arXiv subjects

R. N. Bernard

Publications and source records attributed to R. N. Bernard.

11 recordsLinked to original sources

arXiv2026

Impact of perturbative tensor interactions on the spontaneous fission half-lives of superheavy nuclei

The standard microscopic description of fission, based on the mean-field Hartree-Fock-Bogoliubov approximation and a semi-classical description of tunneling through the fission barrier, has been used to analyse the impact of introducing a (perturbative) tensor term along with the well known Gogny-D1S force in the spontaneous fission half-lives. Calculations in a series of even-even isotopes of superheavy nuclei ranging from nobelium to darmstatium have been carried out. The results show that the tensor term only impacts the height of the first fission barrier and leaves mostly unaffected the pairing properties and therefore the collective inertias. As a consequence of the reduction in the barrier height, the spontaneous fission lifetimes obtained by including the tensor term are significantly smaller than the ones without it bringing the theoretical predictions in closer agreement with experimental data.

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arXiv2026

Microscopic description of the fission process including intrinsic excitations. Part I: 240Pu adiabatic and asymmetric fission path within the Schrodinger Collective Intrinsic Model

This article is the first in a trilogy aimed at presenting the first practical implementation of the Schrodinger Collective-Intrinsic Model (SCIM) applied to nuclear fission. Within the SCIM framework, the many-body wave function explicitly couples collective motion to intrinsic excitations, necessitating sets of Hartree-Fock-Bogoliubov (HFB) configurations that remain continuous and regular across a broad deformation range, from the ground state to scission and beyond. This paper focuses on constructing adiabatic HFB paths suitable for subsequent SCIM dynamical calculations. Standard constrained adiabatic paths often suffer from discontinuities and irregularities, which prevent the direct application of the formalism. To address these challenges, we implement two recently proposed overlap-based protocols, the Link and Drop methods, and combine them into a new numerical procedure.A comparison with the exact Gaussian Overlap Approximation confirms that the resulting adiabatic kernels exhibit properties consistent with the assumptions of the SCIM formalism. The regularized path is then analyzed in the scission region. We identify characteristic structures in the proton and neutron chemical potentials, a pronounced neutron enrichment of the neck at scission, and fragment particle-number distributions displaying a strong odd-even staggering in the proton sector. Finally, using a microscopic fragment-separation procedure formulated in the canonical basis, we extract static scission properties including fragment deformation energies and both Coulomb and nuclear contributions to the fragment interaction energy. These results establish the adiabatic foundations required for future SCIM calculations with intrinsic excitations and provide a microscopic characterization of the scission region in 240Pu.

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arXiv2026

Microscopic description of the fission process including intrinsic excitations. Part II: 240Pu excited and asymmetric fission paths within the Schrodinger Collective

This second article of the trilogy presents the implementation of a third protocol, referred to as Continuous Deflation, designed to construct continuous and regular excited paths within the Schrodinger Collective-Intrinsic Model (SCIM), with applications to nuclear fission. We show that the use of standard 2QP excitations, even when combined with particle-number projection, prevents a consistent application of the SCIM framework. Motivated by the central role of pair breaking in low-energy fission, we explore how to construct intrinsic excited states that incorporate this mechanism while satisfying the continuity and regularity state requirements of the SCIM. To this end, we first analyze the Deflation procedure alone, which constructs excited states through orthogonality constraints. We then extend this construction along a deformation path by introducing an additional continuity constraint, thereby defining the Continuous Deflation method, which generates continuous paths based on excited states. In particular, we construct ten such continuous paths built on top of the adiabatic and asymmetric fission path of 240Pu. The resulting excited states are systematically analyzed in terms of their microscopic structure. We then investigate several fragment properties near scission, including neutron and proton chemical potentials, neutron necking as well as fragment particle-number distributions, and compare them with their adiabatic counterparts.

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arXiv2026

Microscopic description of the fission process including intrinsic excitations. Part III: 240Pu fission dynamics along 1D asymmetric paths within the Schrodinger Collective Intrinsic Model

This last article of the trilogy focuses on the dynamical equation of the Schrodinger Collective-Intrinsic Model (SCIM). First, we motivate and discuss the need to regularize the adiabatic and excited dynamical ingredients entering the collective-intrinsic Hamiltonian, namely the collective potential, the collective inertia tensor, and the collective dissipative tensor. In particular, we introduce a Savitzky-Golay low-pass filter to remove numerical fluctuations incompatible with the second-order truncation in the Symmetric Ordered Product of Operators used to derive the SCIM equations. The diagonal and off-diagonal properties of the three dynamical ingredients are then analyzed along the asymmetric fission path in 240Pu. This study highlights the dominant role of neutron and proton excitation channels, especially in the second well and scission regions, whereas proton-neutron couplings remain essentially negligible. Furthermore, in the adiabatic limit of the SCIM, we perform a comparison with the GOA which reveals very close predictions. Second, we discuss the construction of the initial wave packet and the numerical resolution of the collective-intrinsic Schrodinger equation. Using a continuity equation, we derive the probability fluxes associated with the different components of the wave function, which provide direct access to the contribution of the different excitations to the final observables for the fission problem. The excited states are found to account for more than 80% of the total flux at scission. Finally, we evaluate, the neutron and proton fragment distributions as well as the energy balance, including the total kinetic and excitation energies. The obtained results are found to be consistent with available experimental data and demonstrate the importance of explicitly including intrinsic excitations in the description of fission dynamics.

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arXiv2026

An exact time-dependent generator coordinate method with projection for spontaneous fission reactions

Microscopic descriptions of fission dynamics through the barrier rely on different theoretical frameworks depending on the fission regime, with the time-dependent generator coordinate method (TDGCM) commonly used for induced fission and semiclassical approaches such as the Wentzel-Kramers-Brillouin (WKB) method widely employed for spontaneous fission. In this work, we develop a fully microscopic approach to spontaneous fission based on an exact formulation of the TDGCM, avoiding both the Gaussian overlap approximation and semiclassical treatments. By combining the exact TDGCM with new projection tools and a quasistatic description of spontaneous fission, we derive spontaneous fission lifetimes from a one-dimensional potential energy surface. A detailed analysis of the model parameters shows that they do not introduce uncontrolled phenomenological effects. Remaining discrepancies with experimental lifetimes are traced to possible limitations of the underlying microscopic interaction and to the choice of basis states in the generator coordinate method. The new framework provides a microscopic description of spontaneous fission with reduced empirical input and offers a pathway toward improved predictions through future developments of nuclear interactions, collective coordinates, and the handling of many-body dynamics.

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arXiv2025

Impact of finite-range spin-orbit and tensor terms in Gogny EDF

Energy Density Functionals are of major interest for the study of the atomic nucleus as, coupled with mean-field and beyond N-body approaches, they are applicable to the whole nuclear chart, including superheavy elements. On the one hand, the growing need for nuclear data and, on the other hand, the large amount of experimental data on exotic nuclei explain the work carried out on these phenomenological forms of the nucleon-nucleon interaction to analyze the richness of the nuclear phenomena. In this paper, we propose a fully finite-range extension of the Gogny EDF, including a short-range spin-orbit term and a long-range tensor term. The original fitting protocol of the Gogny interaction has been adapted to include both finite range spin-orbit and tensor terms, adding new constraints and filters linked to relevant data. Nuclear matter, spectroscopic and fission properties are discussed, highlighting ways of improving EDFs when all spin and isospin exchanges are introduced with finite-range terms.

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arXiv2024

Microscopic description of spontaneous fission based on a Gogny energy density functional including tensor contributions

This paper extends previous studies on the impact of tensor forces in fission dynamics of neutron-deficient Thorium isotopes to other isotopic chains of heavy actinides and low-mass super-heavy nuclei. Calculations are carried out within a mean-field framework based on the Gogny-D1S parametrization supplemented with the D1ST2a perturbative tensor term as driving force. Fission barrier heights and spontaneous fission half-lives are used as benchmarks to analyze the impact of the tensor term. A significant reduction of fission barrier heights and half-lives is associated to the tensor component of the force.

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arXiv2022

Smoothing of one- and two-dimensional discontinuities in potential energy surfaces

Background: The generation of potential energy surfaces is a critical step in theoretical models aiming to understand and predict nuclear fission. Discontinuities frequently arise in these surfaces in unconstrained collective coordinates, leading to missing or incorrect results. Purpose: This work aims to produce efficient and physically-motivated computational algorithms to refine potential energy surfaces by removing discontinuities. Method: Procedures based on tree-search algorithms are developed which are capable of smoothing discontinuities in one and two-dimensional potential energy surfaces while minimising their overall energy. Results: Each of the new methods is applied to smooth candidate discontinuities in ${}^{252}\mathrm{Cf}$, ${}^{222}\mathrm{Th}$ and ${}^{218}\mathrm{Ra}$. The effectiveness of each case is analysed both qualitatively and quantitatively. The one-dimensional method is also compared to the adiabatic and linear interpolation approaches which are commonly used to remove discontinuities. Conclusions: The smoothing methods presented in this work are resource-efficient and successful for one- and two-dimensional discontinuities; they will improve the fidelity of potential energy surfaces as well as their subsequent uses in beyond mean-field applications. Complex discontinuities occurring in higher dimensions may require alternative approaches which better utilise prior knowledge of the potential energy surface to narrow their searches.

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arXiv2016

Asymmetry dependence of Gogny based optical potential

An analysis of neutron and proton scattering off $^{40,48}$Ca has been carried out. Real and imaginary potentials have been generated using the Nuclear Structure Method (NSM) for scattering with the Gogny D1S nucleon-nucleon effective interaction. Observables are well described by NSM for neutron and proton elastic scattering off $^{40}$Ca and for neutron scattering off $^{48}$Ca. For proton scattering off $^{48}$Ca, NSM yields a lack of absorption. This discrepancy is attributed to double-charge-exchange contribution and coupling to Gamow- Teller mode which are not included in the present version of NSM. A recipe based on a Perey-Buck fit of NSM imaginary potential and Lane model is proposed to overcome this issue in an approximate way.

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arXiv2015

Electric quadrupole and magnetic dipole moments of odd nuclei near the magic ones in a self-consistent approach

We present a model which describes the properties of odd-even nuclei with one nucleon more, or less, with respect to the magic number. In addition to the effects related to the unpaired nucleon, we consider those produced by the excitation of the closed shell core. By using a single particle basis generated with Hartree-Fock calculations, we describe the polarization of the doubly magic-core with Random Phase Approximation collective wave functions. In every step of the calculation, and for all the nuclei considered, we use the same finite-range nucleon-nucleon interaction. We apply our model to the evaluation of electric quadrupole and magnetic dipole moments of odd-even nuclei around oxygen, calcium, zirconium, tin and lead isotopes. Our Random Phase Approximation description of the polarization of the core improves the agreement with experimental data with respect to the predictions of the independent particle model. We compare our results with those obtained in first-order perturbation theory, with those produced by Hartree-Fock-Bogolioubov calculations and with those generated within the Landau-Migdal theory of finite Fermi systems. The results of our universal, self-consistent, and parameter free approach have the same quality of those obtained with phenomenological approaches where the various terms of the nucleon-nucleon interaction are adapted to reproduce some specific experimental data. A critical discussion on the validity of the model is presented.

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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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