ON NUCLEAR SINGLE-PARTICLE POTENTIALS(Ⅲ)SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL Uαβ=Mαβεβ

  • In this paper the following results are proved:although the single-particle(sp)potential uαβ=Mαβεβ)defined in terms of the mass operator Mαβω) is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=(t+u)|γ>=εγ|γ> are real;moreover,they satisfy exactly the following relation:(εγ=±[EnγN±1)—E0N)] where E0N)denotes the exact ground state energy of a closed-shell nucleus N,and EN±1)are excat energy eigenvalues of its neighbouring N±1 nucleus.Further,in order to determine whether the bound state energies obtained by anyother sp potential may or not satisfy the above relation,a simple method is sugges-ted.It is shown that the amplitude renormalization of the sp Green function canalso be calculated easily by means of this method.
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  • [1] 吴式枢,物理学报,25 (1976), 433.[2] 吴式枢,高能物理与核物理,2 (1978), 10.[3] R. L. Beeker, R. W. Jones. Nucl. Phys., A174 (1971) , 449.[4] S. Ethofer. P. Schuck. Z. Physik. 228 (1969). 264.[5] B. H, Brandow, Rev. Mod. Phys., 39 (1967), 771.[6] A. Klein, "Lectures on the many-body problem”, Vol. 1, ed. E. R. Caianiello (Aeademic Press 1962).[7] 吴式枢,高能物理与核物理,3 (1979), 240.[8] C. B. Dover and R. H. Lemmer, Phys. Rev., 165 (1968), 1105.[9] F. Catara, et al., Nucl. Phys., A276 (1977),433.
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WU SHI-SHU. ON NUCLEAR SINGLE-PARTICLE POTENTIALS(Ⅲ)SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL Uαβ=Mαβεβ)[J]. Chinese Physics C, 1979, 3(4): 469-483.
WU SHI-SHU. ON NUCLEAR SINGLE-PARTICLE POTENTIALS(Ⅲ)SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL Uαβ=Mαβεβ)[J]. Chinese Physics C, 1979, 3(4): 469-483. shu
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Received: 1978-02-18
Revised: 1900-01-01
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ON NUCLEAR SINGLE-PARTICLE POTENTIALS(Ⅲ)SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL Uαβ=Mαβεβ

  • Department of Physics,Jilin University

Abstract: In this paper the following results are proved:although the single-particle(sp)potential uαβ=Mαβεβ)defined in terms of the mass operator Mαβω) is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=(t+u)|γ>=εγ|γ> are real;moreover,they satisfy exactly the following relation:(εγ=±[EnγN±1)—E0N)] where E0N)denotes the exact ground state energy of a closed-shell nucleus N,and EN±1)are excat energy eigenvalues of its neighbouring N±1 nucleus.Further,in order to determine whether the bound state energies obtained by anyother sp potential may or not satisfy the above relation,a simple method is sugges-ted.It is shown that the amplitude renormalization of the sp Green function canalso be calculated easily by means of this method.

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