Units and normalization of abs(dipole)^2 in BSE eigenvalues.dat

[Pradhi Srivastava]

Dear BerkeleyGW developers and users,

I am performing a GW-BSE calculation for an example of a 2D insulator using BerkeleyGW 4.0. I am using absorption.cplx.x with the use_velocity option and would like to calculate the intrinsic radiative lifetime of the first bright exciton.
I would be grateful for clarification regarding the precise definition and normalization of the quantities in the eigenvalues.dat file:
1. What is the exact matrix element represented by Re(dipole) and Im(dipole)? Is it e^⋅⟨0∣r∣S⟩, e^⋅⟨0∣v∣S⟩, or another convention?
2. What are the units of Re(dipole), Im(dipole), and abs(dipole)^2? For example, is abs(dipole)^2 directly in (a_0^2, a_0=Bohr radius)​, or is it a velocity-matrix-element quantity in atomic units?

I would like to ensure that I do not confuse the transition matrix element printed in eigenvalues.dat with the volume-normalized spectral weight used to construct the dielectric function.

Thank you very much for your help.

Regards,

Pradhi