Questions tagged [hyperfine-structure]
The hyperfine-structure tag has no usage guidance.
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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:
$$
H = \frac{p^2}{2m} + V_\text{ECP}...
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Hyperfine structure
In Griffiths, the hyperfine structure is described as follows:
So the hyperfine structure is a result of a mechanism called spin-spin coupling, which is the interaction of the spin of the nucleus (...
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Do excited states of hydrogen give cosmologically relevant hyperfine transitions?
In Griffiths quantum mechanics, there's a discussion of hyperfine splitting for the ground state of hydrogen - this gives rise to a small level splitting corresponding to an emitted wavelength of $21$ ...
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Hyperfine Structure and Symmetries
Can you tell from the hyperfine splitting which symmetries an atom or molecule has?
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How is NMR different from hyperfine structure?
Essentially I've confused myself by trying to understand NMR (nuclear magnetic resonance) as the transition between hyperfine levels and I seem to encounter a contradiction. I'll describe my ...
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A qualitative understanding of how an external magnetic field impacts spectral splitting?
I am trying to build an intuition in my head reg. the various interactions that are mathematically elaborated in standard QM textbooks/courses. I will make some statements below to express my current ...
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On the expression for the hyperfine coupling constant
The hyperfine interaction can be written in the form:
$${\cal{H}}_{\rm{hf}} = {\mu}_I \cdot \vec{h}_{\rm{eff}}= g_{\rm{N}} \mu_{\rm{N}} \vec{I}\cdot{\vec{h}}_{\rm{eff}}$$
where $\mu_I:=g_{\rm{N}}\mu_{\...
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Lamb shift in hydrogen atoms
Has a Lamb shift been observed in any atom other than hydrogen?
I am highly confused. The Lamb shift makes the P1/2 state lower than the S1/2 state. Is Lamb shift observed in other atoms? If not, then ...
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Why Rubidium-87 instead of Rubidium-85 for Atomic Clocks?
The traditional Rubidium isotope of choice for atomic clocks is Rubidium-87, although I have found papers describing clocks built around Rubidium-85. I cannot readily find any references for why 87 is ...
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Spin-Orbit perturbation theory
I'm trying to use pertubation theory to calculate the energy shift due to spin-orbit interaction between the electron and proton in the hydrogen atom. I'm stuck on how to proceed as this hamiltonian ...
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Determining Hyperfine Hamiltonian Term [closed]
I'm having difficulty determining the hyperfine Hamiltonian term for a hydrogen-like atom ($^{87}$Rb & $^{85}$Rb). The hyperfine Hamiltonian is given by:
$${\hat{H}}_{hf}=a_{hf}\left(\frac{1}{2}\...
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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 ...
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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 ...
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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 ...
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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})(...
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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
$$ \hat{H}_{hfs} = \sum_k \mathbf{...
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Neutral hydrogen atoms in inhomogenous magnetic field
In the 1996 gre exam this scenario comes up in a question: a beam of neutral hydrogen atoms in their ground state pass through a region of of strong inhomogenous magnetic field. In the official ...
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How can I calculate the hyperfine structure of a $p$-orbital?
I have a little problem with the calculation of the hyperfine structure of the 3p orbital in the hydrogen atom.
The Hamiltonian is:
Were represents the magnetic moment of the proton and the ...
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Basic labeling of the hyperfine structure of $^{133}$Cs
I am practicing some questions in preparation for an upcoming exam and the following has me stumped:
The D2 line of $^{133}$Cs involves transitions between the ground state $6S_{1/2}$ and the ...
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What exactly is a hyperfine level as mentioned in the definition of a second?
I have a quite simple question: What exactly is a hyperfine level (or a hyperfine structure)?
Maybe my question sounds (or is) stupid $-$ I am not an expert in physics $-$ but I didn't find any ...
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A question on perturbative terms involved in the hyperfine structure of hydrogen
In studying the hyper-fine structure of the hydrogen atom at the 2n level in my notes the following is stated ;
$$\langle W_{mv} \rangle _{2s}=\langle n=2, l=0|- \frac{\hat{P^4}}{8m_e^3c^2}| n=2, ...
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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{...
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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 ...
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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 ...
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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 ...
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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", ...
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Natural linewidth of hyperfine levels? [duplicate]
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 ...
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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 ...
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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 ...
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