Connecting the X(5)-β2\beta^2, X(5)-β4\beta^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)-$\beta^2$, X(5)-$\beta^4$, 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)-$\beta^2$, and X(5)-$\beta^4$ behavior

Systematics of 2+ states in semi-magic nuclei

We propose a simple systematics of low lying 2+ energy levels and electromagnetic transitions in semi-magic isotopic chains Z=28,50,82 and isotonic chains N=28,50,82,126. To this purpose we use a two-level pairing plus quadrupole Hamiltonian, within the spherical Quasiparticle Random Phase Approximation (QRPA). We derive a simple relation connecting the 2+ energy with the pairing gap and quadrupole-quadupole (QQ) interaction strength. It turns out that the systematics of energy levels and B(E2) values predicted by this simple model is fulfilled with a reasonable accuracy by all available experimental data. Both systematics suggest that not only active nucleons but also those filling closed shells play an important role

Transition from the Seniority to the Anharmonic Vibrator Regime in Nuclei

A recent analysis of experimental energy systematics suggests that all collective nuclei fall into one of three classes -- seniority, anharmonic vibrational, or rotational -- with sharp phase transitions between them. We investigate the transition from the seniority to the anharmonic vibrator regime within a shell model framework involving a single large j-orbit. The calculations qualitatively reproduce the observed transitional behavior, both for U(5) like and O(6) like nuclei. They also confirm the preeminent role played by the neutron-proton interaction in producing the phase transition.Comment: 9 pages with 2 tables, submitted to Physical Review C, November 199

Band structure from random interactions

The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the interacting boson model using an ensemble of random one- and two-body interactions. We find a predominance of L(P)=0(+) ground states, as well as strong evidence for the occurrence of both vibrational and rotational band structures. This remarkable result suggests that such band structures represent a far more general (robust) property of the collective model space than is generally thought.Comment: 5 pages, 4 figures, Phys. Rev. Lett., in pres

Smarandache type functions obtained by duality

we extend the Smarandache function from the set N* of positive integers to the set Q of rational

Possible experimental signature of octupole correlations in the 02+^+_2 states of the actinides

$J^{\pi}$= 0$^+$ states have been investigated in the actinide nucleus ${}^{240}$Pu up to an excitation energy of 3 MeV with a high-resolution (p,t) experiment at $E_{p}$= 24 MeV. To test the recently proposed $J^{\pi}$= 0$^+_2$ double-octupole structure, the phenomenological approach of the spdf-interacting boson model has been chosen. In addition, the total 0$^+$ strength distribution and the $0^+$ strength fragmentation have been compared to the model predictions as well as to the previously studied (p,t) reactions in the actinides. The results suggest that the structure of the 0$^+_2$ states in the actinides might be more complex than the usually discussed pairing isomers. Instead, the octupole degree of freedom might contribute significantly. The signature of two close-lying 0$^+$ states below the 2-quasiparticle energy is presented as a possible manifestation of strong octupole correlations in the structure of the 0$^+_2$ states in the actinides.Comment: 6 pages, 5 figures, published in Phys. Rev. C 88, 041303(R) (2013

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.Comment: 8 pages Latex + 8 figs (postscript). In Phys Rev Lett, June 199