How do I assess the linearity of a photomultiplier tube? I have used a scintillation counter coupled with a photo-multiplier tube to record the gamma spectra for sodium-22, cobalt-60, and Cesium-137. 
I need to know how to assess the linearity of the photo-multiplier tube that I used. The photo-multiplier tube is in pulse mode, and multichannel pulse-height analysis is used in the process. 
I already know that the pulse linearity in pulse mode is chiefly dependent on the peak signal current, and that the linearity is limited by the space charge effects in pulse mode. However, I still do not know how to assess the linearity in pulse mode, given the data I have. 
 A: Each of your reference sources should produce a (set of) relatively narrow-energy line(s), whose energy you can discover from an appropriate reference.  In the spectrum from your multichannel analyzer, each of these reference lines should show up as an intensity peak in a particular amplitude channel, which you can read off by eye if it's narrow or by fitting if you want to be more sophisticated.
So your data set consists of a list of MCA channel numbers, each of which corresponds to a known gamma-ray energy.
Fit these data to a straight line.  The slope will be the "gain" of the detector system, with units like keV/channel, and the intercept will give you a "pedestal" channel where a zero-energy event would appear if you allowed your system to trigger on it.
This is enough to tell you whether your system is linear-ish or whether you've got a big gain difference between low- and high-energy events.  How you characterize and respond to any observed nonlinearity depends on just what you're trying to do.
A: Any pulse-counting scheme has a deadtime limitation, so you have an
easily predicted nonlinearity for high count rates, in that deadtime.
This will be determined by the pulse-measuring algorithm and/or any delay-line
preprocessing for baseline restoration.
At low count rates, you can use a calibration source with multiple
filters, or multiple calibration sources, to spot-check the sensitivity
at different (known) count rates.   
If you intend to capture a mixed spectrum, it is possible that the deadtime
for one species will include a gain-modulation of the sensitivity to
another species.  Good regulation of the cathode-to-first-dynode
voltage in your photomultiplier power supply can help.
Because you say 'nonlinearity in the PMT', I assume that you 
know the sensitivity of your scintillator to the various incident radiation(s).
