THE COLLECTIVE EXCITATION SPECTRA IN EVEN-EVEN DEFORMED NUCLEI (Ⅰ) THEORETICAL FORMULATION

WU Chong-Shi; ZENG Jin-Yan

Chinese Physics C> 1984, Vol. 8> Issue(2) : 219-226

THE COLLECTIVE EXCITATION SPECTRA IN EVEN-EVEN DEFORMED NUCLEI (Ⅰ) THEORETICAL FORMULATION

WU Chong-Shi ^, ,
ZENG Jin-Yan

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Starting from the Bohr Hamiltonian we investigate the spectrum of well-deformed nucleus of which the axial asymmetry is not too large. To diagonalize the Bohr Hamiltonian a suitable potential with certain singularity is assumed and the terms of (sin⁴3γ) in the rotational energy operator expanded in powers of sin 3γ are omitted. The usually adopted adiabatic approximation is given up in present treatment. It is shown that the nuclear collective excitation spectrum manifests the vibrational-rotational band structure and can be described by a convenient closed formula. Within a vibrational-rotational band the moment of inertia and the deformation no longer remain constant and the energy spectrum deviates from the I(I+1) rule in varying degrees.

References

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A. Bohr, Nobel Lectures, 1975, Rotational Motion in Xuclei Nordita Publications, No. 632.[2] A. Bohr, Rotational States of Atomic Nuclei, Murksgaard, Copenhagen (1954).[3] A. Bohr and B. R. Mottelson, Nuclear Structure, Vol. I1 (Benjamin, New York, 1975).[4] F. S. Stephens, N. L. Lark and R. M. Diamond, Phys. Rev. Lett., 12(1964), 225.[5] F. S. Stephens, N. L. Lark and R. M. Diamond, Nucl. Phys., 63(1965), 82.[6] S. M. Harris, Phys. Rev. Lett., 13(1964), 663; Phys. Rev., 158(1965), B509.[7]φ Saethre, S. A. Hjorth, A. Johnson, S. Jagare, H. Ryde and Z. Szymanski, Nucl. Phys., A207(1973), 486.[8] B. R. Mottelson, Proc. Intern. Conf. on High Spin Phenomena in Nuclei, Argonne, 1979, ANL/PHY-79-4, p. 1.[9] M. A. J. Mariscotti, G. Scharff-Goldhaber and B. Buck, Phys. Rev., 178(1969), 1864.G. Scharff-Goldhaber, C. Dover and A. L. Goodman, Ann. Rev. Nucl. Sci., 26 (1976), 239.[10] 吴崇试、曾谨言, 待发表.[11] 吴崇试、曾谨言, 待发表.[12] 吴崇试、曾谨言, 待发表.[13] A. Bohr, Dan. Mat. Fys. Medd., 26(1952), no. 14.[14] A. Bohr and B. R. Mottelson, Dan. Mat. Fys. Medd., 27(1953), no. 16.[15] A. S. Davydov and G. F. Filippov, Nucl. Phys., 8(1958), 237.[16] K. Kumar and M. Baranger, Nucl. Phys. A92(1967), 608.[17] G. Gneuss and W. Greiner, Nucl. Phys., A171(1971), 449.[18] L. Wilets and M. Jean, Phys. Rev., 102(1956), 788.[19] F. M. Arscott, Periodic Differential Equations (Pergamon Press, 1964), ch. VIII.[20] A. N. Lowan, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ed. M. Abramowitz and I. A. Stegun, p. 751.[21] 王竹溪、郭敦仁, 特殊函数概论, 科学出版社, 1965年, 第361页.[22] W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer-Verlag, 1966), p. 239.

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[20]	Gu Jin-nan , Wang Zheng-da . THE ROTATIONAL THREE-BAND INTERACTION FOR EVEN-EVEN NUCLEI. Chinese Physics C, 1980, 4(5): 652-660.

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WU Chong-Shi and ZENG Jin-Yan. THE COLLECTIVE EXCITATION SPECTRA IN EVEN-EVEN DEFORMED NUCLEI (Ⅰ) THEORETICAL FORMULATION[J]. Chinese Physics C, 1984, 8(2): 219-226.

WU Chong-Shi and ZENG Jin-Yan. THE COLLECTIVE EXCITATION SPECTRA IN EVEN-EVEN DEFORMED NUCLEI (Ⅰ) THEORETICAL FORMULATION[J]. Chinese Physics C, 1984, 8(2): 219-226. shu

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Received: 1900-01-01
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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

THE COLLECTIVE EXCITATION SPECTRA IN EVEN-EVEN DEFORMED NUCLEI (Ⅰ) THEORETICAL FORMULATION

Corresponding author: WU Chong-Shi,

Received Date: 1900-01-01

Accepted Date: 1900-01-01

Available Online: 1984-04-05

Abstract: Starting from the Bohr Hamiltonian we investigate the spectrum of well-deformed nucleus of which the axial asymmetry is not too large. To diagonalize the Bohr Hamiltonian a suitable potential with certain singularity is assumed and the terms of (sin⁴3γ) in the rotational energy operator expanded in powers of sin 3γ are omitted. The usually adopted adiabatic approximation is given up in present treatment. It is shown that the nuclear collective excitation spectrum manifests the vibrational-rotational band structure and can be described by a convenient closed formula. Within a vibrational-rotational band the moment of inertia and the deformation no longer remain constant and the energy spectrum deviates from the I(I+1) rule in varying degrees.

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THE COLLECTIVE EXCITATION SPECTRA IN EVEN-EVEN DEFORMED NUCLEI (Ⅰ) THEORETICAL FORMULATION

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