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

Wu Shi-shu

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

Abstract
HTML
Reference
Related

PDF

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

[1]

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.

[1]	LIU Shu-Xin , LEI Yi-An , ZENG Jin-Yan . Large Fluctuation in Odd-Even Differences and Nonadditivity of Nuclear Moments of Inertia. Chinese Physics C, 2006, 30(S2): 39-41.
[2]	ZHANG Li , ZHOU Shan-Gu , MENG Jie . Real Stabilization Method and Its Application in Calculating Resonance States. Chinese Physics C, 2006, 30(S2): 59-61.
[3]	XU Fu-Rong . High-Spin Excitations of Atomic Nuclei. Chinese Physics C, 2004, 28(S1): 11-15.
[4]	Gu Jianzhong , Wu Xizhen , Zhao Enguang , Zhuo Yizhong . Nearest Neighbour Level Spacing and Level Curvature Distributions of Single-Particle in Heavy Nuclei. Chinese Physics C, 1997, 21(6): 535-540.
[5]	Ren Jianglong , Ding Linkai . Calculation of Cross-Section and Distribution of Number of Wounded Nucleons in High Energy Hadron-Nucleus Inelastic Collision. Chinese Physics C, 1996, 20(2): 119-123.
[6]	DENG Wei-Zhen , YANG Ze-Sen , WANG Yu-Cheng . A Non-Hermitian Approach of Dyson Boson Expansion to Interacting Boson Model. Chinese Physics C, 1993, 17(10): 907-911.
[7]	LIU Ji-Feng , WU Pei-Yun , SHEN Jian-Ping , LI Guang-Lie . The η-N Interaction Potential and the Potential Well Depth of η-meson in Nuclear Matter. Chinese Physics C, 1991, 15(3): 224-233.
[8]	DOU Zhi-Guo , JING Xiao-Gong , ZHAO Guo-Quan . SINGLE-PARTICLE AND SINGLE-HOLE ENERGIES IN THE ⁴⁰Ca REGION. Chinese Physics C, 1990, 14(11): 1031-1038.
[9]	LI Yang-Guo . ANTIPROTON-NUCLEUS INELASTIC COLLISION. Chinese Physics C, 1989, 13(5): 433-439.
[10]	MA Bo-Qiang , SUN Ji . DIFFERENT TREATMENTS OF NUCLEAR BINDING EFFECT IN DEEP INELASTIC LEPTON NUCLEUS SCATTERING. Chinese Physics C, 1988, 12(6): 786-792.
[11]	JING Xiao-Gong , LI Cheng-Zu , YANG Shan-De , WU Shi-Shu . SINGLE-PARTICLE AND SINGLE-HOLE SPECTRA IN ⁴⁰Ca. Chinese Physics C, 1986, 10(6): 744-751.
[12]	LI Guang-Lie , SHEN Jian-Ping . A Λ-N S WAVE SEPARATION POTENTIAL AND ITS Λ WELL DEPTH IN NUCLEAR MATTER. Chinese Physics C, 1985, 9(4): 442-446.
[13]	SHEN Jian-Ping , LI Guang-Lie . THE POTENTIAL WELL DEPTH OF Λ PARTICLE IN NUCLEAR MATTER DUE TO MESON EXCHANGE POTENTIAL. Chinese Physics C, 1985, 9(3): 307-312.
[14]	WANG KE-XIE , JING XIAO-GONG , WU HUNG-CHU , YANG SHAN-DE , WU SHI-SHU . DEPENDENCE OF SINGLE PARTICLE AND SINGLE HOLE ENERGIES IN THE ¹⁶O REGION ON THE NUCLEAR FORCES. Chinese Physics C, 1982, 6(4): 525-528.
[15]	YANG SHAN-DE , JING XIAO-GONG , WANG KE-XIE , WU SHI-SHU . SINGLE PARTICLE AND SINGLE HOLE ENERGIES IN THE ¹⁶O REGION. Chinese Physics C, 1982, 6(4): 480-490.
[16]	Zheng Yu-ming , Lu Zhao-qi , Chen Yong-shou . THE FOLDING POTENTIAL OF THE DOUBLE WELL-CLUSTER SHELL MODEL. Chinese Physics C, 1980, 4(1): 109-112.
[17]	Wu Shi-shu . A NOTE ON THE THEORY OF SINGLE PARTICLE POTENTIALS. Chinese Physics C, 1980, 4(4): 510-515.
[18]	Zhang Xi-zhen , Chen Yong-shou . QUASIPARTICLE SPECTRUM IN A ROTATING PETENTIAL AND THE BACK-BENDING PHENOMENA. Chinese Physics C, 1980, 4(1): 103-108.
[19]	Wu SHI-SHU . ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅳ) MANY-BODY FORCES. Chinese Physics C, 1979, 3(2): 240-243.
[20]	WU SHI-SHU . ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL U_αβ=M_αβ（ε_β）. Chinese Physics C, 1979, 3(4): 469-483.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1977-06-06
Revised: 1900-01-01

Article Metric

Article Views(1748)
PDF Downloads(290)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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

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） 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.

HTML

Reference (1)

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

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

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

HTML

目录