text:
\section{Introduction}

Unstable nuclei have shown exotic nuclear structures with the development of radioactive beam experiments.
Neutron halo structure is observed in some of the drip-line nuclei, such as $^6$He and $^{11}$Li \cite{tanihata85,tanihata13}.
In unstable nuclei, excess nucleons often form the weakly bound state with respect to the stable core nucleus and they are excited to the unbound states beyond the particle thresholds with small excitation energy.
Hence, the structures of resonances and the responses of continuum states become the important research targets of unstable nuclear physics.
A soft dipole mode including the possibility of resonance has been proposed as a new collective motion with dipole oscillation of excess neutrons against the core nucleus \cite{hansen87,ikeda92}.
Here we define that the core nucleus is kept in the ground state in the soft dipole mode in comparison with the giant dipole resonances, in which the core nucleus is excited.
The Coulomb breakup reaction is useful to investigate the dipole response of unstable nuclei experimentally,
and can bring exotic excitations due to the presence of excess neutrons \cite{nakamura94,aumann99,nakamura06}.

In neutron-rich He isotopes, only two bound states are observed in $^6$He and $^8$He.
The $^8$He nucleus has a large neutron-proton ratio of 3 and consists of the $^4$He core nucleus and four valence neutrons,
which are bound with small separation energy of 3.1 MeV in the ground state \cite{tilley04}.
For the excitations of $^8$He, many experiments have been reported \cite{korsheninnikov93,iwata00,meister02,chulkov05,mueller07,golovkov09,holl21},
and recently, the dipole excitation is examined theoretically \cite{nonaiti22,piekarewicz22}.

In $^8$He, the lowest particle-threshold is the $^6$He+$n$+$n$ three-body channel with the excitation energy of 2.1 MeV,
and the next channel is the $^7$He+$n$ two-body one with the excitation energy of 2.6 MeV, where the ground state of $^7$He is a resonant state of $^6$He+$n$.
Experiments report the candidates of the excited states of $^8$He, which are located above the $^4$He+$n$+$n$+$n$+$n$ five-body channel \cite{golovkov09,holl21}.
From these facts, the excitations of $^8$He lead to the breakups into many-body channels of $^7$He+$n$, $^6$He+$n$+$n$, $^5$He+$n$+$n$+$n$, and $^4$He+$n$+$n$+$n$+$n$.

So far, we have performed the analysis of the neutron-rich He isotopes and their mirror proton-rich unbound nuclei in the $^4$He+$N+N+N+N$ five-body cluster model, where $^4$He is treated as an inert core \cite{myo10,myo12,myo14b,myo21,myo22}.
We solve the motion of multi valence-nucleons around the $^4$He core in the cluster orbital shell model (COSM) \cite{suzuki88,masui06,myo07a,masui12}.
In the COSM, the threshold energies of the particle emissions can be reproduced, namely, the subsystem energies of $^8$He.
This is an important property in the proper description of the multineutron emissions.
Under this condition, we describe many-body resonances using the complex scaling method (CSM) \cite{ho83,moiseyev98,aoyama06,moiseyev11,myo14a,myo20} imposing the correct boundary conditions for decaying states.
In the CSM, one solves the eigenvalue problem of the complex-scaled Hamiltonian using $L^2$ basis functions and obtains the resonances explicitly with complex energy eigenvalues.
Structures of resonances have been successfully investigated using the CSM not only for eigenenergies but also for the strength function applying the Green's function \cite{myo14a,myo20,myo98,myo01,suzuki05,odsuren15}.
For Coulomb breakup reactions of halo nuclei $^6$He and $^{11}$Li, we have successfully investigated the three-body breakup cross sections \cite{myo14a,myo01,kikuchi10,kikuchi13}.
In particular, we can decompose the strength function into the various channels of the direct three-body breakup and the sequential breakup via the subsystems.

In our previous work \cite{myo21}, we predicted four resonances of $^8$He with positive parity in the low excitation energy and the lowest resonance is the $2^+$ state,
whose energy and decay width are consistent with the recent experimental data \cite{holl21}.
In our recent letter \cite{myo22}, we predicted the soft dipole mode of $^8$He ($1^-$) in the electric dipole strength,
which makes a mild peak at the excitation energy of 13 MeV. This mode shows a collective nature of four neutrons oscillating against the $^4$He core.
In this paper, we report the detailed and extended analysis of the electric dipole strength of $^8$He in the low excitation-energy according to the recent letter.
We calculate the $1^-$ states of $^8$He in the COSM and CSM and evaluate the dipole strength function using the Green's function.
For the soft dipole mode, we further explore the possibility of the isolated resonance by searching for the resonance pole carefully in the complex scaling.
We do not discuss the giant resonances in this study, because the configuration of $^4$He is fixed in the five-body cluster model.
The present analysis is useful for the Coulomb breakup experiments of $^8$He \cite{lehr22}.

In section~\ref{sec:method}, we explain the framework of the COSM with the CSM.
In section~\ref{sec:result}, we discuss the results of the electric dipole strength of $^8$He and the possibility of soft dipole resonance.
In section~\ref{sec:summary}, we give a summary.

\section{Method}\label{sec:method}

\subsection{Cluster orbital shell model}

We explain the five-body cluster model of $^8$He with the $^4$He+$n$+$n$+$n$+$n$ COSM.
The relative coordinates of four neutrons are $\{\vc{r}_i\}$ with $i=1,\ldots,4$ as shown in Fig.~\ref{fig:COSM}.
The Hamiltonian is the same as used in the previous studies~\cite{myo10,myo12,myo14b,myo21,myo22}:
\begin{eqnarray}
	H
&=&	t_\alpha+ \sum_{i=1}^{A_v} t_i - t_G + \sum_{i=1}^{A_v} v^{\alpha N}_i + \sum_{i<j}^{A_v} v^{NN}_{ij}
    \\
&=&	\sum_{i=1}^{A_v} \left( \frac{\vc{p}^2_i}{2\mu} + v^{\alpha N}_i \right) + \sum_{i<j}^{A_v} \left( \frac{\vc{p}_i\cdot \vc{p}_j}{A_\alpha m} + v^{NN}_{ij} \right) ,
    \label{eq:Ham}
\end{eqnarray}
where $A_v$ and $A_\alpha$ are the number of valence neutrons and a mass number of $^4$He, respectively.
The total mass number is $A=A_v+A_\alpha$, where $(A_v, A_\alpha)=(4,4)$ for $^8$He.
The kinetic energy operators $t_\alpha$, $t_i$, and $t_G$ are those of $^4$He, one neutron, and the center-of-mass part, respectively.
The operator $\vc{p}_i$ is the relative momentum between $^4$He and a neutron.
The $^4$He--nucleon interaction $v^{\alpha N}$ is given by the microscopic Kanada-Kaneko-Nagata-Nomoto potential \cite{aoyama06,kanada79}.
For nucleon-nucleon interaction $v^{NN}$, we use the Minnesota central potential \cite{tang78}.

\begin{figure}[t]
\centering
\includegraphics[width=4.5cm,clip]{COSM8.eps}
\caption{Coordinate system of the $^4$He+$n$+$n$+$n$+$n$ in the COSM.
The vector $\vc{R}$ is a relative coordinate from the center-of-mass of $^4$He to the center-of-mass of four neutrons.}
\label{fig:COSM}
\end{figure}

In the COSM, the $^8$He wave function $\Psi^J$ with spin $J$ is expanded in the linear combination form of the COSM configuration $\Psi^J_c$ as
\begin{eqnarray}
    \Psi^J
&=& \sum_c C^J_c \Psi^J_c,
    \label{WF0}
    \\
    \Psi^J_c
 &=& {\cal A}' \left\{ \Phi(^4{\rm He}), \Phi^J_c \right\},
    \\
    \Phi^J_c
&=& {\cal A} \left[ \left[ \phi_{p_1}(\vc{r}_1), \phi_{p_2}(\vc{r}_2) \right]_{j_{12}},\left[ \phi_{p_3}(\vc{r}_3),\phi_{p_4}(\vc{r}_4) \right]_{j_{34}} \right]_J .
    \label{WF1}
\end{eqnarray}
We adopt the $(0s)^4$ configuration of the harmonic oscillator wave function for the $\Phi(^4{\rm He})$ of $^4$He.
The range parameter of the $0s$ orbit is 1.4 fm to reproduce the charge radius of $^4$He.
For valence neutrons, the single-particle wave function $\phi_p(\vc{r})$ is a function of relative coordinate $\vc{r}$ and
has a quantum number $p$, the set of $\{n,\ell,j\}$ in the $jj$ coupling scheme.
The label $n$ is for the different radial component explained later and $\ell$ is the orbital angular momentum coupled with a neutron spin as $j=[\ell,1/2]$.
The spins of $j_{12}$ and $j_{34}$ are for the neutron pairs.
The operators for the antisymmetrization ${\cal A'}$ and ${\cal A}$ are between $^4$He and a valence neutron and between valence neutrons, respectively.
The former is treated with the orthogonality condition model \cite{saito69}, where the relative $0s$ orbit is removed in the $\phi_p$.
The label $c$ in Eq.~(\ref{WF0}) means the set of $\{p_1,p_2,p_3,p_4,j_{12},j_{34}\}$.
We superpose the available configurations $\Psi^J_c$ with the amplitude of $C_c^J$ in Eq.~(\ref{WF0}).
The Hamiltonian matrix elements are calculated using the COSM basis states in the analytical form
and one solves the eigenvalue problem of the Hamiltonian:
\begin{eqnarray}
  \sum_{c'}\langle \Psi^J_c |H|  \Psi^J_{c'} \rangle\, C^J_{c'} &=& E^J C_{c}^J  ,
  \label{eq:eigen}
  \\
  \sum_c (C^J_{c})^2&=&1.
\end{eqnarray}
We obtain the amplitudes $\{C^J_c\}$ and the energy eigenvalues $E^J$ of $^8$He
measured from the five-body threshold energy of $^4$He+$n$+$n$+$n$+$n$.

We expand the radial part of $\phi_p(\vc{r})$ with a finite number of Gaussian functions $u(\vc{r},b)$ for each single-particle state:
\begin{eqnarray}
    \phi_p(\vc{r})
&=& \sum_{q=1}^{N_{\ell j}} d^q_p\ u_{\ell j}(\vc{r},b_{\ell j}^q)\, ,
    \label{spo}
    \\
    u_{\ell j}(\vc{r},b_{\ell j}^q)
&=& r^{\ell} e^{-(r/b_{\ell j}^q)^2/2}\, [Y_{\ell}(\hat{\vc{r}}),\chi^\sigma_{1/2}]_{j}\, ,
    \label{Gauss}
	\\
    \langle \phi_p | \phi_{p'} \rangle
&=& \delta_{p,p'}
~=~ \delta_{n,n'}\, \delta_{\ell,\ell'}\, \delta_{j,j'}.
    \label{Gauss2}
\end{eqnarray}
The label $q$ is for the Gaussian range parameter $b_{\ell j}^q$ with $q=1,\ldots, N_{\ell j}$,
where $N_{\ell j}$ is a basis number.
The parameters $\{b_{\ell j}^q\}$ are given in the geometric progression \cite{hiyama03}.
The coefficients $\{d^q_p\}$ in Eq.~(\ref{spo}) are determined using the orthogonal condition of the basis states $\{\phi_p\}$ in Eq.~(\ref{Gauss2}).
The number $N_{\ell j}$ is determined to get the convergence of the solutions and we use $N_{\ell j}=12$ at most
with the range of $b_{\ell j}^q$ from 0.3 fm to around 40 fm.
The multineutron configuration $\Phi^J_c$ in Eq.~(\ref{WF1}) is expanded using the products of the single-particle basis states $\phi_p$.

For the single-particle states $\phi_p$, we include the orbital angular momenta $\ell\le 2$ for the ground state of $^8$He.
This condition gives the two-neutron separation energy of $^6$He($0^+$) with the accuracy of 0.3 MeV
in comparison with the calculation including a large $\ell$.
For $1^-$ states of $^8$He, we increase the configurations including the $\ell=3$ states for the dipole transition.
We use the 173.7 MeV of the repulsive strength of the Minnesota potential $v^{NN}$ instead of the original 200 MeV
to reproduce 0.975 MeV of the two-neutron separation energy of $^6$He.
This condition is the same as used in the previous works \cite{myo10,myo12,myo21,myo22}
and gives a nice reproduction of the energy levels of He isotopes and their mirror nuclei.

\subsection{Electric dipole transition}

We investigate the electric dipole transition from the ground state of $^8$He.
In the present five-body COSM, we fix the configuration of $^4$He,
and consider the dipole transition induced by the motion of valence neutrons around $^4$He.
We introduce the relative coordinate $\vc{R}$ between $^4$He and the center-of-mass of four valence neutrons as shown in Fig. \ref{fig:COSM}.
The operator of the electric dipole ($E1$) transition is expressed in terms of  $\vc{R}$ with $R=|\vc{R}|$ as the recoil effect of $^4$He from the center-of-mass,
\begin{eqnarray}
  \hO_{E1,\mu}&=& -\frac{A_v}{A} eZ_\alpha R\, Y_{1\mu}(\widehat{\vc{R}}),
  \\
  \vc{R}&=& \frac{1}{A_v}\sum_{i=1}^{A_v}\vc{r}_i,
\end{eqnarray}
where $Z_\alpha$ is a proton number of $^4$He.
We consider the completeness relation of the $1^-$ states of $^8$He in the dipole transition,
which brings the non-energy weighted sum-rule value for the cluster model, denoted as $B_{\rm c}(E1)$
and expressed using the mean squared distance between $^4$He and center-of-mass of four valence neutrons in the ground state,
\begin{eqnarray}
  B_{\rm c}(E1)&=& \sum_\mu \langle \wtil{\Phi}_{0^+} | \hO^\dagger_{E1,\mu} \hO_{E1,\mu} |\Phi_{0^+}\rangle
~=~ \frac{3e^2}{4\pi}\cdot \left(\frac{A_vZ_\alpha}{A}\right)^2 \langle \vc{R}^2 \rangle.
\label{eq:SRV}
\end{eqnarray}
The value of $B_{\rm c}(E1)$ is useful to evaluate the amount of dipole strength obtained in the calculation.
For comparison, taking the $A$-nucleon dipole excitations, the ordinary non-energy weighted sum-rule value is
given as $B(E1)=3e^2/(4\pi)\cdot Z_\alpha \langle r^2_p \rangle$
where $\langle r^2_p \rangle$ is a mean squared proton radius of the ground state.
In this study, the excitation of $^4$He is not treated and
this effect is expected to contribute to the dipole strength of $^8$He above the excitation energy of around 20 MeV.

\subsection{Complex scaling method}

We describe resonances and continuum states in the many-body systems with the CSM \cite{ho83,moiseyev98,moiseyev11,aoyama06,myo14a,myo20}.
In this study, resonances are the Gamow states satisfying the outgoing boundary condition with the complex eigenenergies,
and the continuum states are orthogonal to these resonances.
In the CSM, the coordinates $\{\vc{r}_j\}$ in Fig. \ref{fig:COSM} are transformed with a scaling angle $\theta$ as
\begin{eqnarray}
  \vc{r}_j \to \vc{r}_j\, e^{i\theta},\qquad
  \vc{p}_j \to \vc{p}_j\, e^{-i\theta},
  \label{CSM}
\end{eqnarray}
where $\vc{p}_i$ is the conjugate momentum of $\vc{r}_i$ and is used in the Hamiltonian Eq.~(\ref{eq:Ham}).
The complex-scaled Schr\"odinger equation is written with the complex-scaled Hamiltonian $H_\theta$ as
\begin{eqnarray}
	H_\theta   \Psi^J_\theta
&=&     E^J_\theta \Psi^J_\theta ,
	\label{eq:eigen2}
        \\
    \Psi^J_\theta
&=& \sum_c C^J_{c,\theta} \Psi^J_c,
    \label{WF_CSM}
    \\
1&=& \sum_{c} \big(C^J_{c,\theta}\big)^2.
    \label{norm_CSM}
\end{eqnarray}
We solve the eigenvalue problem of Eq.~(\ref{eq:eigen2}) and
obtain the complex-scaled wave function $\Psi^J_\theta$ in Eq.~(\ref{WF_CSM}),
where the coefficients $C_{c,\theta}^J$ are $\theta$-dependent complex numbers.
We obtain the energy eigenvalues $E^J_\theta$ on a complex energy plane according to the so-called ABC theorem proved by Aguilar, Balslev, and Combes \cite{ABC}.

This theorem indicates that the complex scaling transforms the divergent outgoing resonant wave into a damping form.
As a result, the asymptotic boundary condition of resonances in the CSM becomes the same as bound states \cite{aoyama06,myo14a}.
In the CSM, every Riemann branch cut is rotated down by $2\theta$ in the complex energy plane,
according to the momentum transformation in Eq.~(\ref{CSM}).
The branch cuts start from the threshold energies of particle emissions
and the continuum states are obtained on the corresponding $2\theta$ lines.
In the ABC theorem, the energies of bound and resonant states are independent of $\theta$
and the resonance energy eigenvalue is given as $E_r-i\Gamma/2$
with the resonance energy $E_r$ measured from the threshold energy and the decay width $\Gamma$.

In the CSM, one can expand the resonance wave functions with the $L^2$ basis functions
because of the damping boundary condition, being normalized in the condition in Eq.~(\ref{norm_CSM}).
One does not use the Hermitian product according to the bi-orthogonal property of the adjoint states \cite{ho83,moiseyev98,berggren68}.

We calculate the strength function of the electric dipole transition into the unbound states of $^8$He.
For this purpose, we consider the extended completeness relation (ECR) of $^8$He consisting of bound, resonant, and continuum states
with the complex-scaled eigenstates $\Psi^J_\theta$ in Eq.~(\ref{eq:eigen}) \cite{myo01,myo10,berggren68}.
When one adopts a large value of $\theta$, five-body components of $^8$He are classified into several categories,
which construct the five-body ECR of $^8$He as
\begin{eqnarray}
	{\bf 1}
&=&	\sum_{~\nu} \kets{\Psi^J_{\theta,\nu}}\bras{\wtil{\Psi}^J_{\theta,\nu}}
	\nonumber
	\\
&=&	\{\mbox{bound state of $^8${He}}\}
	\nonumber
	\\
&+&	\{\mbox{resonances of $^8${He}}\}
	\nonumber
	\\
&+&	\{\mbox{two-body continuum states of $^7${He}$^{(*)}+n$}\}
	\nonumber
	\\
&+&	\{\mbox{three-body continuum states of $^6${He}$^{(*)}+n+n$}\}
	\nonumber
	\\
&+&	\{\mbox{four-body continuum states of $^5${He}$^{(*)}+n+n+n$}\}
	\nonumber
	\\
&+&	\{\mbox{five-body continuum states of $^4${He} $+n+n+n+n$}\} ,
	\label{eq:ECR}
\end{eqnarray}
where $\{ \Psi^J_{\theta,\nu},\wtil{\Psi}^J_{\theta,\nu} \}$ form biorthogonal bases with the state index $\nu$.

We explain the general procedure to calculate the strength function using the ECR, where we omit the spin notation.
One can define the complex-scaled Green's function ${\cal G}^\theta(E)$ as a function of the energy $E$:
\begin{eqnarray}
	{\cal G}^\theta(E)
&=&	\frac{ {\bf 1} }{ E-H_\theta }
~=~	\sum_{~\nu}
	\frac{|\Psi^\theta_\nu\rangle \langle \wtil{\Psi}^\theta_\nu|}{E-E_\nu^\theta} .
	\label{eq:green1}
\end{eqnarray}
The strength function $S_\lambda(E)$ of the transition operator $\hO_\lambda$ with rank $\lambda$
is represented by using the Green's function without the complex scaling as
\begin{eqnarray}
	S_\lambda(E)
&=&	\sum_{~\nu}
	\bras{\wtil{\Psi}_0}\hO_\lambda^\dagger\kets{\Psi_\nu}\bras{\wtil{\Psi}_\nu}\hO_\lambda\kets{\Psi_0}\,
	\delta(E-E_\nu)
	\label{eq:strength_org}
	\\
&=&	-\frac1{\pi}\ {\rm Im}\left\{ \langle \wtil{\Psi}_0 | \hO^\dagger_\lambda {\cal G}(E) \hO_\lambda | \Psi_0 \rangle \right\},
	\label{eq:strength1}
\end{eqnarray}
where $\Psi_0$ is the initial state.
We apply the complex scaling to the strength function and use ${\cal G}^\theta(E)$ in Eq.~(\ref{eq:green1}).
\begin{eqnarray}
	S_\lambda(E)
&=&     \sum_{~\nu} S_{\lambda,\nu}(E) ,
	\label{eq:strength2}
        \\
        S_{\lambda,\nu}(E)
&=&     -\frac1{\pi}\ {\rm Im}\left\{  \frac{
	\bras{\wtil{\Psi}_0^\theta}  (\hO_\lambda^\dagger)^\theta \kets{\Psi_\nu^\theta}
	\bras{\wtil{\Psi}_\nu^\theta} \hO_\lambda^\theta          \kets{\Psi_0^\theta}
        }{E-E_\nu^\theta}
        \right\}.
	\label{eq:strength3}
\end{eqnarray}
One can extract the contributions of the state $\nu$, $S_{\lambda,\nu}(E)$, in the total strength $S_\lambda(E)$
and classify $S_\lambda(E)$ in terms of the ECR in Eq. (\ref{eq:ECR}).
It is noted that the functions $S_{\lambda}(E)$ and $S_{\lambda,\nu}(E)$ are independent of $\theta$ \cite{myo01,myo10,odsuren15}.
This is because the state $\nu$ is uniquely classified in the ECR in Eq.~(\ref{eq:ECR}) and then $S_{\lambda,\nu}(E)$ is also uniquely obtained.
The complex-scaled Green's function has been widely used in calculations of the scattering amplitudes
\cite{kikuchi10,myo14a,kruppa07,dote13}.

We mention the properties of the strength function $S_{\lambda,\nu}(E)$.
The total strength function $S_{\lambda}(E)$ is the observable and positive definite.
On the other hand, the component $S_{\lambda,\nu}(E)$ is not imposed to keep the positive definite at all energies,
because $S_{\lambda,\nu}(E)$ is non-observable, similar to the complex energies of resonances.
This property means that $S_{\lambda,\nu}(E)$ can show negative values.
We have generally discussed this point of the strength function in the CSM in Refs. \cite{myo98,myo01}.

In this study, many-body continuum states are expanded with the Gaussian functions in Eq.(\ref{Gauss}) similar to the resonances,
and then the states are discretized.
The reliability of the discretization of the unbound states in the CSM has been shown
in terms of the continuum level density \cite{suzuki05,kruppa07,odsuren14,odsuren21}.

\section{Results}\label{sec:result}

\subsection{Energy spectra of He isotopes}

\begin{figure}[b]
\centering
\includegraphics[width=10.5cm,clip]{8He_lev5_color.eps}
\caption{Energy levels of $^{4-8}$He measured from the $^4$He energy \cite{myo21}. Units are in MeV.
  Red (right) and black (left) lines are the values of theory and experiments, respectively.
  Small numbers indicate the decay widths $\Gamma$ of resonances.
  For $^8$He, the experimental data are taken from Refs. \cite{golovkov09,holl21}.}
\label{fig:He}
\end{figure}

We start to discuss the results of the energy spectra of He isotopes to show the validity of the COSM with the complex scaling,
the main parts of which are already reported in the previous work \cite{myo21}.
The energy spectra are useful to confirm the threshold energies of the multineutron emissions in the dipole transition of $^8$He.
The systematic behavior of the energy levels of $^{4-8}$He is shown in Fig. \ref{fig:He}.
For $^8$He, we obtain five states with positive parity; only the ground state is a bound state and the others are resonances.

For the ground $0^+$ state of $^8$He, the relative energy measured from the $^4$He+$n$+$n$+$n$+$n$ threshold is 3.22 MeV and close to the experimental value of 3.11 MeV.
For the $2^+_1$ resonance of $^8$He, we obtain the relative energy of 0.32 MeV and the decay width $\Gamma$ of 0.66 MeV.
These values are consistent with the recent experimental report of the corresponding energy 0.43(6) MeV and decay width $\Gamma$=0.89(11) MeV,
which are derived from the energy dependence of the cross section in the proton inelastic scattering \cite{holl21}.
The dominant configurations of four neutrons in the energy levels are shown in the previous analysis \cite{myo21}.

\begin{table}[t]
  \caption{Radial properties of the ground state of $^8$He in units of fm for matter, proton, neutron, and charge parts.
Comparison with the experiments; a\cite{tanihata92}, b\cite{alkazov97}, c\cite{kiselev05}, d\cite{mueller07}, e\cite{brodeur12}, and f\cite{krauth21}, are shown.
Mean distances between $^4$He and one valence neutron $\alpha\mbox{-}n$ and between $^4$He and four valence neutrons $\alpha\mbox{-}4n$, and the radius of four valence neutrons $4n$, are shown together in fm.
The non-energy weighted sum-rule value $B_{\rm c}(E1)$ of the dipole strength in the cluster model is given in units of $e^2$fm$^2$.}
  \label{tab:radius}
  \centering

    \begin{tabular}{c|cc}
      \noalign{\hrule height 0.5pt}
                       & Theory      & Experiments   \\ \hline
      matter           & 2.53        & 2.49(4)$^{\rm a}$~~~2.45(7)$^{\rm b}$~~~2.49(4)$^{\rm c}$ \\
      proton           & 1.81        &     \\
    ~~neutron~~        & 2.73        &     \\
      charge           & 1.92        & 1.929(26)$^{\rm d}$~~1.959(16)$^{\rm e}$~~1.9559(158)$^{\rm f}$  \\ \hline
$\alpha\mbox{-}n$      & 3.56        &     \\
$\alpha\mbox{-}4n$     & 2.05        &     \\
$4n$                   & 2.91        &     \\ \hline
$B_{\rm c}(E1)$              & 1.01        &     \\
\noalign{\hrule height 0.5pt}
\end{tabular}
\end{table}

In Table \ref{tab:radius}, we summarize the spatial properties of the ground state of $^8$He.
The matter and charge radii of $^8$He are 2.53 and 1.92 fm, respectively, which agree with the experiments.
The mean distance between $^4$He and the center-of-mass of four valence neutrons, $\alpha\mbox{-}4n$, is obtained as $\sqrt{\langle \vc{R}^2 \rangle}=2.05$ fm.
This distance is responsible for the electric dipole transition from the ground state according to Eq.~(\ref{eq:SRV}).
The non-energy weighted sum-rule value for cluster model $B_{\rm c}(E1)$ is obtained as 1.01 $e^2$fm$^2$ using this distance.
The radius of four neutrons in $^8$He is also obtained as 2.91 fm.

\subsection{Electric dipole transition}

We investigate the electric dipole transition strength of $^8$He.
Before showing the results with the complex scaling, first we demonstrate the case without the complex scaling, that is,
the scaling angle $\theta=0^\circ$ and the eigenenergies of the $1^-$ states of $^8$He are discretized on the real energy axis in the bound-state approximation.
The transition strengths are calculated for each discretized state and
we adopt Eq.~(\ref{eq:strength_org}) to calculate the dipole strength
\begin{eqnarray}
  B(E1,\nu)=\bras{\wtil{\Psi}_{0^+}}|\hO_{E1}^\dagger|\kets{\Psi_{1^-,\nu}}\bras{\wtil{\Psi}_{1^-,\nu}}|\hO_{E1}|\kets{\Psi_{0^+}}
\end{eqnarray}
using the reduced matrix elements of the state index $\nu$ in the discretized $1^-$ states.

In Fig.~\ref{fig:disc1}, we show the discretized dipole strength without the complex scaling.
In the distribution, we can confirm the low-energy strengths at around the excitation energies from 3 MeV to 9 MeV
and also at around 14 MeV.
Although the strength distribution is discretized as a function of the energy as shown in Fig.~\ref{fig:disc1},
it becomes continuous by using the Green's function with the complex scaling.
Later, we investigate the properties of the strength using the complex scaling in detail.

\begin{figure}[t]
  \centering
  \includegraphics[width=8.5cm,clip]{E1_disc_02b.eps}
  \caption{Discretized electric dipole strength $B(E1,\nu)$ of $^8$He with the state index $\nu$ as a function of the excitation energy $E_{x,\nu}$ without complex scaling.
    Units are $e^2$fm$^2$.
    For three states with labels A, B, and C, the transition densities are calculated in section \ref{sec:dns}.
  }
  \label{fig:disc1}
\end{figure}
\begin{figure}[t]
  \centering
  \includegraphics[width=8.5cm,clip]{E1_disc_02c.eps}
  \caption{Accumulated electric dipole strength $\sum_\nu B(E1,\nu)$ of $^8$He as a function of the excitation energy without complex scaling.
    The ratio to $B_{\rm c}(E1)$ in Table \ref{tab:radius} is given.}
  \label{fig:disc2}
\end{figure}

In Fig.~\ref{fig:disc2}, we show the accumulated dipole transition strength $\sum_\nu B(E1,\nu)$ as a function of the excitation energy of $^8$He.
This is useful to check the completeness relation of the discretized $1^-$ states.
The results are normalized by $B_{\rm c}(E1)$ shown in Table \ref{tab:radius}.
It is found that at 80 MeV, the accumulated strength is converged and the ratio becomes 0.993 with respect to $B_{\rm c}(E1)$.
This means that the $1^-$ states sufficiently construct the completeness relation in the COSM even without the complex scaling.

Next, we perform the calculation of the electric dipole strength using the complex scaling with a finite $\theta$.
One of the advantages of this calculation is that each eigenstate is distinguishable in the categories of various channels of $^8$He explained in Eq.~(\ref{eq:ECR}).
Another advantage is that the complex scaling provides the correct level density even in the finite number of the basis states \cite{suzuki05}.
By using the Green's function with complex scaling in Eq.~(\ref{eq:green1}),
one can obtain the continuous strength as a function of the excitation energy,
being independent of $\theta$, and the resulting distribution can be compared with the experimental data.

\begin{figure}[b]
\centering
\includegraphics[width=9.0cm,clip]{ene_1-_05e.eps}
\caption{
  Energy eigenvalue distribution of $^8$He ($1^-$) with complex scaling in the complex energy plane
  measured from the ground state energy. The scaling angle $\theta$ is 18$^\circ$ \cite{myo22}. Units are in MeV.
  Some of the channels of multineutron emissions are shown.
}
\label{fig:CSM}
\end{figure}

In Fig. \ref{fig:CSM}, we show the complex energy eigenvalues of $^8$He($1^-$) with complex scaling,
measured from the ground state of $^8$He where the scaling angle $\theta=18^\circ$.
The states are obtained along several lines, which have the angle $2\theta$ with respect to the real axis
and are called the $2\theta$ lines.
The $2\theta$ lines are the branch cuts starting from the thresholds, in the case of $^8$He,
of $^6$He($0^+$)+$n$+$n$, $^7$He($3/2^-$)+$n$, $^4$He+$n$+$n$+$n$+$n$, $^5$He($3/2^-$)+$n$+$n$+$n$, and $^6$He($2^+$)+$n$+$n$,
as the excitation energy increases.
These eigenstates represent the discretized continuum states of each channel.
One can extract the contributions of the individual continuum states to the strength function,
which is handled by using the Green's function with complex scaling and ECR \cite{myo98,myo01,myo14a}.

\begin{figure}[t]
\centering
\includegraphics[width=8.5cm,clip]{E1_dist_05a.eps}
\caption{Distribution of the electric dipole strength $dB(E1)/dE$ of $^8$He
  as a function of the excitation energy using the complex scaling with $\theta=18^\circ$ \cite{myo22}. Units are in $e^2$fm$^2$/MeV.}
\label{fig:dist1}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=8.5cm,clip]{E1_dist_05b.eps}
\caption{Integrated electric dipole strength $B(E1,E)$ of $^8$He using complex scaling up to the excitation energy $E$.
The ratio to $B_{\rm c}(E1)$ in Table \ref{tab:radius} is given.}
\label{fig:dist2}
\end{figure}

In Fig.~\ref{fig:dist1}, we give the electric dipole strength function $dB(E1)/dE$ of $^8$He,
which corresponds to $S_{\lambda=1}(E)$ in Eq.~(\ref{eq:strength2}) as a function of the excitation energy,
where all of the complex-scaled solutions of the $1^-$ states are used.
The line presented in Fig. \ref{fig:dist1}, is obtained by the continuation of discretized strength function shown in Fig. \ref{fig:disc1}.
In the CSM, the strength function obtained with appropriate basis states does not depend on the scaling angle $\theta$.
Some parts of the present analysis have already been reported in the previous letter \cite{myo22}.
It is found that the strength shows a spike at 2.8 MeV and after that, the mild peak is obtained at around 5 MeV.
Above 5 MeV, the strength gradually decreases as the excitation energy increases.

In Fig.~\ref{fig:dist2}, we show the integrated dipole strength up to the excitation energy of $^8$He.
We plot the ratio with respect to $B_{\rm c}(E1)$, similar to the results shown in Fig.~\ref{fig:disc2}.
It is confirmed that at 80 MeV of the excitation energy, the ratio becomes 0.996.
This ensures the completeness relation of the complex-scaled $1^-$ states
and is similar to the case without the complex scaling as shown in Fig. \ref{fig:disc2}.

\begin{figure}[t]
\centering
\includegraphics[width=8.5cm,clip]{E1_dist_PW_02c.eps}
\caption{Distributions of the electric dipole strengths of $^8$He using different conditions of the final $1^-$ states
  with $\theta=18^\circ$.
  (1) plane waves with a blue dashed line,
  (2) without the interactions between valence neutrons ($v^{NN}=0$) with a green dotted line.
  The original results are taken from Fig.~\ref{fig:dist1} with a red solid line.
  }\label{fig:PW}
\end{figure}

In Fig.~\ref{fig:PW}, we further calculate the dipole strength function with complex scaling,
where four valence neutrons in the $1^-$ states of $^8$He are treated as plane waves, namely, no final-state interaction is considered.
We adopt this condition by omitting $v^{\alpha N}$ and $v^{NN}$ in the Hamiltonian in Eq. (\ref{eq:Ham}) for the $1^-$ states.
This calculation is useful to understand the effect of the final-state interaction on the strength function
and we have performed a similar analysis for two-neutron halo nuclei of $^6$He and $^{11}$Li \cite{myo01,myo07b,myo08}.
It is found that the magnitude of strength becomes lower and the distribution is much wider over the excitation energy
in comparison with the original calculation including the interactions.
We confirm a mild bump at a higher excitation energy of around 40 MeV.
This indicates that the interaction effect in the $1^-$ states of $^8$He is important to explain the observed strength below 20 MeV shown in Fig. \ref{fig:dist1}.
It is known that the dipole strength to the plane waves reflects the spatial distribution of the weak-binding neutrons in the ground state \cite{nakamura94,myo98},
but this effect cannot explain the observed strength.
When we omit only the interactions between valence neutrons $v^{NN}$ in the Hamiltonian,
the strength starts to show at around 5 MeV near the $^5$He+$n$+$n$+$n$ threshold energy,
where $^5$He is a $3/2^-$ resonance,
and the peak of the strength shifts to around 10 MeV and the height is reduced from the original one.

\begin{figure}[t]
\centering
\includegraphics[width=8.5cm,clip]{E1_disc_05f.eps
\caption{
  Dipole matrix elements of the $1^-$ eigenstates of $^8$He using the complex scaling with $\theta=18^\circ$ in the complex energy plane, taken from Ref. \cite{myo22}.
  Small red dots indicate the complex eigenenergies.
  The radius of the open circles is the absolute value of the real part of the dipole matrix element for each state in the arbitrary units.}
\label{fig:size}
\end{figure}

To clarify the structures of the original dipole strength,
in Fig.~\ref{fig:size}, we show the distribution of the dipole matrix elements for the $1^-$ eigenstates with the complex energy eigenvalues shown in Fig. \ref{fig:CSM},
which is originally explained in the previous letter \cite{myo22} and complementarily useful in the present analysis.
The size of the open circles is proportional to the real part of the following reduced dipole matrix element,
${\rm Re}\left\{\bras{\wtil{\Psi}^\theta_{0^+}}|\hO_{E1}^{\dagger,\theta}|\kets{\Psi^\theta_{1^-,\nu}}\bras{\wtil{\Psi}^\theta_{1^-,\nu}}|\hO^\theta_{E1}|\kets{\Psi^\theta_{0^+}}\right\}$.
Below 10 MeV of the excitation energy, the two-body continuum states of the $^7$He($3/2^-$)+$n$ channel show a large contribution to the dipole strength.
The strengths from the other channels of $^4$He+$n$+$n$+$n$+$n$, $^5$He+$n$+$n$+$n$, and $^6$He+$n$+$n$ are very minor.

\begin{table}[t]
  \begin{minipage}[t]{0.47\textwidth}
    \caption{Dominant parts of the squared amplitudes $(C_{c,\theta}^J)^2$ of the $1^-$ state of $^8$He with the $^7$He+$n$($s$-wave) configuration.}
    \label{tab:cmp1}
    \centering

    \begin{tabular}{c|ccc}
      \noalign{\hrule height 0.5pt}
      Configuration                            &  $(C_{c,\theta}^J)^2$ \\ \hline
      $(p_{3/2})^3(1s_{1/2})$                 &  $0.918-0.020i$       \\
      $(p_{3/2})(p_{1/2})^2(1s_{1/2})$        &  $0.027+0.001i$       \\
      $(p_{3/2})(d_{5/2})^2(1s_{1/2})$        &  $0.019+0.002i$       \\
      $(p_{3/2})^2(p_{1/2})(1s_{1/2})$        &  $0.014+0.007i$       \\
      \noalign{\hrule height 0.5pt}
    \end{tabular}
  \end{minipage}
  \hspace*{0.6cm}
  \begin{minipage}[t]{0.47\textwidth}
    \caption{Dominant parts of the squared amplitudes $(C_{c,\theta}^J)^2$ of the $1^-$ state of $^8$He with the $^7$He+$n$($d$-wave) configuration.}
    \label{tab:cmp2}
    \centering

    \begin{tabular}{c|ccc}
      \noalign{\hrule height 0.5pt}
      Configuration                            &  $(C_{c,\theta}^J)^2$ \\ \hline
      $(p_{3/2})^3(d_{5/2})$                  &  $0.918-0.013i$       \\
      $(p_{3/2})(p_{1/2})^2(d_{5/2})$         &  $0.028+0.005i$       \\
      $(p_{3/2})(d_{5/2})^3$                  &  $0.017-0.003i$       \\
      $(p_{3/2})(1s_{1/2})^2(d_{5/2})$        &  $0.006+0.002i$       \\
      $(p_{3/2})(d_{3/2})^2(d_{5/2})$         &  $0.004+0.001i$       \\
      \noalign{\hrule height 0.5pt}
    \end{tabular}

  \end{minipage}
\end{table}

In Tables \ref{tab:cmp1} and  \ref{tab:cmp2}, we select the typical $^7$He+$n$ states having relatively large dipole matrix elements
and show the dominant configurations of valence neutrons in these states;
one is $^7$He+$n$($s$-wave) and the other is $^7$He+$n$($d$-wave).
The different radial components in the same orbit are summed up.
It is found that the $^7$He+$n$ channels dominantly have the $(p_{3/2})^3$ configuration for the $^7$He part,
and the last neutron is in the continuum states of $s$-wave or $d$-wave.
Hence, the dipole strengths to the $^7$He$+n$ channels shown in Fig.~\ref{fig:size}
are understood to be caused by the single particle excitation from the ground state of $^8$He.

In Fig.~\ref{fig:size}, several $1^-$ states show the large dipole matrix elements at around 13 MeV of the excitation energy.
In the previous letter \cite{myo22}, it is found that these states have a property of the strong configuration mixing
with the multineutron excitations.
This feature suggests the collectivity of four-neutron ($4n$) excitations and
we assign these states as the soft dipole mode of $4n$ oscillating against the $^4$He core.
The excitation energy of 13 MeV looks high but can be naively understood from the $1\hbar\omega$ excitation of the relative motion
between $4n$ and the $^4$He core estimated using the mean relative distance in the ground state \cite{myo22}.

\begin{figure}[t]
\centering
\includegraphics[width=8.5cm,clip]{E1_dist_05e.eps}
\caption{
  Decomposition of the electric dipole strength of $^8$He using the complex scaling as a function of the excitation energy $E$,
  taken from Ref. \cite{myo22}.
  The components are
  $^7$He(3/2$^-$)+$n$($s$-wave) with a blue solid line,
  $^7$He(3/2$^-$)+$n$($d$-wave) with a green dashed line,
  the soft dipole mode with an orange dash-dotted line,
  in addition to the total strength with a red dotted line.}
\label{fig:cmp}
\end{figure}

In Fig.~\ref{fig:cmp}, we show the results of the decomposition of the dipole strength
into the $^7$He+$n$ channels and the soft dipole mode by using the results of Figs. \ref{fig:CSM} and \ref{fig:size}.
It is confirmed that the $^7$He(3/2$^-$)+$n$ channel is dominant below 10 MeV of the excitation energy,
indicating the sequential breakup process via the $^7$He resonance.
At 13 MeV, the soft dipole mode makes a broad peak in the strength, which explains the total strength above 10 MeV as shown in Fig. \ref{fig:dist1}.

\subsection{Transition density}\label{sec:dns}

Transition density is useful to understand the spatial distribution of multineutron in the dipole excitations of $^8$He \cite{myo22}.
The transition density $\rho_{E1,\nu}(r)$ is defined to be the integrand of the reduced matrix element of the transition to the state $\nu$.
\begin{eqnarray}
  \bras{\wtil{\Psi}_{1^-,\nu}}|\hO_{E1}|\kets{\Psi_{0^+}}
  &=& \int_0^\infty \rho_{E1,\nu}(r)\, r^2 dr \, ,
  \\
\rho_{E1,\nu}(r)
  &=& -\frac{Z_\alpha}{A} e \ \sum_{j=1}^{A_v} \bras{\wtil{\Psi}_{1^-,\nu}}| r_j Y_1(\hat{\vc{r}}_j) \dfrac{\delta(r_j-r)}{r_j^2} |\kets{\Psi_{0^+}}  ,
\end{eqnarray}
where $r$ stands for the distance between $^4$He and a neutron.
It is possible to apply the complex scaling to this quantity, however, the complex scaling changes the spatial distribution of the integrand along the scaled coordinate of $r e^{i\theta}$.
To discuss the spatial property of the transition density $\rho_{E1,\nu}(r)$ directly,
we calculate the transition density with $\theta=0^\circ$ and select the specific states which have the same properties of the configurations as obtained with complex scaling.

\begin{figure}[b]
\centering
\includegraphics[width=8.5cm,clip]{tr_dns_02c.eps}
\caption{
  Transition densities of electric dipole strengths for three $1^-$ states of $^8$He as shown in Fig. \ref{fig:disc1} with labels in units of $e$fm$^{-2}$.
  Three states are shown with their representative configurations of A: $^7$He+$n$($s$-wave) with a blue dashed line, B: $^7$He+$n$($d$-wave) with a green dotted line, and C: soft dipole mode with a red solid line, respectively.}
\label{fig:dns}
\end{figure}

We choose a typical state having the $^7$He+$n$ ($s$-wave) channel with a large dipole matrix element of $^8$He, which is the state with label A in Fig. \ref{fig:disc1}.
In this state, a single neutron is mainly excited from the $p$-state to the $s$-state, and the transition density is shown with the blue dashed line in Fig.~\ref{fig:dns}.
The long tail behaviour is obtained in the distribution because of the separation of one neutron from $^8$He.
The second case is the $^7$He+$n$ ($d$-wave) channel in the state with label B in Fig. \ref{fig:disc1}.
In Fig.~\ref{fig:dns}, this state also shows the long tail behaviour in the green dotted line, indicating the $d$-wave neutron in the continuum.
The last case is the soft dipole mode with label C in Fig. \ref{fig:disc1}.
The transition density in the red solid line shows the large strength concentrating at 3 fm without a long tail,
indicating a soft dipole mode of $4n$ oscillating against the $^4$He core \cite{ikeda92}.

In the summary of the dipole transition densities of $^8$He,
there are two kinds of different excitations; the single-particle excitations to the $^7$He+$n$ channel
and the collective excitation to the soft dipole mode.

\subsection{Possibility of soft dipole resonance}

We locate an isolated $1^-$ resonance that represents the soft dipole mode of $^8$He.
For this purpose, we adopt a larger scaling angle $\theta$ than $18^\circ$ used in Fig. \ref{fig:CSM} in the complex scaling
and try to search for the resonance pole, which is separated from the rotated continuum states in the complex energy plane.
In the calculation of the complex scaling with a large $\theta$, the numerical accuracy generally decreases
because we expand the radial wave function with the finite number of the basis functions.
Due to this reason, several continuum lines in the complex energy plane often deviate from the position at the threshold energies.
It is possible to improve the numerical stability with a large $\theta$
in terms of the complex-range Gaussian basis functions \cite{hiyama03}, which increases the basis number.

\begin{figure}[b]
\centering
\includegraphics[width=8.5cm,clip]{E1_disc_08e.eps
\caption{
  Dipole matrix elements of the $1^-$ eigenstates of $^8$He using the complex scaling with $\theta=26^\circ$ in the complex energy plane measured from the ground state energy.
  Notations are the same as those used in Fig.~\ref{fig:size}.
  The short arrow indicates the eigenenergy of the soft dipole resonance (SDR) with $(E_x,\Gamma)=(14, 21)$ MeV showing the large dipole matrix element.
}
\label{fig:size2}
\end{figure}

In Fig. \ref{fig:size2}, we show the results of the distribution of the dipole matrix elements using $\theta=26^\circ$ in the complex energy plane,
together with the complex energy eigenvalues, similarly to Fig. \ref{fig:size}.
We obtain one candidate of the resonance pole at $(E_x,\Gamma)=(14,21)$ MeV having a large dipole matrix element shown by the large size of the circle.
Here, large $\theta$ values decrease numerical accuracy, so the low-energy continuum lines such as the $^7$He+$n$ channel are slightly shifted to the right direction and not distinguishable clearly.
On the other hand, the resonance pole is stably obtained with this value of $\theta$ in the complex energy plane.
We consider that this resonance becomes the candidate for the soft dipole resonance (SDR) of $^8$He.

We evaluate the radial properties of the SDR in Table \ref{tab:radius2}.
For unbound states with complex energies, the matrix elements can be complex, and if the state is a resonance, its radius is uniquely determined \cite{myo20,burgers96,dote18}.
We can interpret the spatial size of the resonance using the real part of the radius if the imaginary part is relatively smaller than the real part.

It is found that the obtained radial matrix elements of the SDR have larger real parts than the imaginary parts, although this resonance has a very large decay width of 21 MeV.
Using real parts, the resonance shows the large spatial sizes in comparison with those of the ground state as shown in Table \ref{tab:radius}.
The radius of $4n$ in the resonance is 3.71 fm,  which is larger than 2.91 fm in the ground state.
The distance between $^4$He and $4n$ also becomes large as 2.67 fm from 2.05 fm in the ground state.
These results indicate that in the SDR,
the size of $4n$ is expanded from that in the ground state and the mean relative distance also becomes large for dipole oscillation.

\begin{table}[t]
  \caption{Radial properties of the soft dipole resonance of $^8$He in units of fm.
    We show matter, proton, and neutron radii, and mean distance between $^4$He and four valence neutrons $\alpha\mbox{-}4n$,
    and the radius of four valence neutrons $4n$.}
  \label{tab:radius2}
  \centering

    \begin{tabular}{c|ccc}
      \noalign{\hrule height 0.5pt}
      matter         & $3.11+0.86i$  \\
      proton         & $1.97+0.28i$  \\
    ~~neutron~~      & $3.41+0.99i$  \\
$\alpha\mbox{-}4n$   & $2.67+0.84i$  \\
$4n$                 & $3.71+1.14i$  \\
      \noalign{\hrule height 0.5pt}
\end{tabular}
\end{table}

\begin{figure}[t]
\centering
\includegraphics[width=8.5cm,clip]{E1_dist_08c.eps}
\caption{
  Electric dipole strength $dB(E1)/dE$ of $^8$He as a function of the excitation energy using the complex scaling with $\theta=26^\circ$ (blue solid line) and $\theta=18^\circ$ (red dotted line).
  Units are in $e^2$fm$^2$/MeV.
  The contribution of soft dipole resonance (SDR) with $\theta=26^\circ$ is given with an orange dash-dotted line.
  The resonance energy is shown by the black solid circle on the energy axis.}
\label{fig:cmp2}
\end{figure}

Finally, we calculate the electric dipole strength of $^8$He using the complex-scaled solutions including the SDR obtained with $\theta=26^\circ$ in Fig. \ref{fig:cmp2}.
We also compare the results with those obtained using $\theta=18^\circ$.
It is found that strength at around 3 MeV of the excitation energy disappears.
because the continuum states of the $^7$He+$n$ channel are slightly shifted in the complex energy plane as shown in Fig. \ref{fig:size2}.
Above 5 MeV of the excitation energy, the strength is almost common between two results of $\theta=26^\circ$ and $18^\circ$.
We further extract the component of the SDR alone, which is described following Eq.~(\ref{eq:strength3}) as
\begin{eqnarray}
\frac{dB(E1,{\rm SDR})}{dE}&=&-\frac{1}{\pi}{\rm Im}\left\{\frac{M_{\rm R}+iM_{\rm I}}{E-E_{\rm SDR}}\right\}
~=~\frac{1}{\pi}\frac{M_{\rm R}\Gamma/2-M_{\rm I}(E-E_x)}{(E-E_x)^2+\Gamma^2/4},
\label{eq:SDR}
\end{eqnarray}
where
\begin{equation}
E_{\rm SDR}~=~E_x-i\Gamma/2, \qquad
\langle \tilde{\Psi}^\theta_{0^+}||(O^\dagger_{E1})^\theta||\Psi^\theta_{\rm SDR}\rangle
\langle \tilde{\Psi}^\theta_{\rm SDR}||O^\theta_{E1}||\Psi^\theta_{0^+}\rangle~=~M_{\rm R}+iM_{\rm I}.
\end{equation}
The obtained distribution of SDR in Fig. \ref{fig:cmp2} is similar to those of the soft dipole mode as shown in Fig. \ref{fig:cmp}.
This indicates that the SDR is the main component of soft dipole mode in the dipole strength.
The integration of Eq.~(\ref{eq:SDR}) over energy becomes $M_{\rm R}$.

The SDR provides the electric dipole matrix element of $M_{\rm R}+iM_{\rm I}=0.55+0.25i$ ($e^2$fm$^2$)
and the real part $M_{\rm R}$ exhausts about half of the cluster sum-rule value $B_{\rm c}(E1)$=1.01 $e^2$fm$^2$ presented in Table \ref{tab:radius}.
This property represents the strong collectivity of the $4n$ excitation in the SDR from the ground state of $^8$He.
The imaginary part $M_{\rm I}$ determines the deviation of the energy dependence of the strength function from the Breit-Wigner distribution
according to Eq.~(\ref{eq:SDR}) \cite{morimatsu94},
and the peak energy of the strength is shifted from the resonance energy $E_x$ as shown by the solid circle in Fig. \ref{fig:cmp2}.

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

We investigated the possibility of the soft dipole resonance of $^8$He
and its effect on the electric dipole strength using the $^4$He+$n$+$n$+$n$+$n$ five-body cluster model.
We describe the multineutron motion around the $^4$He core in the cluster orbital shell model (COSM) and the complex scaling method (CSM)
and obtain many-body resonant and non-resonant continuum states of $^8$He.
The Green's function is utilized with the complex scaling to calculate the dipole strength function of $^8$He.

It is found that the dipole strength of $^8$He shows the low-energy enhancement and the distribution continues in a wide energy range up to around 20 MeV.
Using the extended completeness relation (ECR) expanded in the complex-scaled eigenstates of $^8$He, the strength is mainly constructed by two components.
Below 10 MeV of the excitation energy, two-body continuum states consisting of the resonance of $^7$He and a neutron contribute to the strength.
This is the single-particle excitations and indicates the sequential breakup process via $^7$He.
At around 13 MeV, the collective excitations of four neutrons ($4n$) make a broad peak in the strength.
From the analysis of the transition densities of the dipole matrix elements,
this excitation causes the soft dipole mode, in which $4n$ are oscillating against the inert $^4$He core \cite{ikeda92},
and is different from the giant dipole resonance, in which the core nucleus is excited.

For the soft dipole mode, we searched for the resonance pole in the complex energy plane by using a large $\theta$ in the complex scaling.
As a result, we found one candidate of the soft dipole resonance at the excitation energy of 14 MeV with the decay width of 21 MeV,
which largely contributes to the dipole strength in the energy region of 13 MeV.
These interesting features of the dipole excitations of $^8$He would be confirmed by experiments, such as the Coulomb breakup reaction of $^8$He \cite{lehr22}.

\section*{Acknowledgments}
This work was supported by JSPS KAKENHI Grants No. JP18K03660, No. JP20K03962, and No. JP22K03643.
Numerical calculations were partly achieved through the use of large-scale computer systems, SQUID, at the Cybermedia Center, Osaka University.

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\nc{\PPNP}[3]   {\JL{Prog. Part. Nucl. Phys.}{#1}{#2}{#3}.}
\nc{\PTEP}[3]   {\JL{Prog. Theor. Exp. Phys.}{#1}{#2}{#3}.}
\nc{\PRep}[3]   {\JL{Phys. Rep.}{#1}{#2}{#3}.}

redpajama_set_name: RedPajamaArXiv


text:
Home > Cases > Gavrić
(Source picture: Moje Vijesti)
Prosecutor's Office of Bosnia and Herzegovina v. Milisav Gavrić
Court Court of Bosnia and Herzegovina (Preliminary Hearing Judge), Bosnia and Herzegovina
Case number KT-RZ-46/07
Decision title Indictment
Decision date 4 June 2008
Prosecutor's Office of Bosnia and Herzegovina
Milisav Gavrić
Categories Crimes against humanity, Genocide
Keywords Crimes against humanity; deportation; enforced disappearance; genocide; inhumane acts; persecution; Srebrenica; Cinkara factory; Potocari
Milisav Gavrić was born on 18 November 1948. He was a member of the Bratunac Police Station, and the Deputy Chief of the Srebrenica Police Station. On 4 June 2008, Gavrić was indicted by the Prosecutor's Office of Bosnia and Herzegovina. According to the allegations, Gavrić, acting alone or together with other members of the military of the Republika Srpska, committed crimes against Bosniak civilians in the Srebrenica enclave between 10 July and 19 July 1995. The specific crimes included capturing Bosniaks and inflicting injuries on them, the separation of women and men, the transfer of women and children, and the execution of Bosniak men.
On 4 June 2008, a preliminary hearing judge of the Court of Bosnia and Herzegovina issued an indictment against Gavrić, charging him with crimes against humanity.
The Court confirmed the indictment on 11 June 2008. Gavrić remains at large.
Milisav Gavrić was a member of the Bratunac Police Station, and Deputy Chief of the Srebrenica Police Station. The indictment alleged that, together with other members of the military and the police forces of the Republika Srpska, Gavrić took part and assisted in the organised and systematic capture of Bosnian Muslims (Bosniaks) during the period from 10 July to 19 July 1995 in the Srebrenica enclave. In addition, he was also involved in the infliction of injuries on the captured Bosniaks, and in their execution. Gavrić was also accused of having assisted in the forced transportation of thousands of Bosniak women, children and elderly people who were transported to the territory controlled by the army of the Republic of Bosnia and Herzegovina. Moreover, Gavrićtook also part in separating the men from the other civilians (p. 1).
The indictment further alleged that on 12 July 1995, in the town of Srebrenica, the accused participated and assisted in the forced disappearance of one Bosniak civilian, who along with 16 other Bosniak civilians was detained in a house of another civilian (para. 2(a)). As alleged in the indictment, on the same day, Gavrić took out one civilian from the compound of the Battery Factory where wounded Bosniak civilians were kept and separated. This civilian was unaccounted for until the time his body was exhumed from the Zeleni Jadar 5 mass grave (para. 2(b)). Among other things, the indictment alleged that in the late afternoon of 12 July 1995, Gavrić, together with two unidentified Serb soldiers, entered the Cinkara factory in Potočari and on two occasions took out 5 to 10 Bosniak men no older than 25, who have been unaccounted ever since (para. 2(d)).
Could Gavrić be charged with genocide and crimes against humanity?
Criminal Code of Bosnia and Herzegovina, 2003:
Article 171(1)(a) and (b) - Genocide
Article 172(1)(h) - Crimes against Humanity
Article 180(1), (29), and (31) - Individual Criminal Responsibility
Criminal Procedure Code of Bosnia and Herzegovina, 2006:
Article 35(2)(h) - Rights and Duties
Article 226(1) - Issuance of the indictment
On 4 June 2008, Gavrić was indicted by a preliminary hearing judge of the Court of Bosnia and Herzegovina. According to the indictment, Gavrić was charged with counts of genocide, including killing and causing serious bodily or mental harm, and crimes against humanity, including deportation or forcible transfer of population, enforced disappearance of persons, and other inhumane acts.
I. Antić, 'Samir And Ryad Had The Right To Live', Helsinki Charter, 2011, Vol. 151-152, pp. 7-10.
Criminal Code of Bosnia and Herzegovina, 2003
Criminal Procedure Code of Bosnia and Herzegovina, 2006
'Case information - Milisav Gavrić', Court of Bosnia & Herzegovina.
'Indictment Confirmed in the Milisav Gavrić case',Court of Bosnia & Herzegovina, 12 June 2008.
'Indictement against Milisav Gavric', Justice Report, 12 June 2008.
'Tužilaštvo BiH podiglo optužnicu protiv Milisava Gavrića', Blic Online, 12 June 2008.
'An overview of the legal proceedings relating to the 1995 genocide', Hague Justice Portal, 7 August 2008.
'Plea hearing postponed in the Milisav Gavrić case', Court of Bosnia & Herzegovina, 10 August 2009.
'Milisav Gavrić izjasnit će se o krivnji 2. oktobra', MOJEVIJESTI, 10 August 2009.
'Srbija, raj za ratne zločince', E-novine Mobilni, 8 August 2012.
'Srebrenican woman receives two bones as remains of her son', AnadoluAgency, 10 July 2013.
'Bosnia issues new Srebrenica indictment', b92, 12 June 2008.
D. Boric, 'CISTAC"IZ SREBRENICE', Blog dnevnik, 26 June 2008.
'ODGOĐENO IZJAŠNJAVANJE O KRIVICI', Bošnjaci.net, 10 August 2009.
'Two Trials Against Two Serbian War Crimes for Srebrenica Genocide', Bošnjaci.net, 10 August 2009.
M. Ristic, 'Bosnia-Serbia Collaboration Uncovers Strpci Mass Grave', Balkan Transitional Justice, 19 September 2013.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Creating a select tag with size>1 CKEDITOR Plugin My CKEDITOR plugin needs to create <select size="15"><option ...></select>, but the size attribute is not directly supported by the creation mechanism. I have tried various ways of adding the size attribute after creation, but so far no joy. Here is what I have; the select is created but it does not get the size attribute.
CKEDITOR.dialog.add('macrosDialog', function(editor) {
  return {
    // Basic properties of the dialog window: title, minimum size.
    title: 'Cadenza Macros',
    resizable: CKEDITOR.DIALOG_RESIZE_BOTH,
    minWidth: 400,
    minHeight: 200,

    // Dialog window contents definition.
    contents: [
      {
        // Definition of the Basic Settings dialog tab (page).
        id: 'tab-basic',
        label: 'Basic Settings',

        // The tab contents.
        elements: [
          {
              type: 'select',
              id: 'groups',
              name: 'groups',
              label: 'Groups',
              style: "height: 300",
              items: [ [ 'Core Scala' ], [ 'Create Courses with Micronautics Cadenza' ], [ 'Java / Scala Interoperability' ], [ 'Play Framework' ] ],
              'default': 'Play Framework'
          },
          {
            // Text input field for the macro title (explanation).
            type: 'text',
            id: 'macroComment',
            label: 'Comment',
            validate: CKEDITOR.dialog.validate.notEmpty("Explanation field cannot be empty")
          }
        ]
      }
    ],

    onLoad: function(e) {
      var groups = editor.document.getElement("groups");
      groups.setAttribute("size", 15);
      //$("#groups").setAttr("size", 15);
    },

    onChange: function(e) {
      alert('Group: ' + this.getValue());
    },

    // This method is invoked once a user clicks the OK button, confirming the dialog.
    onOk: function() {
      // The context of this function is the dialog object itself.
      // http://docs.ckeditor.com/#!/api/CKEDITOR.dialog
      var dialog = this;

      // Creates a new <abbr> element.
      var abbr = editor.document.createElement('abbr');

      // Set element attribute and text, by getting the defined field values.
      abbr.setAttribute('title', dialog.getValueOf('tab-basic', 'title'));
      abbr.setText(dialog.getValueOf('tab-basic', 'abbr'));

      // Finally, inserts the element at the editor caret position.
      editor.insertElement(abbr);
    }
  };
});

A: I used the html element to insert whatever I wanted:
contents: [
  {
    id: 'macrosDialog',
    label: 'Basic Settings',

    // The tab contents.
    elements: [
      {
        type: 'hbox',
        id: 'lists',
        //style: "vertical-align: top",
        widths: [ '25%', '25%', '25%', '25%' ],
        children: [
          {
            type: 'html',
            id: 'groups',
            name: 'groups',
            html: '<select size="15"></select>'
          },{
            type: 'html',
            id: 'courses',
            name: 'courses',
            html: '<select size="15"></select>'
          },{
            type: 'html',
            id: 'sections',
            name: 'sections',
            html: '<select size="15"></select>'
          },{
            type: 'html',
            id: 'lectures',
            name: 'lectures',
            html: '<select size="15"></select>'
          },
        ],
        onLoad: function(data) {
          var dialog = this.getDialog();
          var groups = dialog.getContentElement('macrosDialog', 'lists', 'groups');
          console.log(groups);
          var courses = dialog.getContentElement('macrosDialog', 'lists', 'courses');
          console.log(courses);
          var sections = dialog.getContentElement('macrosDialog', 'lists', 'sections');
          console.log(sections);
          var lectures = dialog.getContentElement('macrosDialog', 'lists', 'lectures');
          console.log(lectures);
        }
      }
    ]
  }
]

redpajama_set_name: RedPajamaStackExchange


What do cats actually see when they're all jacked up on catnip? And what exactly is catnip in the first place? I'm not a veterinarian, so I can only speculate.
Perhaps a portal to another world opens up to them. A world in which 1-UP mushrooms sprout from the ground and the sun looks like the Two Scoops of Raisins mascot. A world in which fauns prance and beckon you to give chase.
Or catnip might just make them really hyper. As I said, I'm not a veterinarian.
Last Friday, I happened to get a nice surprise – my first piece of CAAATS! fan art!
This portrayal of Olive was done by Andrew Fraser, who also happens to have a webcomic of his own, called Bridgette's Belly. You can check it out here.
So are there any other artists out there who are fans of CAAATS!? If so, send in some artwork and I'll post it to the blog! And thanks again to Andrew for the awesome art!
So one week ago, I was in Chicago for a comic convention called C2E2 (Chicago Comic & Entertainment Expo). For the uninitiated, a comic convention is an event in which comic geeks gather by the thousands to get the latest news in the comic world, buy overpriced convention food and dress up in unflattering spandex outfits in the hopes of getting their picture taken.
Though it may sound like a twisted nightmare to some (my wife), there is actually a lot of fun to be had by die hard comic fans. A highlight for me was attending a panel featuring Chris Hemsworth, star of the upcoming Thor movie. The panel featured a Q & A session in which Chris very gracefully fielded questions from rabid geeks. Hilarity ensued.
When someone asked him if he would ever play Aquaman in a film, a woman bolted up from her seat and shouted, "All Aquaman does is come up out of the water and flop around like a fish out of water!" She returned to her seat. The hall erupted with laughter. Chris Hemsworth smiled and nodded. Surely, someone had warned him about all this.
Another highlight of conventions is getting to meet other comic creators. People will sometimes stand in line for hours just to get one of their favorite books signed by the writer and/or artist. Many convention-goers like to track down artists at their tables and ask for personalized artwork.
This year, I was lucky enough to snag a sketch of Olive and Hazel (pictured above) from the very talented Katie Cook. They appear to really love each other in this sketch, which really means they're about to do battle.
All in all, the show was a great time spent with great friends. I even got to meet some folks who read CAAATS! Thanks to both of you for reading! Nyuck, nyuck.
So, would I do it all again? Absolutely. Would I ever wear spandex so that people take my picture? Not in a million years.


text:
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Round One of Idlib Campaign, by Fabrice Balanche
Round One of Idlib Campaign May Target Turkish-Backed Rebels
By Fabrice Balanche Assistant professor and research director at the University of Lyon 2.
https://www.washingtoninstitute.org/policy-analysis/view/round-one-of-idlib-campaign-may-target-turkish-backed-rebels
If Assad and his allies stick with their past strategy, the initial offensive will likely be limited, though it will still spur massive refugee flows and a serious breach between Turkey and Russia.
The Assad regime's brewing offensive against Idlib, the last major rebel pocket in Syria, will take place soon. Army troops have been massing on the enclave's border for weeks, while preparatory airstrikes and shelling have begun. Various international actors publicly oppose the imminent campaign, including Turkey, which wants to protect its local rebel proxies and long-term strategic interests in Syria. Yet Damascus and its allies in Moscow and Tehran seem indifferent to Ankara's dissatisfaction, and they will not be deterred by other outside warnings either.
IDLIB REBELS ARE NUMEROUS BUT DIVIDED
In March 2016, rebel forces numbered between 50,000 and 90,000 in the Idlib pocket. The broad range in this estimate was due to ambiguities in combatant status: while some 50,000 of these rebels were full-time fighters belonging to top groups, another 40,000 were casual fighters belonging to small local factions that may not be willing or able to appreciably affect a major battle. These fighters have been reinforced by about 20,000 other rebels expelled from Aleppo, Ghouta, Deraa, and Rastan, areas the regime and its allies have retaken in the past two years. Yet some of the rebels in the pocket have since been killed, left Syria, or moved to areas occupied by Turkey (Afrin, Azaz, Jarabulus, or al-Bab). Evaluating the exact number in Idlib today is therefore difficult, but it is certainly much larger than the 30,000 figure generally quoted, probably double that.
The rebels are split into two coalitions of more or less equal numbers: Hayat Tahrir al-Sham (HTS), led by al-Qaeda affiliates, and Jabhat al-Wataniya al-Tahrir (JWT, aka the National Front for Liberation). Turkey created the latter coalition this May to weaken HTS, rally its opponents, and prevent it from taking over the entire pocket, since Ankara's initial goal of dissolving HTS proved unsuccessful. JWT's eleven factions include remnants of the Free Syrian Army and Ahrar al-Sham.
Until earlier this year, HTS was content to control the border with Turkey, Idlib city, the province's main lines of communication, and various strategic points, effectively extending its grip over most of the pocket. In February, however, conflict broke out between HTS and Turkish-backed rebels, resulting in a more heterogeneous division of territory after their May ceasefire. HTS now controls most of northern Idlib, while it has had to abandon the southern part of the pocket and the western periphery of Aleppo to JWT. Yet the southern rebels are isolated, caught between the hammer of HTS and the anvil of the Syrian army. Ankara can hardly supply them—in fact, the Turkish military has to negotiate with HTS just to send soldiers and equipment to its own observation posts on the frontlines with the Syrian army. JWT would therefore be the first target if the offensive begins in the south, which appears to be the most logical strategy for Damascus and its allies.
ATTACKING THE WEAKEST SPOT FIRST
Although Bashar al-Assad seemingly aims to retake all of Idlib, he will likely be content at first with a limited offensive given the size of the rebel forces there (not to mention the political value of keeping the HTS threat alive but contained, as discussed in greater detail below). The regime's primary purpose is to provide better protection for Latakia and the Russian base at Hmeimim, which have been targeted regularly by rebels located around Jisr al-Shughour. Its second objective is to push rebels further away from Hama by seizing the entire southern part of the Idlib pocket up to Maarat al-Numan. Another objective may be to clear rebels from the western periphery of Aleppo.
Given these apparent objectives, the Turkish-backed rebels will likely be the first targets of the coming offensive. Recent shelling may indicate that Jisr al-Shughour is another potential early target, but any Syrian army thrust there would involve confronting Uighur fighters from the Islamic Party of Turkestan, a faction that is poorly integrated with other rebels given its ethnic particularism yet still dangerous on its own—and, like leading elements of HTS, loyal to al-Qaeda. Moreover, the terrain surrounding the city is steep and would take months to retake with infantry, as was the case in Salma to the west of Jisr al-Shughour. The difficulty of any such operation may deter the army from trying to seize the city immediately; the current shelling there may instead be intended to neutralize the Uighurs.
In contrast, the army would have an easier time seizing al-Ghab plain and the low areas around Jabal al-Zawiya, where air and armored forces can crush rebel defenses. Syrian troops from the west could then converge with those coming from Abu Duhur to seize Maarat al-Numan, essentially cutting the Idlib pocket in half. The remaining pro-Turkish rebels in the south would find themselves encircled and forced to surrender, perhaps with an offer of refuge in Turkish-controlled areas such as Afrin or Jarabulus. The army has previously used this strategy in Ghouta, Aleppo, Rastan, and Deraa: that is, dividing a rebel territory by attacking the weakest faction first, then negotiating with separate factions individually. The army and its allies are likely counting on HTS to remain largely neutral at first, calculating that the coalition will quietly watch its rivals get eliminated and then absorb their disappointed remnants for round two of the battle for Idlib.
TURKEY'S DILEMMA
Ankara is of course sharply opposed to this strategy. Such a campaign would exact the heaviest toll on JWT, damaging Turkey's credibility with local allies who have committed to stand against HTS. Ankara demands that the offensive be postponed, but Damascus, Tehran, and Moscow argue that Turkey has not fulfilled its commitment to eliminate HTS, so they have no choice but to cleanse Idlib themselves.
In fall 2017, a regime offensive against the Idlib pocket allowed Damascus to retake a southeastern slice of it, including Abu Duhur military base. Turkish president Recep Tayyip Erdogan was furious about that operation and publicly threatened Damascus for attacking his proxies. In the end, Russia appeased him by giving him a green light to attack the Kurdish area of Afrin. Damascus may intend to offer similar compensation for the next Idlib campaign, well aware that eliminating the Kurdish People's Defense Units (YPG) remains Turkey's top priority in Syria. Yet the U.S. military presence in the northeast would prevent any new Turkish offensive against the Kurds even if Erdogan received another green light from Moscow, so it is unclear how far he will take his opposition to the next Idlib campaign.
Whatever the case, eliminating JWT would enable Damascus to get rid of a few more factions that might have represented the opposition at the negotiating table. As part of the counterinsurgency strategy it has followed since 2011, the regime has steadily targeted moderate rebel groups so that only radical factions like HTS remain. The international community is fearful of such radicals and does not consider them a political alternative to the regime or a viable negotiating partner. Assad may therefore be willing to keeping hemming them in without confronting them head on in order to stave off outside efforts to topple him.
For its part, Turkey has tried in vain to convince HTS to break with jihadist ideology and integrate with JWT. Had it succeeded, Ankara would have gained strong leverage over Damascus, perhaps enough to make the Idlib pocket a Turkish protectorate like north Aleppo and incorporate it into the buffer zone Erdogan has been forming on Syria's side of the border. Yet the fact that HTS has pushed JWT and other rivals almost entirely out of northern Idlib calls this scenario into question, since this would essentially mean creating a sanctuary for al-Qaeda.
Many unknowns remain about the scale and outcome of the coming battle for Idlib. Yet if Damascus and its allies stick with their past strategy, the upcoming offensive will likely be limited, albeit for strategic rather than humanitarian reasons. Hundreds of thousands of civilians will still flee to the north of the province, requiring a major humanitarian response in a zone controlled by hostile radicals. Yet the battle itself might not be so bloody—at least the first round against Turkish-backed rebels.
If and when a second round is launched against HTS in northern Idlib, it could be a different order of magnitude. Moscow, Tehran, and Damascus would likely try to use overwhelming force there, arguing that the goal of eliminating al-Qaeda from the area would justify gross humanitarian violations. Although this Machiavellian plan might succeed in military terms, it would seriously damage relations between Russia and Turkey. The battle for Idlib may therefore represent an opportunity for U.S. rapprochement with Ankara, especially if Syrian or Russian forces target the Turkish observation posts dotting the rebel pocket.
Fabrice Balanche is an assistant professor and research director at the University of Lyon 2.


It's looking like a beautiful weekend to go camping! Get outside and enjoy the weather at one of these featured campsites.
There are a bunch of rustic cabins in this week's preview, AND a cottage in Temagami!
Point Farms Provincial Park turns 50 this Saturday! Swing by the park on August 15 to join the celebrations!
Continue reading Point Farms turns 50!


text:
The Learn Tracker
...life-long learning: structured, organized, searchable...
Lectures Watched
Since January 1, 2014
A History of the World since 1300 (67)
History of Rock, 1970-Present (50)
A Brief History of Humankind (48)
The Modern World: Global History since 1760 (35)
Chinese Thought: Ancient Wisdom Meets Modern Science (33)
The Bible's Prehistory, Purpose, and Political Future (28)
Introduction aux éthiques philosophiques (27)
Roman Architecture (25)
Jesus in Scripture and Tradition (25)
Sexing the Canvas: Art and Gender (22)
Descubriendo la pintura europea de 1400 a 1800 (22)
Introduction aux droits de l'homme (19)
Buddhism and Modern Psychology (18)
Calvin: Histoire et réception d'une Réforme (17)
The Ancient Greeks (16)
The French Revolution (15)
À la découverte du théâtre classique français (15)
Key Constitutional Concepts and Supreme Court Cases (14)
Letters of the Apostle Paul (14)
Christianisme et philosophie dans l'Antiquité (13)
Egiptología (12)
Western Music History through Performance (10)
Phenomenology and the Conscious Mind (9)
Human Evolution: Past and Future (9)
Greek and Roman Mythology (9)
The Great War and Modern Philosophy (9)
The Rise of Superheroes and Their Impact On Pop Culture (9)
Villes africaines: la planification urbaine (8)
Masterpieces of World Literature (8)
Programming Mobile Applications for Android (7)
Introduction to Psychology (7)
Fundamentos de la escritura en español (7)
MongoDB for Node.js Developers (7)
Pensamiento Científico (7)
Greeks at War: Homer at Troy (7)
Lingua e cultura italiana: avanzata (6)
A Beginner's Guide to Irrational Behavior (6)
The Emergence of the Modern Middle East (6)
Reason and Persuasion Through Plato's Dialogues (6)
Fake News, Facts, and Alternative Facts (6)
Karl der Große - Pater Europae (6)
The Rooseveltian Century (6)
Exploring Beethoven's Piano Sonatas (5)
Dinosaur Paleobiology (5)
Understanding Einstein: The Special Theory of Relativity (5)
L'avenir de la décision : connaître et agir en complexité (5)
Designing Cities (4)
Problèmes métaphysiques à l'épreuve de la politique, 1943-1968 (4)
The Kennedy Half Century (4)
Introduction to Public Speaking (4)
Emergence of Life (4)
War for the Greater Middle East (4)
Postwar Abstract Painting (3)
Découvrir l'anthropologie (3)
Analyzing the Universe (3)
The Music of the Beatles (3)
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Initiation à la programmation en Java (3)
Formation of the Universe, Solar System, Earth and Life (3)
History of Rock and Roll, Part One (3)
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Devenir entrepreneur du changement (3)
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Notes on video lecture:
Kennedy and the Catholic Issue
The Kennedy Half Century
Larry J. Sabato, University of Virginia
Notes taken by Edward Tanguay on May 18, 2014 (go to class or lectures)
Choose from these words to fill the blanks below:
young, Texas, Frontier, Constitution, ring, 47, Bobby, Rome, pathways, nominating, Irish, Ministerial, unopposed, region, Protestant, Democratic, Vatican, Smith, health, Eisenhower, tolerance, tremendous, Pope
after 1960 nominating convention, Kennedy turned to convincing the American people to elect him
Kennedy was popular with the young
elderly were interested in his support of a national health insurance for the aged
picked Lyndon Johnson as running mate
over objections from his brother Bobby
but without Texas and a "good chunk of the South", Kennedy could not possible defeat Nixon
LBJ wanted to be president, and history had shown that being vice president was one of the best pathways to the White House
LBJ was put in charge of JFK's strategy in the South
the two toured the South, but LBJ made most of the speeches
Nixon was unopposed
first poll showed Nixon leading by 6%
JFK's youth bothered some voters
but Nixon was only 47 while Kennedy 43
religion loomed largest
nation was overwhelmingly Protestant
Kennedy "went into lion's den" and accepted invitation to speak at the Greater Houston Ministerial Association
Nixon was also invited by declined
September 12, 1960 gave speech
visibly tense
300 skeptical Protestant ministers glared at him
Kennedy knew that this speech could make or break his campaign
delivered a memorable plea for religious tolerance
played down his connection to the Catholic church
he used this speech to win the public relations battle
in election, religion played a tremendous role
Kennedy received 80% of the Catholic vote
Nixon got 69% of the Protestant vote
more than race or region, religion explained the 1960 election results
Catholics were traditionally Democratic
even Elenore Roosevelt wondered aloud whether Kennedy could make decisions without the approval of the Pope in the Vatican
in 1928, Catholic Al Smith was swamped by Herbert Hoover, Democrats didn't want to repeat this
Kennedy came out against ties with the Vatican
attacked the Eisenhower administration for being insufficiently tough on the Soviets
argued to strength military forces to face the Soviets
asked: if elected President, if he would be torn between two loyalties, church and state
I would not, I has sworn to uphold the Constitution, the first amendment states that one cannot make laws which favor a religion
Article 6 of the Constitution states that no religious test should be required to qualify for office
it turned out that introducing JFK as Irish Catholic instead of Roman Catholic made a difference with voters
61% in West Virginia
Democratic Convention in Los Angeles
name of JFK's program and administration: "The New Frontier"
after election, Kennedy's Catholicism wore off, became less important
everyone understood that the Pope was not calling the shots
to this day, Kennedy has been the only Catholic president
in June 1963, Kennedy met in Rome with Pope Paul VI succeeding Pope John XXIII
when Catholics meet the Pope, they are supposed to kneel and kiss his ring, Kennedy did not, he simply shook his hand
#########################Pope Paul VI (1897-1978)
Pope from 1963-1978, continued the Second Vatican Council, improved relations with Eastern Orthodox Church and Protestants
succeeded Pope John XXIII
JFK's Rise to Power
1953-1960 Kennedy's Legislative Career
JFK Takes to the National Stage
Site time: 2020-01-20 20:00:22 CET, LEARN TRACKER created by Edward Tanguay


INNOtec Systems GmbH is your competent partner for innovative train and wayside monitoring under operating conditions.
We develop, produce and distribute mobile and stationary monitoring systems for monitoring the track position, the collection of load profiles, the rad accurate noise detection to condition-based maintenance and fully automatic monitoring, analysis and evaluation of the wheel-rail contact (wheel-force diagnostic systems - WFDS, wayside monitoring systems WMS). Everything under real operating conditions. Economic, operational and quality benefits can be maximized by our forward-looking, self-calibrating maintenance and comprehensive wheel management systems. Through our direct access to the track and our global network, we are constantly on the pulse of time and bring innovations in a very short time into our systems.
"Monitoring of rail transport will help to keep traffic noise even beyond 2020 permanently at least halved level"
"We are confident that our main goal - no more noisy trains until 2020 - is reached on time"
Erwin Rüddel: "A milestone in the fight against traffic noise". Heimischer Bundestagsabgeordneter spricht von einem "technischen Quantensprung"
On 09/10/2014 took place in the Rhineland-Palatinate Ministry of Environment a non-public workshop about train noise measurement / rail noise monitoring. Siegfried Pieper held the last of the papers and turned on themselves live on a system.
After we monitor the suburban trains from Frankfurt and Stuttgart 5 respectively 3 years, were added in early 2014. Leipzig and Berlin. The entire Berlin S-Bahn network is monitored now with 4 Lascas and we expect a significant improvement in the way qualities.
The INNOtec systems are certified and approved by the German Ministry of Railways (EBA), TÜV Rheinland and LGA (Technical Inspection Institutes), DB (TM) and MOR (China). INNOtec products meet the highest quality standards in material, application and processing.
standards and have introduced the quality management system.


IQS Directory implements a thorough list of titanium rod manufacturers and suppliers in Virginia. Utilize our listing to examine and sort top titanium rod manufacturers with previews of ads and detailed descriptions of each product. Any titanium rod company can design, engineer, and manufacture titanium rods to meet your companies specific qualifications. An easy connection to reach titanium rod companies through our fast request for quote form is provided on our website. The company information includes website links, company profile, locations, phone, product videos and product information. Customer reviews are available and product specific news articles. This source is right for you whether it's for a manufacturer of titanium alloys, titanium pipes, and titanium tubing.
Established 1925, A.D. MACKAY, Inc. has been the most trustworthy supplier of high purity metals, alloys and inorganic chemicals in the world. Today, we remain dedicated to providing the finest materials to our countless friends in the Research & Development community. Our inventory - Aluminum to Zirconium in all available forms - is the most extensive anywhere in the world. Titanium Rods in North Carolina.
Accro-Met is a woman owned small business supplying an excellent range of titanium, such as titanium sheet, and services. Serving customers nationwide, we are a growing metal distributorship dedicated to fast, courteous service and quality materials. We are familiar with & will certify to the following, ASTM, ASME, AMS, MIL, QQ & DOD Specs, BOEING, LOCKHEED & GENERAL ELECTRICS. Contact us today! Titanium Rods in North Carolina.
ATI Specialty Metals produces titanium and titanium alloys. We can provide you with titanium bars, titanium ingots, titanium wire, slabs, custom shapes and more. Our titanium is developed to be used for aerospace, dental, industrial and medical applications. Some grades have cold formability or fatigue strength. Titanium Rods in North Carolina.
Serving the aerospace and aircraft industries, we provide stainless steel, aluminum, nickel, copper, titanium and a host of other metals and alloys in rod, bar, sheet, strip, plate, wire, forgings, rings, tubing, castings, and more. At Aviation Metals, the customer is always number one, and we are ISO9001:2000 and Aerospace AS9100 certified. Titanium Rods in North Carolina.


text:
HomeFaith and Culture
Faith and CultureOutdoors
Alabama's Black Belt Birding Festival getting bigger in 2022
Michael Sznajderman
(Matthew Grcic/Alabama Audubon)
This summer, folks from across the region flew to Greensboro for the 2021 Black Belt Birding Festival – a sold-out event that has organizers with Alabama Audubon already working to expand the festival in 2022.
Indeed, the bigger event planned for next year follows what turned out to be an immensely successful 2021 festival for local businesses, artists and makers who enjoyed a unique opportunity to showcase their products, creations and community to a new audience.
"The Black Belt Birding Festival brought together community members and visitors from in and around the state, demonstrating the many birding opportunities Alabama's historic Black Belt region has to offer, and bringing in a large weekend of sales for our Greensboro business community," said Meg Ford, Black Belt coordinator for Alabama Audubon, the event host.
"When birders gather together, we can truly make a positive difference for birds and the people who love them – and we hope to make an even larger impact with a full weekend of Black Belt birding and an expansion of offerings for next year's festival," Ford said.
The 2022 Black Belt Birding Festival is slated for July 29-31, with a second day added to accommodate more birders and more activities. Details about the expanded festival will be coming soon, Ford said.
While the field trips to the diverse bird habitats that the Black Belt offers sold out quickly during the 2021 festival, the free in-town events attracted birders and nonbirders alike.
The festival is part of Alabama Audubon's Black Belt Birding Initiative, designed to highlight the benefits of bird-based ecotourism for the Black Belt region. The Alabama Power Foundation was among the supporters of this year's festival.
Among the special guests this year was Christian Cooper, a Black birder and member of the board of directors of NYC Audubon in New York. Cooper is a key organizer of National Black Birders Week, which celebrates Black nature enthusiasts but also points out the dangers they can face when enjoying the outdoors.
This year's Black Belt Birding Festival, which took place in August, was Alabama Audubon's first major event in more than a year because of the COVID-19 pandemic. The organization, celebrating its 75th anniversary this year, is now back with a full slate of scheduled activities.
Learn more about Alabama Audubon here.
(Courtesy of Alabama NewsCenter)


L'Union Fait La Force is the Haitian motto meaning "Unity Makes Strength." This motto embodies what CARIBBEAN APPAREL™ represents in unifying all, no matter where you are from we are all one. We must learn about one another and respect each other. The statue is of Le Negre Marron, a statue in Haiti on Boulevard Champs de Mars. The "Negre Marron" is shown with left leg extended (broken chain on his ankle); a machete is in his right hand, and his left hand holds a conch shell to his lips. The conch shell was often used as a trumpet to assemble people. Created by the Haitian sculptor/architect, Albert Mangones (1917-2002) in 1968 or 1969.


I love vintage shopping. From the first time I discovered vintage clothes were actually a thing in a Topshop concession stand to yesterday when I saw a striped Vivienne Westwood dress on Retromania's Instagram. I find that vintage clothes often have a more vibrant pattern, have an interesting fit or have that edge that often can't be found on modern clothing on the high street. I thought I would share a few places I like to shop for vintage.
Retromania: Both charity shopping and vintage shopping are favourite pastimes of mine. So when I can combine the two, it's brilliant. Fara have a shop in Pimlico called Retromania which is a place for the best of the vintage donations. From Vivienne Westwood to Comme des Garçon to Gucci. It was at Retromania that I tried to shove my foot into the most amazing vintage cowboy boots because they were just perfect, but sadly it wasn't meant to be. This is definitely a place to go often as you never know what has been recently donated. They also, on occasions, have a sale in which everything is FIVE POUNDS (*insert all the high-five and heart eye emojis right here*). Follow them on Instagram for a truckload of vintage loveliness.
Rokit: As well as all the lovely vintageness in Rokit. I also love their upcycled section. Last autumn I picked up an upcycled jumper I ended up throwing on over most my outfits throughout December. The jewellery on offer is great (humongous gold hoops are still my favourite), I want all the denim Rokit has to offer (I'm forever eyeing up the slouchy but wonderful short dungarees) and beautiful, spangly dresses fill the rails. It's definitely THE place for outfit inspiration as autumn quickly approaches.
Beyond Retro: This is the shop I think of when it comes to vintage shopping. It was one of my favourite haunts at university. Forget Oceana. My money went to Beyond Retro and in exchange I got bloody wonderful sequinned jumpers, floral jumpsuits and tropical shirts. I went to university in Brighton so I am well acquainted with the humongous Brighton Beyond Retro but now it's a little far for Saturday shopping so I mainly visit the Soho branch which is just as shiny, retro and brilliant.
Hidden in charity shops: The most satisfying type of vintage shopping is when you find a retro piece hidden amongst all the modern clothes in charity shops. There ain't no better feeling than finding a 70's floaty dress/colourful 80's t-shirt/*insert the best of vintage here* in the most unexpected of places.
Where are your favourite places to find vintage?


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Listed companies' analysis | Ranking | Industry ratios | Ratios (NCI) | Statements (NCI)
Navigant Consulting, Inc. (NCI) financial statements (2023 and earlier)
Business Address 150 NORTH RIVERSIDE PLAZA
SIC 8742 - Management Consulting Services (benchmarking)
Cash, cash equivalents, and short-term investments 207 8 8 9 3 2 1
Cash and cash equivalents 207 8 8 9 3 2 1
Receivables 180 271 264 220 254 223 253
Prepaid expense and other current assets ✕ ✕ ✕ ✕ ✕ ✕ 25
Other current assets 18 21 18 17 15 20 ✕
Other undisclosed current assets 5 9 9 10 (41) (33) (37)
Total current assets: 409 309 300 255 231 211 243
Property, plant and equipment 63 89 83 77 61 44 45
Long-term investments and receivables 3
Due from related parties 3
Intangible assets, net (including goodwill) 437 658 654 661 595 626 636
Goodwill 422 637 625 623 568 615 620
Intangible assets, net (excluding goodwill) 14 21 29 38 27 11 16
Deferred costs 2
Other noncurrent assets 9 24 18 23 17 23 ✕
Prepaid expense and other noncurrent assets ✕ ✕ ✕ ✕ ✕ ✕ 17
Assets held-for-sale, long lived ✕ ✕ ✕ ✕ ✕ 1
Other undisclosed noncurrent assets (6) 13
TOTAL ASSETS: 918 1,080 1,055 1,016 903 904 954
Accounts payable and accrued liabilities 112 128 136 112 108 106 122
Accounts payable 13 12 12 9 12 13 18
Accrued liabilities 16 14 16 11 11 13 12
Employee-related liabilities 70 97 107 92 83 79 85
Taxes payable 13 5 2 2 1 7
Restructuring reserve 0 ✕ ✕
Business combination, contingent consideration, liability (1) ✕ ✕
Deferred revenue and credits ✕ 19 21 20
Other liabilities 34 39 39 32 53 32 36
Other undisclosed current liabilities (19) (21) (20)
Total current liabilities: 146 167 175 144 160 138 157
Long-term debt and lease obligation 133 135 174 110 57 134
Long-term debt, excluding current maturities 133 135 174 110 57 134
Liabilities, other than long-term debt 59 93 110 105 100 123 116
Deferred revenue and credits ✕ 9 11 11
Deferred tax liabilities, net 34 61 78 76 76 87 68
Off-market lease, unfavorable 2
Other undisclosed noncurrent liabilities (9) (11) (13)
Total noncurrent liabilities: 59 226 245 278 201 169 237
Total liabilities: 205 393 420 422 361 307 395
Stockholders' equity attributable to parent 709 687 634 594 543 597 560
Treasury stock, value (161) (224) (181) (297) (276) (247) (217)
Additional paid in capital 664 660 645 628 612 599 582
Accumulated other comprehensive loss (7) (19) (25) (17) (12) (9) (9)
Retained earnings 212 271 196 279 218 255 203
Stockholders' equity attributable to noncontrolling interest 4
Total stockholders' equity: 713 687 634 594 543 597 560
TOTAL LIABILITIES AND EQUITY: 918 1,080 1,055 1,016 903 904 954
Revenues 744 1,032 1,034 919 860 836 845
Revenue, net ✕ 1,032 1,034 919 860 836 845
(Cost of Goods and Services Sold) (550) (747) (728) (658) (519) (488) (495)
Other undisclosed gross profit 6 11 13
Gross profit: 199 296 320 262 340 348 350
Operating expenses (145) (176) (181) (156) (269) (123) (157)
Other operating expense, net (3) (4) (2)
Other undisclosed operating loss (26) (40) (40) (14) (104) (122) (109)
Operating income (loss): 25 76 97 92 (33) 103 84
Nonoperating income (expense) 2 (1) 2 1 1 0 1
Investment income, nonoperating 2 0 0 0 0 0 1
Foreign currency transaction gain, before tax 0
Other nonoperating income (expense) (0) (1) 2 1 0 (0) 0
Interest and debt expense (3) (5) (5) (5) (6) (4) (5)
Other undisclosed loss from continuing operations before equity method investments, income taxes (0)
Income (loss) from continuing operations before income taxes: 24 71 93 88 (38) 99 79
Income tax expense (benefit) (9) 4 (35) (28) 1 (44) (33)
Income (loss) from continuing operations: 15 75 58 60 (37) 55 46
Income (loss) from discontinued operations 106 1 (0)
Net income (loss): 121 75 58 60 (36) 55 46
Other undisclosed net loss attributable to parent (3)
Net income (loss) available to common stockholders, diluted: 121 75 58 60 (36) 52 46
Other comprehensive income (loss) 13 6 (9) (4) (3) (1) 4
Comprehensive income (loss): 134 81 49 56 (39) 54 50
Other undisclosed comprehensive loss, net of tax, attributable to parent (3)
Comprehensive income (loss), net of tax, attributable to parent: 133 81 49 56 (39) 52 50


The film centers around Raja Krishnappa Bairya a boy born into poverty, after becoming an orphan, he arrives to Bombay(present Mumbai) in the 1960s on a quest for power and wealth as desired by his dying mother. After establishing himself as"Rocky" a famous goon, he gets involved with the gold mafia there.He is recruited to kill Garuda, the oppressive heir-in-waiting, in Kolar Gold Fields. In the process of his recruition he falls for Reena Desai, daughter of Rajendra Desai(the person who recruited him for this work). The rest of the story is how Rocky kills Garuda with that highest security and how he wins the hearts of hundreds of slaves working under Garuda.


what do I run as admin?
and what should the file run out of. I have it runnign out of my internet explorer but Idk if thats right. It dosn't work.
2.If Windows Vista find the file and right click, chose "run as admin"
but all it says is open no run as admin.??????????
here is download link to guid: CLICK ME!!!!
i know I did all that but it still dosn't say run as admin.???????? I still said open and it dosent work. My computer is screwed up.
or um...updates for the hack ?
when u goin to post new hacks? Just wondering bcuz none of them work and I can't wiat to start hacking.
thats cool. I cant wiat for some hacks!!!!