intensities in resfields, high-temp limit

[stestoll]

There is an inconsistency with intensity scaling in the high-temperature limit in resfields for systems with multiple electron spins. (resfields_perturb does not support multiple electrons.)

In the following script, the numerical values in I1 and I2 should be identical, but they are not. I1T and I2T are correct.

clear, clc

g = [2 2.1];
Sys.S = 1/2;
Sys.g = g;
Sys.lw = 1;

Sys2.S = [1/2 1/2];
Sys2.g = [g; g];
Sys2.ee = 1;
Sys2.lw = Sys.lw;

Exp.Range = [310 350];
Exp.mwFreq = 9.5;

Exp.MolFrame = [0 0 0];

Exp.Temperature = [];
[~,I1] = resfields(Sys,Exp)
[~,I2] = resfields(Sys2,Exp)

Exp.Temperature = 293;
[~,I1T] = resfields(Sys,Exp)
[~,I2T] = resfields(Sys2,Exp)

I1 =
    6.6649
I2 =
   13.3298
   13.3298
I1T =
    0.0052
I2T =
    0.0052
    0.0052

[stestoll]

The transition rate for Sys2 is twice the transition rate for Sys1, because the Sx operators are not normalized. Therefore, the transition rate depends on the number of spins,

[stestoll]

Here is an example that illustrates the issue. The 2-spin and 1-spin spectra have different area ratios, depending on whether Exp.Temperature is set to a finite temperature or not.

clear, clc

g1 = 2;
g2 = 2.1;
Sys1.S = 1/2;
Sys1.g = (g1+g2)/2;
Sys1.lw = 0.3;

Sys2.S = [1/2 1/2];
Sys2.g = [g1 g2];
Sys2.ee = 100;
Sys2.lw = Sys1.lw;

Exp.Range = [310 350];
Exp.mwFreq = 9.5;
Exp.Harmonic = 0;

Exp.MolFrame = [10 20 30]*pi/180;

Exp.Temperature = 293;
[B,spc1a] = pepper(Sys1,Exp);
[B,spc2a] = pepper(Sys2,Exp);

Exp.Temperature = NaN;
[B,spc1b] = pepper(Sys1,Exp);
[B,spc2b] = pepper(Sys2,Exp);

sum(spc2a)/sum(spc1a)
sum(spc2b)/sum(spc1b)

tiledlayout('vertical')
nexttile
plot(B,spc1a,B,spc2a);
legend('1 spins','2 spins')
title('Exp.Temperature = 293')

nexttile
plot(B,spc1b,B,spc2b);
legend('1 spins','2 spins')
title('Exp.Temperature = NaN')