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Interrelationship of Isospin and Angular Momentum | | L. Zamick
; A.Z. Mekjian
; S.J. Lee
; | | Date: |
25 Feb 2004 | | Journal: | J.Korean Phys.Soc. 47 (2005) 18-22 | | Subject: | nucl-th | | Abstract: | It is noted that the simple interaction in isospin variables $a (1/4 - t(i)cdot t(j))$, in a single $j$ shell calculation, can also be written with angular momentum variables. For the configuration $(j^2) J_A$ for even $J_A$ the isospin is one; for odd $J_A$ it is zero. Hence the above interaction can also be written as $a (1 - (-1)^{J_A})/2$. For the I=0 state of an even-even Ti isotope with $n$ neutrons, the hamiltonian matrix element of this interaction is $ra [J’J’]_0 |H| [JJ]_0ket/a = (n+1) delta_{JJ’} - (n+1) (j^n Jj|j^{n+1} j) (j^n J’j|j^{n+1} j)$. The eigenvalues of this interaction can be found by using the isospin form of the interaction. They are $(n+1)a$ for $T = |N-Z|/2$ and zero for $T = |N-Z|/2 + 2$. One can apply this to some extent to obtain the number of pairs of nucleons with given total angular momentum $J_A$ in a given Ti isotope. | | Source: | arXiv, nucl-th/0402089 | | Services: | Forum | Review | PDF | Favorites | |
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