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Register a new userInteracting Boson Model plus broken-pairs description of high-spin dipole bands
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The Interacting Boson Model with broken-pairs has been extended to include mixed proton-neutron configurations in the fermion model space. The extended version of the model has been used to describe high-spin bands in the transitional nucleus $^{136}$Nd. Model calculations reproduce ten bands of positive and negative parity states, including the two dipole high-spin structures based on the $(pi h_{11/2})^2$ $( u h_{11/2})^2$ configuration.
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Recent interest in spectroscopic factors for single-neutron transfer in low-spin states of the even-odd Xenon $^{125,127,129.131}$Xe and even-odd Tellurium, $^{123,125,127,129,131}$Te isotopes stimulated us to study these isotopes within the frame work of the Interacting Boson-Fermion Model. The fermion that is coupled to the system of bosons is taken to be in the positive parity $3s_{1/2}$, $2d_{3/2}$, $2d_{5/2}$, $1g_{7/2}$ and in the negative $1h_{11/2}$ single-particle orbits, the complete 50-82 major shell. The calculated energies of low-spin energy levels of the odd isotopes are found to agree well with the experimental data. Also B(E2), B(M1) values and spectroscopic factors for single-neutron transfer are calculated and compared with experimental data.
The interpretation of the recently reported low-lying excited bands in $gamma$-soft odd-mass nuclei as wobbling bands is examined in terms of the interacting boson-fermion model that is based on the universal nuclear energy density functional. The predicted mixing ratios of the $Delta{I}=1$ electric quadrupole ($E2$) to magnetic dipole ($M1$) transition rates between yrast bands and those yrare bands previously interpreted as wobbling bands in $^{135}$Pr, $^{133}$La, $^{127}$Xe, and $^{105}$Pd nuclei are consistently smaller in magnitude than the experimental values on which the wobbling interpretation is based. These calculated mixing ratios indicate the predominant $M1$ character of the transitions from the yrare bands under consideration to the yrast bands, being in agreement with the new experimental data, which involve both the angular distribution and linear polarization measurements. The earlier wobbling assignments are severely questioned.
The selfconsistent cranking approach is extended to the case of rotation about an axis which is tilted with respect to the principal axes of the deformed potential (Tilted Axis Cranking). Expressions for the energies and the intra bands electromagnetic transition probabilities are given. The mean field solutions are interpreted in terms of quantal rotational states. The construction of the quasiparticle configurations and the elimination of spurious states is discussed. The application of the theory to high spin data is demonstrated by analyzing the multi quasiparticle bands in the nuclide-s with $N=102,103$ and $Z=71,72,73$.
Rotational $SU(3)$ algebraic symmetry continues to generate new results in the shell model (SM). Interestingly, it is possible to have multiple $SU(3)$ algebras for nucleons occupying an oscillator shell $eta$. Several different aspects of the multiple $SU(3)$ algebras are investigated using shell model and also deformed shell model based on Hartree-Fock single particle states with nucleons in $sdg$ orbits giving four $SU(3)$ algebras. Results show that one of the $SU(3)$ algebra generates prolate shapes, one oblate shape and the other two also generate prolate shape but one of them gives quiet small quadrupole moments for low-lying levels. These are inferred by using the standard form for the electric quadrupole transition operator and using quadrupole moments and $B(E2)$ values in the ground $K=0^+$ band in three different examples. Multiple $SU(3)$ algebras extend to interacting boson model and using $sdg$IBM, the structure of the four $SU(3)$ algebras in this model are studied by coherent state analysis and asymptotic formulas for $E2$ matrix elements. The results from $sdg$IBM further support the conclusions from the $sdg$ shell model examples.
The connections between the X(5)-models (the original X(5) using an infinite square well, X(5)-$beta^8$, X(5)-$beta^6$, X(5)-$beta^4$, and X(5)-$beta^2$), based on particular solutions of the geometrical Bohr Hamiltonian with harmonic potential in the $gamma$ degree of freedom, and the interacting boson model (IBM) are explored. This work is the natural extension of the work presented in [1] for the E(5)-models. For that purpose, a quite general one- and two-body IBM Hamiltonian is used and a numerical fit to the different X(5)-models energies is performed, later on the obtained wave functions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce well the results for energies and B(E2) transition rates obtained with all these X(5)-models, although the agreement is not so impressive as for the E(5)-models. From the fitted IBM parameters the corresponding energy surface can be extracted and it is obtained that, surprisingly, only the X(5) case corresponds in the moderate large N limit to an energy surface very close to the one expected for a critical point, while the rest of models seat a little farther.
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