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

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

WU SHI-SHU

Department of Physics,Jilin University

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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）— E ₀（ N）] where E ₀（ 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

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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 POTENTIALU_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）potentialu_αβ=M_αβ（ε_β）defined in terms of the mass operatorM_αβ（ω） is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equationh|γ>=（t+u）|γ>=ε_γ|γ>are real;moreover,they satisfy exactly the following relation:（ε_γ⁼±[E_nγ（N±1）—E₀（N）] whereE₀（N）denotes the exact ground state energy of a closed-shell nucleusN,andE_nγ（N±1）are excat energy eigenvalues of its neighbouringN±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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ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIALU_αβ=M_αβ（ε_β）

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

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

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