The Expectation Value of S(1).S(2)-Wave Functions Don't Matter
Nuclear Theory
2016-09-13 v2
Abstract
We consider the expectation value of the quantity [3+ \sigma (1).\sigma (2)]/4 . This has a value +1 for 2 nucleons with spin S=1and zero for S=0. We show that for the jj coupling 2 particle configuration [j(1) j(2)]^{J} the expectation value has the structure A+B J(J+1) where A and B are constants. We then show that for a 2proton-2neutron configuration with total angular momentum I the expectation value per pair is independent of the details of the wave function and has a similar structure A' +B' I(I+1) with B'=B/6.
Cite
@article{arxiv.1608.08272,
title = {The Expectation Value of S(1).S(2)-Wave Functions Don't Matter},
author = {L. Zamick},
journal= {arXiv preprint arXiv:1608.08272},
year = {2016}
}