Renormalization for collective motion within a truncated space of the spherical shell model. II. Projected frame in a schematic model

Energy minimization is not sufficient to determine whether a nucleus is spherical or deformed. The quantal zero-point motion can make a nucleus spherical even if the potential energy has a deformed minimum. However, some general conditions give deformed shape as the natural state of atomic nuclei. They are spherical only under some special conditions. Some general criteria for distinguishing spherical nuclei from deformed, as well as some advantages of using a deformed-shell model rather than a spherical-shell model, are presented.

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Viscosity Stratification and a 3-D Compressible Spherical Shell Model of Mantle Evolution

High Performance Computing in Science and Engineering ’03 ◽

10.1007/978-3-642-55876-4_4 ◽

2003 ◽

pp. 27-67 ◽

Cited By ~ 2

Author(s):

Uwe Walzer ◽

Roland Hendel ◽

John Baumgardner

Keyword(s):

Spherical Shell ◽

Shell Model ◽

Mantle Evolution

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Validity of an algebraic-variational approach to the theory of collective motion for an exactly soluble shell model with R(5) symmetry

Nuclear Physics A ◽

10.1016/0375-9474(73)90283-2 ◽

1973 ◽

Vol 210 (3) ◽

pp. 429-442 ◽

Cited By ~ 19

Author(s):

Carlos Dasso ◽

F. Krejs ◽

Abraham Klein ◽

P.K. Chattopadhyay

Keyword(s):

Shell Model ◽

Variational Approach ◽

Collective Motion

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Collective motion in the nuclear shell model III. The calculation of spectra

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1963.0071 ◽

1963 ◽

Vol 272 (1351) ◽

pp. 557-577 ◽

Cited By ~ 133

Keyword(s):

Shell Model ◽

Collective Motion ◽

Mass Region ◽

Wave Functions ◽

Nuclear Shell Model ◽

Matrix Elements ◽

One Dimensional ◽

The One ◽

Nuclear Shell ◽

Main Pattern

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

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