Michel Vallieres

New method for studying the microscopic foundations of the interacting boson model

Abstract We describe (i) A mapping, using a multishell seniority basis, from a prescribed subspace of a shell model space to an associated boson space. (ii) A new dynamical procedure for selecting the collective variables within the boson space, based on the invariance of the trace. (iii) A comparison with exact calculations for a multi-level pairing model, to demonstrate that the method works.

A thermal LBGK model for large density and temperature differences

We present a new lattice-Boltzmann method for hydrodynamic simulations, which is capable of handling very large density and temperature gradients. Unlike other LBGK models, the discrete velocities we used center at the local mean flow velocity, and their values vary according to the local temperature. The adiabatic index of the gas can be easily controlled by a parameter.

Structure of alternative supersymmetry schemes in nuclei

Abstract The structural differences of two group chain decompositions for a multi- j IBA supersymmetry applicable to nuclei in an O(6) region are discussed in terms of core polarization, and compared to data for 197 Pt. It is shown that the wave functions for the lowest two representations are identical in the two chains. This is interpreted in terms of the concept of stretched configurations and leads to suggested experiments to better distinguish the two alternative supersymmetries. Analogous results for an SU(5) region are briefly outlined.

Relationship Between the Interacting Boson Model and the Bohr Collective Hamiltonian

It is demonstrated that the Interacting Boson Model I (IBM), which is described by a Hamiltonian of six coupled harmonic oscillators, (one s-boson and 5 d-bosons), where the total number of bosons, N, is constant of the motion, can be transformed into a Bohr-Mottelson model (BMM) described by a Hamiltonian with the familiar five dimensional quadrupole oscillator degrees of freedom. The correspondence is one-to-one for a BMM acting in a sub-space of the full five-dimensional harmonic oscillator space. The proof depends on a well-known non-linear realization of the generators of SU(6) (which are the basic building blocks of the IBM) in terms of the five BMM bosons and the number N. The orthonormal basis vectors of the BMM are obtained. The relationship between the limiting symmetries of the IBM and the geometrically simple limits of the BMM is described with the aid of the concept of potential energy surface. The form of the BMM Hamiltonian is given for the adiabatic limit. Finally we show that previous work on this problem involving coherent states and the generator coordinate method is incomplete.

Selfconsistent semiclassical calculations using the partial h̵ resummation method

Abstract Selfconsistent semiclassical calculations using the partial resummation technique have been performed for a number of spherical nuclei. The results are found in very good agreement with those obtained in the more lengthy selfconsistently Strutinsky averaged Hartree-Fock approach. Our method has also been applied to the determination of liquid drop parameters associated with effective forces of the Skyrme type.

The multi-j nuclear dynamical supersymmetry U(620)☆

Abstract A U ( 6 20 ) supersymmetry model is proposed to describe nuclei with protons in the j = 1 2 , 3 2 , 5 2 and 7 2 levels in the Pt mass region. The spectra of 196Pt and 197Au are fitted and compared with spectra obtained for the same nuclei in a previously proposed U ( 6 4 ) supersymmetry scheme. Calculations for both models are carried out in the SO(6) limit.

Capture by stabilized continuum: Classical and quantum aspects

We review here the results of our investigations concerning chaotic atomic scattering in the presence of a laser field. Particular emphasis is put on the existence of classical stable resonance structures, induced by the intense laser field, which are embedded in the field-free continuum. We show that phase space structures in the vicinity of a resonance island play an important role in the chaotic scattering behavior and form the basis for a mechanism to enhance the lifetimes of the collisional partners. Quantum calculations, based on a wave packet propagation method, show that quantum solutions are strongly influenced by the classical phase space structures. More specifically, a wave packet is found to spread differently in the regular and chaotic regions; in the latter case it spreads exponentially with time until saturation occurs, defining the saturation time. We also investigate theħ dependence of the spreading rates in both the regular and chaotic regimes. Calculations with an ensemble of classical trajectories are also presented to further illustrate the smoothing effects of varyingħ.

Dynamical supersymmetry and collective nuclear structure physics

Abstract The symmetry principles of the Interacting Boson Model (even-even nucleus) and the Interacting Bose-Fermi Model (even-odd nucleus) are reviewed. Dynamical supersymmetry is introduced as the unifying symmetry for the above two nuclear systems. Experimental tests of dynamical supersymmetry are discussed in detail.

Symmetry and application of SU(mn)⊃SU(m)×SU(n) coefficients of fractional parentage

Abstract A method is given for calculating the SU( mn )⊃SU( m )×SU( n ) many-particle coefficients of fractional parentage (CFP) in terms of the single-particle CFP without using the SU( m ) and SU( n ) Racah coefficients. Some remarkable symmetries of the SU( mn ) ⊃ SU( m ) × SU( n ) CFP are obtained on the grounds that they are at the same time the isoscalar factor for the permutation group chain S( f 1 + f 2 )⊃S( f 1 )⊗S( f 2 ). The application of the SU( mn )⊃SU( m )×SU( n ) CFP to the quark model of nuclei is illustrated. It is shown that the transformation coefficients between the symmetry basis and the physical basis of two nuclear clusters are simply products of two SU( mn )⊃ SU( m )×SU( n ) CFP.

Shell model structure of mid-heavy even–even Sn isotopes

We reconstruct the single-shell states and the corresponding matrix elements needed for describing mid-heavy Sn isotopes within the sdgh major shell in the framework of the nuclear shell model. This reconstruction allows us to calculate the coefficient of fractional parentage (CFP) for mid-heavy Sn isotopes by reducing the calculation requirements. Then, we have carried out the shell model calculations in the sdgh major shell for the even?even 110,112,114,116Sn isotopes by using CD-Bonn and Nijmegen1 two-body effective nucleon?nucleon (NN) interactions. The results are compared to the most recent experimental data and found to be in good agreement with experiments.