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Register a new userTransition probabilities in the U(6) limit of the Symplectic Interacting Vector Boson Model
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The tensor properties of the algebra generators and the basis are determined in respect to the reduction chain $Sp(12,R) supset U(6)% supset U(3)otimes U(2)supset O(3)otimes (U(1)otimes U(1))$, which defines one of the dynamical symmetries of the Interacting Vector Boson Model. The action of the Sp(12,R) generators as transition operators between the basis states is presented. Analytical expressions for their matrix elements in the symmetry-adapted basis are obtained. As an example the matrix elements of the E2 transition operator between collective states of the ground band are determined and compared with the experimental data for the corresponding intraband transition probabilities of nuclei in the actinide and rare earth region. On the basis of this application the important role of the symplectic extension of the model is analyzed.
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The case of U(5)--$hat{Q}(chi)cdothat{Q}(chi)$ mixing in the configuration-mixed Interacting Boson Model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively.
Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that for sufficiently strong attractive interactions this system develops a first-order phase transition via formation of Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. The thermodynamical characteristics of the system are calculated for the liquid-gas and condensed phases. The energy density exhibits a jump at the critical temperature.
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.
It has been a puzzle whether quarks may exist in the interior of massive neutron stars, since the hadron-quark phase transition softens the equation of state (EOS) and reduce the neutron star (NS) maximum mass very significantly. In this work, we consider the light U-boson that increases the NS maximum mass appreciably through its weak coupling to fermions. The inclusion of the U-boson may thus allow the existence of the quark degrees of freedom in the interior of large mass neutron stars. Unlike the consequence of the U-boson in hadronic matter, the stiffening role of the U-boson in the hybrid EOS is not sensitive to the choice of the hadron phase models. In addition, we have also investigated the effect of the effective QCD correction on the hybrid EOS. This correction may reduce the coupling strength of the U-boson that is needed to satisfy NS maximum mass constraint. While the inclusion of the U-boson also increases the NS radius significantly, we find that appropriate in-medium effects of the U-boson may reduce the NS radii significantly, satisfying both the NS radius and mass constraints well.
We propose a method to incorporate the coupling between shape and pairing collective degrees of freedom in the framework of the interacting boson model (IBM), based on the nuclear density functional theory. To account for pairing vibrations, a boson-number non-conserving IBM Hamiltonian is introduced. The Hamiltonian is constructed by using solutions of self-consistent mean-field calculations based on a universal energy density functional and pairing force, with constraints on the axially-symmetric quadrupole and pairing intrinsic deformations. By mapping the resulting quadrupole-pairing potential energy surface onto the expectation value of the bosonic Hamiltonian in the boson condensate state, the strength parameters of the boson Hamiltonian are determined. An illustrative calculation is performed for $^{122}$Xe, and the method is further explored in a more systematic study of rare-earth $N=92$ isotones. The inclusion of the dynamical pairing degree of freedom significantly lowers the energies of bands based on excited $0^+$ states. The results are in quantitative agreement with spectroscopic data, and are consistent with those obtained using the collective Hamiltonian approach.
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