Questions tagged [hyperfine-structure]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
2answers
97 views

The most precise analytic solution of the hydrogen energy levels [closed]

Consider the problem where we want to calculate the energy levels of an electron in a hydrogen atom and we want to find the most precise analytic (i.e. a closed-form solution) solution that matches ...
1
vote
1answer
90 views

Hyperfine Splitting

What does Hyperfine Splitting exactly mean? I am having a bit of trouble understanding the concept of hyperfine splitting. I solved the problem of including hyperfine interaction for the ground state ...
1
vote
0answers
31 views

How to work in the states $|F,m_F\rangle$ in hyperfine structure?

Suppose that we have two atoms with one proton one electron each, and these electrons interact with each other. The states for the electrons are the singlet ($S=0$) and the triplet states ($S=1$). My ...
0
votes
0answers
12 views

Is there a table for hyperfine interaction tensor?

I'm doing research in biophysics and I need to find the hyperfine interaction tensors for ascorbic acid radical, FADH-, and oxigen radical (O2-). Is there a place where I can find the hyperfine ...
0
votes
0answers
31 views

Why cant we treat electron as a dipole in nucleus' magnetic field in this way in hyperfine structure?

In hyperfine structure modifications, the magnetic field due to magnetic moment of nucleus couples with the orbital angular momentum of the electron. The interaction(perturbation) term of the ...
2
votes
0answers
72 views

What are good quantum numbers for the Hyperfine Hamiltonian?

The hyperfine hamiltonian for an atom with one electron in valence shell is of the form: $ H = H_0 + A_1\vec{S}\cdot\vec{L} + A_2\vec{L}\cdot\vec{I} + A_3\vec{S}\cdot\vec{I} + A_4(\vec{I}\cdot\hat{r})(...
1
vote
0answers
82 views

Hyperfine Structure Derivation

Multiple sources, including the prodigal paper on the topic, "Theory of Hyperfine Structure" by Charles Schwartz, state that the hyperfine interaction can be written $$ \hat{H}_{hfs} = \sum_k \mathbf{...
0
votes
1answer
47 views

Neutral hydrogen atoms in inhomogenous magnetic field

In the 1996 gre exam this scenario comes up in a question: a beam of neutral hydrogen atoms in their ground state pass through a region of of strong inhomogenous magnetic field. In the official ...
1
vote
0answers
77 views

How can I calculate the hyperfine structure of a $p$-orbital?

I have a little problem with the calculation of the hyperfine structure of the 3p orbital in the hydrogen atom. The Hamiltonian is: Were represents the magnetic moment of the proton and the ...
0
votes
1answer
65 views

Basic labeling of the hyperfine structure of $^{133}$Cs

I am practicing some questions in preparation for an upcoming exam and the following has me stumped: The D2 line of $^{133}$Cs involves transitions between the ground state $6S_{1/2}$ and the ...
3
votes
4answers
4k views

What exactly is a hyperfine level as mentioned in the definition of a second?

I have a quite simple question: What exactly is a hyperfine level (or a hyperfine structure)? Maybe my question sounds (or is) stupid $-$ I am not an expert in physics $-$ but I didn't find any ...
0
votes
1answer
58 views

A question on perturbative terms involved in the hyperfine structure of hydrogen

In studying the hyper-fine structure of the hydrogen atom at the 2n level in my notes the following is stated ; $$\langle W_{mv} \rangle _{2s}=\langle n=2, l=0|- \frac{\hat{P^4}}{8m_e^3c^2}| n=2, ...
5
votes
3answers
977 views

Fine structure Hamiltonian from Dirac equation

The Hamiltonian for fine structure (the atom with $\text{Z}$ protons and with electron interaction terms included) is $$H=\frac{\text{Z}^2}{ r}+\underbrace{\frac{p^2}{m}+\frac{p^4}{m^3}}_{\text{...
3
votes
1answer
168 views

Feshbach -Resonance why are hyperfine structures important?

The hyperfine structure of energy levels around the ground state seem to enable Feshbach and be intrinsic to it. Why do we need hyperfine levels? I.e. why is Feshbach specific to ultracold atoms in ...
0
votes
2answers
752 views

Hyperfine Interaction Hamiltonian

I didn't had any course on hyperfine interactions and now I am having trouble in solving the Anisotropic Hyperfine Hamiltonian. The problem is of matrix dimensions that have to be considered in the ...
5
votes
0answers
57 views

Where can I find data about hyperfine levels of a given atom?

The NIST Atomic Spectra Database is an excellent resource for finding the energy levels of atoms and the transitions between them, and (together with the DLMF) is a good candidate for the number-one ...
4
votes
1answer
496 views

Natural linewidth of hyperfine transitions

I'm referring to this question: Natural linewidth of hyperfine levels? Let's take Rubidium-85 for example. It's written everywhere that the D2 line has a linewidth of around 6 MHz. But the D2 "line", ...
8
votes
0answers
484 views

Natural linewidth of hyperfine levels?

The D2 line of $^{87}\mathrm{Rb}$ is the transition between the $5^2\mathrm P_{3/2}$ and the $5^2\mathrm S_{1/2}$ states. Its linewidth $\Gamma$ is always quoted to be $\sim 6\ \mathrm{MHz}$. But both ...
1
vote
1answer
165 views

Sub-structure of hyperfine levels

In studying introductory atomic physics I have come across fine structure splittings in energy levels due to spin-orbit coupling. Which has a sub-structure called hyperfine structure which comes from ...
2
votes
1answer
331 views

Hydrogen Hyperfine Structure: General Expression

I was looking at the hyperfine structure for the hydrogen atom. I checked pretty much every textbook I knew but none of them gave me the general expression for the energy correction due to the ...