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Interrelationship of Isospin and Angular Momentum
Larry Zamick,Suk-Joon Lee,A. Z. Mekjian 한국물리학회 2005 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.47 No.1
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 h[J0J0]0|H|[JJ]0i/a = (n + 1)JJ0 − (n + 1)jnJj|}jn+1jjnJ0j|}jn+1j. 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.