Abstract
We count the number of pairs in the single-j-shell model of for various interactions. For a state of total angular momentum I, the wave function can be written as , where is the probability amplitude that the protons couple to and the neutrons to . For there are three states with () and one with (). The latter is the double analog of . In that case (), the magnitude of is the same as that of a corresponding two-particle coefficient of fractional parentage. In counting the number of pairs with an even angular momentum J, we find a new relationship is obtained by diagonalizing a unitary nine-j symbol. We are also able to get results for the “no-interaction” case for states, for which it is found, e.g., that there are fewer () pairs than on the average. Relative to this no-interaction case, we find that for the most realistic interaction used there is an enhancement of pairs with angular momentum , and 7, and a depletion for the others. Also considered are interactions in which only the () pair state is at lower energy, interactions where only the () pair state is lowered, interactions where both are equally lowered, and the interaction. We are also able to obtain simplified formulas for the number of pairs for the states in and by noting that the unique state with isospin is orthogonal to all the states with isospin .
- Received 7 October 2004
DOI:https://doi.org/10.1103/PhysRevC.71.034317
©2005 American Physical Society