Questions tagged [hyperfine-structure]

33 questions
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3 answers

Why Rubidium-87 instead of Rubidium-85 for Atomic Clocks?

The traditional Rubidium isotope of choice for atomic clocks is Rubidium-87, although I have found papers describing clocks built around Rubidium-85. I cannot readily find any references for why 87 is preferred in clocks. Rubidium-85 is the…
14
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1 answer

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 useful resource they don't tell you about in…
9
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3 answers

Lamb shift in hydrogen atoms

Has a Lamb shift been observed in any atom other than hydrogen? I am highly confused. The Lamb shift makes the P1/2 state lower than the S1/2 state. Is Lamb shift observed in other atoms? If not, then why?
9
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1 answer

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 states have hyperfine splittings. The transition…
7
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5 answers

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 description in the Internet which I understood. (Or…
6
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3 answers

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{kinetic}}+\underbrace{\frac{\text{Z} \ L\cdot…
6
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1 answer

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 hyperfine perturbation Hamiltonian. All of them only…
5
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1 answer

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", a transition between fine structure levels, is…
4
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1 answer

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 $$ \hat{H}_{hfs} = \sum_k \mathbf{T}^{(k)}_n \cdot \mathbf{T}^{(k)}_e $$ where the…
3
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Energy after changing to uncoupled basis

Suppose we are looking at the valence electron of a Hydrogenic atom for which $I = 3/2,\ J = 1/2$ (and hence $L = 0$). Our Hamiltonian for this setting is given by: $$ H = \frac{p^2}{2m} + V_\text{ECP} + \eta LS + hA_\text{hfs} I J $$ where…
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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})(\vec{S}\cdot\hat{r})$ where $H_0$ is the kinetic…
3
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1 answer

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 ground stae, why would a magnetic field in any gas…
2
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1 answer

Help understanding Feshbach resonance

Currently this is my understanding of feshbach resonance, I know that free unbound atoms are coupled to a molecular state in which the atoms are tightly bound. The closer this molecular level lies with respect to the energy of two free atoms, the…
2
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2 answers

Hyperfine structure

In Griffiths, the hyperfine structure is described as follows: So the hyperfine structure is a result of a mechanism called spin-spin coupling, which is the interaction of the spin of the nucleus (proton in this case) with the spin of the…
2
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Spin-Orbit perturbation theory

I'm trying to use pertubation theory to calculate the energy shift due to spin-orbit interaction between the electron and proton in the hydrogen atom. I'm stuck on how to proceed as this hamiltonian does not commute with L or S, however I have read…
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