Station Taxis occupies a large premises at Riverside Road in Southwick, Sunderland.We have recently purchased and installed a new state of the art telephone system which enables us to be more efficient when dealing with our customers calls.
We also operate using an automated dispatch system which means when you contact Station Taxis the system can automatically send the closest available car to you cutting down the time you wait for your taxi.
We also have taxi offices located at the Park Lane bus interchange and outside of the Sunderland train station so if you're in town and you need a taxi you can call into either of these offices and we will be happy to arrange a taxi for you.
Sunderland's best and biggest Oriental Buffet Restaurant. Set in comfortable, modern surrounding. With Over 80 Varieties Of Different Dishes Served Daily. Wine & Beer A Available From Our Fully Licenced Bar. Seating Over 250 People, Karaoke Function Room are avaerable, Party Bookings Welcome!
The waterfront in Sunderland has been transformed in recent years by extensive redevelopment including the impressive Marina complex at North Dock. Originally constructed by Brunel in 1837, the Dock has been renovated and extended to provide the modern Marina we now enjoy.
Sunderland Marina aims to provide top class facilities combined with friendly, efficient service. The Marina is staffed 24 hours a day, 7 days a week, all year round and is dedicated to provide a personal service to all users and their families.
The Marina consists of 113 fore-and-aft moorings, 26 un-serviced berths and 88 fully serviced pontoon berths.
At Rustico we pride ourselves for offering an wholesome take on contemporary Italian cuisine to suit all tastes and occasions. We've created a simple and affordable menu such as our finest homemade meatballs & pate, traditionally stone baked pizzas & delicious pasta dishes by using only the finest Italian and local ingredients in the accompany of award winning Italian wines and beers to deliver an unforgettable experience..
We are situated on one the major routes in and out of the Sunderland city centre close to Saint Peter's metro station, slap bang in the middle of North Bridge Street. Inside, it's a little haven from the hustle and bustle outside with its traditional Italian restaurant charm.
Providing both casual and fine dining Rustico is very much an upbeat destination for all food lovers. There is also an elegant bar offering a bar menu with a mouth watering choice of regional Italian wines.
Sunderland's only four star hotel is the Sunderland Marriott. Located on the seafront overlooking the sandy beaches at Seaburn two miles north of the city centre. A full-service hotel offering modern, high quality accommodation for business and leisure travellers alike. All bedrooms have en-suite facilities - many enjoying sea views. The hotel also boasts three luxurious suite style rooms complete with a glazed rotunda overlooking the sea. The Sunderland Marriott Hotel features banqueting and conference facilities, cocktail bar, fine dining restaurant, private parking and superb leisure facilities. The hotel has recently undergone a £0.5 million bedroom refurbishment, completely upgrading a third of our existing bedrooms incorporating contemporary and modern design.
Al Pacino is located in Sunderland, on Church Street. Now with Just-Eat.co.uk you're able to place your order online in a smart way with no extra costs. Amazing offers & glorious dishes are available on our menu. All you favourite Pizzas are only a few clicks away from you. So place your order now for collection or delivery & enjoy it ! Al Pacino is open every day from 17:00 to 01:00.
Alan has a long history as an award winning chef, working all around the globe. His latest ventures have seen him travel to war torn countries such as Africa, Iraq and Afghanistan and working in the British Embassy in Afghanistan. Alans latest job was an Operations Manager for the British Royal Marines and American Marines in Afghanistan where he oversaw 1,200 staff preparing 45,000 meals a day for our troops.
Grant is an ex-Royal Marine, who has also worked in personal security and managed a bar in Sunderland.
Together they have combined their experience to open Signatures, which specialises in wonderful home cooked traditional English dishes with a modern twist.
Welcome to Asiana Fusion Restaurant Asiana Fusion Restaurant takes inspiration from the finest of pan Asian cuisine.,br.


Our manager got interviewed for HERSTORY magazine November edition. This magazine mainly focus on women doing business and introduces their stories. I recommend you this magazine to get more information about the women working force that we have here in Japan.
SUiTO will be broadcasted on RKB channel tonight at 12:50 pm. They will introduce you our restaurant space and kimono dress up experience.


text:
Accelerators & Coworking
Michigan School Honored as Top Entrepreneurship School
By Amanda Lewan on November 19th, 2015 / Comments
We're not surprised to hear the news that this Michigan University program is ranked high for entrepreneurship.
According to Entrepreneur Magazine and The Princeton Review, the Zell Lurie Institute for Entrepreneurial Studies at the University of Michigan is ranked the Number 4 Graduate Program in Entrepreneurship. This is the sixth year running it's been ranked a top five program for entrepreneurship. Also, worth noting, is the undergraduate entrepreneurship program was ranked number 7.
The school has recently expanded it's offerings to sharpen the minds of students interest in entrepreneurship.
"As interest in entrepreneurship grows at a rapid pace, we at Michigan Ross are here to help students learn and determine if entrepreneurship is the right choice for them," said Alison Davis-Blake, dean of the University of Michigan's Ross School of Business. "Our focus on action-based learning, and the opportunity to manage real funds, develop real projects and interact with mentors who are successful entrepreneurs and venture capitalists themselves is what sets Ross apart."
On campus are two startup incubators, TechArb and the new Bharat Desai Family Accelerator, both working with the Zell Lurei Institute. In July 2015, the Zell Lurie Institute received a pledge of $60 million from the Zell Family Foundation, which provides additional endowed support for the continued delivery and development of entrepreneurship programs for students and alumni.
Learn more about this entrepreneurial program here: http://www.zli.bus.umich.edu/
Amanda Lewan
Editor @michipreneur. Co-founder Bamboo Detroit. Follow me @Amanda_Jenn. I love telling the story of entrepreneurs and innovators.
MHacks Hosting Weekend Long Hackathon in Detroit
TechArb Graduates Class of Tech Entreprenerus
University of Michigan Invests in 5 Transportation Technologies
Follow Michipreneur
Michipreneur Newsletter
Michigan's Startup Community. For Innovators, Creatives, and Doers.
Michipreneur © 2015, All Right reserved. | Powered by Momentum

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Mocking MQ connector in munit (mule 4) causing test to try connecting to the MQ and test fails I am able to mock MQ connector in munit, no issues. When MQ is actually up and running, munit tests are successful, however if MQ is shut down, testing fails as it is not able to connect to the MQ. I want the munit tests to succeed even if MQ is down, it is already mocked, so not need to connect anyways. This happens only when publishing to a queue for me, but tests publishing to a topic are fine.
Any clues?

redpajama_set_name: RedPajamaStackExchange


text:
'50 Shades of Grey' Movie Casting Drama: Jamie Dornan Is A Better Christian Grey Than Charlie Hunnam, Says Wife Of 'Fifty Shades' Producer
By Rebecka Schumann @RebeckaSchumann
When news broke in September that actor Charlie Hunnam would take on the role of Christian Grey in the "Fifty Shades of Grey" film, some fans revolted against that casting decision. And they must have been happy when the "Sons of Anarchy" TV star later decided to quit the film due to his "immersive" filming schedule. Among those not sorry to see him opt out was the wife of "Fifty Shades" producer Michael De Luca, Angelique De Luca, who recently unleashed her true feelings regarding Hunnam playing the sexually sadistic, Seattle billionaire.
A self-professed fan of the erotic book series the film is based on, De Luca hasn't kept quiet regarding the casting process. "To be honest, to me, [Charlie] wasn't a great fit," said De Luca on Twitter Oct. 12, following fansite comments that they were sad to hear Hunnam had quit. When prompted to explain, De Luca said, "He didn't have that CG [Christian Grey] demeanor inside or outside. CG exudes a certain sexual intensity that comes from his eyes. I just feel like that actor has to make us all feel it and it wasn't going to come from [Charlie Hunnam]."
While Hunnam may have not had a fan in De Luca, an entrepreneur and philanthropist, she has stated her public approval for the film's new lead, "Once Upon a Time" star Jamie Dornan. "My wish came true! I'm proud & beyond hot for my new boyfriend (yes Mike knows ;) @JamieDornan1 to be CG!!" she posted on Twitter on Oct. 24, also calling the native Irish actor "very talented."
On Friday, "Fifty Shades of Grey" author E.L. James announced on Twitter that "True Blood" actor Luke Grimes would be joining Dornan and his on-screen lover, actress Dakota Johnson, in the film. According to one of De Luca's most recent social media posts, she is pleased with her husband's decision to cast Grimes in the film as Christian Grey's adoptive brother, Elliot Grey. "Have you seen the Grey brother? They look great, don't they?" Twitter user @lilcaribou asked De Luca Friday, to which she replied, saying, "I totally agree!"
Due to the recent casting shake-up, the filming schedule for "Fifty Shades of Grey" has been moved from its original start date of Nov. 1 to Dec. 2, according to a report from the Hollywood Reporter Monday. It has yet to be confirmed if the film will still premiere on its original release date of Aug. 1, 2014.
'50 Shades Of Grey' Movie First Set Photo: E. L. James Tweets Picture Of Charlie Tango
'50 Shades Of Grey' Cast News: 5 Reasons Dakota Johnson May Quit 'Fifty Shades' Movie Like Charlie Hunnam


This Day I Uploaded 15 images also all are in Full HD version. From different picture in Cancer and taurus compatibility photos, you can have Wedding with decor. Anyway, if you don't appropriate with ideas, you could still take a look inspiration. Even so I promote you would probably use as an dream design, although together with has inspiring decoration design. Don't forget for share this Cancer and taurus compatibility synastry romantic chemistry calculator thats that bullsht best men\\\'s wedding bands to girl friend or your family. So they are can get with to create they Wedding. I am glad would probably share as well as plus to you all. Perhaps you would probably find which to date are you search.


Welcome to Stories of Hope, where you can follow fearlessHOPE families as they take a journey from their child's diagnosis of visual impairment or loss, through treatments, surgeries, community support, helpful resources, and more.
If your child has been diagnosed with visual impairment or loss, please consider reaching out to fearlessHOPE or any of these families to learn more about this inclusive network of support.
A blog dedicated to the life of Hazel Wiede from the perspective of her loving parents. Hazel has a chromosome deletion on her 6th Chromosome (6p 25.3 through 25.2).


text:
Hand-Lists of Books Printed by London Printers, 1501-1556 by Bibliographical Society (Great Britain)
Hand-Lists of Books Printed
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible.MoreThis work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. Hand-Lists of Books Printed by London Printers, 1501-1556 by Bibliographical Society (Great Britain)
Terraria Guide For Beginners: Learn The Basics of Terraria Game, Explore Biomes, Find Materials, Bui
The Scene is Dead
Madocs Prickly Problem
Hals Ueber Kopf Roman (Temperance Brennan, #9)
Rising Fears
Brother-Making in Late Antiquity and Byzantium: Monks, Laymen, and Christian Ritual
West Nile Virus: Detection, Surveillance, and Control
A Mile in My Shoes
De latere reizen van Robinson Crusoe naar zijn eiland en de wereld rond
Queens Agent: Sir Francis Walsingham and the Rise of Espionage in Elizabethan England
Korte geschiedenis van het bedrog: de verhalen
めすいぬずかん コミックス版
Premonitions: When the Universe Shifts, Expect the Unexpected
Tied Up At Work: BDSM Erotica
Dynamic Testing: The Nature and Measurement of Learning Potential
lef : loopbaancoach voor vrouwen
Panorama of the Western Front


Key Features and Benefits:Home ownershipAre you selling or buying a home? This software will guide you through maximizing your deductions for home mortgage interest and real estate taxes.InvestmentsThis software will guide you through your sale of stocks, bonds and mutual funds. And, it will help you report your dividends or capital gain distributions.Retirement incomeGet help reporting income from your retirement plan and rollovers, payments from your IRAs, annuities, disability, pension and life insurance proceeds, etc.Refund revealExplains the changes in your refund amount so you always know you are getting the maximum refund.Life changesGet advice for key tax benefits after big changes in your life such as marriage, the birth of a child, getting a new job, going to college, etc.Charitable donationsWhether you;ve donated money or clothing to your local charity, or need to report mileage for volunteer work, this software will help you track and report those donations to optimize tax savings.
Usually the software worked great and I prefer it to Turbotax. However, on several occasions the instructions confounded me. Usually these instructions were to go to a different screen and do something; but the words used for that something were different than in the instructions or else hidden in a corner so it took forever to navigate and produced great confusion and stress. Two similar examples from the email "Your Federal Return has Been Accepted". The email states that you will receive a confirmation number but no number is forthcoming. The email also states that you can "write a product review" but after clicking this link, it takes 5 minutes of hunting to find the review area when clicking on "write a product review" should take you right to the place you want to go. I would suggest that you test your product by "grabbing people off the street". The people who provide "chat help" are knowledgeable and efficient but getting connected to them using the program is another challenge.
Overall this is very good program. Interview instructions are clear and concise and it is easy to navigate around to any topic. As with other software, one expects to see incremental improvement and added functionality each year. Not the case with this program, unfortunately. Below is a list of features I'd like to see in next year's edition: 1. Ability to quickly transform an already completed MFJ return to a MFS/HoH return for either spouse. Currently, the program lets you reduce a MFJ return to a MFS/HoH return for only the primary/first spouse. 2. Ability to see and print the current tax year's key data (important data for next year's tax return). 3. Ability to enter a comment for every non-blank entry field for user's future recall or reference (e.g., a note to remember how you arrived at the value you entered in a field). 4. Option to increase the font size of the instructions. 5. The "Plan" section of the software needs a lot of work. The instructions in this section are horrible.
I've been using using H&R block At Home/TaxCut for a number of years now so importing my pervious tax information was straight forward and relaivtely painless. Also, the entry of this years infomation was pretty easy as well due the the well laid out menus and such. However, when it came time to file, unlike with previous years, I did owe a little bit this year so I decided to go with the online credit card payment method. This instructions provided for this were absoultely HORRENDOUS. You are provided a single instruction "Go to the tax payment website to make a credit card payment." Absoultely no further information about what you need to enter into any of the fields on this website are given. While most of the information requested is pretty straight forward some of it is not, and not having any information on what to put into these fields gave me a "I think I did it right but I'm not really sure feeling". For future versions this is something that should definitely be corrected.
Everything worked smoothly and efficiently except for one thing. Last year I filed an amended return. This caused some confusion and ultimately a rejection of my Federal return. Bottom line is there should be a focused help section telling the user what to do if you have a prior years amended return. For example, at the time of filing, we are asked for the prior years AGI in order for the IRS to accept the return. I entered the final amended value, but IRS actually wanted the ORIGINAL AGI (before the amendment). Also, when entering the State Refund into the Income section, I also entered the final amended value. Well, turns out the ORIGINAL refund value was needed here too, so it matches the state's 1099G. My point is that more questions and instructions should be given along the way, asking if the filer (user) had an amended return and exactly what that means for every form we fill out. Other than that the HR block software does a good job at guiding you through all the IRS forms.
Have used H & R for many years without any significant problems until this year. While trying to file my daughter and her husband's return the AGI from 2014 which was done on H & R, was incorrect with no means to correct the number. Upon review the figures from 2014 were all messed up and thank goodness I retained the completed return along with all worksheets. These numbers were correct so no way to figure out how the AGI carried forward got this messed up. Was furious that was told by " Chat" that I could not correct the number and had to go through IRS.gov and obtain e-filing Pins for both she and her husband and re-file the return. A major inconvenience and leaves me feeling less than confidant in the whole program. I will be filing my own return in the next couple of days and will check the figures very closely to assure that 2014 will be brought forward correctly. Just about ready to go to Tax Cut next year although will be a major pain to have to manually input all numbers.


On March 22, 2016, UNHRC president Choi Kyong-lim (S. Korea) sent a letter to all 47-member states at the United Nations Human Rights Council (UNHRC) recommending professor Stanley Michael Lynk (Western University, London, Ontario) as the new special rapporteur for the Palestinian Territories (Gaza, West Bank and East Jerusalem) effective March 31. He will succeed Indonesian envoy Makarium Wibisono who quit the post in January 2016 blaming the Zionist regime of interfering in his work and demonizing him.
Wibisono's predecessor, American Jewish academic Richard Falk, was targeted for six years by the Organized Jewry including HRW and UN Watch.
Michael Lynk and the leading candidate for the position, Jewish professor Penny Green (Queen Mary University, London), were both declared anti-Israel by the Geneva-based UN Watch Jewish group.
On March 16, the Winnipeg Jewish Review published an Open Letter to Canada's prime minister Justin Trudeau demanding that he disqualify both candidates for their criticism of the Zionist regime. The joke is Canada is not a member of UNHRC, but Saudi Arabia is.
A Jewish group from Harper's Tories asked Justin Trudeau to immediate take action on complaint in the said open letter and asked Ottawa to follow orders from the Jewish Lobby. It was so threatening that country's foreign minister Stephane Dion called upon UNHRC to review the appointment of professor Michael Lynk as its special rapporteur on human rights in Palestine.
On Friday, Ronald S. Lauder, president World Jewish Congress slammed UNHRC for the appointment of Michael Lynk. "It's entirely predictable, but regrettable move which further undermines the council's credibility, which is close to zero," he said.
Incidentally, on Thursday, the Geneva-based council voted to create a database of all Israeli and international firms operating directly or indirectly in the West Bank, East Jerusalem and the Golan Heights. The resolution was tabled by Pakistan with 32 votes in favor, none against, and 15, pro-USrael countries abstaining.
Danny Danon, the Israeli ambassador to the UN, said the database was a blacklist accusing the UN body of behaving "obsessively" against Tel Aviv.
Benjamin Netanyahu also issued a statement on Thursday evening, calling UNHRC an anti-Israel circus.
US Ambassador to the UN Keith Harper described the resolution as especially disturbing – adding it only serves to reinforce the council's one-sided actions against Israel.
Ibrahim Khreisheh, Palestinian envoy to the UNHRC, called the vote a message of hope for our people.
Dr. Stanley Michael Lynk is internationally renowned law professor, who had written critical views on human rights abuses in Palestine (here).
. But we all know that criticizing West's Holy Cow of Human right abuses, is an unforgiveable sin.
"Whether Lynk on the job is as vocal a critic of Israeli policies as Falk and Wibisono remains to be seen," Steve Lendman, American Jewish writer, author and radio talk-show host wrote on March 24.


text:
II Marine Expeditionary Force
This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Please help to improve this article by introducing more precise citations. (March 2018) (Learn how and when to remove this template message)
The II Marine Expeditionary Force (II MEF) is a Marine Air-Ground Task Force consisting of ground, air and logistics forces capable of projecting offensive combat power ashore while sustaining itself in combat without external assistance for a period of 60 days. The II Marine Expeditionary Force is commanded by a Lieutenant General, who serves under U.S. Marine Corps Forces Command, providing Marine fighting formations and units to European Command, Central Command and Southern Command.
II MEF insignia
23 October 1962 – present
Expeditionary combat forces
United States Marine Corps Forces Command
Garrison/HQ
Marine Corps Base Camp Lejeune
Operation Desert Storm
Global War on Terror
Lieutenant General Brian D. Beaudreault
Higher headquartersEdit
II MEF falls under the command of U.S. Marine Corps Forces Command (MARFORCOM), and is a service retained force, meaning it is not assigned or allocated to any of the Geographic Combatant Commands. However, II MEF regularly provides subordinate units in support of operations and exercises throughout the U.S. European Command, U.S. Africa Command, and U.S. Southern Command Areas of Responsibility, as well as in support of other U.S. unified and NATO commands. II MEF units are available for and prepared to respond to contingency requirements worldwide.
EmploymentEdit
In addition to the option of being employed in its entirety as a MEF-sized unit, II MEF has the capability of forming task-organized Marine Air-Ground Task Forces (MAGTF) of lesser size such as a MEF (Forward), a brigade-sized MAGTF (Marine Expeditionary Brigade or "MEB") about one-third the size of a MEF or a Marine Expeditionary Unit (MEU), about one-third the size of a MEB. The size and composition of any MAGTF will be dependent upon the mission assigned. One mission that could be assigned to the MEB would be assignment for planning, deployment and utilization of equipment stored aboard Maritime Prepositioning Ships (MPS). The MPS program involves the forward deployment of the MPS Squadron of four or five ships loaded with a brigade's worth of combat equipment and supplies and the airlifting of the MEB to the designated objective area to link up with the MPS Squadron. At the same time, tactical aircraft of the MEB are flight ferried to an airfield in or near the area of operation. The MEB can be sustained for 30 days by the supplies aboard the ships.
The only routinely deployed MAGTFs, the 22d, 24th and 26th MEUs deploy on a rotating basis to the Mediterranean Sea area to serve as the landing force for the Commander, 6th Fleet. The MEU consists of approximately 2,200 Marines and Sailors, is capable of rapid response in a variety of possible contingencies, and if the situation requires, can serve as the forward element of a larger MAGTF.
Structure of II MEF 2018
UnitsEdit
II Marine Expeditionary Force Information Group: Command element
II Marine Expeditionary Force Headquarters
2nd Intelligence Battalion
2nd Law Enforcement Battalion
2nd Radio Battalion
8th Communications Battalion
2nd Air Naval Gunfire Liaison Company (ANGLICO)
2nd Marine Division: Ground combat element
2nd Marine Aircraft Wing: Aviation combat element
2nd Marine Logistics Group: Logistics combat element
2nd Marine Expeditionary Brigade
22nd Marine Expeditionary Unit
Wikimedia Commons has media related to II Marine Expeditionary Force.
United States Marine Corps portal
Julian C. Smith Hall
II MEF's official website
Retrieved from "https://en.wikipedia.org/w/index.php?title=II_Marine_Expeditionary_Force&oldid=901812130"


In my never ending pursuit of good coffee (because let's face it, being a full time nerd is tiring) I stumbled across The Black Lab Coffee House in Clapham. A close friend of mine, who also happens to be a coffee nut, stopped in London for a weekend visit and I decided we should try out new coffee place.
I'm not a black coffee drinker but I was able to have a little of this before giving in and adding milk. If you're not normally a black coffee fan, this is the way to go if you're thinking of trying it. We also ordered something to eat; I had a pumpkin, feta and greens sandwich drizzled with balsamic, which was pretty good. My friend had oatmeal with fresh fruit and cream and really enjoyed it. They have a decent selection of pastries and fresh sandwiches. AeroPressed coffee costs £2.80 and my sandwich cost £4.95, not an unreasonable amount for lunch in London. Yes, they have wifi and they also sell AeroPresses, fresh ground coffee and other types of coffee makers on site. The staff are well versed in coffee brewing, friendly and avid coffee lovers. If you're a coffee aficionado, looking for a place to chat over a cup with a friend or have a coffee while getting a little work done, this is a great little gem in the South. Don't pass it up. I will definitely be back here.


text:
\section{Introduction\label{sec:intro}}
The detailed study of unstable nuclei was a major subject in nuclear physics during recent decades. $\beta$ decay measurements provide not only important information on the structure of the daughter and parent nuclei, but  can also be used to inform  nuclear astrophysics  studies and probe fundamental subatomic symmetries \cite{Hardy2015}. The link between experimental results and theory is given by the reduced transition probabilities, $ft$. Experimental $ft$ values involve three measured quantities: the half-life, $t_{1/2}$, the $Q$ value of the transition, which determines the statistical phase space factor $f$, and the branching ratio associated with that transition, $BR$.

In the standard $\mathcal{V\!\!-\!\!A}$ description of  $\beta$ decay, $ft$ values are related to the fundamental constants of the weak interaction and the matrix elements through this equation:

\begin{equation}
ft=\frac{\mathcal{K}}{g_V^2|\langle f|\tau|i\rangle|^2+g_A^2|\langle f|\sigma\tau|i\rangle|^2} ,
\label{eq:theo_ft}
\end{equation}

where $\mathcal{K}$ is a constant and $g_{V(A)}$ are the vector (axial) coupling constants of the  weak interaction; $\sigma$ and $\tau$ are the spin and isospin operators, respectively. Thus, a comparison of the experimental $ft$ values with the  theoretical ones obtained from the calculated matrix elements is a good test of the nuclear wave functions obtained with model calculations. However, to reproduce the $ft$ values measured experimentally, the axial-vector coupling constant $g_A$ involved in Gamow-Teller transitions has to be renormalized \cite{Wilkinson1973,WILKINSON1973_2}. The effective coupling constant $g'_A=q\times g_A$ is deduced empirically from experimental results and depends on the mass of the nucleus: The quenching factor is $q=0.820(15)$ in the $p$ shell \cite{Chou1993}, $q=0.77(2)$ in the $sd$ shell \cite{Wildenthal1983}, and $q=0.744(15)$ in the $pf$ shell \cite{Martinez1996}. Despite  several theoretical approaches attempting to reveal the origin of the quenching factor it is still not fully understood \cite{Brown2005}.

Another phenomenon which shows the limitations of our theoretical models is the so-called \emph{$\beta$-decay mirror asymmetry}. If we assume that the nuclear interaction is independent of  isospin, the theoretical description of $\beta$ decay is identical for the decay of a proton ($\beta^+$) or a neutron ($\beta^-$) inside a nucleus. Therefore, the $ft$ values corresponding to analog transitions should be identical. Any potential asymmetries are quantified by the asymmetry parameter $\delta=ft^+/ft^-1$, where the $ft^\pm$  refers to the $\beta^\pm$ decays in the mirror nuclei. The average value of this parameter is $(4.8\pm0.4)\%$ for $p$ and $sd$ shell nuclei  \cite{Thomas2004}. From a theoretical point of view the mirror asymmetry can have two origins: (a) the possible existence of exotic \emph{second-class currents} \cite{Wilkinson1970447,PhysRevLett.38.321,WilkinsonEPJ}, which are not allowed within the framework of the standard  $\mathcal{V\!\!-\!\!A}$ model of the weak interaction and (b) the breaking of the isospin symmetry between the initial or final nuclear states. Shell-model calculations were performed to test the isospin non-conserving part of the interaction in $\beta$ decay \cite{Smirnova2003441}. The main contribution to the mirror asymmetry from the nuclear structure was found to be from the difference in the matrix elements of the Gamow-Teller operator ($|\langle f|\sigma\tau|i\rangle|^2$), because of isospin mixing and/or differences in the radial wave functions.

Large mirror asymmetries  have been reported for transitions involving  halo states \cite{Tanihata2013}. For example, the asymmetry parameter for the  $A=17$ mirror decays $^{17}$Ne$\rightarrow^{17}$F and $^{17}$N$\rightarrow^{17}$O  to the first excited states of the respective daughters was  measured to be $\delta=(-55\pm9)\%$ and $\delta=(-60\pm1)\%$  in two independent experiments \cite{Borge1993, Ozawa1998}. This result was  interpreted as evidence for a proton halo in the first excited state of $^{17}$F assuming that the fraction of the $2s_{1/2}$ component of the valence nucleons remains the same in $^{17}$Ne and $^{17}$N. However, a different interpretation was also given in terms of charge dependent effects which increase  the $2s_{1/2}$ fraction in  $^{17}$Ne by about 50\% \cite{PhysRevC.55.R1633}. The latter result is also consistent with the high cross section obtained in the fragmentation of $^{17}$Ne \cite{Ozawa199418,Ozawa199663}, suggesting the existence of a halo in  $^{17}$Ne. More recently Kanungo \emph{et al.} reported the possiblity of a two-proton halo in $^{17}$Ne \cite{Kanungo200321}.
An extremely large mirror asymmetry was also observed in the mirror decay of $A=9$ isobars $^{9}$Li$\rightarrow^{9}$Be and $^{9}$C$\rightarrow^{9}$B. A value of $\delta=(340\pm70)\%$ was reported for the $^{9}$Li and $^{9}$C $\beta$-decay transitions to the 11.8 and 12.2 MeV levels of their respective daughters, which is the largest ever measured \cite{Bergmann2001427,Prezado2003}. Despite  the low experimental interaction cross sections measured with various targets in attempts to establish the halo nature of $^{9}$C \cite{Ozawa199663,Blank1997242}, recent results at intermediate energies \cite{Nishimura2006}, together with the anomalous magnetic moment \cite{Matsuta1995c153} and theoretical predictions \cite{0256-307X-27-9-092101,PhysRevC.52.3013,Gupta2002}, make $^{9}$C a proton halo candidate.
The potential relationship between large mirror asymmetries and halos is therefore clear. Precision measurements of mirror asymmetries in states involved in strong, isolated, $\beta$-decay transitions might provide a technique to probe halo nuclei that is complementary to total interaction cross section and momentum distribution measurements in knockout reactions \cite{Tanihata2013}.

Moreover, $\beta$ decay of proton-rich nuclei can be used for nuclear astrophysics studies. Large $Q_\beta$-values of  these nuclei not only allow the population of the bound excited states of the daughter, but also open  particle emission channels. Some of these levels correspond to astrophysically significant resonances which cannot be measured directly because of limited radioactive beam intensities. For example, the $^{25}\mathrm{Al}(p,\gamma)^{26}\mathrm{Si}$ reaction \cite{Wrede_2009} plays an important role in the abundance of the cosmic $\gamma$-ray emitter $^{26}\mathrm{Al}$.  The effect of this reaction is to  reduce the amount of ground state $^{26}\mathrm{Al}$, which is bypassed by the sequence $^{25}\mathrm{Al}(p,\gamma)^{26}\mathrm{Si}(\beta\nu)^{26m}\mathrm{Al}$, reducing therefore the intensity of the 1809-keV $\gamma$-ray line characteristic of the  $^{26}\mathrm{Al}$  $\beta$ decay \cite{Iliadis_96}. Thus it is important to constrain the $^{25}\mathrm{Al}(p,\gamma)^{26}\mathrm{Si}$ reaction rate.

 $^{26}$P is the most proton-rich bound phosphorus isotope. With a half-life of $43.7(6)$~ms and a $Q_{EC}$ value of $18258(90)$~keV \cite{Thomas2004}  the $\beta$ decay can be studied over a wide energy interval. $\beta$-delayed $\gamma$-rays  and protons from excited levels of $^{26}$Si  below and above  the proton  separation energy of $5513.8(5)$~keV \cite{AME2012} were observed directly in previous experiments \cite{Thomas2004,Cable_83,Cable_84} and, more recently, indirectly from the Doppler broadening of peaks in  the $\beta$-delayed  proton-$\gamma$ spectrum \cite{Schwartz2015}. The contribution of novae to the abundance  of $^{26}\mathrm{Al}$ in the galaxy was recently constrained by using  experimental data  on the $\beta$ decay of  $^{26}$P \cite{Bennett2013}.

In addition, $^{26}\mathrm{P}$ is a candidate to have a proton halo \cite{Brown1996,Ren1996,Gupta2002,Liang2009}. Phosphorus isotopes are the lightest nuclei expected to have a ground state with a dominant contribution of a $\pi s_{1/2}$ orbital. Low orbital angular momentum orbitals enhance the halo effect, because higher
$\ell$-values give rise to a confining centrifugal barrier. The low separation energy of  $^{26}$P (143(200)~keV \cite{AME2012}, 0(90)~keV\cite{Thomas2004}),   together with the narrow momentum distribution and enhanced cross section observed in proton-knockout reactions \cite{Navin1998} give some experimental evidence for the  existence of a proton halo in $^{26}$P.

In this paper, we present a comprehensive summary of the $\beta$-delayed $\gamma$ decay of $^{26}$P
 measured at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University during a fruitful experiment for which selected  results have already been reported in two separate shorter papers \cite{Bennett2013,Schwartz2015}. In the present work, the Gamow-Teller strength, $B(GT)$, and the experimental $ft$  values are compared to theoretical calculations and to the decay of the mirror nucleus  $^{26}$Na to investigate the  Gamow-Teller strength and mirror asymmetry, respectively. A potential relationship between  the mirror asymmetry and the existence of a proton halo in $^{26}$P is also discussed. Finally, in the last section, the calculated thermonuclear $^{25}$Al$(p,\gamma)^{26}$Si reaction rate, which was used in Ref. \cite{Bennett2013} to estimate the contribution of novae to the abundance of galactic $^{26}$Al, is tabulated for completeness.

\section{Experimental procedure\label{sec:experiment}}

\begin{figure}[t]
\centering
\includegraphics[width=0.45\textwidth]{Fig1.eps}%
\caption{\label{fig:Setup} Schematic view of the experimental setup. The thick arrow indicates the beam direction. One of the  16 SeGA detectors was removed to show the placement of the GeDSSD.}
 \end{figure}

The experiment was carried out at the National Superconducting Cyclotron Laboratory (NSCL). A 150~MeV/u 75~pnA primary beam of $^{36}\mathrm{Ar}$ was delivered from the Coupled Cyclotron Facility and impinged upon a 1.55~g/cm$^2$ Be target. The $^{26}\mathrm{P}$ ions were in-flight separated from other fragmentation products according to their magnetic rigidity by the A1900 fragment separator \cite{Morrissey200390}. The Radio-Frequency Fragment Separator (RFFS) \cite{Bazin2009314} provided a further increase in beam purity before the beam was implanted into a 9-cm diameter, 1-cm thickness planar germanium double-sided strip detector (GeDSSD) \cite{Larson201359}. To detect signals produced by both the implanted ions and the $\beta$ particles emitted during the decay, the GeDSSD was connected to two parallel amplification chains. This allowed the different amounts of energy deposited in implantations (low gain) and decays (high gain) to be detected in the GeDSSD. The GeDSSD was surrounded by the high purity germanium detector array SeGA \cite{Mueller2001492} in its barrel configuration which was used to  measure the $\beta$-delayed $\gamma$ rays (see Fig.\ref{fig:Setup}).

\begin{figure}[b]
 \includegraphics[trim=0cm 0mm 0cm 1cm, clip=true,width=.5\textwidth]{Fig2.eps}%

 \caption{\label{fig:PID} Particle identification plot obtained for a selection of runs during the early portion of the experiment, before the beam tune was fully optimized. The energy loss was obtained from one of the PIN detectors and the time of flight between the same detector and the scintillator placed at the focal plane of the A1900 separator. A low-gain energy signal in the GeDSSD condition was used. The color scale corresponds to the number of ions.}
 \end{figure}

  The identification of the incoming beam ions was accomplished using   time-of-flight and energy loss signals. The energy loss signals were provided by a pair of  silicon PIN detectors  placed slightly upstream of the decay station. The time of flight was measured between one of these PINs and a plastic scintillator placed 25~m upstream, at the A1900 focal plane. Figure  \ref{fig:PID} shows a two-dimensional cluster  plot of the  energy loss versus the time of flight for the incoming  beam taken prior to a re-tune that improved the beam purity substantially for the majority of the experiment. A coincidence condition requiring a low-gain signal in the GeDSSD was applied to ensure the ions were implanted in the detector. It shows that the main contaminant in our beam was the radioactive isotone $^{24}\mathrm{Al}$ ($\sim$13\%). During the early portion of the experiment, a small component of $^{25}\mathrm{Si}$ was also present in the beam. We estimated its ratio and it was on average 2.1\%, but this value was diluted to 0.5\% after incorporating the data acquired after the re-tune.  Small traces of lighter isotones like $^{22}\mathrm{Na}$ and $^{20}\mathrm{F}$ were also present ($\sim$2.5\%). The total secondary beam rate was on average 80~ions/s and the  overall purity of the implanted  beam was 84\%. This value of the beam purity differs from the previous reported values in Ref. \cite{Bennett2013}, in which the implant condition was not applied The  $^{26}\mathrm{P}$ component was composed of the ground state and the known  164.4(1)~keV isomeric state \cite{Nishimura2014,DPL2016}. Because of the short half-life of the isomer [120(9)~ns] \cite{Nishimura2014} and the fact that it decays completely to the ground state of $^{26}\mathrm{P}$, our $\beta$-decay measurements were not affected by it.

The data were collected event-by-event using the NSCL digital acquisition system \cite{Prokop2014}. Each channel provided its own time-stamp signal, which allowed coincidence gates to be built between the different detectors. To select $\beta$-$\gamma$ coincidence events, the high-gain energy signals from the GeDSSD were used to indicate that a $\beta$ decay occurred. The subsequent $\gamma$ rays emitted from excited states of the daughter nuclei were selected by setting a 1.5-$\mu$s coincidence window. The 16  spectra obtained by each of the elements of SeGA were then added together after they were gain  matched  run-by-run to account for  possible gain drifts during the course of the experiment.

\begin{figure*}
\centering
 \includegraphics[trim=2cm 5mm 5mm 2mm, clip=true,width=.85\textwidth]{Fig3.eps}%

 \caption{\label{fig:spec} $\gamma$-ray spectrum observed by the SeGA array in coincidence with a $\beta$ particle in the GeDSSD.  Photopeaks have been labeled by the emitting nucleus and its energy rounded to the closest keV integer. Peaks labeled with one (two) asterisks correspond to single (double) escape peaks.}
 \end{figure*}

\section{Data Analysis and Experimental Results \label{sec:data}}

As   mentioned in  Sec. \ref{sec:intro}, the data presented in this paper are from the same experiment described in Refs. \cite{Bennett2013,Schwartz2015}, but independent sorting and analysis routines were developed and employed. The values extracted are therefore slightly different, but consistent within uncertainties. New values derived in the present work are not intended to supersede those from Refs. \cite{Bennett2013,Schwartz2015}, but rather to complement them. In this section, the analysis procedure is described in detail and the experimental results are presented.

Figure  \ref{fig:spec} shows the cumulative $\gamma$-ray spectrum observed in all the detectors of the SeGA array in coincidence with a $\beta$-decay signal in the GeDSSD. We have identified 48 photopeaks, of which 30 are directly related to the decay of $^{26}$P. Most of the other peaks were assigned to the $\beta$ decay of the main contaminant of the beam,  $^{24}$Al. Peaks in the spectrum have been labeled by the $\gamma$-ray emitting nuclide. Twenty-two of the peaks correspond to $^{26}$Si, while eight of them  correspond to  $\beta$-delayed proton decays to  excited states of $^{25}$Al followed by $\gamma$-ray emission. In this work we will focus on the decay to  levels of $^{26}$Si as the $^{25}$Al levels have already been discussed in Ref. \cite{Schwartz2015}.

\begin{figure}

 \includegraphics[trim=5mm 1cm 1cm 0mm, clip=true,width=.5\textwidth]{Fig4.eps}%
 \caption{\label{fig:calibr}(Upper panel) Energy calibration of SeGA $\gamma$-ray spectra using the  $\beta$-delayed $\gamma$ rays emitted by $^{24}\mathrm{Al}$. The solid line is the result of a second degree polynomial fit. Energies and uncertainties are taken from \cite{Firestone20072319}. (Lower panel) Residuals of the calibration points with respect to the calibration line.}
 \end{figure}

\subsection{$\bm{\gamma}$-ray Energy Calibration}

The energies of the $\gamma$ rays emitted during the experiment were determined from a calibration of the SeGA array. As mentioned in  Sect. \ref{sec:experiment} and in Refs. \cite{Schwartz2015,Bennett2013} a gain-matching procedure was performed to align all the signals coming from the 16 detectors comprising the array. This alignment was done with the strongest background peaks, namely the 1460.8-keV line (from the  $^{40}\mathrm{K}$ decay) and the 2614.5-keV one (from the $^{208}\mathrm{Tl}$ decay). The gain-matched cumulative spectrum was then absolutely calibrated \emph{in situ} using the well-known energies of the $^{24}$Al  $\beta$-delayed $\gamma$ rays emitted by $^{24}\mathrm{Mg}$, which cover a wide range in energy from 511~keV to almost 10~MeV \cite{Firestone20072319}. To account for possible non-linearities in the response of the germanium detectors, a second degree polynomial fit was used as a calibration function.  Results of the calibration are shown in Fig.~\ref{fig:calibr}. The standard deviation for this fit is 0.3~keV, which includes the literature uncertainties associated with  the energies of $^{24}\mathrm{Mg}$. The systematic uncertainty was estimated from the residuals of room background peaks not included in the fit. The lower panel of Fig.~\ref{fig:calibr} shows that these deviations are below 0.6~keV, with an average of 0.2~keV. Based on this, the systematic uncertainty was estimated to be 0.3~keV.

\begin{figure}

 \includegraphics[trim=5mm 1cm 1cm 0mm, clip=true,width=.5\textwidth]{Fig5.eps}%
 \caption{\label{fig:eff}SeGA photopeak efficiency. (Top panel) Results of a {\sc Geant4} simulation [solid line (red)] compared to the efficiency measured with absolutely calibrated sources (black circles) and the known $^{24}\mathrm{Mg}$ lines (empty squares). The simulation and the $^{24}\mathrm{Mg}$ data have been scaled to match the source measurements. (Bottom panel) Ratio between the simulation and the experimental data. The shaded area (yellow) shows the adopted uncertainties.}
 \end{figure}

\subsection{Efficiencies}

\subsubsection{$\beta$-particle Efficiency \label{sec:betaeff}}
The $\beta$-particle detection efficiency of the GeDSSD can be determined  by taking the ratio between the number of counts under a certain photopeak in the $\beta$-gated $\gamma$-ray singles spectrum and the ungated one. In principle, the $\beta$ efficiency depends on  $Q_\beta$. To investigate this effect, we calculated the ratios between the gated and the ungated spectra for all the $^{24}\mathrm{Mg}$ peaks, which have different combinations of $Q_\beta$, and found it to be independent of the end-point energy of the $\beta$ particles, with an average ratio of $\varepsilon_\beta(^{24}\mathrm{Mg})=(38.6\pm0.9)\%$. Because of the different implantation depths for $^{24}\mathrm{Al}$ and $^{26}\mathrm{P}$ ($^{24}\mathrm{Al}$ barely penetrates into the GeDSSD), we also calculated the gated to ungated ratios of the strongest peaks of $^{26}\mathrm{Si}$ (1797~keV) and its daughter $^{26}\mathrm{Al}$ (829~keV) obtaining a constant, average, value for the efficiency of $\varepsilon_\beta=(65.2\pm0.7)\%$. The singular value for $^{26}\mathrm{Si}$ and $^{26}\mathrm{Al}$ is explained by their common decay point in the GeDSSD.

\subsubsection{$\gamma$-ray  Efficiency}

To obtain  precise measurements of the $\gamma$-ray intensities, we determined  the photopeak efficiency  of  SeGA. The photopeak efficiency was  studied over a wide energy range between 400 keV and 8 MeV. The results of a {\sc Geant4} \cite{Agostinelli2003250} Monte-Carlo simulation were compared with the relative intensities of the well-known $^{24}\mathrm{Mg}$ lines used also in the energy calibration. The high energy lines of this beam contaminant made it possible to benchmark the simulation for energies higher than  with standard sources. In addition,  the comparison of the simulation to data taken offline with absolutely-calibrated $^{154,155}\mathrm{Eu}$ and $^{56}\mathrm{Co}$ sources allowed us to scale the simulation to determine the  efficiency at any energy. The scaling factor was 0.91. The statistical uncertainty of this scaling factor was inflated by  a scaling factor of $\sqrt{\chi^2/\nu}$  yielding an uncertainty of 1.5\%, which was propagated into the efficiency. The magnitude of this  factor is consistent with {\sc Geant4} simulations of the  scatter associated with coincidence summing effects \cite{Semkow1990}.  Figure \ref{fig:eff} shows the adopted efficiency curve compared to the source data, and the  $^{24}\mathrm{Mg}$ peak intensities. The accuracy of this photopeak efficiency was estimated to be $\delta\varepsilon/\varepsilon=1.5\%$ for energies below 2800~keV and 5\% above that energy.

\subsection{$\bm{\gamma}$-ray intensities \label{subsec:intensities}}
\begin{figure}[t]

 \includegraphics[trim=0mm 1cm 1cm 0mm, clip=true,width=.5\textwidth]{Fig6.eps}%
 \caption{\label{fig:fit} (Top panel) Example of a typical fit to the 1960-keV peak, using the function of Eq. (\ref{eq:EMG}). The dashed line corresponds to the background component of the fit. (Bottom panel) Residuals of the fit in terms of the standard deviation $\sigma$.}
 \end{figure}

The intensities of the $\gamma$ rays emitted  in the $\beta$ decay of $^{26}\mathrm{P}$ were obtained from the areas of the photopeaks shown in the spectrum of Fig. \ref{fig:spec}. We used an exponentially modified Gaussian (EMG) function to describe the peak shape together with a linear function to model the local background:

\begin{equation}
F=B+\frac{N}{2\tau}e^{\frac{1}{2\tau}\left (2\mu+\frac{\sigma^2}{\tau} -2x \right )}\mathrm{erfc}\!\left[\frac{ \sigma^2+\tau(\mu-x)}{\sqrt{2}\sigma\tau}\right ],
\label{eq:EMG}
\end{equation}

where $B$ is a linear background, $N$ is the area below the curve, $\mu$ and $\sigma$ are the centroid and the width of the Gaussian, respectively, and $\tau$ is the decay constant of the exponential; erfc is the complementary error function.
 The parameters describing the width of the Gaussian ($\sigma$) and the exponential constant ($\tau$) were determined by fitting narrow isolated peaks at various energies. The centroids and the areas below the peaks were obtained from the fits. When multiple peaks were very close, a multi-peak fitting function was applied using  the same values for the $\tau$ and $\sigma$ parameters for all the peaks in the region. In general the fits were very good, with reduced chi-squared ($\chi^2/\nu$) close to  unity. In those cases where  $\chi^2/\nu$ was bigger than one, the statistical uncertainties were inflated by multiplying them by $\sqrt{\chi^2/\nu}$. Fig. \ref{fig:fit} shows an example of the fit to the 1960-keV peak.

\subsubsection{Absolute normalization}
The total number of $^{26}\mathrm{P}$ ions  implanted and subsequently decaying in the GeDSSD is, in principle, needed to obtain an absolute normalization of the $\gamma$-ray intensities, and hence the $\beta$ branchings of $^{26}\mathrm{Si}$ levels. The number of $\gamma$ rays observed  at energy $E$ is:
\begin{equation}
N_\gamma(E)=N_0 \times \varepsilon_{\gamma}(E)\times \varepsilon_{\beta}(E) \times I_{\gamma}(E)
\label{eq:abs_intensity}
\end{equation}

\begin{table
 \caption{\label{tab:levels} Data on $^{26}$Si energy levels and  $^{26}\mathrm{P}(\beta\gamma)$ decay. A total of 12 levels and 22 $\gamma$ rays have been identified. The first column shows the level energies  obtained from the laboratory $\gamma$-ray energies shown in the fifth column and include the nuclear recoil correction factor. The second column shows the $\beta$-branches. The third and fourth columns show the spin and parity of the initial and final state, respectively. The last column corresponds to the absolute intensities of the $\gamma$ rays.}
 \begin{ruledtabular}

\begin{tabular}[c]{d d c c d d}
\multicolumn{1}{c}{$E_x$ (keV)} & \multicolumn{1}{c}{$\beta$-Branch (\%)} & $_iJ_n^\pi$ & $_fJ_n^\pi$ & \multicolumn{1}{c}{ $E_\gamma$ (keV)} & \multicolumn{1}{c}{$I$ (\%)} \\
\hline
1797.1(3)   & \multicolumn{1}{c}{ 41(3) }  & $2_1^+$    & $0_1^+$     &  1797.1(3)       &\multicolumn{1}{c}{ 58(3)}    \\
2786.4(3)   & \textless0.39\footnote[3]{95\% confidence level.}       & $2_2^+$    & $2_1^+$     &  989.0(3)     & 5.7(3)   \\
            &                     &            & $0_1^+$     &  2786.5(4)\footnote[1]{Transition never observed in $^{26}$P $\beta$ decay}       & 3.4(2)   \\
3756.8(3)   & 1.9(2)              & $3_1^+$    & $2_2^+$     &  970.3(3)        & 1.15(9)   \\
            &                     &            & $2_1^+$     &  1959.8(4)       & 1.7(1)   \\
4138.6(4)   & 6.2(4)              & $2_3^+$    & $2_2^+$     &  1352.2(4)\footnotemark[1]       & 0.48(7)   \\
            &                     &            & $2_1^+$     &  2341.2(4)       & 4.7(3)   \\
            &                     &            & $0_1^+$     &  4138.0(5)\footnotemark[1]       & 1.0(1)   \\
4187.6(4)   & 4.4(3)              & $3_2^+$    & $2_2^+$     &  1401.3(3)       & 3.8(2)   \\
            &                     &            & $2_1^+$     &  2390.1(4)\footnotemark[1]       & 2.2(1)   \\
4445.1(4)   & 0.8(2)\footnotemark[1]              & $4_1^+$    & $2_2^+$     &  \multicolumn{1}{l}{ 1660(2)\footnotemark[1]}         & 0.08(6)   \\
            &                     &            & $2_1^+$     &  2647.7(5)\footnotemark[1]       & 1.7(1)   \\
4796.4(5)   & 0.56(9)\footnotemark[1]             & $4_2^+$    & $2_2^+$     &  2999.1(5)\footnotemark[1]        & 0.56(9)   \\
4810.4(4)   & 3.1(2)\footnotemark[1]              & $2_4^+$    & $2_2^+$     &  2023.9(3)\footnotemark[1]        & 3.1(2)   \\
5146.5(6)   & 0.18(5)\footnotemark[1]              & $2_5^+$    & $2_2^+$     &  2360.0(6)\footnotemark[1]        & 0.18(5)   \\
5288.9(4)   & 0.76(7)\footnotemark[1]             &  $4_3^+$   &  $4_1^+$    &  842.9(3)\footnotemark[1]         & 0.33(7)  \\
            &                     &            & $3_1^+$     &  1532.1(5)\footnotemark[1]        & 0.43(7)   \\
            &                     &            & $2_1^+$     & \multicolumn{1}{l}{  3491\footnote[2]{Not observed.}}   &\textless0.12\footnotemark[3]   \\
5517.3(3)   & 2.7(2)\footnotemark[1]              &  $4_4^+$   &  $4_1^+$    &  1072.1(5)\footnotemark[1]         & 0.69(9)  \\
            &                     &            & $3_2^+$     &  1329.9(3)\footnotemark[1]         & 1.4(1)   \\
            &                     &            & $3_1^+$     &  1759.7(5)\footnotemark[1]         & 0.47(6)   \\
            &                     &            & $2_2^+$     &  2729.9(5)\footnotemark[1]         & 0.29(5)   \\
5929.3(6)   & 0.15(5) \footnote[4]{Only the $\gamma$ branch has been measured.}             &  $3_3^+$   &  $3_2^+$    &  1741.7(9)         & 0.15(5)   \\
 \end{tabular}
 \end{ruledtabular}
 \end{table}

where  $N_0$  is the total number of ions decaying, $\varepsilon_{\gamma(\beta)}$ are the efficiencies to detect $\gamma$ rays ($\beta$ particles), and $I_{\gamma}$ is the absolute $\gamma$-ray intensity. To circumvent the uncertainty associated with the  total number of ions decaying,  we  used  the ratio of the number of $\beta$ decays of $^{26}\mathrm{P}$ to its daughter $^{26}\mathrm{Si}$ [$61(2)\%$] \cite{Thomas2004}, and the absolute intensity of the 829-keV $\gamma$-rays emitted in the $\beta$ decay of  $^{26}\mathrm{Si}$, $[21.9(5)\%]$ \cite{Endt19981}, to calculate the intensity of the 1797-keV line, which is the most intense $\gamma$ ray emitted in the decay of $^{26}\mathrm{P}$ (see Table \ref{tab:levels}). To do so, we applied Eq. (\ref{eq:abs_intensity}) to these two $\gamma$ rays :

\begin{equation}
\label{eq:intensity_Al}
N_\gamma(829) = N_{^{26}\mathrm{Si}} \varepsilon_{\gamma}(829) \varepsilon_{\beta}(829)  I_{\gamma}(829)
\end{equation}
\begin{equation}
N_\gamma(1797) = N_{^{26}\mathrm{P}} \varepsilon_{\gamma}(1797) \varepsilon_{\beta}(1797)  I_{\gamma}(1797)
\label{eq:intensity_Si}
\end{equation}

By taking the ratio between Eqs. (\ref{eq:intensity_Al}) and (\ref{eq:intensity_Si}), the only unknown is the intensity of the 1797-keV $\gamma$ ray, because the $\beta$ efficiencies can be obtained from the  $\beta$-gated to ungated ratios discussed in Sec. \ref{sec:experiment}. The value obtained for the intensity of the 1797-keV $\gamma$ ray is thus 58(3)\%, which is in agreement with the value 52(11)\% reported in Ref. \cite{Thomas2004} and more precise. The rest of the  $\gamma$-ray intensities  were determined with respect to this value by employing the efficiency curve and they are  presented in Table \ref{tab:levels}. We also report an upper limit on the intensity of one $\gamma$ ray which was expected to be near the theshold of our sensitivity given the intensity predicted by theory.

\subsection{$\bm{\beta}$-$\bm{\gamma}$-$\bm{\gamma}$ coincidences \label{subsec:coincidences}}
\begin{figure}[t]

 \includegraphics[trim=0mm 5mm 1cm 0mm, clip=true,width=.5\textwidth]{Fig7.eps}%
 \caption{\label{fig:Coincidences2} (Color online) $\beta$-$\gamma$-$\gamma$ coincidence  spectrum gating on   the 1797 keV $\gamma$-rays (blue). The hatched histogram (green) shows  coincidences with continuum background in a relatively broad region above the peak gate.  The background bins are 16 keV wide and are normalized to the expected background per 2 keV from random coincidences. The strongest peaks corresponding to $\gamma$ rays emitted in coincidence are indicated.}
 \end{figure}

 The 16-fold granularity of SeGA  allowed us  to obtain $\beta$-$\gamma$-$\gamma$ coincidence spectra,  which helped to interpret the $^{26}\mathrm{P}$ decay scheme. Fig. \ref{fig:Coincidences2} shows the gamma coincident spectrum gated on the 1797-keV peak, where we can see several peaks corresponding to $\gamma$ rays detected  in coincidence. To estimate the background from random coincidences, we have created another histogram gated on the background close to the peak and normalized  to the number of counts within the gated regions. At some energies the background estimate is too high. This is because of a contribution from real $\gamma$-$\gamma$ coincidences involving Compton background, which should not be normalized according to the random assumption.

\begin{figure*}

\centering
 \includegraphics[trim=0mm 2mm 1cm 9mm, clip=true,width=.75\textwidth]{Fig8.eps}%
 \caption{\label{fig:Coincidences} Selected sample of  $\beta$-$\gamma$-$\gamma$ coincidence  peaks gating on different $\gamma$ rays: (a) 989~keV, (b) 1401~keV, (c) 2024~keV, and (d)  2341~keV. The hatched histogram shows  normalized coincidences with continuum background in a relatively broad region above the peak gates. The background bins are 8-keV wide  and are normalized to the expected background per keV.}
 \end{figure*}

   Fig. \ref{fig:Coincidences} presents a sample of  peaks observed in  coincidence when gating on  some other intense $\gamma$ rays observed. From this sample we can see that the  coincidence technique helps to  cross-check the decay scheme. For example Fig. \ref{fig:Coincidences}(a) shows clearly that the 1401-keV $\gamma$ ray is emitted in coincidence with the 989-keV $\gamma$ ray, indicating that the former $\gamma$ ray comes from a  higher-lying level. In the same way, we can see in  Fig. \ref{fig:Coincidences}(b)  that the 1330-keV $\gamma$-ray  is emitted from a level higher than the 4187-keV level. From the gated spectra, some information can  also be extracted from the missing peaks. As  Fig. \ref{fig:Coincidences}(c) shows, by gating on the 2024-keV $\gamma$ ray the 970-keV peak disappears, displaying only the 989-keV peak, which means that the 970-keV $\gamma$ ray comes from a level which is  not connected with these two levels by any $\gamma$-ray cascade. Fig. \ref{fig:Coincidences}(d) shows clearly the coincidence between the  $\gamma$ ray emitted from the first  $2^+$ state at 1797~keV to the ground state of $^{26}$Si and the  2341-keV $\gamma$ ray from the third $2^+$ state to the first excited state.

 These coincidence procedures were systematically analyzed for all possible combinations of $\gamma$ rays and the results are summarized in Table \ref{tab:coincidence} in the form of a 2D matrix, where a checkmark (\checkmark) means the $\gamma$ rays were detected in coincidence. The condition for a $\gamma$ ray to be listed in coincidence with another is for it to be at least 3$\sigma$ above the estimated random-coincidence background. It is  worth noting  that this background estimate is somewhat conservative, therefore  the significance of some of the peaks is underestimated.

\begin{table*
 \caption{\label{tab:coincidence}  Coincidence matrix of all the $\gamma$ rays measured in the $\beta$ decay of $^{26}\mathrm{P}$. The first column corresponds to the  $\gamma$-ray energy on which the gate is set. The following columns indicate the $\gamma$ rays observed in the gated spectrum. $\gamma$ rays observed in coincidence are indicated with a checkmark (\checkmark) if the detection is larger than $3\sigma$ above background. $\gamma$-ray energies have been rounded to the closest integer and are given in keV.}
 \begin{ruledtabular}

\begin{tabular}[c]{ccccccccccccccccccccccc}
	&843	&  970  &   989  &   1072  &  1330  &  1352  &  1401 &   1532&    1660  &  1742  &  1760  &  1797 &   1960  &  2024  &  2341 &   2360 & 2390	&  2648  &  2730  &  2787  &  2999  &  4138 \\
\hline
843	&	&  -	&   \checkmark	 &   -    &  -    &  -    &  -   &	 -  &	  -	&  -	 &  -    &  -   &   \checkmark     &  -    &  -   &	 -   &   -	&  \checkmark	 &  -    &  \checkmark     &  -    &  -   \\
970	&-	&	&   \checkmark	 &   \checkmark     &  -    &  -    &  -   &	 -   &	  -	&  -	 &  \checkmark	  &  \checkmark    &   -    &  -    &  -   &	 -   &   -	&  -	 &  -    &  -    &  -    &  -   \\
989	&\checkmark&  \checkmark&	 &   \checkmark     &  \checkmark  &  \checkmark  &  \checkmark    &\checkmark   &\checkmark	&  -	 & \checkmark& \checkmark &   -  &\checkmark&  - &\checkmark &   -	&  -	 &  \checkmark&  \checkmark&  -   &  -   \\
1072	&-	&  -	&   \checkmark	 &	   &  -    &  -    &  \checkmark    &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &  -    &  -   &	 -   &   -	&  \checkmark	 &  -    &  -    &  \checkmark     &  -   \\
1330	&-	&  -	&   \checkmark	 &   -    &	    &  -    &  \checkmark    &	 -  &	  -	&  -	 &  -    &  \checkmark    &   \checkmark     &  -    &  -   &	 -   &   -	&  -	 &  -    &  -    &  -    &  -   \\
1352	&-	&  -	&   \checkmark	 &   -    &  -    &	     &  -   &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &  -    &  -   &	 -   &   -	&  -	 &  -    &  \checkmark     &  -    &  -   \\
1401	&\checkmark	&  -	& \checkmark& \checkmark & \checkmark &  -  & & -  &	  -	& \checkmark\footnote[1]{Not 3$\sigma$, but 99.6\% C.L.} &  -    & \checkmark & \checkmark &  -    &  -   &	 -   &   -	& -&  -  &\checkmark  &  -    &  -   \\
1532	&\checkmark	&  \checkmark	&   \checkmark	 &   --   &  -    &  -    &  -   &	     &	  -	&  -	 &  -    &  \checkmark    &   \checkmark     &  -    &  -   &	 -   &   -	&  -	 &  -    &  -    &  -    &  -   \\
1660	&\checkmark	&  -	&   -   &   \checkmark     &  -    &  -    &  -   &	 -  &	 	&  -	 &  -    &  \checkmark    &   -    &  -    &  -   &	 -   &   -	&  -	 &  -    &  \checkmark     &  -    &  -   \\
1742	&-	&  -	&   -	 &   -    &  -    &  -    &  \checkmark    &	 -  &	  -	&	 &  -    &  -    &   -    &  -    &  -   &	 -   &   -	&  -	 &  -    &  -     &  -    &  -   \\
1760	&-	&  \checkmark	&   \checkmark	 &   -    &  -    &  -    &  -   &	 -  &	  -	&  -	 &	  &   \checkmark   &   \checkmark     &  -    &  -   &	 -   &   -	&  -	 &  -    &  -    &  -    &  -   \\
1797	&-	&  -	&   \checkmark	 &   -     &  -     &  -  &  \checkmark    &	 -   &	  -	&  -	 &  -	  &	  &   \checkmark     &  \checkmark     &  \checkmark   & -   &   \checkmark	&  \checkmark	 &  -	  &  -    &  -     &  -   \\
1960	&\checkmark	&  -	&   -   &   -    &  \checkmark     &  -    &  -   &	 \checkmark   &	  -	&  -	 &  \checkmark	  &  \checkmark    &	    &  -    &  -   &	 -   &   -	&  -	 &  -    &  -    &  -    &  -   \\
2024	&\checkmark	&  -	&   \checkmark	 &   -    &  -    &  -    &  -   &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &	     &  -   &	 -   &   -	&  -	 &  -    &  \checkmark     &  -    &  -   \\
2341	&-	&  -	&   -   &   -    &  \checkmark     &  -    &  -   &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &  -    &	     &	 -   &   -	&  -	 &  -    &  -    &  -    &  -   \\
2360	&-	&  -	&   -   &   -    &  -    &  -    &  -   &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &  -    &  -   &	      &   -	&  -	 &  -    &  \checkmark     &  -    &  -   \\
2390	&-	&  -	&   -   &   -    &  \checkmark     &  -    &  -   &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &  -    &  -   &	 -   &  	&  -	 &  -    &  -    &  -    &  -   \\
2648	&\checkmark	&  -	&   -   &   \checkmark     &  -    &  -    &  -   &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &  -    &  -   &	 -   &   -	&	 &  -    &  -    &  -    &  -   \\
2730	&-	&  -	&   \checkmark	 &   -    &  -    &  -    &  -   &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &  -    &  -   &	 -   &   -	&  -	 &	  &  -    &  -    &  -   \\
2787	&\checkmark	&  \checkmark	&   -   &   -    &  \checkmark     &  \checkmark     &  \checkmark    &	 -  &	  -	&  -	 &  \checkmark	  &  -   &   -    &  \checkmark     &  -   &	 -   &   -	&  -	 &  -    &	   &  -    &  -   \\
2999	&-	&  -	&   -   &   -    &  -    &  -    &  -   &	 -  &	  -	&  -	 &  -    &  \checkmark    &   -    &  -    &  -   &	 -   &   -	&  -	 &  -    &  -    &	    &  -   \\
4138	&-	&  -	&   -   &   -    &  -    &  -    &  -   &	 -  &	  -	&  -	 &  -    &  -   &   -    &  -    &  -   &	 -   &   -	&  -	 &  -    &  -    &  -    &	    \\

 \end{tabular}
 \end{ruledtabular}
 \end{table*}

\subsection{Decay scheme of $\bm{^{26}\mathrm{P}}$}

Fig. \ref{fig:decay} displays the $^{26}\mathrm{P}$ $\beta$-decay scheme deduced from the results obtained in this experiment. Only those levels populated in the $\beta$ decay are represented. This level scheme was  built in a self-consistent way by taking into account the  $\gamma$-ray energies and intensities observed in the singles spectrum of Fig. \ref{fig:spec} and the $\beta$-$\gamma$-$\gamma$ coincidence spectra described in Sec. \ref{subsec:coincidences}.

\begin{figure*}
\centering
 \includegraphics[trim=0mm 5mm 1cm 0mm, clip=true,width=\textwidth]{Fig9.eps}%
 \caption{\label{fig:decay} (Left) $^{26}$P decay scheme as deduced from the experimental data acquired in the present work. $\gamma$-ray transition labels correspond to the absolute intensities. $\beta$-decay branches corresponding to each populated level are also given (red). The branches to the unbound $3^+$ state and the particle unbound states (asterisks) were taken from literature \cite{Thomas2004,Schwartz2015}. (Right) $^{26}$Si levels populated in $^{26}$P $\beta$ decay obtained from a USDB shell-model calculation.  Level energies are given in keV.}
 \end{figure*}

The excitation energies of $^{26}\mathrm{Si}$  bound levels, their $\beta$-feedings, the energies of the $\gamma$ rays, and the absolute intensities measured in this work are shown in Table \ref{tab:levels}.

\subsubsection{$^{26}\mathrm{Si}$ level energies, spins and parities }

 Level energies of $^{26}\mathrm{Si}$ populated  in the $\beta$ delayed $\gamma$ decay of  $^{26}\mathrm{P}$  were obtained from the measured $\gamma$-ray energies  including a correction for the nuclear recoil. The excitation energy values of the  levels listed in Table \ref{tab:levels}  were obtained from the weighted average of all the possible $\gamma$-ray cascades coming from that level. To assign spins and parities we compared the deduced level scheme with USDB shell-model calculations and took into account $\beta$-decay angular momentum  selection rules, showing a 1 to 1 correspondence for all the levels  populated by allowed transitions, with a fair agreement in the level energies within theoretical uncertainties of a few hundred  keV (see Fig. \ref{fig:decay} ).

\subsubsection{ $\beta$-feedings}
 The $\beta$ branching ratio to the $i$-th excited energy level can be determined from the $\gamma$-ray intensities:

\begin{equation}
\label{eq:BR}
BR_i = I_{i,\text{out}}-I_{i,\text{in}},
\end{equation}
where $I_{i,\text{out}}(I_{i,\text{in}})$ represents the total $\gamma$-ray intensity  observed decaying out of (into) the $i$-th level. The $\beta$-decay branches deduced from this experiment are given in Table \ref{tab:BR}, where they are also compared to previous measurements of $^{26}\mathrm{P}$  $\beta$ decay \cite{Thomas2004}. To investigate  the possible  missing intensity from the Pandemonium effect \cite{Hardy1977}, we have used a shell-model calculation to estimate the  $\gamma$-ray intensities of all possible transitions from  bound states  feeding each particular level, and found them to be on the order of the uncertainty or (usually) much lower.
 \begin{table*}[t
 \caption{\label{tab:BR} Comparison of the $\beta$-branches and $\log\! ft$ values obtained in the present work with previous determinations and shell-model calculations. Values previously unknown are indicated by a dash.}

 \begin{ruledtabular}

\begin{tabular}[c]{l d d d d d d}
\multicolumn{1}{c}{$E_x$ (keV)} & \multicolumn{3}{c}{ $\beta$-Branch (\%) }    &\multicolumn{3}{c}{ $\log\! ft$}\\
\cline{2-4}\cline{5-7}
& \multicolumn{1}{c}{Present work}&\multicolumn{1}{c}{Ref. \cite{Thomas2004} }   &\multicolumn{1}{c}{Theory}  &
\multicolumn{1}{c}{Present work}&\multicolumn{1}{c}{Ref. \cite{Thomas2004} }  &\multicolumn{1}{c}{Theory} \\
\hline
1797   & 41(3) 		  	      & 44(12)  & 47.22			&  4.89(3) & 4.89(17)			   &4.81  	\\
2786   &\textless0.39   	      & 3.3(20) & 0.37			& \multicolumn{1}{c}{ $>$6.76} & 5.87(72)  &6.77  	\\
3757   & 1.9(2) 		      & 2.68(68)& 1.17 			& 5.94(4) & 5.81(15) 			   & 6.135	\\
3842   & \multicolumn{1}{c}{not obs.} & 1.68(47)& \multicolumn{1}{c}{--}& \multicolumn{1}{c}{not obs.} & 6.00(17) & \multicolumn{1}{c}{--}	 \\
4139   & 6.2(4) 		      & 1.78(75)& 2.97 			& 5.37(3) & 5.93(32) 			   & 5.634	\\
4188   & 4.4(3) 		      & 2.91(71)& 8.88 			& 5.51(3) & 5.71(14) 			   & 5.182	\\
4445   & 0.8(2) 		      &\multicolumn{1}{c}{--}& 1.11	& 6.23(8) &\multicolumn{1}{c}{--}  	   & 6.071	\\
4796   & 0.56(9) 		      &\multicolumn{1}{c}{--}&	0.06	&  6.31(7) &\multicolumn{1}{c}{--}	   & 7.274	\\
4810   & 3.1(2) 		      &\multicolumn{1}{c}{--}&	4.45	&  5.57(3) & \multicolumn{1}{c}{--}	   & 5.934	\\
5147   & 0.18(5) 		      &\multicolumn{1}{c}{--}& 0.03	&  6.7(1) &\multicolumn{1}{c}{--} 	   &7.474 	\\
5289   & 0.76(7) 		      &\multicolumn{1}{c}{--}&	0.60	& 6.09(6) & \multicolumn{1}{c}{--}	   &6.158 	\\
5517   & 2.7(2) 		      &\multicolumn{1}{c}{--}&	3.96	&  5.51(4) & \multicolumn{1}{c}{--}	   &5.262 	\\
5929   & 0.15(5)\footnote[1]{Only the $\gamma$ branch was measured} & 17.96(90)\footnote[2]{Only the proton branch was measured}&10.08 &  6.7(1)\footnotemark[1] & 4.60(3)\footnotemark[2] 	   &4.810      \\
 \end{tabular}
 \end{ruledtabular}
 \end{table*}

\section{ Discussion}

\subsection{Comparison to  previous values of  $\bm{^{26}\mathrm{Si}}$ level energies}

 We compare in Table  \ref{tab:energies} the  energies and the spins and parities deduced in this work with previous values available in the literature \cite{Thomas2004,PhysRevC.75.062801,Komatsubara2014,Doherty2015}. The results of Ref. \cite{Thomas2004} correspond to $\beta$ decay, thus the same levels are expected to be populated. We observed six  levels of  $^{26}\mathrm{Si}$ for the first time in the $\beta$ decay of  $^{26}\mathrm{P}$. These six levels were previously reported using  nuclear reactions  to populate them \cite{PhysRevC.75.062801,Komatsubara2014,Doherty2015}. The previously reported energies for these levels are in  good agreement with  the results obtained in this work. However, it is worth  mentioning a significant discrepancy (up to 6~keV) with energies obtained in Refs. \cite{PhysRevC.75.062801,Doherty2015} for the  two $\gamma$ rays  emitted from the $4_4^+$ state to the  $3_1^+$ and  $2_2^+$ states (1759.7 and 2729.9~keV, respectively). Despite these discrepancies in the $\gamma$-ray energies, the excitation energy of the level reported is in excellent agreement with our results. However, it should be noted that the $\gamma$-ray branching ratios are inconsistent for the 1759.7-keV transition.

 The 3842-keV level reported in \cite{Thomas2004} was not observed in the present work. In agreement with \cite{PhysRevC.75.062801,Komatsubara2014,Doherty2015} we show that  this level does not exist, as the 2045-keV $\gamma$ ray emitted from this level to the first excited state is not seen either  in the spectrum of Fig. \ref{fig:spec} nor the coincidence spectrum with the 1797-keV peak (Fig.~\ref{fig:Coincidences2}).

The 4810-keV level was  previously tentatively assigned to be a $2^+$ state, but this assignment was not clear, because of the proximity to another level at 4830~keV assigned as a $0^+$. The fact that the 2024-keV line  appears in the spectrum confirms that the spin and parity is $2^+,3^+$ or $4^+$. If this level was  $0^+$, the $\beta$-decay transition which populates this level would be second forbidden ($\Delta J=3$,$\Delta\pi=0$) and  highly suppressed.

 We  observed also the  two levels located  just above the proton separation energy ($S_p=5513.8$~keV). The first one corresponds to a $4^+$ state with an energy of 5517~keV. This level was also reported in Refs. \cite{PhysRevC.75.062801,Komatsubara2014}. The second level  at 5929~keV was previously observed in $\beta$-delayed proton emission  by Thomas \emph{et al.} \cite{Thomas2004} and more recently reported in our previous paper describing the present experiment \cite{Bennett2013}. The results presented here with the same set of data, but with an independent analysis, confirm the evidence for the observation of a $\gamma$ ray emitted from that level in the present experiment.

\begin{table*
 \caption{\label{tab:energies} Excitation energies, spins and parities  of $^{26}\mathrm{Si}$ levels from the present work compared to previous $\gamma$-ray work and to the allowed $^{26}\mathrm{P}(\beta\gamma)$ transitions predicted by the shell model. Only the states below 6~MeV are listed. Values not observed  are indicated by a dash.}

 \begin{ruledtabular}

\begin{tabular}{c d c d c d c d c d c c}
\multicolumn{2}{c}{Present work  } &\multicolumn{2}{c}{ Ref. \cite{Thomas2004}} &\multicolumn{2}{c}{  Ref. \cite{PhysRevC.75.062801}} &  \multicolumn{2}{c}{  Ref. \cite{Komatsubara2014}}&  \multicolumn{2}{c}{  Ref. \cite{Doherty2015}}&\multicolumn{2}{c}{Theory}\\
\multicolumn{2}{c}{ $^{26}\mathrm{P}(\beta\gamma)$}&\multicolumn{2}{c}{ $^{26}\mathrm{P}(\beta\gamma)$}&\multicolumn{2}{c}{ $^{16}\mathrm{O}(^{12}\mathrm{C},2\mathrm{n}\gamma)$}&
\multicolumn{2}{c}{ $^{\mathrm{nat}}\mathrm{Mg}(^{3}\mathrm{He},\mathrm{n}\gamma)$}&\multicolumn{2}{c}{ $^{\mathrm{24}}\mathrm{Mg}(^{3}\mathrm{He},\mathrm{n}\gamma)$}&\multicolumn{2}{c}{ $^{26}\mathrm{P}(\beta\gamma)$}\\
\cline{1-2}\cline{3-4}\cline{5-6}\cline{7-8}\cline{9-10}\cline{11-12}
$J_n^\pi$ &\multicolumn{1}{c}{$E_x$ (keV)} &$J_n^\pi$ &\multicolumn{1}{c}{$E_x$ (keV)} &$J_n^\pi$ &\multicolumn{1}{c}{$E_x$ (keV)} & $J_n^\pi$ &\multicolumn{1}{c}{$E_x$ (keV)}& $J_n^\pi$ &\multicolumn{1}{c}{$E_x$ (keV)}& $J_n^\pi$ &\multicolumn{1}{c}{$E_x$ (keV)} \\
\cline{1-2}\cline{3-4}\cline{5-6}\cline{7-8}\cline{9-10}\cline{11-12}
$2_1^+$ & 1797.1(3) & $2_1^+$ & 1795.9(2) & $2_1^+$ & 1797.3(1) & $2_1^+$ & 1797.4(4)&$2_1^+$ &1797.3(1) &$2_1^+$ &1887	     \\
$2_2^+$ & 2786.4(3) & $2_2^+$ & 2783.5(4) & $2_2^+$ & 2786.4(2) & $2_2^+$ & 2786.8(6)&$2_2^+$ &2786.4(2) &$2_2^+$ &2948	     \\
\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}& $0_2^+$ & 3336.4(6) & $0_2^+$ & 3335.3(4)&$0_2^+$ & 3336.4(2)&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}\\
$3_1^+$ & 3756.8(3) & $(3_1^+)$ & 3756(2) & $3_1^+$ & 3756.9(2) & $3_1^+$ & 3756.9(4)& $3_1^+$ & 3757.1(3)&$3_1^+$ &3784\\
\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}& $(4_1^+)$ & 3842(2) &\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}\\
$2_3^+$ & 4138.6(4) & $2_3^+$ & 4138(1) & $2_3^+$ & 4139.3(7) & $2_3^+$ & 4138.6(4)& $2_3^+$ & 4138.8(13)    &$2_3^+$ &4401\\
$3_2^+$ & 4187.6(4) & $3_2^+$ & 4184(1) & $3_2^+$ & 4187.1(3) & $3_2^+$ & 4187.4(4) & $3_2^+$ & 4187.2(4) &$3_2^+$ &4256\\
$4_1^+$ & 4445.1(4) & \multicolumn{1}{c}{--}&\multicolumn{1}{c}{--} & $4_1^+$ & 4446.2(4) & $4_1^+$ & 4445.2(4)& $4_1^+$ & 4445.5(12)   &$4_1^+$ &4346\\
$4_2^+$ & 4796.4(5) & \multicolumn{1}{c}{--}&\multicolumn{1}{c}{--} & $4_2^+$ & 4798.5(5) & $4_2^+$ & 4795.6(4) & $4_2^+$ & 4796.7(4)  &$4_2^+$ &4893\\
$2_4^+$ & 4810.4(4) & \multicolumn{1}{c}{--}&\multicolumn{1}{c}{--} & $(2_4^+)$ & 4810.7(6) &$(2_4^+)$ & 4808.8(4)&$2_4^+$ & 4811.9(4)&$2_4^+$ &4853\\
\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}& $(0_3^+)$ & 4831.4(10) & $(0_3^+)$ & 4830.5(7) & $0_3^+$ & 4832.1(4)&\multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}\\
$2_5^+$ & 5146.5(6) & \multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}& $2_5^+$ & 5146.7(9) & $2_5^+$ & 5144.5(4) & $2_5^+$ & 5147.4(8)&$2_5^+$ &5303 \\
$4_3^+$ & 5288.9(4) & \multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}& $4_3^+$ & 5288.2(5) & $4_3^+$ & 5285.4(7)& $4_3^+$ & 5288.5(7) &$4_3^+$ &5418 \\
$4_4^+$ & 5517.3(3) & \multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}& $4_4^+$ & 5517.2(5) & $4_4^+$ & 5517.8(11)& $4_4^+$ & 5517.0(5)&$4_4^+$ &5837 \\
\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}& $1_1^+$ & 5677.0(17)& $1_1^+$ & 5673.6(10) & $1_1^+$ & 5675.9(11)&\multicolumn{1}{c}{--}& \multicolumn{1}{c}{--} \\
\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--} & $0_4^+$ & 5890.0(10)& $0_4^+$ & 5890.1(6)& \multicolumn{1}{c}{--}& \multicolumn{1}{c}{--}\\
$3_3^+$ & 5929.3(6) & $3_1^+$ & 5929(5)\footnote{$^{26}\mathrm{P}(\beta\mathrm{p})$.} & \multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&\multicolumn{1}{c}{--}&$3_3^+$ &6083 \\

\end{tabular}
\end{ruledtabular}
\end{table*}

\subsection{$\bm{ft}$ values and Gamow-Teller strength}
As mentioned in Sec. \ref{sec:intro}, the calculation of the experimental $ft$ values requires the measurement of three fundamental quantities: (a) the half-life, (b) the branching-ratio, and (c) the $Q$ value of the decay. The experimental value of the half-life and  the semiempirical $Q$-value, are $t_{1/2}=43.7(6)$~ms and $Q_{EC}=18250(90)$~keV, respectively. Both values were taken from Ref. \cite{Thomas2004}. The branching ratios from the present work  are listed in Table \ref{tab:levels}. The partial half-lives $t_i$, are thus calculated as:
\begin{equation}
\label{eq:partial_half_life}
t_i = \frac{t_{1/2}}{BR_i}(1+P_{EC}),
\end{equation}

 where $BR_i$ is the $\beta$-branching ratio of  the $i$-th level and $P_{EC}$ the fraction of electron capture, which can be neglected for the light nuclide $^{26}$P. The statistical  phase space factors $f$ were calculated with the parametrization reported in \cite{Wilkinson197458} including  additional radiative  \cite{WILKINSON1973_2} and diffuseness corrections \cite{PhysRevC.18.401}. The uncertainty associated with this calculation is 0.1\%, which is added quadratically to the uncertainty derived from the 0.5\% uncertainty of the $Q_{EC}$ value. Table \ref{tab:BR} shows the $\beta$ branches and $\log\!ft$ values for the transitions to excited levels of $^{26}$Si  compared to the previous values reported in \cite{Thomas2004}. For the first excited  state, our estimation of the $\beta$ feeding  is consistent with the previous result. In the case of the second excited state, the previous value is one order of magnitude larger than our upper limit. This  is because of the new levels we  observed. The large branching ratios observed for the $2_3^+$ and the $3_2^+$ states compared to previous results, 6.2(4)\% and 4.4(3)\%, respectively, are noteworthy. The reason for that difference is the observation of new $\gamma$ rays emitted by those levels which have now been accounted for. The new levels together with the unobserved state at 3842~keV explain all the discrepancies between the results reported here and literature values \cite{Thomas2004}.
 As far as the $\log\! ft$ values are concerned the agreement for the first excited state is very good, but when going to higher energies, the discrepancies in the $\log\! ft$ values are directly related to those in the branching ratios.

\subsubsection{Comparison to theory}

Theoretical calculations were also performed using a shell model code. Wave functions of $^{26}$P were deduced using a full $sd$-shell model with the USDB interaction and their corresponding beta decay transitions to $^{26}$Si levels.

Fig. \ref{fig:decay} shows the comparison  between the $^{26}\mathrm{Si}$ level energies  deduced in this $^{26}$P $\beta$-decay work to the same levels predicted by the calculation. We observe a fair  agreement in the level energies, but the theoretical values are systematically higher. The r.m.s. and maximum deviations between theory and experimental results are 109 and 320~keV, respectively. From a direct comparison we also see that in this work we have measured all the states populated in the allowed transitions predicted by the shell-model calculation.

The experimental $\log\! ft$ values presented in Table \ref{tab:BR} were determined from the measured  branching ratios combined with the known values of $Q_{EC}$ and half-life \cite{Thomas2004}.  Theoretical Gamow-Teller strengths were obtained from the matrix elements of the transitions to states of $^{26}$Si populated in the $\beta$ decay of $^{26}$P. To compare them to the experimental results, the experimental $B(GT)$ values were calculated from the   $ft$ values through the expression,

\begin{equation}  \label{eq:BGT}
 B(GT)=\frac{2\mathcal{F}t}{ft},
\end{equation}

\begin{table}[b]
  \caption{Comparison of the experimental and theoretical $B(GT)$ values obtained in the present work. The quenching factor applied to theory is $q^2=0.6$.}
  \label{tab:bgt}
 \begin{ruledtabular}
  \begin{tabular}{d  d c d d }
\multicolumn{2}{c}{Present work}& &\multicolumn{2}{c}{Theory}\\
\cline{1-2} \cline{4-5}
\multicolumn{1}{c}{$E_x$ (keV)} & \multicolumn{1}{c}{ $B(GT)$}& $I_n^\pi$ &
\multicolumn{1}{c}{$E_x$ (keV)}   & \multicolumn{1}{c}{ $B(GT)$}
\\
\hline
1797  & 0.048(3)		&$2_1^+$ &1887   &0.0606 \\
2786  &\textless0.0007  	&$2_2^+$ &2948   &0.0007 \\
3757  & 0.0044(4)		&$3_1^+$ &3784   & 0.0029 \\
4139  & 0.016(1)		&$2_3^+$ &4401   & 0.009 \\
4188  & 0.0117(1)		&$3_2^+$ &4256   & 0.0256\\
4445  & 0.0023(4)		&$4_1^+$ &4346   & 0.0033\\
4796  & 0.0018(3)		&$4_2^+$ &4893   & 0.0002\\
4810  & 0.0103(7)		&$2_4^+$ &4853   & 0.0161\\
5147  & 0.0007(2)		&$2_5^+$ &5303   &0.0001  \\
5289  & 0.0031(4)		&$4_3^+$ &5418   & 0.0027\\
5517  & 0.012(1)		&$4_4^+$ &5837   & 0.0213\\

  \end{tabular}
 \end{ruledtabular}
\end{table}

where $\mathcal{F}t= 3072.27\pm0.62$~s \cite{Hardy2015} is the average corrected $ft$ value from $T=1$ $0^+\rightarrow 0^+$ superallowed  Fermi $\beta$ decays. Table \ref{tab:bgt} shows the comparison between the  experimental and theoretical $B(GT)$ values. A quenching factor $q=0.77$ ($q^2=0.6$) was applied to the shell-model calculation \cite{Wildenthal1983}. Theoretical predictions overestimate the experimental values for  the transitions to the $2^+_1$, $3^+_2$, $4^+_1$, $2^+_4$, and $4^+_4$ states. Experimental $B(GT)$ values are slightly underestimated for the rest of the states up to 5.9~MeV.   The most significant differences are in the $4_2^+$  and the $2_5^+$ levels for which the  predicted $B(GT)$ values differ by almost  one order of magnitude with the experimental ones. A possible explanation for this difference is the mixing between different levels.

\begin{figure}[t]

 \includegraphics[trim=0mm 5mm 2mm 0mm, clip=true,width=.45\textwidth]{Fig10.eps}%
 \caption{\label{fig:BGT}  Summed Gamow-Teller strength distribution of the $\beta$ decay of $^{26}$P up to 5.9~MeV excitation energy. The results of the present experiment are compared to previous results \cite{Thomas2004} and Shell-Model calculations. A quenching factor $q^2=0.6$ was used in the theoretical calculation.}
 \end{figure}

\begin{table*}
  \caption{Comparison of experimental $ft$ values for the $\beta$ decay of $^{26}$P and its mirror $^{26}$Na \cite{PhysRevC.71.044309}. The mirror asymmetry $\delta$ is also listed and compared to the previous experimental results \cite{Thomas2004}, where applicable.}
  \label{tab:mirror}
 \begin{ruledtabular}
  \begin{tabular}{d c  c  d c d d}
\multicolumn{2}{c}{ $^{26}\mathrm{P}(\beta\gamma)^{26}\mathrm{Si}$}& &\multicolumn{2}{c}{ $^{26}\mathrm{Na}(\beta\gamma)^{26}\mathrm{Mg}$ \cite{PhysRevC.71.044309}}& \multicolumn{2}{c}{ $\delta (\%)$}\\
\cline{1-2} \cline{4-5} \cline{6-7}
\multicolumn{1}{c}{$^{26}\mathrm{Si}\;E_x$ (keV)}  & \multicolumn{1}{c}{$ft^+$ (s) } & $I_n^\pi$&
\multicolumn{1}{c}{$^{26}\mathrm{Mg}\;E_x$ (keV)}  & \multicolumn{1}{c}{$ft^-$ (s) } & \multicolumn{1}{c}{Present work}&\multicolumn{1}{c}{Ref.\cite{Thomas2004}}
\\
\hline
1797  & 7.9(5)$\times 10^4$ 	& $2_1^+$ &1809 &5.23(2)$\times 10^4$  & 51(10) &50(60)\\
3757  & 8.7(8)$\times 10^5$ 	& $3_1^+$ &3941  &7.5(2)$\times 10^5$  &16(11)&10(40)  \\
4139  & 2.4(2)$\times 10^5$ 	& $2_3^+$ &4332  &4.22(9)$\times 10^5$  &-43(5)&110(160)  \\
4188  & 3.2(2)$\times 10^5$  	& $3_2^+$ &4350  &2.16(4)$\times 10^5$   & 50(10) &110(70)\\
4445  & 1.7(7)$\times 10^6$ 	& $4_1^+$ &4319  &1.43(3)$\times 10^6$  &20(50) \\
4796  & 2.1(3)$\times 10^6$ 	& $4_2^+$ &4901  &1.63(7)$\times 10^6$  & 29(18)\\
4810  & 3.7(3)$\times 10^5$ 	& $2_4^+$ &4835  &1.85(2)$\times 10^5$  & 100(16)\\
5147  & 5.6(20)$\times 10^6$  	& $2_5^+$ &5291  &2.0(3)$\times 10^7$ &  -72(11)\\
5289  & 1.2(2)$\times 10^6$ 	& $4_3^+$ &5476  &7.9(40)$\times 10^7$ & -98(1)\\
5517  & 3.2(3)$\times 10^5$  	& $4_4^+$ &5716&  1.71(3)$\times 10^5$&87(18) \\

  \end{tabular}
 \end{ruledtabular}
\end{table*}

 Fig. \ref{fig:BGT} shows the summed Gamow-Teller strength distribution of the decay of $^{26}$P for  bound levels up to 5517~keV. In this figure we compare the results obtained in this work with the previous results and the shell-model calculation.  We can see that the agreement with the previous experimental results is good for the first excited state, with a small difference that is consistent within uncertainties. As the energy increases the differences become more significant, with our results slightly below the previous ones until the contribution of the new levels is added. For energies above 4.1 MeV, the results from the previous experiment are clearly below our results. If we compare the present data with the theoretical prediction using the typical quenching factor of $q^2=0.6$, we see that the theoretical prediction overestimates the summed Gamow-Teller strength in the excitation energy region below 5.9~MeV.
If a quenching factor of 0.47 were applied to the shell model calculations instead, the agreement would be almost perfect in this energy region. However, this does not necessarily imply that the value of $q^2=0.6$ is inapplicable because only a small energy range was considered for the normalization. In fact, most of  the Gamow-Teller strength is to unbound states which have not been measured in the present work. Furthermore, according to shell model calculations, only $\sim$21\% of the total Gamow-Teller strength is in the $Q$-value window.

\subsection{Mirror asymmetry and $\bm{^{26}\mathrm{P}}$ proton halo}

The high precision data on the $\beta$ decay of the mirror-nucleus $^{26}$Na from Ref. \cite{PhysRevC.71.044309}, together with the results obtained in the present work made it possible to calculate finite values of the mirror asymmetry for $\beta$-decay transitions from the  $A=26$, $T_z=\pm2$ mirror nuclei to low lying states of their respective daughters. Table \ref{tab:mirror} shows the results of the $ft$ values obtained for the $\beta$ decay of $^{26}$P and its mirror nucleus, and the corresponding asymmetry parameter,  compared to the previous experimental results reported in Ref. \cite{Thomas2004}. We see that for the low lying  states, the agreement between previous data and our results is good, but our results are  more precise, yielding the first finite values for this system. For the higher energy states, we report the first values for the mirror asymmetry. We observe  large and significant   mirror asymmetries with values ranging from $-98\%$ up to $+100\%$. As mentioned in Sec. \ref{sec:intro}, mirror asymmetries can be related to isospin mixing and/or differences in the radial wavefunctions. It was also shown that halo states produce  significant mirror asymmetries. The $51(10)\%$ asymmetry observed for the transition to the first excited state could be further evidence for a proton halo in $^{26}$P \cite{Navin1998}. Higher lying states are not as useful because of possible mixing between nearby states.

To investigate this effect more quantitatively, we performed  two different shell model calculations with the USDA and USDB interactions. For the transition to the first excited state, these two interactions  predict mirror asymmetries of 3\% and 2.5\%, respectively: far from  experimental result. If we lower the energy of the $2s_{1/2}$ proton orbital by 1~MeV  to account for the low proton separation energy of $^{26}$P, the mirror asymmetries we obtain  for the first excited state are 60\%  and 50\% for the USDA and USDB interactions, respectively, in agreement with the experimental result and supporting the  hypothesis of a halo state \cite{Brown1996}. Before firm conclusions can be made, however, more detailed calculations are needed to evaluate the contributions of the  other effects that may produce mirror asymmetries.

\section{ $\bm{^{25}\mathrm{Al}(\mathrm{p},\gamma)^{26}\mathrm{Si}}$ Reaction rate calculation}

As reported in Ref. \cite{Wrede_2009}, the $\beta$ decay of $^{26}$P to $^{26}$Si provides a convenient means for determining parameters of the astrophysically relevant reaction $^{25}$Al$(p,\gamma)^{26}$Si  in novae. In these stellar environments, the nuclei are assumed to have a Maxwell-Boltzmann distribution of energies characterized by the temperature $T$ from which the  resonant reaction rate can be described by a sum over the different resonances:

\begin{equation}
\label{eq:Reaction rate}
\langle \sigma v\rangle=\left (\frac{2\pi}{\mu kT}\right )^{3/2}\hbar^2\sum_r(\omega\gamma)_re^{-E_r/kT},
\end{equation}

where $\hbar$ is the reduced Planck constant, $k$ is the Boltzmann constant, $\mu$ is the reduced mass, and $E_r$ is the energy of the resonance in the center-of-mass frame. $(\omega\gamma)_r$ is the resonance strength, which is  defined as

\begin{equation}
\label{eq:Res_stength}
(\omega\gamma)_r=\frac{(2J_r+1)}{(2J_p+1)(2J_{\text{Al}}+1)}\left(\frac{\Gamma_p\Gamma_\gamma}{\Gamma} \right )_r.
\end{equation}

\begin{table}

  \caption{Thermonuclear $^{25}$Al$(p,\gamma)^{26}$Si reaction rate, $N_A\langle\sigma v\rangle$, in units of cm$^3$s$^{-1}$mol$^{-1}$ as a function of stellar temperature $T$, including resonant capture contributions from  resonances and direct capture. The first and last columns labeled ``Low'' and ``High'', respectively, correspond to the 1 standard deviation uncertainty limits, while the ``Central'' one corresponds to the recommended rate.}
  \label{tab:rate}

 \begin{ruledtabular}
  \begin{tabular}{ d n{2}{2} n{2}{2} n{2}{2} }

\multicolumn{1}{c}{$T$ (GK)}	&	\multicolumn{1}{c}{Low}		&       	\multicolumn{1}{c}{Central}&       	\multicolumn{1}{c}{High}	     \\
\hline
0.01	&	1.10E-37	&	1.57E-37	&	2.04E-37	\\
0.015	&	7.00E-32	&	1.00E-31	&	1.30E-31	\\
0.02	&	3.19E-28	&	4.56E-28	&	5.93E-28	\\
0.03	&	1.23E-23	&	1.75E-23	&	2.28E-23	\\
0.04	&	9.42E-21	&	1.34E-20	&	1.75E-20	\\
0.05	&	1.40E-18	&	1.93E-18	&	2.88E-18	\\
0.06	&	1.16E-16	&	2.42E-16	&	6.17E-16	\\
0.07	&	5.64E-15	&	1.50E-14	&	4.30E-14	\\
0.08	&	1.27E-13	&	3.59E-13	&	1.06E-12	\\
0.09	&	1.46E-12	&	4.23E-12	&	1.25E-11	\\
0.1	&	1.03E-11	&	3.01E-11	&	8.95E-11	\\
0.11	&	5.06E-11	&	1.48E-10	&	4.40E-10	\\
0.12	&	1.99E-10	&	5.53E-10	&	1.64E-09	\\
0.13	&	5.80E-10	&	1.68E-09	&	4.98E-09	\\
0.14	&	1.55E-09	&	4.36E-09	&	1.28E-08	\\
0.15	&	4.04E-09	&	1.03E-08	&	2.92E-08	\\
0.16	&	1.14E-08	&	2.43E-08	&	6.24E-08	\\
0.17	&	3.46E-08	&	6.23E-08	&	1.34E-07	\\
0.18	&	1.02E-07	&	1.79E-07	&	3.14E-07	\\
0.19	&	2.84E-07	&	5.41E-07	&	8.44E-07	\\
0.2	&	7.80E-07	&	1.60E-06	&	2.42E-06	\\
0.21	&	2.07E-06	&	4.47E-06	&	6.75E-06	\\
0.22	&	5.21E-06	&	1.15E-05	&	1.75E-05	\\
0.23	&	1.23E-05	&	2.76E-05	&	4.21E-05	\\
0.24	&	2.72E-05	&	6.17E-05	&	9.40E-05	\\
0.25	&	5.67E-05	&	1.29E-04	&	1.97E-04	\\
0.26	&	1.12E-04	&	2.55E-04	&	3.89E-04	\\
0.27	&	2.09E-04	&	4.78E-04	&	7.30E-04	\\
0.28	&	3.74E-04	&	8.55E-04	&	1.31E-03	\\
0.29	&	6.42E-04	&	1.47E-03	&	2.24E-03	\\
0.3	&	1.06E-03	&	2.43E-03	&	3.71E-03	\\
0.31	&	1.70E-03	&	3.88E-03	&	5.93E-03	\\
0.32	&	2.63E-03	&	6.01E-03	&	9.19E-03	\\
0.33	&	3.96E-03	&	9.06E-03	&	1.39E-02	\\
0.34	&	5.82E-03	&	1.33E-02	&	2.04E-02	\\
0.35	&	8.36E-03	&	1.91E-02	&	2.92E-02	\\
0.36	&	1.18E-02	&	2.69E-02	&	4.10E-02	\\
0.37	&	1.62E-02	&	3.70E-02	&	5.66E-02	\\
0.38	&	2.19E-02	&	5.01E-02	&	7.66E-02	\\
0.39	&	2.92E-02	&	6.67E-02	&	1.02E-01	\\
0.4	&	3.83E-02	&	8.75E-02	&	1.34E-01	\\
0.42	&	6.32E-02	&	1.44E-01	&	2.21E-01	\\
0.44	&	9.94E-02	&	2.27E-01	&	3.47E-01	\\
0.46	&	1.50E-01	&	3.42E-01	&	5.22E-01	\\
0.48	&	2.17E-01	&	4.96E-01	&	7.58E-01	\\
0.5	&	3.06E-01	&	6.97E-01	&	1.06E+00	\\

  \end{tabular}
 \end{ruledtabular}
\end{table}

$J_{r(p,\mathrm{Al})}$ are the spins of the resonance (reactants), $\Gamma_{p(\gamma)}$ are the proton ($\gamma$-ray) partial widths of the resonance and $\Gamma=\Gamma_p+\Gamma_\gamma$ is the total width. It was previously predicted \cite{Iliadis_96} that the levels corresponding to significant resonances  at nova temperatures in  the $^{25}$Al$(p,\gamma)^{26}$Si reaction are the $J^\pi = 1_1^+,4_4^+,0_4^+$, and $3_3^+$  levels. In our previous work \cite{Bennett2013} we reported the first evidence for the observation of $\gamma$ rays emitted from the $3_3^+$ level. The determination of the strength of the $3_3^+$ resonance in $^{25}$Al$(p,\gamma)^{26}$Si based on the experimental measurements of the partial proton width  ($\Gamma_p$) \cite{Peplowski2009} and the  $\gamma$-ray branching ratio ($\Gamma_\gamma/\Gamma$) \cite{Bennett2013}  was also performed and used  to determine the amount of $^{26}$Al ejected in novae. In this work, we have confirmed the evidence for the 1742-keV $\gamma$ ray emitted from the  $3_3^+$ level to the $3_2^+$ level in $^{26}$Si with an intensity of $0.15(5)\%$. To some extent, the present paper is a follow-up of our previous work, thus we present here (see Table \ref{tab:rate}) for completeness the results of the full reaction rate calculation used to obtain the astrophysical results published in \cite{Bennett2013}. The table shows the total thermonuclear $^{25}$Al$(p,\gamma)^{26}$Si reaction rate as a function of temperature including contributions from the relevant resonances, namely $1_1^+,0_4^+$, and $3_3^+$  and the direct capture. For the  $1^+$ and $0^+$ resonances and the direct capture, values are adopted from Ref. \cite{Wrede_2009}. Our table includes the rate limits calculated from a 1 standard deviation variation of the parameters.

\section{Conclusions}

We have measured the absolute $\gamma$-ray intensities and deduced the $\beta$-decay branches for the decay of $^{26}$P to bound states and low-lying  resonances of $^{26}$Si. We have observed six new $\beta$-decay branches and 15 $\gamma$-ray lines never observed before in $^{26}$P  $\beta$ decay, likely corresponding to most of all the allowed  Gamow-Teller transitions between the ground state and 5.9~MeV. The energies measured for the excited states show good agreement with previous results obtained using various nuclear reactions to populate these states. We have calculated the $\log\! ft$ values of all these new transitions and compared them to USDB shell-model calculations. The reported values  show  good agreement with the theoretical calculations. In addition, the Gamow-Teller strength function was calculated and compared to theoretical values, showing that the  summed Gamow Teller strength is locally overestimated  with the standard  $sd$ shell quenching of 0.6. The mirror asymmetry was also investigated by calculating the $\beta$-decay asymmetry parameter $\delta$ for 10 transitions. The significant asymmetries observed, particularly for the transition to the first excited states of $^{26}$Si and its mirror $^{26}$Mg ($\delta=(51\pm10)\%$) might be further evidence for the existence of a proton halo in the $^{26}$P.  Finally, we have tabulated the total $^{25}$Al$(p,\gamma)^{26}$Si reaction rate at nova temperatures used to estimate the galactic production of $^{26}$Al in  novae in Ref. \cite{Bennett2013}.

\begin{acknowledgments}
The authors gratefully acknowledge the contributions of the NSCL staff.
This work is supported by the U.S. National Science Foundation under grants PHY-1102511,  PHY-0822648, PHY-1350234, PHY-1404442, the U.S. Department of Energy under contract No. DE-FG02-97ER41020, the U.S. National Nuclear Security Agency under contract No. DE-NA0000979 and the Natural Sciences and Engineering Research Council of Canada.
\end{acknowledgments}

\providecommand{\noopsort}[1]{}\providecommand{\singleletter}[1]{#1}%

redpajama_set_name: RedPajamaArXiv


Deluxe Reclining Front Bucket Seats Includes driver manual height and lumbar adjuster and passenger fold flat front seat with hard back.
Front Air Conditioner Includes electronic controls.
Radio: AM/FM Stereo w/Single CD/MP3 Playback Includes seek and scan, clock, Radio Data System (RDS) and auxiliary input jack for iPod/MP3 player.
Transmission: 4-Speed Automatic w/OD Flat towable.