Partial dynamical symmetry as a selection criterion for many-body interactions

Abstract

We propose the use of partial dynamical symmetry (PDS) as a selection criterion for higher-order terms in situations when a prescribed symmetry is obeyed by some states and is strongly broken in others. The procedure is demonstrated in a first systematic classification of many-body interactions with SU(3) PDS that can improve the description of deformed nuclei. As an example, the triaxial features of the nucleus 156 Gd are analyzed. Many-body forces play an important role in quantum many-body systems [1]. They appear either at a fundamental level or as effective interactions which arise due to restriction of degrees of freedom and truncation of model spaces. A known example is the structure of light nuclei, where two-nucleon interactions are insufficient to achieve an accurate description and higher-order interactions between the nucleons must be included [2]. Given the difficulty in constraining the nature of such higher-order terms from experiments, one is faced with the problem of their determination. One way, currently the subject of active research [3], is to determine them from chiral effective field theory applied to quantum chromodynamics. This establishes a hierarchy of inter-nucleon interactions according to their order. In light-medium nuclei, these interactions serve as input for ab-initio methods (e.g., the no-core shell model (NCSM) [4]) to generate, by means of similarity transformations, A-body effective Hamiltonians in computational tractable model spaces.The situation is more complex in heavy nuclei, where ab-initio methods are limited by the enormous increase in size of the model spaces required to accommodate correlated collective motion of many nucleons. One possible approach to circumvent this problem, is to augment the NCSM method through a symplectic symmetry-adapted choice of basis [5]. A second approach is to employ energy density functionals and incorporate beyond mean-field effects by mapping to collective Hamiltonians [6], e.g., the interacting boson model (IBM) [7]. In both approaches the Hilbert spaces are based on particular dynamical algebras which lead to a dramatic reduction of the basis dimension. Nevertheless, even with such simplification, the number of possible interactions in the effective Hamiltonians grows rapidly with their order, and a selection criterion is called for. In this Rapid Communication, we suggest a method to select possible higher-order terms which is based on the idea of partial dynamical symmetry (PDS).The concept of PDS [8] is a generalization of that of a dynamical symmetry (DS) [9] where the conditions of the latter (solvability of the complete spectrum, existence of exact quantum numbers for all eigenstates, and predetermined structure of the eigenfunctions) are relaxed and apply to only part of the eigenstates and/or of the quantum numbers. PDSs have been identified in various dynamical systems involving bosons and fermions (for a review, see Ref.[8]). They play a role in diverse phenomena including nuclear and molecular spectroscopy [10][11][12], q...

Lifetime measurements in Gd156

“…Another recent development describes nuclei at the point of phase change from spherical to deformed in terms of β and γ shape parameters, or the SU(3) symmetry [17,18,20] or the pseudo-SU(3) [35]. There is also the possibility of Partial Dynamical Symmetries where the SU(3) symmetry is obeyed by some of the states and broken in others [46]. A systematic theoretical study of even-even deformed nuclei in the Hartree-Fock-Bogoliubov approach extended by the generator coordinate method and mapped into a five-dimensional collective Hamiltonian for even-even nuclei from Z = 10 − 110, provides guidelines to distinguishing between coexistence and β vibrational oscillations.…”

“…Numerous other studies included electron, proton, and photon scattering [51,52]. The 156 Gd nucleus was used for comparisons with early tests of the Interacting Boson Model numerical studies for the SU(3) limit [53] as well as the later tests of Partial Dynamical Symmetry tests [46]. The focus of this paper is the excited K π = 0 + bands.…”

Partial dynamical symmetry and odd-even staggering in deformed nuclei

“…The essential idea is to relax the stringent conditions of complete solvability, so that only part of the eigenspectrum retains all the DS quantum numbers. Various types of bosonic and fermionic PDS are known to be relevant to nuclear spectroscopy [4][5][6][7][8][9][10][11][12][13]. In the present contribution we demonstrate the relevance of PDS to the odd-even staggering in the γ-band of 156 Gd [13].…”

“…The two classes of SU(3)-PDS Hamiltonians demonstrate the increase in flexibility obtained by generalizing the concept of DS to PDS. In fact, in the IBM more than half of all possible interactions have an SU(3) PDS [13]. In summary, we have presented several classes of IBM Hamiltonians with SU(3) PDS, and obtained an improved description of signature splitting in the γ band of 156 Gd.…”

Linking partial and quasi dynamical symmetries in rotational nuclei

“…This situation, referred to as partial dynamical symmetry (PDS) [4], was shown to be relevant to specific nuclei [4][5][6][7][8][9][10][11][12] and molecules [13]. In parallel, the notion of quasi dynamical symmetry (QDS) was introduced and discussed in the context of nuclear models [14][15][16][17][18][19][20][21].…”