Formal Aspects of Nuclear Moment-of-Inertia Theory

William A. Friedman; Lawrence Wilets

doi:10.1103/PhysRevC.2.892

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Formal Aspects of Nuclear Moment-of-Inertia Theory

William A. Friedman and Lawrence Wilets^*

Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540

^*Present and permanent address: Department of Physics, University of Washington, Seattle, Washington 98105.

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Phys. Rev. C 2, 892 – Published 1 September, 1970

DOI: https://doi.org/10.1103/PhysRevC.2.892

Abstract

Projected Hartree-Fock states are used as a representation in calculating nuclear wave functions. The rotational energy is determined consistently through $\frac{J (J + 1)}{〈 J^{2} 〉}$ , and the moment of inertia thus obtained is compared with the expressions of other authors. The formulas of Peierls and Yoccoz and Thouless and Valatin yield approximately the same results as ours, but all of these formulas exhibit discrepancies with the Inglis independent-particle cranking-model formula. We find that the spurious state $J_{x} | φ 〉$ plays a dominant role, in agreement with Banerjee, D'Oliveira, and Stephenson. Interesting observations are made for the case of the soluble $SU (3)$ model of Elliott.

References (16)

D. R. Inglis, Phys. Rev. 103, 1786 (1956)
D. J. Thouless, Nucl. Phys. 21, 225 (1960) D. J. Thouless and J. G. Valatin, 31, 211 (1962)
M. Baranger, Caragese Lectures in Theoretical Physics, 1962 (W. A. Benjamin, Inc., New York, 1963)
G. E. Brown, Unified Theory of Nuclear Models and Nucleon-Nucleon Forces (North-Holland Publishing Company, Amsterdam, The Netherlands, 1967)
M. K. Banerjee, D. D'Oliveira, and G. J. Stephenson, Jr., Phys. Rev. 181, 1404 (1969)
R. E. Peirels and J. Yoccoz, Proc. Phys. Soc. (London) A70, 381 (1957)
J. Yoccoz, Proc. Phys. Soc. (London) A70, 388 (1957) Many-Body Description of Nuclear Structure and Reactions, Proceedings of the International School of Physics "Enrico Fermi," Course XXXVI, edited by C. Bloch (Academic Press Inc., New York, 1966)
F. Villars, in Many-Body Description of Nuclear Structure and Reactions, Proceedings of the International School of Physics "Enrico Fermi," Course XXXVI, edited by C. Bloch (Academic Press Inc., New York, 1966)
Y. Y. Sharon, Ph.D. thesis, Princeton University, 1965 (unpublished)
G. Ripka, in Lectures in Theoretical Physics, edited by P. D. Kunz and W. E. Brittin (University of Colorado Press, Boulder, Colorado, 1966), Vol. VIII C Advances in Nuclear Physics, edited by M. Baranger and E. Vogt (Plenum Press, Inc., New York, 1968), Vol. I
S. M. Harris, Phys. Rev. 138, B509 (1965)
F. Villars, in Nuclear Physics, Proceedings of the International School of Physics, "Enrico Fermi," Course XXIII, edited by V. F. Weisskopf (Academic Press Inc., New York, 1963)
F. Villars and N. C. Rogerson, to be published
R. E. Peierls and D. J. Thouless, Nucl. Phys. 38, 154 (1962)
J. P. Elliott, Proc. Roy. Soc. (London) A245, 128, 562 (1958) M. Harvey, in Advances in Nuclear Physics, edited by M. Baranger and E. Vogt (Plenum Press, Inc., New York, 1968), Vol. I
S. G. Nilsson and O. Prior, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 32, No. 16 (1960) J. J. Griffin and M. Rich, Phys. Rev. Letters 3, 342 (1960)

[c1] D. R. Inglis, Phys. Rev. 103, 1786 (1956)

[c2] D. J. Thouless, Nucl. Phys. 21, 225 (1960) D. J. Thouless and J. G. Valatin, 31, 211 (1962)

[c3] M. Baranger, Caragese Lectures in Theoretical Physics, 1962 (W. A. Benjamin, Inc., New York, 1963)

[c4] G. E. Brown, Unified Theory of Nuclear Models and Nucleon-Nucleon Forces (North-Holland Publishing Company, Amsterdam, The Netherlands, 1967)

[c5] M. K. Banerjee, D. D'Oliveira, and G. J. Stephenson, Jr., Phys. Rev. 181, 1404 (1969)

[c6] R. E. Peirels and J. Yoccoz, Proc. Phys. Soc. (London) A70, 381 (1957)

[c7] J. Yoccoz, Proc. Phys. Soc. (London) A70, 388 (1957) Many-Body Description of Nuclear Structure and Reactions, Proceedings of the International School of Physics "Enrico Fermi," Course XXXVI, edited by C. Bloch (Academic Press Inc., New York, 1966)

[c8] F. Villars, in Many-Body Description of Nuclear Structure and Reactions, Proceedings of the International School of Physics "Enrico Fermi," Course XXXVI, edited by C. Bloch (Academic Press Inc., New York, 1966)

[c9] Y. Y. Sharon, Ph.D. thesis, Princeton University, 1965 (unpublished)

[c10] G. Ripka, in Lectures in Theoretical Physics, edited by P. D. Kunz and W. E. Brittin (University of Colorado Press, Boulder, Colorado, 1966), Vol. VIII C Advances in Nuclear Physics, edited by M. Baranger and E. Vogt (Plenum Press, Inc., New York, 1968), Vol. I

[c11] S. M. Harris, Phys. Rev. 138, B509 (1965)

[c12] F. Villars, in Nuclear Physics, Proceedings of the International School of Physics, "Enrico Fermi," Course XXIII, edited by V. F. Weisskopf (Academic Press Inc., New York, 1963)

[c13] F. Villars and N. C. Rogerson, to be published

[c14] R. E. Peierls and D. J. Thouless, Nucl. Phys. 38, 154 (1962)

[c15] J. P. Elliott, Proc. Roy. Soc. (London) A245, 128, 562 (1958) M. Harvey, in Advances in Nuclear Physics, edited by M. Baranger and E. Vogt (Plenum Press, Inc., New York, 1968), Vol. I

[c16] S. G. Nilsson and O. Prior, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 32, No. 16 (1960) J. J. Griffin and M. Rich, Phys. Rev. Letters 3, 342 (1960)

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Formal Aspects of Nuclear Moment-of-Inertia Theory

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