arXiv subjects

H. Flocard

Publications and source records attributed to H. Flocard.

12 recordsLinked to original sources

arXiv2007

Large-amplitude Qn-Qp collectivity in the neutron-rich oxygen isotope 20O

By means of HFB calculations with independent constraints on axial neutron and proton quadrupole moments Q_n and Q_p, we investigate the large amplitude isoscalar and isovector deformation properties of the neutron-rich isotope 20O. Using the particle-number and angular-momentum projected Generator Coordinate Method, we analyze the collective dynamics in the {Q_n, Q_p} plane. The parameterization SLy4 of the Skyrme interaction is used for all calculations in connection with a density-dependent zero-range pairing interaction. Our results show that already for this moderately neutron-rich nucleus the transition moments are modified when independent neutron and proton collective dynamics are allowed.

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arXiv2003

Beyond-mean-field-model analysis of low-spin normal-deformed and superdeformed collective states of S32, Ar36, Ar38 and Ca40

We investigate the coexistence of spherical, deformed and superdeformed states at low spin in S32, Ar36, Ar38 and Ca40. The microscopic states are constructed by configuration mixing of BCS states projected on good particle number and angular momentum. The BCS states are themselves obtained from Hartree-Fock BCS calculations using the Skyrme interaction SLy6 for the particle-hole channel, and a density-dependent contact force in the pairing channel. The same interaction is used within the Generator Coordinate Method to determine the configuration mixing and calculate the properties of even-spin states with positive parity. Our calculations underestimate moments of inertia. Nevertheless, for the four nuclei, the global structural properties of the states of normal deformation as well as the recently discovered superdeformed bands up to spin 6 are correctly reproduced with regard to both the energies and the transition rates.

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arXiv2001

GCM Analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of Pb208. In this study, we rely on a coherent approach based on the Generator Coordinate Method including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF+BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations.

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arXiv1998

Temperature Dependence of Even-Odd Effects in Small Superconducting Systems

Generalized BCS equations which consistently include the projection on the particle-number parity are derived from a systematic variational method. Numerical solutions are given that are illustrative of ultra-small metallic grains. Compared to the BCS approximation, the pairing is slightly enhanced in even and noticeably inhibited in odd systems. In the latter case, the gap increases with T near T=0; for a suitably small pairing this can result in a reentrance phenomenon. Paramagnetic effects are evaluated as functions of the temperature and the magnetic field.

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arXiv1997

Extended BCS Theories

Extensions of the Hartree-Fock-Bogoliubov theory are worked out which are tailored for, (i) the consistent evaluation of fluctuations and correlations and (ii) the restoration through projection of broken symmetries. For both purposes we rely on a single variational principle which optimizes the characteristic function. The Bloch equation is used as a constraint to define the equilibrium state, and the trial quantities are a density operator and a Lagrangian multiplier matrix which is akin to an observable. The conditions of stationarity are respectively a Schrödinger-like equation and a Heisenberg-- like equation with an imaginary time running backwards. General conditions for the trial spaces are stated that warrant the preservation of thermodynamic relations. When the trial spaces are chosen to be of the independent-quasi-particle type, the ensuing coupled equations provide an extension of the Hartree-Fock-Bogoliubov approximation, which optimizes the characteristic function. Variational expressions for thermodynamic quantities or characteristic functions are also obtained with projected trial states, whether an invariance symmetry is broken or not. In particular, the projection on even or odd particle number is worked out for a pairing Hamiltonian, which leads to new equations replacing the BCS ones. Qualitative differences between even and odd systems, depending on the temperature $T$, the level density and the strength of the pairing force, are investigated analytically and numerically.

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arXiv1997

Particle-unstable nuclei in the Hartree-Fock theory

Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.

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arXiv1996

Deformation of Nuclei Close to the Two-Neutron Drip Line in Mg Region

We perform the Hartree-Fock-Bogoliubov (HFB) calculations for ground states of even Mg isotopes using the Skyrme force and a density-dependent zero-range pairing force. The HFB equation is solved in a three-dimensional cartesian mesh, and a convergence of deformation is carefully examined with respect to a cut-off radius for a check of the calculations. We discuss systematics of the two-neutron separation energy, deformation and root-mean-square radius. We have found that 36,38,40Mg have appreciable static deformation, where 40Mg is a two-neutron drip-line nucleus in our calculation, and the deformations of the neutron and proton are different in these three nuclei. The deformation property is analyzed on the basis of the single-particle diagram. It is shown that N=28 is not a closed shell in Mg as well as Si.

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arXiv1996

Superdeformed Bands of Odd Nuclei in A=190 Region in the Quasiparticle Picture

We study the properties of the superdeformed (SD) bands of 195Pb and 193Hg by the cranked Hartree-Fock-Bogoliubov method. Our calculations reproduce the flat behavior of the dynamical moment of inertia of two of the SD bands of 195Pb measured recently. We discuss possible configuration assignments for the observed bands 3 and 4 of 195Pb. We also calculate the two interacting SD bands of 193Hg. Our analysis confirms the superiority of a density-dependent pairing force over a seniority pairing interaction.

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arXiv1995

3D Solution of Hartree-Fock-Bogoliubov Equations for Drip-Line Nuclei

We investigate the possibility of describing triaxial quadrupole deformations for nuclei close to the two-neutron drip line by the Hartree-Fock Bogoliubov method taking into account resonances in the continuum. We use a Skyrme interaction to describe the Hartee-Fock hamiltonian and a density-dependent zero-range interaction to evaluate the pairing field. The mean-field equations are solved in a three-dimensional cubic mesh. We study the stability of the two-neutron separation energies and of the description of the nuclear surface as a function of the number of active mean-field orbitals and of the size of the mesh. The even Ni isotopes are used as a test case and the accuracy as a function of quadrupole deformation is studied by performing constrained calculations. A first application to the study of the two-neutron separation energies in Ni isotopes up to the drip line is presented.

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arXiv1995

Microscopic study of superdeformation in the A=150 mass region

The cranked Hartree-Fock-Bogoliubov method presented in previous studies of superdeformed bands in Hg and Pb isotopes is applied to the study of superdeformed bands in Gd150, Dy152, Dy151 and Tb151. The same density-dependent zero-range pairing interaction used in the A=190 mass region leads to a similarly good agreement with the experimental data. In particular, our results confirm the importance of a correct treatment of pairing correlations in Gd150 to reproduce its experimental dynamical moment of inertia. The quasi-particle spectra obtained for all the nuclei studied here are compatible with the experimental results obtained for excited bands in this mass region. The quality of our results opens the possibility of studying microscopically very subtle phenomena like the properties of identical bands.

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arXiv1993

Superdeformed rotational bands in the Mercury region; A Cranked Skyrme-Hartree-Fock-Bogoliubov study

A study of rotational properties of the ground superdeformed bands in \Hg{0}, \Hg{2}, \Hg{4}, and \Pb{4} is presented. We use the cranked Hartree-Fock-Bogoliubov method with the {\skm} parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of \Hg{2}.

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arXiv1993

Microscopic approach to collective motion

An overview of a microscopic framework based on the Hartree-Fock description of the mean field is presented which, starting from an effective interaction allows a description of collective motions. A study of the isotope shifts in the Pb region illustrates the importance of the effective interactions and points to their limitations. Such forces should be improved in order to achieve a better description of nuclei properties especially with the coming availability of exotic beam facilities. The coupling of collective quadrupole and octupole degrees of freedom in $^{194}$Pb is analyzed within the Generator Coordinate Method, which represents a step beyond the simple mean-field approximation. As a last example, we present a study of nuclear rotations. First we discuss results on superdeformed rotating bands in $^{192}$Hg, $^{194}$Hg and $^{194}$Pb obtained without including a treatment of pairing correlations. Preliminary calculations are also presented with these correlations included as well as an approximate projection on nucleon number. Email contact: paul@amoco.saclay.cea.fr

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