Hyperfine Coupling Tensor&Constant (A)

[HaticeHatipoglu]

Hello,
I want to define a system which includes an alkali metal atom like 87 Rubidium. You all know that alkali atoms have only one valance electron. So I want to calculate Hamiltonian of the system under magnetic field B (along z-axis)

Code: Select all

Sys.S=1/2
Sys.g=2.0023 (value of gfree)
B=[0;0;350]

For Hyperfine coupling Hamiltonian term, I must define a nucleus/isotope.

Code: Select all

Sys.Nucs='87Rb'

At that time I must write Hyperfine coupling constant or tensor (A). But I have no idea about that. It does not need to be a precise value because I will make an assumption about Hperfine coupling constant and I will assume it is isotropic. How can I calculate simple Hyperfine coupling constant of an isotope or where can I find Hyperfine coupling constants of isotopes?

Note: There are always 1 electron in my system. Therefore, we can think that Hyperfine interaction Hamiltonian caused only between 1 electron and 1 nuclei&isotope.

Best Regards,
Hatice Hatipoğlu
haticehatipogluu@gmail.com

[Stefan Stoll]

The hyperfine constant for rubidium is well known - you'll it by googling "rubidium hyperfine". It's about 1 GHz.

To convert to another Rb isotopes (neglecting any potential isotope effects on the electron distribution), use EasySpin's nucgval: A_87Rb = A_85Rb/nucgval('85Rb')*nucgval('87Rb').

This code snippet:

Code: Select all

clear
Rb.S = 1/2;
Rb.Nucs = '85Rb';
Rb.A = 1012;  % MHz
B = [0 0 0];  % mT
H = ham(Rb,B);
E = eig(H)/1e3  % -> GHz

shows that at zero field, the hyperfine interaction splits the electronic 2S_1/2 ground state of Rb into a lower-lying quintet (F=2) and a higher-lying septet (F=3).

Here is a level diagram:

Code: Select all

clear
Rb.S = 1/2;
Rb.Nucs = '85Rb';
Rb.A = 1012;  % MHz
levelsplot(Rb,'z',[0 1000],9.5);

Note that you might want to look up the exact g value for Rb. It is probably slightly different from the free-electron g value 2.0023.