2003/12/18 by L. Zamick, E. Moya de Guerra, Zamick, L. +8
Mathematics · Physics and Astronomy · #Analytic Number Theory Research #FOS: Physical sciences #Nuclear Theory (nucl-th) #Nuclear physics research studies #Random Matrices and Applications #nucl-th
paper · pdf · doi:10.48550/arxiv.nucl-th/0312077
17 pages
arxiv created 2003/12/18 · openalex publication_date 2003/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We count the number of pairs in the single j-shell model of 44Ti for various interactions. For a state of total angular momentum I, the wave function can be written as Ψ=∑JP JN D(JP JN) [(j2)JP(j2)JN]I, where D(JP JN) is the probability amplitude that the protons couple to JP and the neutrons to JN. For I=0 there are three states with (I=0, T=0) and one with (I=0, T=2). The latter is the double analog of 44Ca. In that case (T=2), the magnitude of D(JJ) is the same as that of a corresponding two particle fractional parentage coefficient. In counting the number of pairs with an even angular momentum JA we find a new relationship obtained by diagonalizing a unitary nine-j symbol. We are also able to get results for the 'no-interaction' case for T=0 states, for which it is found that there are less (J=1, T=0) pairs than on the average. Relative to this 'no-interaction case' we find for the most realistic interaction used that there is an enhancement of pairs with angular momentum JA=0,2,1 and 7, and a depletion for the others. Also considered are interactions in which only the (J=0, T=1) pair state is at lower energy, only the (J=1, T=0) pair state is lowered and where both are equally lowered.