Introduce yourself – tell us a bit about you and your blog.
My name is Meg and I write the gluten free, vegetarian blog, Beard and Bonnet. My household consists of 1 gluten free vegetarian husband, 1 preteen daughter that will eat just about anything except for cheese, a toddler with a severe gluten allergy and a love for all things meaty, and our 2 pets who are also on a gluten free diet for health reasons. Me? Well, I can eat pretty much anything except for shellfish and processed soy.
It may seem like there is a lot of going without in our kitchen, but what I can promise you is that we don't feel like we are missing out at all. My goal has always been to cook 1 meal everyday that not only meets all of our dietary restrictions, but pleases everyone at the dinner table then I share all of those recipes on my site for our readers.
In the past few years of writing B&B there have been plenty of memorable meals, but some of our family favorites are my "Pulled" Cauliflower BBQ Sandwich, Sweet Potato Taquitos, and Asian Lettuce Wraps.
My passion for cooking began at an early age; my mother is an accomplished pastry chef and my grandparents were avid gardeners so I was always surrounded by food! I can vividly remember picking corn and green beans in my grandparents garden then sitting under their tree with my grandmother and a glass of tea as we tipped and tailed the beans and shucked the corn.
Whenever I think of those times with her I can still recall the smell of the fresh beans and corn and how in that moment with my grandmother nothing else really mattered. Because of all of this inspiration from the amazing cooks around me I wrote my first cookbook when I was 9 complete with pictures and illustrations, my mom still has that tattered cookbook at her house.
I can find recipe inspiration from almost anywhere. Whether it's seasonal vegetables at the farmers market or the desire to recreate an old family favorite from my childhood there really is no one particular place that I find inspiration.
Any ingredients you can't stand? Which one can't you live without?
Can't stand? That would have to be dill pickles. I had a bad experience with them as a child and it has stuck with me all of these years. I can't even stomach the taste of dill, which is sad because I would love to cook with it. If I had to pick one ingredient that I can't live without it would have to be limes. I use them every day, they are always in my water and served alongside meals at my table. There is just something about that little oomph that they give finished dishes that I can't get enough of.
I don't care what type of food you are cooking it is almost always enhanced with a little squeeze of lime or a sprinkling of lime zest.
Are there any cooking techniques, dishes or styles that particularly intimidate you and you have yet to try?
I was so inspired by it that I committed to overcome my fear and to learn as much as I could about Thai cooking. So many recipes that I have created over the last few months now have been influenced by the new techniques and ingredients I have learned about! One of my favorites is my Roasted Spring Vegetable Curry, it has a mild heat factor which makes it perfect for my kids and is equally delicious with a little sriracha and fresh chilies added for Todd and I.
Share your worst cooking nightmare. Any epic recipe failures?
I don't have one particular failure or nightmare that stands out. I prefer to think of them as learning experiences, ha! I can say that for me it comes in waves; it seems like when I am on a roll and the recipes are flowing it feels like there is no stopping me, but every now and then I hit a wall for a few days and it seems like nothing is turning out right.
It's during those times that I find it really key to find new inspiration; whether that comes from the farmer's market, a new cookbook, or finding a new blog to pour myself into. I find that if I focus my attention on finding new inspiration that the wall comes down and I can get back in the kitchen.
What's the most adventurous dish you've ever eaten?
I grew up in the South surrounded by men that loved to hunt and cook. My grandfather had a ritual of always making breakfast for the family whenever we would visit him in Columbia, TN. One Saturday morning he served up homemade biscuits with a fried medallion of meat. Being only 10 or 11 at the time I figured it was some type of pork because that was his favorite breakfast meat.
Turns out it was squirrel that he had hunted himself, I don't think I have been the same since.
If I'm only going to make one dish from your blog, which one should it be?
Hush Puppy Tacos. They are the perfect fusion of my southern upbringing and my love of fresh California cooking. All I can really say about these tacos are that they are a flavor explosion that everyone should experience at least once.
You made the adjustment to gluten free eating due to your son's gluten intolerance. How difficult was this transition?
I'm not going to lie, in the beginning it was very hard to wrap my brain around! We were very much a baguette with dinner, pasta 2 – 3 times a week, and sandwich obsessed family. Watching our son get better everyday that gluten was out of our diets was well worth the transition though and actually became a huge source of inspiration for me. I feel fortunate that I can taste the foods that he sees and wants to try then I can go home and recreate them for him. One of his favorite treats that I have recreated for him are my cinnamon sugar donuts, they are dangerously addictive!
You seem to have moved around a lot over the years, has this affected your cooking style in any way?
I have lived in 14 different places in the past 12 years and have taken inspiration from each and every one of them. I love exploring our new environments for fresh local flavors, new to me ingredients, and building lasting friendships with the people I meet in each place over food. You can't beat that type of life experience, but I will say that the moving itself has become harder over the years and more draining on us physically and emotionally.
We are finally back home in Southern California where we feel at home and have no plans on moving again in the future.
Bio: Meg van der Kruik is the blogger, photographer, and recipe developer behind Beard & Bonnet, a gluten-free vegetarian blog that celebrates style, design, food, and family. Meg has been cooking vegetarian dishes for over 7 years, but it wasn't until her son was born with a gluten intolerance that she delved into the world of gluten-free cooking. Meg's goal is to show others that gluten-free, vegetarian living can be easy, fulfilling, and delicious! Meg's recipes have been published in Southern Living and Go Gluten Free Magazine. Along with her husband, she's also one half of the duo behind the award-winning eco-design studio Union Eighteen, whose recycled rugs have garnered international acclaim.
Follow Beard & Bonnet on : Pinterest, Facebook, Instagram, and Twitter to receive daily updates on what's happening in her kitchen and in front of her camera!
Thank you so much for featuring Beard and Bonnet on your site today!


text:
\section{Introduction}

In recent studies of nuclear excitations in stable and unstable nuclei,
low-energy dipole (LED) strength, which has been found in lower energy regions than giant dipole resonances,
has attracted experimental~\cite{1402-4896-2013-T152-014012,Bracco:2015hca,Bracco:2019gza} and theoretical~\cite{Paar:2007bk} attention.
The LED strengths has been observed in some $N=Z$ nuclei~\cite{Harakeh:1981zz,Poelhekken:1992gvp,Youngblood:1999zz,John:2003ke} and in various neutron-rich nuclei such as $^{18}$O~\cite{PhysRevC.43.2127,Manley:1991zz}, $^{20}$O~\cite{Nakatsuka:2017dhs}, and $^{26}$Ne~\cite{Gibelin:2007fda,Gibelin:2008zz}.
Properties and origins of the LED excitations have been often discussed in relation with symmetry energy of nuclear matter~\cite{Brown:2000pd,Piekarewicz2014,Colo2014}, neutron skin thickness in neutron-rich nuclei~\cite{Piekarewicz:2006ip,Inakura:2011mv,Piekarewicz:2012pp,Tamii:2011pv,Birkhan:2016qkr}, and neutron capture rate from astrophysical interests~\cite{Goriely:1998utv,Goriely:2004qb,Tonchev:2017ily}, but they have been not clarified yet.

In theoretical studies of the LED excitations, a couple of kinds of LED modes have been proposed.
For example, the Pygmy mode in $N> Z$ nuclei, in which excess neutrons oscillate in an opposite direction to
the core~\cite{Ikeda:pygmy}, is considered to contribute isovector dipole (IVD) strengths ~\cite{Mohan:1971tz,10.1143/PTP.83.180,VanIsacker:1992zz}.
Another type is toroidal dipole (TD) mode characterized by a vortical nature suggested by Refs.~\cite{Dubovik:toroidal,Semenko:toroidal}.
The toroidal mode can produce isoscalar dipole (ISD) strength and is expected to appear in both of neutron-rich and $N=Z$ nuclei.
In the recent years, the TD mode is intensively studied by microscopic models~\cite{Vretenar:2001te,Ryezayeva:2002zz,0954-3899-29-4-312,Reinhard:2013xqa}.
Kvasil {\it et al.} have introduced the TD operator to measure the toroidal feature
and demonstrated that it is a sensitive probe for the TD mode~\cite{0954-3899-29-4-312}
though experimental observation of the TD strength has not been confirmed yet.
The third candidate is cluster excitation mode.
As pointed out by Chiba {\it et al.}~\cite{Chiba:2015khu}, the ISD strength can be enhanced in the cluster excitation mode.
In the low-energy spectra, these different kinds of dipole modes do not necessarily appear as identical states but may mix with each other in the low-energy $1^-$ spectra.

In deformed nuclei, further interesting features of the LED excitations can be found due to
coupling of the dipole modes with nuclear deformation.
In a strong coupling regime, the dipole excitations can be classified by $K$ quanta, which indicates
the $z$-component of total angular momentum in a body-fixed frame.
Nesterenko {\it et al.} investigated the LED excitations in deformed nuclei with a mean field approach
\cite{Kvasil:2013yca,Nesterenko:2016qiw,Nesterenko:2017rcc}, and showed that compressional dipole and TD modes appear as
$K=0$ and $K=1$ states, respectively.
The LED excitations in a deformed system of ${}^{10}\textrm{Be}$ have been also discussed in our
previous work~\cite{Shikata:2019wdx}, in which properties of LED have been discussed in terms of
$K$ quanta in the prolately deformed system.

Our future goal is to investigate LED excitations in various nuclei including stable and unstable nuclei
with a microscopic framework and to reveal their fundamental features and origins.
For this aim, it is essential to describe various LED modes such as
the Pigmy, TD, and cluster excitation modes in general nuclei with and without deformations.

In this paper, we propose a new method of variation after $K$-projection in a framework of the
$\beta$-constraint antisymmetrized molecular dynamics (AMD) for the study of LED excitations.
By using the AMD wave function,
the energy variation is performed after the parity- and $K$-projections under constraint of the
quadrupole deformation.
The AMD is a useful microscopic approach for structure study of light nuclei, which can describe developed cluster structures, shell-model-like states, and their intermediate states ~\cite{Kanada-Enyo:2001yji,KANADAENYO2003497,Kimura:2016fce}.
For study of deformed nuclei, the AMD has been developed to the $\beta$-constraint and $\beta\gamma$-constraint versions,
in which quadrupole deformation parameters $\beta$ and $(\beta,\gamma)$ are constrained, respectively, in the energy variation~\cite{Dote:1997zz,10.1143/PTP.106.1153,Suhara:2009jb}.
The latter, $\beta\gamma$-constraint AMD, is a better approach than the former $\beta$-constraint
for detailed description of deformations, in particular, axial asymmetric structures.
However, it needs numerical cost because of a huge number of basis wave functions in the two dimensional space of the constraint parameters
and may encounter difficulty in application to heavy-mass nuclei.
In the present method, we improved the $\beta$-constraint by performing the $K$-projection in the energy variation to
efficiently obtain basis wave functions essential to LED excitations.

As a test case of a light deformed nuclei, we first apply the present method to ${}^{10}\textrm{Be}$.
Structure of ${}^{10}\textrm{Be}$ has been investigated by
many theoretical studies, e.g., cluster model~\cite{Fujimura:1999zz,Descouvemont:2002mnw}, molecular orbital model~\cite{vonOertzen1996,Itagaki:2000nn}, and AMD~\cite{Kanada-Enyo:1999bsw,Kanada-Enyo:2015knx},
which show $2\alpha+nn$ cluster structures of low-energy states.
We compare results of the $\beta$-constraint AMD with and without the $K$-projection as well as the
$\beta\gamma$-constraint AMD and show the applicability of the $K$-projection method.
Then we apply the method to study dipole excitations of ${}^{16}\textrm{O}$.

This article is organized as follows.
In Sect.\ \ref{sec:formalism}, the present formalism of $K$-projection after variation in the AMD framework is explained.
The generator coordinate method (GCM) and expression of dipole operators are also described.
The interactions used in the present calculation are expressed in Sect.\ \ref{sec:effective_int}.
Section\ \ref{sec:10Be} shows application to ${}^{10}\textrm{Be}$.
In Sect.\ \ref{sec:16O}, the LED excitations in ${}^{16}\textrm{O}$ are investigated with the present method.
Finally, this article is summarized in Sect.\ \ref{sec:summary}.

\section{Formalism} \label{sec:formalism}

In order to investigate the dipole excitations,
we propose a new method of a constraint AMD with variation
after the $K$-projection as well as the parity projection. That is,
energy variation is performed for the AMD wave function projected
onto the parity and the $z$ component of angular momentum eigen state
under the quadrupole constraint ($\beta$ or $\beta\gamma$).
After the energy variation, thus obtained AMD wave functions are superposed with GCM. For details of the AMD framework,
the reader is referred to Refs.~\cite{Kanada-Enyo:1998onp, Kanada-Enyo:2001yji, 10.1143/PTP.106.1153}.

\subsection{AMD}
An AMD wave function is given by a slater determinant:
\begin{eqnarray}
\Phi = \mathcal{A}\left[\psi_1\psi_2\cdots\psi_A\right],
\end{eqnarray}
where $\psi_i\ (i=1,2,\cdots,A)$ is the $i$th single-particle wave function given by a localized Gaussian wave packet as
\begin{eqnarray}
\psi_i\ &=& \phi(\vector{Z}_i)\chi(\vector{\xi}_i)\tau_i, \\
\phi(\vector{Z}_i) &=& \left(\frac{2\nu}{\pi}\right)^{\frac{3}{4}}\exp\left[ -\nu\left(\vector{r} - \frac{\vector{Z}_i}{\sqrt{\nu}}\right)^2 \right],\\
\chi(\vector{\xi}_i)&=&\xi_{i\uparrow}|\uparrow\rangle + \xi_{i\downarrow}|\downarrow\rangle, \\
\tau_i &=&p\ \textrm{or}\ n.
\end{eqnarray}
$\vector{Z}_i$ and $\vector{\xi}_i$ indicate Gaussian centroids and nucleon-spin orientations, respectively, and they are treated independently as variational parameters determined by the energy optimization.
$\nu$ is the width parameter and is taken to be common with all nucleons.

In a simple version of AMD, the energy variation,
\begin{eqnarray}
\delta\left(\frac{\langle\Psi|\hat{H}|\Psi\rangle}{\langle\Psi|\Psi\rangle} \right) = 0 \label{eq:var}
\end{eqnarray}
is performed for the parity-projected AMD wave function $|\Psi\rangle = \hat{P}^{\pi}|\Phi\rangle$ with the parity projection operator $\hat{P}^{\pi}$.

\subsection{Quadrupole constraint AMD}
In order to perform the $K$-projection, energy variation is performed under constraint of the quadrupole deformation parameter $\beta$ or $\beta\gamma$.
The deformation parameters $\beta$ and $\gamma$ are defined as
\begin{eqnarray}
\beta\cos\gamma &=& \frac{\sqrt{5}}{3}\frac{2\langle z^2\rangle - \langle x^2\rangle - \langle y^2\rangle}{R^2}, \\
\beta\sin\gamma &=& \sqrt{\frac{5}{3}}\frac{\langle x^2\rangle - \langle y^2\rangle}{R^2}, \\
R^2 &=& \frac{5}{3}(\langle x^2\rangle + \langle y^2\rangle + \langle z^2\rangle),
\end{eqnarray}
where $\langle \vector{r} \rangle$ represents an expectation value of operator $\hat{\vector{r}}$ by the AMD wave function without any projection.

In this paper, we perform two kinds of constraint AMD.
One is $\beta\gamma$-constraint AMD($\beta\gamma$-AMD)~\cite{Suhara:2009jb} and the other is the $\beta$-constraint AMD($\beta$-AMD)~\cite{10.1143/PTP.106.1153}.
For a given constraint value $\beta_0$ (or values ($\beta_0,\gamma_0$)), the energy variation is done by
imposing the constraint $\beta=\beta_0$ ($\beta=\beta_0,\gamma=\gamma_0$).
Here we keep the condition for the
off-diagonal components of moment of inertia as $\langle xy\rangle=\langle yz\rangle=\langle zx\rangle=0$.
After the energy variation, the optimized AMD wave function with the given quadrupole deformation
$|\Phi(\beta_0)\rangle$ ($|\Phi(\beta_0,\gamma_0)\rangle$)  is obtained.

\subsection{K-projection VAP}
In the present method, the energy variation in eq.\ \eqref{eq:var} is performed for the $K$ and parity projected AMD wave function $|\Psi\rangle=\hat{P}_{K}\hat{P}^{\pi}|\Phi\rangle$ instead of $|\Psi\rangle=\hat{P}^{\pi}|\Phi\rangle$ without the $K$ projection.
Here,
$\hat{P}_K$ is the $K$-projection operator given as
\begin{eqnarray}
\hat{P}_K = \frac{1}{2\pi}\int_0^{2\pi}d\theta\ e^{-iK\theta}\hat{R}(\theta),
\end{eqnarray}
where $\hat{R}(\theta)$ is the rotation operator around the principal axis in body-fixed frame.
We call the present method "K-VAP" and the conventional method "P-VAP" to distinguish the two methods.
As a result of K-VAP, it is expected that the AMD wave function can be optimized for the given parity and $K$ quantum number.
In order to describe the ground states wave functions of ${}^{10}\textrm{Be}$ and ${}^{16}\textrm{O}$,
the $K^\pi=0^+$ projection is performed in K-VAP, and the
resultant AMD wave function is called $K^{\pi}=0^+$ basis.
For the dipole excitations, i.e., the $1^-$ excitation states, $K^\pi=0^-$ and $K^\pi=1^-$ projections are performed, and the obtained AMD wave functions are called $K^{\pi}=0^-$ and $K^{\pi}=1^-$ bases, respectively.
The obtained AMD wave function of $\beta$-AMD($\beta\gamma$-AMD) with K-VAP is denoted as
$|\Phi_K^\pi(\beta)\rangle$($|\Phi_K^\pi(\beta,\gamma)\rangle$).

\subsection{GCM}
In order to construct wave functions for the ground and $1^-$ states,
GCM is applied for $\beta$-AMD with K-VAP with respect to the  generator coordinate $\beta$.
It means that the basis wave functions are superposed as
\begin{eqnarray}
\Psi^{\pi}(J_m) = \sum_{K,K'}\sum_{\beta}c_{KK'}(\beta)\hat{P}_{MK'}^J\hat{P}^{\pi}|\Phi_K^{\pi}(\beta)\rangle ,
\end{eqnarray}
where the parity projection and total angular momentum projection $\hat{P}_{MK'}^J$ are performed.
Note that, for the $1^-$ states, $K=0$ and $K=1$ bases are adopted and mixing of $K'$ components is taken into account.
The coefficients $c_{KK'}(\beta)$ are determined by solving the Hill-Wheeler equation~\cite{Hill:1952jb,Griffin:1957zza}.
 In a similar way, the GCM calculation with the P-VAP bases wave functions, $|\Phi^{\pi}(\beta_0)\rangle$,
is also performed for comparison.
For the width parameter, we set $\nu = 0.235\ \textrm{fm}^{-2}$ for ${}^{10}\textrm{Be}$ and $\nu = 0.19\ \textrm{fm}^{-2}$ for ${}^{16}\textrm{O}$ which are same in Refs.~\cite{Shikata:2019wdx, Kanada-Enyo:2019hrm}.

\subsection{dipole operator}
To analyze the LED excitation, we use the three dipole operators:
$E1$, compressive dipole (CD), and toroidal dipole (TD) operators~\cite{0954-3899-29-4-312} defined as
\begin{eqnarray}
\hat{M}_{E1}(\mu) &=& \frac{N}{A}\sum_{i\in p}r_iY_{1\mu}(\hat{\vector{r}}_{i}) - \frac{Z}{A}\sum_{i\in n}r_iY_{1\mu}(\hat{\vector{r}}_{i}), \\
\hat{M}_{\textrm{CD}}(\mu) &=& \frac{-1}{10\sqrt{2}c}\int d\vector{r}\ \nabla\cdot\vector{j}_{\textrm{nucl}}(\vector{r})\ r^3Y_{1\mu}(\hat{\vector{r}}), \label{eq:CD_op}\\
\hat{M}_{\textrm{TD}}(\mu)&=&\frac{-1}{10\sqrt{2}c} \int d\vector{r}\ (\hat{\nabla}\times\vector{j}_{\textrm{nucl}}(\vector{r}))\cdot r^3\vector{Y}_{11\mu}(\hat{\vector{r}}), \label{eq:TD_op}
\end{eqnarray}
where $\vector{j}_{\textrm{nucl}}$ is convection nuclear current and $\vector{Y}_{jL\mu}(\hat{\vector{r}})$ is vector spherical given as
\begin{eqnarray}
\vector{j}_{\textrm{nucl}}(\vector{r}) &=& \frac{-i\hbar}{2m}\sum_{k=1}^A\{ \vector{\nabla}_k\delta(\vector{r}-\vector{r}_k) + \delta(\vector{r}-\vector{r}_k)\vector{\nabla}_k \},  \label{eq:current} \\
\vector{Y}_{jL\mu}(\hat{\vector{r}}) &=& \sum_{\alpha,\beta}\langle L\alpha,1\beta|j\mu\rangle Y_{L\alpha}(\hat{\vector{r}})\vector{e}_\beta .
\end{eqnarray}
The transition strength of the dipole operator $\hat{M}_D$ for the $0_1^+\rightarrow 1_k^-$ transition
is given as
\begin{eqnarray}
B(D;0_1^+\rightarrow 1_k^-) = |\langle 1_k^-||\hat{M}_D||0_1^+\rangle|^2 .
\end{eqnarray}
The TD and CD operators are IS type rank-1 operators.
The former can probe the nuclear vorticity as discussed in Ref.~\cite{Nesterenko:2016qiw}.
The latter is a good probe for the compressional mode and corresponds to the ordinary ISD operator
\begin{eqnarray}
\hat{M}_{\textrm{ISD}}(\mu)=\int d\vector{r}\ \rho(\vector{r})r^3Y_{1\mu}(\hat{\vector{r}})
\end{eqnarray}
with the relation of
\begin{eqnarray}
B(\textrm{CD};0_1^+\rightarrow 1_k^-) &=& \left(\frac{1}{10}\frac{E_k}{\hbar c}\right)^2B(\textrm{ISD};0_1^+\rightarrow 1_k^-),
\end{eqnarray}
where $E_k$ is the excitation energy of the $1_k^-$.

\section{Effective interaction} \label{sec:effective_int}
The hamiltonian of total system is given as
\begin{eqnarray}
H = \sum_i t_i - T_G + \sum_{i<j}v_{ij}^{\textrm{coulomb}} + V_{\textrm{eff}} ,
\end{eqnarray}
where $t_i$ and $T_G$ are the kinetic energy of the $i$th nucleon and the center of mass motion, respectively.
$v_{ij}^{\textrm{coulomb}}$ is the two-body coulomb potential which is approximated by a seven-range Gaussian form.
$V_{\textrm{eff}}$ is effective nuclear interaction of the central and spin-orbit forces.
We use the effective interactions same as Refs.~\cite{Kanada-Enyo:2011ldi,Shikata:2019wdx} for
${}^{10}\textrm{Be}$, and those as Refs.~\cite{Kanada-Enyo:2017ers,Kanada-Enyo:2019hrm} for ${}^{16}\textrm{O}$.
That is, for the ${}^{10}\textrm{Be}$, we use the Volkov No.2 force~\cite{Volkov:1965zz} with $W = 1-M = 0.6$ and $B=H=0.125$ for the central force and
the G3RS force~\cite{Yamaguchi:1979hf,Tamagaki:1968zz} with $u_1=-u_2=-1600$\ MeV for the spin-orbit force.
This parameter set describes well the energy spectra of ${}^{10}\textrm{Be}$.
For the case of ${}^{16}\textrm{O}$, we use the MV1 central force
with the case1 parametrization of $W = 1-M = 0.62$ and $B=H=0$, and
the G3RS spin-orbit force  with $u_1=-u_2=-3000$\ MeV, which describe energy spectra of ${}^{12}\textrm{C}$ with the AMD calculation~\cite{Kanada-Enyo:2006rjf}.
The Volkov central force is the finite-range 2-body interaction, which describes the $\alpha$-$\alpha$ scattering phase shifts, and often used for light nuclei, but it has an over-binding problem in application to heavy-mass nuclei.
The MV1 central force consists of the finite-range 2-body and zero-range 3-body terms and can systematically
reproduce the binding energies of $\alpha$, ${}^{12}\textrm{C}$, and ${}^{16}\textrm{O}$~\cite{Kanada-Enyo:2017ers}
without the over-binding problem.

\section{Application to ${}^{10}\textrm{Be}$} \label{sec:10Be}

We apply the newly developed method, that is, $\beta$-AMD with K-VAP for ${}^{10}\textrm{Be}$.
We also apply the $\beta\gamma$-AMD with P-VAP and K-VAP for comparison, and discuss
how the new method works for dipole excitations.

\subsection{energy surfaces and Energy spectra}
For detail analysis, we here discuss energy surfaces on the $\beta$-$\gamma$ plane
obtained by $\beta\gamma$-AMD with K-VAP and that with P-VAP.
In Fig.\ \ref{fig:bg_plane_10Be}, the calculated energy surfaces are shown.
Figures\ \ref{fig:bg_plane_10Be}\ (a) and (b) show the P-VAP result for the positive- and negative-parity projections, respectively, and
Figs.\ \ref{fig:bg_plane_10Be}\ (c), (d), and (e) show the K-VAP result with $K^{\pi}=0^+,\ K^{\pi}=0^-$, and $K^{\pi}=1^-$, respectively.
The K-VAP energy surfaces show a broad flat region around the energy minimum area.
It should be noted that an energy minimum area is located at $\gamma\sim0$ in the  P-VAP energy surfaces
corresponding to a prolate minimum, but it extends (or shifts) toward a triaxial deformation area ($\gamma\sim 30^{\circ}$) in the $K^{\pi}=0^+$ and $K^{\pi}=0^-$ energy surfaces (Figs.\ \ref{fig:bg_plane_10Be} (c) and (d)).
This indicates that the axial symmetric deformation is favored before the $K$-projection but the triaxial deformation is favored after the $K$-projection.

\begin{figure}[!h]
\begin{center}
\includegraphics[width=12cm]{graph/Energy_surface_bg_10Be.pdf}
\includegraphics[width=18cm]{graph/Energy_surface_bg_Kbase_10Be.pdf}
\end{center}
\caption{(color online)
energy surfaces of ${}^{10}\textrm{Be}$ obtained by $\beta\gamma$-AMD with P-VAP and K-VAP.
Panels (a) and (b) are positive- and negative-parity projected energy surfaces, respectively, for the bases of $\beta\gamma$-AMD with P-VAP.
Panels (c), (d), and (e) are $K^{\pi}=0^+,\ 0^-,\ $and $1^-$ projected one, respectively, for bases of $\beta\gamma$-AMD with K-VAP.
The solid lines with filled circles represent the $(\beta,\gamma)$ paths for $\beta$-AMD bases, which
are obtained by optimizing $\gamma$ for each $\beta$ value.
Color mapping is shown in the unit of MeV.
}
\label{fig:bg_plane_10Be}
\end{figure}

The solid lines with filled circle represent the $\gamma$-optimized paths for bases of
$\beta$-AMD, where $\gamma$ is optimized for each $\beta$ value.
In the case of P-VAP, the path goes along the $\gamma=0$ line meaning that $\beta$-AMD with P-VAP gives approximately axial symmetric states.
On the other hand, in the K-VAP result,
the path goes through a $\gamma\ne 0$ area in the energy valley.
It means that  triaxially deformed configurations can be obtained by K-VAP even in the $\beta$-AMD.
As shown later, those triaxial configurations are essential to describe the $K^{\pi}=0^-$ dipole mode.

\begin{figure}[!h]
\begin{center}
\includegraphics[width=12cm]{graph/Energy_spectrum_10Be.pdf}
\end{center}
\caption{
Energy spectra of  ${}^{10}\textrm{Be}$ obtained by the GCM calculation of $\beta\gamma$-AMD and $\beta$-AMD with
P-VAP and K-VAP bases. The experimental energy spectra of the corresponding states are shown for
comparison.
}
\label{fig:spectrum_10Be}
\end{figure}

We perform the GCM calculation for $\beta\gamma$-AMD ($\beta$-AMD) with P-VAP and K-VAP by superposing the obtained basis wave functions to obtain the energy spectra and final wave functions of ${}^{10}\textrm{Be}$.
The calculated energy spectra are shown in Fig.\ \ref{fig:spectrum_10Be} compared with the experimental spectra for corresponding states.
In the K-VAP result, energies are globally lower by about a few MeV than the P-VAP result for all states meaning that
further energy optimization is achieved by the $K$-projection.
For dipole states, two $1^-$ states ($1_{1,2}^-$) are obtained in both the $\beta\gamma$-AMD and $\beta$-AMD
calculations with K-VAP.
However in the case of P-VAP, the $1_2^-$ state is obtained only by $\beta\gamma$-AMD but not
by $\beta$-AMD because the latter calculation ($\beta$-AMD with P-VAP) does not contain triaxially deformed bases
as shown in the $\gamma$-opimized path in Fig.\ \ref{fig:bg_plane_10Be}\ (b).

\begin{figure}[!h]
\begin{center}
\includegraphics[width=10cm]{graph/density_Pbase_10Be.pdf}
\end{center}
\caption{(color online) Intrinsic densities of ${}^{10}\textrm{Be}$  at given $\beta$ values
obtained by $\beta$-AMD with P-VAP.
The optimized values of $\gamma$ for each $\beta$ are written in the panels.
Panels (a) and (b) show the densities of the positive-parity bases and (c) and (d) show those of the negative-parity bases.
}
\label{fig:density_P_10Be}
\end{figure}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=10cm]{graph/density_Kbase_10Be.pdf}
\end{center}
\caption{(color online) Intrinsic densities of ${}^{10}\textrm{Be}$  at given $\beta$ values
obtained by  $\beta$-AMD with K-VAP.
Top, middle, and bottom panels show the densities of the $K^{\pi}=0^+,\ 0^-,\ $and $1^-$ bases, respectively.
}
\label{fig:density_K_10Be}
\end{figure}

\subsection{properties of dipole excitations}

\begin{table}[htbp]
\begin{center}
\begin{tabular}{llcccc} \toprule
&&$E_x\ $(MeV)&$B(\textrm{TD})\ (\textrm{fm}^4)$&$B(\textrm{CD})\ (\textrm{fm}^4)$&$B(E1)\ (\textrm{fm}^2)$ \\ \midrule
P-VAP&$1_1^-$ &9.05&$2.66\times10^{-3}$&$6.79\times10^{-5}$&$6.42\times10^{-3}$ \\
&$1_2^-$&-&-&-&- \\
&&&&& \\
K-VAP&$1_1^-$ &7.96&$2.39\times10^{-3}$&$2.39\times10^{-4}$&$6.92\times10^{-3}$ \\
&$1_2^-$&14.9&$2.59\times10^{-4}$&$2.89\times10^{-4}$&$2.47\times10^{-1}$ \\
&&&&& \\
exp.&$1_1^-$ &5.96&-&-&$2.72\times10^{-6}$ \\
&$1_2^-$&-&-&-&- \\
\bottomrule
\end{tabular}
\end{center}
\caption{The excitation energies and transition strengths in ${}^{10}\textrm{Be}$ obtained by $\beta$-AMD with P-VAP and K-VAP, and experimental data~\cite{PhysRevC.80.034318}.
}
\label{tab:strength_10Be}
\end{table}

In this subsection, we discuss properties of dipole excitations mainly based on the result of $\beta$-AMD with K-VAP.
The excitation energies and dipole transition strengths for the $E1$, CD, and TD operators are shown in Table\ \ref{tab:strength_10Be}.
The intrinsic densities of basis wave functions obtained by $\beta$-AMD with K-VAP and P-VAP
are shown in  Fig.\ \ref{fig:density_K_10Be} and Fig.\ \ref{fig:density_P_10Be}, respectively.
In the K-VAP result, the $0_1^+$ state has a largest overlap with the configuration at $(\beta,\gamma)=(0.60,4.6^{\circ})$ in Fig.\ \ref{fig:density_K_10Be}\ (a), whereas the $1_1^-$ state dominantly contains the $K=1$ component of the intrinsic state at $(\beta,\gamma)=(0.72,1.7^{\circ})$ in Fig.\ \ref{fig:density_K_10Be}\ (f).
They show approximately axial-symmetric shapes ($\gamma\sim 0$) with an $\alpha+{}^6\textrm{He}$-like structure.
In these states, two clusters are close to each other and
not well-developed.
The $1_1^-$ state has the strong TD transition and can be regarded as the $K=1$ excitation built on the compact $\alpha+{}^6\textrm{He}$ state. This remarkable TD strength is caused by vortical current in the transition current density and it is considered that the excitation mode to the $1_1^-$ is the vortical mode consistent with that discussed in Refs.~\cite{Kanada-Enyo:2017uzz,Shikata:2019wdx}.
For  the $0_1^+$ and $1_1^-$ states, the P-VAP result shows similar features
to the K-VAP result in the TD transition, but differs from the K-VAP result in the CD strength.
Namely, the K-VAP calculation shows three times larger CD strength for the $1^-_1$ than the P-VAP calculation
because of significant mixing of the $K=0$ component of triaxially deformed configurations
(see Fig.\ \ref{fig:density_K_10Be}\ (c)).

The $1_2^-$ state is dominantly formed by the $K=0$ component of
triaxially deformed configurations obtained by $\beta$-AMD with K-VAP for the $K^\pi=0^-$. It
has the dominant overlap  ($\sim$ 70\ \%) with the basis wave function at $(\beta,\gamma)=(0.84,5.5^{\circ})$
with a remarkably developed $\alpha+{}^6\textrm{He}$ cluster structure
as shown in Fig.\ \ref{fig:density_K_10Be}\ (d).
It also has significant overlap ($\sim$ 52\ \%) with the base at $(\beta,\gamma)=(0.48,29^{\circ})$
in Fig.\ \ref{fig:density_K_10Be}\ (c). In these configurations,
the ${}^6\textrm{He}$ cluster is deformed in a tilted or perpendicular orientation from the $Z$ axis
contributing the triaxiality of the total system. The $K=0$ component projected from these triaxial configurations play a crucial role in generating the $1_2^-$ state.

In the transition properties,  the remarkable $E1$ strength is obtained for the $1_2^-$:
Energy-weighted strength ($EB(E1:0_1^+\rightarrow 1_2^-)$) accounts for about 10\ $\%$ of the TRK sum rule.
It also has the significant CD transition strength because of the $K=0$ component of the developed $\alpha+{}^6\textrm{He}$ cluster structure.
Furthermore, as a result of mixing of the large triaxial configuration in Fig.\ \ref{fig:density_K_10Be}\ (c), the CD strength and also  $E1$ strength are
 enhanced because the excitation from the ground state to such triaxial configuration involves spatial expansion of excess neutron distribution in ${}^6\textrm{He}$, which induces the $E1$ and CD strengths as described in Ref.~\cite{Shikata:2019wdx}.

In the application to ${}^{10}\textrm{Be}$, we can say that $\beta$-AMD combined with K-VAP is useful to efficiently
generate important bases for the low-energy dipole excitations, $1^-_1$ and $1^-_2$ states, and can obtain the equivalent result
to the  $\beta\gamma$-AMD. In particular, the K-VAP treatment can get
the triaxial configurations within the $\beta$-AMD, which are essential for the $1^-_2$ state ($K=0$ mode).
This is an advantage against $\beta\gamma$-AMD to save computational costs, and superior to the standard $\beta$-AMD with the P-VAP framework,
which favors axial-symmetric configurations rather than axial-asymmetric ones.

\section{Results of ${}^{16}\textrm{O}$} \label{sec:16O}
In the previous section, we demonstrated applicability of $\beta$-AMD with K-VAP in description of
dipole excitations in ${}^{10}\textrm{Be}$.
We apply the same method to ${}^{16}\textrm{O}$ and present the obtained results for LED excitations
in this section.
\subsection{energy surfaces and intrinsic structures}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=\hsize]{graph/Energy_surface_bc_16O.pdf}
\end{center}
\caption{(color online) The energy surfaces obtained by $\beta$-AMD as a function of $\beta$ in ${}^{16}\textrm{O}$.
Panels (a), (b), and (c) show the $K^{\pi}=0^+,\ 0^-,$ and $1^-$ projected energy surfaces, respectively.
The solid lines with filled circle are the result of K-VAP, and those with filled square represent the P-VAP result.
}
\label{fig:ES_bc_16O}
\end{figure}

$K$-projected energy curves obtained by $\beta$-AMD with K-VAP are shown in Fig.\ \ref{fig:ES_bc_16O}
compared with the P-VAP result.
Figures\ \ref{fig:ES_bc_16O}\ (a), (b), and (c) show the $K^{\pi}=0^+,\ 0^-,\ $and $1^-$ projected energy surfaces, respectively.
In all the cases, the energy minimum corresponds to the normal deformation(ND) around $\beta=0.2$--$0.4$ indicating
a relatively smaller deformation in ${}^{16}\textrm{O}$ than ${}^{10}\textrm{Be}$.
In the negative-parity results,
the energy difference between the $K=0$ and $K=1$ bases is only a few MeV at the energy minimum,
but it gets larger as $\beta$ increases: the energy curve for $K^{\pi}=0^-$($K^{\pi}=1^-$) bases
is soft(steep) against $\beta$.

In Fig. \ref{fig:density_K_16O}, intrinsic densities of K-VAP bases are shown.
In all cases of $K^{\pi}=0^+,$ $0^-$, and  $1^-$, an $\alpha$ cluster is formed at the surface of
a $^{12}$C core in the ND region, and it develops as $\beta$ increases.
The $K^{\pi}=0^+$ bases around the energy minimum at $\beta\sim0.4$ has a tetrahedral-like structure
as shown in Fig.\ \ref{fig:density_K_16O}\ (a), which contributes to the ground state obtained by the
GCM calculation.
In a large $\beta$ region, the $K^{\pi}=0^+$ bases show a developed ${}^{12}\textrm{C}+\alpha$ cluster structure (see Fig.\ \ref{fig:density_K_16O}\ (b)),
which dominantly contributes to the $0_2^+$ state.
In the $K^{\pi}=0^-$ and $K^{\pi}=1^-$ bases,
intrinsic configurations at $\beta\sim 0.4$ (ND region) are similar to each other as shown  in
Figs.\ \ref{fig:density_K_16O} (c) and (e).
These two bases have large overlaps with the $1_1^-$ state obtained by the GCM calculation.
At large $\beta$ values, $K^{\pi}=0^-$ and $K^{\pi}=1^-$ bases have
developed ${}^{12}\textrm{C}+\alpha$ cluster configurations, where
the ${}^{12}\textrm{C}$ cluster is deformed with tilted orientation against the ${}^{12}\textrm{C}$-$\alpha$ $(Z)$ axis
as shown  in
Figs.\ \ref{fig:density_K_16O} (d) and (f).
Consequently, the total system becomes axial asymmetric.
The $K^{\pi}=0^-$ bases with this axial asymmetric cluster structure
play an important role to construct the $1_2^-$ state as discussed later.

\begin{figure}[!h]
\begin{center}
\includegraphics[width=\hsize]{graph/density_Pbase_16O.pdf}
\end{center}
\caption{(color online) Intrinsic densities of  ${}^{16}\textrm{O}$ at given $\beta$ values obtained by $\beta$-AMD with P-VAP.
The optimized values of $\gamma$ for each $\beta$ are also written.
Panels (a) and (b) show the densities of the positive- and negative-parity bases, respectively.
}
\label{fig:density_P_16O}
\end{figure}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=\hsize]{graph/density_Kbase_16O.pdf}
\end{center}
\caption{(color online) Intrinsic densities of  ${}^{16}\textrm{O}$ at given $\beta$ values
obtained by the $\beta$-AMD with K-VAP.
Top, middle, and bottom panels show the densities of the $K^{\pi}=0^+,\ 0^-,\ $and $1^-$ bases, respectively.
}
\label{fig:density_K_16O}
\end{figure}

\subsection{GCM results and LED strengths}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=12cm]{graph/Energy_spectrum_16O.pdf}
\end{center}
\caption{Energy spectra of  ${}^{16}\textrm{O}$ obtained by the GCM calculation of $\beta$-AMD with
P-VAP and K-VAP bases. The experimental energy spectra of the corresponding states are shown for
comparison.
}
\label{fig:spectrum_16O}
\end{figure}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=\hsize]{graph/squared_overlap_16O.pdf}
\end{center}
\caption{ (color online)
GCM amplitudes as functions of $\beta$ for the K-VAP results of ${}^{16}\textrm{O}$.
In panel (a), GCM amplitudes for the $0_1^+$ and $0_2^+$ states are plotted by square
and circle points, respectively.
Panels (b) and (c) show the amplitude for the $1_1^-$ and $1_2^-$, respectively.
The $K=0$ component of GCM amplitude for the $K^{\pi}=0^-$ basis and
the $K=1$ component of GCM amplitude for the $K^{\pi}=1^-$ basis are plotted by
square and circle points, respectively.
}
\label{fig:SO_16O}
\end{figure}

Energy spectra obtained by the GCM calculation with K-VAP bases are shown in Fig.\ \ref{fig:spectrum_16O}
compared with the experimental data.
In Fig.\ \ref{fig:SO_16O}, GCM amplitudes, which are given by squared overlaps of the  GCM states with
K-VAP bases, are shown as functions of $\beta$.
In Fig.\ \ref{fig:SO_16O}\ (a),
the GCM amplitudes for the $0_1^+$ and $0_2^+$ states are shown by square and circle points, respectively.
In Figs.\ \ref{fig:SO_16O}\ (b) and (c), the GCM amplitudes for the $1_1^-$ and $1_2^-$ states are shown, respectively, with square(circle) points for $K^{\pi}=0^-(1^-)$ bases.

The calculated binding energy of the ground state is $120.3$\ MeV which slightly underestimates
the experimental value $127.6$\ MeV.
The ground state has the largest GCM amplitude as $\sim 90$\ $\%$
with the base at $\beta=0.4$ as shown in Fig.\ \ref{fig:density_K_16O}\ (a).
The lowest $1^-$ state at the excitation energy 9.8\ MeV largely contains the $K^\pi=0^-$ and $K^\pi=1^-$ components in the $\beta\sim0.4$ (ND) region (see Fig.\ \ref{fig:SO_16O}\ (b)).
The $0_2^+$ state at 10.55\ MeV and the $1_2^-$ state at 12.47\ MeV
are constructed from the $K^{\pi}=0^+$ and  $K^{\pi}=0^-$ bases with the developed
$\alpha + {}^{12}\textrm{C}$ cluster structure, respectively,
as can be seen in their large
GCM amplitudes at 0.6$\lesssim\beta\lesssim0.8$ region (see Figs.\ \ref{fig:SO_16O}\ (a) and (c)).
This result is consistent with the cluster model assignment of the
 $0_2^+$ and  $1_2^-$  states as the band-head states of the parity doublet
($K^{\pi}=0^+$ and $K^{\pi}=0^-$) $\alpha + {}^{12}\textrm{C}$ cluster bands.

\begin{table}[htbp]
\begin{center}
\begin{tabular}{llccc} \toprule
&&$E_x\ $(MeV)&$B(\textrm{TD})\ (\textrm{fm}^4)$&$B(\textrm{CD})\ (\textrm{fm}^4)$ \\ \midrule
P-VAP&$1_1^-$ &9.88&$2.93\times10^{-3}$&$3.49\times10^{-3}$ \\
&$1_2^-$&13.20&$3.98\times10^{-3}$&$1.65\times10^{-5}$ \\
&&&& \\
K-VAP&$1_1^-$ &9.78&$3.62\times10^{-3}$&$2.87\times10^{-3}$ \\
&$1_2^-$&12.47&$3.80\times10^{-3}$&$9.35\times10^{-5}$ \\ \bottomrule
\end{tabular}
\end{center}
\caption{The excitation energies and transition strengths in ${}^{16}\textrm{O}$.}
\label{tab:strength_16O}
\end{table}

The calculated dipole transition strengths are shown in Table\ \ref{tab:strength_16O}.
The present calculation obtains significant TD and CD strengths of the $1_1^-$.
This result for the $1_1^-$ state is qualitatively
consistent with the previous AMD result obtained by the variation after spin-parity projections
\cite{Kanada-Enyo:2017ers}. The TD strength is also shared by the $1_2^-$ state
via mixing of the TD mode and $\alpha + {}^{12}\textrm{C}$ cluster mode.
More details of the two dipole modes are discussed later.

\subsection{comparison between K-VAP and P-VAP methods}
For comparison, we also perform $\beta$-AMD with P-VAP of ${}^{16}\textrm{O}$ for comparison with the
present K-VAP method.
The $K$-projected energy curves obtained from P-VAP bases are shown in Fig.\ \ref{fig:ES_bc_16O}
by square points, and intrinsic densities of P-VAP bases are shown in Fig.~\ref{fig:density_P_16O}.
The K-VAP energy curves are generally lower than the P-VAP result
indicating that additional energy gains are obtained with the K-VAP method.
In particular, the significant energy gain is obtained for $K^{\pi}=1^-$ bases because P-VAP
bases for the negative-parity projection contains the dominant  $K=0$ component but minor
$K=1$ component. This is a general trend of the P-VAP method, which favor
axial-symmetric configurations, i.e.,  $K=0$ dominant bases in various nuclei.
Indeed, as shown in the intrinsic densities of Fig. \ref{fig:density_K_16O}, P-VAP
bases show approximately axial symmetric configurations.

In the GCM energies of  ${}^{16}\textrm{O}$ states obtained by superposing K-VAP or P-VAP bases,
all the GCM states obtained by K-VAP bases gain $1$-$2$ MeV energies  compared with the P-VAP result.
For example, the binding energy of the  K-VAP result is 1.4 MeV larger than the P-VAP result.
Further energy gain is obtained for ${}^{12}\textrm{C}+\alpha$ ($K^{\pi}=0^-$) cluster band because of the rotational degree of freedom of the deformed ${}^{12}\textrm{C}$ cluster in K-VAP bases.
In Table\ \ref{tab:strength_16O}, the properties of dipole excitations are compared between the
P-VAP and K-VAP results. The two methods give qualitatively similar results for excitation energies and
TD and CD transition strengths of the $1^-_1$ and $1^-_2$ states. It means that,
in the case of ${}^{16}\textrm{O}$, the essential bases for low-energy dipole states can be obtained
by the P-VAP method, even though the K-VAP method obtains some amount of extra energy gain due to higher order effects.

\subsection{excitation modes and origin of strengths}
We analyze dipole modes and discuss origins of the significant dipole strengths in the present K-VAP result
of ${}^{16}\textrm{O}$. For this aim,
we define an ``intrinsic state'' of each GCM state as a specific base state having the largest GCM amplitude.
For the $0_1^+$ state, the intrinsic state is defined as the $K^{\pi}=0^+$ base at $\beta = 0.4$ shown in Fig.\ \ref{fig:density_K_16O}\ (a).
In the $1_1^-$ state, the $K^{\pi} = 0^-$ and $K^{\pi} = 1^-$ bases at the $\beta\sim 0.4$ (ND) region are strongly mixed and
both have large GCM amplitudes, and therefore,
two choices of the intrinsic states are possible: one is the  $K^{\pi} = 0^-$ base
at $\beta=0.40$ shown in Fig.\ \ref{fig:density_K_16O}\ (c)
and the other is the $K^{\pi} = 1^-$ base at $\beta=0.32$ shown in Fig.\ \ref{fig:density_K_16O}\ (e).
We call these intrinsic states as $0_\textrm{gs}^+$, $1_\textrm{ND}^-(K=0)$, and $1_\textrm{ND}^-(K=1)$.
The $1_2^-$ contains mainly the $K^{\pi}=0^-$ components with the developed
$\alpha+{}^{12}\textrm{C}$ structure.
Therefore, as the intrinsic state of the $1_2^-$ state,
we choose the  $K^{\pi}=0^-$  base at $\beta= 0.92$ (Fig.\ \ref{fig:density_K_16O}\ (f)), which we label as $1_\textrm{cl}^-$.

In order to clarify the dipole excitation modes, we calculate transition current densities $\vector{j}^K(\vector{r})$
and local matrix elements of the CD and TD operators $\hana{M}_D^K(\vector{r})\ (D = \textrm{CD}\ \textrm{or}\ \textrm{TD})$
for transitions between $K$-projected states in the intrinsic frame defined as,
\begin{eqnarray}
\vector{j}^K(\vector{r}) &\equiv & \langle f^K|\hat{\vector{j}}_{\textrm{nucl}}(\vector{r})|i\rangle ,\\
\hana{M}_{\textrm{TD}}^{K=0}(\vector{r})&=& \frac{1}{c}\left[ (2X^2+2Y^2+Z^2)j^{K=0}_Z - ZXj^{K=0}_X - YZj^{K=0}_Y \right],\label{eq:SD_TD_0} \\
\hana{M}_{\textrm{TD}}^{K=1}(\vector{r})&=& \frac{1}{c}\left[ (X^2+2Y^2+2Z^2)j^{K=1}_X - XY j^{K=1}_Y - ZXj^{K=1}_Z \right],\label{eq:SD_TD_1} \\
\hana{M}_{\textrm{CD}}^{K=0}(\vector{r})&=& \frac{1}{c}\left[ -(X^2+Y^2+3Z^2)j^{K=0}_Z - 2ZXj^{K=0}_X - YZj^{K=0}_Y \right],\label{eq:SD_CD_0} \\
\hana{M}_{\textrm{CD}}^{K=1}(\vector{r})&=& \frac{1}{c}\left[ -(3X^2+Y^2+Z^2)j^{K=1}_X - 2XY j^{K=1}_Y - 2ZXj^{K=1}_Z \right],\label{eq:SD_CD_1}
\end{eqnarray}
where the initial state $|i\rangle$ is taken to be $\hat{P}^{K=0}|0_\textrm{gs}^+\rangle$, and the final state $|f^K\rangle$ is chosen to be either of $\hat{P}^{K}|f\rangle$ with
$|f\rangle=|1_\textrm{ND}^-(K=0)\rangle$, $|1_\textrm{ND}^-(K=1)\rangle$, and $|1_\textrm{cl}^-\rangle$.
$\hana{M}_{\textrm{TD(CD)}}^{K}$ is the local matrix element at $\vector{r}$ corresponding to integrand of the TD(CD) strength
and called "TD(CD) strength density" in the present paper.
Here, we specify the $\mu$ component of the dipole
operator in the TD strength, $\vector{Y}_{11\mu=0}$ with the label $K=0$
and $-(\vector{Y}_{11\mu=1}-\vector{Y}_{11\mu=-1})/\sqrt{2}$ with $K=1$,
and that in the CD strength, $Y_{1\mu=0}$ with the label $K=0$ and $-(Y_{1\mu=1}-Y_{1\mu=-1})/\sqrt{2}$ with $K=1$.

\begin{figure}[!h]
\begin{center}
\includegraphics[width=13cm]{graph/current_16O.pdf}
\end{center}
\caption{(color online) The transition current densities for the $K$-projected intrinsic states of ${}^{16}\textrm{O}$.
Panels (a) and (b) show the transition currents to the $1_\textrm{ND}^-(K=0)$ and $1_\textrm{ND}^-(K=1)$, respectively.
The densities are plotted on the $Z$-$X$ plane.
}
\label{fig:current_16O}
\end{figure}

The calculated transition current densities for  $0_\textrm{gs}^+\to 1_\textrm{ND}^-(K=0)$ and $0_\textrm{gs}^+\to 1_\textrm{ND}^-(K=1)$ transitions
are shown in Fig.\ \ref{fig:current_16O}.
In the vector plot of $\vector{j}^K(\vector{r})$ in Fig.\ \ref{fig:current_16O},
one can see two kinds of dipole modes characterized by $K$ quanta.
One is the $K=0$ oscillation mode and the other is the $K=1$ vortical mode.
The former shows translational current along the $Z$ direction (see Fig.\ \ref{fig:current_16O}\ (a)) caused by the $\alpha$ cluster oscillation relative to the $^{12}$C$(3\alpha$) core, which is understood as a $K^\pi=0^-$ excitation of the relative motion between two asymmetric clusters.
The latter shows the remarkable vortical current (see Fig.\ \ref{fig:current_16O}\ (b)) arising from the tilted ${}^{12}\textrm{C}$ configuration in Fig.\ \ref{fig:density_K_16O}\ (e).
It should be noted that, in the $J^\pi=1^-$ projected states,
these two dipole modes of the $K=0$ and $K=1$ components are not orthogonal to but somewhat overlap
with each other,
and both are significantly contained in the $1_1^-$.
It means that the $1_1^-$ has the dual nature of dipole excitations characterized by $K$-quanta:
the $K=1$ vortical mode and the $K=0$ oscillation mode.

In order to discuss contributions of these two dipole modes to the TD and CD transition strengths,
we show in Fig.\ \ref{fig:strength_density_16O} the strength densities in the $Z$-$X$ plane at $Y=0$, $\hana{M}_{\textrm{TD}}^{K}(X,0,Z)$ and $\hana{M}_\textrm{CD}^{K}(X,0,Z)$, defined in eqs.\ \eqref{eq:SD_TD_0}-\eqref{eq:SD_CD_1}.
Upper and lower panels of Fig.\ \ref{fig:strength_density_16O} show
the calculated results of the TD and CD strengths, respectively,
for the transitions from the $0_\textrm{gs}^+$ to the three $1^-$ states: $1_\textrm{ND}^-(K=0)$, $1_\textrm{ND}^-(K=1)$, and $1_\textrm{cl}^-$.
The $K=0$ oscillation, i.e., the $\alpha$ cluster oscillation, generates the strong CD strength density as seen in Fig.\ \ref{fig:strength_density_16O} (b),
whereas the $K=1$ vortical current contributes to the TD strength density as can be seen in Fig.\ \ref{fig:strength_density_16O} (c).
Compared with the $0_\textrm{gs}^+\to 1_\textrm{ND}^-(K=0)$ and $0_\textrm{gs}^+\to 1_\textrm{ND}^-(K=1)$ transitions,
the strength densities $\hana{M}_D^K(\vector{r})$ are very weak in the $1_\textrm{cl}^-$ excitation (see Figs.\ \ref{fig:strength_density_16O}\ (e) and (f)) because of the small overlap between the initial and final states, that is, the compact ground state and the developed cluster state.

\begin{figure}[!h]
\begin{center}
\includegraphics[width=\hsize]{graph/strength_density_16O.pdf}
\end{center}
\caption{(color online) The heat maps for the TD and CD strength densities in ${}^{16}\textrm{O}$ with respect to the $K$-projected intrinsic states in $Z$-$X$ plane at $Y=0$.
Panels (a)-(b) and (c)-(d) show the matrix elements from the $0_\textrm{gs}^+$ to the $1_\textrm{ND}^-(K=0)$ and $1_\textrm{ND}^-(K=1)$, respectively.
Panels (e) and (f) show the one to the $1_\textrm{cl}^-$.
Color mapping is shown in the range $[-1\ \textrm{fm},1\ \textrm{fm}]$.
}
\label{fig:strength_density_16O}
\end{figure}

In the present analysis of the dominant intrinsic configurations,
the pure $K^\pi=0^-$ cluster excitation does not generate strong TD and CD strengths.
The $K^\pi=0^-$ cluster component is the main component of the $1_2^-$ state.
Nevertheless, the $1_2^-$ state has the significant TD strength in the GCM result as shown previously, because it is not a pure $K^\pi=0^-$ cluster state
but contains significant mixing ($\sim 30\%$) of the $K=1$ component at the $\beta\sim 0.4$ (ND) region, which contributes to the
significant TD strength.
In other words, the TD strength of the $1_2^-$ state comes from mixing of the $K^\pi=1^-$ vortical mode in the dominant
$K^\pi=0^-$ cluster mode.

The TD strength of the  $1_2^-$ state is sensitive to the mixing ratio of the $K=1$ configuration.
To see the sensitivity, we artificially vary the mixing ratio by changing the strength $V_{LS}$ of the spin-orbit force
as $V'_{LS} = \lambda V_{LS}$. We perform the GCM calculation with
$\lambda=0.8$ and 0.9 for 80\% and 90\% weaker spin-orbit strengths. As $\lambda$ decreases,
the energy interval between the $1_1^-$ and $1_2^-$ states increases and the mixing becomes small.
As a result, the TD strength is concentrated on the $1_1^-$ state.
For instance, in the
$\lambda = 0.8$ case, the TD strengths are
 $B(\textrm{TD};0_1^+\rightarrow 1_1^-)=8.30\times10^{-3}$\ $\textrm{fm}^4$ and $B(\textrm{TD};0_1^+\rightarrow 1_2^-)=1.41\times10^{-3}$\ $\textrm{fm}^4$.
From this analysis, one can see that the present result
of $B(\textrm{TD};0_1^+\rightarrow 1_1^-)=3.62\times10^{-3}$\ $\textrm{fm}^4$ and $B(\textrm{TD};0_1^+\rightarrow 1_2^-)=3.80\times10^{-3}$\ $\textrm{fm}^4$
for the original strength ($\lambda = 1.0$) is a transient situation of the
level crossing between the lower $K^\pi=1^-$ vortical mode and higher $K^\pi=0^-$ cluster mode,
where the TD strength from the $K^\pi=1^-$ vortical mode is fragmented into the $1^-_1$ and $1^-_2$ states.
Since there remains model ambiguity in effective interaction parameters in the present framework,
we can not give a conclusion for the mixing ratio.
In order to understand detailed properties of low-energy dipole excitations in ${}^{16}\textrm{O}$,
further experimental informations are needed.

\section{Summary}\label{sec:summary}

We proposed a new method, $\beta$-AMD with K-VAP, in which variation is performed after the $K$-projection as well as the parity projection under the $\beta$-constraint, and applied this method for low-energy dipole excitations of ${}^{10}\textrm{Be}$ and ${}^{16}\textrm{O}$.

In the application to ${}^{10}\textrm{Be}$, we showed that the new method works well to efficiently obtain essential
configurations for low-energy dipole excitations and can obtain
better results compared with the standard $\beta$-AMD with P-VAP (without
$K$-projection). In particular,
$\beta$-AMD with K-VAP can describe triaxially deformed configurations,
whereas the $\beta$-AMD with P-VAP favors only the axial-symmetric ($\gamma\sim0$) configurations.
In the GCM calculation, the present $\beta$-AMD with K-VAP can obtain
the equivalent result to the GCM result of full  $\beta\gamma$-AMD configurations
for the $1_1^-$ and $1_2^-$ states.
It indicates that the present method of $\beta$-AMD with K-VAP is a useful approach to save numerical cost
in describing low-energy dipole excitations.

In the application of ${}^{16}\textrm{O}$, the present method obtains two LED states, $1_1^-$ and $1_2^-$.
The ground state and $1_1^-$ state are dominantly contributed by small deformation bases and
the $1_1^-$ state possesses the significant TD and CD transition strengths.
On the other hand, the $1_2^-$ state is mainly composed by $\alpha + {}^{12}\textrm{C}$ cluster developed bases and regarded as the band-head state of the $K^\pi=0^-$ cluster band.
By analysis of the strengths and current densities of these two types (TD and CD) of dipole transitions,
we discussed properties of the dipole excitations and showed that the $K=0$ and $K=1$ natures play important roles.
Namely, the $1_1^-$ state has the duality of the $K=0$ and $K=1$ modes: the $K=0$ oscillation mode is described by relative motion between asymmetric clusters, and $K=1$ vortical mode is generated by the tilted configuration of the deformed ${}^{12}\textrm{C}$ cluster.
The $1_2^-$ state is dominantly described by the $K=0$ dipole motion of the $\alpha$ cluster relative to the ${}^{12}\textrm{C}$ cluster.

The present method was found to be a useful tool for study of LED in light nuclei.
We will apply this method to $Z\neq N$ nuclei in $sd$-shell region such as $^{18}$O and $^{20}$O in future study.
It is also an remaining issue to discuss experimental signal of the TD mode.
For instance, transverse charge form factors would be useful experimental information as a
sensitive probe for the TD transition strengths as pointed out by Nesterenko {\it et al.} \cite{Nesterenko:2019dnt}.

\section*{Acknowledgement}

The authors thank to Dr.~Nesterenko and Dr.~Chiba for fruitful discussions.
The computational calculations of this work were performed by using the
supercomputer in the Yukawa Institute for theoretical physics, Kyoto University.
This work was supported by
JSPS KAKENHI Grant Nos. 18J20926, 18K03617, and 18H05407.

\bibliographystyle{ptephy}

redpajama_set_name: RedPajamaArXiv


text:
Six Student Senators Resign In Two Days
Alex Shedd/Fourth Estate
Five of six chair positions are left vacant following resignations
BY ABIGAIL ADCOX, ASSISTANT NEWS EDITOR AND JACK HARVEY, STAFF WRITER
In the span of a week's time, six student senators have resigned from their positions within Student Government.
Among the six senators to resign, five were chairs for various committees, including Dustin Cone, chair of the University Services Committee, Leah Hoffman, chair of the University Life Committee, Joseph Fernando, chair of the Government and Community Relations Committee, Erica Kelly, chair of the University Academics Committee and McKenna Bates, chair of the Administrative and Financial Affairs Committee. The sixth senator who resigned was Zachary Wolfson.
Prior to the March 21 student senate meeting, former chair of the University Life Committee Leah Hoffman sent an email on Tuesday, March 19 to senate leadership expressing grievances with Student Body President Bekah Pettine.
"The President of the Student Body has had increasing relations in my department to the point that I am uncomfortable with working with her," Hoffman wrote in the email, "Unlike any other department in Student Government, [President Bekah Pettine] is consistently involved in the planning and implementing of projects which are outside of her scope. This includes, but is not limited to, communicating with offices which fall under my department."
Hoffman then went on to allege an incident that took place last fall between her and Pettine, which concerned the First of All We Vote event on Nov. 1. The event was hosted by Student Government, Alpha Phi Alpha Fraternity, Inc. and Mason Votes, and was comprised of a debate between College Republicans (CRs) and George Mason Democrats (GMU Dems) on a number of crucial issues ahead of the 2018 national midterm elections.
Hoffman, who is a member of CRs and represented them as a participant in the debate, claimed in the email that Pettine provided her with the debate questions prior to the event.
"Bekah sent me the questions for First of All We Vote in November," Hoffman alleged. "After Bekah sent me these questions, I immediately sent them to [Senator Elijah Nichols], because I know the action of sending them to me was immoral as I was debating for the Republicans." Nichols, who represented GMU Dems in the debate, confirmed with Fourth Estate that Hoffman had sent him the questions.
Text messages obtained by Fourth Estate from Oct. 31 appear to show that Pettine sent a document titled "Debate Questions" to Hoffman.
In response to the document allegedly sent by Pettine, Hoffman replied, "Did you read these questions??? Talk about bias!!!!!," to which Pettine replied, "I know, that's why I wanted to show them to ya'll."
Fourth Estate reached out to Pettine to verify the text message exchange, but Pettine declined to comment on the conversation. She is currently seeking legal representation to resolve these accusations. Pettine has stated that these accusations are uncorroborated and unwarranted.
In an earlier interview with Fourth Estate on Saturday, March 23, Pettine said, "I don't know where that's coming from; "First of All We Vote happened six months ago, and frankly, it wasn't something that I was involved with in planning. I don't have a lot of information on it," in response to a question about allegations of her leaking the document.
Pettine went on to say, "I did everything in my power to resolve the situation for all parties involved and to ensure that the questions were rewritten."
The questions were ultimately rewritten prior to the event, after Student Government learned that both organizations had obtained the first set of debate questions. According to Nichols, Kara Kline, president of GMU Dems, notified Tim O'Shea, executive secretary for government and community relations, that they had obtained the first set of debate questions.
Hoffman resigned from her position as chair of the University Life Committee in the student senate meeting on March 21 with a formal statement. In an act of solidarity with Hoffman, former Chair of the University Academics Committee Erica Kelly also resigned during the March 21 student senate meeting.
"I believe it is time for me to go, because I do this in solidarity with Chairwoman Hoffman and Chairwoman Bates, because the next administration and the student body must know that bullying, harassment and misconduct have no place in Student Government," Kelly said in her statement before the student senate. "I encourage all of you to take the action that you see fit to hold this administration and all others accountable in the future."
Following Hoffman, former Chair of the Administrative and Financial Affairs Committee McKenna Bates announced her resignation via the student senate listserv Wednesday, March 20.
Bates sent an email to students alleging that Senate Speaker Claire Olivier had attempted to "harm [Bates'] relationships with other senators through breaches of confidentiality [and] dissemination of false information."
Bates alleged specifically that Olivier revealed details of a disciplinary measure taken against Bates by Olivier and Speaker pro tempore Cedric Price to fellow senators. Bates stated that this took place during a Mason Hillel trip over spring break to Israel called Fact Finders, which several Student Government members took part in.
Kelly backed this allegation, stating that Olivier divulged this confidential information to multiple senators on the trip, including Kelly, on more than one occasion.
On Thursday, March 21, Olivier stated to Fourth Estate, "The allegations are false," adding that she had no further comment. Olivier has not responded to several other attempts by Fourth Estate for comment. An attorney claiming to represent Olivier, however, stated, that "all the allegations are baseless, uncorroborated and untrue."
Price did not respond for comment to verify the conversation between him and Olivier.
Former Senator Zachary Wolfson also resigned during the March 21 student senate meeting. In response to why he decided to resign, Wolfson said, "The main reason that I decided to resign actually ended up stemming from the resignation of former Admin and Finance Chairwoman McKenna Bates; the former chairwoman basically decided to resign for her own personal reasons."
Wolfson continued, "It's also important to note that the resignation that she offered did go and mention another senator, had dealt with similar problems to what she was mentioning, and I'm actually that other senator… This actually relates to the speaker of the current student senate, at least in the sense that she is not being supportive of other senators and supporting the student body."
Former Chair of the University Services Committee Dustin Cone joined the others in resigning at the March 21 meeting. Cone expressed a general dissatisfaction with the way Student Government was run, stating, "I devoted my time with (sic) Student Government, seven, ten-plus hours, working with University Services… I personally have felt harassed, have felt attacked, have been cursed, all while being in Student Government while doing my job. My mental health has gone down to do good for the university. That shouldn't go hand-in-hand."
While Cone's resignation was apparently not directly tied to those of Hoffman and Bates, he did express solidarity with them when interviewed by Fourth Estate.
Joseph Fernando, former chair of the government and community relations committee, was also one of the five senators to resign during the student senate meeting March 21. Fernando attributed his resignation to that of Cone. "I could not, in good conscience … continue working in a very toxic environment," he said.
Pettine spoke about how she plans to finish out the last few weeks of her term in the wake of the six resignations during Saturday's interview.
"Something that I established as president this year is an anonymous complaint form as a way for members to bring forth their concerns, which goes straight to the advisor," she said. "I really want to keep referring people to that and encouraging them to use it. In addition, I believe this year's department meetings between executive secretaries, chairs and undersecretaries have been a great way to encourage further transparency and communication between branches."
Pettine also said about her time within Student Government, "I really am proud of the work we're doing. I'm just hoping that the culture and the way we speak to each other as an organization can be greatly improved."
In wake of the resignations, in next week's student senate meeting, only one of six chair positions will be occupied, which requires five elections to be held to fill the vacancies.
Correction (4.08): the reporters stated that details regarding a disciplinary action against McKenna Bates were confidential. To clarify, Senators Bates and Kelly only alleged that this information was confidential. However, it was only confidential via Student Government community norms, not official bylaws. Additionally, an attorney representing Senator Olivier has clarified that the disciplinary action against Senator Bates was appropriate due to a breach of Student Government rules, and the decision to enact the measure was allegedly solely Speaker Pro Tempore Price's. The attorney also clarified that Senator Bates accepted the disciplinary action via email and stated that she would not appeal it.
39th Student Senate Mason Student Government resignations student body president
South Sudan Still in Crisis
Right, Wrong or Indifferent
160 LIGHTS INSTALLED ACROSS CAMPUS AS PART OF STUDENT GOVERNMENT INITIATIVE
Student Government Elections to Take Place Online
Student Government Update

redpajama_set_name: RedPajamaCommonCrawl


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Candidate should be a B.E. (Mech) or B.E. (Instrumentation) with 2+ years of experience.
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I recently wrote a post about how frustrating pregnancy can be, but I thought it was only fair to talk about some of the awesome things that have been happening to me as well. Pregnancy is a stressful time, but there's also loads of amazing things to enjoy, and now I'm in my third trimester, I'm reflecting on how much I've actually enjoyed being pregnant!
Now I'm well into my third trimester, the reality of labour and birth is really starting to hit home. Instead of thinking about the next stage of pregnancy – the next trimester – I'm thinking about the inevitable end bit, where baby koala makes an appearance. Needless to say, my anxiety levels have been gradually increasing as the number of weeks to go has gradually decreased.
There is a tonne of stuff you could run out and buy when you find out you're pregnant – and I've certainly treated myself to some new bits and bobs – but I've discovered there are some things worth your pennies, and some things you just don't need. Here I'm sharing my first half of pregnancy favourites – the things that got me through the first and second trimester (yeah I know that's more than half – so sue me).


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Search only speeches by Stephen Hammond Search all speeches
Results 141–160 of 3000 for (in the 'Commons debates' OR in the 'Westminster Hall debates' OR in the 'Lords debates' OR in the 'Northern Ireland Assembly debates') speaker:Stephen Hammond
Government Mandate for the NHS (25 Apr 2019)
Stephen Hammond: My hon. Friend is right. At the heart of the long-term plan is the emphasis on primary care and prevention. Providing care for people in their own homes undoubtedly achieves better outcomes for patients and he is right to welcome it.
Stephen Hammond: The hon. Gentleman is right to point out that a consultation is being undertaken on various aspects of the long-term plan and the legal framework that needs to be put in place. It is entirely up to local CCGs to make decisions on their procurement policy.
Stephen Hammond: My hon. Friend and I have sometimes disagreed on certain things, but one thing we agree on is his advocacy for his constituents, and he is right that I have been to see for myself the issues in Kettering in terms of the current configuration of the accident and emergency department. He is right to press for that urgent care centre, and he knows that he has impressed the case on my mind.
Stephen Hammond: The hon. Lady knows that the House and her Committee will have the fullest opportunity to scrutinise the document as and when it is published. She also knows that there is a commitment to publish it soon. She also rightly points out that it will deliver on the need to ensure that health and social care are integrated.
Stephen Hammond: The Government are not trying to hide anything. The hon. Lady is right that it is an important document, and it is important therefore that we get it absolutely correct. I refer her to what the chief executive of NHS England said yesterday. He said: "We have an agreed direction in the long-term plan…We have the budget set for the next year, and we have the NHS annual planning...
Stephen Hammond: The hon. Lady does a great injustice to my right hon. Friend. He is today—
Stephen Hammond: In the hon. Lady's fantasy world, that may be true, but my right hon. Friend is in fact addressing a conference in Manchester, talking about the gender pay gap and how this side will close it in the NHS. I would have thought she would welcome that, rather than shouting at me.
Women and Equalities: Women's Life Expectancy (25 Apr 2019)
Stephen Hammond: Preventing health problems is the best way to improve life expectancy. We are taking action on childhood obesity, diabetes and cardiovascular disease and action to reduce smoking rates. Later this year, my Department will produce a prevention Green Paper, which will set out cross-Government plans for prevention in greater detail.
Stephen Hammond: The hon. Lady raises an important point. We know that we need to make it easier to book appointments and more convenient for women to attend them. That is why Sir Mike Richards is undertaking a comprehensive review of screening programmes. It will look at how we can improve the uptake and set out clear recommendations on how we can make those screening programmes more accessible.
Stephen Hammond: The conclusion I draw is to look at Public Health England's recent review, which made it clear that it is not possible to attribute the slowdown in the improvement of life expectancy to any single cause. That is why we are not complacent, as I said in answer to the hon. Member for Newcastle upon Tyne Central (Chi Onwurah). The Budget saw us fully fund the situation with a big cash boost,...
Stephen Hammond: As I said in response to the hon. Member for Newcastle upon Tyne Central (Chi Onwurah), the Government have already put in place prevention programmes to ensure a reduction in smoking rates. The prevention vision and the prevention Green Paper will set out the means by which smoking can be reduced further to support people, pregnant or otherwise.
Stephen Hammond: I answered that question just a moment ago. As I said, Public Health England's recent review made it clear that it is not possible to attribute the slowdown to any one cause. It is therefore important to tackle all the causes of the deterioration in life expectancy, which is why the Government will publish a prevention Green Paper later this year.
Women and Equalities: Domestic Abuse: Medical Training (25 Apr 2019)
Stephen Hammond: Tackling domestic abuse is a key priority for this Government. That is why we have put £2 million into expanding the pilot programme, which will create a model health response for survivors of domestic violence and abuse. Training for frontline medical staff to help identify domestic abuse is included in a wide range of training and education curriculums for health staff.
Stephen Hammond: I commend the hon. Lady's work on the all-party parliamentary group on domestic violence and abuse. She will know that the Department produced a domestic abuse resource for health professionals that advises them on how best to support adults and young people over 16 who are experiencing domestic abuse, and that training is available now.
Stephen Hammond: My hon. Friend is right. The definition, which also includes factors such as mental health and economic issues, will make things much clearer for frontline staff and help them to understand and look for incidents of domestic violence and abuse.
Stephen Hammond: The hon. Gentleman raises an important point, and he will know that the Government have committed extra money to ensure women prisoners get the support they need for neuro problems when they enter prison.
Stephen Hammond: My hon. Friend raises an important point, because domestic violence clearly impacts the whole of family life, and there is evidence that children are also affected. We need to ensure that there are no legal barriers to sharing data to protect children or vulnerable adults, and we need to ensure that the £8 million we are spending will help those children recover from domestic violence.
Stephen Hammond: The hon. Lady raises an important point. We need to ensure that people are properly triaged for all sorts of diseases when they turn up at A&E, including domestic violence. I will reflect on her point and talk to NHS England about it.
Women and Equalities: Topical Questions (25 Apr 2019)
Stephen Hammond: My hon. Friend is exactly right. The evidence is clear that the MMR vaccine is safe and effective. Mums and dads should ensure that their children are vaccinated.
Healthcare (International Arrangements) Bill (Changed to Healthcare (European Economic Area and Switzerland Arrangements) Bill): Power to make healthcare payments (26 Mar 2019)
Stephen Hammond: Given that I just said that we have accepted the amendment that would remove the powers, that argument is hardly powerful. I also suspect that the Opposition Spokesperson and the other members of the Committee will be surprised to hear that they had not fulfilled their role when they sat through the hours of scrutiny in Committee. In conclusion, I offer my thanks to hon. Members from across...
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A two-day German-Russian conference "Methods of efficient production in the agricultural sector - the key to success in the future" was held in Voronezh. The event was attended by owners, managers and top managers of agricultural enterprises of Russia and Germany.
At the meeting the current topic of production efficiency in the agricultural sector was raised.
Konstantin Khoroshev, First Deputy Director of the Office for Investment Promotion and Strategic Projects Supports, presented the investment attractiveness of the agro-industrial complex of the Voronezh region to the participants. He spoke about the results achieved by regional farmers in the field of animal husbandry. To date, more than 200 investment projects are being implemented in animal husbandry. Voronezh region ranks 3rd place in the country in terms of the number of pigs. The leaders of the industry in the region are such large companies as: LLC «AgroEko», which is among the ten largest producers of pork, LLC «Zarechnoye», which ranks second place among the largest producers of beef in the Russian Federation. GK «Verkhnekhavsky Agroholding» and LLC «Donskoy Bekon» are also among the leaders.
It was also noted that at present in the region there is a two-tier system of industrial parks. 3 state ("Maslovsky", "Liskinsky", Bobrovsky ") and 1 private industrial park "Perspectiva" have been created. In total, taking into account small and medium businesses, 90 residents are placed with a total investment of over 35 billion rubles in the existing industrial parks of the region.
In 2018 a territory of advanced socio-economic development was created in the mono-city Pavlovsk. On the territory of the industrial park "Maslovsky" a platform has been allocated for small and medium businesses. Also, the regional government is working to create a special economic zone of an industrial-production type "Center".
In conclusion of his speech, Konstantin Khoroshev said that it is planned to create a high-tech cluster of agricultural engineering in the region. The strategy of the cluster of agricultural machinery is aimed at the implementation of measures to transform the industry into an advanced sector of industry that meets the needs of the Russian agro-industrial complex in highly efficient machinery and equipment of its own production.
It is planned that such international companies as «Kuhn», «Agrostroj Pelhrimov», «Claas» will become participants in the regional cluster.


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text:
emma 16
mansfield_park 11
persuasion 5
pride_and_prejudice 7
heir 1
heroine 10
narrator 4
married 6
unmarried 22
widowed 4
landed gentry 13
middle-aged 6
young married 2
naval officer 1
Admiral Croft 1
Catherine Morland 2
Elizabeth Bennet 1
Emma Woodhouse 2
Frank Churchill 1
Henry Crawford 2
John Thorpe 1
Lady Bertram 1
Lady Catherine de Bourgh 2
Margaret Dashwood 1
Mary Crawford 3
Miss Bates 1
Mr. Bennet 1
Mr. Knightley 1
Mr. Woodhouse 1
Mrs Jennings 1
Mrs. Allen 1
Mrs. Weston 1
Narrator as "Somebody" 2
Narrator as Anne Elliot 1
Narrator as Elizabeth Bennet 1
Narrator as Emma Woodhouse 2
Narrator as Fanny Price 1
Narrator as Henry Crawford 1
Narrator as Mr. Weston 1
"I honour your circumspection. A fortnight's acquaintance is certainly very little. One cannot know what a man really is by the end of a fortnight. But if we do not venture somebody else will; and after all, Mrs. Long and her daughters must stand their chance; and, therefore, as she will think it an act of kindness, if you decline the office, I will take it on myself."
Character: Mr. Bennet
"Very true, indeed; and now, my dear Jane, what have you got to say on behalf of the interested people who have probably been concerned in the business? Do clear them too, or we shall be obliged to think ill of somebody."
Character: Elizabeth Bennet
to stand up with somebody else,
Character: Narrator as Elizabeth Bennet
About the middle of the next day, as she was in her room getting ready for a walk, a sudden noise below seemed to speak the whole house in confusion; and, after listening a moment, she heard somebody running upstairs in a violent hurry, and calling loudly after her. She opened the door and met Maria in the landing place, who, breathless with agitation, cried out—
Character: Narrator
"Mrs. Collins, you must send a servant with them. You know I always speak my mind, and I cannot bear the idea of two young women travelling post by themselves. It is highly improper. You must contrive to send somebody. I have the greatest dislike in the world to that sort of thing. Young women should always be properly guarded and attended, according to their situation in life. When my niece Georgiana went to Ramsgate last summer, I made a point of her having two men-servants go with her .— Miss Darcy, the daughter of Mr. Darcy, of Pemberley, and Lady Anne, could not have appeared with propriety in a different manner. I am excessively attentive to all those things. You must send John with the young ladies, Mrs. Collins. I am glad it occurred to me to mention it; for it would really be discreditable to you to let them go alone."
Character: Lady Catherine de Bourgh
"Oh! Your uncle! He keeps a man-servant, does he? I am very glad you have somebody who thinks of these things. Where shall you change horses? Oh! Bromley, of course. If you mention my name at the Bell, you will be attended to."
One morning, about a week after Bingley's engagement with Jane had been formed, as he and the females of the family were sitting together in the dining-room, their attention was suddenly drawn to the window, by the sound of a carriage; and they perceived a chaise and four driving up the lawn. It was too early in the morning for visitors, and besides, the equipage did not answer to that of any of their neighbours. The horses were post; and neither the carriage, nor the livery of the servant who preceded it, were familiar to them. As it was certain, however, that somebody was coming,
They had nearly done breakfast, when the sound of a carriage, (almost the first they had heard since entering Lyme) drew half the party to the window. It was a gentleman's carriage, a curricle, but only coming round from the stable-yard to the front door; somebody must be going away. It was driven by a servant in mourning.
Novel: Persuasion
any tolerably pleasing young woman who had listened and seemed to feel for him would have received the same compliment. He had an affectionate heart. He must love somebody.
Character: Narrator as Anne Elliot
"Now he must begin all over again with somebody else. I think we must get him to Bath. Sophy must write, and beg him to come to Bath. Here are pretty girls enough, I am sure. It would be of no use to go to Uppercross again, for that other Miss Musgrove, I find, is bespoke by her cousin, the young parson. Do not you think, Miss Elliot, we had better try to get him to Bath?"
Character: Admiral Croft
She stopped, regretting with a deep blush that she had implied so much; but less would hardly have been sufficient. Mrs Smith would hardly have believed so soon in Mr Elliot's failure, but from the perception of there being a somebody else. As it was, she instantly submitted, and with all the semblance of seeing nothing beyond; and
to lose no time, lest somebody else should come in.
Character: Narrator as Henrietta Musgrove
"I wish we had any — it would be somebody to go to."
Character: Catherine Morland
"No more there are, indeed. How very provoking! But I think we had better sit still, for one gets so tumbled in such a crowd! How is my head, my dear? Somebody gave me a push that has hurt it, I am afraid."
Character: Mrs. Allen
"No, indeed, it looks very nice. But, dear Mrs. Allen, are you sure there is nobody you know in all this multitude of people? I think you must know somebody."
"That is a good one, by Jove! I asked you as soon as I came into the room, and I was just going to ask you again, but when I turned round, you were gone! This is a cursed shabby trick! I only came for the sake of dancing with you, and I firmly believe you were engaged to me ever since Monday. Yes; I remember, I asked you while you were waiting in the lobby for your cloak. And here have I been telling all my acquaintance that I was going to dance with the prettiest girl in the room; and when they see you standing up with somebody else, they will quiz me famously."
Character: John Thorpe
She was not deceived in her own expectation of pleasure; the comedy so well suspended her care that no one, observing her during the first four acts, would have supposed she had any wretchedness about her. On the beginning of the fifth, however, the sudden view of Mr. Henry Tilney and his father, joining a party in the opposite box, recalled her to anxiety and distress. The stage could no longer excite genuine merriment — no longer keep her whole attention. Every other look upon an average was directed towards the opposite box; and, for the space of two entire scenes, did she thus watch Henry Tilney, without being once able to catch his eye. No longer could he be suspected of indifference for a play; his notice was never withdrawn from the stage during two whole scenes. At length, however, he did look towards her, and he bowed — but such a bow! No smile, no continued observance attended it; his eyes were immediately returned to their former direction. Catherine was restlessly miserable; she could almost have run round to the box in which he sat and forced him to hear her explanation. Feelings rather natural than heroic possessed her; instead of considering her own dignity injured by this ready condemnation — instead of proudly resolving, in conscious innocence, to show her resentment towards him who could harbour a doubt of it, to leave to him all the trouble of seeking an explanation, and to enlighten him on the past only by avoiding his sight, or flirting with somebody else — she took to herself all the shame of misconduct, or at least of its appearance, and was only eager for an opportunity of explaining its cause.
But many were the tedious hours which must yet intervene. She shuddered, tossed about in her bed, and envied every quiet sleeper. The storm still raged, and various were the noises, more terrific even than the wind, which struck at intervals on her startled ear. The very curtains of her bed seemed at one moment in motion, and at another the lock of her door was agitated, as if by the attempt of somebody to enter. Hollow murmurs seemed to creep along the gallery, and more than once her blood was chilled by the sound of distant moans. Hour after hour passed away, and the wearied Catherine had heard three proclaimed by all the clocks in the house before the tempest subsided or she unknowingly fell fast asleep.
"that somebody would give us all a large fortune apiece!"
Character: Margaret Dashwood
"Lord! my dear, how calmly you talk of it; and can the Colonel wait two or three months! Lord bless me! — I am sure it would put ME quite out of patience! — And though one would be very glad to do a kindness by poor Mr. Ferrars, I do think it is not worth while to wait two or three months for him. Sure somebody else might be found that would do as well; somebody that is in orders already."
Character: Mrs Jennings
"I am very glad I did think of her. It was very lucky, for I would not have had poor James think himself slighted upon any account; and I am sure she will make a very good servant: she is a civil, pretty-spoken girl; I have a great opinion of her. Whenever I see her, she always curtseys and asks me how I do, in a very pretty manner; and when you have had her here to do needlework, I observe she always turns the lock of the door the right way and never bangs it. I am sure she will be an excellent servant; and it will be a great comfort to poor Miss Taylor to have somebody about her that she is used to see. Whenever James goes over to see his daughter, you know, she will be hearing of us. He will be able to tell her how we all are."
Character: Mr. Woodhouse
Harriet Smith was the natural daughter of somebody. Somebody had placed her, several years back, at Mrs. Goddard's school, and somebody had lately raised her from the condition of scholar to that of parlour-boarder. This was all that was generally known of her history. She had no visible friends but what had been acquired at Highbury, and was now just returned from a long visit in the country to some young ladies who had been at school there with her.
"though I have kept my thoughts to myself; but I now perceive that it will be a very unfortunate one for Harriet. You will puff her up with such ideas of her own beauty, and of what she has a claim to, that, in a little while, nobody within her reach will be good enough for her. Vanity working on a weak head, produces every sort of mischief. Nothing so easy as for a young lady to raise her expectations too high. Miss Harriet Smith may not find offers of marriage flow in so fast, though she is a very pretty girl. Men of sense, whatever you may chuse to say, do not want silly wives. Men of family would not be very fond of connecting themselves with a girl of such obscurity—and most prudent men would be afraid of the inconvenience and disgrace they might be involved in, when the mystery of her parentage came to be revealed. Let her marry Robert Martin, and she is safe, respectable, and happy for ever; but if you encourage her to expect to marry greatly, and teach her to be satisfied with nothing less than a man of consequence and large fortune, she may be a parlour-boarder at Mrs. Goddard's all the rest of her life—or, at least, (for Harriet Smith is a girl who will marry somebody or other,) till she grow desperate, and is glad to catch at the old writing-master's son."
Character: Mr. Knightley
"I must see somebody very superior to any one I have seen yet, to be tempted; Mr. Elton, you know,
Character: Emma Woodhouse
He wanted to marry well, and having the arrogance to raise his eyes to her, pretended to be in love; but she was perfectly easy as to his not suffering any disappointment that need be cared for. There had been no real affection either in his language or manners. Sighs and fine words had been given in abundance; but she could hardly devise any set of expressions, or fancy any tone of voice, less allied with real love. She need not trouble herself to pity him. He only wanted to aggrandise and enrich himself; and if Miss Woodhouse of Hartfield, the heiress of thirty thousand pounds, were not quite so easily obtained as he had fancied, he would soon try for Miss Somebody else with twenty, or with ten.
Character: Narrator as Emma Woodhouse
the advantage of such an addition to their confined society in Surry; the pleasure of looking at somebody new; the gala-day to Highbury entire, which the sight of him would have made;
Character: Narrator as Mr. Weston
Oh! and I had almost forgotten one idea that occurred to me— this pianoforte that has been sent here by somebody —though we have all been so well satisfied to consider it a present from the Campbells, may it not be from Mr. Knightley? I cannot help suspecting him. I think he is just the person to do it, even without being in love."
Character: Mrs. Weston
This would be a trial. He was no dancer in general. If he were to be very alert in engaging Jane Fairfax now, it might augur something. There was no immediate appearance. No; he was talking to Mrs. Cole— he was looking on unconcerned; Jane was asked by somebody else, and he was still talking to Mrs. Cole.
Somebody said that
Miss Gilbert was expected at her brother's, and must be invited with the rest.
Character: Narrator as "Somebody"
Somebody else believed
Mrs. Gilbert would have danced the other evening, if she had been asked.
"She must be under some sort of penance, inflicted either by the Campbells or herself. There is great fear, great caution, great resolution somewhere.—She is not to be with the Dixons. The decree is issued by somebody. But why must she consent to be with the Eltons?—Here is quite a separate puzzle."
In a few minutes the carriage returned.—Somebody talked of rain.—
"Indeed you did. I remember it perfectly. You mentioned it as what was certainly to be very soon. Mrs. Perry had told somebody, and was extremely happy about it.
Character: Frank Churchill
"If you please, my dear. With all my heart. I am quite ready. I was ready to have gone with her, but this will do just as well. We shall soon overtake her. There she is—no, that's somebody else. That's one of the ladies in the Irish car party, not at all like her.—Well, I declare—"
Character: Miss Bates
She was again roused from disagreeable musings by sudden footsteps: somebody was coming at a quick pace down the principal walk. She expected Mr. Rushworth, but it was Julia, who, hot and out of breath, and with a look of disappointment, cried out on seeing her,
Novel: Mansfield Park
On the tragic side were the Miss Bertrams, Henry Crawford, and Mr. Yates; on the comic, Tom Bertram, not quite alone, because it was evident that Mary Crawford's wishes, though politely kept back, inclined the same way: but his determinateness and his power seemed to make allies unnecessary; and, independent of this great irreconcilable difference, they wanted a piece containing very few characters in the whole, but every character first-rate, and three principal women. All the best plays were run over in vain. Neither Hamlet, nor Macbeth, nor Othello, nor Douglas, nor The Gamester, presented anything that could satisfy even the tragedians; and The Rivals, The School for Scandal, Wheel of Fortune, Heir at Law, and a long et cetera, were successively dismissed with yet warmer objections. No piece could be proposed that did not supply somebody with a difficulty, and on one side or the other it was a continual repetition of,
"Phoo! phoo! This is only because there were no tall women to compare her with, and because she has got a new gown, and you never saw her so well dressed before. She is just what she was in October, believe me. The truth is, that she was the only girl in company for you to notice, and you must have a somebody. I have always thought her pretty —not strikingly pretty—but 'pretty enough,' as people say; a sort of beauty that grows on one. Her eyes should be darker, but she has a sweet smile; but as for this wonderful degree of improvement, I am sure it may all be resolved into a better style of dress, and your having nobody else to look at; and therefore, if you do set about a flirtation with her, you never will persuade me that it is in compliment to her beauty, or that it proceeds from anything but your own idleness and folly."
Character: Mary Crawford
"You must think of somebody else too, when you wear that necklace,"
It was a heavy, melancholy day. Soon after the second breakfast, Edmund bade them good-bye for a week, and mounted his horse for Peterborough, and then all were gone. Nothing remained of last night but remembrances, which she had nobody to share in. She talked to her aunt Bertram— she must talk to somebody of the ball; but her aunt had seen so little of what had passed, and had so little curiosity, that it was heavy work. Lady Bertram was not certain of anybody's dress or anybody's place at supper but her own.
"She could not recollect what it was that she had heard about one of the Miss Maddoxes, or what it was that Lady Prescott had noticed in Fanny: she was not sure whether Colonel Harrison had been talking of Mr. Crawford or of William when he said he was the finest young man in the room— somebody had whispered something to her; she had forgot to ask Sir Thomas what it could be."
Character: Lady Bertram
"suppose you were to have one of the Miss Owens settled at Thornton Lacey; how should you like it? Stranger things have happened. I dare say they are trying for it. And they are quite in the light, for it would be a very pretty establishment for them. I do not at all wonder or blame them. It is everybody's duty to do as well for themselves as they can. Sir Thomas Bertram's son is somebody; and now he is in their own line. Their father is a clergyman, and their brother is a clergyman, and they are all clergymen together. He is their lawful property; he fairly belongs to them. You don't speak, Fanny; Miss Price, you don't speak. But honestly now, do not you rather expect it than otherwise?"
"but I do not think I have had a volume of Shakespeare in my hand before since I was fifteen. I once saw Henry the Eighth acted, or I have heard of it from somebody who did, I am not certain which. But Shakespeare one gets acquainted with without knowing how. It is a part of an Englishman's constitution. His thoughts and beauties are so spread abroad that one touches them everywhere; one is intimate with him by instinct. No man of any brain can open at a good part of one of his plays without falling into the flow of his meaning immediately."
Character: Henry Crawford
his hoping soon to have an assistant, a friend, a guide in every plan of utility or charity for Everingham: a somebody that would make Everingham and all about it a dearer object than it had ever been yet.
Character: Narrator as Henry Crawford
"I wish I left you in stronger health. Is there anything I can do for you in town? I have half an idea of going into Norfolk again soon. I am not satisfied about Maddison. I am sure he still means to impose on me if possible, and get a cousin of his own into a certain mill, which I design for somebody else. I must come to an understanding with him. I must make him know that I will not be tricked on the south side of Everingham, any more than on the north: that I will be master of my own property. I was not explicit enough with him before. The mischief such a man does on an estate, both as to the credit of his employer and the welfare of the poor, is inconceivable. I have a great mind to go back into Norfolk directly, and put everything at once on such a footing as cannot be afterwards swerved from. Maddison is a clever fellow; I do not wish to displace him, provided he does not try to displace me; but it would be simple to be duped by a man who has no right of creditor to dupe me, and worse than simple to let him give me a hard-hearted, griping fellow for a tenant, instead of an honest man, to whom I have given half a promise already. Would it not be worse than simple? Shall I go? Do you advise it?"
It was parting with somebody of the nature of a friend; and though, in one light, glad to have him gone, it seemed as if she was now deserted by everybody; it was a sort of renewed separation from Mansfield;
Character: Narrator as Fanny Price