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Pierre-Francois Loos 2020-02-03 16:30:00 +01:00
parent 09aff3b148
commit fbea44ea73
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BSE-PES.tex
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@ -347,7 +347,6 @@ In Eq.~\eqref{eq:W}, $\eta$ is a positive infinitesimal, and $\OmRPA{m}{\IS}$ a
\begin{subequations} \begin{subequations}
\label{eq:LR_RPA} \label{eq:LR_RPA}
\begin{align} \begin{align}
\label{eq:LR_RPA}
\ARPA{ia,jb}{\IS} & = \delta_{ij} \delta_{ab} (\eHF{a} - \eHF{i}) + 2 \IS \ERI{ia}{jb}, \ARPA{ia,jb}{\IS} & = \delta_{ij} \delta_{ab} (\eHF{a} - \eHF{i}) + 2 \IS \ERI{ia}{jb},
\\ \\
\BRPA{ia,jb}{\IS} & = 2 \IS \ERI{ia}{bj}, \BRPA{ia,jb}{\IS} & = 2 \IS \ERI{ia}{bj},
@ -361,7 +360,6 @@ so that $W^{\lambda}$ reduces to the bare Coulomb potential. In that limit, t
\begin{subequations} \begin{subequations}
\label{eq:LR_RPAx} \label{eq:LR_RPAx}
\begin{align} \begin{align}
\label{eq:LR_RPAx}
\ARPAx{ia,jb}{\IS} & = \delta_{ij} \delta_{ab} (\eHF{a} - \eHF{i}) + \IS \qty[ 2 \ERI{ia}{jb} - \ERI{ij}{ab} ], \ARPAx{ia,jb}{\IS} & = \delta_{ij} \delta_{ab} (\eHF{a} - \eHF{i}) + \IS \qty[ 2 \ERI{ia}{jb} - \ERI{ij}{ab} ],
\\ \\
\BRPAx{ia,jb}{\IS} & = \IS \qty[ 2 \ERI{ia}{bj} - \ERI{ib}{aj} ]. \BRPAx{ia,jb}{\IS} & = \IS \qty[ 2 \ERI{ia}{bj} - \ERI{ib}{aj} ].