English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A proton-neutron symplectic model of collective motions, based on the non-compact symplectic group $Sp(12,R)$, is introduced by considering the symplectic geometry of the two-component many-particle nuclear system. The possible classical collective motions are determined by different dynamical groups that can be constructed from the symplectic generators. The relation of the $Sp(12,R)$ irreps with the shell-model classification of the basis states is considered by extending of the state space to the direct product space of $SU_{p}(3) \otimes SU_{n}(3)$ irreps, generalizing in this way the Elliott's $SU(3)$ model for the case of two-component system. The $Sp(12,R)$ model appears then as a natural multi-major-shell extension of the generalized proton-neutron $SU(3)$ scheme which takes into account the core collective excitations of monopole and quadrupole, as well as dipole type associated with the giant resonance vibrational degrees of freedom. Each $Sp(12,R)$ irreducible representation is determined by a symplectic bandhead or an intrinsic $U(6)$ space which can be fixed by the underlying proton-neutron shell-model structure, so the theory becomes completely compatible with the Pauli principle. It is shown that this intrinsic $U(6)$ structure is of vital importance for the appearance of the low-lying collective bands with both the positive and negative parity. The full range of low-lying collective states can then be described by the microscopically based intrinsic $U(6)$ structure, renormalized by coupling to the giant resonance vibrations.

The proton-neutron symplectic model of nuclear collective motions