Unified pair-coupling theory of fermion systems

Rowe, D.J.; Song, Ting-Ting; Chen, H.

doi:10.1103/physrevc.44.r598

Cited by 15 publications

(27 citation statements)

References 14 publications

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“…[1,2,15]. It follows from Claim 1 that the VCS wave function for a one quasi-particle state u j α † jm |x has values given by…”

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

“…It turns out, as shown in refs. [1,2] that the function Φ s n is well-known in the theory of symmetric polynomials [15] as a Schur function (or S-function); such functions are the characters of fully antisymmetric irreps of the unitary groups and easy to derive. The definition…”

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

“…[1,2], this recursion relation is solved by making a change of variables from {z j } to the symmetric power functions…”

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

“…However, it can be restored with relative ease in a coherent-state representation [1,2] in a manner that preserves much of the elegance and simplicity of the models.…”

Section: Introductionmentioning

confidence: 99%

“…However, the methods extend to the general HB theory by the number projection methods given in ref. [1].…”

Section: Introductionmentioning

confidence: 99%

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Restoration of particle number as a good quantum number in BCS theory

Rowe

2001

Nuclear Physics A

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As shown in previous work, number projection can be carried out analytically for states defined in a quasi-particle scheme when the states are expressed in a coherent state representation. The wave functions of number-projected states are well-known in the theory of orthogonal polynomials as Schur functions. Moreover, the functions needed in pairing theory are a particularly simple class of Schur functions that are easily constructed by means of recursion relations. It is shown that complete sets of states can be projected from corresponding quasi-particle states and that such states retain many of the properties of the quasi-particle states from which they derive. It is also shown that number projection can be used to construct a complete set of orthogonal states classified by generalized seniority for any nucleus.

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“…[1,2,15]. It follows from Claim 1 that the VCS wave function for a one quasi-particle state u j α † jm |x has values given by…”

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

“…[1,2], this recursion relation is solved by making a change of variables from {z j } to the symmetric power functions…”

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

“…However, it can be restored with relative ease in a coherent-state representation [1,2] in a manner that preserves much of the elegance and simplicity of the models.…”

Section: Introductionmentioning

confidence: 99%

“…However, the methods extend to the general HB theory by the number projection methods given in ref. [1].…”

Section: Introductionmentioning

confidence: 99%

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Restoration of particle number as a good quantum number in BCS theory

Rowe

2001

Nuclear Physics A

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Fermion to boson mappings revisited

Ginocchio

Johnson

1996

Physics Reports

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We briefly review various mappings of fermion pairs to bosons, including those based on mapping operators, such as Belyaev-Zelevinskii, and those on mapping states, such as Marumori; in particular we consider the work of Otsuka-Arima-Iachello, aimed at deriving the Interacting Boson Model. We then give a rigorous and unified description of state-mapping procedures which allows one to systematically go beyond Otsuka-Arima-Iachello and related approaches, along with several exact results.

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