What is Nuclear spin: Definition and 27 Discussions

In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model is a model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels. The first shell model was proposed by Dmitry Ivanenko (together with E. Gapon) in 1932. The model was developed in 1949 following independent work by several physicists, most notably Eugene Paul Wigner, Maria Goeppert Mayer and J. Hans D. Jensen, who shared the 1963 Nobel Prize in Physics for their contributions.
The shell model is partly analogous to the atomic shell model which describes the arrangement of electrons in an atom, in that a filled shell results in greater stability. When adding nucleons (protons or neutrons) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. This observation, that there are certain magic numbers of nucleons (2, 8, 20, 28, 50, 82, 126) which are more tightly bound than the next higher number, is the origin of the shell model.
The shells for protons and for neutrons are independent of each other. Therefore, "magic nuclei" exist in which one nucleon type or the other is at a magic number, and "doubly magic nuclei", where both are. Due to some variations in orbital filling, the upper magic numbers are 126 and, speculatively, 184 for neutrons but only 114 for protons, playing a role in the search for the so-called island of stability. Some semi-magic numbers have been found, notably Z = 40 giving nuclear shell filling for the various elements; 16 may also be a magic number.In order to get these numbers, the nuclear shell model starts from an average potential with a shape something between the square well and the harmonic oscillator. To this potential, a spin orbit term is added. Even so, the total perturbation does not coincide with experiment, and an empirical spin orbit coupling must be added with at least two or three different values of its coupling constant, depending on the nuclei being studied.

Nevertheless, the magic numbers of nucleons, as well as other properties, can be arrived at by approximating the model with a three-dimensional harmonic oscillator plus a spin–orbit interaction. A more realistic but also complicated potential is known as Woods–Saxon potential.

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  1. B

    A Technical question about AMO experiment in a paper

    Hello! This is quite technical, but any advice would be greatly appreciated (@Twigg ?). It is about this paper: https://arxiv.org/pdf/1909.02650.pdf. In principle, beside the EDM, we also have spin dependent parity violating (time-reversal conserving) effects. This is always true, as we need a...
  2. J

    Possible spins and parities of an odd-odd nucleus

    I'm actually not even 100% sure about the formulas, as in my book they explain j, s and l quite unclearly. Could anyone give me a proper explanation as how to see these and if I'm using them correctly. What i tried to do was determine the proton and neutron angular momentum, spin and parity...
  3. H

    I Nuclear spin coupling in molecular (protium) hydrogen

    I'm not sure where this post belongs--here, or nuclear chemistry, quantum mechanics, NMR spectroscopy, etc. Moderator--please feel free to move it to a better location. I'm wondering if a container of liquid hydrogen subjected to a strong magnetic field would have both nuclei of each atom...
  4. S

    Total Angular Momentum of an odd-parity shell-model state

    Homework Statement A certain odd-parity shell-model state can hold up to a maximum of 4 nucleons. What are its values of J and L? What about an odd-parity shell-model state with a maximum of 6 nucleons? Homework Equations Parity = (-1)L J = L+S Total angular momentum, J, is equal to orbital...
  5. F

    NMR nuclear spin absorption/emission question

    NMR textbooks often state that an ensemble of nuclei cannot absorb the excitation radiowaves if the spin population is "saturated" (wherein "saturated" is often described as equal spin population in all energy states, or a population inversion). But these same NMR textbooks show that a 180...
  6. Spinnor

    I Noble gases with even nuclear spin form superfluids?

    Other than Helium do Noble gases with even nuclear spin form superfluids? Is there a simple quantum mechanical explanation why the difference below of the Melting point and Boiling point of the Noble gases is roughly the same value? A yes or no would suffice. From...
  7. nomadreid

    I Uranium isotopes with m in superscript

    On the page https://en.wikipedia.org/wiki/Isotopes_of_uranium, some of the superscripts have, besides the atomic number, also an "m". For example, besides the usual isotope 234U with spin 0+, there is also the isotope 234mU (with nuclear spin 6-). What is this "m"? While I am at it, what is the...
  8. Nouki

    A Nuclear spin of Fluorine 19

    Can anyone explain to me why angular momentum of F-19 equals to J=1/2, but if we calculate J with the shell model the result is J=5/2. Thank you
  9. M

    Electron and Nuclear spin interaction

    Homework Statement Hello, I'm asked to show the equivalence of the given Hamiltonian below which describes the interaction between an electron and a nucleus and the following Hamiltonian The Attempt at a Solution [/B] I've simply written down each Hamiltonian as a sum of four tensor...
  10. Garlic

    Different stable nuclear spins for the same isotope

    Hello everyone, When I look at the isotope lists, I always see only one nuclear spin for a specific isotope. (Why) can't an isotope have different nuclear spin types that are stable? I know metastable isotopes exist, but I am asking about the stable isotopes. Can't there be a case where the...
  11. U

    What is the nuclear spin of this atom?

    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} =...
  12. J

    Nuclear Spin and Magnetic Resonance Imaging

    Hi pf, Please could someone kindly answer a few questions about proton spin in the context of MRI. As I understand it when an external static magnetic field is applied to a patient the magnetic dipole moments of the protons in the hydrogen nuclei will experience a torque causing them to align...
  13. M

    Stern Gerlach and Nuclear Spin?

    So, my current understanding of spin is that when particles with a certain spin state hit a stern gerlach device, their wavefunction is split into components, deflection associated with one of the pure spin states aligned with the device. For spin 1/2 particles, there are only supposed to be two...
  14. Clear Mind

    What is the Nuclear Spin of Fluorine-19 and How is it Calculated?

    I was trying to calculate the ##^{19}_{9}F_{10}## nuclear spin using the nuclear shell method. From what i know the nuclear spin for a nucleous with odd ##A## is the total angular momentum ##J## of the stand-alone nucleon: P: ##(1d_{5 \backslash 2})^1## (stand-alone nucleon) N: ##(1d_{5...
  15. T

    Nuclear Spin and Selection Rules

    Suppose we define the total angular momentum as F = I+J where I is the nuclear spin angular momentum and J is the total electronic angular momentum. mF and mJ are the respective magnetic quantum numbers. The relevant F selection rules are delta_mF = 0, 1 and -1, delta_F = 0, 1 and -1. And...
  16. kawkaw

    How Is Nuclear Spin Calculated for Alkali Atoms?

    hello, i am new in this forum , :) i want to ask if anyone know how to calculate the nuclear spin of an atom in general, i searched in google i didnt find any method of calculation :/ can anyone help me please, thanks
  17. Demon117

    Total nuclear spin of deuteron

    Hello all, I am having trouble understanding how this works. In Krane there arises a discussion on total angular momentum I of the deuteron. While it is true it has three components, namely the individual spins of the neutron and proton, but also the orbital angular momentum l of the nucleons...
  18. G

    Understanding Nuclear Spin: Odd Proton and Neutron Counts

    hi i have a question about nuclear spin if the number of protons and neutrons is even, then my chemistry book says, that the nuclear spin is always zero. i guess that the reason is, that there are always 2 protons and 2 neutrons in one state with opposite spin and therefore the overall...
  19. jaketodd

    Atoms with non-zero nuclear spin

    What are the criteria for an atom to have non-zero nuclear spin? This is not homework. Thanks, Jake
  20. N

    Calculating Nuclear Spin: Oxygen-17

    Homework Statement Oxygen 17, work out j (nuclear spin)Hi. Assume oxygen 17 atom. j is supposed to be 5/2. How does one work this out? from what i gather, l for protons is 1, and l for neutrons is 2. How does one work out j, and what would s be? Partly what I'm confused about is for the...
  21. L

    Magnetic field due to nuclear spin

    Hi all. Can anyone tell me why in the equation of the magnetic field due to a nuclear's spin has radius dependence? How come? B=-u0 uI / 2 pi R^3 (sorry about the typing, I don't know how to type a porper equation..) Thanks in advance
  22. L

    Whats the difference between nuclear spin and isospin?

    hey I am a bit confused re the difference between nuclear spin and isospin. are they the same thing? thanks
  23. S

    Temperature in a nuclear spin 1/2 system?

    Temperature in a nuclear spin 1/2 system?? Homework Statement A solid at temperature T contains 10^20 protons which have a spin I = 1/2 and a nuclear g-factor of 5.59. Calculate the temperature such that 75% of the protons have their magnetic dipole moment aligned parallel to the applied...
  24. B

    How is nuclear spin determined?

    Is there a formula for determining the total spin of a nucleus? I know protons and neutrons have 1/2 spin and I know even number A nuclei have 0 spin. But I don’t know how the spin is determined for values larger than 1/2. For example: 55Fe spin 3/2 56Co spin 4 57Co spin 7/2...
  25. quasinerd

    Exploring Quantum Gates and Nuclear Spin

    After reading Seth Lloyd's book “Programming the Universe”(only once) I came up with a few questions. The way I understand it... He describes the fabric of space-time as consisting of an endless array of casual space (wires) and matter(quantum gates). The wires tell information where to go and...
  26. S

    What Determines the Spin and Parity of a Nucleus with Multiple Excited Nucleons?

    I understand that the spin and parity of the nucleus is determined by looking at hte unpaired nucleon (is that the correct way of saying it?). But what if we were looking at nulceus where 2 or more nucleons were excited from the ground state?? What would the spin and parity of the nucleus be...
  27. T

    Predicting Nuclear Spin with Shell Model: How is it Calculated and Validated?

    How would one predict the total spin of a nucleus given Z, N and the shell model? Does it have to to do with even-even, even-odd, odd-odd nuclei?