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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沈阳化工大学材料科学与工程学院沈阳 110142

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 functionG_αβ(ω) may be separated into two parts:G_αβ(ω)=G_αβ^d(ω)+G_αβ^c(ω). AlthoughG_αβ^d(ω) is a meromorphic function,G_αβ^c(ω) contains branch cuts. In ourprevious discussion of the non-hermitian sp potentialu_αβ=M_αβ(ε_β) defined in termsof the mass operatorM_αβ(ω), we have only consideredG_αβ^d(ω) explicitly. This corres-ponds to a truncation approximation. In this paper, the consequences due toG_αβ^c(ω)are further investigated. It is shown that besides a few new conclusions, all the resultsobtained previously remain true.