What is the difference between parallel and antiparallel spins for a pair of nucleons?
My understanding is that nucleons have a strong tendency to pair – proton with proton, neutron with neutron, proton with neutron. When they pair their spins either:
cancel (spins pair antiparallel) pairing of a spin-up and spin-down nucleon
add (spins pair parallel) pairing of two nucleons with both spin up or both spin down
Am I understanding this correctly? – I'm thinking I might be missing something in regards to the Pauli Exclusion Principle. How can two nucleons with the same spin state pair?
Best Answer
It simply means that nucleons can be parallel in spin or opposite nature of spin- example of two nucleons
( up , up ) or ( down , down ) or ( up , down ) or (down, up)
if they are parallel total spin S = s(1) +s(2) = 1 a triplet state
if they are anti -parallel
total spin S = s(1) +s(2) = 0 a singlet state
the spin-spin or spin-orbit interactions will be different for two states.
which may affect the nuclear force.
the scattering cross sections for two states will give different results.
As nucleons are added in a nucleus in a specific state the nucleons get paired and the final spin state of the nucleus is decided by the odd nucleon (its spin). In case of even number nucleus the total spin is zero.
Spin-spin coupling is the coupling of the intrinsic angular momentum (spin) of different particles. Examples are- Such coupling between pairs of nuclear spins is an important feature of (NMR) spectroscopy as it can provide detailed information about the structure and conformation of molecules. Spin-spin coupling between nuclear spin and electronic spin is responsible for hyperfine structure in atomic spectral transitions.
Due to the similarity in mass and nuclear properties between the proton and neutron, they are sometimes considered as two symmetric types of the same object, a nucleon.
The symmetry relating the proton and neutron is known as isospin and denoted I (or sometimes T).
Isospin is an SU(2) symmetry, like ordinary spin, so is completely analogous to it.
The proton and neutron form doublet, with a downstate (↓) being a neutron, and an up (↑) state is a proton.
A pair of nucleons can either be in an antisymmetric state of isospin called singlet or in a symmetric state called triplet.
An example-
Therefore one may try constructing the wave function of deuteron holding the Pauli principle and the ground state of deuteron will come to a triplet state of nucleons with Binding of about 2.2 MeV.