arXiv subjects

L. M. Robledo

Publications and source records attributed to L. M. Robledo.

At least 91 records · Page 5Linked to original sources

arXiv2014

Shape evolution and shape coexistence in Pt isotopes: comparing interacting boson model configuration mixing and Gogny mean-field energy surfaces

The evolution of the total energy surface and the nuclear shape in the isotopic chain $^{172-194}$Pt are studied in the framework of the interacting boson model, including configuration mixing. The results are compared with a self-consistent Hartree-Fock-Bogoliubov calculation using the Gogny-D1S interaction and a good agreement between both approaches shows up. The evolution of the deformation parameters points towards the presence of two different coexisting configurations in the region 176 $\leq$ A $\leq$ 186.

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arXiv2014

Combinatorial level densities by the real-time method

Levels densities of independent-particle Hamiltonians can be calculated easily by using the real-time representation of the evolution operator together with the fast Fourier transform. We describe the method and implement it with a set of Python programs. Examples are provided for the total and partial levels densities of a heavy deformed nucleus (Dy-164). The partial level densities that may be calculated are the projected ones on neutron number, proton number, azimuthal angular momentum, and parity.

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arXiv2014

Accurate nuclear masses from a three parameter Kohn-Sham DFT approach (BCPM)

Given the promising features of the recently proposed Barcelona-Catania-Paris (BCP) functional \cite{Baldo.08}, it is the purpose of this paper to still improve on it. It is, for instance, shown that the number of open parameters can be reduced from 4-5 to 2-3, i.e. by practically a factor of two. One parameter is tightly fixed by a fine-tuning of the bulk, a second by the surface energy. The third is the strength of the spin-orbit potential on which the final result does not depend within the scatter of the values used in Skyrme and Gogny like functionals. An energy rms value of 1.58 MeV is obtained from a fit of these three parameters to the 579 measured masses reported in the Audi and Waspra 2003 compilation. This rms value compares favorably with the one obtained using other successful mean field theories. Charge radii are also well reproduced when compared with experiment. The energies of some excited states, mostly the isoscalar giant monopole resonances, are studied within this model as well.

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arXiv2013

Spin constraints on nuclear energy density functionals

The Gallagher-Moszkowski rule in the spectroscopy of odd-odd nuclei imposes a new spin constraint on the energy functionals for self-consistent mean field theory. The commonly used parameterization of the effective three-body interaction in the Gogny and Skyrme families of energy functionals is ill-suited to satisfy the spin constraint. In particular, the Gogny parameterization of the three-body interaction has the opposite spin dependence to that required by the observed spectra. The two-body part has a correct sign, but in combination the rule is violated as often as not. We conclude that a new functional form is needed for the effective three-body interaction that can take into better account the different spin-isospin channels of the interaction.

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arXiv2013

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.

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arXiv2012

Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction

As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov (HFB) theory, we have developed a new calculational tool to find the HFB minima of odd-A nuclei based on the gradient method and using interactions of Gogny's form. The HFB minimization includes both time-even and time-odd fields in the energy functional, avoiding the commonly used "filling approximation". Here we apply the method to calculate neutron pairing gaps in some representative isotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82 spherical chains and the Z=62 and 92 deformed chains. We find that the gradient method is quite robust, permitting us to carry out systematic surveys involving many nuclei. We find that the time-odd field does not have large effect on the pairing gaps calculated with the Gogny D1S interaction. Typically, adding the T-odd field as a perturbation increases the pairing gap by ~100 keV, but the re-minimization brings the gap back down. This outcome is very similar to results reported for the Skyrme family of nuclear energy density functionals. Comparing the calculated gaps with the experimental ones, we find that the theoretical errors have both signs implying that the D1S interaction has a reasonable overall strength. However, we find some systematic deficiencies comparing spherical and deformed chains and comparing the lighter chains with the heavier ones. The gaps for heavy spherical nuclei are too high, while those for deformed nuclei tend to be too low. The calculated gaps of spherical nuclei show hardly any A-dependence, contrary to the data. Inclusion of the T-odd component of the interaction does not change these qualitative findings.

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arXiv2012

Microscopic description of quadrupole-octupole coupling in Sm and Gd isotopes with the Gogny Energy Density Functional

The interplay between the collective dynamics of the quadrupole and octupole deformation degree of freedom is discussed in a series of Sm and Gd isotopes both at the mean field level and beyond, including parity symmetry restoration and configuration mixing. Physical properties like negative parity excitation energies, E1 and E3 transition probabilities are discussed and compared to experimental data. Other relevant intrinsic quantities like dipole moments, ground state quadrupole moments or correlation energies associated to symmetry restoration and configuration mixing are discussed. For the considered isotopes, the quadrupole-octupole coupling is found to be weak and most of the properties of negative parity states can be described in terms of the octupole degree of freedom alone.

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arXiv2012

Octupole deformation properties of actinide isotopes within a mean field approach

We discuss the octupole deformation properties of many even-even actinide isotopes. The analysis is carried out in the mean field framework (Hartree-Fock-Bogoliubov approximation) by using the axially symmetric octupole moment as a constraint. A one-dimensional octupole collective Hamiltonian is used to obtain properties like excitation energies or $E1$ and $E3$ transition probabilities of the negative parity band-heads associated to the lowest lying $1^{-}$ and $3^{-}$ states. The evolution of these values with neutron number is discussed and a comparison with available experimental data is made. In order to minimize the uncertainties associated to the energy density functional used, the calculations have been carried out for an assorted set ranging from the BCP1 functional to the finite range Gogny interaction with the D1S, D1N and D1M parametrization.

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arXiv2012

Shape coexistence in Lead isotopes in the interacting boson model with Gogny energy density functional

We investigate the emergence and evolution of shape coexistence in the neutron-deficient Lead isotopes within the interacting boson model (IBM) plus configuration mixing with microscopic input based on the Gogny energy density functional (EDF). The microscopic potential energy surface obtained from the constrained self-consistent Hartree-Fock-Bogoliubov method employing the Gogny-D1M EDF is mapped onto the coherent-state expectation value of the configuration-mixing IBM Hamiltonian. In this way, the parameters of the IBM Hamiltonian are fixed for each of the three relevant configurations (spherical, prolate and oblate) associated to the mean field minima. Subsequent diagonalization of the Hamiltonian provides the excitation energy of the low-lying states and transition strengths among them. The model predictions for the $0^{+}$ level energies and evolving shape coexistence in the considered Lead chain are consistent both with experiment and with the indications of the Gogny-EDF energy surfaces.

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arXiv2012

Electromagnetic transition strengths in soft deformed nuclei

Spectroscopic observables such as electromagnetic transitions strengths can be related to the properties of the intrinsic mean-field wave function when the latter are strongly deformed, but the standard rotational formulas break down when the deformation decreases. Nevertheless there is a well-defined, non-zero, spherical limit that can be evaluated in terms of overlaps of mean-field intrinsic deformed wave functions. We examine the transition between the spherical limit and strongly deformed one for a range of nuclei comparing the two limiting formulas with exact projection results. We find a simple criterion for the validity of the rotational formula depending on $<Δ\vec{J}^2>$, the mean square fluctuation in the angular momentum of the intrinsic state. We also propose an interpolation formula which describes the transition strengths over the entire range of deformations, reducing to the two simple expressions in the appropriate limits.

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arXiv2012

Pairing in finite systems: beyond the HFB theory

The Hartree-Fock-Bogoliubov approximation is very useful for treating both long- and short-range correlations in finite quantum fermion systems, but it must be extended in order to describe detailed spectroscopic properties. One problem is the symmetry-breaking character of the HFB approximation. We present a general and systematic way to restore symmetries and to extend the configuration space using pfaffian formulas for the many-body matrix elements. The advantage of those formulas is that the sign of the matrix elements is unambiguously determined. It is also helpful to extend the space of configurations by constraining the HFB solutions in some way. A powerful method for finding these constrained solutions is the gradient method, based on the generalized Thouless transformation. The gradient method also preserves the number parity of the Bogoliubov transformation, which facilitates the application of the theory to systems with odd particle number.

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arXiv2011

Symmetry restoration in Hartree-Fock-Bogoliubov based theories

We present a pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shell.

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arXiv2011

Collective structural evolution in neutron-rich Yb, Hf, W, Os and Pt isotopes

An interacting boson model Hamiltonian determined from Hartree-Fock-Bogoliubov calculations with the new microscopic Gogny energy density functional D1M, is applied to the spectroscopic analysis of neutron-rich Yb, Hf, W, Os and Pt isotopes with mass $A\sim 180-200$. Excitation energies and transition rates for the relevant low-lying quadrupole collective states are calculated by this method. Transitions from prolate to oblate ground-state shapes are analyzed as a function of neutron number $N$ in a given isotopic chain by calculating excitation energies, $B$(E2) ratios, and correlation energies in the ground state. It is shown that such transitions tend to occur more rapidly for the isotopes with lower proton number $Z$, when departing from the proton shell closure Z=82. The triaxial degrees of freedom turn out to play an important role in describing the considered mass region. Predicted low-lying spectra for the neutron-rich exotic Hf and Yb isotopes are presented. The approximations used in the model and the possibilities to refine its predictive power are addressed.

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arXiv2011

Exactly solvable pairing Hamiltonian for heavy nuclei

We present a new exactly solvable Hamiltonian with a separable pairing interaction and non-degenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one related to an interaction cutoff and the other to the pairing strength. These two parameters can be adjusted to give an excellent reproduction of Gogny self-consistent mean-field calculations in the canonical basis.

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arXiv2011

Global systematics of octupole excitations in even-even nuclei

We present a computational methodology for a theory of the lowest octupole excitations applicable to all even-even nuclei beyond the lightest. The theory is the well-known generator-coordinate extension (GCM) of the Hartree-Fock-Bogoliubov self-consistent mean field theory (HFB). We use the discrete-basis Hill-Wheel method (HW) to compute the wave functions with an interaction from the Gogny family of Hamiltonians. Comparing to the compiled experimental data on octupole excitations, we find that the performance of the theory depends on the deformation characteristics of the nucleus. For nondeformed nuclei, the theory reproduces the energies to about 20 % apart from an overall scale factor of about 1.6. The performance is somewhat poorer for (quadrupole) deformed nuclei, and for both together the dispersion of the scaled energies about the experimental values is about 25 %. This compares favorably with the performance of similar theories of the quadrupole excitations. Nuclei having static octupole deformations in HFB form a special category. These nuclei have the smallest measured octupole excitation energies as well as the smallest predicted energies. However, in these cases the energies are seriously underpredicted by the theory. We find that a simple two-configuration approximation, the Minimization After Projection method, (MAP) is almost as accurate as the full HW treatment, provided that the octupole-deformed nuclei are omitted from the comparison. This article is accompanied by a tabulation of the predicted octupole excitations for 818 nuclei extending from dripline to dripline, computed with several variants of the Gogny interaction.

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arXiv2011

Microscopic description of cluster radioactivity in actinide nuclei

Cluster radioactivity is the emission of a fragment heavier than $α$ particle and lighter than mass 50. The range of clusters observed in experiments goes from $^{14}$C to $^{32}$Si while the heavy mass residue is always a nucleus in the neighborhood of the doubly-magic $^{208}$Pb nucleus. Cluster radioactivity is described in this paper as a very asymmetric nuclear fission. A new fission valley leading to a decay with large fragment mass asymmetry matching the cluster radioactivity products is found. The mass octupole moment is found to be more convenient than the standard quadrupole moment as the parameter driving the system to fission. The mean-field HFB theory with the phenomenological Gogny interaction has been used to compute the cluster emission properties of a wide range of even-even actinide nuclei from $^{222}$Ra to $^{242}$Cm, where emission of the clusters has been experimentally observed. Computed half-lives for cluster emission are compared with experimental results. The noticeable agreement obtained between the predicted properties of cluster emission (namely, clusters masses and emission half-lives) and the measured data confirms the validity of the proposed methodology in the analysis of the phenomenon of cluster radioactivity. A continuous fission path through the scission point has been described using the neck parameter constraint.

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arXiv2011

Application of the gradient method to Hartree-Fock-Bogoliubov theory

A computer code is presented for solving the equations of Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the need for efficient and robust codes to calculate the configurations required by extensions of HFB such as the generator coordinate method. The code is organized with a separation between the parts that are specific to the details of the Hamiltonian and the parts that are generic to the gradient method. This permits total flexibility in choosing the symmetries to be imposed on the HFB solutions. The code solves for both even and odd particle number ground states, the choice determined by the input data stream. Application is made to the nuclei in the $sd$-shell using the USDB shell-model Hamiltonian.

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arXiv2011

Spectroscopic calculations of the low-lying structure in exotic Os and W isotopes

Structural evolution in neutron-rich Os and W isotopes is investigated in terms of the Interacting Boson Model (IBM) Hamiltonian determined by (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the Gogny-D1S Energy Density Functional (EDF). The interaction strengths of the IBM Hamiltonian are produced by mapping the potential energy surface (PES) of the Gogny-EDF with quadrupole degrees of freedom onto the corresponding PES of the IBM system. We examine the prolate-to-oblate shape/phase transition which is predicted to take place in this region as a function of neutron number $N$ within the considered Os and W isotopic chains. The onset of this transition is found to be more rapid compared to the neighboring Pt isotopes. The calculations also allow prediction of spectroscopic variables (excited state energies and reduced transition probabilities) which are presented for the neutron-rich $^{192,194,196}$W nuclei, for which there is only very limited experimental data available to date.

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