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Register a new userRelationship between X(5)-models and the interacting boson model
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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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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.
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.
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.
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.
Background: The lead region, Po, Pb, Hg, and Pt, shows up the presence of coexisting structures having different deformation and corresponding to different particle-hole configurations in the Shell Model language. Purpose: We intend to study the importance of configuration mixing in the understanding of the nuclear structure of even-even Po isotopes, where the shape coexistence phenomena are not clear enough. Method: We study in detail a long chain of polonium isotopes, 190-208Po, using the interacting boson model with configuration mixing (IBM-CM). We fix the parameters of the Hamiltonians through a least-squares fit to the known energies and absolute B(E2) transition rates of states up to 3 MeV. Results: We obtained the IBM-CM Hamiltonians and we calculate excitation energies, B(E2)s, electric quadrupole moments, nuclear radii and isotopic shifts, quadrupole shape invariants, wave functions, and deformations. Conclusions: We obtain a good agreement with the experimental data for all the studied observables and we conclude that shape coexistence phenomenon is hidden in Po isotopes, very much as in the case of the Pt isotopes.
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