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

WU SHI-SHU

Chinese Physics C> 1979, Vol. 3> Issue(4) : 469-483

ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL U_αβ=M_αβ（ε_β）

WU SHI-SHU

Department of Physics,Jilin University

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Abstract：
In this paper the following results are proved:although the single-particle（sp）potential u_αβ=M_αβ（ε_β）defined in terms of the mass operator M_αβ（ω） is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=（t+u）|γ>=ε_γ|γ> are real;moreover,they satisfy exactly the following relation:（ε_γ⁼±[E_nγ（N±1）—E₀（N）] where E₀（N）denotes the exact ground state energy of a closed-shell nucleus N,and E_nγ（N±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.

References

[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 U_αβ=M_αβ（ε_β）[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 U_αβ=M_αβ（ε_β）[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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沈阳化工大学材料科学与工程学院沈阳 110142

ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL U_αβ=M_αβ（ε_β）

WU SHI-SHU

Department of Physics,Jilin University

Received Date: 1978-02-18
Accepted Date: 1900-01-01
Available Online: 1979-08-05

Abstract: In this paper the following results are proved:although the single-particle（sp）potential u_αβ=M_αβ（ε_β）defined in terms of the mass operator M_αβ（ω） is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=（t+u）|γ>=ε_γ|γ> are real;moreover,they satisfy exactly the following relation:（ε_γ⁼±[E_nγ（N±1）—E₀（N）] where E₀（N）denotes the exact ground state energy of a closed-shell nucleus N,and E_nγ（N±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.