ThermalDistributionModel amplitude instead just works like center

[acerbjorn]

Hi, hope I am writing this in the right place.

The ThermalDistributionModel lineshape is defined, as far as I can tell,

real(1/(amplitude*exp((x - center)/not_zero(kt)) + offset + tiny*1j))

However, this means that amplitude serves the same function as the center variable. By rewriting amplitude into the exponential, one gets

1/(exp( (x-center + log(amplitude)*kT)/kT ) + offset)

I think, given the name that amplitude is probably meant to be in the numerator, so it can control the height of the lineshape, So something like

real(amplitude/(exp((x - center)/not_zero(kt)) + offset + tiny*1j))

[newville]

@acerbjorn I see your point, and don't disagree that amplitude could be moved in this definition. That change would break backward compatibility, which we should be reluctant to do ;).

This model was added from a PR from @mpmdean, so I think we should get their opinion on this too.

Anyone have any preferences for whether to change thermal_distribution() in this way?

[mpmdean]

The reason that amplitude appears as it does is to match the common form in physics at the link seen in the docs.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disfcn.html

i.e. amplitude serves as was a written as A.

It's very reasonable to raise the question of whether this is good notation. In light of the comment, it might be better to rename it as A?

I also have some sympathy about the idea of changing it.

[newville]

@mpmdean Thanks!

It does seem like amplitude should be an overall scale factor here.

We could make a new function (or 3 separate functions for boltzmann, bose, and fermi distributions?) with amplitude as an overall scale factor. Or we could change thermal_distribution, which would break back compatibility.

Any preferences?

[mpmdean]

I don't have strong preferences, but I think it might be better to avoid changing the thermal_distribution in a way that might not be noticed.

[newville]

@acerbjorn @mpmdean I propose adding new, separate model functions/lineshapes for Maxwell-Botzmann, Bose-Einstein, and Fermi-Dirac lineshapes, without the form keyword.