diff --git a/BSE-PES.tex b/BSE-PES.tex
index 1a518ac..38b8f03 100644
--- a/BSE-PES.tex
+++ b/BSE-PES.tex
@@ -337,6 +337,7 @@ with $\epsilon_{\lambda}$ the dielectric function at coupling constant $\lambda$
 	\\
 	\times  \qty(\frac{1}{\omega - \OmRPA{m}{\IS} + i \eta} - \frac{1}{\omega + \OmRPA{m}{\IS} - i \eta}),
 \end{multline}
+
 where the spectral weights at coupling strength $\lambda$ read
 \begin{equation}
 	\sERI{pq}{m} =  \sum_i^{\Nocc} \sum_a^{\Nvir} \ERI{pq}{ia} (\bX{\IS}_m + \bY{\IS}_m)_{ia}.
@@ -344,6 +345,7 @@ where the spectral weights at coupling strength $\lambda$ read
 
 In Eq.~\eqref{eq:W},  $\eta$ is a positive infinitesimal, and $\OmRPA{m}{\IS}$ are the direct (\ie, without exchange) RPA neutral excitation energies computed by solving the linear eigenvalue problem \eqref{eq:LR} with the following matrix elements
 \begin{subequations}
+\label{eq:LR_RPA}
 \begin{align}
 	\label{eq:LR_RPA}
 	\ARPA{ia,jb}{\IS} & = \delta_{ij} \delta_{ab} (\eHF{a} - \eHF{i}) +   2 \IS \ERI{ia}{jb},
@@ -357,6 +359,7 @@ The relation between the BSE formalism and the well-known RPAx approach can be o
 %namely setting  $\epsilon_{\lambda}({\bf r},{\bf r}'; \omega) = \delta({\bf r}-{\bf r}')$ 
 so that   $W^{\lambda}$ reduces to the bare Coulomb potential. In that limit,  the $GW$ quasiparticle energies reduce to the Hartree-Fock eigenvalues, and Eqs.~\ref{eq:LR_BSE} to the RPAx equations: 
 \begin{subequations}
+\label{eq:LR_RPAx}
 \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} ],