Hyperfine interaction Hamiltonian.

Hhf = ham_hf(Sys)
Hhf = ham_hf(Sys,eSpins,nucSpins)
Hhf = ham_hf(Sys,eSpins,nucSpins,'sparse')

ham_hf constructs the hyperfine interaction part of the spin Hamiltonian of spin system spin system Sys, that is

The operator matrix Hhf is in units of MHz. If eSpins and nucSpins are specified, they select the electron and nuclear spins to include. For eSpins, 1 indicated the first electron spin. For nucSpins, 1 indicates the first nuclear spin. For example, for a system with 3 electron spins and 2 nuclei, eSpins=2 and nucSpins=[1 2] indicates the hyperfine interactions of electron 2 with both nuclei.

If 'sparse' is given as third argument, the Hamiltonian matrix is returned in sparse format instead of full format.

For a two-spin system AB

AB = struct('S',1/2,'Nucs','23Na','g',[2 2 2],'A',[230 210 200]);
AB.AFrame = [23 45 67]*pi/180;

with a hyperfine coupling matrix tilted with respect to the standard molecular frame, the eigenvalues of the hyperfine Hamiltonian are

E = eig(ham_hf(AB))

E =
 -270.1785
 -267.8967
 -262.5431
  146.7712
  150.1785
  157.8967
  172.5431
  173.2288

Obviously the slight anisotropy in A causes the states of the combined spin S+I to split in zero field.

ham, ham_cf, ham_ee, ham_ez, ham_ezho, ham_nn, ham_nq, ham_nz, ham_oz, ham_so, ham_zf