Dual characterization of critical fluctuations: Density functional theory & nonlinear dynamics close to a tangent bifurcation

We improve on the description of the relationship that exists between critical clusters in thermal systems and intermittency near the onset of chaos in low-dimensional systems. We make use of the statistical-mechanical language of inhomogeneous systems and of the renormalization group (RG) method in nonlinear dynamics to provide a more accurate, formal, approach to the subject. The description of this remarkable correspondence encompasses, on the one hand, the density functional formalism, where classical and quantum mechanical analogues match the procedure for one-dimensional clusters, and, on the other, the RG fixed-point map of functional compositions that captures the essential dynamical behavior. We provide details of how the above-referred theoretical approaches interrelate and discuss the implications of the correspondence between the high-dimensional (degrees of freedom) phenomenon and low-dimensional dynamics.Comment: 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

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