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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?

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

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.

Stefan Stoll wrote: ↑Tue Mar 26, 2024 9:54 pm

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?

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.