Relations for four nucleons in a single j shell

doi:10.1103/PHYSREVC.75.024307

Title: Relations for four nucleons in a single j shell

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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.

Authors:

Zamick, L. ^[1]

Department of Physics and Astronomy, Rutgers University, New Brunswick, New Jersey 08903 (United States)

Publication Date:: Thu Feb 15 00:00:00 EST 2007

OSTI Identifier:: 20991008

Resource Type:: Journal Article

Resource Relation:: Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevC.75.024307; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; ANGULAR MOMENTUM; ISOSPIN; NUCLEONS; PARTICLES; SHELLS

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                    Zamick, L. Relations for four nucleons in a single j shell.  United States: N. p., 2007. 
        Web.  doi:10.1103/PHYSREVC.75.024307.

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                    Zamick, L. Relations for four nucleons in a single j shell.  United States.  doi:10.1103/PHYSREVC.75.024307.

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                    Zamick, L. Thu .  
        "Relations for four nucleons in a single j shell".  United States.  
        doi:10.1103/PHYSREVC.75.024307.

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@article{osti_20991008,

  title        = {Relations for four nucleons in a single j shell},

  author       = {Zamick, L.},

  abstractNote = {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.},

  doi          = {10.1103/PHYSREVC.75.024307},

  journal      = {Physical Review. C, Nuclear Physics},

  number       = 2,

  volume       = 75,

  place        = {United States},

  year         = {Thu Feb 15 00:00:00 EST 2007},

  month        = {Thu Feb 15 00:00:00 EST 2007}

}

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DOI: 10.1103/PHYSREVC.75.024307

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Isospin relations for four nucleons in a single j shell

Zamick, L. ; Escuderos, A. - 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. - 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. - 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 ; ... - 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. - 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).