arXiv subjects

R. F. Casten

Publications and source records attributed to R. F. Casten.

35 records · Page 2Linked to original sources

arXiv2009

SU(3) quasidynamical symmetry underlying the Alhassid--Whelan arc of regularity

The first example of an empirically manifested quasi dynamical symmetry trajectory in the interior of the symmetry triangle of the Interacting Boson Approximation model is identified for large boson numbers. Along this curve, extending from SU(3) to near the critical line of the first order phase transition, spectra exhibit nearly the same degeneracies that characterize the low energy levels of SU(3). This trajectory also lies close to the Alhassid-Whelan arc of regularity, the unique interior region of regular behavior connecting the SU(3) and U(5) vertices, thus offering a possible symmetry-based interpretation of that narrow zone of regularity amidst regions of more chaotic spectra.

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arXiv2009

Regularities and symmetries of subsets of collective 0+ states

The energies of subsets of excited 0+ states in geometric collective models are investigated and found to exhibit intriguing regularities. In models with an infinite square well potential, it is found that a single formula, dependent on only the number of dimensions, describes a subset of 0+ states. The same behavior of a subset of 0+ states is seen in the large boson number limit of the Interacting Boson Approximation (IBA) model near the critical point of a first order phase transition, in contrast to the fact that these 0+ state energies exhibit a harmonic behavior in all three limiting symmetries of the IBA. Finally, the observed regularities in 0+ energies are analyzed in terms of the underlying group theoretical framework of the different models.

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arXiv2008

What can we learn from the Interacting Boson Model in the limit of large boson numbers?

Over the years, studies of collective properties of medium and heavy mass nuclei in the framework of the Interacting Boson Approximation (IBA) model have focused on finite boson numbers, corresponding to valence nucleon pairs in specific nuclei. Attention to large boson numbers has been motivated by the study of shape/phase transitions from one limiting symmetry of IBA to another, which become sharper in the large boson number limit, revealing in parallel regularities previously unnoticed, although they survive to a large extent for finite boson numbers as well. Several of these regularities will be discussed. It will be shown that in all of the three limiting symmetries of the IBA [U(5), SU(3), and O(6)], energies of 0+ states grow linearly with their ordinal number. Furthermore, it will be proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0_2^+)=E(6_1^+), E(0_3^+) =E(10_1^+), E(0_4^+)=E(14_1^+), the energy ratio E(6_1^+) /E(0_2^+) turning out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first- and second-order transitions. The energies of 0+ states near the point of the first order shape/phase transition between U(5) and SU(3) will be shown to grow as n(n+3), where n is their ordinal number, in agreement with the rule dictated by the relevant critical point symmetries studied in the framework of special solutions of the Bohr Hamiltonian. The underlying dynamical and quasi-dynamical symmetries are also discussed.

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arXiv2008

0+ states in the large boson number limit of the Interacting Boson Approximation model

Studies of the Interacting Boson Approximation (IBA) model for large boson numbers have been triggered by the discovery of shape/phase transitions between different limiting symmetries of the model. These transitions become sharper in the large boson number limit, revealing previously unnoticed regularities, which also survive to a large extent for finite boson numbers, corresponding to valence nucleon pairs in collective nuclei. It is shown that energies of 0_n^+ states grow linearly with their ordinal number n in all three limiting symmetries of IBA [U(5), SU(3), and O(6)]. Furthermore, it is proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0_2^+)=E(6_1^+), E(0_3^+)=E(10_1^+), E(0_4^+)=E(14_1^+), while the energy ratio E(6_1^+) /E(0_2^+) turns out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first- and second-order transitions. The energies of 0_n^+ states near the point of the first order shape/phase transition between U(5) and SU(3) are shown to grow as n(n+3), in agreement with the rule dictated by the relevant critical point symmetries resulting in the framework of special solutions of the Bohr Hamiltonian. The underlying partial dynamical symmetries and quasi-dynamical symmetries are also discussed.

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arXiv2008

Exactly separable version of the Bohr Hamiltonian with the Davidson potential

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum) and a stiff harmonic oscillator for u(gamma) centered at gamma=0. In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, gamma band and 0_2^+ band are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare earth and actinide nuclei using two parameters (beta_0, gamma stiffness). Insights regarding the recently found correlation between gamma stiffness and the gamma-bandhead energy, as well as the long standing problem of producing a level scheme with Interacting Boson Approximation SU(3) degeneracies from the Bohr Hamiltonian, are also obtained.

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arXiv2008

Simple, empirical order parameter for a first order quantum phase transition in atomic nuclei

A simple, empirical signature of a first order phase transition in atomic nuclei is presented, the ratio of the energy of the 6+ level of the ground state band to the energy of the first excited 0+ state. This ratio provides an effective order parameter which is not only easy to measure, but also distinguishes between first and second order phase transitions and takes on a special value in the critical region. Data in the Nd-Dy region show these characteristics. In addition, a repeating degeneracy between alternate yrast states and successive excited 0+ states is found to correspond closely to the line of a first order phase transition in the framework of the Interacting Boson Approximation (IBA) model in the large N limit, pointing to a possible underlying symmetry in the critical region.

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arXiv2008

Unified description of 0+ states in a large class of nuclear collective models

A remarkably simple regularity in the energies of 0+ states in a broad class of collective models is discussed. A single formula for all 0+ states in flat-bottomed infinite potentials that depends only on the number of dimensions and a simpler expression applicable to all three IBA symmetries in the large boson number limit are presented. Finally, a connection between the energy expression for 0+ states given by the X(5) model and the predictions of the IBA near the critical point is explored.

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arXiv2006

Empirical Proton-Neutron Interactions and Nuclear Density Functional Theory: Global, Regional and Local Comparisons

Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.

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arXiv2005

Anomalous behavior of the first excited 0$^{+}$ state in $N \approx Z$ nuclei

A study of the energies of the first excited $0^+$ states in all even-even $Z$ $\geq$ 8 nuclei reveals an anomalous behavior in some nuclei with $N$ = $Z$, $Z$ $\pm$ 2. We analyze these irregularities in the framework of the shell model. It is shown that proton-neutron correlations play an important role in this phenomenon.

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arXiv2004

Alternative Interpretation of Sharply Rising E0 Strengths in Transitional Regions

It is shown that strong 0+2 -> 0+1 E0 transitions provide a clear signature of phase transitional behavior in finite nuclei. Calculations using the IBA show that these transition strengths exhibit a dramatic and robust increase in spherical-deformed shape transition regions, that this rise matches well the existing data, that the predictions of these E0 transitions remain large in deformed nuclei, and that these properties are intrinsic to the way that collectivity and deformation develop through the phase transitional region in the model, arising from the specific d-boson coherence in the wave functions, and that they do not necessarily require the explicit mixing of normal and intruder configurations from different IBA spaces.

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arXiv2004

Generalization of the $N_pN_n$ Scheme and the Structure of the Valence Space

The $N_pN_n$ scheme, which has been extensively applied to even-even nuclei, is found to be a very good benchmark for odd-even, even-odd, and doubly-odd nuclei as well. There are no apparent shifts in the correlations for these four classes of nuclei. The compact correlations highlight the deviant behavior of the Z=78 nuclei, are used to deduce effective valence proton numbers near Z=64, and to study the evolution of the Z=64 subshell gap.

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arXiv2004

A test of X(5) for the gamma degree of freedom

We present the first extensive test of the critical point symmetry X(5) for the gamma degree of freedom, based in part on recent measurements for the gamma-band in 152 Sm. The agreement is good for some observables including the energies and most intra- and interband transitions, but there is also a serious discrepancy for one transition.

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arXiv2001

Singular Character of Critical Points in Nuclei

The concept of critical points in nuclear phase transitional regions is discussed from the standpoints of Q-invariants, simple observables and wave function entropy. It is shown that these critical points very closely coincide with the turning points of the discussed quantities, establishing the singular character of these points in nuclear phase transition regions between vibrational and rotational nuclei, with a finite number of particles.

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arXiv2000

Robust Nuclear Observables and Constraints on Random Interactions

The predictions of the IBM two-body random ensemble are compared to empirical results on nuclei from Z=8 to 100. Heretofore unrecognized but robust empirical trends are identified and related both to the distribution of valence nucleon numbers and to the need for and applicability of specific, non-random interactions. Applications to expected trends in exotic nuclei are discussed.

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arXiv2000

Quadrupole shape invariants in the interacting boson model

In terms of the Interacting Boson Model, shape invariants for the ground state, formed by quadrupole moments up to sixth order, are studied in the dynamical symmetry limits and, for the first time, over the whole structural range of the IBM-1. The results are related to the effective deformation parameters and their fluctuations in the geometrical model. New signatures that can distinguish vibrator and gamma-soft rotor structures, and one that is related to shape coexistence, are identified.

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arXiv1999

Phase Transitions in Finite Nuclei and the Integer Nucleon Number Problem

The study of spherical-deformed ground--state phase transitions in finite nuclei as a function of N and Z is hindered by the discrete values of the nucleon number. A resolution of the integer nucleon number problem, and evidence relating to phase transitions in finite nuclei, are discussed from the experimental point of view and interpreted within the framework of the interacting boson model.

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arXiv1998

Odd-spin yrast states as multiple quadrupole-phonon excitations

The wavefunctions of the lowest odd spin positive parity yrast states in the IBA are shown to be nearly pure multiple quadrupole-phonon excitations even outside the three dynamical symmetries. The empirical data for collective nuclei with 30 < Z < 80 confirm these predictions. The quadrupole-phonon purity of the 2^+_1 state can be measured from E2-branching ratios of the 3^+_1 state. These data show a high correlation to the 2^+_1 Q-phonon purity deduced from the E2-decay of 2^+ states.

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