Hyperfine structure - Hamiltonian and bases

I
Thread starter Teri
Start date Jan 5, 2019
Tags

Atomic Bases Hamiltonian Hyperfine Hyperfine structure Structure

In summary, hyperfine structure is a phenomenon in atomic spectra where closely spaced energy levels are split into finer levels due to interactions between electrons and the nucleus. The Hamiltonian in hyperfine structure is a mathematical operator used to calculate energy levels and transition probabilities. It can be solved using perturbation theory and numerical methods. There are two main bases used to describe hyperfine structure: the uncoupled basis and the coupled basis. Practical applications of hyperfine structure include atomic clocks, nuclear magnetic resonance spectroscopy, and laser cooling and trapping, as well as providing information for testing fundamental physics theories and studying the universe.

Jan 5, 2019

Teri

Hi, could you please explain me, how to copmute the yellow parts? Thank you very much.

Physics news on Phys.org

Jan 6, 2019

vanhees71

Science Advisor

Insights Author

Gold Member

2023 Award

I guess, it might help to read about the addition of angular momenta and Clebsch-Gordon coefficients. Your question is too vague to be answered in a forum posting.

1. What is hyperfine structure?

Hyperfine structure is the splitting of atomic energy levels due to the interaction between the magnetic moments of the nucleus and the electrons. This phenomenon is caused by the coupling between the nuclear spin and the electronic spin.

2. What is the Hamiltonian in hyperfine structure?

The Hamiltonian in hyperfine structure is a mathematical operator that describes the total energy of a system. It takes into account the interaction between the nuclear spin, electronic spin, and other factors such as the magnetic field and the nuclear quadrupole moment.

3. How is the Hamiltonian used to calculate hyperfine structure?

The Hamiltonian is used to solve the Schrödinger equation, which describes the behavior of quantum systems. By solving this equation, the energy levels of the hyperfine structure can be calculated.

4. What are the bases used in hyperfine structure calculations?

The bases used in hyperfine structure calculations are usually the eigenstates of the electronic and nuclear spin operators. These bases are known as the |F, mF> basis, where F is the total angular momentum and mF is its projection along the z-axis.

5. How does hyperfine structure affect atomic spectra?

Hyperfine structure causes the energy levels of atoms to split, resulting in multiple spectral lines instead of a single line. This splitting is usually too small to be observed with the naked eye, but it can be detected with precise spectroscopic techniques.