Relations for four nucleons in a single j shell

doi:10.1103/PHYSREVC.75.024307

Abstract

In previous works we considered the number of pairs of particles with angular momentum J{sub 12} for systems with total angular momentum zero. Here we extend the the work to states of any total angular momentum. We find simplified relations satisfied for a system of four nucleons with isospins zero and two.

Isospin relations for four nucleons in a single j shell

Zamick, L. ; Escuderos, A. October 2005 - Physical Review. C, Nuclear Physics

We had previously used techniques involving isospin to count the number of states for three identical fermions in a single j shell with total angular momentum I=j. We generalize this to all I, but the main thrust of this work is to consider now a four-fermion system. As before, one evaluates the eigenvalues of the Hamiltonian {sigma}{sub i<j}[a+bt(i){center_dot}t(j)] from both an isospin point of view and an angular momentum point of view. In the four-particle case, we get a more limited result than in the three-particle case, namely the number of T=0 states minus twice the number of T=2 states,more » all of a given angular momentum I.« less
DOI: 10.1103/PhysRevC.72.044317
ALLOWED VALUES OF COUPLED ANGULAR MOMENTUM AND i-SPIN FOR NUCLEONS IN A SINGLE SHELL IN j--j COUPLING.

Hubbard, L.B. January 1970 - Comput. Phys. Commun. 1: 453-6(Dec 1970).
DOI: 10.1016/0010-4655(70)90020-2
CORRECTION TERM FOR THE BINDING ENERGY FORMULA OF IDENTICAL NUCLEONS IN A SINGLE j SHELL.

Nomura, M. January 1970 - Progr. Theor. Phys. (Kyoto) 43: 555-6(Feb 1970).
DOI: 10.1143/PTP.43.555
Number of states for nucleons in a single-j shell

Zhao, Y.M. ; Cyclotron Center, Institute of Physical Chemical Research ; Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000 ; ... December 2005 - Physical Review. C, Nuclear Physics

In this paper we obtain number of states with a given spin I and a given isospin T for systems with three and four nucleons in a single-j orbit, by using sum rules of six-j and nine-j symbols obtained in earlier works.
DOI: 10.1103/PhysRevC.72.064333
RESIDUAL INTERACTION AND THE SENIORITY SCHEME OF THREE- AND FOUR-NUCLEONS IN A SINGLE SHELL. (in Japanese)

Nomura, M. January 1969 - pp 211 of Contributions to the International Conference on Properties of Nuclear States, Montreal, Canada, August 25--30, 1969. Montreal Les Presses de l'Universite de Montreal (1969).

Title: Relations for four nucleons in a single j shell

Abstract

Citation Formats

Isospin relations for four nucleons in a single j shell

ALLOWED VALUES OF COUPLED ANGULAR MOMENTUM AND i-SPIN FOR NUCLEONS IN A SINGLE SHELL IN j--j COUPLING.

CORRECTION TERM FOR THE BINDING ENERGY FORMULA OF IDENTICAL NUCLEONS IN A SINGLE j SHELL.

Number of states for nucleons in a single-j shell

RESIDUAL INTERACTION AND THE SENIORITY SCHEME OF THREE- AND FOUR-NUCLEONS IN A SINGLE SHELL. (in Japanese)