2004/02/29 by L. Zamick, A. Z. Mekjian, S. J. Lee
Physics and Astronomy · #nucl-th
published as J.Korean Phys.Soc. 47 (2005) 18-22 · 7 pages
arxiv created 2005/03/04 · arxiv updated 2009/12/01
It is noted that the simple interaction in isospin variables a (1/4 - t(i)⋅ t(j)), in a single j shell calculation, can also be written with angular momentum variables. For the configuration (j2) JA for even JA the isospin is one; for odd JA it is zero. Hence the above interaction can also be written as a (1 - (-1)JA)/2. For the I=0 state of an even-even Ti isotope with n neutrons, the hamiltonian matrix element of this interaction is \bra [J'J']0 |H| [JJ]0\ket/a = (n+1) δJJ' - (n+1) (jn Jj|\ jn+1 j) (jn J'j|\ jn+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 JA in a given Ti isotope.