text:
\section{Introduction}

Studies related to confined atoms are important for a broad range of possible applications. The spatial entrapment of atoms or molecules is
possible in nature as well as artificially;  e.g., impurity
atoms in mesoscopic scale semiconductor artificial structures, molecular zeolite sieves, fullerenes, quantum devices, etc.  \cite{imp-1,imp-2}.
The confinement of atoms lead to distinct and interesting changes in their electronic structures and other properties. Endohedral entrapment of
an atom inside fullerene cage can be synthesized in laboratory owing to rapid developments in the modern technologies. These endohedral
fullerenes unveil interesting physical and chemical properties that can be significantly different from the encapsulated atom or the fullerene
itself. Although studies of confined endohedral atoms in any fullerene are interesting, but confined atoms particularly in the C$_{60}$
fullerene has drawn more attention these days. This is because C$_{60}$ can be assumed as a spherical ball with the confined atom at the center.
Therefore, the energy levels of a confined atom can still be described using a spherical potential as for a free atom by suitably choosing an
effective potential.

Using R-matrix method in the non-relativistic theory, Haso\u glu {\it et al.} \cite{STM-1} had calculated cross-sections for the photoionization
process of a confined Ca atom and reported the influence of potential well depth on near threshold photoionization cross-sections. Following
this work, Kumar et al \cite{HV-1} had investigated non-dipole effects in photoionization of outer 4$s$ shell of the entrapped Ca atom in a
spherical attractive well potential in the relativistic random phase approximation (RRPA). Recently, Haso\u glu {\it et al.} \cite{Zuo} have
investigated electron correlation effects of endohedral confinement on the energy levels of Be, Mg, and Ca atoms in the non-relativistic
framework using multi-configuration Hartree-Fock (MCHF) method. Haso\u glu {\it et al.} have argued in their work about the possibility of
confinement of Ca atom at the center of the C$_{60}$ shell, giving rise to a stable equilibrium. It is, therefore, imperative to understand
energy levels of such an environment on the structure of a captured Ca atom more accurately by employing a powerful relativistic
many-body method before carrying out experiment.

It is very challenging to get accurate results for the atomic properties of the Ca atom even when it is isolated from any external mediation
owing to strong correlations between its two valence $s$ electrons. For example, it has been found earlier that the lower-order relativistic
perturbative theories underestimate the electric dipole polarizability ($\alpha_0$) value of the Ca atom while RRPA overestimates it
compared to the experimental value \cite{yashpal1}. As mentioned above, only a few less powerful many-body methods are employed to account for
electron correlation effects in the confined Ca atom. To guide future experiment on the confined Ca atom, it is necessary to study its
spectroscopic properties by applying a more accurate theory. In this work, we have calculated many properties such as electron correlation
energy, ionization potential (IP) and $\alpha_0$ of the of the confined Ca atom in the endohedral fullerene C$_{60}$ cluster
and show their variation with the attractive potential depth. These calculations are performed within the framework of the Dirac-Hartree-Fock
(DF) method, relativistic second-order many-body perturbation theory (RMBPT(2) method), RRPA and relativistic coupled-cluster (RCC) theory.
We employ the lower-order methods like DF and RMBPT(2) methods in order to find out role of electron correlations in the above properties
by comparing results from these methods. The RCC theory is an all-order perturbative method
that obeys proper scaling with the number of electrons even when it is approximated in contrast to the truncated configuration interaction
(CI) method or its variants like the MCHF method \cite{szabo,bartlett,bishop}. It also includes core-polarization effects to all-order as
in RRPA along with other physical effects. To ascertain accuracies of the results, we first perform calculations of the aforementioned properties
of the free Ca atom and compare them with their corresponding experimental values. We also compare our calculations of self-consistent field
(SCF) energy and energies of the 4$s$, 3$p_{3/2}$, 3$p_{1/2}$ and 3$s$ orbitals at various depths of the confining annular potential well with
the earlier reported results by Kumar {\it et al.} using the DF method \cite{HV-1}.

Because of experimental feasibility to prepare confined atoms, the interest in electron elastic collision with entrapped atoms is increasing
now-a-days \cite{Dolmatov-1,Dolmatov-2,Fassen1,Fassen2}. However, there have been few theoretical studies reported in the context of elastic
scattering of electrons from confined atom A@C$_{60}$. Dolmatov et al. have studied elastic collision of low energy electrons with A@C$_{60}$
and demonstrated the role of polarizability of an atom $+$ C$_{60}$ \cite{Dolmatov-1} and that of atoms alone \cite{Dolmatov-2}. In fact,
Dolmatov {\it et al.} have given a full account of the previous related works in Refs. \cite{Dolmatov-1,Dolmatov-2} on the same. However,
these studies were carried out using non-relativistic Hartree-Fock theory and at low projectile electron energies. Here, we have performed
calculations of the elastic collision cross-sections for the intermediate projectile electrons scattered from the endohedrally confined Ca atoms
in the relativistic theory framework. Furthermore, we have used electron charge densities from the DF method, DF method with core-polarization
(CP) potential (DFCP method) and RCC theory to show the differences in the results due to various approximations in the many-body methods.
It to be noted that RCC theory includes CP potential to all-orders along with electron correlations due to non-CP type of interactions. In all
these approaches, we take into account the quantum mechanical exchanges between the projectile and atomic electrons as well as polarizability of
the atom as a function of potential depth. Since we focus only on the effect of confinement of Ca on electron scattering process, we have
neglected the impact of polarizability of C$_{60}$ by the incident electron in these calculations. The results are reported for differential
cross-sections (DCSs) and integrated cross-sections (ICSs). We compare our results for the free Ca atom with the available experimental
data \cite{Ca-expt} and other reported calculations using the DFCP method \cite{hasan} in order to gauge accuracies of the results for the
confined atom.

\section{Methods for Calculations}
\subsection{Atomic properties}

In the DF method, we obtain the mean-field wave function $|\Phi_0 \rangle$ using the $V^N$ potential of the $[3p^{6}4s^2]$ configuration of
the Ca atom. All the DF and DFCP results are obtained using this wave function and $\alpha_0= 169\ ea_0^3$ from experiment \cite{exp-pol}. The
exact wave function in the RCC theory is expressed using $|\Phi_0 \rangle$ as the reference determinant as \cite{cizek}
\begin{equation} \label{exp}
| \Psi_0 \rangle = e^{\hat{T}} | \Phi_0 \rangle ,
\end{equation}
where $\hat T$ is known as the RCC excitation operator given by
\begin{eqnarray} \label{Texp}
\hat T  &=&  \sum\limits_{k=1}^N  \hat T_k = \sum\limits_{\stackrel{a_1 < a_2 \dots < a_k}{i_1 < i_2 \dots < i_k}} t^{a_1 a_2 \dots a_k}_{i_1 i_2 \dots i_k}   a^+_1 i^-_1 a^+_2 i^-_2 \dots a^+_k i^-_k  \ \ \ \
\end{eqnarray}
with $+$ and $-$ superscripts on the second quantization operators represent for creation and annihilation of electrons in the virtual (denoted by $a$) and occupied (denoted by $i$) orbitals,
respectively, and $t$ are the amplitudes in the excitation process in an $N$ electron system. The RCC approaches considering up to $T_N$ operators with $N = 2, 3, 4, \dots$, known as the RCC
singles and doubles (RCCSD), RCC singles, doubles, and triples (RCCSDT), RCC singles, doubles, triples, and quadruples (RCCSDTQ), etc. methods constitute a hierarchy, which converges to the exact
solution of the wave function in the given one-particle basis set.

 The amplitudes $t$ of the RCC operators are obtained by projecting bra determinants $\langle \Phi^{a_1 a_2 \dots a_k}_{i_1 i_2 \dots i_k} | e^{-\hat{T}}=$ $\langle \Phi_0^N | a^+_1 i^-_1 a^+_2 i^-_2 \dots  a^+_k i^-_k e^{-\hat{T}} $ from the
left of the Schr\"odinger equation $\hat H |\Psi_0 \rangle = E_0 |\Psi_0 \rangle$, with the ground state energy $E_0$, as
\begin{eqnarray}\label{CCeq}
\langle \Phi^{a_1 a_2 \dots a_k}_{i_1 i_2 \dots i_k} \vert \overline{H} \vert \Phi_0 \rangle &=& E_0 \delta_{k,0}, \;\;\;\; (k=1, \dots N) ,
\end{eqnarray}
where $ \overline{H}=e^{-\hat{T}} \hat H e^{\hat{T}}=(\hat H e^{\hat{T}})_c$ for the subscript $c$ means connected terms between the atomic
Hamiltonian $\hat H$ with the $\hat T$ operators are only retained.

We have considered the Dirac-Coulomb (DC) Hamiltonian in our calculation for the free atom, which in atomic units (a.u.) is given by
\begin{eqnarray}
H &=& \sum_{i=1}^{N} \left [ c\mbox{\boldmath$\alpha$}_i\cdot \textbf{p}_i+(\beta_i -1)c^2 + V_{n}(r_{i}) \right]
   +  \frac{1}{2} \sum_{i,j} \frac{1}{r_{ij}}  \nonumber \\
  \label{NSDeq}
\end{eqnarray}
where $\mbox{\boldmath$\alpha$}$ and $\beta$ are the Dirac matrices, $c$ is the speed of light, the nuclear potential $V_{n}(r)$ is determined
using the Fermi-charge distribution, and $r_{ij}$ is the radial distance between the electrons located at $r_i$ and $r_j$. To obtain wave
function of the endohedral confined atom, we introduce a short range spherical model potential $U$ along with the DC Hamiltonian defining as
\begin{eqnarray}
U(r) =
\left\{\begin{array}{ll}
 -U_0, & \mbox{for $r_0 \le r \le r_0 + \Delta $}\\
0, & \mbox{otherwise}
\end{array}\right.
\label{Ur}
\end{eqnarray}
where $r_0$ is the inner radius, $\Delta$ is the thickness and $U_0$ is the depth of the potential well.

The IP of an electron of orbital $a$ in the atom is estimated in the RCC theory by expressing \cite{nandy1}
\begin{eqnarray}
|\Psi_a \rangle = e^T (1+ R_a) |\Phi_a \rangle,
\end{eqnarray}
where the reference state is constructed as $|\Phi_a \rangle = a_a |\Phi_0 \rangle$ with $a_a$ is the corresponding annihilation operator
for the electron in orbital $a$ and $R_a$ is another RCC operator introduced to take care of the extra correlation effects that was
included through the detached electron. The IP ($E_a$) and amplitude solving equations for the $R_a$ wave operators
are given by
\begin{eqnarray}
\langle \Phi_a^*| [(H e^T)-E_a] \{1+R_a\}|\Phi_a\rangle &=& \delta_{a,*}
\end{eqnarray}
where $|\Phi_a^* \rangle$ designates excited configuration determinants from $|\Phi_a\rangle$ for the $R_a$ amplitude determination else
it corresponds to $|\Phi_a\rangle$ to estimate IP of the electron from orbital $a$. This equation contains non-linear terms and also both
the energy and amplitude determining equations are inter-dependent. These solutions are obtained adopting the self-consistent procedure.

The excited states ($|\Psi_K(J, \pi) \rangle$) of the Ca atom with angular momentum $J$ and parity $\pi$ is obtained by operating
excitation operators $\Omega_K$ on $|\Psi_0 \rangle$ as \cite{nandy2}
\begin{eqnarray}
 |\Psi_K(J, \pi) \rangle = \Omega_K(J, \pi) |\Psi_0\rangle ,
\end{eqnarray}
where $K$ corresponds to level of excitations. The eigenvalue ($E_L$) and eigenfunction for the $L^{th}$ excited state are obtained
by diagonalizing the above equation as
{\small{
\begin{eqnarray}
\langle \Phi_L (J, \pi) | (H e^T) \Omega_K (J, \pi) |\Phi_0 \rangle = E_L \langle \Phi_L (J, \pi) | \Omega_L (J, \pi) |\Phi_0 \rangle .
\end{eqnarray}}}
In this expression, $|\Phi_L\rangle$ has a definite value of $J$ and $\pi$ and solutions are obtained in the iterative procedure using the
Davidson's diagonalization algorithm for the non-symmetric matrix \cite{hirao}.

We evaluate $\alpha_0$ by expressing the RCC wave function as \cite{bijaya1}
\begin{eqnarray}
 |\tilde{\Psi}_0 \rangle =e^{\hat{T}^{(0)}+ |\vec{\mathcal E}| \hat{T}^{(1)}} |\Phi_0 \rangle,
\end{eqnarray}
where $\hat{T}^{(0)}$ represents the RCC operator that accounts for electron correlation effects due to the electromagnetic interactions
only and $\hat{T}^{(1)}$ takes care of correlation effects due to both the electromagnetic interaction and the $D$ operator, respectively,
to all-orders. In the perturbative expansion, this corresponds to
\begin{eqnarray}
 |\Psi_0^{(0)} \rangle = e^{\hat{T}^{(0)}} |\Phi_0 \rangle
\ \ \ \
\text{and}
\ \ \ \
 |\Psi_0^{(1)} \rangle = e^{\hat{T}^{(0)}} \hat{T}^{(1)} |\Phi_0 \rangle.
 \label{eqt1}
\end{eqnarray}
Both $|\Psi_0^{(0)} \rangle$ and $|\Psi_0^{(1)} \rangle$ can be determined by obtaining amplitudes of the $\hat{T}^{(0)}$ and $\hat{T}^{(1)}$
RCC operators. The amplitude determining equation for $\hat{T}^{(0)}$ is same as Eq. (\ref{CCeq}) for the DC Hamiltonian. The $\hat{T}^{(1)}$
amplitude determining equation is given by
\begin{eqnarray}
 \langle \Phi^{a_1 a_2 \dots a_k}_{i_1 i_2 \dots i_k} \vert \overline{H}^{DC} \hat{T}^{(1)}+ \overline{D} \vert \Phi_0 \rangle =0 \label{eq37} .
\end{eqnarray}
It to be noted that for solving the amplitudes of $\hat{T}^{(0)}$, the projected $\langle \Phi^{a_1 a_2 \dots a_k}_{i_1 i_2 \dots i_k} \vert$
determinants have to be even parity whereas they are the odd-parity for evaluating the $\hat{T}^{(1)}$ amplitudes. We have considered
the RCCSD method approximation in the RCC theory.

After obtaining these solutions, we evaluate $\alpha_0$ as \cite{yashpal1,yashpal2}
\begin{eqnarray}
\alpha_0  &=& 2 \langle\Phi_0 | e^{T^{(0)\dagger}} D e^{T^{(0)}} T^{(1)} | \Phi_0 \rangle_{fc} ,
\label{eqccx}
\end{eqnarray}
where $fc$ stands for the fully-contracted terms. The above expression contains a non-terminating series $e^{T^{\dagger (0)}} D e^{T^{(0)}}$. This is computed self-consistently as discussed in
our earlier works \cite{yashpal2,bijaya2}. We also perform calculation of $\alpha_0$ using the RMBPT(2) and RRPA methods adopting the procedures
described in Refs. \cite{yashpal1,yashpal2,yashpal3}. From the differences between the results obtained by the RRPA and RCCSD method, we can find
out contributions due to the non-core-polarization correlations to all-orders.

\begin{figure*}[t]
\begin{center}
\includegraphics[trim = 0cm 5cm 5cm 0cm,scale=0.7]{fig-1.eps}
\end{center}
\caption{(Color online) Probability densities of the 3$p_{1/2}$, 3$p_{3/2}$ and 4$s$ orbitals are shown in (a), (b) and (c), respectively,
and (d) shows charge density ($\rho(r)$)  as function of the radial distance ($r$) and  the confining potential $U$ (in a.u.).
The insets in (d) magnify the crossing of curves around 5 a.u. and large radial distances.}
\label{wavefunctions}
\end{figure*}
\subsection{Cross-section calculations}
\label{Model-Potential-theory}

If the interaction potential $V(r)$ of the projectile electron with the target is approximated to be
spherically symmetric then the method of partial wave expansion can be employed and the entire scattering process
can be described by the direct and spin-flip scattering amplitudes as
\begin{eqnarray}
\label{direct}
f(k,\theta) &=& \frac{1}{2 \iota k} \sum_{l=0} ^\infty \left (
(l+1) (e^{2\iota \delta^+} -1) \right. \nonumber \\
&& + \left. l (e^{2\iota \delta^-} -1) \right) P_l(\cos\theta)
\end{eqnarray}
and
\begin{eqnarray}
\label{spin-flip}
g(k,\theta) = \frac{1}{2 \iota k} \sum_{l=0} ^\infty \left (
 e^{2\iota \delta^-} -e^{2\iota \delta^+} \right)
 P_l^1(\cos\theta),
\end{eqnarray}
respectively. Here $k$ is the relativistic wave number, $\delta^{\pm}$ are the scattering phase shifts with
$+$ ($-$) sign refers to up (down) spin of the projectile electron, $\theta$ is the scattering angle, and $P_l(\cos\theta)$ and
$P_l^1(\cos\theta)$ are the Legendre polynomials and associated Legendre functions, respectively. The phase shifts are calculated by
solving the Dirac radial equation in the field of $V(r)$ and analyzing the large-$r$ behavior of the Dirac spherical waves.

The DCS per unit solid angle for spin unpolarized electrons are calculated by
\begin{eqnarray}
\label{dcs}
\frac{d\sigma}{d\Omega} = |f(k,\theta)|^2 + |g(k,\theta)|^2 .
\end{eqnarray}
We obtain the ICS by integrating the DCS over the solid angle. For the computational simplicity,
we express the interaction potential as $V(r) = V_{st}(r) + V_{ex}(r)- \iota V_{ab}(r)$, where $V_{st}$, $V_{ex}(r)$ and $V_{ab}$ are
known as the static, exchange and absorption potentials, respectively. The static potential at a general point $r$ is evaluated using
the following expression
\begin{eqnarray}
\label{vstatic}
V_{st}(r) = -\frac{Z}{r} -\left(\int_0^r \rho(r') 4\pi r'^2 dr'
                        + \int_r^\infty \rho(r') 4\pi r' dr'
                        \right).
\end{eqnarray}
Here $Z$ is the nuclear charge of the atom and $\rho(r)$ is the charge densities of the confined Ca atom. We determine $\rho(r)$ first
in the mean-field procedure using the DF method and then, we take into account the electron screening effects through the RCC method by
including the electron correlation effects. After evaluating $V_{st}(r)$, the exchange potential is calculated using
the charge density and energy dependent form suggested
by Furness and McCarthy \cite{Ve_FM}. In the elastic scattering process, there is still finite probability of occurrence of
inelastic processes which we take into
account through the absorption potential $V_{ab}(r)$. We define this potential in the local density approximation (LDA) as suggested by
Salvat \cite{salvat}.

As some of the previous studies were carried out using the DFCP method (e.g. see Refs. \cite{hasan,ls-1,ls-2}), we also employ the DFCP method in our
calculations to demonstrate differences between the results from this method and the RCC theory by introducing the CP
potential ($V_{cp}(r)$) in the interaction potential as $V(r) = V_{st}(r)+V_{ex}(r)+V_{cp}(r)-\iota V_{ab}(r)$. Here $V_{st}(r)$ and
$V_{ex}(r)$ are determined using $\rho(r)$ from the DF method. This approximation for $ V(r) $ may suit better for slow incident electrons as
they can polarize the charge cloud of atom more causing interaction of the induced dipole moment of the atom with the projectile electron.
The CP potential can be divided into two parts as short-range ($V_{sr}$) and long range ($V_{lr}$)  as discussed by Salvat \cite{salvat}.
Here, we define $V_{sr}(r)$ in LDA  \cite{lda} considering the parameters given by Pedrew
and Zunger \cite{cp_sr}. Buckingham potential \cite{Buckingham} is employed to describe $V_{lr}(r)$ which
depends upon the static dipole polarizability $ \alpha_{0} $. It is evident now that to define interaction potential $V(r)$ reliably
it is necessary to obtain $\rho(r)$, $\alpha_0$ and also excitation energies (which are required to determine $V_{ab}(r)$) as accurately
as possible. Moreover, their dependencies on the well depth of the endohedral confinement need to be investigated precisely in order
to study elastic scattering from the confined atom.

\section{Results and Discussion}\label{RnD}

\subsection{Atomic properties}

In the present work, we model the endohedral confinement potential in Eq.~(\ref{Ur}) by using the values of $r_0$ and $\Delta$
to be 5.8 a.u. and 1.89 a.u., respectively, as suggested by Xu et al \cite{Xu}. As mentioned earlier, Haso\u glu {\it et al.}
\cite{STM-1} had investigated spectroscopic properties of the confined Ca atom using the MCHF method. Here, we intend to show the
differences in some of the results due to our relativistic methods compared to the MCHF calculations. We use Gaussian type orbitals
(GTOs) in the DF method to obtain the single particle orbital wave functions and energies. The $k^{th}$ GTO in an atomic orbital expansion is
defined as
\begin{eqnarray}
f_k(r) = e^{-\eta_k r^2},
\end{eqnarray}
where $\eta_k$ is an arbitrary parameter chosen suitably to produce the orbitals accurately. Using the even tempering condition as
$\eta_k = \eta_0 \zeta^k$, we consider $\eta_0=0.00715$ and $\zeta=1.92$ to define GTOs in our calculations. From these calculations, we
observe that increasing the potential depth does not affect much the inner shell orbitals wave functions. However, for outer shell 4$s$ the effect
of change in the value of $U$ is quite significant; more pronounced in the vicinity of the radial distances $r_0 -\Delta$ and
$r_0 +\Delta$. To demonstrate this, we have plotted variation of probability densities of the inner 3$p_{1/2}$ and 3$p_{3/2}$ and outer 4$s$ shells
in Figs. \ref{wavefunctions}(a)-(c), respectively, from the DF method. As seen, the peak of the probability density curve shifts for the $4s$
orbital towards larger $r$ as the well deepens. All the curves cross one another nearly at inner radius $r_0$ of the potential well. Our
results are in very good agreement with the numerical calculations by Kumar et. al. \cite{HV-1}. Figure \ref{wavefunctions}(d) shows the
electronic charge density  $\rho(r)$ as a function of $r$ at various depths. This shows the probability density of the 4$s$ orbital, $\rho(r)$,
also changes dramatically close to the inner-radius of the potential well. In the inset of Fig. \ref{wavefunctions}(d), we show how all the
curves cross approximately around $r = 5$ a.u.. This shows with increasing $U$ value, $\rho(r)$ first decreases slowly up to $r = 10$ a.u.
and falls off faster beyond 10 a.u.. After discussing wave functions, we show variation of the single particle orbital energies
with the potential depth. In this case also we find that the trends match well with the results of Kumar et. al. \cite{HV-1} as quoted
in Table \ref{tab1}. This implies that we have correctly implemented the confined potential in our calculations.

\begin{table}
\caption{Comparison of single particle orbital energies from our analytical calculations using GTOs (given as I) and numerical values reported
by Kumar et al \cite{HV-1} (given as II) for different confined potential strength U (in a.u.).}
\begin{tabular}{c c c c c c c c c}\hline \hline
U & \multicolumn{2}{c}{4$s$}     & \multicolumn{2}{c}{$3p_{1/2}$} & \multicolumn{2}{c}{$3p_{3/2}$}& \multicolumn{2}{c}{$3s$} \\
         & I & II & I & II & I & II & I & II \\ \hline
         & & \\
0.000	& 5.34	& 5.34		&36.71	& 36.71	& 36.28	& 36.29	& 61.55	& 61.55 \\
0.005	& 5.37	& 5.37		&36.75	& 36.75	& 36.33	& 36.34	& 61.59	& 61.59 \\
0.010	& 5.40	& 5.40		&36.79	& 36.79	& 36.37	& 36.37	& 61.63	& 61.63 \\
0.050	& 5.65	& 5.65		&37.14	& 37.14	& 36.72	& 36.72	& 61.97	& 61.97 \\
0.090	& 5.93	& 5.93		&37.54	& 37.53	& 37.12	& 37.10	& 62.36	& 64.35 \\
0.130	& 6.24	& 6.24		&38.00	& 37.95	& 37.59	& 37.53	& 62.82	& 62.77 \\
0.140	& 6.35	& 6.33		&38.09	& 38.06	& 37.67	& 37.64	& 62.90	& 62.88 \\
0.170	& 6.62	& 6.60		&38.45	& 38.41	& 38.03	& 37.99	& 63.26	& 63.22 \\
0.200	& 6.91	& 6.88		&38.65	& 38.77	& 38.44	& 38.35	& 63.67	& 63.57 \\
0.200	& 7.02	& 6.98		&38.99	& 38.89	& 38.58	& 38.47	& 63.80	& 63.69 \\
0.220	& 7.13	& 7.09		&39.13	& 38.01	& 38.71	& 38.59	& 63.93	& 63.81 \\
0.250	& 7.47	& 7.41		&39.54	& 39.39	& 39.12	& 38.96	& 64.33	& 64.18 \\
0.290	& 7.96	& 7.87		&40.10	& 39.88	& 39.64	& 39.46	& 64.90	& 64.66 \\
0.310	& 8.23	& 8.11		&40.34	& 40.12	& 39.92	& 39.70	& 65.12	& 64.90 \\
0.330	& 8.50	& 8.36		&40.60	& 40.35	& 40.20	& 39.93  & 65.40& 65.13 \\\hline \hline
\end{tabular}
\label{tab1}
\end{table}

After testing single particle orbital energies and wave functions from our DF method, we now compare the electron self-consistent field (SCF)
and correlation energies with the MCHF calculations in Table \ref{corr}. We find our SCF energy of the free Ca atom is about 3 a.u. larger than
the SCF energy reported using the MCHF method in Ref. \cite{Zuo}. We also perform numerical calculation of the SCF energy using the GRASP2K
package \cite{grasp2k} to validate our result. There is a good agreement between both the calculations in the relativistic approach. This
justifies that the difference between the SCF energies from our calculations and the MCHF results of Haso\u glu {\it et al.} \cite{Zuo} is due to the relativistic
effects. Again, the correlation energies obtained using the RMBPT(2) and RCCSD methods for both the isolated and confined Ca atoms are found
to be considerably different than the values given by the MCHF method. It suggests that the relativistic and correlation corrections
are inefficiently included in the MCHF method. We also find that the correlation energies from the RMBPT(2) and RCCSD methods are very close
to each other and they are decreasing with the increasing value of the potential depth.

\begin{table}
\caption{Demonstration of trends of SCF and correlation energies (absolute values) as function of $U$. We also compare our SCF energy for
the free Ca atom from the non-relativistic calculation reported by Haso\u glu et al \cite{Zuo} and using GRAS2K code \cite{grasp2k}.
Similarly, magnitudes of the correlation energies are also compared between the calculations using the RMBPT(2), RCCSD and MCHF methods. All the quantities are
given in a.u.}
\begin{tabular}{lccccc}\hline\hline
$U$ & \multicolumn{2}{c}{SCF Energy} & \multicolumn{3}{c}{Correlation Energy}\\\cline{2-6}
    &         This work & Others              & RMBPT(2)    & RCCSD & MCHF \cite{Zuo} \\\hline
    & & \\
 0.00       & 679.71  &  676.76 \cite{Zuo}      & 0.7302    &   0.7487	& 0.223\\
	    &  & 679.71 \cite{grasp2k} & & &\\
   0.01   &    676.79   & &  0.7297    &   0.7483		& 0.222\\
   0.05   &      679.72  &	&   0.7276   &     0.7465 	& 0.221\\
   0.10   &      679.74 &  &  0.7247   &    0.7442		& 0.219\\
    0.15   &     679.76   & &	 0.7218   &    0.7419	& 0.217\\
    0.20    &     679.79  &  &	 0.7189  &     0.7399	& 0.215\\
    0.25   &     679.82   &  &	0.7162    &   0.7379		& 0.213\\
    0.30   &      679.85  &   &	0.7138   &    0.7369		& 0.212\\
    0.35    &    679.89    &	&	0.7119    &   0.7379		& 0.211\\
    0.40     &    679.93  & &	  0.7107   &    0.7410 	& 0.210\\\hline \hline
\end{tabular}
\label{corr}
\end{table}

We now show the trends of IP of the confined Ca atom with well depth in Table \ref{ipeng} from the DF, RMBPT(2) and RCCSD methods. We have also given its
value for the free atom and compared with the experimental value \cite{exp-ip} in the same table. The RPMBT(2) result seems
closer to the RCCSD result. We anticipate that inclusion of triple excitations in the RCC theory will improve the RCCSD result, but
inclusion of these excitations demands for large computational resources. Furthermore, carrying out calculations including triple excitations
for a range of well depths are too time taking. Thus, we show trends of the IP only using the RCCSD method approximation in the RCC theory
framework.

\begin{figure*}[t]
\begin{center}
\includegraphics[trim = 0cm 1cm 5cm 0cm,scale=0.8]{fig-2.eps}
\end{center}
\caption{(Color online) Comparison of our DCSs and ICSs from the DF, DFCP and RCCSD methods with the experimental value
\cite{Ca-expt} and other available calculation \cite{hasan} for the elastic scattering of an electron from an isolated Ca atom.}
\label{free-ca}
\end{figure*}

\begin{table}
\caption{Trends of ionization potential (IP) in cm$^{-1}$ from the DF, RMBPT(2) and RCCSD methods as function of $U$ (in a.u.). We
also compare our results for the free Ca atom with the experimental value.}
\begin{tabular}{c c c c c}\hline \hline
     $U$   &  DF       &    RMBPT(2)     &     RCCSD      &    Experiment \cite{exp-ip} \\\hline
 & & \\
    0.00 &    43085.69   &    49769.48    &     50138.51  &   49305.95 \\
    0.01 &  43544.77    &   50157.94     &    50520.24	&\\
  0.05   & 45528.67     &  51864.55      &   52180.95		&\\
   0.10  &   48356.92   &    54371.71    &     54654.27	&\\
   0.15  &   51588.43   &   57330.23     &    57645.79		&\\
   0.20  &   55227.19   &   60759.73     &    61198.35	&\\
   0.25  &   59264.59   &   64659.86     &   65301.45		&\\
   0.30  &    63682.83  &    69015.21    &     70031.23	&\\
  0.35   & 	68458.74     & 73801.28       &  75508.26		&\\
   0.40    &   73566.84    &  78987.77     &    81725.72	& \\\hline \hline
\end{tabular}
\label{ipeng}
\end{table}

\begin{table}[b]
\caption{Correlation trends of dipole polarizability of the free and confined Ca atoms using the DF, RMBPT(2), RRPA and RCCSD methods.
Results are given in a.u.}
\begin{tabular}{c c c c c c}\hline \hline
       $U$ &    Experiment \cite{exp-pol}   &   DF    &    RMBPT(2)   &  RRPA   &     RCCSD \\\hline
& & \\
    0.00    &       169$\pm$17  &    122.89   &    151.73  &    182.80 	&     157.03 \\
    0.01    &                  &       125.82  &     155.72  &    187.60  & 161.12\\
    0.05    &                  &       138.81  &     173.28  &    208.52  & 180.29\\
    0.10    &                &          158.06  &   198.98   &   238.60   &   209.61\\
   0.15   &                  &        180.85   &    228.86  &    272.71  &   245.47\\
    0.20   &                  &         207.13   &    262.56  &  310.07   &   288.69\\
    0.25  &                  &         236.54   &    299.30  &    349.55  &  Diverge\\
   0.30    &                  &         268.38   &    337.94  &  389.80   &  Diverge\\
   0.35   &                  &        301.61    &   377.09   &   429.48  &  Diverge\\
    0.40   &                  &          335.01  &     415.3  &   467.49  &   Diverge \\\hline \hline
    \end{tabular}
\label{dipp}
\end{table}

Determining $\alpha_0$ value of an atomic system accurately in the {\it ab initio} approach is very challenging. We have carried out
calculations of $\alpha_0$ values for a variety of atomic systems precisely using our perturbative RCC method \cite{yashpal1,yashpal2,yashpal3}.
In our investigations, we had found RRPA can give $\alpha_0$ values of atomic systems with inert gas configurations very close to the
calculations using the RCCSD method and experimental values \cite{bijaya3}. However, RRPA overestimates the $\alpha_0$ values in other
atomic systems while the RCCSD method is able to give very accurate results \cite{yashpal3,bijaya3}. From the computational point of view,
RRPA takes much less time than the RCCSD method to carry out these calculations. Since experimental value of $\alpha_0$ of free Ca atom is
not available precisely, we perform calculation of this quantity using the DF, RMBPT(2), RRPA and RCCSD methods. These values are given in
Table \ref{dipp} along with the experimental result. It shows the DF method gives a lower value of $\alpha_0$ in the free Ca atom, while its
result increases gradually in the RMBPT(2) method and RRPA. However, the RCCSD method gives an intermediate value between the RMBPT(2) and
RRPA calculations implying that there are strong cancellations between the core-polarization and other correlation effects in the RCCSD
method. Our RCCSD result is also within the error bar of the experimental value \cite{exp-pol}. We find similar trends in the $\alpha_0$
values from the DF, RMBPT(2), RRPA and RCCSD methods for finite value of the potential depth of the confined Ca atom. We also see the $\alpha_0$ value of the confined
Ca atom increases rapidly with increasing value of the potential depth and the perturbed amplitudes in the RCC method do not converge for
relatively large magnitudes of the potential depth. In order to estimate this quantity accurately for large $U$ values, one can extrapolate
our RCCSD results from the trends of the RMBPT(2) and RRPA calculations.

\begin{figure*}
\begin{center}
{\includegraphics[trim = 0cm 5cm 5cm 0cm,scale=0.8]{fig-3.eps}}
\caption{(Color online) Demonstration of DCSs and ICSs using the DFCP method for the elastic scattering of an electron from a confined Ca atom
as function of confining potential ($U$).}
\label{conf-ca}
\end{center}
\end{figure*}

\subsection{Elastic Scattering Cross-sections}

In this sub-section, we would like to demonstrate the effects of endohedral confinement of Ca on the electron elastic scattering cross-section.
In order to assess the accuracy of our atomic structure calculations, we have calculated first DCSs for the electron and free Ca atom elastic
scattering at the incident electron energies of 10, 20, 40, 60 and 100 eV and compare these calculations with the measurements reported by
Milisavlijevi\'c et al \cite{Ca-expt} as well as those obtained using the optical model potential approach by Hasan et al \cite{hasan}.
As mentioned in Sec. \ref{Model-Potential-theory}, we perform calculations using the charge densities from the DF and RCCSD methods.

In Fig. \ref{free-ca}, we plot our DCS results for the isolated Ca atom along with the other reported values in Refs. \cite{Ca-expt}
and \cite{hasan}. Calculations of Hasan et al \cite{hasan} are equivalent to our DFCP results and therefore, the two sets of results
overlap on each other. At 10 eV, the RCCSD results explain the measurements better in comparison to the DFCP calculations in the scattering
angle range 70$^o$ - 110$^o$. Also, the RCC results agree better with experimental data at 20 eV as well in the range 110$^o$ - 130$^o$. This
indicates that the wave functions obtained using the RCCSD method give more reliable results at lower energies. At 20 eV, the DCS
results are not reported by Hasan et al \cite{hasan} and hence, they are not shown in Fig. \ref{free-ca}(b). In general, our RCC and DFCP
results are in good agreement with the measurements up to 70$^o$ electron scattering angle. Between 70$^o$ - 120$^o$ our results are slightly
deviated in magnitude but agree in shape with the experimental values \cite{Ca-expt}. Beyond 120$^0$ our all the DCS, except at 60 eV, lie
within the experimental error bars. Further, as expected the correlation effects play important role in the forward scattering region and at low
projectile electron energy. Therefore, as the energy increases the difference between the DF and DFCP calculations diminish. We also observed that
the RCC results are slightly higher in the forward scattering range. This can be due to slightly higher value of $\alpha_0$ obtained by the
RCCSD method in comparison to the DF method. In Fig. \ref{free-ca}(f), we have compared ICSs from our calculations and the experimental values.
The DFCP results are in better agreement with the experimental data while cross-sections from the RCCSD method are slightly higher than
the values obtained using the DFCP method. This is again due to higher values of DCSs from the RCCSD method at small angles. Agreement
of the DFCP results with the experimental values could be coincidental, but we anticipate that inclusion of contributions from the higher level
excitations in our RCC theory could improve the RCCSD results. Nevertheless, we find an overall agreement of the present calculations for
electron and free Ca atom elastic scattering with the previous experimental \cite{Ca-expt} and other theoretical calculations \cite{hasan}.

Figure \ref{conf-ca} displays behavior of DCS as a function of confining potential $U$ in the electron energy range 10-100 eV. Although we
have performed DCS calculations using the DF, DFCP and RCCSD methods, we present here only the DFCP calculations. We have used our calculated
$\alpha_0$ values of the confined Ca atom to obtain polarization potentials at different $U$.
It can be seen from the figure that the magnitude of DCS increases with increasing potential depth in the forward scattering direction. This
reflects the fact that dipole polarizability of the target Ca atom increases with increasing well depth. Also, this could be due to rise
in the charge density, as shown in Fig.~\ref{wavefunctions}, on increasing depth of the confining potential. The shape of the DCS curves at
various values of $U$ differ significantly at low incident electron energy. This difference diminishes with the increasing energy of
the projectile electron. At 10 eV the first two dips near 35$^o$ and 80$^o$ become more pronounced and deeper with increasing $U$.
In Fig-\ref{conf-ca} (d), the ICS are shown as function of well depth at various incident electron energy. As can be seen from the figure,
there is a consistent increase in the cross-sections with increasing attractive potential. At low electron energy, the rise in ICS is more
with increasing value of $U$ and the cross-section increases by 131\% at 10 eV energy for a change in the value of $U$ from 0.01 to 0.4 a.u..
However, this rise in ICS becomes slower for projectile electrons with more energy and for 100 eV ICS increases by 69\% only. Thus, the slope
of these cross-section curves decreases with increasing electron energy. It shows that the influence of the presence of the endohedral
environment on the cross-section is more significant for slower projectile.

\section{Conclusions}\label{conclusions}

We have carried out a detailed study of atomic structure and dynamics of endohedral confinement of Ca atom in C$_{60}$ cage using
relativistic many-body methods. Since no experimental data is available for atomic properties of the above encapsulated atom, we have evaluated
self-consistent energy, correlation energy, ionization potential and dipole polarizability of this atom at different levels of
approximations in the many-body methods. We found that deepening of the attractive potential well results into more tightening of
the electrons to the nucleus and hence, increase in the ionization potentials. We also compared our single particle orbital energies
for different values of potential depth with the corresponding results reported using numerical calculations and found very good agreement
between them. Our ionization potential and dipole polarizability results for the free Ca atom agree well with the measurements. We also
compared our self-consistent and correlation energies with the reported non-relativistic calculations and observe that the
relativistic effects influence these results significantly.

The behavior of probability density and electronic charge density at various potential depths of the confined Ca atom obtained
using the mean-field calculations are analyzed and it shows that these quantities show spectacular changes with strengthening of the
confining potential. We found the probability density of the valence 4$s$ shell spreads over to a broader radial distance with increase
in $U$ in contrast to the inner shells for which it remains unaffected in the presence of the potential well. Utilizing the
electronic charge densities calculated by the Dirac-Fock method and relativistic coupled-cluster theory, the differential
and integrated cross-sections of elastic scattering of an electron from the free and confined Ca atoms in the incident electron energy
range from 10 to 100 eV are investigated. We found our results using the core-polarization potential with the Dirac-Fock wave function
and wave functions from the relativistic coupled-cluster theory are in good agreement with the measurements and previous calculations
for the free Ca atom. The differential cross-sections are found to be slightly better in the relativistic coupled-cluster theory at the
incident electron energies 10 and 20 eV. This shows the effectiveness of the all-order perturbative coupled-cluster theory in the low energy regime.
It also emphasizes the crucial role played by the many-body methods for accurate determination of the atomic wave functions in explaining
the experimental data. Further, variations in the differential and integrated cross-sections with increasing potential strength are
shown. It shows differential cross-sections change dramatically; particularly at low projectile energies.

\section*{Acknowledgement}
SB is thankful to the Ministry of Human Resources and Development (MHRD), Govt. of India for fellowship.
RS and LS are grateful to the SERB-DST and CSIR, New Delhi, Govt. of India for the supporting research grants.
B. K. S. acknowledges use of Vikram-100 HPC cluster of Physical Research Laboratory (PRL), Ahmedabad, India for the computations.

redpajama_set_name: RedPajamaArXiv


Saturday, November 29th, from 1pm – 4pm in the Library. Photo by Kris Krug Throughout this holiday weekend there will be Drawings, Prizes, and Local Holiday Treats available at various locations within the building.
Monthly Potluck Grant Dinner which supports local good causes. Bring a food dish and a $10 donation of which the selected grant recipient gets 100%.
The First Street Community Center of Mount Vernon, Iowa is pleased to host an Evening of Celtic Music with Lilywren. The live performance will take place 7pm, Friday, March 13th, 2015.
This Sunday, April 26, 2015 the First Street Community Center in Mount Vernon, Iowa get's quite the exciting treat for children of all ages.
Bob Campagna, a former long time resident of Mount Vernon, describes his Mount Vernon business, Abbe Creek Press, as "on hiatus" in Loveland, Colorado.
At our educational event we provide hearing screenings and cover numerous topics including basic ear anatomy and physiology, tinnitus, types of hearing loss, hearing aid styles, hearing aid technology, and the side effects of untreated hearing loss.
Looking to be creative? Join us Saturday, November 28th, 11am - 2pm to paint a winter barn scene.
Students will receive step by step instructions on creating this amazing barn using acrylic paint on a wood board. All supplies will be provided. The class will be located in the library of the First Street Community Center. Feel free to bring a beverage and snack.
NOTE: Hillary Clinton will not be at this event. However, you are encouraged to come and learn what the women of the Senate think about Hillary Clinton. Come listen to them and ask them your questions.
This Friday, January 15th from 12:15-1:30pm. This event is held in the Library at the First Street Community Center in Mount Vernon, Iowa.
The First Street Community Center in Mount Vernon, Iowa is pleased to announce that we've got a live musical performance by Lilywren Saturday, April 30th at 7pm in our Library performance space upstairs.
Discover your inner artist as you create a beautiful small painting under the guidance of acrylic artist Lianne Westcot. This is a great way to learn the beginnings of shape and depth.
Bring a photo of your own or select one provided at the beginning of class. You'll be amazed as you follow a few simple steps to complete your own small wonder!
Registration Deadline: REGISTRATION & PAYMENT is required by Wed, July 6th by 6:30pm so the instructor can prepare materials.
Alcohol ink is a bright and fun medium for the beginner or advanced artist. The perfect medium for those who have little or no art training as well as the experienced artist who wants to relax, unwind and allow their creativity to flow!
Linda will instruct students on a variety of alcohol ink techniques to complete your final projects.
If you have had previous alcohol ink class, you will be shown new methods and techniques. Bring your sense of fun as well as a beverage of choice!
Registration Deadline: Registration & Payment is required by Wednesday, July 13th at 7pm so the instructor can prepare materials.
Jump into Summer by painting this Stargazer Lily! You will be using acrylics while painting this delightful flower on a 9" x 12" canvas board.
In this monthly "Flower Series" class, you will be painting a different fun and vibrant version of one your favorite flowers, following step-by-step instructions. A variety of color options are available for this series.
Registration Deadline: Class minimum of 5 must be met by Thursday, July 14th at 9:30am so the instructor can prepare materials.
For the beginner or advanced, learn new Alcohol Ink painting techniques on Yopu paper and on tiles.
With this unconventional method of painting, you will be amazed at what you can accomplish with straws and packing peanuts instead of a brush. If you love color, and trying new things, this class will intrigue you!
Registration Deadline: REGISTER EARLY--Class minimum of 5 must be reached by Thursday, July 21st at 10am for instructor to prepare materials.
Paint this lively and whimsical floral in an enjoyable and social atmosphere. Come by yourself, or bring your fun and crazy friends. With the stroke of fun, you will be unleashing your creativity in no time.
Linda will show you various techniques using acrylics on a 9 x 12 canvas.
Registration Deadline: Class minimum of 5 must be met by Wednesday, July 27th at 7pm so the instructor can prepare materials.
Alcohol ink is a fun medium for the beginner or an advanced artist. The perfect medium for those who have little or no art training as well as the experienced artist who wants to relax, unwind and allow their creativity to flow!
Linda will instruct students on a variety of alcohol ink techniques to complete your final projects. If you have had previous alcohol ink class, with Linda, you will be shown new methods and techniques. Bring your sense of fun as well as a beverage of choice!
Registration Deadline: & Payment is required by Thursday, August 18th by 7pm So the instructor can get materials ready.
Come by yourself, or bring your fun and crazy friends. With the stroke of fun, you will be unleashing your creativity in no time. Paint this lively and whimsical floral in an enjoyable and social atmosphere.
Registration Deadline: Payment is required by Wednesday, Aug 24th by 7pm, So the instructor can get materials ready.
For all you cat lovers out there…. Instructor Linda Bild, will be teaching you to paint this fun and whimsical Laura Burch inspired cat in acrylics paint.
No prior art experience is necessary as this is aimed for beginners over the age of 10 or for the young at heart! Come to relax, enjoy and have fun while exploring your creative side.
Registration Deadline: Payment is required by Thursday, Aug 25th. So the instructor can get materials ready.
Come by yourself, or bring your fun and crazy friends. With the stroke of fun, you will be unleashing your creativity in no time. Paint these colorful moonlit flowers in an enjoyable and social atmosphere.
Linda will show you various techniques using acrylics on a 9 x 12 canvas. Join Canvas, Cocktails & Coffee every month and begin your own home gallery. Come paint with us, we'll have the coffee pot on!
Who doesn't need a new pair of earrings?
In this intro to Jewelry Making class you will learn an introduction to wirework in creating 3 pairs of earrings. The first technique is making a closed wrapped loop that allows you to make earrings and pendants. The second technique is making a closed wrapped loop inside of a closed loop, allowing you to attach dangles to chains.
Each student will complete 3 pairs of earrings incorporating glass, semiprecious stones, pearls, Czech beads and Swarovski crystals. Make a pair of earrings for yourself and give the others as gifts!
In this fun and exciting Flower Series class, students will be painting a vibrant version of one of their favorite flowers.
Offered monthly, this class is for both beginners, who have never created art or drawn before, as well as advanced painters wishing to learn new Acrylic painting techniques.
Instructor, Linda Bild will show you a step-by-step approach using Acrylics while painting this stunning floral on a 12"x 12" canvas board.
Eek, a mouse!! At East End Art we think that it's time to start thinking about your Halloween decorations. These cute mouse trick-or-treaters are a unique and personal way to add flair to your home during Halloween.
Nina Scott will instruct each participant to complete a felt mouse by hand sewing, and then decorate with the costume of your choice.
Grandparents, spend a fun-filled morning with your grandchildren painting this fun and whimsical butterfly in acrylic paint.
No prior art experience is necessary as this is aimed for beginners over the age of 10 or for the young at heart!
Come to relax, enjoy and have fun while exploring your creative side. Acrylics and oil markers will be used on a 9x12" canvas board. Afterwards you can proudly mount this in a child's room, your office cubicle or wherever you need a touch of fun and whimsy.
For the beginner or advanced, unleash your creative spirit using Alcohol Ink painting techniques.
Linda will instruct her students a variety of techniques to complete 3-5 amazing final projects on Yupo paper and tiles.
New methods and techniques will be shown for those who have taken a previous Alcohol Ink class. Come create with us, it's good for your soul!
Please join East End Art for our First Friday Art Reception for Sri Rao on Friday, October 7th, from 5:30pm to 7:30pm.
Light refreshments and wine served for this casual event. Come meet Sri and see her exhibit of beautiful Iowa landscapes as well as her new collection of jewelry.
Reception is held in the Library (next to the gallery) at the First Street Community Center in Mount Vernon.
Just in time for Halloween! Paint this Happy Halloween scene in an enjoyable and social atmosphere.
Come by yourself, or bring your fun and crazy friends. With the stroke of fun, you will be unleashing your creativity in no time.
Alcohol Inks is the perfect medium for those who have little or no art training as well as the experienced artist who wants to relax, unwind and allow their creativity to flow!
Students will be instructed on a variety of alcohol ink techniques and complete several projects.
If you have had a previous alcohol ink class with Linda, you will be shown new methods and techniques.
Bring all of your friends and a sense of fun to Alcohol Inks with Alcohol Drinks !
Please join East End Art for our First Friday Art Reception for Denise Murphy on Friday, November 4th from 5:30pm to 7:30pm in the Library (adjacent to the gallery) in the First Street Community Center.
Light refreshment served, for this casual (come as you are) meetup. The public is welcome. Come and meet Denise, she has a great collection of her current project "365 Series."
The Mount Vernon Area Arts Council (MVAAC) is sponsoring a Community Mural, a project that includes soliciting input from students and residents. The MVAAC Board invites you to participate in a mural discussion at 7 pm, Thursday, January 26, 2017, at the First Street Community Center's (old Middle School) library.
The purpose of the meeting is to generate ideas and themes for the mural, which will be located on the concrete wall that separates the parking lots south of Main Street. Currently you can see temporary signage at this location; you may have seen "Coming Spring 2017 Community Mural" on this wall just off Hwy 1.
Come join us to hear Andy McGuire's plan and vision for running for governor. This will give us an opportunity to hear from one of many candidates running.
Jim will speak to our group about his organization. He has the pleasure to represent Iowa Legal Aid. They help assist for elderly and low incomes families as well as disabled.
City Council candidate, Stephanie West, will be interviewed Saturday, November 4, at 10:30 a.m. in the library of the First Street Community Center. You're welcome to attend in person. If you would like you can submit questions to Klrose718@gmail.com by noon on Friday, Nov. 3.
Come learn, listen and contribute! We'll learn about South East Linn Community Center (SELCC) and talk about our next steps and priorities for 2018.
The Mount Vernon / Lisbon Unit of the Linn County League of Women Voters meets the third Tuesday of every month 4:15 - 5:30pm in the library at the First Street Community Center.
Anyone (including men, students, young voters) interested in "encouraging informed and active participation in government, working to increase understanding of major public policy issues, and influencing public policy through education and advocacy" is welcome to attend!
Come on out after the Mount Vernon farmer's market to enjoy FREE ice cream, socialize and meet Christian Andrews, candidate for Iowa House District 95. Local musicians Leah and Josh Woosley will perform live! People who sign up to volunteer for the campaign will be entered into a drawing for prizes from local businesses.
Contact Helios Stitches N Stuff for more info.


The game sells for $215 used and $440 new.
The game sells for $26 used and $110 new.
The game sells for $41 used and $99 new.
The game sells for $40 used and $??? new. We haven't seen a new version of this game yet. But this one is signed and will probably sell for several hundred dollars.


text:
District attorney to seek death penalty for man…
District attorney to seek death penalty for man accused of killing Hayward cop
Mark Estrada as he appeared in court for his arraignment at the Hayward Hall of Justice in Hayward, Calif., Friday, July 24, 2015. Estrada is accused of fatally shooting Hayward Police Sgt. Scott Lunger.
By Angela Ruggiero | aruggiero@bayareanewsgroup.com | Bay Area News Group
PUBLISHED: August 23, 2018 at 3:18 pm | UPDATED: August 23, 2018 at 3:51 pm
OAKLAND — In a rare move, the Alameda County District Attorney's Office is seeking the death penalty against a man accused of killing a Hayward police sergeant in 2015.
In only the second time in her career, District Attorney Nancy O'Malley will pursue the death penalty for defendant Mark Estrada, accused of killing Sgt. Scott Lunger, 48, a Brentwood father of two. Lunger was fatally shot in the head and thigh shortly after he approached a white Chevrolet Silverado he had stopped for swerving in the roadway at 3:15 a.m. July 22, 2015, in Hayward.
Hayward police Sgt. Scott Lunger was killed during a traffic stop on July 22, 2015. (Hayward Police Department) (Hayward Police Department)
In court on Thursday afternoon for motions to change his attorneys, Estrada, 24, appeared in red and white striped jail clothes, his once longer shoulder-length hair cut short in a buzzcut.
His trial date is expected for Nov. 26. However, Judge James Cramer granted his motion to remove one of his retained attorneys on record, Christopher Morales, which could potentially affect the trial date.
In May 2017, Estrada was held to answer on all his charges, including murder with the special circumstances of lying in wait and drive by shooting, which qualified him for the death penalty. The District Attorney's Office typically assembles a team of prosecutors, including O'Malley herself and in this case John Brouhard, who is prosecuting Estrada's case. After a meeting, O'Malley makes the final decision on whether seek the death penalty.
Since she was appointed top prosecutor in 2009, O'Malley has only sought death for one other defendant, Darnell Williams, who was convicted in May 2016 for the deaths of 8-year-old Alaysha Carradine and 22-year-old Anthony Medearis in separate instances. The jury in that case recommended death. Brouhard also prosecuted that case.
During Estrada's preliminary hearing, Brouhard argued that Estrada had enough time to prepare and arm himself with his gun.
"When his prey is close enough to kill, he immediately takes action," said Brouhard during the hearing in 2017.
Alleged cop killer ordered to trial in death of Hayward police Sgt. Scott Lunger
Friend describes alleged Hayward cop killer arriving wounded at doorstep
Oakland man accused of killing Hayward police officer pleads not guilty
Lunger, who had been on the force for 15 years, had pulled over the truck that night in what was described as a routine traffic stop, after the vehicle was seen swerving.
Officer Justin Green said in testimony that he knew something wasn't right. Green had already begun running toward the truck when he heard a gunshot fired from inside the cab and saw Lunger collapse.
Estrada, hysterically sobbing and bleeding, showed up at his friend's doorstop in East Oakland a little more than an hour later, a friend testified. Estrada told his friend he had been shot by a cop, and refused to go to the hospital, that he wanted to sleep through it instead. He had a gunshot wound to the lower back and reeked of alcohol. His friend testified that it was out of character for Estrada, who has no criminal record.
2015 Homicides
Angela Ruggiero
Angela Ruggiero covers criminal justice and the Alameda County Superior Court. She previously covered the Tri-Valley cities of Pleasanton, Dublin, Livermore and Danville.
Follow Angela Ruggiero	@Aeruggie
Men robbed outside Oakland City Hall
Two men were robbed at gunpoint early Thursday morning in Frank Ogawa Plaza outside Oakland City Hall.
Federal Monitor Robert Warsaw had already overturned Kirkpatrick's light discipline against the officers, but the extent of the discipline he wanted in the shooting were unknown until the documents were released Thursday. Likewise, the commission's decision on the matter was not public until Thursday.

redpajama_set_name: RedPajamaCommonCrawl


As the Chair of Governors at Ysgol Tanyfron Primary School. It gives me great pleasure to explain our role to current parents/guardians, prospective families and any visitors to the school website. I am also delighted to share with you the current make up of the governing body for the 2018-19 academic year.
Our Governing body works very closely with school, parents/guardians and most importantly our pupils; to provide the best educational setting we can. We pride ourselves on our mission statement of 'Making a difference together', through embracing an open door policy, family engagement and supporting the school's needs.
The governing body has established a number of committees and statutory panels. We meet as a Full Governing Body every half term. The Governing Bodies committees also meet together every term to review and discuss the details of the school life.
As Governors we also share a common objective which is the wider school community. To achieve this, and to carry out our role as Governors effectively, we need to know what issues are important to you (so we remain responsive) and ensure that you know what issues Governors are discussing (so that we remain accountable).That is why as Governors we work closely with Mr Lloyd and Staff to ensure that we continue to deliver a high standard of education to our children at Ysgol Tanyfron.
If you have a concern or a point of view to share please let us know. We can be contacted via the School Office, by e-mail mailbox@tanyfron-pri.wrexham.sch.uk or by approaching any of the governing body on the school yard.


text:
OCONOMOWOC NEWS
Oconomowoc's Eric Jensen, the longtime Milwaukee Bucks public address announcer, will be featured in the NBA 2K22 video game
Evan Frank
"All right, Milwaukee, it's time for Bucks basketball!"
Oconomowoc resident Eric Jensen, who is the longtime public address announcer for the Milwaukee Bucks, will now play a part in a popular video game franchise. Jensen will provide in-game calls, live commentary and other announcements for NBA 2K22, which will be released later this month.
According to the NBA 2K Twitter account, the game will take on a "new level of realism" by including every NBA team's public address announcer. In a separate tweet from the Milwaukee Bucks, Jensen said in a video interview that his sons were excited about the announcement.
"My sons are really into it, especially my 15-year-old," Jensen said. "He plays all the time. Out of all the things I've done in my career, this is the most excited he's been about anything. He's really fired up about this whole thing."
Jensen, who has lived in Oconomowoc for 19 years, has worked in radio since college and currently serves as a producer and on-air talent at 102.9 The Hog. About 25 years ago, Jensen was asked to be the public address announcer for the Milwaukee Wave.
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Jensen spent a few years with the Wave and auditioned for the Bucks public address announcer position when it became available in 1999.
Jensen said he was influenced by the Bucks former public address announcer Jack Gallo.
"I wanted my announcing to stand up to what Jack Gallo had built that to," Jensen said. "He had a way of announcing that I kind of emulate a little bit, and I use some things that I heard Jack do as a kid growing up. When the Bucks are climbing their way back into a game and then they hit a shot that ties it up, I stole Jack's line that is, 'And this game is tied.' Then you say the score and the crowd usually gives you a nice applause for that one. That was a Jack Gallo staple."
Jensen said you have to bring your own personality into public address announcing.
"You can't be yelling the whole time," Jensen said. "If everything is crazy and fantastic, nothing is. You have to pick your spots, get excited when the fans are going to get excited. I think that's a way you can bring the arena to a better level of intensity."
NBA 2K22 will launch Sept. 10 for PlayStation 5, Xbox Series X|S, PS4, Xbox One, Switch and PC.
Contact Evan Frank at (262) 361-9138 or evan.frank@jrn.com. Follow him on Twitter at @Evanfrank_LCP.


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Our Location28-C, Block E-1, Gulberg-III, Lahore
Phone042-111-111-476
Emailinfo@hsm.com.pk
BIO FERTILIZER
BAGASSE
DIRECTORS PROFILE
PATTERN OF SHAREHOLDING
DIRECTORS CODE OF CONDUCT
EMPLOYEES CODE OF CONDUCT
FINANCIAL HIGHLIGHTS 2020
INTERIM ACCOUNTS
FREE FLOAT SHARES
CORPORATE BRIEFING
INVESTOR GRIEVANCES
STOCK EXCHANGE & SYMBOL
Pursue Excellence & Success Will Follow
Excellence is the Result of Habitual Integrity
If You Don't Value Excellence You Wont Achieve Excellence
Welcome To Husein Sugar
Husein Sugar, incorporated in 1966, in Karachi is one of Pakistan's oldest and most renowned sugar factories. Having completed more than fifty years of business, the company is listed on the Pakistan Stock Exchange with security symbol, HSM. The company has had the honor of being award the Top 25 Companies of Pakistan award twice. Here, on the Web Site, you can see the latest news and updates with regard to the company.
Sugar comprises of the majority of the company's sale. Sugar, or the generic name given to the family of various sweet-tasting
Molasses is the residual liquid food obtained in the manufacturing of raw sugar. This by-product of sugar is mostly sold to distilleries
Husein Sugar produces high quality Bio-Fertilizer that can be used by farmers to enrich the soil before cultivation of crops
Bagasse, which is the fiber residue of sugarcane post the extraction of sucrose juice in the milling stage is an excellent
Husein Sugar Mills Limited (The Company) was incorporated on February 14, 1966 in Karachi and received its Certificate for Commencement of Business on April 16, 1966.The Company is listed on the Pakistan Stock Exchange and has received the award for Top 25 Companies of Pakistan twice in its fifty-year history. The Company commenced trial production on January 22, 1968 and went into commercial production on February 15, 1968, making it one of the pioneers of Pakistan's sugar industries. Given the rich history of the company, which is now in its third generation, it enjoys cordial and familial relations with the sugarcane growers of the area.
Years Operated
Share Market Price
Mrs. Sadia Ali Tariq
Mrs. Sadia Ali Tariq is a non –executive director of Husein Sugar Mills Limited. Mrs. Sadia Ali Tariq is also a Director of Tariq Welfare Foundation, a Company Registered under Section 42 with the Securities and Exchange Commission of Pakistan (SECP). She has completed her Directors Training Program from the Lahore University of Management Sciences.
MR. MUHAMMAD IMRAN KHAN
Mr. Muhammad Imran Khan joined the Board on 31 May 2018. He is currently serving as independent director on Husein Sugar's Board of Directors, and as the Member of the Board's Audit Committee.
MR. SAIF HASAN
Mr. Saif Hasan is an experienced executive in the global textile and fashion industry with a background in technology operations and management. He is also serving as a Director of Intermoda Brands Pvt. Ltd and is an executive at Matrix Sourcing, Triple Tree Solutions, and Lulusar. Previously, Mr. Hasan has worked in Silicon Valley. He completed his higher education at The George Washington University in Washington DC. He has also completed executive courses at the London School of Economics and the Lahore University of Management Sciences. Mr. Hasan joined the Board of Directors of Husein Sugar Mills Limited on the Dec 19, 2019.
MR. TAUFIQ AHMED KHAN
Mr. Khan is a highly decorated executive of Pakistan's pharmaceutical industry. Serving as the independent director on Husein Sugar's Board of Directors, and as the Chairman of the Board's Audit Committee.
MRS. MARYAM HABIB
Mrs. Maryam Habib was elected as a director on the board of Husein Sugar Mills in March of 2017. Mrs. Habib pursued her higher education at Kinnaird College Lahore. She is currently serving as the Executive Director of the company.
MIAN MUSTAFA ALI TARIQ
Mian Mustafa Ali Tariq is the Chief Executive Officer of the company. He completed his higher education at the University of California, Los Angeles and was awarded with a Bachelor of Arts degree in Economics.
MIAN AHMED ALI TARIQ
Mian Ahmed Ali Tariq is the Chairman of the Board of Directors of the company. He completed his higher education at the Lahore University of Management Sciences and was awarded with a Bachelors of Science (Honors) degree.
Mr. Muhammad Imran Khan joined the Board on 31 May 2018. He is currently serving as independent director on Husein Sugar's Board of Directors, and as the Member of the Board's Audit Committee. Mr. Khan's contributions to the company are of the utmost importance .Mr. Khan serves as CEO/Founder of Sule International and brings in several years of experience in commodities trading domestic and internationally. . He was Co-Founder of Amber Road Trading Co New York with focus on trading between South East Asia, North America and England. Mr. Khan also serves on the board of Admaxim a global digital advertising technology company. Mr. Khan holds a bachelor's degree from Government College (Lahore, Pakistan) and has completed a business management and marketing certification from the University of California Los Angeles. .
Mr. Khan is a highly decorated executive of Pakistan's pharmaceutical industry. Serving as the independent director on Husein Sugar's Board of Directors, and as the Chairman of the Board's Audit Committee, Mr. Khan's contributions to the company are of the utmost importance. He pursued his higher education at the University of Exeter where he was rewarded with a Bachelors of Science Degree in Economics Mr. Khan is also a director of Highnoon Laboratories Ltd., one of Pakistan's largest pharmaceutical manufacturers. He is also the Chief Executive Officer of Curexa Health Pvt. Ltd, a wholly owned subsidiary of Highnoon Labs. After completing the necessary requirements as per the Code of Corporate Governance, The Pakistan Institute of Corporate Governance has also certified Mr. Khan. Given his vast capabilities and wide-ranging exposure, Mr. Khan is an invaluable member of the Board of Directors.
Mrs. Maryam Habib was elected as a director on the board of Husein Sugar Mills in March of 2017. Mrs. Habib pursued her higher education at Kinnaird College Lahore. She is currently serving as the Executive Director of the company. In her short time at the company, she has been instrumental in initiating and implementing various programs of the company.
Mian Mustafa Ali Tariq is the Chief Executive Officer of the company. He completed his higher education at the University of California, Los Angeles and was awarded with a Bachelor of Arts degree in Economics. He has also been certified by the Lahore University of Management Sciences for successfully completing their course on Enhancing Board Effectiveness. He is a member of the HR&R Committee of the Board.
He is also a trustee of his family's non-profit social welfare organization. The family's education trust, which operates Mian Mohammad Ali Tariq College and Mian Nazir Husein School, has provided financial aid and scholarships to thousands of children since its inception. The family's healthcare trust operates a non-profit hospital that provides low-cost and free health care services.
Mian Ahmed Ali Tariq is the Chairman of the Board of Directors of the company. He completed his higher education at the Lahore University of Management Sciences and was awarded with a Bachelors of Science (Honors) degree. Mian Tariq is also a certified director from the Institute of Cost and Management Accountants of Pakistan (ICMAP). He has been associated with the company for more than a decade, and has served in an executive capacity since 2009. Mian Ahmed's vision and leadership at Husein has played a critical role in the company's growth, success, and development. An industry leader, Mian Ahmed also serves on the Executive Committee of The Pakistan Sugar Mills Association for Punjab.
Mian Tariq's is a strong advocate of giving back to the community. Under his leadership, Husein Sugar Mills has expanded its commitment and contribution towards social welfare and development. His family trust has providing quality education and healthcare for generations at affordable prices through substantial scholarships and financial aid.
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Ninja Warrior returns to the Universal Studios backlot for the fourth year
They'll tape the LA Qualifiers and City Finals on March 6 and 7.
By Nikki Lee@anwnation Feb 15, 2019, 10:15am PST
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As American Ninja Warrior fans anxiously awaited the arrival of the season 11 taping dates and locations, there was one thing they were pretty confident about. Ninja Warrior likes to kick things off in Los Angeles. In fact, all 10 seasons of the show have started somewhere in the Los Angeles area. Up till season seven, that was usually the Venice Beach boardwalk. But for season eight, the show looked for a different type of quintessential LA backdrop and found it on the Universal Studios backlot.
For the past three years, Ninja Warrior start started taping each season in this location, transforming the part of the backlot usually reserved for NYC-themed filming into the Ninja course. (In season 10, the Dallas episode aired first, but LA was still recorded first.)
The Universal Studios backlot is much more isolated than the rest of the cities. It provides a controlled environment as the Ninjas and crew jump back into things. Also, it looks very, very cool as the crew can customize almost every element around them. For season 11, the show will set up there for the fourth time, filming the LA Qualifiers and City Finals on March 6 and 7.
We feel like the fans are pretty familiar with the history of this location. But just to jog your memory, here are the LA recaps from the last three seasons, as well a few of the well-known runs. It definitely reminded us that LA tends to set the tone for the season, and something exciting usually gets things off on the right foot.
Season eight:
Ninja Warrior is back! Los Angeles Qualifying Recap
LA city finals recap: A gut punch to your emotions
Season nine:
America Ninja Warrior Los Angeles City Qualifier recap: Time to cannonball into season nine
American Ninja Warrior Los Angeles City Finals recap: No smooth rides on this Elevator
Season 10:
Los Angeles Qualifiers recap: The dinos roared but the Ninjas delivered
Los Angeles City Finals recap: Redemption for some, heartbreak for others
Unfortunately, we don't think we'll get the fantastic dinosaur set that we saw in season 10. After all, there aren't any Jurassic World movies coming out this year. But we're sure the hardworking crew behind the show is till putting together a gorgeous debut episode.