dorsal/arxiv
View SchemaInterrelationship of Isospin and Angular Momentum
| Authors | L. Zamick, A. Z. Mekjian, S. J. Lee |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0402089 |
| URL | https://arxiv.org/abs/nucl-th/0402089 |
| Journal | J.Korean Phys.Soc. 47 (2005) 18-22 |
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 $\bra [J'J']_0 |H| [JJ]_0\ket/a = (n+1) \delta_{JJ'} - (n+1) (j^n Jj|\} j^{n+1} j) (j^n J'j|\} j^{n+1} j)$. 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.
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"abstract": "It is noted that the simple interaction in isospin variables $a (1/4 -\nt(i)\\cdot t(j))$, in a single $j$ shell calculation, can also be written with\nangular momentum variables. For the configuration $(j^2) J_A$ for even $J_A$\nthe isospin is one; for odd $J_A$ it is zero. Hence the above interaction can\nalso be written as $a (1 - (-1)^{J_A})/2$. For the I=0 state of an even-even Ti\nisotope with $n$ neutrons, the hamiltonian matrix element of this interaction\nis $\\bra [J\u0027J\u0027]_0 |H| [JJ]_0\\ket/a = (n+1) \\delta_{JJ\u0027}\n - (n+1) (j^n Jj|\\} j^{n+1} j)\n (j^n J\u0027j|\\} j^{n+1} j)$. The eigenvalues of this interaction can be found by\nusing the isospin form of the interaction. They are $(n+1)a$ for $T = |N-Z|/2$\nand zero for $T = |N-Z|/2 + 2$. One can apply this to some extent to obtain the\nnumber of pairs of nucleons with given total angular momentum $J_A$ in a given\nTi isotope.",
"arxiv_id": "nucl-th/0402089",
"authors": [
"L. Zamick",
"A. Z. Mekjian",
"S. J. Lee"
],
"categories": [
"nucl-th"
],
"journal_ref": "J.Korean Phys.Soc. 47 (2005) 18-22",
"title": "Interrelationship of Isospin and Angular Momentum",
"url": "https://arxiv.org/abs/nucl-th/0402089"
},
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