I have an energy spectrum for various gamma sources. What software programs are recommended for background extraction and peak fitting in this case?
The recommendations posted will depend on who is using the software already. Some commonly recommended commercial software for what you ask include the following:
Origin - widely used but general purpose (must roll your own routines)
Igor Pro - great to generate publication-ready graphics (must roll your own routines)
SigmaPlot - general purpose
PeakFit - dedicated solely to peak fitting (less emphasis on quality of results than e.g. Igor Pro)
Mathematica - general computing system that has a wide array of fitting functions.
Some freeware include the following:
Fityk - focused on a specific set of peak fitting options
MagicPlot - a lightweight app for general non-linear regression fitting
Peak-O-Mat - touts its utility for batch fitting of spectra
You can find some reviews (and other random recommendations) at these links:
arXiv -- specifically about analysis of gamma spectra
ResearchGate - reviews of general peak fitting in spectrscopy
WindowsReport - reviews of curve fitting software for Windows
for that you can use for example "Origin" or you can look if there is a python library, which does that for you, since Origin costs money.