Intensity output of resfreqs and resfields

[gdold]

I'm relatively new to the field, and am trying to understand the meaning of the intensity output from the resfreqs (and resfields) solvers. The doc page does not state what the value specifically corresponds to (other than some parameterisation of the strength of the transition), and the resfreqs and resfields solvers appear to give different values for the same transition.

Looking a simple example of a free electron:

Code: Select all

Sys = struct('g',2.002319,'S',.5); % Free electron

Exp = struct('Field',50); % mT
[Freq,Int] = resfreqs_matrix(Sys,Exp);
fprintf('Resfreqs: Freq = %f MHz, Int = %f\n',Freq,Int);

Exp = struct('mwFreq',1.401247369,'Range',[0,100]); % GHz
[Freq,Int] = resfields(Sys,Exp);
fprintf('Resfields: Freq = %f MHz, Int = %f\n',Freq,Int);

outputs two different intensities:

Code: Select all

Resfreqs: Freq = 1401.247369 MHz, Int = 196.349419
Resfields: Field = 50.000000 mT, Int = 7.006237

Could anyone help clarify what these intensities mean, what are the units, and how they correspond to something physically measurable? The spin system I'm working on is significantly more complex than this and it would be very useful to be able to convert these intensities to something physical or to normalise them against something.

[Stefan Stoll]

The numbers are based on Fermi's Golden Rule. Below is a code snippet that demonstrates what is going on. If you want the full details, check out this PRL paper.

Code: Select all

clear, clc
Sys.S = 1/2;
Sys.g = 2;
Exp.Field = 50; % mT

% The frequency-domain intensity is obtained from Fermi's Golden Rule.
%-----------------------------------------------------------------------
[nu,Intnu] = resfreqs_matrix(Sys,Exp);

% Here is the corresponding explicit calculation.
H = sham(Sys,[0;0;50]);  % Hamiltonian, in MHz
[V,E] = eig(H);
Sx = sop(Sys.S,'x'); % unitless
MatrixElement = V(:,1)'*Sx*V(:,2);  % unitless
c = Sys.g*bmagn/planck/1e9;  % MHz/mT
Intnu_ = (MatrixElement*c)^2;  % (MHz/mT)^2

[Intnu Intnu_]

% For the field-domain intensity, a factor proportional to 1/g is
% included to account for the frequency-to-field conversion of the
% lineshapes.
%-----------------------------------------------------------------------
Exp.mwFreq = 9.5;
Exp.Range = [300 400];
[B,IntB] = resfields(Sys,Exp);

% Here is the explicit calculation.
IntB_ = Intnu_/c; % MHz/mT

[IntB IntB_]