Chinese Physics C > 1978, Vol. 2 > Issue(1): 10-22

ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅱ) THE NONHERMITIAN CHOICE

Wu Shi-shu

Department of Physics, Jilin University

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Abstract：
The cancellation properties of the nonhermitian single-particle （SP） potential u_αβ= M_αβ（ ε_β） [or M_αβ（ ε_α）] according to the principle of maximal cancellation of perturbation diagrams are investigated in detail. The mass operator M_αβ（ ω） is separated into two parts M_αβ^on（ ω） and M_αβ^off（ ω） as usual, however, a new criterion for their definition will be proposed. It is shown that the exact mass operator insertion is equal to the sum of the following three types of terms:（1） terms contributed by the poles of M_αβ^off（ ω）. They are truly non-factorizable and must be considered separately,（2） terms which can be cancelled to all orders by the nonhermitian choice u_αβ= M_αβ（ ε_β） [or M_αβ（ ε_α）]. Hence, they serve to define u_αβ,（3） the remaining terms, which can be summed to all orders in a simple way and may be interpreted as amplitude renormalization of the SP Green function.In order to illustrate the usefulness of the above results, we have considered the renormalized random phase approximation （RRPA） for the particle-hole Green function as an example. Related formulae are derived. In RRPA, not only the SP propagator renormalization which includes all the effects except those contributed by the poles of M_αβ^off（ ω）, but also the off energy shell property of the G matrix elements have been taken into account.

References

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P. J. Ellis, E. Osnes, Phys. Lett., 41B (1972), 97.[2] B. H. Brandow. Phys. Rev., 152 (1966), 863; Ann. of Phys., 57 (1970), 214.[3] M. W. Kirson, Nucl. Phys., A115 (1968), 49; A139 (1969), 57.[4] R. L. Becker, K. T. R. Davies, M.R. Patterson, Phys. Rev., C9 (1974), 1221.[5] R. W. Jones, F. Mohling, Nucl. Plys., A151 (1970), 420.[6] A. Klein, Phys. Rev., 121 (1960), 950.[7] R. W. Jones, F. Mohling, R. L. Becker, Nucl. Phys., A220 (1974), 45.[8] 昊式枢，物理学报，25 (1976), 433.[9] M. W. Kirson, Ann. of Phys., 66 (1971), 624; 82 (1974), 345.[10] 李政道、杨振宁，Phys. Rev., 117 (1960), 22.[11] S. Ethofer, P. Schuck, Z. Physik, 228 (1969), 264.[12] 吴式枢，物理学报，22(1966), 377.[13] P. Schuck, F. Villare, P. Ring, Nucl. Phys., A208 (1973), 302.[14] 吴式枢，中国科学，1973, 3, 255; 1974, 5, 471.

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Wu Shi-shu. ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅱ) THE NONHERMITIAN CHOICE[J]. Chinese Physics C, 1978, 2(1): 10-22.

Wu Shi-shu. ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅱ) THE NONHERMITIAN CHOICE[J]. Chinese Physics C, 1978, 2(1): 10-22. shu

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Received: 1977-06-06
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

ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅱ) THE NONHERMITIAN CHOICE

Wu Shi-shu

Department of Physics, Jilin University

Received Date:1977-06-06
Accepted Date:1900-01-01
Available Online:1978-02-05

Abstract:The cancellation properties of the nonhermitian single-particle （SP） potentialu_αβ=M_αβ（ε_β） [orM_αβ（ε_α）] according to the principle of maximal cancellation of perturbation diagrams are investigated in detail. The mass operatorM_αβ（ω） is separated into two partsM_αβ^on（ω） andM_αβ^off（ω） as usual, however, a new criterion for their definition will be proposed. It is shown that the exact mass operator insertion is equal to the sum of the following three types of terms:（1） terms contributed by the poles ofM_αβ^off（ω）. They are truly non-factorizable and must be considered separately,（2） terms which can be cancelled to all orders by the nonhermitian choiceu_αβ=M_αβ（ε_β） [orM_αβ（ε_α）]. Hence, they serve to defineu_αβ,（3） the remaining terms, which can be summed to all orders in a simple way and may be interpreted as amplitude renormalization of the SP Green function.In order to illustrate the usefulness of the above results, we have considered the renormalized random phase approximation （RRPA） for the particle-hole Green function as an example. Related formulae are derived. In RRPA, not only the SP propagator renormalization which includes all the effects except those contributed by the poles ofM_αβ^off（ω）, but also the off energy shell property of the G matrix elements have been taken into account.