Microscopic description of fission in neutron-rich plutonium isotopes with the Gogny-D1M energy density functional

The most recent parametrization D1M of the Gogny energy density functional is used to describe fission in the isotopes $^{232-280}$ Pu. We resort to the methodology introduced in our previous studies [Phys. Rev. C \textbf{88}, 054325 (2013) and Phys. Rev. C \textbf {89}, 054310 (2014)] to compute the fission paths, collective masses and zero point quantum corrections within the Hartree-Fock-Bogoliubov framework. The systematics of the spontaneous fission half-lives t$_{SF}$, masses and charges of the fragments in Plutonium isotopes is analyzed and compared with available experimental data. We also pay attention to isomeric states, the deformation properties of the fragments as well as to the competition between the spontaneous fission and $\alpha$-decay modes. The impact of pairing correlations on the predicted t$_{SF}$ values is demonstrated with the help of calculations for $^{232-280}$Pu in which the pairing strengths of the Gogny-D1M energy density functional are modified by 5 $\%$ and 10 $\%$, respectively. We further validate the use of the D1M parametrization through the discussion of the half-lives in $^{242-262}$Fm. Our calculations corroborate that, though the uncertainties in the absolute values of physical observables are large, the Gogny-D1M Hartree-Fock-Bogoliubov framework still reproduces the trends with mass and/or neutron numbers and therefore represents a reasonable starting point to describe fission in heavy nuclear systems from a microscopic point of view.Comment: 14 pages, 11 figures. arXiv admin note: text overlap with arXiv:1312.722

Microscopic description of fission in Uranium isotopes with the Gogny energy density functional

The most recent parametrizations D1S, D1N and D1M of the Gogny energy density functional are used to describe fission in the isotopes $^{232-280}$ U. Fission paths, collective masses and zero point quantum corrections, obtained within the constrained Hartree-Fock-Bogoliubov approximation, are used to compute the systematics of the spontaneous fission half-lives $t_\mathrm{SF}$, the masses and charges of the fission fragments as well as their intrinsic shapes. The Gogny-D1M parametrization has been benchmarked against available experimental data on inner and second barrier heights, excitation energies of the fission isomers and half-lives in a selected set of Pu, Cm, Cf, Fm, No, Rf, Sg, Hs and Fl nuclei. It is concluded that D1M represents a reasonable starting point to describe fission in heavy and superheavy nuclei. Special attention is also paid to understand the uncertainties in the predicted $t_\mathrm{SF}$ values arising from the different building blocks entering the standard semi-classical Wentzel-Kramers-Brillouin formula. Although the uncertainties are large, the trend with mass or neutron numbers are well reproduced and therefore the theory still has predictive power. In this respect, it is also shown that modifications of a few per cent in the pairing strength can have a significant impact on the collective masses leading to uncertainties in the $t_\mathrm{SF}$ values of several orders of magnitude.Comment: 22 pages, 17 figures; Minor modifications to previous versio

Microscopic description of fission in nobelium isotopes with the Gogny-D1M energy density functional

Constrained mean-field calculations, based on the Gogny-D1M energy density functional, have been carried out to describe fission in the isotopes $^{250-260}$No. The even-even isotopes have been considered within the standard Hartree-Fock-Bogoliobov (HFB) framework while for the odd-mass ones the Equal Filling Approximation (HFB-EFA) has been employed. Ground state quantum numbers and deformations, pairing energies, one-neutron separation energies, inner and outer barrier heights as well as fission isomer excitation energies are given. Fission paths, collective masses and zero-point quantum vibrational and rotational corrections are used to compute the systematic of the spontaneous fission half-lives t$_\mathrm{SF}$ both for even-even and odd-mass nuclei. Though there exists a strong variance of the predicted fission rates with respect to the details involved in their computation, it is shown that both the specialization energy and the pairing quenching effects, taken into account within the self-consistent HFB-EFA blocking procedure, lead to larger t$_\mathrm{SF}$ values in odd-mass nuclei as compared with their even-even neighbors. Alpha decay lifetimes have also been computed using a parametrization of the Viola-Seaborg formula. The high quality of the Gogny-D1M functional regarding nuclear masses leads to a very good reproduction of $Q_{\alpha}$ values and consequently of lifetimes.Comment: 13 pages, 9 figure

A variational approach to approximate particle number projection with effective forces

Kamlah's second order method for approximate particle number projection is applied for the first time to variational calculations with effective forces. High spin states of normal and superdeformed nuclei have been calculated with the finite range density dependent Gogny force for several nuclei. Advantages and drawbacks of the Kamlah second order method as compared to the Lipkin-Nogami recipe are thoroughly discussed. We find that the Lipkin-Nogami prescription occasionally may fail to find the right energy minimum in the strong pairing regime and that Kamlah's second order approach, though providing better results than the LN one, may break down in some limiting situations.Comment: 16 pages, 8 figure

Remarks on the use of projected densities in the density dependent part of Skyrme or Gogny functionals

I discuss the inadequacy of the "projected density" prescription to be used in density dependent forces/functionals when calculations beyond mean field are pursued. The case of calculations aimed at the symmetry restoration of mean fields obtained with effective realistic forces of the Skyrme or Gogny type is considered in detail. It is shown that at least for the restoration of spatial symmetries like rotations, translations or parity the above prescription yields catastrophic results for the energy that drive the intrinsic wave function to configurations with infinite deformation, preventing thereby its use both in projection after and before variation.Comment: To be published as a contribution to J. Phys G, Special Issue, Focus Section: Open Problems in Nuclear Structur

Spectroscopy of quadrupole and octupole states in rare-earth nuclei from a Gogny force

Collective quadrupole and octupole states are described in a series of Sm and Gd isotopes within the framework of the interacting boson model (IBM), whose Hamiltonian parameters are deduced from mean field calculations with the Gogny energy density functional. The link between both frameworks is the ($\beta_2\beta_3$) potential energy surface computed within the Hartree-Fock-Bogoliubov framework in the case of the Gogny force. The diagonalization of the IBM Hamiltonian provides excitation energies and transition strengths of an assorted set of states including both positive and negative parity states. The resultant spectroscopic properties are compared with the available experimental data and also with the results of the configuration mixing calculations with the Gogny force within the generator coordinate method (GCM). The structure of excited $0^{+}$ states and its connection with double octupole phonons is also addressed. The model is shown to describe the empirical trend of the low-energy quadrupole and octupole collective structure fairly well, and turns out to be consistent with GCM results obtained with the Gogny force.Comment: 17 pages, 12 figures, 4 table

Shape evolution and the role of intruder configurations in Hg isotopes within the interacting boson model based on a Gogny energy density functional

The interacting boson model with configuration mixing, with parameters derived from the self-consistent mean-field calculation employing the microscopic Gogny energy density functional, is applied to the systematic analysis of the low-lying structure in Hg isotopes. Excitation energies, electromagnetic transition rates, deformation properties, and ground-state properties of the $^{172-204}$Hg nuclei are obtained by mapping the microscopic deformation energy surface onto the equivalent IBM Hamiltonian in the boson condensate. These results point to the overall systematic trend of the transition from the near spherical vibrational state in lower-mass Hg nuclei close to $^{172}$Hg, onset of intruder prolate configuration as well as the manifest prolate-oblate shape coexistence around the mid-shell nucleus $^{184}$Hg, weakly oblate deformed structure beyond $^{190}$Hg up to the spherical vibrational structure toward the near semi-magic nucleus $^{204}$Hg, as observed experimentally. The quality of the present method in the description of the complex shape dynamics in Hg isotopes is examined.Comment: 19 pages, 14 figures, revised version including new results and discussions, title changed, accepted for publication in Phys. Rev.