In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to interaction between the nucleus and electron clouds.
In atoms, hyperfine structure arises from the energy of the nuclear magnetic dipole moment interacting with the magnetic field generated by the electrons and the energy of the nuclear electric quadrupole moment in the electric field gradient due to the distribution of charge within the atom. Molecular hyperfine structure is generally dominated by these two effects, but also includes the energy associated with the interaction between the magnetic moments associated with different magnetic nuclei in a molecule, as well as between the nuclear magnetic moments and the magnetic field generated by the rotation of the molecule.
Hyperfine structure contrasts with fine structure, which results from the interaction between the magnetic moments associated with electron spin and the electrons' orbital angular momentum. Hyperfine structure, with energy shifts typically orders of magnitudes smaller than those of a fine-structure shift, results from the interactions of the nucleus (or nuclei, in molecules) with internally generated electric and magnetic fields.
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 question is if i have to keep the nuclear spin of the protons parallel when i write the states, for...
I was reading a paper on Radical-Pair mechanism (2 atoms with 1 valence electron each) and the author used the hyperfine hamiltonian $$H_{B}=-B(s_{D_z}+s_{A_z})+As_{D_x}I_x+As_{D_y}I_y+as_{D_z}I_z$$ and found the following eigenvalues: a/4 (doubly degenerate) , a/4±B , (-a-2B±2√(A^2+B^2)) ...
If caesium 133 frequency for its hyperfine structure is 9 192 631 770, and hydrogen is 1 420 405 751.7667 what are the frequencies for the other elements and their isotopes? Is there a list on line some were because this would be a long list. Any help on where to look on line would be...
Homework Statement
Hi everybody! Here is the problem:
Hyperfine splitting of Deuterium Balmer alpha line:
Consider the ##3p_{3/2}## to ##2s_{1/2}## transition in deuterium. Find the number of transition lines and their frequency shifts with respect to the transition without hyperfine...
Does anybody have more insights regarding
https://www.nature.com/articles/ncomms15484
High precision hyperfine measurements in Bismuth challenge bound-state strong-field QED
Does this really challange QED? Or does this mean that we miss certain contributions to QED calculations?
The authors...
Homework Statement
I've been given the worked answer to a very similar question, but there's a step I don't understand so I can't apply it. My question asks:
An energy level with ##J=\frac{11}{2}## has six hyperfine sub-levels with these relative energies...
What is the cause of hyperfine line splitting?
I saw somewhere that it was because of spin quantum number and somewhere else that it was because of how electrons interact in the atom.
And relative intensity of spectral lines?
I'd assume it's due to the probability of electron jumps being more...
I'm looking for the theoretical calculation of the hyperfine structure transition frequency of Ca-133 which is used in atomic clocks to define the second according to SI-Units. Google, Google... there is a lot about the hyperfine Hamiltonian of hydrogen, but couldn't find none about that of...
Homework Statement
Derive the Breit-Rabi equation in the case that the quantum number j is equal to 1/2, specifically the 1S_1/2 state of Hydrogen. This is the equation describing hyper-fine and Zeeman splitting of the energy levels in an applied magnetic field.
Homework Equations
We are given...
Consider the Dirac equation for bounded electron in hydrogen atom.
I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum.
Kinetic and Coulombic potential and rest energies are the first terms and easy to identify.
Then we...
Homework Statement
A transition happens for ##\lambda = 494nm## in the Cesium ions (##^133 Cs##) between a term in the ##5p^5 6s## configuration and term in the ##5p^5 6p## configuration. Five components are observed with the following energies (relative to the transition of least energy): 0...
Homework Statement
A singly ionized atom exhibits hyperfine structure in a ##^3P_1 \rightarrow ^3S_1## transition. Assuming ##I## is greater than ##J## and given that the ##^3S_1## levels are split by ##66~GHz## and ##54~GHz##, find the nuclear spin ##I##.
Homework Equations
E_{HFS} =...
Good day all,
I'm taking a course on hyperfine interactions this semester. It is organised in the alternative way that we, the students prepare some part of the course notes (e.g. treat magnetic dipole term, electric quadrupole term etc.).
The problem I have is that the course notes we...
Homework Statement
(a)Find splitting between F=0 and F=1 in hydrogen
(b) Find the constant ##A## and nuclear magnetic moment
Homework EquationsThe Attempt at a Solution
Hyperfine splitting is given by:
H_{hf} = \frac{A}{2} \left[ F(F+1) - I(I+1) - J(J+1) \right]
The intervals are given by...
I have read from DJ Griffiths Quantum Mechanics that the electron-positron annihilation process will enlarge the hyperfine splitting of the positronium ground state. More precisely, the actual splitting is larger than that we calculated only considering the spin interaction between the positron...
1. Problem:
Consider Hydrogen in its ground state in a magnetic field of magnitude B.
Compute the effect of the magnetic field on the hyperfine structure of Hydrogen
(that is you should include the interaction of both the proton and electron magnetic
moments with the applied magnetic field)...
We know this tiny splitting in degenerate levels in Hydrogen spectrum due to magnetic interactions between spins of electron and proton. but is that true the proton spin is independent of energy in this (hyperfine) splitting? I want to understand the physics of this splitting and how the spin...
Hi guys
As far as I have understood the technique of optical puming (OP), then if we look at the hyperfine state F=2 (for example), then OP can be used to prepare the atoms in the state F=2, mF=2, but not any other (i.e., lower) mF. Is there no technique for preparing atoms in a state with a...
Hello...
I was just reading about that, and I have one question.
In the chapter I've jut read about, the overall headline is about one electron atoms, so I was just wondering, since the overall equation got Z (Atomic number) in it, if this was for larger atoms as well, or ONLY one electron...
Hello,
my name is Artemis. These days I study at University of Science and Technology in Cracow. Due to the fact that semester is almost over one of my tutors asked me to do a quick presentation about "Ways of measuring hyperfine interactions". I would appreciate it a lot if anyone of you could...
Hi Anyone,
This is my first post here and i have a bit of a quandry.
I'm doing some work related to hyperfine transition levels in Rubidium.
Ive been looking and asking but no-one can explain to me satisfactorly how hyperfine splits occur.
Mostly i get answers like " you should find out...
microwave can be used to engineering potentials for alkali atoms
i find that in the literature, people only take the magnetic dipole transition into account
why the electric dipole transition is neglected?
is it forbidden?
Homework Statement
Hyperfine structure is the splitting of energy levels due to the coupling of the magnetic moment of the atomic nucleus and the electron’s total angular momentum.
In a hypothetical atom called “hypogen” the electron is replaced by a negatively
charged pion (π-) which has...
Homework Statement
Derive the hyperfine Hamiltonian starting from \hat{H}_H_F = -\hat{\mu}_N \cdot \hat{B_L} . Where \hat{\mu}_N is the magnetic moment of the nucleus and
\hat{B_L} is the magnetic field created by the pion’s motion around the nucleon. Write down the Hamiltonian in the...
A detailed picture of the Hydrogen red line shows a lot of detail:
The difference in the 2 largest peaks is the fine structure, the lamb shift is clearly noted, but what are the other 2 bumps just below the lamb shift in the upper chart. I was thinking hyperfine, but I don't think that...
[SOLVED] Hyperfine splitting of deuterium
Homework Statement
Calculate the wavelength of the photon emitted under a hyperfine transition in the ground state (n=1) of deuterium. Deuterium is a proton and a neutron in the nucleus, but still one electron. The spin of deuterium is 1.Homework...
Homework Statement
I am trying to see if I understand these corrections to the hydrogen atom:
To explain the fine structure correction, we go to the electrons frame of reference, in which the proton is moving with velocity v. This produces a magnetic field according to Maxwell's equations the...
I'm having some problems with the Fine and Hyperfine splitting (FS and HFS). For example the 3s3p Configuration, I understand the FS:
*****************************_______Mj=1
************1P________J=1*****_______ Mj=0
*****************************_______ Mj=-1
*
*
************3P______ Is...
What are the approximate relative sizes of the following energies?
a) The n = 1 to n = 2 energy difference in hydrogen and the rest mass mc^2 of an electron
b) The n = 1 to n = 2 energy difference in hydrogen and a typical fine structure splitting in hydrogen
c) A typical fine...