text:
\section{Introduction}
In atomic nuclei, strongly correlated nucleons compose spatially localized
subsystems, namely the nuclear clusters \cite{horiuchi86}. The relative motion
between the $\alpha$-clusters is the fundamental mode of dynamics in various
nuclear systems, such as $^8$Be, $^{12}$C, $^{16}$O, and $^{20}$Ne. These
clustering states have been studied by using different theoretical models, as
reviewed in Refs.~\cite{zhou19, freer18, ren18, tohsaki17, schuck16, kimura16,
funaki15, ito14, enyo12, horiuchi12}.

The Beryllium isotopes are well known for their clustering structures in the
ground states, as discussed in previous theoretical studies \cite{Eny95,
Eny99, Ita00, Ito04, myo14, myo15, fun02, Lyu15, Lyu16}. In these works, many
interesting physical phenomena, including the formation of two $\alpha$
clusters \cite{Eny95,Eny99}, occupation of nuclear molecular orbits by the
valence neutrons \cite{Ita00}, di-cluster configurations \cite{ito14},
contribution from tensor force \cite{myo14, myo15}, and nonlocalized dynamics
of the two $\alpha$-clusters \cite{Lyu16}, have been studied. It is found that
the low lying spectrum of the $^{8-10}$Be isotopes can be well described by
the Tohsaki-Horiuchi-Schuck-R{\"o}pke (THSR) wave functions \cite{fun02,
Lyu15, Lyu16}, which were originally proposed for the description of
$\alpha$-condensate states \cite{tohsaki01} and have been applied to many
clustering phenomena in nuclei \cite{fun02, Lyu15, Lyu16, zhao18, zhao19,
zhou13, zhou14, zhou16}.

In previous works, the physical properties of cluster states in nuclei, such
as the energy spectrum and the charge radii, have been reproduced by
theoretical calculations. In addition, for probing the clustering effects,
observables in various cluster-involved nuclear reactions have been
investigated, such as the monopole transition strengths \cite{yang14, chi15},
the proton induced $\alpha$-knockout cross section \cite{lyu18, lyu19}, and
the $\alpha$-emission cross sections in the fusion-evaporation reactions
\cite{wang19}. In this work, we propose to probe the evolution of the
$\alpha$-clustering structure through the momentum distributions in the
$^{8-10}$Be isotopes. In general, the momentum distributions could be
extracted from the electron scattering reactions \cite{ciofi96}.

In recent decades, the electron scattering observables have been adopted to
study the high-momentum components \cite{ciofi96, hen14, ciofi15, hen17} or
the deformation \cite{wang20, liu19} of nuclei. It is found that the tensor
and short-range components of inter-nucleon correlations, induced by the
nuclear force, dominate at the momentum regions at about 2 fm$^{-1}$ and 4
fm$^{-1}$, respectively \cite{lyu19b}. Comparing to the inter-nucleon
correlations, the $\alpha$-correlation dominates at much lower momentum
region, and hence we may connect the $\alpha$-cluster dynamics to the nucleon
momentum distributions below the Fermi momentum of $1.4$ fm$^{-1}$.
Especially, due to the antisymmetrization effect between $\alpha$-clusters, we
expect that the momentum distribution would be depressed or enhanced in the
compact systems where $\alpha$-clusters have strong spatial overlap with each
other, by analogy with the inter-nucleon contacts in the correlated $NN$ pairs
\cite{zhao19b}. Through the momentum distributions in the $^{8-10}$Be
isotopes, we expect to reveal the evolution of the corresponding clustering
structure, from the dilute gas-like state to the compact one with cluster
dissolution.

For the theoretical description of Beryllium isotopes, we adopt the THSR wave
function developed in our previous works \cite{Lyu15, Lyu16}. In
Ref.~\cite{hirai11}, the momentum distribution of $^{9}$Be was discussed
through the Antisymmetrized Molecular Dynamics (AMD) wave function, but the
center-of-mass component is not treated in the formulation. In this work, the
momentum distributions are predicted by using the analytical derivation
formulated recently in Ref.~\cite{lyu19b}, with subtraction of center-of-mass
motion.

This paper is organized as follows. In Sec.~\ref{sec:formulation}, we
introduce the formulation of the clustering wave functions and nucleon
momentum distributions for the $^{8-10}$Be isotopes. We note that the one-body
momentum distributions of nucleons are investigated in this work, which are
affected by the inter-nucleon and clustering correlations. In
Sec.~\ref{subsec:brink}, the relation between the $\alpha$-$\alpha$ distance
and the nucleon momentum distribution is discussed through Brink type wave
functions of two $\alpha$-cluster system. In Sec.~\ref{subsec:res-thsr}, we
discuss the nucleon momentum distribution for the $^{8-10}$Be isotopes
predicted by using the physical THSR wave functions, and present their
relation with the evolution of $\alpha$-clustering structure. The last
Sec.~\ref{sec:conclusion} contains the conclusion.

\section{Formulations}
\label{sec:formulation}
We introduce briefly the formulations for the clustering wave functions of the
$^{8-10}$Be isotopes and the corresponding nucleon momentum distributions.
Detailed introductions can be found in Refs.~\cite{Lyu15, Lyu16, lyu19} for
the wave functions and in Ref.~\cite{lyu19b} for the nucleon momentum
distributions.

\subsection{Wave functions of $^{8-10}$Be isotopes}
\label{subsec:wave functions}
We start by writing the Brink wave function of the $^{8}$Be nucleus as
\cite{Bri66}
\begin{equation}\label{eq:brink}
	\begin{aligned}
		\Psi^{\textup{Brink}}(^{8}\text{Be}) = \sqrt{\frac{4!\cdot4!}{8!}} \mathcal{A}
		\{\phi_{\alpha_1}(\bm{R}_1)\phi_{\alpha_2}(\bm{R}_2)\},
	\end{aligned}
\end{equation}
where $\mathcal{A}$ is the antisymmetrizer and the wave function of each alpha
cluster $\phi_\alpha(\bm{R})$ is defined as
\begin{equation}\label{eq:alpha}
	\phi_\alpha(\bm{R}) = \frac{1}{\sqrt{4!}} \mathcal{A}
	\{\phi_{1}(\bm{r}_1,\bm{R})\dots\phi_{4}(\bm{r}_4,\bm{R})\}.
\end{equation}
The single nucleon wave functions $\phi(\bm{r}, \bm{R})$ with the position
$\bm{r}$ are defined as the Gaussian wave packets
\begin{equation}\label{eq:wf-nucleon}
  \phi(\bm{r},\bm{R})
  = (2\nu/\pi)^{3/4} e^{-\nu(\bm{r}-\bm{R})^2}\chi_{\sigma,\tau}
\end{equation}
with centroids $\bm{R}$ and width parameter $\nu=0.27$ fm$^{-2}$ to reproduce
the binding energy of $\alpha$-cluster. The component $\chi_{\sigma,\tau}$ is
for the spin $\sigma$ and isospin $\tau$ of each nucleon.

The Brink wave function in Eq.~(\ref{eq:brink}) describes the localized
configuration of two $\alpha$-clusters in the $^{8}$Be nucleus. In physical
nuclei, it is known that the $\alpha$-clusters perform nonlocalized motion,
which is confined by the Gaussian container in the THSR wave function
\cite{zhou14}
\begin{equation}\label{eq:thsr-8be}
	\begin{aligned}
		\Psi^{\textup{THSR}}(^{8}\text{Be})
    & = \int d\bm{R}_1 d\bm{R}_{2}
    \mathcal{G}(\bm{R}_{1},\bm{\beta}_{\alpha})
    \mathcal{G}(\bm{R}_{2},\bm{\beta}_{\alpha})
		\\
    &\qquad\,\times \mathcal{A}\{
      \phi_{\alpha,1}(\bm{R}_1)\phi_{\alpha,2}(\bm{R}_2)
    \},
	\end{aligned}
\end{equation}
where the container function $\mathcal{G}$ is the deformed Gaussian
\begin{equation}\label{eq:Gauss}
  \mathcal{G}(\bm{R},\bm{\beta})=
  \exp \left(-\frac{R_{x}^{2}
    +R_{y}^{2}}{\beta_{xy}^{2}}
  -\frac{R_{z}^{2}}{\beta_{z}^{2}}
  \right).
\end{equation}
Here, the size of the Gaussian container is determined by the width parameters
${\beta}_{xy}$ and ${\beta}_{z}$ in each direction. For the $^{9,10}$Be
isotopes, we introduce additional valence neutrons into the THSR wave function
as
\begin{align}
\Psi^{\textup{THSR}}(^{9}\text{Be})
  & = \int d\bm{R}_1 d\bm{R}_{2}
    \mathcal{G}(\bm{R}_{1},\bm{\beta}_{\alpha})
    \mathcal{G}(\bm{R}_{2},\bm{\beta}_{\alpha})
    \nonumber\\
  &\qquad\,\times \mathcal{A}\{
      \phi_{\alpha,1}(\bm{R}_1)\phi_{\alpha,2}(\bm{R}_2)
      \phi_{9}^{\pi}
    \},\label{eq:9be}\\
\Psi^{\textup{THSR}}(^{10}\text{Be})
  & = \int d\bm{R}_1 d\bm{R}_{2}
    \mathcal{G}(\bm{R}_{1},\bm{\beta}_{\alpha})
    \mathcal{G}(\bm{R}_{2},\bm{\beta}_{\alpha})
    \nonumber\\
  &\qquad\,\times \mathcal{A}\{
      \phi_{\alpha,1}(\bm{R}_1)\phi_{\alpha,2}(\bm{R}_2)
      \phi_{9}^{\pi}\phi_{10}^{\pi}
    \}.\label{eq:10be}
\end{align}
where $\phi_{9,10}^{\pi}$ are the wave functions of valence neutrons occupying
$\pi$-orbits, which are formulated as
\begin{align}
\phi^{\pi}_{9}(\bm{r})
  &=\int d\bm{R}_{9}
    \mathcal{G}(\bm{R}_{9},\bm{\beta}_{n})
    e^{ i\phi_{\bm{R}_{9}}}
    \phi_{n\uparrow}(\bm{r}_{9},\bm{R}_{9}),
    \label{eq:pi-9be}\\
\phi^{\pi}_{10}(\bm{r})
  &=\int d\bm{R}_{10}
    \mathcal{G}(\bm{R}_{10},\bm{\beta}_{n})
    e^{- i\phi_{\bm{R}_{10}}}
    \phi_{n\downarrow}(\bm{r}_{10},\bm{R}_{10}).
    \label{eq:pi-10be}
\end{align}
Here $\phi_{n\uparrow}$ and $\phi_{n\uparrow}$ are neutron wave functions
defined in Eq.~(\ref{eq:wf-nucleon}) with spin up and down, respectively, and
$\phi_{\bm{R}}$ is the azimuthal angle of the neutron generator coordinate
$\bm{R}$. The exponential factors $e^{ \pm i\phi_{\bm{R}}}$ is introduced to
reproduce the negative parity of the $\pi$-orbit \cite{Lyu15}. More details
for the formulation of Eqs.~(\ref{eq:pi-9be}) and (\ref{eq:pi-10be}) can be
found in Ref.~\cite{Lyu15}. The deformation parameters $\bm{\beta}$ are
optimized by variational calculation for each isotope \cite{Lyu15,Lyu16}.

\subsection{Momentum distribution of the wave functions}
The nucleon momentum distribution operator $\hat{n}(\bm{k})$ for mass number
$A$ is defined in the momentum space as
\begin{equation}
\hat{n}(\bm{k})\equiv
  \sum_{i=1}^{A}\delta\left(\bm{k}_{i}-\bm{k}_{\textrm{G}}-\bm{k}\right),
\end{equation}
where $\bm{k}_{i}$ is the single-nucleon momentum and $\bm{k}_{G}$ is the
center-of-mass momentum
\begin{equation}
  \bm{k}_{\textrm{G}}=\sum_{i=1}^{A}\bm{k}_{i}.
\end{equation}
For the AMD wave functions
\cite{enyo12}
\begin{equation}\label{eq:amd}
\Psi^{\text{AMD}}=
  \mathcal{A}\left\{
    \prod_{i=1}^{A} \phi_{i}(\bm{r}_{i},\bm{R}_{i})
  \right\},
\end{equation}
the nucleon momentum distribution with correct treatment for the
center-of-mass motion is written as \cite{lyu19b}
\begin{equation}\label{eq:amd-momentum}
\begin{aligned}
n(\bm{k})
&=\braket{\Psi^{\text{AMD}}|\hat{n}(\bm{k})|\Psi^{\text{AMD}}}\\
&=\sum_{i=1}^{A}n_{i}(\bm{k}),
\end{aligned}
\end{equation}
where $n_{i}(\bm{k})$ is the momentum distribution of each nucleon
\begin{equation}\label{eq:amd-momentum2}
\begin{aligned}
&n_{i}(\bm{k})=
  \left(\frac{1}{2\pi\nu\epsilon}\right)^{3/2}\\
&\qquad\quad\times
  \sum_{j=1}^{A}\exp\left[
      -\frac{1}{2\nu\epsilon}\left(
          \bm{k}-i\nu(\bm{R}^*_{i}-\bm{R}_{j})
        \right)^{2}
  \right]B_{ij}B^{-1}_{ji},
\end{aligned}
\end{equation}
$\epsilon=(A-1)/A$, and $B_{ij}=\braket{\phi_{i}|\phi_{j}}$ is the overlap
matrix of single nucleon states. We note that in this formulation, the
center-of-mass motion is correctly treated, as discussed in
Ref.~\cite{lyu19b}. The momentum distribution $n(\bm{k})$ in
Eq.~(\ref{eq:amd-momentum}) satisfies the normalization condition
\begin{equation}
  \int d\bm{k}\, n(\bm{k})=A.
\end{equation}
Similarly, we define the proton momentum distribution as
\begin{equation}
n^{P}(\bm{k})=
  \sum_{i\in p}n_{i}(\bm{k}),
\end{equation}
where subscript $i$ denotes all the protons. For the superposed AMD wave
function $\ket{\Psi} = \sum_{a}c_{a} \ket{\Psi_{a}}$, the corresponding
nucleon momentum distribution is given as
\begin{equation}\label{eq:amd-sum}
\begin{aligned}
n(\bm{k})=&
  \frac{1}
    {\braket{\Psi|\Psi}}
  \sum_{a,b}
    c_{a}^{*}c_{b}\braket{\Psi_{a}|\widehat{n}|\Psi_{b}},\\
\end{aligned}
\end{equation}
where $c_{a}$ and $c_{b}$ are superposition coefficients.

Mathematically, the Brink wave function in Eq.~(\ref{eq:brink}) can be written
as a special case of the AMD wave function
\begin{equation}\label{eq:brink-amd}
\begin{aligned}
&\Psi^{\textup{Brink}}(^{8}\text{Be}) \\
&\quad= \sqrt{\frac{1}{8!}} \mathcal{A}
  \{\phi_{1}(\bm{r}_{1},\bm{R}_1)\dots\phi_{4}(\bm{r}_{4},\bm{R}_1)\\
&\qquad\qquad\quad\
  \times\phi_{5}(\bm{r}_{5},\bm{R}_2)\dots\phi_{8}(\bm{r}_{8},\bm{R}_2)\},
\end{aligned}
\end{equation}
which has the same format as Eq.~(\ref{eq:amd}). In addition, the THSR wave
functions in Eqs.~(\ref{eq:thsr-8be}), (\ref{eq:9be}), and (\ref{eq:10be}) are
mathematically equivalent to the superposed AMD wave functions. As an example,
we write the case for $^{9}$Be as
\begin{align}\label{eq:9be-amd}
&\Psi^{\textup{THSR}}(^{9}\text{Be})=\nonumber\\
&\quad\int d\bm{R}_1 d\bm{R}_{2}
  \mathcal{G}(\bm{R}_{1},\bm{\beta}_{\alpha})
  \mathcal{G}(\bm{R}_{2},\bm{\beta}_{\alpha})
  \nonumber\times\\
&\qquad\int d\bm{R}_{9}
  \mathcal{G}(\bm{R}_{9},\bm{\beta}_{n})
  e^{ i\phi_{\bm{R}_{9}}}
  \nonumber\times\\
&\qquad\quad\
  \mathcal{A}\{
  \phi_{1}(\bm{r}_{1},\bm{R}_1)\dots\phi_{8}(\bm{r}_{8},\bm{R}_2)
    \phi_{n\uparrow}(\bm{r}_{9},\bm{R}_{9})
  \}.
\end{align}
Hence, the momentum distributions of the Brink or THSR wave functions in this
work can be calculated using the analytical formulations in
Eqs.~(\ref{eq:amd-momentum}) and (\ref{eq:amd-sum}).

\section{Results}
\subsection{Nucleon momentum distribution of the $\alpha$-$\alpha$ system}
\label{subsec:brink}
We first show the nucleon momentum distribution of two free $\alpha$-clusters
as the solid curve in Fig.~\ref{fig:brink-curve}. It is found that the
momentum of free $\alpha$-clusters distributes in a Gaussian form, which is
the Fourier transformation of the $\alpha$-cluster wave function in
Eq.~(\ref{eq:alpha}). We note that this Gaussian distribution is only valid in
low momentum region less than the Fermi momentum $k_{\rm{F}}=1.4$ fm$^{-1}$.
As predicted in Ref.~\cite{lyu19b}, the high-momentum region is dominated by
the tensor and short-range correlations around $k\approx 2$ fm$^{-1}$ and
$k\approx 4$ fm$^{-1}$, respectively. In this work, we focus on the clustering
correlation and choose the effective Volkov $NN$ interaction which does not
include the tensor component or the short-range repulsion, and we limit our
discussion on the momentum with up to $k_{\rm{F}}$ to avoid the effect from the
high-momentum component. In addition, the G3RS term is adopted for the
spin-orbit interaction. Parameters of the interactions are taken from
Ref.~\cite{Ita00}.

\begin{figure}[h]
  \centering

	\includegraphics[width=0.5 \textwidth]{brink-curve.eps}
	\caption{The intrinsic momentum distributions of the $^{8}$Be nucleus
  described by the Brink wave function along the $z$-axis. ``$D_z$'' is the
  relative distance between $\alpha$ clusters in $z$-axis. ``2 free
  $\alpha$-clusters'' denotes the nucleon momentum distribution of two free
  $\alpha$-clusters.}
	\label{fig:brink-curve}
\end{figure}

For the $^{8}$Be nucleus, we calculate the intrinsic momentum distribution
along the $z$-axis described by the $\alpha$-$\alpha$ Brink wave function in
Eq.~(\ref{eq:brink}). This is a toy model with the relative motion of two
$\alpha$-clusters localized around the relative distance
$\bm{D}=\bm{R}_{1}-\bm{R}_{2}$. The $z$-axis is set as the symmetry axis, hence
the relative distance of two $\alpha$-clusters is determined by the parameter
$D_z$. We show in Fig.~\ref{fig:brink-curve} and \ref{fig:brink-xy} the
nucleon momentum distributions of $^{8}$Be with $\alpha$-$\alpha$ distances
$D_z=\{4,3,2,1\}$ fm, which correspond to the evolution from the weak to the
strong overlap between the two $\alpha$-clusters.

In Fig.~\ref{fig:brink-curve}, the solid and dotted curves are used to
illustrate the momentum distribution of two $\alpha$-clusters without
antisymmetrization between them, where the solid curve shows the distribution
of two free $\alpha$-clusters as discussed before, and the dotted one is for
the $\alpha$-$\alpha$ Brink wave function at infinite distance
$(\bm{D}\to\infty)$.  These two curves have the Gaussian shape, but the one of
the Brink wave function has an enhanced tail part and a smaller value at the
zero momentum. This difference arises from the effect of the localization of
the inter-cluster motion in the $\alpha$-$\alpha$ Brink wave function.
Analytically using Eq.~(\ref{eq:amd-momentum2}), we derive the momentum
distribution $n(k)$ of two free $\alpha$-clusters as
\begin{equation}\label{eq:free-2-alpha}
n^{\textrm{Free}}_{2\alpha}(\boldsymbol{k})
  = \left(\frac{8}{3 \pi \nu}\right)^{3 / 2}
  \textup{exp}\left(-\frac{2}{3 \nu} \boldsymbol{k}^2\right),
\end{equation}
where $\epsilon=3/4$ for both $\alpha$-clusters. For the $\alpha$-$\alpha$
Brink wave function at infinite distance $D\to\infty$, we obtain
\begin{equation}\label{eq:brink-2-alpha}
n^{\textrm{Infinite-Brink}}_{2\alpha}(\boldsymbol{k})
  = \left(\frac{16}{7 \pi \nu}\right)^{3 / 2}
  \textup{exp}\left(-\frac{4}{7 \nu} \boldsymbol{k}^2\right),
\end{equation}
where $\epsilon=7/8$. The coefficient in Eq.~(\ref{eq:brink-2-alpha}) is
smaller than the one in Eq.~(\ref{eq:free-2-alpha}), which results in a
smaller value at the center for the dotted curve as compared to the solid
curve shown in Fig.~\ref{fig:brink-curve}.

For the curve with finite $D_z=4$ fm in Fig.~\ref{fig:brink-curve}, a Gaussian
shape, which is similar to the dotted curve with infinite $D_{z}$, is observed
but with a slight depression near $k=0$ fm$^{-1}$. This could be explained by
the small overlap between two $\alpha$-clusters and the nucleons are excited
to the relatively higher momentum because of the inter-cluster
antisymmetrization. By further reducing the $\alpha$-$\alpha$ distance $D_z$,
it is clearly seen that the momentum distribution becomes more peripheral and
a dip structure appears at zero-momentum, which corresponds to a rather
compact system where the nucleon excitation is most significant. This process,
in which the Gaussian form of momentum distribution is broken, shows the
dissolution of two $\alpha$-clusters when they are in large spatial overlap
with each other.

\begin{figure}[h]
	\centering

	\includegraphics[width=\figwidth]{brink-xy.eps}\\
  \caption{The intrinsic nucleon momentum distributions of the
  $\alpha$-$\alpha$ Brink wave function as functions of the $\alpha$-$\alpha$
  distance $D_{z}$ in the $x$-$z$ cross section.}
	\label{fig:brink-xy}
\end{figure}

The nucleon dynamics within the overlapped $\alpha$-clusters can be more
clearly demonstrated by the intrinsic density distribution in the momentum
space. The corresponding density values in the $x$-$z$ cross section are shown
in Fig.~\ref{fig:brink-xy} for different $\alpha$-$\alpha$ distances $D_{z}$.
With large distance $D_{z}=4$ fm, the momentum distribution of two
$\alpha$-clusters is almost spherical, which is similar to the Gaussian
distribution predicted for the free $\alpha$-cluster. As the the inter-cluster
distance is decreased, the spherical symmetry is found to be broken and a
large deformation of momentum distribution emerges. The most intriguing
observation is that in the most compact configuration with $D_{z}=1$ fm, a
``cluster structure'' is observed in the intrinsic momentum distribution of
two $\alpha$-clusters, which is astonishing when considering the fact that the
$\alpha$-clusters are strongly dissolved in the coordinate space under this
short relative distance.

\subsection{Nucleon momentum distribution of Beryllium isotopes}
\label{subsec:res-thsr}
We calculate the nucleon momentum distribution for the $^{8-10}$Be isotopes by
using the corresponding THSR wave function for each nucleus, as formulated in
Sec.~\ref{subsec:wave functions}. In our previous works \cite{fun02, Lyu15,
Lyu16}, the accuracy of the THSR wave functions has been proved by reproducing
the physical properties of the $^{8-10}$Be isotopes, such as the energy
spectra and radii. The Hamiltonian is adopted from Ref.~\cite{Lyu15} and the
THSR wave function is variationally determined for each nucleus. The
$\bm{\beta}$ parameters in the optimized THSR wave functions are listed in
Table \ref{table:para}. The resonant state of the $^{8}$Be nucleus is
simulated by a weakly bounded solution that corresponds to a local energy
minimum in the variation of THSR wave function \cite{fun02}.

\begin{table}[h]
	\begin{center}
    \caption{Components of the deformation parameter $\bm{\beta}$ in the
     optimized THSR wave functions of $^{8-10}$Be isotopes. All units are in
     fm.}
    \label{table:para}

    \begin{tabular*}{6.5cm}{ @{\extracolsep{\fill}} l c c c l }
			\hline
      \hline
			& ${\beta}_{\alpha,xy} $ & ${\beta}_{\alpha,z} $ & ${\beta}_{n,xy}$ &
			${\beta}_{n,z}$\\
			\hline
			$^8$Be & 1.0 & 11.0  & - & - \\
			\hline
			$^9$Be & 0.1 & 4.2 & 2.5 & 2.8 \\
			\hline
			$^{10}$Be & 0.1 & 2.5 & 1.9 & 2.9 \\
			\hline
		\end{tabular*}
	\end{center}
\end{table}

\begin{figure}[h]
	\centering

	\includegraphics[width=\figwidth]{thsr-xy.eps}\\
  \caption{The intrinsic proton momentum distributions of $^{8-10}$Be isotopes
   in the $x$-$z$ cross section.}
	\label{fig:thsr-intrinsic}
\end{figure}

From Table \ref{table:para}, it is clearly shown that the $\bm{\beta}$
parameter shrinks when introducing additional valence neutrons into the
nucleus, which corresponds to an evolution from the dilute cluster gas in
$^{8}$Be to the compact structure in $^{10}$Be. The motion of
$\alpha$-clusters in the Be isotopes is demonstrated by the proton momentum
distribution of $^{8-10}$Be isotopes, as shown in
Fig.~\ref{fig:thsr-intrinsic}. For the dilute $^{8}$Be, we obtain spherical
Gaussian distribution for the protons while clear deformation is observed for
the compact $^{10}$Be nucleus, which is similar to the Brink model discussed
in Fig.~\ref{fig:brink-xy}. We note that the deformation in the THSR wave
function of $^{8}$Be is weaker than the Brink wave functions in
Sec.~\ref{subsec:brink}, which is due to the spatially extended motion of
$\alpha$-clusters in $^{8}$Be described by the THSR wave functions.

\begin{figure}[h]
	\centering

	\includegraphics[width=0.5\textwidth]{proton-curve.eps}\\
  \caption{The nucleon momentum distributions of the two $\alpha$-clusters
  within the $^{8-10}$Be isotopes. Curves denoted with parentheses are for the
  $^8$Be ($0_{1}^+$), $^9$Be ($3/2_{1}^-$), and $^{10}$Be ($0_{1}^+$) nuclei
  in the laboratory frames. Curves denoted with ``intrinsic" are for the
  intrinsic frames before angular momentum projections. }
	\label{fig:proton-curve}
\end{figure}

To obtain the distribution of two $\alpha$-clusters for the $^{8-10}$Be
isotopes in the laboratory frame, we calculate the angle-averaged momentum
distribution on the sphere surface $S$ with the radius $k$, which is defined
as
\begin{equation}
  n(k)=\frac{1}{4\pi k^{2}}
        \int_{|\boldsymbol{k}|=k} n(\boldsymbol{k}) {\rm d} S.
\end{equation}
The THSR wave functions are adopted for the $^8$Be$(0_{1}^+)$, $^9$Be$(3/2_{1}^-)$,
and $^{10}$Be$(0_{1}^+)$ isotopes after angular momentum projection
\cite{horiuchi86}, and the calculated distributions are shown in
Fig.~\ref{fig:proton-curve}. In addition, corresponding curves for the
intrinsic frames are also included for comparison, where only slight
differences before and after angular momentum projection are observed.

For the compact cluster state in $^{10}$Be, the depression at zero-momentum
and the enhanced tail region are observed once again in
Fig.~\ref{fig:proton-curve}, as compared to the Gaussian-like curve of
$^{8}$Be. The depression in the distribution of the two $\alpha$-clusters in
$^{10}$Be is not strong enough to produce a dip structure, but the large
deviation from the $^{8}$Be curve shows clearly the strong antisymmetrization
between $\alpha$-clusters. In $^{9}$Be, relatively weaker $\alpha$-$\alpha$
overlap is found from the intermediate zero-momentum depression.

\begin{figure}[htbp]
	\centering

	\includegraphics[width=0.5\textwidth]{nucleon-curve.eps}\\
	\caption{The total momentum distributions of the $^8$Be$(0_{1}^+)$,
  $^9$Be$(3/2_{1}^-)$, and $^{10}$Be$(0_{1}^+)$ isotopes with THSR wave
  function.}
	\label{fig:nucleon-curve}
\end{figure}

We also calculate the momentum distribution of all nucleons in each isotope,
as shown in Fig.~\ref{fig:nucleon-curve}. The solid curve for the $^{8}$Be
nucleus is not changed from Fig.~\ref{fig:proton-curve}, except the different
amplitude. However, the dip structures appear in the curves of $^{9}$Be and
$^{10}$Be isotopes, with further enhanced tail region, as compared to
Fig.~\ref{fig:proton-curve}. In Ref.~\cite{ciofi96}, similar dip structures
have been observed in experimental results for $^{12}$C and $^{16}$O nuclei.
We note that the dip structures in Fig.~\ref{fig:nucleon-curve} are also
contributed by the $p$-shell occupation by valence neutrons, in addition to
the $\alpha$-$\alpha$ antisymmetrization which is the major origin of dip
structure in Fig.~\ref{fig:brink-curve}. This conjecture is proved by the
decomposition of the momentum distribution in $^{10}$Be, as shown in
Fig.~\ref{fig:components}. Here, the momentum component contributed by the
$\alpha$-clusters and the valence neutrons are calculated by replacing the
summation over $i$ in Eq.~(\ref{eq:amd-momentum}) with the corresponding set
of nucleon indices. In this figure, the contribution from valence neutrons is
presented by the blue dotted curve, in which the node structure of $p$-wave is
clearly observed. It is also found that the valence neutrons contribute mostly
around $k\approx0.5$ fm$^{-1}$, which enhances the tail region in
Fig.~\ref{fig:nucleon-curve}. We note that using the relation $\braket{k}=2\nu
D$ in Ref.~\cite{myo17e}, this $k$ corresponds to the high-momentum excitation
of neutron with imaginary shift of about $D=1$ fm in coordinate space, which
is the mean location of valence neutron measured from the center of mass.

\begin{figure}[htbp]
	\centering

	\includegraphics[width=0.5\textwidth]{decomposition.eps}\\
  \caption{Decomposition of momentum distributions in $^{10}$Be ($0_{1}^{+}$)
  into components contributed by $\alpha$-clusters and valence neutrons.}
	\label{fig:components}
\end{figure}

\section{Conclusion}
\label{sec:conclusion}
We investigated the evolution of clustering structure through the momentum
distributions in the $^{8-10}$Be isotopes, which are calculated by using the
analytical expressions formulated in our recent work. The general features of
the nucleon dynamics within two $\alpha$-cluster system under
antisymmetrization have been discussed via the momentum distribution of a
Brink type $\alpha$-$\alpha$ wave function. For the state with a strong
inter-cluster overlap at small relative distance, we observed a significant
depression with a dip structure at zero-momentum and an enhanced tail at
relatively higher momentum region, which is a clear manifestation for the
nucleon momentum excitation induced by the antisymmetrization between two
$\alpha$-clusters. The most interesting observation is that the momentum
distribution of the extremely compact $\alpha$-$\alpha$ system shows a
``cluster structure'' in the intrinsic frame of momentum space, which is
complementary to its significant $\alpha$-cluster dissolution in the
coordinate space because of the strong antisymmetrization.

For the physical nuclei, we adopted the THSR wave functions for the clustering
states in the $^{8-10}$Be isotopes, which provided successful descriptions for
these nuclei in our previous works. The evolution from the dilute gas-like
state to the compact one with $\alpha$-cluster dissolution was demonstrated by
the calculated nucleon distribution for the two $\alpha$-clusters within the
Be isotopes, where the successive depression at zero-momentum was observed in
the curves of $^{9-10}$Be, as compared to the curve of $^{8}$Be. We also
calculated the momentum distribution of total nucleons for the $^{8-10}$Be
isotopes, and observe a significant depression at zero-momentum for the
compact $^{10}$Be nucleus. We performed the decomposition for the momentum
distribution and found that both the inter-cluster antisymmetrization and the
$p$-orbit occupation by the valence neutrons contribute to the dip structure
at zero-momentum in the $^{10}$Be nucleus. In this study, we propose a new
window for the investigations of $\alpha$-clustering structures in the
$^{8-10}$Be isotopes by connecting the lower region of momentum distributions
with the nuclear clustering structures, which could be extended to the future
studies of heavier nuclear clustering states.

\section*{Acknowledgments}
The authors would like to thank Prof.~Hiroki Takemoto, Dr.~Niu Wan,
Prof.~Masaaki Kimura and Prof.~Bo Zhou for the valuable discussions, and also
the anonymous reviewer for the valuable comments. This work is supported by
the National Key Research and Development Program of China (Grants No.
2018YFA0404403 and No. 2016YFE0129300), the National Natural Science
Foundation of China (Grants No. 11975167, No. 11961141003, No. 11761161001,
No. 11535004, No. 11881240623, No. 11822503 and No. 11575082), the Science and
Technology Development Fund of Macau under Grant No. 008/2017/AFJ, and the
JSPS KAKENHI Grants No. JP18K03660. The author M.L. acknowledges the support
from the RCNP theoretical group for his stay in RCNP and the fruitful
discussions with the members, and the support from the Yozo Nogami Research
Encouragement Funding. The author Q.Z. is grateful to the members of the
nuclear theory group in Hokkaido University for fruitful discussions.

\def\JL#1#2#3#4{ {{\rm #1}} \textbf{#2}, #3 (#4)}
\nc{\PR}[3]     {\JL{Phys. Rev.}{#1}{#2}{#3}}
\nc{\PRC}[3]    {\JL{Phys. Rev.~C}{#1}{#2}{#3}}
\nc{\RMP}[3]    {\JL{Rev. Mod. Phys.}{#1}{#2}{#3}}
\nc{\PRA}[3]    {\JL{Phys. Rev.~A}{#1}{#2}{#3}}
\nc{\PRL}[3]    {\JL{Phys. Rev. Lett.}{#1}{#2}{#3}}
\nc{\NP}[3]     {\JL{Nucl. Phys.}{#1}{#2}{#3}}
\nc{\NPA}[3]    {\JL{Nucl. Phys.}{A#1}{#2}{#3}}
\nc{\PL}[3]     {\JL{Phys. Lett.}{#1}{#2}{#3}}
\nc{\PLB}[3]    {\JL{Phys. Lett.~B}{#1}{#2}{#3}}
\nc{\PTP}[3]    {\JL{Prog. Theor. Phys.}{#1}{#2}{#3}}
\nc{\PTPS}[3]   {\JL{Prog. Theor. Phys. Suppl.}{#1}{#2}{#3}}
\nc{\PTEP}[3]   {\JL{Prog. Theor. Exp. Phys.}{#1}{#2}{#3}}
\nc{\PRep}[3]   {\JL{Phys. Rep.}{#1}{#2}{#3}}
\nc{\PPNP}[3]   {\JL{Prog.\ Part.\ Nucl.\ Phys.}{#1}{#2}{#3}}
\nc{\JPG}[3]    {\JL{J. of Phys. G}{#1}{#2}{#3}}
\nc{\andvol}[3] {{\it ibid.}\JL{}{#1}{#2}{#3}}

redpajama_set_name: RedPajamaArXiv


text:
Q: JS Progress Bar not working in InAppBrowser I am using progressbar.js Progress Bar in a Cordova app.
My cordova app opens a remote html page (same network, but remote to the device) using the 'inAppBrowser' plugin.
All works as expected when I debug/test in Ripple, but when on the Android device, the progress bar just fails to initialise when this page is viewed in the 'inAppBrowser'.
I have tried two different Android devices with the same result.
When the same page with progress bar is viewed on Android in the normal Chrome browser, it works as expected. My app just navigates to this page using the 'inAppBrowser', and that is where it breaks.
All other JS works fine in pages viewed by the 'inAppBrowser', so it is something specific to progressbar.js .
I am not sure how to debug this one, as it's most certainly a javascript error being thrown somewhere, but I can't debug the 'inAppBrowser' page on the Android device at all. (Or better, I don't know how/if I can do it?)
Chrome remote debugging makes use of running your code in Chrome on the Android device, and that is where my page actually runs so I can't see how that will help me.
Any advice?
Thanks

A: Inpect with chrome developer tools chrome://inspect/#devices will allow remote debugging of any page loaded in chrome on the android device, so assuming that you use inappbrowser to load the page into chrome this will allow you to see what is going on.

A: Having looked at the documentation
it looks like you can use:
inAppBrowserRef.addEventListener('loaderror', loadErrorCallBack);

function loadErrorCallBack(params) {

$('#status-message').text("");

var scriptErrorMesssage =
   "alert('Sorry we cannot open that page. Message from the server is : "
   + params.message + "');"

inAppBrowserRef.executeScript({ code: scriptErrorMesssage }, executeScriptCallBack);

inAppBrowserRef.close();

inAppBrowserRef = undefined;

}

redpajama_set_name: RedPajamaStackExchange


text:
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Ancient grains may have been left on the sidelines for a few generations, but they're definitely making a comeback. Brace yourself because what you will learn about ancient grains could possibly and positively change your lifestyle!
Ancient Grains: What You Know Could Save You!
With the recent popularity of chia seeds, quinoa, and amaranth, interest in these ancient grains have since increased. And with my propensity to be drawn to anything 'healthy', I've included quinoa and chia seeds in my diet.
Of course, before I went nuts over these foods, I did my own searching and found more positive revelations about these healthy grains. Not only are they an excellent food source, they're also perfect for my homesteading lifestyle. Read on to know what ancient grains are, what's in it, and why they're still enjoying popularity today.
Ancient grains or heritage grains are a grouping of seed- or fruit-based cereals which trace its roots as far as the beginning of civilization. These heritage grains have been cultivated for thousands of years but didn't achieve the prominence modern grains like corn, rice, and wheat got.
However, unlike modern grains, these grains changed so little over the millennia. Perhaps, farmers preference for faster-growing crops like corn and wheat spared these grains from crop manipulation and selective breeding.
Ancient grains were once important crops in different cultures, though they've lost that distinction over the years. For example, quinoa was once revered by the Incas, farro grains was mentioned in the Bible, and barley and oats were once essential crops during 19th century-Europe.
With their recent rediscovery in the West, their popularity is expected to rise and continue. So much so that they could be our food of tomorrow.
What's The Fuss With Ancient Grains?
With the belief that the Paleo diet is healthier, plus the old-world romanticism of 'slow food', heritage grains are making a revival. While cultivation of these crops has been limited, they are increasingly taking over shelves in stores and the market. You can now easily find pasta, artisan bread, and cereal made from heritage grains.
Luckily, heritage grains have been continually cultivated organically in different communities around the globe. Because these grains remained natural, they are the stuff of healthy-eater dreams. They make a great choice and a healthy addition to grains and carbs since they are less refined and apparently contain a higher amount of essential nutrients.
Organic, higher fiber and nutritional content, gluten-free, and protein-rich are just some of the characteristics ancient grains boast.
Perhaps, being unchanged from selective cropping and biotechnological research, they've managed to be just as they were for the past centuries–just as healthy. In short, ancient grains are non-GMO—great news for health watchers and organic growers.
PALEO CERTIFIED AND PALEO APPROVED SNACKS! The Paleo Healthy Snacks Care Package by The Good Grocer is a collection of 25 grab-n-go snacks. These healthy snacks contain no added sugar and are gluten, grain, soy and dairy free. Each snack is All Natural and free from artificial colors, flavors and preservatives. This Paleo snack box includes a variety of nutrient dense savory and sweet snacks that everyone will love.
PERFECT GIFT FOR ANYONE ON THE PALEO DIET: Paleo snacks that you can trust. Perfect for Cross Fit athletes, students, military, college care packages, get well soon care packages, office break rooms, road trips, college dorms, colleague and client appreciation gifts and more! Great for holidays, birthdays or housewarming gifts too! This Paleo Healthy Snacks Care Package is a fun and hip alternative to gift baskets.
BEAUTIFULLY PACKAGED: Snacks come packaged in our awesome gift box. It's really cute and earth-friendly too! All of our boxes are made from 100% recycled materials. Expertly packed with care in The Good Grocer gift box, this assortment of premium Paleo snacks is sure to impress anyone.
Have You Tried These Ancient Grains?
Technically, not all of the heritage grains are grains, but they have been classified along with grains since they are prepared in the same manner. Sorghum, oats, rye, barley, millet and wild rice are considered grains while buckwheat, chia, amaranth, and quinoa are pseudocereals.
Generally, heritage grains are all said to be more nutritious and healthier than modern grains. They are said to contain more protein, perfect for vegans who need plant-based protein in their diet.
However, the nutritional properties of grains are varied and sometimes unique to a variety. For example, oats have a hefty level of thiamine, chia doubles in fiber content compared to other grains, and spelt has a high level of manganese.
Ancient grains, often referred to as 'super grains', are said to be rich in protein, antioxidants, and omega-3 fatty acids. Ongoing research shows that these healthy grains are likely to decrease the cholesterol level in consumers. It has been also shown to help prevent diabetes and certain cancers, specifically colon and breast cancer.
Some grains are celebrated for being gluten-free, but not all ancient grains are gluten-free. Millet, teff, buckwheat, quinoa, and amaranth are gluten-free, but oats and the ancient kinds of wheat like Khorasan and Spelt are not.
Packaged & Shipped on dedicated Top 11 Allergen Free equipment in Rhode Island by our Specialy trained staff. Country of Origin: USA. Whole Sorghum is organically grown & certified organic from USDA; however Gerbs does not have Organic Certification thus the product will not be packaged as organic.
Gerbs Allergen Declaration: Product is FREE from the following: Gluten, Wheat, Peanuts, Tree Nuts, Soy, Eggs, Milk/Dairy, Fish, Crustacean, Mustard and Sesame.
Gerbs All-Natural Pledge = No Trans-fats, No chemicals, No preservatives, Non-GMO, & Nothing artificial Ever! The way mother nature intended our foods to be, our ingredient list is always very basic without added shelf life stabalizers ie chemicals!
As we have time and again pointed out, every homesteader is practically a survivalist. It should be clear by now that ancient grains are not only hardy, for indeed they have withstood the test of time.
They grow in some of the harshest conditions and they practically thrive on neglect. Most heritage grains are also long-storing, like buckwheat, kamut, and spelt which survive for as long as 30 years or longer when stored properly. With that said, ancient grains are definitely your ultimate survival food item.
Now, I can safely conclude that these ancient food sources could be the food of today and tomorrow. Not only did these foods survive without intervention and manipulation, they've nourished our ancestors and can nourish us just as well.
Get familiar with these ancient grains out in their natural environment so you know where and what to look for in any survival situation. Knowing about ancient grains can definitely save your life, health-wise and survival-wise.
Now you know a great deal more about the 'super grains' ancient grains. Whether you are looking forward to a healthier lifestyle, looking for variety in your food choices, or looking for a survival food item, you got it with ancient grains!
What do you think about the ancient grains? Share your thoughts about it in the comments section below!


text:
\section{Introduction}
\label{introduction}

Polycyclic aromatic hydrocarbons (PAHs) are a large class of conjugated
$\pi$\textendash electron systems of great importance in many research areas, such as
combustion and environmental chemistry, materials science, and astrochemistry.
In the astrophysical context, in particular, PAHs are found in carbonaceous
meteorites \cite{hah88}, in interplanetary dust particles \cite{cle93}, and
are tentatively identified in the atmospheres of Titan and Jupiter
\cite{sag93} and in the coma of Halley's comet \cite{mor94cla04}. In the
study of the interstellar medium (ISM) PAHs have been considered well before
any IR observations of interstellar objects were available. Complex molecular
aggregates with dimensions of $\sim$10~\AA{} were first proposed to contribute to
the interstellar extinction \cite{pla56}. Large condensed\textendash ring hydrocarbons
were later recognised as the ``Platt particles'', precursors of small graphite
grains \cite{don68}.
The similarity between the vibration of C\textendash C and C\textendash H bonds in large fused\textendash ring
aromatic molecules and on the surface of interstellar carbon particles was
then put forward to explain the origin of some emission bands observed
in the near and mid\textendash IR in the spectra of many astronomical objects,
excited by vis\textendash UV photons \cite{dul81}.

The observed spectra required temperatures unattainable in thermal
equilibrium by solid\textendash state particles, suggesting molecule\textendash sized carriers,
subject to large temperature fluctuations.
From abundance, photo\textendash stability, and spectral constraints PAHs and related
species were thus suggested as the most natural carriers of the whole family
of these so\textendash called ``Aromatic Infrared Bands'' (AIBs) observed near 3.3, 6.2,
7.7, 8.6, 11.3, and 12.7~$\mu$m \cite{leg89all89}. Following the stochastic
absorption of single vis\textendash UV photons, a typical PAH quickly converts most
or all of the electronic excitation energy into vibrational energy of
low\textendash lying electronic states (typically the ground\textendash state or the first excited
state).
Due to its low heat capacity \cite{and78sel84} the molecule is transiently
heated to peak temperatures of the order of 10$^3$~K. In a collision\textendash free
environment it then loses its energy through the emission of radiation; IR
fluorescence, in particular, is the proposed explanation for the observed
AIBs \cite{leg89all89}. The observations of the AROME balloon\textendash borne experiment
\cite{gia88ris94} already suggested the ubiquitous presence of AIBs in our
Galaxy as well as in external galaxies. This is now confirmed by the large
wealth of observations made with several space\textendash based missions, such as the
Infrared Space Observatory (ISO)\footnote{The official ISO web page is
\texttt{http://www.iso.vilspa.esa.es}}
and the Spitzer Space
Telescope\footnote{\texttt{http://www.spitzer.caltech.edu}},
which show that the AIBs dominate the near and medium\textendash IR spectrum of many
interstellar and circumstellar objects whose radiation field intensities
differ by several orders of magnitude \cite{bou98pee04}.

PAHs are estimated to account for a substantial fraction of the total
interstellar carbon budget \cite{bou99}, and are seen as an intermediate
stage between the gas and dust phases of the ISM, i.e., large molecules or
very small grains. As such, they are included in some form
in all interstellar dust models \cite{models} and are thought to play a
role also in the chemistry \cite{chemistry}.
They are
expected to exist in a wide variety of environments, in a complex statistical
equilibrium of different charge and hydrogenation states \cite{baklep}.
We remark that in the astrophysical context and, consequently, in
the astrophysical literature, the term ``PAHs'' does not correspond to the
strict definition as given in chemistry textbooks, but should be read
more like ``PAHs and related species'', including partially dehydrogenated
species and molecules in which one or more peripheral hydrogen atoms have
been substituted by other functional groups.
Although several open questions remain opened (their formation mechanisms,
their size distribution, their charge and hydrogenation state, etc.)
this subject has motivated a large number of observational, experimental,
quantum\textendash chemical, and modelling studies \cite{rev}. These, in turn, led to
the further speculation that PAHs could account for other unidentified
spectral features of interstellar origin:
\begin{enumerate}
\item
since large neutral PAHs and all ionised PAHs absorb in the visible, they were
proposed as plausible candidate carriers of (at least) a subset of diffuse
interstellar bands (DIBs) \cite{dibs1}, about 300 absorption
features observed in the near\textendash UV, visible, and near\textendash IR spectra of reddened
stars \cite{dibs2};
\item
mixtures of gaseous PAHs (present as ions, radicals as well as neutral species)
could give an important contribution to the 217.5~nm bump and to the far\textendash UV
rise of the interstellar extinction curve \cite{job};
\item
PAHs are known to be efficient emitters in the visible through fluorescence
and/or phosphorescence mechanisms \cite{bir70}. On the basis of matrix
isolation spectroscopy \cite{mis} and gas\textendash phase experiments \cite{oss}, PAHs
and their cations seem to be good candidates to account for the optical
emission bands observed in peculiar interstellar objects \cite{rr} and
related to some DIBs;
\item
small neutral PAHs such as anthracene
(C$_{14}$H$_{10}$) and pyrene (C$_{16}$H$_{10}$), have been tentatively identified
in the protoplanetary Red Rectangle nebula \cite{bl} and in other ordinary
reflection nebulae \cite{vij05b}, based on the observation of a blue
luminescence (BL), an emission band extending from 360 up to $480$~nm;
\item
PAH dications \cite{dications} are believed to contribute to the extended red
emission (ERE), a broad emission band observed from 540 to about 900~nm in a
large number of dusty interstellar environments \cite{ere}.
\end{enumerate}

\subsection{Collecting the spectral properties of PAHs}

The knowledge of the molecular parameters for a large sample of PAHs in all
their relevant ionisation and hydrogenation states is of fundamental
importance for our understanding of the physics and chemistry of the ISM
\cite{rev}.

In the last few years we have started a long\textendash term project to produce an atlas
of synthetic spectra of \emph{individual} PAHs to be compared with
astronomical observations both in absorption in the visible \cite{mal03} and
in emission in the IR \cite{atlas}. To this end we need the previous knowledge
of some key molecular parameters for a large number of species, and use them
as a basis to run Monte\textendash Carlo simulations \cite{job02,mc} of their
photophysics in specific interstellar environments. Such an approach enabled
us to perform a cross\textendash check for the identification of small neutral PAHs in
the Red Rectangle nebula \cite{bl} by comparing our quantitative prediction
for the IR emission spectrum of each given molecule and the available ISO data
\cite{mul06a}. In addition, these simulations provide an
important preparatory work for the forthcoming Herschel Space Observatory
mission\footnote{\texttt{www.sron.nl/divisions/lea/hifi/directory.html}},
in the attempt to identify specific PAHs through their low\textendash frequency
vibrational modes involving the whole skeleton of the molecule in a
collective vibration \cite{atlas,zha96pir06}. Resolving the rotational
structure of these so\textendash called ``flopping'' or ``butterfly'' modes provides one
more crucial identification element for interstellar PAHs \cite{atlas}.

Taking advantage of the great advances realised over the past years in
computer performances, we have started a systematic theoretical study of
the spectral properties of a large sample of PAHs in different charge states
\cite{mal}. We used in a uniform way well\textendash known and established
quantum\textendash chemical techniques for the study of the electronic
ground\textendash state and excited\textendash state properties needed for astrophysical
applications (see next Section for technical details).

Here we present a homogeneous database of the computed molecular properties
for a sample of 40 different PAHs. For each molecule in the sample and for its
charge states -1, 0, +1 and +2, our spectral database presents in tabular or
visual form the energetic, rotational, vibrational, and electronic properties.
This database is freely accessible on\textendash line and is suitable for further
accumulation of new data. It can be found at the following web\textendash pages:
\begin{itemize}
\item
\textsf{http://astrochemistry.ca.astro.it/database/} \\
at the INAF\textendash Osservatorio Astronomico di Cagliari (Italy) and its mirror site
at:
\item
\textsf{http://www.cesr.fr/$\sim$joblin/database/} \\
at the Centre d'~Etude Spatiale des Rayonnements of Toulouse (France).
\end{itemize}
In Sect.~\ref{database} we describe the molecular properties available and the
theoretical methods we used to obtain them (Sect.~\ref{theory}), the sample of
different species included until present (Sect.~\ref{sample}), and the general
structure of the database (Sect.~\ref{structure}). Section~\ref{future}
presents our concluding remarks.

\section{The database}
\label{database}

\subsection{Molecular properties and theoretical methods}
\label{theory}

Motivated mainly by basic research in astrophysics, a large number of papers
devoted to the experimental \cite{exp1,exp2,exp3,exp4} and theoretical study
\cite{pahs1,pahs2,pahs3} of the spectral properties of PAHs and related
species have appeared in the literature over the last decade.
Due to the large number of electrons in the molecules considered (416 in the
largest one, circumovalene), an \emph{ab initio} study based on the direct
solution of the many\textendash electron Schr\"odinger equation currently has prohibitive
computational costs. We here used the density functional theory (DFT)
\cite{jon89} and its time\textendash dependent extension (TD\textendash DFT) \cite{mar04}, which
are the methods of choice for the study, respectively, of the ground\textendash state
and the excited\textendash state properties of such complex molecules as PAHs.

At present, the computed molecular properties of individual PAHs that can be
found in our database are:
\begin{enumerate}
\item \label{item1} harmonic vibrational frequencies and integrated IR
absorption cross\textendash sections;
\item \label{item2} rotational constants at the optimised ground\textendash state
geometry;
\item \label{item3} electron affinities;
\item \label{item4} first and second ionisation energies;
\item \label{item5} permanent dipole moments;
\item \label{item6} vis\textendash UV photo\textendash absorption cross\textendash sections up to $\sim30$~eV.
\item \label{item7} static dipole polarisabilities;
\end{enumerate}
These are the most relevant molecular parameters needed for astrophysical
purposes. The set of PAHs for which \emph{all} of the above data are
simultaneously available from laboratory experiments is relatively small.
Thanks to the ever increasing computational power available, the use of
quantum\textendash chemical tools is the next best alternative and can be furthermore
useful as a guide for future experimental work.

All calculations for the electronic ground\textendash state have been performed using
the Density Functional Theory module of the Gaussian\textendash based code
\textsc{nwchem} \cite{str05}. In particular, we employed the widely used
hybrid B3LYP functional, a combination of the Becke's three parameters
exchange functional \cite{bec93} and the Lee\textendash Yang\textendash Parr gradient\textendash corrected
correlation functional \cite{lee88}. We first optimised the ground\textendash state
geometries using the relatively inexpensive \mbox{4\textendash31G} basis set, followed
by the full vibrational analyses (item~\ref{item1}) to confirm the geometries
obtained to be global minima on the potential energy surface. The combination
\mbox{B3LYP/4\textendash31G} was shown to give good results in the study of the
vibrational properties of PAHs, scaling all frequencies by the same empirical
scale\textendash factor \cite{lan96,bau97}. We thus adopted the same uniform scaling
procedure derived by these authors for all of the PAHs under study in their
-1, 0, +1 and +2 charge states. Since for  open\textendash shell systems analytical
second derivatives are not yet implemented in the version of \textsc{nwchem}
that we used (version 4.7), we performed the vibrational analyses for
all the anions, cations, and dications triplets, using the \textsc{Gaussian03}
quantum chemistry package \cite{g03}.

We then started from the optimal geometries and the corresponding
self consistent field solution obtained in the previous step to refine the
optimisation with the larger \mbox{6\textendash31+G$^\star$} basis\textendash set, a valence double
zeta basis set augmented with $d$ polarisation functions and $s$ and $p$
diffuse functions to each carbon atom \cite{fri84}. The rotational constants
(item~\ref{item2}) have been derived from the optimised
B3LYP/\mbox{6\textendash31+G$^\star$} geometries.
Although basis set convergence is not yet expected at this level, in view of
the large systems under study some compromise between accuracy and
computational costs had to be made.

We thus computed the adiabatic and vertical values of both the electron
affinity (item \ref{item3}) and the first and second ionisation energy
(item \ref{item4}). Adiabatic values are evaluated as the difference between
the total energies of the neutral and the corresponding ion minima,
respectively; these quantities, therefore, take into account the structural
relaxation of the molecule following the ionisation process. The vertical
values, computed at the optimised geometry of the neutral molecule, neglect
structural relaxation but include wavefunctions relaxation due to the addition
of one electron  (anion) or the removal of one (cation) or two (dication)
electrons.
All neutral and singly\textendash ionised species were computed as singlet and doublet,
respectively, while for dications we computed both their singlet and triplet
ground states. This enabled us to predict the relative energies of electronic
states having different multiplicities. For almost all of the molecules under
study (34 out of a total of 40), our calculations predict the dication overall
ground\textendash state to be the singlet \cite{mal06}.
Whenever available, we list the experimental electron affinities and single
ionisation energies as reported in the NIST Chemistry WebBook \cite{lia05}.
As to the second ionisation energies we report the values obtained in the only
available experimental measurements of the second ionization energies of the
PAHs we considered \cite{tob94,sch01,den06}. For polar species we list also
the corresponding permanent dipole moments (item \ref{item5}), which might be
relevant for the astronomical search of PAHs in the microwave region through
their pure rotational spectrum \cite{lov05}.

Concerning item~\ref{item6} in the above list, we already presented a
collection of individual vis\textendash UV photo\textendash absorption spectra computed in a
uniform way for a large sample of anionic, neutral, cationic, and dicationic
PAHs \cite{mal}.  We used a real\textendash time real\textendash space implementation of the
Time\textendash Dependent Density Functional Theory (TD\textendash DFT) \cite{yab99} as given in
the \textsc{octopus} computer code \cite{mar03}.
Our results are in good agreement with the only available measurements of
photo\textendash absorption cross\textendash sections of neutral PAHs from the visible to
the vacuum\textendash UV spectral domain \cite{job}. While experimental spectra in the
far\textendash UV are needed for a similar direct validation for PAH ions, our
theoretical data for neutral species reproduce the overall far\textendash UV behaviour,
including the broad absorption peak dominated by $\sigma^*\gets\sigma$ transitions, which
matches well both in position and width. The computed vertical excitations of
$\pi\to\pi^\star$ character falling in the low\textendash energy range are expected to be precise
to within a few tenths of an eV, which are the typical accuracies of TD\textendash DFT
calculations using the currently available exchange\textendash correlation functionals
\cite{hir99,hir03}. With respect to other theoretical studies of the
electronic excitations of PAHs, the main step forward achieved by our work is
represented by the spectral range covered, that extends up to $\sim$30~eV. This
piece of information has proven to be particularly useful for astrophysical
modelling when laboratory data are missing \cite{mul06a,mul06b,mul06c}. On the
other hand, the main drawback is that we do not obtain independent information
for each excited electronic state, such as its symmetry and its description in
terms of promotion of electrons in a one\textendash electron picture. With the
\textsc{octopus} code we also obtain the static dipole polarisabilities
(item \ref{item7}), whose knowledge is important in the study of chemical
reactivity.

More technical details about the calculations
we performed with both the \textsc{octopus} and \textsc{nwchem} codes, as well
as on the expected accuracy achieved, can be found elsewhere \cite{mal}.

\subsection{The sample of molecules}
\label{sample}

A wide range of PAHs and related species are thought to exist in the ISM
\cite{tie05}. The total of 40 molecules selected in this work, ranging in size
from naphthalene and azulene (C$_{10}$H$_{8}$) to circumovalene (C$_{66}$H$_{20}$),
cover an ample range of structures inside the two large classes of
pericondensed and catacondensed species. Although non\textendash compact PAHs are
expected to be less stable than compact ones with the same number of benzenoid
rings, we extended the present study to both classes, including also large
oligoacenes such as pentacene (C$_{22}$H$_{14}$) and hexacene (C$_{26}$H$_{16}$).
In addition we included some PAHs with five\textendash membered rings, namely fluorene
(C$_{13}$H$_{10}$), fluoranthene (C$_{16}$H$_{10}$) and corannulene (C$_{20}$H$_{10}$).
Whenever possible, the known symmetry of the molecular geometry was
assumed during calculations, e.g.,
C$_{2v}$ for phenanthrene (C$_{14}$H$_{10}$), C$_{2h}$ for chrysene (C$_{18}$H$_{12}$),
D$_{3h}$ for triphenylene (C$_{18}$H$_{12}$), D$_{2h}$ for ovalene (C$_{32}$H$_{14}$),
D$_{6h}$ for coronene (C$_{24}$H$_{12}$), hexabenzocoronene (C$_{42}$H$_{18}$) and
circumcoronene (C$_{54}$H$_{18}$) and so forth).
In the case of some of the molecules with a more than 2\textendash fold
symmetry axis, symmetry breaking was observed upon single and double
ionization, as expected from Jahn\textendash Teller distortion \cite{kat99}.
More specifically, we obtained a symmetry reduction from D$_{6h}$ to D$_{2h}$
point group for coronene, hexabenzoronene, and circumcoronene, from  D$_{3h}$
to C$_{2v}$ for triphenylene and from C$_{5v}$ to  C$_{s}$ for corannulene.

\begin{comment}
The complete set of the 40 molecules considered and their symmetry point
groups are reported in Table~\ref{mols}.

\begin{table}
\begin{center}
\caption{\label{mols}
Complete set of different PAHs considered in this work.}
\begin{tabular}{lc}
\hline \hline
\noalign{\smallskip}
Name (Formula) & Symmetry group \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
Azulene (C$_{10}$H$_{8}$) & D$_\mathrm{2h}$\\[-4pt]
Naphthalene (C$_{10}$H$_{8}$) &  D$_\mathrm{2h}$\\[-4pt]
Acenaphthylene (C$_{12}$H$_{8}$)& C$_\mathrm{2v}$\\[-4pt]
Biphenylene (C$_{12}$H$_{8}$) & D$_\mathrm{2h}$ \\[-4pt]
Acenaphthene (C$_{12}$H$_{10}$)& C$_\mathrm{2v}$\\[-4pt]
Fluorene (C$_{13}$H$_{10}$)& C$_\mathrm{2v}$\\[-4pt]
Anthracene (C$_{14}$H$_{10}$) & D$_\mathrm{2h}$\\[-4pt]
Phenanthrene (C$_{14}$H$_{10}$)& C$_\mathrm{2v}$\\[-4pt]
Pyrene (C$_{16}$H$_{10}$) & D$_\mathrm{2h}$\\[-4pt]
Tetracene (C$_{18}$H$_{12}$) & D$_\mathrm{2h}$\\[-4pt]
Chrysene (C$_{18}$H$_{12}$)& C$_\mathrm{2h}$\\[-4pt]
Triphenylene (C$_{18}$H$_{12}$)& D$_\mathrm{3h}$\\[-4pt]
Benzo[a]anthracene (C$_{18}$H$_{12}$)& C$_\mathrm{s}$\\[-4pt]
Corannulene (C$_{20}$H$_{10}$)& C$_\mathrm{5v}$\\[-4pt]
Benzo[a]pyrene (C$_{20}$H$_{12}$)& C$_\mathrm{s}$\\[-4pt]
Benzo[e]pyrene (C$_{20}$H$_{12}$)& C$_\mathrm{2v}$\\[-4pt]
Perylene (C$_{20}$H$_{12}$) & D$_\mathrm{2h}$\\[-4pt]
Anthanthrene (C$_{22}$H$_{12}$)& C$_\mathrm{2h}$\\[-4pt]
Benzo[g,h,i]perylene (C$_{22}$H$_{12}$) & D$_\mathrm{2h}$\\[-4pt]
Pentacene (C$_{22}$H$_{14}$) & D$_\mathrm{2h}$\\[-4pt]
Coronene (C$_{24}$H$_{12}$) & D$_\mathrm{6h}$\\[-4pt]
Dibenzo[b,def]chrysene (C$_{24}$H$_{14}$) & C$_\mathrm{2h}$\\[-4pt]
Dibenzo[cd,lm]perylene (C$_{26}$H$_{14}$) & D$_\mathrm{2h}$\\[-4pt]
Hexacene (C$_{26}$H$_{16}$) & D$_\mathrm{2h}$\\[-4pt]
Bisanthene (C$_{28}$H$_{14}$) & D$_\mathrm{2h}$\\[-4pt]
Benzo[a]coronene (C$_{28}$H$_{14}$) & D$_\mathrm{2h}$\\[-4pt]
Dibenzo[bc,kl]coronene (C$_{30}$H$_{14}$) & D$_\mathrm{2h}$\\[-4pt]
Dibenzo[bc,ef]coronene (C$_{30}$H$_{14}$) & C$_\mathrm{2v}$\\[-4pt]
Terrylene (C$_{30}$H$_{16}$) & D$_\mathrm{2h}$\\[-4pt]
Ovalene (C$_{32}$H$_{14}$) & D$_\mathrm{2h}$\\[-4pt]
Tetrabezo[bc,ef,kl,no]coronene (C$_{36}$H$_{16}$) & D$_\mathrm{2h}$\\[-4pt]
Circumbiphenyl (C$_{38}$H$_{16}$) & D$_\mathrm{2h}$\\[-4pt]
Circumanthracene (C$_{40}$H$_{16}$) & D$_\mathrm{2h}$\\[-4pt]
Quaterrylene (C$_{40}$H$_{20}$) & D$_\mathrm{2h}$\\[-4pt]
Circumpyrene (C$_{42}$H$_{16}$) & D$_\mathrm{2h}$\\[-4pt]
Hexabenzocoronene (C$_{42}$H$_{18}$)& D$_\mathrm{6h}$\\[-4pt]
Dicoronylene (C$_{48}$H$_{20}$) & D$_\mathrm{2h}$\\[-4pt]
Pentarylene (C$_{50}$H$_{8}$) & D$_\mathrm{2h}$\\[-4pt]
Circumcoronene (C$_{54}$H$_{18}$)& C$_\mathrm{6h}$\\[-4pt]
Circumovalene (C$_{66}$H$_{20}$) & D$_\mathrm{2h}$\\[-4pt]
\hline
\end{tabular}
\end{center}
\end{table}
\end{comment}

Although
some studies show interstellar PAHs to be on average larger than the species
we considered \cite{bou99}, we restricted ourselves to molecules containing
up to a maximum of 66~carbon atoms, since computational costs steeply scale
with dimensions (e.g., about 3000 CPU hours on an IBM SP5 for the
circumovalene ions, which were the most expensive species considered).

\subsection{General structure of the database}
\label{structure}

The main\textendash pages \textsf{http://astrochemistry.ca.astro.it/database/} and \\
\textsf{http://www.cesr.fr/$\sim$joblin/database/} contain the full list of
molecules considered; they are ordered by incrasing masses. Direct links
to the official web\textendash pages of the packages and computing resources used are
given.
A separate page can then be accessed for each given species. The latter
includes a graphical representation of the selected molecule and the links to
the following pages:
\begin{enumerate}
\item[(i)]
The corresponding NIST web\textendash page (if available).
\item[(ii)]
The html table of the harmonic vibrational analyses for each of the four
charge states considered (item \ref{item1} in the list of the previous
section); a pdf version of the table can also be downloaded.
\item[(iii)]
The table of the general parameters of the molecule (items \ref{item2} to
\ref{item6}) with the addition of its symmetry properties
(symmetry properties, irreducible representations $\Gamma_\mathrm{3N}$ and
$\Gamma_\mathrm{vib}$, and IR\textendash active modes).
\item[(iv)]
The plots of the vis\textendash UV photo\textendash absorption cross\textendash sections (item \ref{item7})
for each charge\textendash state; all of the spectra can also be downloaded in ascii
format.
\item[(v)]
A list with some of the more representative papers related to the given
molecule; more than 500 references are currently included, each of
them pointing to the official web\textendash page of the journal (when available).

\end{enumerate}

As to the last point, in particular, many references are likely to have
been missed in our bibliographic search. We will be thankful to anyone who
will send us more relevant references.

\subsection{Related links}

There are several other internet resources reporting relevant data and
bibliographic references on the spectral properties of PAHs. Among them, we
refer the reader to the official web-page of the Astrochemistry Laboratory
at NASA Ames Research Center \textsf{http://www.astrochemistry.org/}
and the Polycyclic Aromatic
Hydrocarbon Structure Index \textsf{http://ois.nist.gov/pah/} and the
Chemistry WebBook \textsf{http://webbook.nist.gov/chemistry/}
of the National Institute of Standards and Technology. Up to date references
and direct links to personal web pages can also be found in the web-page
\textsf{http://www.astrochymist.org/}, which is devoted to the field of
astrochemistry in general.

\section{Future perspectives}
\label{future}

In the near future we will extend our database towards two main directions.
We will include larger PAHs and, at the same time, we will study some
derivatives of the molecules already considered. In particular, we plan to
study de\textendash hydrogenated \cite{vuo00,dul06} or super\textendash hydrogenated species
\cite{ber96sno98}, and species including heteroatoms such as oxygen
\cite{bau98b}, nitrogen \cite{polar} or organometallic compounds
\cite{szc06,ell99}.
Better levels of theory (e.g., larger bases and/or newly developed
exchange\textendash correlation functionals) will be employed for the calculation of some
of the molecular
properties considered. In addition, we plan to compute other poorly known
molecular parameters, such as the anharmonic correction to vibrational terms
and rotational constants \cite{bar} and the vibronic structure of electronic
absorption and emission spectra \cite{die}. On a parallel track, all of
these data will be used to produce synthetic spectra to compare with actual
astronomical observations. Of course, external contributions to be included
in the database, either experimental or theoretical results, are also very
welcome. We therefore invite anybody interested in having their results
made available on our database to submit their contributions following the
contact links in the on\textendash line web\textendash pages; the appropriate
citation to the owner of the data will be reported.

\section*{Acknowledgements}
G.~Malloci aknowledges the financial support by INAF\textendash Ossevatorio Astronomico
di Cagliari and the ``Minist\`ere de la Recherche''. We warmly thank the authors
of \textsc{octopus} for making their code available under a free license. We
acknowledge the High Performance Computational Chemistry Group for the use of
\textsc{nwchem},
A Computational Chemistry Package for Parallel Computers, Version~4.7
(2005), PNNL,  Richland, Washington, USA. Part of the simulations were
carried out at CINECA (Bologna) and CALMIP (Toulouse)
supercomputing facilities.


Because of its appeal, Rehoboth is clearly being targeted now as a high potential and vulnerable jurisdiction for investor-owned mini-hotels and mega-houses in the established residential areas of the city. . . The most obvious choice to actually protect residentially zoned neighborhoods is to add a maximum occupancy limit regardless of the numbers of bedrooms. . . Henlopen Acres' action [capping occupancy in any house at 12] was an eloquent statement about the nature of residential neighborhoods and their preservation, not a compromise about balancing neighborhoods with the ambitions and business plans of would-be investors in mini-hotels in their neighborhoods. The Acres just said "no" to mini-hotels. In Rehoboth, unlike Henlopen Acres, we include, and are proud of, our commercial areas and the operators of our businesses, just as we are of our neighborhoods. Still, this immediate discussion about occupancy limitsis primarily about neighborhoods in Rehoboth and I trust our elected representatives will treat their protection as a priority in the actions they take.
"The whole character of Rehoboth is being changed by the mini-hotel," said James Horty, who owns a home on Henlopen Avenue."
From a Letter to the Editor, Cape Gazette, by Stan Heuisler, July 17, 2015.


text:
Posts Tagged 'the fed'
The Federal Reserve's Last Stand
Texas Straight Talk
Rep. Ron Paul (R) – TX 14
The remarkable confluence of recent events has brought unprecedented but very welcome attention to both U.S. monetary policy and the global political economy in general. First, Federal Reserve Board Chairman Ben Bernanke recently announced that the Fed would embark upon another round of monetary easing by purchasing $600 billion worth of U.S. treasury debt. This amounts to admission that markets have run out of patience with our profligacy and therefore our own central bank literally must serve as the buyer of last resort for treasury debt.
Second, World Bank President Robert Zoellick openly suggested that gold could play a helpful role in the global monetary system by serving as reference against more volatile fiat currencies. This is almost heresy coming from a neoconservative globalist like Mr. Zoellick. It hints at an obvious but unspoken truth that is anathema to politicians and central bankers alike, namely, that gold could be viewed as money.
Finally, Mr. Obama attended the G20 summit in South Korea last week and found a very chilly reception for his vision of American economic policy. Mr. Obama argued for continued worldwide stimulus via continued debasing of the U.S. dollar to bolster American exports. Several powerful European and Asian finance ministers however rejected this approach out of hand as nothing short of a currency war. They are committed to austerity measures at home and don't want to let the U.S. simply monetize its past sins at their expense.
All these events culminated in a tremendous amount of political and media scrutiny aimed at the Fed. Ordinary Americans are demanding answers and accountability and they are putting heat on their political representatives in Washington to end the cozy independence from congressional oversight the Fed has enjoyed for so long.
In the 35 years I have been studying, speaking and writing about monetary policy I have never before seen Congress or the financial press pay much attention to the Fed. Monetary policy has always been considered boring on Capitol Hill, something left to remote policy wonks far away from the den of presidential or congressional politics. Congress always has been eager to leave Fed governors well alone with no oversight or accountability as long as they played along and papered over the growing budget deficits.
But it's amazing what a global economic meltdown will do to the political and media landscape. In just two short years the Fed has become the hot topic and a lightning rod for criticism. While it is gratifying to see so many formerly uninterested politicians, economists, talk show hosts and pundits suddenly rally to attack the Fed, one can only wonder whether they truly understand that central banking is inherently incompatible with our Constitution and a free market economy.
In other words, it's not enough to show outrage at the latest Fed action or argue about the relative merits of Mr. Bernanke compared to his predecessors. To reclaim our dollar and our economy Americans must oppose central banking per se. Fiat currencies cannot be reformed or managed. They are fundamentally subject to ruinous debasement courtesy of the political and ruling class. History shows that this is true in all nations, at all times.
Posted in Congress, Federal Reserve, House of Representatives, Monetary Policy | Tags: End the Fed, Federal Reserve, Monetary Policy, QE2, Ron Paul, the fed | Comments Off on The Federal Reserve's Last Stand
Fed Independence or Fed Secrecy?
Texas Straight Talk – A weekly column
Last week I was very pleased that hearings were held on the independence of the Federal Reserve system. My bill HR 1207, known as the Federal Reserve Transparency Act, was discussed at length, as well as the general question of whether or not the Federal Reserve should continue to operate independently.
The public is demanding transparency in government like never before. A majority of the House has cosponsored HR 1207. Yet, Senator Jim DeMint's heroic efforts to attach it to another piece of legislation elicited intense opposition by the Senate leadership.
The hearings on Capitol Hill provided us with a great deal of information about the types of arguments that will be levied against meaningful transparency and how the secretive central bankers will defend the status quo that is so beneficial to them.
Claims are made that auditing the Fed would compromise its independence. However, by independence, they really mean secrecy. The Fed clearly cherishes its vast power to create and spend trillions of dollars, diluting the value of every other dollar in circulation, making deals with other central banks, and bailing out cronies, all to the detriment of the taxpayer, and to the enrichment of themselves. I am happy to challenge this type of "independence".
They claim the Fed is endowed with special intellectual abilities with which to control the market and that central bankers magically know what the market needs. We should just trust them. This is patently ridiculous. The market is a complex and intricate thing. No one knows what the market needs other than the market itself. It sends signals, such as prices, that should be reacted to and respected, not thwarted and controlled. Bankers are not all-knowing and cannot ignore the rules of supply and demand. They might act as if they are, but their manipulation of the market just ends up throwing it wildly off balance, which gives us the boom and bust cycles.
They claim the Fed must remain apolitical. No organization is apolitical that relies on the President to appoint the Chairman. In fact, it is subject to the worst sort of politics – power to create trillions of dollars and affect the value of every dollar in the country without the accountability of direct elections or meaningful oversight! The Fed typically enacts monetary policy that is favorable to particular administrations close to elections, to the detriment of long term considerations. They do this partly because of the political appointee process for the Chairmanship.
The only accountability the Federal Reserve has is ultimately to Congress, which granted its charter and can revoke it at any time. It is Congress's constitutional duty to protect the value of the money, and they have abdicated this responsibility for far too long. This was the issue that got me involved in politics 35 years ago. It is very encouraging to finally see the issue getting some needed exposure and traction. It is regrettable that it took a crisis of this magnitude to get a serious debate on this issue.
Posted in Federal Reserve | Tags: financial stability, HR 1207, Monetary Policy, the fed, Transparency | Comments Off on Fed Independence or Fed Secrecy?
Fed Intends to Hire Lobbyist in Campaign to Buttress Its Image
By Robert Schmidt
June 5 (Bloomberg) — The Federal Reserve intends to hire a veteran lobbyist as it seeks to counter skepticism in Congress about the central bank's growing power over the U.S. financial system, people familiar with the matter said.
Linda Robertson currently handles government, community and public affairs at Johns Hopkins University in Baltimore, and headed the Washington lobbying office of Enron Corp., the energy trading company that collapsed in 2002 after an accounting scandal. She was also an adviser to all three of the Clinton administration's Treasury secretaries.
Robertson would help the Fed manage relations with lawmakers seeking greater oversight of a central bank that has used emergency powers to prevent Wall Street's demise. While she wasn't tied to Enron's fraud, her association with the firm may raise questions, analysts said.
"Some members of Congress think there are votes in attacking the Fed" after it "unnecessarily and unwisely entangled monetary policy with fiscal policy," said former St. Louis Fed President William Poole. "The Fed is going to have a tricky time of unwinding what has been done" and will need to "keep in touch with members of Congress more thoroughly," said Poole, now senior fellow with the Cato Institute in Washington.
Robertson served under Treasury Secretaries Lawrence Summers, Robert Rubin and Lloyd Bentsen. She didn't return calls seeking comment.
Summers Tie
Summers now heads the White House National Economic Council. Along with Treasury Secretary Timothy Geithner, he is leading Obama administration efforts to broaden the economic rescue and overhaul financial regulation. He has been mentioned as a possible successor to Fed Chairman Ben S. Bernanke should Bernanke not be renominated when his term ends in January.
Robertson is likely to start at the Fed in July and have the title of senior adviser to the Board of Governors, the people familiar with the situation said.
She was considered for a senior post under Geithner at the Treasury but ran up against the Obama administration's restrictions on hiring lobbyists, the people said.
"People have been asking whether the Fed is capable of getting its job done right," said Lynn Turner, a former chief accountant at the Securities and Exchange Commission. "Hiring a former lobbyist from Enron will surely make one wonder."
Lawmaker Pressure
Robertson would confront a range of issues in the newly created position. Congress is looking to subject the Fed to more scrutiny, and some lawmakers have suggested that district bank presidents should be confirmed by the Senate.
Some legislators have also expressed opposition to the Obama administration's attempt to make the Fed the regulator in charge of financial companies deemed too-big-to-fail.
In addition, the central bank has been become a target to some members of Congress who've posted online videos of their interrogations of Fed officials during public hearings.
One YouTube clip, of Florida Democratic Representative Alan Grayson's grilling of Inspector General Elizabeth Coleman, has garnered almost 500,000 views in about a month.
Robertson is expected to advise the Fed on communications strategy, the people said. In recent months, Bernanke has pushed to make the traditionally secretive institution more open. He's done a television interview with CBS's "60 Minutes" program and taken questions from reporters at a National Press Club function in Washington.
According to her biography on the Johns Hopkins Web site, Robertson has spent more than 25 years working on federal legislative issues.
While Robertson's Hopkins biography makes no mention of her work at Enron, federal disclosure documents show she joined the company in 2000 after working at the Treasury. Robertson, who signed some of the forms, said she lobbied on energy and tax issues.
Posted in Federal Reserve | Tags: money, the fed, Transparency | Comments Off on Fed Intends to Hire Lobbyist in Campaign to Buttress Its Image


Chicken and Waffles Casserole - Frugal Mom Eh!
This Chicken and Waffles Casserole features hand breaded, oven fried chicken and waffles layered together and baked for an amazing breakfast recipe your whole family will love!
With Easter and March break coming up there is ample opportunity to serve my family amazing breakfast and brunches.
I decided to shake it up a little bit and turn chicken and waffles into a dish perfect for serving at brunch by oven frying my fresh Canadian chicken and turning it into a Chicken and Waffles Casserole. It's great to make the night before and then just pop it into the oven in time to enjoy for a family brunch.
The best part about this casserole is that the oven fried chicken retains its flavour and crunch, and is so much healthier than traditionally fried chicken. Mmmm. So satisfying!
I was actually browsing around Chicken.ca, looking for other delicious chicken breakfast recipes and I found some others to check out including Chicken and Egg Ramekins, Chicken and Cheese Breakfast Muffins, Savoury Asparagus & Chicken Bread Pudding and Speedy Breakfast Quesadilla. Chicken and breakfast? Who knew!
Line two baking sheets with parchment paper and spray with the cooking spray.
Mix together the flour, chilli powder, garlic powder, mustard powder, a pinch each of salt and pepper in a shallow bowl.
Crack 3 eggs into another shallow bowl and beat well.
Place the panko breadcrumbs into a third shallow bowl.
Toss the chicken in the flour to coat, then dip into the egg, and then place in the panko, turning to coat. Place onto the prepared baking sheets and repeat with the rest of the chicken.
Spray the chicken with the cooking spray then bake, turning the chicken over halfway through, for about 20 minutes or until the chicken is cooked through. Set aside.
Grease an 8×13 inch baking dish.
Add half of the cubed waffles in a single layer.
Top with half of the chicken and 1/2 of the cheese then layer the remaining waffles and chicken and cheese.
Whisk together 6 eggs, milk, maple syrup, a pinch each of salt,and pepper in a medium bowl until combined then pour the egg mixture evenly over the chicken and waffles.
If desired refrigerate overnight (or bake immediately).
Spray the chicken with the cooking spray then bake, turning the chicken over halfway through, for about 20 minutes or until the chicken is cooked through.
Grease an 8x13 inch baking dish.
This looks really yummy and I'm going to have to try it soon!
Wow,what an interesting dish looks delicious !
I've never done anything like this….definitely curious! I'm pretty sure my guys would love it….
I had never thought of having chicken for breakfast but we have bacon occasionally so why not chicken? I love your recipe and I know I will try it. Thank you so much for thls and other recipies.
Oh wow this looks so good, I would love to make this some time, would be a great weekend dinner!!
ELizabeth, I am planning this for Mother's Day brunch.Since I like the texture of the dish in the pictures, can you please tell me if you let this sit overnight with the egg mixture or exactly when did you compile 100% of the ingredients together. I do not want the chicken to dry out so please solve this dilemma, Elizabeth. Thank you!
When I made it for this post I did not let it sit at all, I baked the chicken and then compiled all the ingredients and threw it in the oven.
I just had my first experience with chicken & waffles at a pub last month & it was heavenly!! It is now a favorite for me. Honestly I've never seen it in a casserole & I know I will love this 100%!
Hi Elizabeth, this looks delicious. Do you have any idea how it reheats if I were to make this ahead for the week?


text:
News tagged with strontium
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(Phys.org)—A combined team of researchers from Columbia University in the U.S. and the University of Warsaw in Poland has found that there appear to be flaws in traditional theory that describe how photodissociation works. ...
Fukushima site still leaking after five years, research shows
Five years after the Fukushima nuclear accident, there is still no U.S. federal agency responsible for studies of radioactive contaminants in the ocean. But scientific data about the levels of radioactivity in the ocean ...
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Mechanical properties of nanomaterials can be altered due to the application of voltage, University of Wyoming researchers have discovered.
Storage advance may boost solar thermal energy potential
Engineers at Oregon State University have identified a new approach for the storage of concentrated solar thermal energy, to reduce its cost and make it more practical for wider use.
Energy & Green Tech
New study highlights valuable tool for studying living and extinct animals
University of Cincinnati scientists are reporting a significant finding that could open up entirely new explorations in the fields of ecology and paleoecology.
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A team of physicists has defied conventional wisdom by inducing stable ferroelectricity in a sheet of strontium titanate only a few nanometers thick.