Nucleon pair approximation of the nuclear collective motion

We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = J max pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I ≤ 2j. For I = 0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.

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“…(4), say, Eq. (5.8) of [9], we expect that the "integer" eigenvalues appear not only in even systems but also appear in odd-A systems.…”

Section: Integer Eigenvaluesmentioning

confidence: 99%

General pairing interactions and pair truncation approximations for fermions in a single-jshell

2003

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“…It also indicates that κ πν for these three nuclei is not as strong as the values predicted by empirical formulas (see Appendix B in Ref. [37] 109 Te acquire the experimental value (within the experimental error) of 762 and 595 e 2 fm 4 , as shown in Fig. 6 and Table II.…”

Section: Theoretical Frameworkmentioning

confidence: 52%

Nucleon pair approximation description of the low-lying structure of108,109Te and109I

Jiang

Lei

et al. 2013

Phys. Rev. C

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“…It corresponds to a rearrangement of the configuration space to decouple the most important part from the rest of the space. There are many different schemes of truncating a shellmodel space 5,6,7,8,9,10 . Although these schemes differ very much in details in the way of building the model bases and/or choosing effective interactions, they share the common character that the model space is first constructed by some physical guidance.…”

Section: The Projected Shell Modelmentioning

confidence: 99%

Shell Model for Heavy Nuclei and Its Application in Nuclear Astrophysics

Sun

2006

Int. J. Mod. Phys. E

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Performing shell model calculations for heavy nuclei is a long-standing problem in nuclear physics. The shell model truncation in the configuration space is an unavoidable step. The Projected Shell Model (PSM) truncates the space under the guidance of the deformed mean-field solutions. This implies that the PSM uses a novel and efficient way to bridge the two conventional methods: the deformed mean-field approximations, which are widely applied to heavy nuclei but able to describe the physics only in the intrinsic frame, and the spherical shell model diagonalization method, which is most fundamental but feasible only for small systems. We discuss the basic philosophy in construction of the PSM (or generally PSM-like) approach. Several examples from the PSM calculations are presented. Astrophysical applications are emphasized.

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Nucleon pair approximation of the nuclear collective motion

Cited by 90 publications

References 34 publications

General pairing interactions and pair truncation approximations for fermions in a single-jshell

General pairing interactions and pair truncation approximations for fermions in a single-jshell

Nucleon pair approximation description of the low-lying structure of108,109Te and109I

Shell Model for Heavy Nuclei and Its Application in Nuclear Astrophysics

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