text:
\section{Introduction}

It is possible for an atom or a molecule to eject a bound electron and become ionized due to the scattering of a slow, heavy particle, such as weakly interacting massive particle (WIMP) dark matter. Such electrons can be detected, although the momentum transfer values involved in this process are very high on the atomic scale.
This type of scattering is particularly relevant for the analysis of the anomalous DAMA annual modulation signal.

The DAMA Collaboration uses a scintillation detector to search for possible dark matter (DM) interactions within NaI crystals (see Ref.~\cite{Bernabei2013} and references therein).
The data from the combined DAMA/LIBRA and DAMA/NaI experiments indicates an annual modulation in the event rate at around 3 keV electron-equivalent energy deposition with a 9.3$\sigma$ significance  (the low-energy threshold for DAMA is $\sim2$ keV) \cite{Bernabei2013}.
The phase of this modulation agrees very well with the assumption that the signal is due to the scattering of DM particles (e.g., WIMPs) present in the DM galactic halo.
This result stands as the only enduring DM direct-detection claim to date.

On the other hand, null results from several other, more sensitive, experiments (e.g., Refs.~\cite{Aprile2012,Akerib2014,AgneseSCDMS2014}) all but rule out the possibility that the DAMA signal is due to a WIMP--nucleus interaction.
While the DAMA experiment is sensitive to scattering of DM particles off both electrons and nuclei, most other DM detection experiments reject pure electron events in order to search for nuclear recoils with as little background as possible.
This means that DM particles that interact favorably with electrons rather than nucleons could potentially explain the DAMA modulation without being ruled out by the other null results.
This possibility has been considered previously in the literature---see, e.g.,~Refs.~\cite{Bernabei2008a,Kopp2009}.

In Ref.~\cite{Kopp2009}, a theoretical analysis concluded that due to a suppression in the WIMP--electron-scattering ionization cross section, loop-induced WIMP--nucleus scattering would dominate the relevant event-rate, even if the DM particles only interacted with leptons at tree level. In this case,  the previous constraints from nuclear recoil experiments \cite{Aprile2012,Akerib2014,AgneseSCDMS2014} still apply.
However, these conclusions are based on calculations that employed simple nonrelativistic wave functions.
A rigorous {\em ab initio} relativistic treatment of the atomic structure has not yet been implemented, and, as we demonstrate in this work, is crucial.

A recent analysis of data from the XENON100 experiment has also investigated WIMP-induced electron-recoil events~\cite{XENONcollab2015,XENONcollab2015a}, and also observed modest evidence for an annual modulation (at the $2.8\sigma$ level).
However, based on their analysis of the average unmodulated event-rate, DM that interacts with electrons via an axial-vector coupling was excluded as an explanation for the DAMA result at the $4.4\s$ level \cite{XENONcollab2015}.
This means that for DM--electron scattering to be consistent with both the DAMA and XENON experiments, both event rates would have to have a very large modulation fraction.
It has been suggested that electron-interacting ``mirror'' DM may satisfy this criteria \cite{Foot2015} (see also Ref.~\cite{Foot2014}).
By assuming the DAMA result was due to an axial-vector coupling, and using the theoretical analysis from Ref.~\cite{Kopp2009}, the corresponding modulation amplitude that would be expected in the XENON experiment was calculated in Ref.~\cite{XENONcollab2015a}.
The observed amplitude was smaller than this by a factor of a few, and it was concluded that the XENON results were inconsistent with the DAMA results at the $4.8\s$ level \cite{XENONcollab2015a}.
We note, however, these conclusions are not entirely model independent, and a rigorous relativistic analysis is required.
We also note that there is no {\em a priori} reason to believe that the fraction of the modulated signal should be small or proportional to the fractional annual change in the DM velocity distribution.
In fact, the scattering amplitude is very highly dependent on the values of momentum transfer involved, which depend on the velocity of the DM particles.
As we shall show, electron relativistic effects must be taken into account properly to recover the correct momentum-transfer dependence of the cross section.

In this work, we demonstrate the applicability of the Born approximation to such scattering processes, and demonstrate that the expected exponential suppression of the relevant electron matrix elements is lifted.
This essentially amounts to an effective enhancement of the scattering rate due to the behaviour of the electron wave functions at very small distances (i.e., close to the nucleus).
Crucially, we also show that relativistic effects actually give the dominant contribution to the scattering cross section. This means that an analysis that only considers nonrelativistic electron wave functions may underestimate the size of the effect by several orders of magnitude, which may have significant implications for the interpretation of electron-recoil experiments, such as DAMA {and XENON}.
A more complete {\em ab initio} {relativistic many-body} calculation of the scattering cross section and ionization rate will be presented in a later work.

As well as the DAMA and XENON100 experiments, our results also have implications for the interpretation
of other experiments which are sensitive to electron recoils, such as XENON10 \cite{Essig2012a,*Essig2012,Angle2011} and CoGeNT \cite{CoGeNT2013,*CoGeNT2014}. They will also be useful for the planning and interpretation of future experiments, in particular for those proposed to search for light DM for which electron recoils are significant \cite{Essig2012a,*Essig2012,Essig2015}.

\section{Scattering amplitude}\label{sec:ampl}

We consider the scattering amplitude and the resulting cross section for the ionization of an atom or molecule via the scattering of a slow, heavy particle $\chi$ (e.g., a dark-matter WIMP), off the atomic electrons; see Fig.~\ref{fig:scattering}.
By heavy and slow, we mean that the mass of the incident particle is much greater than the electron mass, $M_\chi \gg m_e$, while the typical velocity of the DM particle $V$ is much smaller than the characteristic electron velocity,
$V\ll v_e$, where $v_e\sim\a c$ ($\a \approx1/137$ is the fine-structure constant and $c\approx3\E{8}\;{\rm ms}^{-1}$ is the speed of light).

\begin{figure}
		\includegraphics[height=0.25\textwidth]{Scatter}
		\caption{Effective amplitude for scattering of a heavy particle ($M_\chi\gg m_e$) off an electron, via a short-range interaction. We consider the case corresponding to atomic ionization, where $\psi_i$ is a bound electron state and $\psi_f$ is a state in the continuum.}
		\label{fig:scattering}
\end{figure}

For simplicity, we take the effective interaction between the particle $\chi$ and the electron to be a pure contact interaction
\eq{eq:veff}{
\hat V_{\rm eff}=\a_{\chi}\delta\left( \v{r}-\v{R} \right),
}
where $\v{r}$ and $\v{R}$ are the position vectors of the electron and the heavy particle, respectively, and $\a_\chi $ is the strength constant.
(Considering a finite-range interaction does not affect our conclusions; see the Appendix.)
Assuming that the interaction is weak, the amplitude
is given by the Born approximation,
\aln{
M&=\a_\chi\int \Exp{-i\v{k}'\cdot\v{R}}\psi_f^*(\v{r})\delta\left( \v{r}-\v{R} \right) \Exp{i\v{k}\cdot\v{R}}\psi_i(\v{r})\d^3\v{r}\d^3\v{R} \notag\\
&=\a_\chi\bra{f}\Exp{-i\v{q}\cdot\v{r}}\ket{i},\label{eq:M}
}
where $\v{k}$ and $\v{k}'$ are the initial and final momenta of the heavy particle, respectively, and $\v{q}=\v{k}'-\v{k}$ is the momentum transfer (we use units in which $\hbar =1$).

From Eq.~(\ref{eq:M}), the scattering cross section is expressed as
\eq{eq:dsig}{
\d\s =
\frac{2\pi}{V}\a_\chi^2\abs{\bra{f}\Exp{-i\v{q}\cdot\v{r}}\ket{i}}^2\delta\left(\frac{k^2-k'^2}{2M_\chi}-\omega\right)\frac{\d^3k'}{(2\pi)^3}\d\nu_f,
}
where $V=k/M_\chi $, $\omega=\ec_f-\ec_i$ is the change in energy between the initial and final electron states, and $d\nu_f$ is the density of final electron states. Assuming that the heavy particle is incident along the $z$ axis, we obtain from Eq.~(\ref{eq:dsig}),
\eq{eq:born-r}{
\d\s=\frac{\a_\chi^2}{V^2}\abs{\bra{f}\Exp{-i\v{q}\cdot\v{r}}\ket{i}}^2\frac{q\d q\d\phi }{(2\pi)^2}\d\nu_f
,}
where $q^2=k'^2+k^2-2k'k\cos \theta $, $\theta $ is the heavy-particle scattering (polar) angle, $\phi $ is the azimuthal angle, and $k'=\sqrt{k^2-2M_\chi \omega }$. The total cross section is obtained from Eq.~(\ref{eq:born-r}) by integration over $q$ and $\phi $ and summation/integration over the initial and final electron states.

Since the energy of the DM particle is much greater than the typical electron transition energy $\omega $, the smallest momentum transfer is $q_{\rm min}=|k'-k|\simeq \omega /V$. The corresponding vector $\v{q}$ is in the negative $z$ direction. For low incident velocities $V$ this momentum is much larger than the typical electron momentum $p_e$:
$q_{\rm min}\gtrsim m_ev_e^2/V=p_e(v_e/V)\gg p_e$. In this case the Fourier transform in the amplitude
(\ref{eq:M}) is suppressed and the momentum transfers essential for the total cross section are such that $q\ll k$ (though formally Eq.~(\ref{eq:born-r}) is integrated up to $q_{\rm max}=k+k'$).
Hence, we can write the momentum transfer vector as $\v{q}=-(\omega /V)\hat{\v{e}}_z+\v{q}_\perp$, where $\v{q}_\perp$ is the component perpendicular to $z$.
This also implies $q\d q\d\phi =\d^2q_\perp $.
Changing the electron wave functions from the coordinate to momentum space (e.g., $\widetilde \psi _i (\v{p})=\int \Exp{-i\v{p}\cdot \v{r}}\psi _i(\v{r})\d^3\v{r}$), we have from Eq.~(\ref{eq:born-r}):
\aln{
\d\s=&\frac{\a_\chi^2}{V^2}
\abs{\int\widetilde\psi_f^*(\v{p}-\v{q})\widetilde\psi_i(\v{p})\frac{{\rm d}^3p}{(2\pi)^3}}^2
\frac{{\rm d}^2q_\perp}{(2\pi)^2}\d\nu_f
\label{eq:born-q}
.
}

Let us now derive this result using a different approach, i.e., the time-dependent perturbation theory, and treating the motion of the heavy particle classically.
We assume that this particle moves in a straight line, $\v{R}=\v{\rho }+\v{V}t$, where $\v{\rho }$ is the impact parameter vector perpendicular to $\v{V}$. The probability of the transition $i\to f$ induced by the interaction (\ref{eq:veff}) is then given by $\d w=\abs{M_{\rm td}}^2\d\nu_f$, where the transition amplitude is \cite{LLVol3}
\eq{eq:tdamp}{
M_{\rm td}=\a_\chi\int^\infty_{-\infty}\Exp{i\omega t}\bra{f}\delta\left(\v{r}-\v{\rho}-\v{V} t\right)\ket{i}\d t
.}
Replacing the electron wave functions with their momentum-space counterparts, $\widetilde \psi _i (\v{p})$ and $\widetilde \psi _f (\v{p}')$, and integrating over $\v{r}$ and $t$ gives the amplitude in the form
\eq{eq:Mtd}{
M_{\rm td}=\frac{\a_\chi}{V}
\iint
\Exp{i\v{q}_\perp\cdot\v{\rho}}\widetilde\psi_f^*(\v{p}-\v{q})\widetilde\psi_i(\v{p})\frac{{\rm d}^3p}{(2\pi)^3}\frac{{\rm d}^2q_\perp}{(2\pi)^2},
}
where we introduced $\v{q}=\v{p}-\v{p}'$, whose $z$ component (i.e., that in the direction of $\v{V}$) is fixed by integration over time and given by $q_z=-\omega /V$.

The differential cross section is obtained by integrating the transition probability over the impact parameters:
\eq{eq:semicl}{
\d\s =\int \abs{M_{\rm td}}^2 \d\nu_f\d^2\v{\rho}.
}
Inserting the amplitude from Eq.~(\ref{eq:Mtd}) immediately leads to the cross section (\ref{eq:born-q}), derived earlier using the Born approximation.

This equivalence confirms the validity of the Born approximation, ensuring that Eq.~(\ref{eq:born-r}) can be used to calculate the cross section and event-rates.
At the same time, the time-dependent picture provides additional understanding of the smallness of the ionization cross section by WIMPs (beyond the overall factor $\a_\chi^2$).
It is known that if the time scale of the perturbation $T$ is much larger than the characteristic period $\tau $ of the system, the effect of the perturbation is suppressed \cite{LLVol3}.
In our case $T=a_0/V$ and $\tau \sim 1/\omega $, where $a_0$ is the Bohr radius (or, more generally, the radius of the electron orbit).
Their ratio is $T /\tau \sim a_0\omega /V \sim q_{\rm min}/p_e \gg 1$
\cite{[{In atomic collisions this is known as the Massey adiabatic criterion; see }]Massey1949},
which means that the cross section is suppressed.
This suppression is in general exponential, unless the potential in which the particles
move has a singularity, which changes the suppression into a power law.
This is demonstrated explicitly
 in the next sections.

\section{Exponential suppression \\(and lack thereof)}\label{sec:supp}

The large magnitude of the momentum transfer $q$ relative to the typical electron momenta means that the exponent in the atomic structure factor $\bra{f}\Exp{-i\v{q}\cdot\v{r}}\ket{i}$ oscillates much more rapidly than the electron wave functions involved.
The value of this integral is thus determined by small electron--nucleus separations, and the dominant contribution to the cross section is proportional to the probability of finding the electron close to the nucleus.

In general, rapid oscillations of $\Exp{-i\v{q}\cdot\v{r}}$ lead to an exponential suppression of the amplitude. The simplest way to see this is by assuming that the electron wave functions have an oscillator-like behaviour, $\psi_{i,f}(r)\sim A\Exp{-\beta r^2}$.
The matrix element for large $q$ will then be
\eq{eq:suppress}{
\bra{f}\Exp{-i\v{q}\cdot\v{r}}\ket{i}\propto \Exp{-{q^2}/{8\beta}},
}
which is exponentially suppressed.
This behaviour will be observed for any electron wave functions that are smooth near the origin.
As mentioned
above,
exponential suppression of the amplitude for large $v_e/V$ is also the general result of the adiabatic nature of the perturbation by a slow projectile \cite{LLVol3,Massey1949}.

We demonstrate, however, that the behaviour of the electron wave functions near the origin of the Coulomb field leads to contributions to the amplitude that are not exponentially suppressed. These terms are proportional to the nuclear charge $Z$ and decrease only as a power of $q$ at large $q$.

Consider the ejection of an electron with energy $\ec $ from an atomic orbital $nl$. The contribution of the final-electron partial wave $l'$ to the amplitude (\ref{eq:M}) is proportional to the radial integral
\eq{eq:rad}{
\int _0^\infty R_{\ec l'} (r) R_{nl}(r)j_L(qr)r^2\d r,
}
where $R_{nl}(r)$ and $R_{\ec l'}(r)$ are the radial wave functions of the initial and final states, $j_L(x)$ is the spherical Bessel function, the values of $l$, $l'$ and $L$ must satisfy the triangle inequality, and $l+l'+L$ must be even due to parity selection. The leading contribution to this integral at large $q$ comes from small $r\sim 1/q$, where the radial functions behave as (in atomic units: $a_0=1$, $c=1/\a\approx 137$)
\eq{eq:R_nl}{
R_{nl}(r)\simeq A r^{l}\left[1-\frac{Z}{l+1}r+\dots \right],
}
$A$ being the normalization factor, and with a similar expression for $R_{\ec l'}(r)$. From Eqs.~(\ref{eq:rad}) and (\ref{eq:R_nl}), it appears that the leading contribution to the amplitude at high $q$ is proportional to
\eq{eq:rad_1}{
\int _0^\infty r^{l+l'+2}j_L(qr)\d r=
\frac{1}{q^{l+l'+3}}\int _0^\infty x^{l+l'+2}j_L(x)\d x.
}
However, the integral
\eq{eq:Bes_int}{
\int _0^\infty x^{l+l'+2}j_L(x)\d x=2^{l+l'+1}\sqrt{\pi }
\frac{\Gamma\left[ \frac{3}{2}+\frac{1}{2}(L+l+l')\right]}{\Gamma\left[ \frac{1}{2}(L-l-l')\right]}\notag
}
is identically zero for even $l+l'+L$, since the gamma function in the denominator has poles for nonpositive integer arguments. This also shows that including any even-power corrections to the small-$r$ expansion of the wave functions, Eq.~(\ref{eq:R_nl}) (which appear for any potential regular at the origin), also leads to zero contributions. Therefore the amplitude in this case would decrease faster than any power of $q$, i.e., exponentially.

On the other hand, the lowest-order, linear correction in either $R_{nl}(r)$ and $R_{\ec l'}(r)$, is proportional to $Z$ [see Eq.~(\ref{eq:R_nl})], and the integral $\int _0^\infty x^{l+l'+3}j_L(x)\d x$ is \textit{nonzero}. This determines the leading asymptotic behaviour of the amplitude,
\eq{eq:rad2}{
\int_0^\infty R_{\ec l'} (r) R_{nl}(r)j_L(qr)r^2\d r\propto \frac{Z}{q^{l+l'+4}}.
}
This shows that the largest cross section for large $q$ (i.e., the least suppression,
$\abs{\bra{f}\Exp{-i\v{q}\cdot\v{r}}\ket{i}}^2\propto q^{-8}$)
is obtained for both initial and final $s$ states ($l=l'=L=0$).
{Similar integrals arise in the problem of atomic photoionization at high energies, see, e.g., Ref.~\cite{Dalgarno1992,Forrey1995}.}

This power, instead of the exponent, emerges due to the Coulomb singularity of the electron wave function at the nucleus.
The singularity for the $s$-wave electrons is stronger than in higher partial waves, whose expansions contain extra powers of $r$.
The ionization by slow, heavy particles is thus dominated by $s$-wave contributions from small electron--nuclear distances.
This means that there is an effective atomic-structure enhancement of such scattering processes involving $s$-waves, and that relativistic effects may be significantly larger than expected.

\section{Relativistic Enhancement}\label{sec:rel}

Indeed, the situation in the relativistic case is quite different.
Consider the Dirac wave function for an electron in the central field of the atom,
\eq{eq:diracwf}{
\psi_{n\k m}=
\twocomp{F_{n\k}(r)\,\Omega_{\k m}(\theta_r,\phi_r)}{i G_{n\k}(r)\, \Omega_{-\k, m}(\theta_r,\phi_r)},
}
where $\k$ is the Dirac quantum number [$\k=-(l+1)$ for $j=l+1/2$, and
$\kappa =l$ for $j=l+1/2$, $j$ being the total angular momentum], and $\Omega_{\k m}$ is the two-component spherical spinor. At small $r$, the radial functions of the large and small Dirac components behave as \cite{LLvol4}
\begin{subequations}
\aln{
F_{n\k}(r)&\simeq B \, r^{\g-1}   \,(\g-\k+Cr+\dots ), \label{eq:diracF}
\\
G_{n\k}(r)&\simeq -Z\alpha B \, r^{\g-1}(1+Dr+\dots ), \label{eq:diracG}
}
\end{subequations}
where $B$ is a normalization constant, $\g=\sqrt{\k^2-(Z\a)^2}$,
\eq{eq:C}{
C=-\frac{Z}{2\g +1}[1+(2\g -2\k +1)(1+\a^2\ec _{n\k})],
}
$\ec _{n\k}$ is the electron energy, and
$D\sim C$.

In the nonrelativistic limit ($Z\a \rightarrow 0$, $\g =|\k|$) $G_{n\k}$ vanishes, and Eq.~(\ref{eq:diracF}) reduces to Eq.~(\ref{eq:R_nl}).
However, the corrections in $\g=|\k |-(Z\a)^2/2|\k|+\dots $ actually change the power of $r$ that appears in the expansion.
As a result, the lowest-order in $r$ term, which vanished in the nonrelativistic case [see Eq.~(\ref{eq:rad_1})], now becomes
\eq{}{
\int _0^\infty r^{\g+\g'}j_L(qr)\d r
=\frac{2^{\g+\g'-1}}{q^{\g+\g'+1}}\sqrt{\pi }
\frac{\Gamma\left[\frac{1}{2}(L+\g+\g'+1)\right]}{\Gamma\left[ \frac{1}{2}(L-\g-\g'+2)\right]},\notag
}
which is {\em nonzero}.
For example, for the initial and final $s$-wave states [$\k=-1$, $\g=\g '\simeq 1-(Z\a)^2/2$], we have
\eq{}{
\int _0^\infty r^{2\g }j_0(qr)\d r=\frac{\Gamma(2\g)\sin[\pi(1-\g)]}{q^{2\g+1}}
\simeq \frac{\pi(Z\a)^2}{2 \, q^{3-(Z\a)^2}}.
}
The power of $q$ remains the same for scalar, pseudoscalar, vector, and pseudovector interactions, and if $p$ states are considered; see the Appendix.

Thus we see that not only is the exponential suppression removed, but even the power suppression is significantly weaker than that found in the nonrelativistic case.
Note that the cross section goes as the square of the amplitude, meaning that the momentum-transfer dependence of the leading atomic structure contribution to the cross section is proportional to $q^{-6+2(Z\a)^2}$
(compared to $q^{-8}$ in the nonrelativistic case, and $\Exp{-(q/p_e)^2}$ in the ``naive'' adiabatic case; see also the Appendix).
This result indicates that relativistic effects actually give the dominating contribution to the amplitude, and that therefore a nonrelativistic treatment of such problems can greatly underestimate the size of the effect.

\begin{figure}
		\includegraphics[width=0.425\textwidth]{relEnhancement}
		\caption{The ratio $R$ of the atomic structure factor
		$\abs{\bra{\ec s_{1/2}}\Exp{-i\v{q}\cdot\v{r}}\ket{3s_{1/2}}}^2$
for the ionization of $3s_{1/2}$ electrons in iodine ($I_{3s_{1/2}}=1.1$~keV, $\ec =2$~keV) calculated with relativistic (hydrogen-like Dirac) wave functions to that obtained with nonrelativistic wave functions, using the true nuclear charge $Z=53$.
(The momentum conversion is $1~\mbox{MeV}/c \approx 268$ a.u.)}\label{fig:enhancement}
\end{figure}

We have verified this enhancement numerically.
In Fig.~\ref{fig:enhancement}, we plot the ratio of the atomic structure factor  calculated using relativistic Dirac-Coulomb wave functions to those calculated using nonrelativistic Schr\"odinger functions.
The calculations were performed for the $3s$ state of iodine, which would give the dominant contribution to the ionization rate due to WIMP--electron scattering at the energy scale relevant to the DAMA experiment \cite{Kopp2009} {(the $1s$ and $2s$ electrons are bound too tightly in I and Xe to become ionized with the energy deposition observed by DAMA)}.
We use the true nuclear charge ($Z=53$ for iodine) instead of the effective nuclear charge $\widetilde Z$.
The standard definition $\widetilde Z=n\sqrt{2 I_{nl}}$, where $n$ is the principal quantum number and $I_{nl}$ is the electron ionization energy, provides a sensible approximation for the wave function at intermediate distances.
At very small distances, however, the nuclear charge is essentially unscreened. Therefore, the atomic wave functions at small distances are proportional to the pure Coulomb wave functions.
Given the importance of small electron--nuclear separations, such processes are strongly dependent on the atomic number, and using a too-small $\widetilde Z$ can lead to orders-of-magnitude underestimation of the probability.
{The best way to treat this problem is to use a self-consistent field approach, such as the relativistic Hartree-Fock method.}

\section{Conclusion}

We have demonstrated the equivalence of the first Born approximation and semiclassical treatment for the problem of ionization of atoms or molecules by slow, heavy particles, such as WIMPs, and have shown that relativistic effects (which were previously neglected) give the dominant contribution to the event rate.
Our calculations have implications for the interpretation of the anomalous annual modulation result of the DAMA and XENON collaborations in terms of DM particles scattering off the atomic electrons.

One might suspect that this is a less-likely explanation, due to the supposed {large} suppression from the electron wave function at high momentum.
We show, however, that this suppression is not as strong {as expected}, leading to an effective enhancement coming from the contribution of $s$-wave electrons at very small distances.
The effect is thus highly-dependent on the nuclear charge, which is mostly unscreened at such small distances. Therefore, there are implications for simple calculations that employ screened hydrogen-like functions with an effective nuclear charge $\widetilde Z$; it is more appropriate to employ a fully self-consistent approach, such as the relativistic Hartree-Fock method.
Crucially, relativistic corrections to such a process are significantly larger than may have been expected due to the different radial dependence of the Dirac wave functions (compared to the Schr\"odinger wave functions) at small distances.
A nonrelativistic treatment of such problems can therefore greatly underestimate the size of the effect.
Several new experiments designed to test the DAMA results are currently under way \cite{Bernabei2015,Amare2015b,*Amare2015,*Amare2015a,Xu2015}; it is crucial that the relevant theory required for their interpretation is correct.
There are also implications for the planning and interpretation of future experiments, in particular for those proposed to search for light DM, for which electron recoils are significant \cite{Essig2012a,*Essig2012,Essig2015}.

\acknowledgements
\paragraph*{Acknowledgements---}
This work was supported in part by the Australian Research Council.
We would like to thank J.~C.~Berengut, M.~Pospelov, and Y.~V.~Stadnik for helpful discussions,
and M.~Schumann for his comments on the manuscript.
BMR and VVF are grateful to the Mainz Institute for Theoretical Physics (MITP), where part of this work was completed, for its hospitality and support.

redpajama_set_name: RedPajamaArXiv


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text:
What Is a Hydraulic Winch & How Does It Work
Last Updated on July 2, 2021
What is a Hydraulic Winch?
How Does s Hydraulic Winch Work?
Features of hydraulic winch
Hydraulic Winch Part Examples
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One of the best attributes of the winch is its ability to pull for longer periods without overheating. Which is longer than an electric winch.
Hydraulic winch is ideally suited for heavy-duty marine applications to perform anchoring, towing as well as lifting and hauling heavy objects. It can be adapted to both offshore and onshore applications.
The main benefit of hydraulic winch is that they have a 100% duty cycle and are fully submersible. Having a 100% duty cycle means that without any negative effects, it can run constantly.
Suggested Read:
Warn Hydraulic Winch Reviewed
What To Look For in A Hand Winch
Best Winch For Truck
Hydraulic winch works by using a fluid in a confined space. It uses a pump to create a pressure differential.
This pressure differential involves having a low-pressure fluid stored in a reservoir before the pump that becomes supported inside of the pump which moves to the driven component and back to the reservoir.
Along with the reservoir, pump, and lines, there will be several valves that control the flow in the system.
Another noticeable advantage of the hydraulic winch in vehicle-mounted applications is its beneficial operation in cold weather. It is because of the power steering pump, the hydraulic fluid is warmed before it is about to enter to the winch motor.
The warm winch is able to pull harder than a cold winch and makes a better result. The warm hydraulic fluid keeps the motor warm and ready to operate even in cold weather conditions.
In practical situations, a winch can be pulled as hard as it can be, until it is completed. The hydraulic winches are designed in a way that they will not be overheated with a hard pull.
Hydraulic winch is made to operate with complete power for a long period of time. The battery system of any vehicle is supposed to operate at a high-power for only a short period of time.
A normal winch design will work best when the engine of the vehicle is on. In some instances, It's winch usage can be terminated considering this fact.
The major fact while working with a hydraulic winch design is to deeply observe where you are going to use it. The size and weight of the vehicle must also be taken under consideration, where the winch will be mounted.
High efficiency- This winch can work easily even after long term use and heating conditions.
High performance- Comparing to an electric winch, hydraulic winch will not be overheated with a long-time hard pull.
High strength- Hydraulic winch especially is designed for the most challenging task on both land and sea. It has a strong construction with a long working life.
Reliability and durability- Hydraulic winch can work perfectly in the harshest environments. It can operate for a long time with complete power.
Features like automatic braking, emergency stop button, drum locking system, pawl brake and over travel prevention system will provide maximum protection.
1. Rope Drum Assembly
2. Drum Locking System
3. Removable Cover Assembly
4. UnderCover Mesh
5. Pawl Pin
6. Pawl Operating Lever
7. Handle Stopper
8. Machined Connection Beam
9. Wire Rope
10. Top Overtravel Limit Valve
11. Interlock Valve Support
12. STD S/S Hinge
13. Hydraulic Pipe
The hydraulic winch is more efficient than an electric winch. This type of winch is more suitable for tough jobs on land and water. This heavy-duty winch is commonly used on boats, on the shore to carry out a number of different tasks and at docks.
Marine Hydraulic Winch
The hydraulic winch, as the name suggests, is powered by a hydraulic system. It is able to deliver great power in order to handle a big job. Energy efficiency is very important while choosing a winch for marine applications.
Electric winches use power directly from generator sets.
On the contrary, hydraulic winches use fluid power to work which utilizes hydraulic systems and a motor pump between the generator set and the winch.
Hydraulic winch has the capacity to carry huge loads. This type of winches has generator sets large enough for crane loads.
Hydraulic winches are the better option for vessels that need to move heavy cargo. Because of the size of hydraulic system equipment hydraulic winch is the best option for larger vessels.
So, now you know what is a hydraulic winch and the operating principle of hydraulic winches. If you have any more questions about the hydraulic winch system or hydraulic winch working principle, then just drop a comment below.
You may also like to read our reviews of electric winches:
X-Bull electric Winches
Smittybilt Waterproof Winches
KFI products Winches
Best winches for car hauler
Best hitch mounted winch

redpajama_set_name: RedPajamaCommonCrawl


text:
package com.inet.lib.less;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map.Entry;

/**
 * A HashMap that hold multiple values for a single key.
 *
 * @param <K>
 *            The key type
 * @param <V>
 *            the values type
 */
class HashMultimap<K, V> {

    private final HashMap<K, List<V>> map = new HashMap<>();

    private HashMultimap<K, V> parent;

    /**
     * Default constructor
     */
    HashMultimap() {
    }

    /**
     * Constructor with parent
     *
     * @param parent
     *            parent, will be hold by reference
     */
    HashMultimap( HashMultimap<K, V> parent ) {
        this.parent = parent;
    }

    /**
     * Add a value to this map. If the map previously contained a mapping for the key, then there are two values now.
     * @param key the key
     * @param value the value
     */
    void add( K key, V value ) {
        List<V> rules = map.get( key );
        if( rules == null ) {
            rules = new ArrayList<>();
            map.put( key, rules );
        }
        rules.add( value );
    }

    /**
     * Get all values for the given key. If no key exists then null is return.
     *
     * @param key
     *            the key
     * @return the list or null
     */
    List<V> get( K key ) {
        List<V> result = map.get( key );
        if( parent != null ) {
            List<V> resultParent = parent.get( key );
            if( result == null ) {
                return resultParent;
            } else if( resultParent == null ){
                return result;
            } else {
                for( V value : resultParent ) {
                    if( !result.contains( value ) ) {
                        result.add( value );
                    }
                }
            }
        }
        return result;
    }

    /**
     * Add all values of the mappings from the specified map to this map.
     *
     * @param m
     *            mappings to be stored in this map
     */
    void addAll( HashMultimap<K, V> m ) {
        if( m == this ) {
            return;
        }
        for( Entry<K, List<V>> entry : m.map.entrySet() ) {
            K key = entry.getKey();
            List<V> rules = map.get( key );
            if( rules == null ) {
                rules = new ArrayList<>();
                map.put( key, rules );
            }
            for( V value : entry.getValue() ) {
                if( !rules.contains( value ) ) {
                    rules.add( value );
                }
            }
        }
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public String toString() {
        return map.toString();
    }
}

redpajama_set_name: RedPajamaGithub


What happens if we want more/fewer cookies in the batch?
What happens if we want more/fewer chips in each cookie?
Again matching the requirements of real business, the students are asked to act as consultants and, based on the data they gather, advise the company about the number of chocolate chips to put in the mixture.
This task leads naturally into one way mathematics is applied in business. A question is posed, data is collected and analysed and decisions are made. The card suggests doing the experiment 'several times' - deliberately not defining several because a critical question for mathematicians is How much data is enough?. We want the students to carry out the trials and record results so that they get a feel for the random elements of the situation and so that they have sufficient data to make a reasoned judgement. Here are the results for 10 trials of making a batch of 6 cookies with a minimum of 3 chips per cookie.
Remember these figures are the number of chips to put in the mixture for a batch of six cookies so that the minimum is 3 chips per cookie. That will be the advertising claim - 'At least 3 chocolate chips in every cookie!'.
How would you advise the client (D-Licious Cookie Company)?
Is ten trials enough data on which to make a decision?
How should the data be displayed to help guide the decision?
What statistics (range, mode, median, mean) could be used to analyse the data?
Should outliers (the very largest and very smallest results) be ignored?
If we choose a figure likely to give three chips per cookie, then will be at least one cookie in the batch of six that has three chips. But what number might be in the other cookies? For example, the 38 result above produced cookies with 8, 3, 5, 9, 9 & 4 chips. Is it possible to make a cookie with 9 chips, or would it basically be a 'piece of chocolate'?
How much do chocolate chip cookies cost anyway? This would be part of the manufacturing costs. Whatever the best mathematical result may be, can the client afford to use that number of chips per batch?
In a sense, it doesn't matter what the students choose as the best number to put into the batch, provided they can justify the decision on the basis of the data and can make intelligent comment about some of the related questions.
You will need one dice for each pair of students, counters or something else to be used as chocolate chips and scrap paper to use as a tray of 6 cookies. If you have one Poly Plug for each student in your class and they each use their red board, you will have plenty of 'chocolate chips' for the 6 cookies/3 chips trials.
One way to start this whole class lesson is from the journals of students who have used this task in your regular task session. This means you will have to wait until a few pairs of students have tried the task and recorded their results and thoughts. This might take three or four weeks of making sure that the task is used regularly.
Invite students who have used the task to introduce it to the class. This can work quite well in a 'fishbowl situation' at a central table using the board supplied with the task. The introduction will produce one outcome.
So, in this trial we found that there needed to be ... chocolate chips in the mixture to get a batch of six cookies to have at least 3 chips in every cookie. Do you think that would be the result if we did another trial?
At this point build a list on the board of student predictions about the best number of chips to put into a 6/3 mixture. Using a stem and leaf plot is a good idea, in fact, the data can be used to introduce this tool. Obviously the few students who have used the task will (probably) have a better idea than those who have only seen one trial, but the purpose of making this list is to see how an increasing amount of data effects predictions. If you plan your board space appropriately, you can record this set of predictions, and the ones later in the session as a back to back stem and leaf plot.
(This is a stem and leaf plot of the ten trials listed above.
In a second part of the board start a stem and leaf plot headed Actual Data and enter the one result from the introduction.
That's not much data to predict from. Let's get some more.
Ask each pair to fold their paper into six sections numbered 1 to 6 and carry out one trial. As they finish they add their result to the stem and leaf plot. Soon there will be 10 or more results.
Our challenge is to advise the company about the number of chocolate chips to put in the mixture for 6 cookies, so that we can tell our customers that every cookie has at least three chocolate chips. If you only had this data, what advice would you give?
Discuss whether this is enough data. Encourage further discussion with a question like: Would we tell the company to put 18 chips in each batch? or Would we tell the company to put (maximum so far) into each batch? When it is suggested that more data is needed, include the data from one of the journal records.
This is where you use the Back to Back plot, or use a third part of the board to gather the data under the heading Prediction 2. Discuss what has influenced any changes when compared with the first prediction.
We are fortunate that some of our workers have already carried out more trials when they were using the task. I am going to ask them to add their results to the Actual Data and while they are doing that every group can run one more trial and include their data as well.
Discuss ways to analyse this data including such statistics as range, mode, median and mean. Also, if appropriate to the age, discuss how to deal with outliers. On the basis of this final set of data and the discussion, challenge each pair to prepare a report, with evidence, to the general manager of D-Licious Cookie Company. This report could be submitted for assessment, in which case you might want to include discussion of a rubric for assessment. Rubric and other assessment tools can be found in the Assessment section of the site.
What happens if the machinery in the factory changes and can now make cookies in batches of 10, or if the boss decides to advertise a different minimum number of chips in each cookie?
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 58, Chocolate Chip Cookies. This lesson plan suggests using a real packet of chocolate chip cookies as the stimulation for the lesson. After initial prediction, the students carefully eat their way through a cookie and count the chips. The lesson is also supported by software that can run many trials of many different No. of cookies / Minimum number of chips scenarios.


Earn your online Bachelor of Science in Finance degree from Regis University, and prepare yourself for and exciting career in the world of finance. This fully online degree in finance has been created to develop its students' understanding of the global financial world, and prepare them for career with organizations such as, banks, investment companies, government agencies, consulting firms, insurance firms, and small and large corporations.
This is an excellent degree program for individuals who are wanting to begin building or further strengthen their fundamental financial skills. This program has been designed in order to give its student the knowledge they need for a successful financial career, and prepare them for specialty certification such as Series 7.
The coursework in this online degree in finance examines a variety of element that affect the world of finance such as, financial analysis and planning, investment decisions, financing decisions, and the management of financial resources, while incorporating current trends, techniques and practices that are found in contemporary global finance.
All applicants of this program must have at least a High School Diploma or GED equivalent as highest level of education, as well as 3+ years of professional experience.


text:
package com.tngtech.jgiven.junit.de;

import org.junit.ClassRule;
import org.junit.Rule;

import com.tngtech.jgiven.junit.ScenarioExecutionRule;
import com.tngtech.jgiven.junit.ScenarioReportRule;
import com.tngtech.jgiven.lang.de.SzenarioTestBasis;

public class SzenarioTest<GEGEBEN, WENN, DANN> extends SzenarioTestBasis<GEGEBEN, WENN, DANN> {
    @ClassRule
    public static final ScenarioReportRule writerRule = new ScenarioReportRule();

    @Rule
    public final ScenarioExecutionRule scenarioRule = new ScenarioExecutionRule( writerRule, this, getScenario() );

}


Cue the plastic spoon! I already have a million and one ways that I use plastic spoons when working with chocolate. I guess now it's a million and two!
Line up a bunch of spoons and knock these out in no time at all. Make them in advance and store in an airtight container at room temp for up to three months.
Draw a small circle on the back of a plastic spoon to create an outline for the pupil. Draw a larger circle around that circle to create the iris.
Pour melted white candy melts into a parchment paper cone (or piping bag or squirt bottle – whatever you're most comfortable with). Flip the spoon over and pipe a tiny white dot within the small circle, but a little off center. This will be the little glint in your chocolate eye. It's such a tiny detail, but it's what gives the eyeball realism.
Pipe black candy melts over the tiny white dot, filling in the small circle. Set aside to dry.
Pipe colored candy melts around the black dot, filling in the lines of the larger circle. Set aside to dry completely before moving on to the next step.
Fill in the rest of the spoon with white candy melts and, again, set aside to dry.
Make sure all of the layers of chocolate are completely set before popping the chocolate eyeball out of the spoon. Run your fingers around the sides of the eyeball to smooth over any rough edges.
Smoosh a chocolate eyeball onto a freshly iced cupcake and allow the frosting to billow up over the sides. Use a small icing spatula to smooth down the icing over the edges of the eyeball.
Wanna make these together? Join me live on my Facebook page on Friday, October 16th at 10am and that's exactly what we'll do! I'll be demo'ing the whole project, start to finish. Including my super fancy eyeball smooshing technique. ;P I'll also be answering any and all of your Halloween baking and treat making questions.
Eye hope to see you there! Muuuuahahahaha!


Highly recommended for keeping cuticles in tip-top shape! A beautiful rich consistency which glides on to nails without stickiness.
Soothing Shea & Cocoa Butters nourish and repair dry, splitting cuticles.
Portable tin can travel anywhere. Use daily for maintenance, or as an intensive overnight cuticle treatment.
Treat your nails and cuticles kindly with this naturally restorative balm.
Olea Europaea (Organic Extra Virgin Olive Oil), Ricinis Communis (Castor Oil), Cera Flava (Beeswax), Elettaria Cardomomum (Cardomom essential oil), Zingiber Officinalis (ginger essential oil), Cymbopogan Schoenanthus (Lemongrass essential oil), Litsea Cubeba (litsea cubeba essential oil), Citrus Nobilis (Mandarin essential oil), Pelargonium Graveolens (Geranium essential oil), Rosmarinus officinalis (rosemary essential oil), Hippophae Rhamnoides (Seabuckthorn berry CO2 extract), Butyrospermum parkii (Wild african shea butter).
Rub into cuticles and watch soothing Shea Butter give excellent results. Use regularly for beautiful nails.


Since Halloween season, aka pumpkin everything, is coming up, I'll be uploading a bunch of different pumpkin recipes these coming weeks! I've been testing these cookies all week long and finally made the perfect recipe!
I initially was going to do a cream cheese icing, but it just wasn't working out. I made my cream recipe several times, but it was too hot in my apartment and as soon as I piped the cream over the cookies it would melt right away, even after having cooled the cookies and the cream over night in the fridge (it's 35C/95 inside my apartment).
So I gave up on the dairy part and just decided to go with a coconut cream. My coconut whipped cream would have melted right away so I added some coconut butter from Artisana to it and it created the perfect thick icing! I sweetened it with stevia and it was perfect!
The secret to making these cookies super moist and crumbly is to leave them in the fridge. If you do make these, please leave them in a tupperware or plastic bag to store.
These cookies are also great as is. If you don't feel like making whoopie pies, you can just have the cookies as a treat! Great in lunch boxes too as dessert. If you'd like to try another dairy-free pumpkin recipe, check out my Paleo pumpkin pie!
In a bowl, combine the almond butter and pumpkin puree together and mix together. Add all of the spices and sweetener and continue mixing. Add the eggs and mix. Add the almond flour and coconut flour and mix until perfectly mixed.
Add a round tip to a large piping bag and transfer the batter inside it. Put some parchment paper over two baking trays and pipe 24 even circles over the parchment paper.
In a bowl, whip the coconut cream for a few minutes. Add the coconut butter and whip an additional minute. Add the stevia and vanilla and combine. Place in the fridge 2+ hours to cool.
Transfer the coconut cream inside a piping bag attached with a round tip. Pipe the coconut icing over 12 cookies and top with the remaining cookies.
Great dairy free recipe. I like the taste of coconut cream, espessialy whipped with coconut butter, yum!
Geez! These look so awesome. I can't wait to try these in the Fall. Good idea to add the coconut butter to the coconut whip to give it more stability – the icing looks great.
These are so much fun! I have never made Whoopie Pies before but I've always wanted to. I know my kids would be so excited to try these.
My kids are always asking for these…and you make it look easy!! Thanks for healthier version!
These are so so cute! I loooove woopie pies and so I'm so excited to to find a paleo version. Yum.
I'm sorry about your difficulties creating this recipe, but I'm glad that you came up with a dairy free version. I think coconut and pumpkin are great together!
Oooooh my goodness. Those look dangerous! Haha.
I am drooling. So pretty. And sooooo yum!
Whoopie pies are SO fun! And I'm one of those people who loves pumpkin year-round, not just in the fall, so these are perfect for me!
Oooo almond butter and pumpkin?!? Now that's a winning combo! These look fantastic!
Hi, you can get it in wholefoods market or on amazon.


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text:
Hot Book
Home >> The star with 1000 faces >> The star with 1000 faces Oneshot Page 32
Author:TAKAHASHI Rumiko
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Chapter: The star with 1000 faces Oneshot Next Page: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Previous Next Report
Toriyama Akira Mankan Zenseki
Saitei Megami
Avalon~bitter~ (Anthology)
Omaejan
Koi ni Wazurai
Manga Name:The star with 1000 faces
Categories: Oneshot
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text:
\section{Introduction}

Graphene, a two-dimensional material with a single atomic layer of graphitic carbon,
has attracted great attention recently, due to its novel electronic properties and
potential device applications \cite{santosCPL2011,zouPRL2010,SongNanotech2010}.
Ideal graphene sheet is nonmagnetic, then to use graphene for spintronic applications
the major challenge is to make graphene magnetic. In this sense, the experimental observation of magnetic properties in graphene and related materials \cite{OhldagPRL2007,LuoNanoLett2007, nair2012,freitas2014hyperfine,nair2013dual} has drawn huge interest, especially considering the applications of these materials in spintronics, quantum information processing and others.

Recently theoretical works \cite{yazyev2,ugeda,boukhvalovPRB2011,PalaciosPRB2012,PazSSC2013,felixPRB2014}
have revealed that the magnetic properties in graphene-based systems are associated with the occurrence
of defects such as atomic vacancies, substitutional and chemisorbed species. In particular,
vacancies in graphene sheet giving rise to magnetism depend on
 the density of defects\cite{singhJPCM2009}. Single-atom defects in graphene also lead to the occurrence of
quasi-localized states near the Fermi level \cite{PazSSC2013}. The fact that quasi-localized states
lie at the Fermi level suggests that itinerant magnetism can be induced due to electron exchange
instability \cite {eduwardsJPCM2006}.

Here, we report a systematic investigation of the effects of changing the spatial arrangement of two vacancies in a graphene sheet on its electronic and magnetic properties; the separation between the vacancies as well as their location (with respect to the distinct sites of the bipartite graphene lattice) were studied, while keeping the density of the defects fixed.
Two single vacancies were created in the same sublattice (A0A$i$) or in different sublattices (A0B$i$) with $i$=1, 2, 3 and 4 for different distance between the vacancies.
Spin-polarized DFT calculations with full structural relaxation were performed.
Our findings show that the ground state of the graphene sheet containing two vacancies is indeed magnetic, with a ferromagnetic-like coupling between the magnetic moments associated with the vacancies. However, depending on the creation of the vacancies on the same sublattice or in different sublattices and on the possible topological lattice distortions, different contributions of the $\pi$
 and $\sigma$ orbitals to magnetism are observed.

\section{Calculations}
In this work, we have investigated the interaction between carbon vacancies in a
 graphene monolayer, through first-principles calculations, based on the density
functional theory (DFT)\cite{dft1,dft2}. The spin-polarized DFT calculations were
performed using ultrasoft Vanderbilt pseudopotentials \cite{vanderbilt}, and a
generalized gradient approximation (GGA) for the exchange-correlation potential
\cite{perdew}, as implemented in the VASP code \cite{kresse1,kresse2,kresse3}.
In this calculation we have used a 9$\times$9 supercell with 160 carbon atoms and two atomic vacancies, which were created by removing carbon atom from an pristine graphene sheet. Herein, two different vacancy locations were considered: (a) vacancies in the A
sublattice and (b) vacancies in the B sublattice. The lattice parameter for graphene
obtained from structural optimization was 2.46 \AA. We have used a
plane-wave-cutoff energy of 400 eV and a Monkhorst-Pack \cite{monkhorst} scheme
with a 3$\times$3$\times$1 k-mesh for the Brillouin zone integration. In all calculations the
lattice parameter was kept fixed at the calculated value, whereas the atoms were allowed
to relax until the atomic forces were smaller than 0.025 eV/\AA.

\section{Results and Discussions}

In order to study the effect of the interaction between two vacancies in the graphene
sheet, we have considered several different configurations as shown in Figure \ref{structure}.
It is important to stress that the vacancy concentration was kept fixed in all calculations reported herein.

\begin{figure}[!h]
\begin{center}
\includegraphics[width = 8.5 cm]{fig1.eps}
\caption{Topological configurations of two vacancies on single graphene,
where A{\textit i} and B{\textit i} indicate the position
 of the vacancies created on A and B sublattice, respectively. }
\label{structure}
\end{center}
\end{figure}

First, a single defect vacancy was created in A0 (as indicated in Figure \ref{structure}) and the structure was completely relaxed. The structural relaxation carried out for the entire structure yielded a planar Jahn Teller distorted carbon triangle and local magnetic moment around the vacancy, in accordance with previous work\cite{chenNanoscale2014}. For the carbon triangle (see Figure \ref{spinD}), we found two long bonds with a length of 2.55 \AA~ each and a short bond with a length of 1.98 \AA~ (see table \ref{triangle}), as compared with the value of 2.46 \AA~ for the
undistorted structure. The formation of this short bond points to a reconstruction of the two dangling bonds left after the removal of the carbon atom from the A0 site in the graphene sheet \cite{PazSSC2013}. The ground state of the relaxed system exhibited a magnetic moment 1.16 $\mu_B$, in agreement with previous reports \cite{PalaciosPRB2012}.

The formation energy of a single vacancy in the graphene sheet at the ground state of the system was calculated as

 \begin{equation}
 \label{formation}
 E_f=\frac{1}{n}(E_v-\frac{N-n}{N}E_{g}),
\end{equation}

where $N$ denotes the number of C atoms in the defect-free graphene sheet, $n$
represents the number of vacant C atoms (i.e., $n=1$ for a single vacancy) and $E_{g}$ and  $E_v$ are the total energies
 of the  defect-free and the vacancy-containing  graphene sheets, respectively.
 The formation energy of the graphene sheet containing a single vacancy calculated according to
equation (\ref{formation}) was found to be 7.6 eV, which is in good agreement with
the experimental value of 7.0 eV \cite{mayer} and also with previous results of
DFT calculations \cite{dai,faccio2}.

However, when we created the second vacancy in the graphene sheet the formation energy was found to be 7.50 eV, which is a value somewhat smaller than the one corresponding to a single isolated vacancy \cite{PazSSC2013}. A Jahn-Teller distorted triangle was again observed around each vacancy (see Figure \ref{spinD}). The values of the bond lengths in these triangles for a graphene sheet with two
 vacancies separated by varying distances after a full relaxation of the whole topological configuration (see figure \ref{structure})
are given in Table \ref{triangle}, with the symbols d and L standing for the short bond and the two long bonds, respectively.

\begin{table}[h!]
\begin{center}
\caption{Bond lengths in the carbon triangles formed around each single vacancy in the relaxed graphene structure. The symbols dA$0$ and LA$0$ represent the short bond and the two long bonds in the triangle formed around the A0 site, whereas dX$i$ and LX$i$ represent the corresponding bond lengths in the triangle formed around the second vacancy (X can indicate an A or B site and $i$ ranges from 1 up to 4.)}
\label{triangle}
\begin{tabular}{c c c c c c c}
\hline
\hline
system & dA0(\AA) & \multicolumn{2}{c}{LA0(\AA)}  &dX$i$(\AA)&\multicolumn{2}{c}{LX$i$(\AA)}\\
\hline
\hline
A0 or B0& 1.98    & 2.55      &2.55     & 1.98    & 2.55      &2.55 \\
A0A1     & 1.73    & 2.54      &2.52     & 1.90    & 2.58      &2.65 \\
A0A2     & 1.79    & 2.52      &2.56     & 1.86    & 2.60      &2.68 \\
A0A3     & 1.87    & 2.54      &2.54     & 1.93    & 2.57      &2.57 \\
A0A4     & 1.89    & 2.55      &2.58     & 1.95    & 2.58      &2.65 \\
A0B1     & 1.91    & 2.61      &2.64     & 1.91    & 2.61      &2.64 \\
A0B2     & 1.84    & 2.53      &2.60     & 1.82    & 2.56      &2.57 \\
A0B3     & 1.97    & 2.57      &2.59     & 1.95    & 2.55      &2.55 \\
A0B4     & 2.08    & 2.57      &2.64     & 1.93    & 2.55      &2.57 \\
\hline
\hline
\end{tabular}
\end{center}
\end{table}

From the data displayed in Table \ref{triangle}, one can note that the average lengths of the two long bonds are in general larger than 2.55 \AA~(value corresponding to a single isolated vacancy) for all configurations. Also, for systems with two vacancies, it can be verified that the length of the short bond in the carbon triangles increases with the increase of the distance between the vacancies; however, the average length of this short bond calculated from the lengths associated with each vacancy (dX$i$ and dA0) remains in most cases below the value corresponding to an isolated vacancy (1.98 \AA).

In order to investigate the effect of the creation of the second vacancy on the ground state of the system and on its total magnetic moment, different configurations were considered in terms of the relative location of each vacancy (A0A$i$ or A0B$i$ configurations) and of the separation between the vacancies (different      $i$ values), as indicated in Figure \ref{structure}.
In this sense, the total energy difference between states with distinct magnetic couplings involving the magnetic moments associated with each vacancy was determined. The values of the calculated total energy differences considering ferromagnetic (FM) and antiferromagnetic (AFM) coupling for all configurations studied herein are shown in Figure \ref{energy}.

\begin{figure}[h]
\begin{center}
\includegraphics[width = 8.5 cm]{fig2.eps}
\caption{Total energy difference between AFM and FM states ($\Delta E_{AFM-FM}$) as a function
 of the distance (D) between the single vacancies.}
\label{energy}
\end{center}
\end{figure}

The results plotted in Figure \ref{energy} clearly show that the FM state is more energetically
stable than the AFM state for the case of the two vacancies created on the same sublattice (A0A$i$ configuration). The ferromagnetic coupling between the magnetic moments associated with the two single vacancies can be seen in Figure \ref{spinD}a in the case of the ground state of the A0A1 topological configuration, where only spin up (yellow) electron states are observed around the vacancies. On the other hand, for vacancies created on different sublattices, the AFM state is more energetically
stable than the FM state, which follows closely Lieb's theorem for bipartite lattices \cite{LiebPRL1989}.
For the ground state of the A0B1 configuration (see Figure \ref{spinD}b), one can observe the presence of contributions due to spin up (yellow) and spin down (blue) states on A and B sublattices, respectively, as expected for an antiferromagnetic coupling. These results are in good agreement with previous theoretical works\cite{yazyev2,helm,chenNanoscale2014},
where DFT calculations predict antiferromagnetic order in the case of vacancies on different sublattices and ferromagnetic order otherwise.
One can also note for both FM and AFM states that for all topological configurations the magnitude of the total energy difference
 $\vert \Delta E_{AFM-FM}\vert$ decreases with the increase of the distance
between the single vacancies, becoming negligible for distances D larger than 7 \AA. This finding helps to explain the difficulty (or the impossibility, in some cases) to observe experimentally the occurrence of magnetic order in graphene-based systems, since the defect concentration needs to be considerably high so as to produce a significant energy imbalance between FM and AFM states. For instance, Nair et al. recently reported the occurrence of paramagnetic behavior down to liquid helium temperatures in graphene samples presenting high defect concentrations (close to $10^{20} g^{-1}$), with the average separation between magnetic moments estimated at 10 nm \cite{nair2012}. The present results clearly show that this spacing is about 10 times larger than the threshold above which the energy difference between AFM and FM couplings becomes negligible. Thus, one could expect that, in graphene-based materials with this range of vacancy concentration, any indication of magnetic order can be completely ruled out. For vacancies randomly created on A and B sublattices and separated by distances above ca. 10 \AA, the results of our calculations clearly indicate there will be no definite magnetic order in the system.

\begin{figure}[!h]
\begin{center}
\includegraphics[width=8.5cm]{fig3.eps}
\caption{Net spin density distribution for the ground states of the (a) A0A1 and (b) A0B1 configurations. The spin up and spin down states are represented by yellow and blue colors, respectively.}
\label{spinD}
\end{center}
\end{figure}

Furthermore, we explored the effect of changing the distance between the two vacancies on the net magnetic moment of the system, in the case of the A0A$i$ configurations (where the ground state corresponds to FM coupling). Figure \ref{moment} shows there is a reduction of the total magnetic moment as the distance between the vacancies grows. It is also important to note that the net magnetic moment approaches a value equal to twice the magnetic moment of an isolated vacancy when the vacancies become too far apart. Thus, as the long range interaction between the two vacancies becomes negligible, the magnetic moment per vacancy is similar to the one corresponding to a single isolated vacancy located at the same sublattice. Moreover, one can also observe that for D around 5 \AA~, the A0A$1$ configuration, the total magnetic moment is somewhat higher than the double of the total magnetic moment of the isolated vacancy, clearly showing the effect of the FM coupling between the magnetic moments in this case. For all topological configurations, one can see that local magnetic moments are induced around the vacancies (as illustrated in Figure \ref{spinD}a) and the total magnetic moment has contributions from $\sigma$ and $\pi$ states. These results are in general agreement with previous calculations conducted in similar systems \cite{faccio2,francis2015nonchalant}. However, it is important to stress that the maximum values of the total magnetic moment in all cases here described are well below the values recently reported by Francis et al. \cite{francis2015nonchalant}, where total magnetic moments of ca. 3 $\mu_B$ are found for two vacancies located at the same sublattice and separated by more than 6.0 \AA. In contrast, our results show that the largest magnetic moment, which is ca. 14 $\%$ above the value corresponding to twice the magnetic moment of a single isolated vacancy, is found only for two vacancies quite close to each other (separation D around 5 \AA~, corresponding to the A0A$1$ configuration).
 It is clearly observed in Figure \ref{magmom}a,
that there is a strong spin splitting of $\pi$ orbitals, especially in the A0A1 case, which is due to the interaction
between the neighboring vacancies. This leads to an increase of the $\pi$ orbital contribution to the total magnetic
moment, making it larger as compared to twice the value corresponding to a single isolated vacancy. This effect of spin
splitting of $\pi$ orbitals is reduced with the increase of the
distance between the two vacancies  (see  Figure \ref{magmom}a and b), which is accompanied by the reduction of the net magnetic moment shown in Figure \ref{moment}.

\begin{figure}[!h]
\begin{center}
\includegraphics[width = 8.5 cm]{fig4.eps}
\caption{Total magnetic moment as a function of distance (D) between two vacancies on same sublattice.}
\label{moment}
\end{center}
\end{figure}

These results are in good agreement with what is known about the ground state of graphene-based systems with vacancy-induced magnetism, which is related to Stoner instability giving rise to ferromagnetism due to delocalized $\pi$ electrons and localized moments of $\sigma$ dangling bonds \cite{ozakiPRB2014}. Then, the ground state of a graphene sheet containing two vacancies on the same sub-lattice is spin-polarized with
net magnetic moment varying according to the topological configuration. Additionally, for defects
created on different sublattices, our results follow closely the prediction of Lieb's theorem, which indicates
the imbalance between the two sublattices is the origin of magnetism in graphene,
leading to an antiferromagnetic ground state in these cases.

\begin{figure}[!h]
\begin{center}
\includegraphics[width=8.5cm]{fig5.eps}
\caption{ Projected density of states (PDOS) on p$_z$ orbital of the carbon atoms in a graphene sheet with two vacancies in A0A$i$ configuration:
(a) A0A1 (b) A0A4.}
\label{magmom}
\end{center}
\end{figure}

\section{Conclusion}

In summary, we have used spin-polarized DFT calculations to investigate the magnetic interaction between two atomic vacancies in a graphene sheet for different topological configurations, keeping fixed the defect concentration. In this study, we have considered
vacancies created either on the same or on different sublattices for various distances between them. The general conclusion emerging from this analysis was that the ground state of the system corresponds to a ferromagnetic or antiferromagnetic coupling of the magnetic moments associated with the interacting vacancies in the case of vacancies created on the same sublattice or in different sublattices, respectively.
The results revealed that the net magnetic moment for
the case of two vacancies on different sublattices moves towards the double of the magnetic moment of the isolated
vacancy with the increase of the vacancy separation. This trend indicates that the vacancy-vacancy interaction becomes negligible for long distances and that the magnetic moment per vacancy is similar to the case of a single isolated vacancy.  However, for the configurations with a short distance between the two vacancies, the
 interaction between the magnetic moments associated with the vacancies  conduct to different effects on the total magnetic moment for each type of configuration. This effect is attributed to the magnitude of the spin splitting of $\pi$ states.
Finally, our results have clearly evidenced how difficult it would be to observe experimentally the emergence of magnetic order in graphene-based systems containing randomly created atomic vacancies, since the energy difference between cases of antiferromagnetic and ferromagnetic order decreases quickly with the increase in the distance separating each vacancy pair.

\section*{Acknowledgments}

The authors acknowledge the support from Brazilian
 agencies CNPq and CAPES; we thank also to CENAPAD-SP for computer time.


text:
HomeOrganicsAnaerobic DigestionComparison of Anaerobic Digestion in the EU vs. the U.S. - Part Two
Comparison of Anaerobic Digestion in the EU vs. the U.S. - Part Two
James Miller, Christine Mejia Arbogast, Kris Ferguson | Jan 14, 2022
In addition to energy sales, revenues for AD facilities primarily derive from two other sources: (1) disposal tipping fees and (2) from the sales of compost and soil amendments which differ considerably between the EU and the U.S. The following discusses the impact of those two factors on AD development.
Historic and Current Market Factors in the EU
In the absence of regulations affecting pricing, landfill disposal is usually a less expensive end destination for organics. Therefore, relative tipping fees are a significant factor for assessing the business case for AD. The higher the landfill tipping fee, the more attractive and cost competitive AD becomes, as explained below.
Primarily due to governmental levies and dwindling landfill space, tipping fees in the EU are on average significantly higher than in the U.S. For instance, landfill tipping fees in Sweden and Denmark (with taxes included) are $185/ton and $125/ton respectively. Germany is the only EU country that does not impose levies, but its landfill tipping fees are still a relatively high $165/ton even without them.
By contrast, the U.S. has substantial available landfill space, and tipping fees are much lower. The Environmental Research & Education Foundation (EREF) maintains a database of landfills and their tipping rates throughout the United States[1]. According to the EREF database, in 2020 the average tipping fee for 493 landfills across the country was $53.72/ton.
In California, while landfill tipping fees are slightly higher than the low national average (compared to the EU), large amounts of the waste stream flow through transfer stations with much higher rates making the financial case for AD development better. In the San Francisco Bay area, nearly all of the major transfer stations charge higher than $100 per ton for disposal.
Where gate fees are even higher, such as in the Northeast, AD is cost competitive, and a few states in that region have also enacted legislation requiring organics collection and processing. This has led to considerable interest in the development of AD facilities.
Elsewhere across the country, tipping fees are typically lower and well below those in the EU. The combination of low tipping fees and abundant landfill space are a disincentive for organics diversion and processing.
Another important market consideration is the sales of compost and soil amendments. In most EU countries, petrochemical products, including fertilizer, are relatively more expensive than in the U.S. As a result, EU markets for compost and soil amendments and the resulting sales revenues are stronger, steadier, and more predictable.
Waste Generation, Feedstocks
The feedstocks that power AD facilities must also be considered. For example, is the composition of food wastes different in the EU compared to the U.S.? The simple answer is yes. In the EU, there is less food packaging and more emphasis on Extended Producer Responsibility, or EPR. In Germany, the Closed Substance Cycle and Waste Management Act (Act) was passed in 1996 requiring producers to take responsibility for end-of-life management of their products.[1] These types of EPR laws are starting to appear across the United States, as in Maine which became the first state to sign EPR legislation into law for plastics and packaging materials, with Oregon passing a similar law in August of 2021.[2] There are also less below-sink garbage disposals in the EU compared to the United States, so a higher percentage of food waste enters the collected waste stream. Collection and post-collection practices (i.e., a larger percentage of separate color-coded containers for food waste are found in Germany vs. the U.S.) may also vary.
As it relates to feedstocks, a measurable difference between the EU and U.S. waste streams is the level of contamination in the organics stream itself. Source-separated organic waste streams in the EU are generally cleaner than within the U.S. due to better understanding and participation among generators, a result of 20 years of practice.
However, there are more similarities between European and U.S. waste streams than differences. Thus, technologies and systems that were developed for processing European waste streams can also be successful when applied to U.S. waste streams.
Influence of Waste-to-Energy
Another important consideration when discussing the benefits of AD is the presence (or lack thereof) of Waste-to-energy (WTE) facilities. In most areas of the EU, solid refuse fuel (SRF) is a valuable product derived from organic waste that cannot be digested or composted. Biodegradable materials that do not make it into the organics stream for composting or AD can be converted to SRF and have a positive commercial value. With only about 71 WTE facilities in operation in the U.S.[3] and particularly in California (which only has two), those materials will almost always be disposed into a landfill and therefore have a negative commercial value.
Economic feasibility is the primary factor behind the discrepancy between the development of AD facilities in the EU and the U.S. Tip fees needed to cover the costs to develop and operate AD facilities can be competitive compared to the high landfill tipping fees throughout the EU. Lower landfill tipping fees as well as lower energy costs in the U.S. make it financially difficult to develop AD facilities without enforceable regulatory requirements and financial incentives.
In the EU, AD markets are driven in part by government policies that have not been in existence in the U.S. This includes high electricity prices for renewable electricity driven by feed-in tariffs.[1] Development and implementation of AD in the EU, which for the most part is 20 years ahead of the U.S., required government foresight and intervention. Due to market factors such as high fuel and landfill costs, the business case for AD is much stronger in the EU than in the United States. The driver for incentives and regulatory mandates includes the many environmental benefits of AD.
One of the most important environmental benefits is the ability of an AD facility to significantly reduce or eliminate greenhouse gas emissions. By capturing methane gas that would have otherwise been emitted into the atmosphere, AD facilities displace fossil fuels that contribute to climate change. A secondary benefit is the production and sale of beneficial end use products and applications.
Strong regulatory mandates for organics diversion from landfills, such as those being implemented pursuant to SB 1383 in California, coupled with government funding and financial incentives and/or tariffs for renewable energy are what is needed in the U.S. to try replicating the advancement of AD development in the EU. Similar government intervention and incentives have been gaining traction in the U.S. with increased attention on climate change, and while there are features of the AD industry in Europe that we cannot expect to duplicate in the U.S., much can be learned and emulated, and the demand for AD will continue to grow and provide those benefits here.
James Miller is the CEO of JR Miller & Associates. He can be reached at [email protected].
Jim is one of the Featured Speakers at the Organics Recycling Conference & Food Recovery Forum at WasteExpo, May 9-12, Las Vegas. For more information on the conference programs click here.
Editor's note: Part one of this series on anaerobic digestion focuses on background, regulations and incentives. Part two covers historic and current market factors in the EU, feedstocks and the influence of waste-to-energy.
[7] MSWLF-Tipping-Fees-2020_FINAL-m2yyxt.pdf (erefdn.org)
[8] THE CLOSED SUBSTANCE CYCLE AND WASTE MANAGEMENT ACT (iisd.org)
[9] Maine Becomes First State to Sign Extended Producer Responsibility Law for Packaging, Other States with Plastics and Packaging Bills May Follow Shortly (bdlaw.com)
[10] Is Waste to Energy Set to Increase in the Coming Years? | AltEnergyMag
[11] Anaerobic Digestion Evaluation Study (recyclingandenergy.org)


text:
The Ghana Education Service has oversight responsibility over the day to day administration of education in the district. The District Assembly however, plays a facilitative role through the provision of certain basic infrastructure and the creation of enabling environment for the progress of education in the district.
Type of Educational Facilities in the District
The socio-economic development of any district is largely depended on the quality of its educational delivery. This is inherent in the quality and adequacy of educational facilities and infrastructure within the district. In all the district has 55 Kindergarten, 55 Primary Schools, 45 Junior High Schools, 4 Senior High Schools, 1 Vocational/Technical School, 2 tertiary 6 ICT Centres and 3 Libraries..
A survey conducted in 2014 in the district revealed that some of the basic schools have educational facilities such as classrooms, urinals and toilet facilities. However ancilliary facilities such as computer laboratories, water tanks, football pitches, furniture, kitchen, staff common rooms and new classroom blocks need to be provided to create conducive atmosphere for teaching and learning.
The survey also revealed that Amadu, Akaka, Soboyo and Mobia communities in the Temate Electoral Area ought to be provided with basic school facilities to spare the pupils from travelling as far as Temate/Nkwanta to access education. This has however resulted in the increased enrolment in the A.M.E Zion Educational Complex in Nkwanta.
The Assembly should however make plans of increasing and improving the educational facilities in the District to hold the growing population of the school-going age. The siting of educational facilities should also be considered in order to provide for communities/settlements which lack these facilities. Table 1.47 Provides analysis of the types of educational facilities in the district.
Basic School Enrolment
The total enrolment in basic schools in the district for the 2013/2014 academic year is 17,823 of which 9,362 corresponding to 53.0 percent are boys and 8,461 representing 47.0 percent are girls. Out of the total basic school enrolment of 17,823, 4,323 which represent 24.0 percent are in the pre-school (KG). This is made up of 51.0 percent (2,196) boys and 49.0 percent (2,127) girls. Also 9,807 (55.0%) pupils constituting 53.0 percent of boys (5,170) and 47.0 percent of girls (4,637) are in the Primary School. Thus, the total enrolment in the Junior High School is 3,693 (21.0%) comprising of 1,996 (54.0%) boys and 1,697 (46.0%) girls.
It could be observed from above that girls' enrolment in all levels of basic education is generally lower than the boys' enrolment. Regardless of the gap between boys and girls enrolment in basic schools in the district is very narrow which explains that girls' participation in basic schools in the district is encouraging.
Table 2.30 and figure 1.16 below provide more detailed analysis on basic school enrolment in the district for both private and public basic schools.
The total enrolment in Senior High School and Vocational/Technical School in the district as at 2013/2014 academic year is 4,775 constituting of 57 percent (2,736) males and 43 percent (2,039) females. Out of this number, 4,738 (99%) comprising of 57 percent (2,701) males and 56.7 percent (2,037) females are in the Senior High School. The remaining 37 (1.0%) consisting of 96 percent (35) males and 4.0 percent (2) females are in the Technical/Vocational School.
It is clear from this analysis that the boys-girls enrolment in the basic schools follows the same trend in boys-females' enrolment in Senior High School in the district. The data also indicates that parents are gradually accepting the need to educate their girl child which is a great potential for the district in addressing the issue of gender inequality and ensuring full participation of both sexes in active decision making for sustainable development.
Table 2.31 and Figure 1.17 present analysis of Senior High School and Technical/Vocational School in the both public and private institutions in the district.
Number of Teachers
Data gathered revealed that the district has a total number of 1,324 teachers. In effect, the teacher-pupils' ratio in the district is 1:16 and the teacher-students ratio is 1:18 which show that teachers are more than available in the district. There is an issue however, to do with the geographical distribution of teachers in the district in that greater percentages of these teachers are located in the Southern part of the district to the neglect of the Northern part. There is the need to put in place certain conscious mechanisms in the form of incentives such as allowances and accommodations among others to attract teachers to these deprived areas.
Of the total number of teachers 60.0 percent corresponding to 792 teachers are trained whilst the remaining 40.0 percent corresponding to 532 teachers are untrained. In general, it could be concluded that the district has more trained teachers than untrained teachers and for that matter the issue of trained teachers should be taken on a lighter weight.
However, further analysis indicates that trained teachers in the district are skewed in terms of the level of school (i.e. Pre-School, Primary, JHS or SHS), type of school (i.e. Secondary or Vocational/Technical), type of institution or ownership (i.e. private or public) and geographical distribution or location (i.e. Southern or Northern part). With respect to the level of school the JHS has the highest proportion of trained teachers of 253 followed by primary with 239 teachers. Thus, the vocational level has the lowest number of trained teachers of 6 teachers.
It is also obvious from the analysis that whereas the public institution (school) has 68.0 percent trained teachers the private sector has only 16.0 percent trained teachers. This situation calls for immediate intervention from the government. This could be in the form of intensive training workshop to abreast these untrained teachers with the vital professional and pedagogical skills required to promote quality teaching and effective learning.
Table 2.33 provide detailed analysis of the teacher situation in the district.
Classroom blocks
The district has 80 No 3 unit, 263 No 6 unit and 124 No 3 unit classroom blocks for public K.G. Primary and Junior High Schools respectively as shown in table 1.51 below. Comparing these figures to the number of public K.G. Primary and Junior High schools in the district (i.e. 55, 55 and 45 respectively) it is apparent that these classroom blocks are woefully inadequate. Notwithstanding this, most of these classrooms especially in the Northern part are dilapidated and in very poor conditions. There is the need to provide additional stock of classroom blocks and rehabilitate existing ones that are in very poor conditions.
2.20.6	Circuits in the District
There are 5 circuits in the district. Table 2.35 below gives names of circuits in the district and the number of schools under each circuit.
It could be observed from the above table that there are seven (7) and five (5) Junior High School in the Banko and Besoro Circuits respectively. It is therefore possible that these Junior High Schools in these circuits cannot contain the enrolments levels of pupils from the primary schools. To curb this situation more JHS should be provided in these areas. It is also highly recommended that most of the schools should be considered for the School Feeding Programme to boost the enrolment level in these deprived areas.
Furniture Situation in the District
The total number of furniture in the district does not commensurate with the number of enrolment in the various schools. There is the need to provide additional furniture stock. Table 1.53 shows the furniture situation in the district on circuit basis.
School Feeding Programme & Capitation Grant
The Sekyere Kumawu District school feeding programme cover fifteen schools. These schools are;
1.Kumawu Anglican primary
2.Kumawu Benevolent Islamic Basic
3.Kumawu R/C primary
4.Kumawu presby primary
5.Woraso D/A primary
6.Bodomase Methodist Ka/primary
7.Woraso D/A kG/primary
8.Woraso presby kG/primary
9.Sekyere D/A Saviour kg/primary
10.Banko D/A KA/Primary
11.Besoro D/A primary
12.Oyoko D/A primary
13.Nkwanta A.M.E. Zion primary
14.Sekyere D/A Basic school
15.Bodomase D/A Primary
Problems and Challenges of Education
•	Some of the classroom blocks are dilapidated and in need of urgent maintenance
•	Large number of unqualified Teachers
•	Unpaid salaries
•	Inadequate office equipment


text:
The Breaking Point by Stephen Koch
Below is the latest in an ongoing series of guest reviews. Our reviewer this time is David Schwartz, author of one of my favorite stories from 2004, "The Lethe Man" (in Say...Why Aren't We Crying?), as well as stories in such places as Strange Horizons and Fortean Bureau.
The Breaking Point: Hemingway, Dos Passos, and the Murder of José Robles by Stephen Koch
a guest review by David J. Schwartz
A novelistic account of the disintegrating friendship between American modernists John dos Passos and Ernest Hemingway, set during the Spanish Civil War, The Breaking Point is as frustrating as it is fascinating. In attempting both literary and personal biographies of his protagonists, Stephen Koch ultimately falls short of doing either very well; the result is an odd hybrid between cloak-and-dagger novel and critical psychoanalysis. Yet as a chronicle of the machinations at work behind the conflict itself, the book points at the deeper resonances of the war. Both as shadow-play and as dress rehearsal for World War II and the Cold War, the conflict between and among the Second Spanish Republic and Nationalists under Franco is at times eerily predictive. In the end it's difficult not to imagine that Koch would have preferred to write a different book; a sobering and sympathetic examination of how well-meaning Americans of letters like Dorothy Parker and Archibald MacLeish were fooled by Stalin's Comintern operatives into believing they were aiding the working class, and in the process laid themselves open to the McCarthy witch hunts. But this is not that story.
The breaking point of the title has to do with the murder of John dos Passos's close friend José Robles Pazos sometime in March of 1937. The particulars of the case are still unclear; the official version was that Robles was arrested, tried, and executed as a fascist spy. Considering that Robles was a lifelong leftist who left his teaching job at John Hopkins University to aid the Republic, Dos Passos didn't buy it. The more likely scenario is that Robles was killed by Stalinist agents because of uncertainty over what he knew and might subsequently report about the real agenda of the Soviet "observers" in Spain. The Republic was not a united front, but a coalition of interests struggling for ultimate control even as they fought the fascists. But again, the death itself is not Koch's focus, nor even are the intrigues behind it. He is most interested in the way Robles's death affected the friendship between "Hem" and "Dos."
By 1937 Dos had reached the apex of his career; he'd appeared on the cover of Time Magazine, and his watershed U.S.A. trilogy was complete. Hem, though slightly behind Dos's curve, had no legitimate reason for professional jealousy; nonetheless, something had already gone very wrong in their friendship. Koch states that much of the original draft of To Have and Have Not contained scathing and libelous attacks on Dos: "[He] is presented as an (of course) unmanly blowhard, a political and artistic poseur, a cuckold, a masochist, and a deadbeat. The book sneers at Dos Passos's method as shallow and artistically trivial." Koch argues that these attacks were a product of Hemingway's insecurity, and the interactions between the Dos Passos character (Richard Gordon) and the Hemingway analogue are clashes between aspects of Hem's own personality. "The key to the novel's dominant bitterness is of course Hemingway's own self-contempt. . . . It is Richard Gordon who glimpses Hem passing by [and] invariably looks down on his rival's wretchedness with contempt. . . . In other words, in To Have and Have Not, Dos Passos is made into the vehicle of Hemingway's own self-loathing."
The book is full of this sort of literary psychoanalysis, and while at times it sheds light on the texts, set against the larger conflict it begins to seem rather beside the point. What is certain is that when Hem and Dos traveled (separately) to Spain to cover the war, their attitudes had already become quite different. When Robles turns up missing, Dos searches for him; Hemingway tells him to leave the matter alone and stop asking questions. "'Don't put your damn mouth into this Robles business,'" he tells Dos upon the latter's arrival in Madrid. "'The fifth column'--covert Franco sympathizers in Madrid--'is everywhere. Just suppose your professor took a powder and joined the other side.'" When Hem learns, thanks to the intercession of one of the Comintern's many pawns, the official "truth" of the matter, he takes great pleasure in humiliating Dos both politically and artistically by casting suspicion upon Dos's friendship with the "fascist traitor."
I must confess that I am one of those who find Hemingway more interesting as a character than as a writer; but the fact that Koch appears to feel similarly does not service his book particularly well. He is less interested in Hem's motives than in the dastardly nature of his betrayals, be they of Dos or of the women in his life. None of which is to suggest that Koch vilifies Hemingway, or that he bears no admiration for his work. There's an air of rueful admiration behind the reportage of Hem's lies and libels--as if the author were shaking his head and smiling as he researched, saying to himself, "That magnificent bastard!" And the lambasting of works like the aforementioned To Have and Have Not is largely motivated by disgust at the waste of indisputable talent. Nevertheless, the text's sympathies lie ultimately with Dos Passos, who is after all the wronged party. Dos is not a legend, though, only a minor modernist with two or three great books to his credit. Hemingway is the larger-than-life figure careening through this story, the self-styled realist taken in by the proletarian fantasies woven by Joris Ivens and other guides and mentors, most of whom Koch believes to have been Comintern operatives.
Koch seems unwilling to peel back the labels of "sadist" and "misogynist" to even guess at Hem's deeper motivations. Describing Hemingway's expectations that a woman "focus exclusively on him and his needs," Koch cops out by saying "The man was just that selfish; and the truth was just that simple." In the end, we are given the archetypal Hemingway and little more, and Dos Passos is--if possible--even less illuminated by the narrative. Cast in the role of the quester, his search is his virtue; his flaw, if he has one, that he is too trusting, too idealistic. By choosing to approach these events as a narrative, Koch makes Hem and Dos into characters; but by only attempting the shallowest of dives into their psychologies, he leaves them flat, unformed, and ultimately not that interesting. (Also frustrating is the inexplicable lack of an index--though there are endnotes--in a book packed with real-life personalities and events. It's as if everyone involved chose to treat this as a work of fiction.)
The character which most stands out in The Breaking Point is the war itself. Even presented in profile, its beginning and end lopped off, limited primarily to the intrigues of Stalin and the left (the Nationalists get off easy in this book), it still comes through as a fascinating microcosm of the Twentieth Century. At times it bears the lingering flavor of tragic romance, at others it reads as a collision of hopeless naïvete with cynical manipulation. Perhaps it was the resonance of this latter opposition which Koch hoped to parallel with his tale of Dos and Hem; I only wish he had scratched deeper beneath their surfaces.
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Worst Last Lines
Dead in the West by Joe R. Lansdale


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