Strength of the Qπ · Qν interaction and the strong-coupled pseudo-SU(3) limit

Draayer, J. P.; Weeks, K.J.; Hecht, K. T.

doi:10.1016/0375-9474(82)90497-3

Cited by 63 publications

(59 citation statements)

References 11 publications

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“…Since then the SU(3) symmetry has been used in a number of models, including the interacting boson model (IBM) [5], the fermion dynamical symmetry model (FDSM) [6], and the interacting vector boson model (IVBM) [7], especially in heavier nuclei, where the LS coupling scheme of the Elliott model breaks down [8]. It also forms the rationale for pseudo-SU(3) [9][10][11][12][13], which we will discuss below. Finally, a quasi-SU(3) symmetry [14,15], based on the smallness of ∆j = 1 matrix elements, leads to an approximate restoration of LS coupling in heavy nuclei.…”

Section: Su(3) and Nuclear Deformation: The Motivation And Naturementioning

confidence: 99%

Proxy-SU(3) symmetry in heavy deformed nuclei

et al. 2017

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Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions:The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

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Section: Su(3) and Nuclear Deformation: The Motivation And Naturementioning

confidence: 99%

Proxy-SU(3) symmetry in heavy deformed nuclei

et al. 2017

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“…2) The approximate SU (3) symmetry described in 1) is complementary to the pseudo-SU (3) symmetry [12,27,28], in which the normal parity orbitals are approximated, while the intruder parity orbitals remain intact, in contrast to the present approximate symmetry, in which the normal parity orbitals remain intact, while the intruder parity orbitals are approximated.…”

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confidence: 98%

Prolate over oblate dominance in deformed nuclei as a consequence of the SU(3) symmetry and the Pauli principle

Bonatsos

2017

Eur. Phys. J. A

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Abstract. We show that the dominance of prolate over oblate shapes in even-even deformed nuclei can be derived from the SU (3) symmetry and the Pauli principle.As remarked in a recent review [1] by Hamamoto and Mottelson, "the observed almost complete dominance of prolate over oblate deformations in the ground states of deformed even-even nuclei is not yet adequately understood".In this letter we suggest that the appearance of prolate (rugby ball shaped) deformations in the ground states of the majority of deformed even-even nuclei, as opposed to the existence of a few oblate (pancake shaped) ground state deformations appearing just below the simultaneous closing of the proton valence shell and the neutron valence shell can be understood in terms of the SU (3) symmetry and the Pauli principle alone.The basic steps needed in this proof are listed here.1) The SU (3) symmetry discovered by Elliott [2,3] in the sd shell, is destroyed in higher shells by the presence of the strong spin-orbit interaction. However, it has been recently realized [4] that the SU (3) symmetry can be approximately recovered in the higher shells by substituting the opposite parity orbitals (except the one lying highest in energy) invading a given shell from above by the normal parity orbitals which have deserted this given shell in order to take refuge in the shell below. Using the Nilsson asymptotic quantum numbers [5,6] one can see that during this replacement all angular momentum projections (projections of orbital angular momentum, spin, total angular momentum) remain unchanged, while only the total number of quanta N and the number of quanta in the z-direction, n z , are reduced by one unit. This approximation is in line with the remark by Mottelson [7] that the asymptotic quantum numbers of the Nilsson model can be seen as a generalization of Elliott's SU (3).2) The SU (3) symmetry being restored, it is known that the ground state will belong to the highest weight irreducible representation (λ, μ) of SU (3) [2,3], occurring a

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“…Since the most important configurations are those with highest spatial symmetry [11], we ignored all configurations that involve an odd number of particles in any of the four spaces and only consider the interplay between those having zero or two protons and/or two neutrons in the unique space. Then, from all the possible couplings we chose those irreducible representations with the highest value for the second order Casimir operator of (pseudo-)SU(3).…”

Section: Results In the Su(3) Model With Active Intruder Levelsmentioning

confidence: 99%

Microscopic Calculations for Waiting-Point Nuclei

Drumev¹,

Bahri²,

Draayer³

2006

AIP Conference Proceedings

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Abstract. Shell-model calculations for upper fp-shell nuclei using realistic interactions are reported. Valence nucleons beyond the N=28=Z core are considered to fill levels of the normal parity upper fp-shell and the unique parity configurations that consists either of the g 9/2 level or the whole gds-shell. These two cases are handled within a standard M-scheme approach and an SU(3) picture, respectively. Results for low-lying energy spectra, single-particle occupancies and symmetry properties of the eigenstates are reported. Various truncations are considered that key on the number of nucleon pairs allowed to occupy the unique-parity space. The calculations demonstrate the importance of the unique-parity space to the structure of upper fp-shell nuclei.

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Strength of the Qπ · Qν interaction and the strong-coupled pseudo-SU(3) limit

Cited by 63 publications

References 11 publications

Proxy-SU(3) symmetry in heavy deformed nuclei

Proxy-SU(3) symmetry in heavy deformed nuclei

Prolate over oblate dominance in deformed nuclei as a consequence of the SU(3) symmetry and the Pauli principle

Microscopic Calculations for Waiting-Point Nuclei

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