Intensity from resfreqs output vs explicit calculation

[Devout_Spin]

I'm trying to find transition intensities in frequency-domain for spin system with S=1/2, I=1/2. By explicit calculations from Fermi's golden rule I get about 2x larger intensity than from resfreqs_matrix output. Could anyone help explain why is there a discrepancy?

Code: Select all

clear, clc

% Spin System
Sys.g = 1;
Sys.A = 500;  % MHz
Sys.S = 1/2;
Sys.Nucs = '31P';

Exp.Field = 50; % mT

% Direct method
[Freq, Int1] = resfreqs_matrix(Sys, Exp);
Int1

% Explicit method
Ham = sham(Sys,[0; 0; Exp.Field]); % Hamiltonian
[V,E] = eig(Ham);
Sx = sop([1/2; 1/2],'xe');
MatrixElement = V(:,1)'*Sx*V(:,4);
Int2 = (Sys.g*bmagn/planck/1e9 * MatrixElement).^2 % (MHz/mT)^2

[Stefan Stoll]

If no temperature is given, EasySpin uses a scaling factor of 1/(2*prod(I+1), where I the vector of all nuclear spins in the system. For a single 31P nucleus, this gives the additional factor of 1/2.

[Devout_Spin]

If no temperature is given, EasySpin uses a scaling factor of 1/(2*prod(I+1), where I the vector of all nuclear spins in the system. For a single 31P nucleus, this gives the additional factor of 1/2.

What does this scaling factor account for when no temperature is given?

[Stefan Stoll]

It makes sure that the total spectra intensity is independent of nuclear spins. For example, 15N and 14N give 2 and 3 lines respectively, to give the same overall intensity, the 15N line intensities are divided by 2, and the 14N by 3.