A NOTE ON THE THEORY OF SINGLE PARTICLE POTENTIALS

Wu Shi-shu

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1980, Vol. 4> Issue(4) : 510-515

A NOTE ON THE THEORY OF SINGLE PARTICLE POTENTIALS

Wu Shi-shu

Jilin University

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Abstract：
It is well known that corresponding to the discrete (d) and continuous (c) energyspectra of the nuclei (N+1) and (N-1), the Lehmann representation of the singleparticle (sp) Green function G_αβ(ω) may be separated into two parts: G_αβ(ω)=G_αβ^d(ω)+G_αβ^c(ω). Although G_αβ^d(ω) is a meromorphic function, G_αβ^c(ω) contains branch cuts. In ourprevious discussion of the non-hermitian sp potential u_αβ=M_αβ(ε_β) defined in termsof the mass operator M_αβ(ω), we have only considered G_αβ^d(ω) explicitly. This corres-ponds to a truncation approximation. In this paper, the consequences due to G_αβ^c(ω) are further investigated. It is shown that besides a few new conclusions, all the resultsobtained previously remain true.

References

[1]

吴式枢,物理学报,25 (1976), 433;高能物理与核物理,2 (1978) 10;同左(待发表).这三文简称为文[I],[II]与[III].[2] N. I. Muskhelishvili, Singular Integral Equations, 1953; H. Bremermanrl, Distributions, Complex Va-riables, and Fourier Transforms, 1965.[3] J. R. Schrieffer, many-body Theory, ANL-6527, 1962.[4] J. R. Taylor, Scattering Theory, Ch. 20, 1972.[5] T. T. S.Kou,私人通讯.

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Wu Shi-shu. A NOTE ON THE THEORY OF SINGLE PARTICLE POTENTIALS[J]. Chinese Physics C, 1980, 4(4): 510-515.

Wu Shi-shu. A NOTE ON THE THEORY OF SINGLE PARTICLE POTENTIALS[J]. Chinese Physics C, 1980, 4(4): 510-515. shu

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Received: 1979-03-13
Revised: 1900-01-01

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A NOTE ON THE THEORY OF SINGLE PARTICLE POTENTIALS

Wu Shi-shu

Jilin University

Received Date: 1979-03-13
Accepted Date: 1900-01-01
Available Online: 1980-08-05

Abstract: It is well known that corresponding to the discrete (d) and continuous (c) energyspectra of the nuclei (N+1) and (N-1), the Lehmann representation of the singleparticle (sp) Green function G_αβ(ω) may be separated into two parts: G_αβ(ω)=G_αβ^d(ω)+G_αβ^c(ω). Although G_αβ^d(ω) is a meromorphic function, G_αβ^c(ω) contains branch cuts. In ourprevious discussion of the non-hermitian sp potential u_αβ=M_αβ(ε_β) defined in termsof the mass operator M_αβ(ω), we have only considered G_αβ^d(ω) explicitly. This corres-ponds to a truncation approximation. In this paper, the consequences due to G_αβ^c(ω) are further investigated. It is shown that besides a few new conclusions, all the resultsobtained previously remain true.