arXiv:nucl-th/0208060 · Physical Review C

A study of randomness, correlations, and collectivity in the nuclear shell model

Víctor Velázquez, Jorge G. Hirsch, Alejandro Frank, A. P. Zuker

Published Mar 24, 2003• 10 citations

Abstract

A variable combination of realistic and random two-body interactions allows the study of collective properties [such as the energy spectra and $B(E2)$ transition strengths] in ${}^{44}\mathrm{Ti},$ ${}^{48}\mathrm{Cr},$ and ${}^{24}\mathrm{Mg}.$ It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the $B(E2)$ values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.

DOI: 10.1103/physrevc.67.034311

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arXiv:nucl-th/0208060 · Physical Review C

A study of randomness, correlations, and collectivity in the nuclear shell model

Víctor Velázquez, Jorge G. Hirsch, Alejandro Frank, A. P. Zuker

Published Mar 24, 2003• 10 citations

arXiv HTML PDF

Abstract

A variable combination of realistic and random two-body interactions allows the study of collective properties [such as the energy spectra and

B(E2)

transition strengths] in

{}^{44}\mathrm{Ti},

{}^{48}\mathrm{Cr},

and

{}^{24}\mathrm{Mg}.

It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the

B(E2)

values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.

DOI: 10.1103/physrevc.67.034311

Related papers

Order, collectivity, structured yrast lines, and correlated energies in random bosonic systems

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The energy systematics of medium and heavy even-even nuclei shows very regular features, such as for example the tripartite classification of nuclear structure into seniority, anharmonic vibrator and rotor regions [1,2]. Traditionally, this regular behavior has been interpreted as a consequence of particular interactions, such as an attractive pairing force in semimagic nuclei and an attractive neutron-proton quadrupole-quadrupole interaction for deformed nuclei. It came as a surprise, therefore, that recent studies of even-even nuclei in the nuclear shell model [3–5] and in the interacting boson model (IBM) [6–8] with random interactions also displayed a high degree of order. Both models showed a statistical preference for L = 0 ground states, despite the random nature of the interactions. In addition, in the shell model evidence was found for the occurrence of pairing properties [5], and in the IBM for vibrational and rotational bands [6,7]. These unexpected results have sparked a large number of investigations to try to understand their origin [9]. In this contribution, we discuss the phenomenom of emerging regular spectral features from the IBM with random interactions, and itsThe energy systematics of medium and heavy even-even nuclei shows very regular features, such as for example the tripartite classification of nuclear structure into seniority, anharmonic vibrator and rotor regions [1,2]. Traditionally, this regular behavior has been interpreted as a consequence of particular interactions, such as an attractive pairing force in semimagic nuclei and an attractive neutron-proton quadrupole-quadrupole interaction for deformed nuclei. It came as a surprise, therefore, that recent studies of even-even nuclei in the nuclear shell model [3–5] and in the interacting boson model (IBM) [6–8] with random interactions also displayed a high degree of order. Both models showed a statistical preference for L = 0 ground states, despite the random nature of the interactions. In addition, in the shell model evidence was found for the occurrence of pairing properties [5], and in the IBM for vibrational and rotational bands [6,7]. These unexpected results have sparked a large number of investigations to try to understand their origin [9]. In this contribution, we discuss the phenomenom of emerging regular spectral features from the IBM with random interactions, and its

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New puzzle for many-body systems with random two-body interactions

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We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast $J=0,2,4,6,8$ states. Previous studies, limited only to $J=0,2,4$ states, had shown strong correlations in boson systems but not fermion systems. By including $J\ensuremath{\geqslant}6$ states and considering different scatter plots, strong correlations between ratios of yrast excitation energies appear in both boson and fermion systems. Such correlations agree with real nuclear data and include the well-known limits of seniority, vibrations, and rotations.We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast $J=0,2,4,6,8$ states. Previous studies, limited only to $J=0,2,4$ states, had shown strong correlations in boson systems but not fermion systems. By including $J\ensuremath{\geqslant}6$ states and considering different scatter plots, strong correlations between ratios of yrast excitation energies appear in both boson and fermion systems. Such correlations agree with real nuclear data and include the well-known limits of seniority, vibrations, and rotations.

arXiv:nucl-th/0612018Physical Review CApr 25, 200726 citations

Collective behavior in random interaction

Calvin W. Johnson, Hai Ah Nam

arXiv:nucl-th/0601093Revista Mexicana de FísicaJan 30, 20061 citation

A variable combination of realistic and random two-body interactions allows the study of collective properties [such as the energy spectra and

B(E2)

transition strengths] in

{}^{44}\mathrm{Ti},

{}^{48}\mathrm{Cr},

and

{}^{24}\mathrm{Mg}.

It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the

B(E2)

Signatures of order and collectivity appear in a broad range of one and two level boson systems. Toy systems of

N

particles on a single

j=3,\,4\dots 7

level, and on 2 levels

(j_1,\,j_2)

with

j_1+j_2 \leq 6

were studied. Surprising novel features in the yrast lines were consistent with boson condensates. Strong signatures of order and collectivity were the norm. These included the usual energy ratios and quadrupole transition strengths for vibrational and rotational bands. There were pronounced correlations in energy ratios, sharp peaks in the Alga ratios and fractional collectivity across all the 1-level systems, as well as signatures of triaxiality

We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast

J=0,2,4,6,8

states. Previous studies, limited only to

J=0,2,4

states, had shown strong correlations in boson systems but not fermion systems. By including $J\ensuremath{\geqslant}6$ states and considering different scatter plots, strong correlations between ratios of yrast excitation energies appear in both boson and fermion systems. Such correlations agree with real nuclear data and include the well-known limits of seniority, vibrations, and rotations.