arXiv subjects

E. A. McCutchan

Publications and source records attributed to E. A. McCutchan.

29 records · Page 2Linked to original sources

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

Complementary descriptions of shape/phase transitions in atomic nuclei

Shape/phase transitions in atomic nuclei have first been discovered in the framework of the Interacting Boson Approximation (IBA) model. Critical point symmetries appropriate for nuclei at the transition points have been introduced as special solutions of the Bohr Hamiltonian, stirring the introduction of additional new solutions describing wide ranges of nuclei. The complementarity of the IBA and geometrical approaches will be demonstrated by three examples. First, it will be shown that specific special solutions of the Bohr Hamiltonian correspond to the borders of the critical region of the IBA. Second, it will be demonstrated that the distinct patterns exhibited in different transitional regions by the experimental energy staggering in gamma-bands can be reproduced both by the IBA and by special solutions of the Bohr Hamiltonian. Third, a first attempt to obtain a IBA SU(3) level scheme from a special solution of the Bohr Hamiltonian will be presented.

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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

Exactly separable version of X(5) and related models

One-parameter exactly separable versions of the X(5) and X(5)-beta^2 models, labelled as ES-X(5) and ES-X(5)-beta^2 respectively, are derived by using in the Bohr Hamiltonian potentials of the form u(beta)+u(gamma)/beta^2. Unlike X(5), in these models the beta_1 and gamma_1 bands are treated on equal footing. Spacings within the gamma_1 band are well reproduced by both models, while spacings within the beta_1 band are well reproduced only by ES-X(5)-beta^2, for which several nuclei with R_{4/2}=E(4_1^+)/E(2_1^+) ratios and [normalized to E(2_1^+)] beta_1 and gamma_1 bandheads corresponding to the model predictions have been found.

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arXiv2006

Connecting the X(5)-$β^2$, X(5)-$β^4$, and X(3) models to the shape/phase transition region of the interacting boson model

The parameter independent (up to overall scale factors) predictions of the X(5)-$β^2$, X(5)-$β^4$, and X(3) models, which are variants of the X(5) critical point symmetry developed within the framework of the geometric collective model, are compared to two-parameter calculations in the framework of the interacting boson approximation (IBA) model. The results show that these geometric models coincide with IBA parameters consistent with the phase/shape transition region of the IBA for boson numbers of physical interest (close to 10). Nuclei within the rare-earth region and select Os and Pt isotopes are identified as good examples of X(3), X(5)-$β^2$, and X(5)-$β^4$ behavior.

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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

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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