Gogny D1S Force Research Articles

Skyrme–Hartree–Fock–Bogoliubov Calculations of Even and Odd Neutron-Rich Mg Isotopes

Using the Skyrme functional with SIII, SKM*, SLy4, and UNE0 sets of parameters and the Hartree–Fock–Bogoliubov mean-field method; the ground-state properties of even-even and even-odd neutron-rich Mg isotopes have been investigated. The results of calculations of the binding energy per nucleon (B/A), the one- and two-neutron separation energies (Sn and S2n), proton and neutron rms radii, neutron pairing gap, and quadrupole deformation parameter (B2) have been compared with the available experimental data, the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny force, and predictions of some nuclear models such as the Finite Range Droplet Model (FRDM) and Relativistic Mean-Field (RMF) model. Our results show good agreements in comparison with the experimental data and the results of the mentioned models.

Woods-Saxon type of mean-field potentials with effective mass derived from the D1S Gogny force

Analytic average mean-field potentials of the Fermi-function (Woods-Saxon) type for the whole nuclear chart with space-dependent effective mass are deduced from the D1S Gogny force. Those ready-for-use potentials are advertised as an alternative to other existing phenomenological mean-field potentials.

Microscopic-macroscopic approach for ground-state energies based on the Gogny force with the Wigner-Kirkwood averaging scheme

In the previous paper I \cite{bhagwat20} we have shown that self-consistent Extended Thomas-Fermi (ETF) potentials and densities associated with a given finite-range interaction can be parametrized by generalized Fermi distributions. As a next step, a comprehensive calculation of ground-state properties of a large number of spherical and deformed even-even nuclei is carried out in the present work using the Gogny D1S force within the ETF scheme. The parametrized ETF potentials and densities of paper I are used to calculate the smooth part of the energy and the shell corrections within the Wigner-Kirkwood semiclassical averaging scheme. It is shown that the shell corrections thus obtained, along with a simple liquid drop prescription, yield a good description of ground-state masses and potential energy surfaces for nuclei spanning the entire periodic table.

Importance of multicranked configuration mixing for angular-momentum-projection calculations: Study of superdeformed rotational bands in Dy152 and Hg194

Recently we investigated an effective method of multicranked configuration mixing for angular-momentum-projection calculations, where several cranked mean-field states are coupled after projection: The basic idea was originally proposed by Peierls and Thouless more than fifty years ago. With this method a good description of the rotational band has been achieved in a fully microscopic manner. In the present work, we apply the method to the high-spin superdeformed band, for which a long rotational sequence is observed, and study how a good description is obtained for the rotational spectrum as well as the ${\mathcal{J}}^{(1)}$ and ${\mathcal{J}}^{(2)}$ moments of inertia as functions of angular momentum. The Gogny D1S force is employed as an effective interaction, and the yrast superdeformed bands in $^{152}\mathrm{Dy}$ and $^{194}\mathrm{Hg}$ are taken as typical examples in the $A\ensuremath{\approx}150$ and $A\ensuremath{\approx}190$ regions, respectively. The effect of pairing correlations is examined by the method of variation after particle-number projection to understand the different behaviors of ${\mathcal{J}}^{(2)}$ moments of inertia observed in these two nuclei. The particle-number projection on top of the angular-momentum projection has been performed for the first time with the multicranked configuration mixing.

Towards an extended Gogny force

In this paper, we present a recent evolution of the analytical form of the Gogny force. The extension of the density-dependent term to a finite range is discussed and has led to the D2 Gogny force. A global refitting of the force has been done but preserving standard good properties of the Gogny force. Indeed the same fitting procedure with the same constraints and filters which have been used to obtain the D1-type parametrizations has been applied. The evolution of global properties (binding energies and nuclear radii) along the N = 8, 20, 28, 40 isotopic chains is discussed at the Hartree-Fock-Bogoliubov approximation level. Results coming from systematic calculations based on 1385 nuclei are also presented. Axial symmetry has been assumed. A comparison with the results obtained using the D1S parametrization, which tends to show that the D2 and the D1S Gogny force display very similar axial deformation properties, is done.

Description of nuclear systems with a self-consistent configuration-mixing approach. II. Application to structure and reactions in even-even sd -shell nuclei

The variational multiparticle-multihole configuration mixing approach (MPMH) to nuclei has been proposed about a decade ago. While the first applications followed rapidly, the implementation of the full formalism of this method has only been recently completed and applied in [C. Robin, N. Pillet, D. Pe\~na Arteaga and J.-F. Berger, Phys. Rev. C 93, 024302 (2016)] to $^{12}$C as a test-case. The main objective of the present paper is to carry on the study that was initiated in that reference, in order to put the MPMH method to more stringent tests. To that aim we perform a systematic study of even-even sd-shell nuclei. The wave function of these nuclei is taken as a configuration mixing built on orbitals of the sd-shell, and both the mixing coefficients of the nuclear state and the single-particle wave functions are determined consistently from the same variational principle. The calculations are done using the D1S Gogny force. Various ground-state properties are analyzed. In particular, the correlation content and composition of the wave function as well as the single-particle orbitals and energies are examined. Binding energies and charge radii are also calculated and compared to experiment. The description of the first excited state is also examined and the corresponding transition densities are used as input for the calculation of inelastic electron and proton scattering. Special attention is paid to the effect of the optimization of the single-particle states consistently with the correlations of the system. Globally, the results are satisfying and encouraging. In particular, charge radii and excitation energies are nicely reproduced. However, the chosen valence-space truncation scheme precludes achieving maximum collectivity in the studied nuclei. Further refinement of the method and a better-suited interaction are necessary to remedy this situation.

Low-energy modification of the γ strength function of the odd-even nucleus In115

Photoactivation yield measurements on $^{115}\mathrm{In}$ have been performed at the ELSA facility with Bremsstrahlung photon beams over a range of endpoint energies between 4.5 and 18 MeV. The measured photoexcitation yields of the $^{115m}\mathrm{In}$ metastable state are compared with calculated yields using cross sections obtained with different models of the photon strength function. It is shown that additional photon strength with respect to the general Lorentzian model is needed at 8.1 MeV for the calculated yields to reproduce the data. The origin of this extra strength is unclear, because it is compatible with additional strength predicted in both $E1$ and $M1$ photon strength distributions by quasiparticle random-phase approximation calculations using the Gogny D1S force.

Realistic description of rotational bands in rare earth nuclei by the angular-momentum-projected multicranked configuration-mixing method

Recently we have proposed a reliable method to describe the rotational band in a fully microscopic manner. The method has recourse to the configuration-mixing of several cranked mean-field wave functions after the angular-momentum-projection. By applying the method with the Gogny D1S force as an effective interaction, we investigate the moments of inertia of the ground state rotational bands in a number of selected nuclei in the rare earth region. As another application we try to describe, for the first time, the two-neutron aligned band in $^{164}$Er, which crosses the ground state band and becomes the yrast states at higher spins. Fairly good overall agreements with the experimental data are achieved; for nuclei, where the pairing correlations are properly described, the agreements are excellent. This confirms that the previously proposed method is really useful for study of the nuclear rotational motion.

Deformation properties with a finite-range simple effective interaction

Deformed and spherical even–even nuclei are studied using a finite-range simple effective interaction within the Hartree–Fock–Bogoliubov mean-field approach. Different parameter sets of the interaction, corresponding to different incompressibility, are constructed by varying the exponent γ of the density in the traditional density-dependent term. Ten of the 12 parameters of these interactions are determined from properties of asymmetric nuclear matter and spin-polarized pure neutron matter. The two remaining parameters are fitted to reproduce the experimental binding energies known in 620 even–even nuclei using several variants of the rotational energy correction. The rms deviations for the binding energy depend on the value of γ and the way the rotational energy correction is treated but they can be as low as 1.56 MeV, a value competitive with other renowned effective interactions of Skyrme and Gogny type. Charge radii are compared to the experimental values of 313 even–even nuclei and the rms deviation is again comparable and even superior to the one of popular Skyrme and Gogny forces. Emphasis is given to the deformation properties predicted with these interactions by analyzing the potential energy surfaces for several well deformed nuclei and the fission barriers of some nuclei. Comparison of the results with the experimental information, where available, as well as with the results of the Gogny D1S force, shows satisfactory agreement.

Infinitesimal cranking for triaxial angular-momentum-projected configuration-mixing calculations and its application to theγvibrational band

Inclusion of time-odd components into the wave function is important for reliable description of rotational motion by the angular-momentum-projection method; the cranking procedure with infinitesimal rotational frequency is an efficient way to realize it. In the present work we investigate the effect of this infinitesimal cranking for triaxially deformed nucleus, where there are three independent cranking axes. It is found that the effects of cranking about three axes on the triaxial energy spectrum are quite different and inclusion of all of them considerably modify the resultant spectrum from the one obtained without cranking. Employing the Gogny D1S force as an effective interaction, we apply the method to the calculation of the multiple gamma vibrational bands in $^{164}$Er as a typical example, where the angular-momentum-projected configuration-mixing with respect to the triaxial shape degree of freedom is performed. With this method, both the $K=0$ and $K=4$ two-phonon gamma vibrational bands are obtained with considerable anharmonicity. Reasonably good agreement, though not perfect, is obtained for both the spectrum and transition probabilities with rather small average triaxial deformation $\gamma\approx 9^\circ$ for the ground state rotational band. The relation to the wobbling motion at high-spin states is also briefly discussed.

A study on the rearrangement corrections to the folding model applied to nucleon inelastic scattering

A study of direct neutron induced reactions off spherical nuclei is given in terms of a folding model. Matter densities stemming from the Random Phase Approxi- mation (RPA), implemented with the Gogny D1S force are used to provide the relevant coupling potentials. The impact of rearrangement corrections on cross sections is studied for direct inelastic nucleon scattering off 16 O and 208 Pb. The rearrangement correction to calculated cross sections is shown to strongly depend on the incident energy and on the excitation multipolarity.

First applications of the Fayans functional to deformed nuclei

First calculations for deformed nuclei using the Fayans functional are carried out for the uranium and lead isotopic chains. The ground state deformations and deformation energies are compared to Skyrme–Hartree–Fock–Bogolyubov HFB-17 and HFB-27 functional results. For the uranium isotopic chain, the Fayans functional property predictions are rather similar to HFB-17 and HFB-27 predictions. However, there is a disagreement for the lead isotopic chain. Both of the Skyrme HFB functionals lead to predictions of rather strong deformations for the light Pb isotopes, which does not agree with the experimental data on charge radii and magnetic moments of the odd Pb isotopes. On the other hand, the Fayans functional leads to the prediction of a spherical ground state for all of the lead isotopes, in accordance with the data and the results known from the literature obtained with the Gogny D1S force and the SLy6 functional as well. The deformation energy curves are calculated and compared against those derived from four Skyrme functionals—SLy4, Sly6, SkM* and UNEDF1—for the 238U nucleus and several lead-deficient Pb isotopes. In the first case, the resulting Fayans functional is rather close to SkM* and UNEDF1, which—in particular the latter—describe the first and second barriers in 238U rather well. For the light lead isotopes, the Fayans deformation energy curves are qualitatively close to those derived from the SLy6 functional.

Low-energy electric dipole response of Sn isotopes

We study the low-energy dipole (LED) strength distribution along the Sn isotopic chain in both the isoscalar (IS) and the isovector (IV, or E1) electric channels, to provide testable predictions and guidance for new experiments with stable targets and radioactive beams. We use the self-consistent Quasi-particle Random-Phase Approximation (QRPA) with finite-range interactions and mainly the Gogny D1S force. We analyze also the performance of a realistic two-body interaction supplemented by a phenomenological three-body contact term. We find that from N=50 and up to the N=82 shell closure (132Sn) the lowest-energy part of the IS-LED spectrum is dominated by a collective transition whose properties vary smoothly with neutron number and which cannot be interpreted as a neutron-skin oscillation. For the neutron-rich species this state contributes to the E1 strength below particle threshold, but much more E1 strength is carried by other, weak but numerous transitions around or above threshold. We find that strong structural changes in the spectrum take effect beyond N=82, namely increased LED strength and lower excitation energies. Our results with the Gogny interaction are compatible with existing data. On this basis we predict that a) the summed IS strength below particle threshold shall be of the same order of magnitude for N=50-82, b) the summed E1 strength up to approximately 12 MeV shall be similar for N=50-82 MeV, while c) the summed E1 strength below threshold shall be of the same order of magnitude for N ~ 64 - 82 and much weaker for the lighter, more-symmetric isotopes. We point out a general agreement of our results with other non-relativistic studies, the absence of a collective IS mode in some of those studies, and a possibly radical disagreement with relativistic models.

Microscopic mean field approximation and beyond with the Gogny force

Fully consistent axially-symmetric-deformed quasiparticle random phase approximation calculations have been performed with the D1S Gogny force. A brief review on the main results obtained in this approach is presented. After a reminder on the method and on the first results concerning giant resonances in deformed Mg and Si isotopes, the multipole responses up to octupole in the deformed and heavy nucleus 238U are discussed. In order to analyse soft dipole modes in exotic nuclei, the dipole responses have been studied in Ne isotopes and in N=16 isotopes, for which results are presented. In these nuclei, the QRPA results on the low lying 2+ states are compared to the 5-Dimensional Collective Hamiltonian ones. © Owned by the authors, published by EDP Sciences, 2014.

Pairing and rotational properties of actinides and superheavy nuclei in covariant density functional theory

The cranked relativistic Hartree-Bogoliubov theory has been applied for a systematic study of pairing and rotational properties of actinides and light superheavy nuclei. Pairing correlations are taken into account by the Brink-Booker part of finite-range Gogny D1S force. For the first time, in the covariant density functional theory (CDFT) framework, the pairing properties of deformed nuclei are studied via the quantities (such as three-point ${\ensuremath{\Delta}}^{(3)}$ indicators) related to odd-even mass staggerings. The investigation of the moments of inertia at low spin and the ${\ensuremath{\Delta}}^{(3)}$ indicators shows the need for an attenuation of the strength of the Brink-Booker part of the Gogny D1S force in pairing channel. The investigation of rotational properties of even-even and odd-mass nuclei at normal deformation, performed in the density functional theory framework in such a systematic way for the first time, reveals that in the majority of the cases the experimental data are well described. These include the evolution of the moments of inertia with spin, band crossings in the $A\ensuremath{\ge}242$ nuclei, the impact of the particle in specific orbital on the moments of inertia in odd-mass nuclei. The analysis of the discrepancies between theory and experiment in the band crossing region of $A\ensuremath{\le}240$ nuclei suggests the stabilization of octupole deformation at high spin, not included in the present calculations. The evolution of pairing with deformation, which is important for the fission barriers, has been investigated via the analysis of the moments of inertia in the superdeformed minimum. The dependence of the results on the CDFT parametrization has been studied by comparing the results of the calculations obtained with the NL1 and NL3* parametrizations.

Prolate shape of140Ba from a first combined Doppler-shift and Coulomb-excitation measurement at the REX-ISOLDE facility

Background: Quadrupole moments of excited nuclear states are important observables for geometrically interpreting nuclear structure in terms of deformed shapes, although data are scarce and sometimes ambiguous, in particular, in neutron-rich nuclides. Purpose: A measurement was performed for determining the spectroscopic quadrupole moment of the 2(1)(+) state of Ba-140 in order to clarify the character of quadrupole deformation (prolate or oblate) of the state in its yrast sequence of levels. Method: We have utilized a new combined technique of lifetime measurement at REX-ISOLDE and MINIBALL using the Doppler-shift attenuation method (DSAM) and a reorientation analysis of Coulomb-excitation yields. Results: On the basis of the new lifetime of tau(2(1)(+)) = 10.4(-0.8)(+2.2) ps the electric quadrupole moment was determined to be Q(2(1)(+)) = -0.52(34) eb, indicating a predominant prolate deformation. Conclusions: This finding is in agreement with beyond-mean-field calculations using the Gogny D1S force and with results from the Monte Carlo shell-model approach.

β-decay measurements forN>40Mn nuclei and inference of collectivity for neutron-rich Fe isotopes

A decay spectroscopic study of the neutron-rich isotopes has been performed using fragmentation of a 86Kr primary beam. Fragments from this reaction have been selected by the LISE2000 spectrometer at the Grand Acc el erateur National d Ions Lourds (GANIL). Half-lives of 29 isotopes, including the first ones identified for 61Ti (15 4 ms), 64V (19 8 ms), and 71Fe (28 5 ms), have been determined and compared with model predictions. 67,68Mn -delayed rays were observed for the first time. The branching for the -delayed neutron emission was measured to be greater than 10(5)% in the 67Mn decay. The 67Fe isomeric level is firmly determined at higher energy than assigned in previous works. The excitation energies of the first (2+) and (4+) states of 68Fe are suggested to lie at 522(1) and 1389(1) keV, respectively, thus bringing confirmation of assignments based on in-beam -ray spectroscopy. Beyond-mean-field calculations with the Gogny D1S force have been performed for even-mass nuclei through the Fe isotopic chain. Not only 68Fe but most of the neutron-rich Fe isotopes with neutron numbers below N = 50 are interpreted as soft rotors. The calculated mean occupancy of the neutron g9/2 and d5/2 orbitals in correlated ground statesmore » is steadily growing with increasing neutron number throughout the isotopic chain. Interpretation of 67Fe data is based upon the present calculations for the 66Fe and 68Fe even cores.« less

Microscopic model approach to (n,xn) pre-equilibrium reactions for medium-energy neutrons

We report on microscopic model calculations of the first step of direct pre-equilibrium ($n$,$x$$n$) emission in neutron interaction with $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$ below 20 MeV. Our model is based on both an accurate description of the target excited states, provided by the self-consistent random-phase approximation (RPA) method implemented with the Gogny D1S force, and well-established in-medium two-body forces to represent the residual nucleon-nucleon interaction for the inelastic processes. Two goals have been achieved: The present microscopic approach provides a unified description of collective state excitations and the pre-equilibrium one-step process, and our reaction model reproduces the available data fairly well, without any parameter adjustment.

Particle-particle random-phase approximation applied to beryllium isotopes

This work is dedicated to the study of even-even 8-14 Be isotopes using the particle-particle Random Phase Approximation that accounts for two-body correlations in the core nucleus. A better description of energies and two-particle amplitudes is obtained in comparison with models assuming a neutron closed-shell (or subshell) core. A Wood-Saxon potential corrected by a phenomenological particle-vibration coupling term has been used for the neutron-core interaction and the D1S Gogny force for the neutron-neutron interaction. Calculated ground state properties as well as excited state ones are discussed and compared to experimental data. In particular, results suggest the same 2s_1/2-1p_1/2 shell inversion in 13Be as in 11Be.

Microscopic description of nuclear structure aroundZr80

A new approach for the calculation of angular momentum projected potential energy surfaces (AMPPESs) is proposed which combines the projected shell model with a quadrupole constrained relativistic Hartree-Bogoliubov (RHB) theory in which the NL3 effective interaction is chosen for the relativistic mean-field effective Lagrangian and a separable Gogny D1S interaction for the pairing force (QCRHB-NL3 + separable Gogny D1S force theory). We apply this approach to compute the AMPPESs of 80,82,84 Zr nuclei up to high spins and investigate the spin-induced shape transitions and decay out of the superdeformed (SD) bands in these nuclei. We find that the shape transitions occur in 80 Zr and 84 Zr, which are driven by the rotational alignments of the nucleons in the 1g 9/2 orbitals, and a strong shape mixing happens in 82 Zr. Moreover, it is shown that the barrier separating the SD states and normal deformed (or spherical) states becomes lower and narrower for 82 Zr and 84 Zr at high spins, indicating that the decay out of the SD bands could occur at high spins. For 80 Zr, however, there is no decay out of the SD band because the barrier is so high and thick. Meanwhile, the QCRHB-NL3 + separable Gogny D1S force theory is employed to calculate the ground-state potential energy surfaces and the single-particle levels of these nuclei, which in turn are used to determine and analyze the equilibrium shapes and discuss the shape coexistence of these nuclei. In addition, this theory is compared with other state-of-the-art mean-field theories to justify its use to study the ground-state potential energy surfaces of 80,82,84 Zr.