Angular dependent energy distribution (modelling TNSA)

Hi to everyone,

I am trying to model the proton beams obtained from target normal sheath acceleration TNSA.
I am using general particle source so to use as energy distribution some measured spectra we got in the lab.

The point is that in TNSA the energy distribution varies also according to the angle (Redirecting). Higher energies near the propagation axis, lower energies at larger angles.

I would like to implement this angular energy dependece by using gps. Is that even possible?
I red some old posts and it was suggested to switch to particlegun, but I was wondering if gps could be used instead.

I also tested the example 23 here: https://hurel.hanyang.ac.kr/Geant4/Geant4_GPS/reat.space.qinetiq.com/gps/examples/examples.html
(That I think now is included in the extedend examples in eventgenerator->exgps)
but I am not sure it does what I need, I don’t really get what I should use as Ehi and Weight.

/gps/ang/type user
/gps/hist/type phi (or theta)
/gps/hist/point E_hi weight

Geant4 Version: 11.2.2 (same issue with 10.5.1)
Operating System: Ubuntu 20.04
Compiler/Version: gcc version 9.4.0 (Ubuntu 9.4.0-1ubuntu1~20.04.2)
CMake Version: 3.16.3

Thank you for your help!