  Resonant inelastic X-ray scattering (RIXS) has become an important scientific
tool. Nonetheless, conventional high-resolution RIXS measurements (<100 meV),
especially in the soft x-ray range, require large and low-throughput grating
spectrometers that limits measurement accuracy and simplicity. Here, we
computationally investigate the performance of a different method for measuring
RIXS, Photoelectron Spectrometry for Analysis of X-rays (PAX). This method
transforms the X-ray measurement problem of RIXS to an electron measurement
problem, enabling use of compact, high-throughput electron spectrometers. In
PAX, X-rays to be measured are incident on a converter material and the energy
distribution of the resultant photoelectrons, the PAX spectrum, is measured
with an electron spectrometer. The incident X-ray spectrum is then estimated
through a deconvolution algorithm that leverages concepts from machine
learning. We investigate a few example PAX cases. Using the 3d levels of Ag as
a converter material, and with 10$^5$ detected electrons, we accurately
estimate features with 100s of meV width in a model RIXS spectrum. Using a
sharp Fermi edge to encode RIXS spectra, we accurately distinguish 100 meV FWHM
peaks separated by 45 meV with 10$^7$ electrons detected that were photoemitted
from within 0.4 eV of the Fermi level.
