arXiv subjects

Marcella Grasso

Publications and source records attributed to Marcella Grasso.

At least 19 recordsLinked to original sources

arXiv2026

Recent applications of the subtracted second RPA method

In this review, we discuss the most recent developments and applications of the Subtracted Second RPA (SSRPA), an extension of the Second RPA (SRPA), which overcomes its pathological issues encountered within the Energy Density Functional theory. After recalling the formal properties of the SRPA and SSRPA, the anomalous behavior of SRPA is shown and discussed by presenting several applications with different kinds of nuclear interactions. The most recent pathology-free SSRPA studies are then presented both for charge-conserving and charge-exchange nuclear excitations. The comparison with experimental data is presented to assess and quantify the improvement introduced by the SSRPA with respect to the RPA and SRPA. The impact of beyond-mean-field correlations induced in SSRPA is also qualitatively estimated in connection with the modeling of the nuclear equation of state. We conclude by discussing the future perspectives of the SSRPA, focusing on its potential connections with some current experimental challenges and outlining necessary theoretical extensions and numerical developments.

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arXiv2025

Nuclear $\beta$-decay half-lives within the subtracted second random-phase approximation

We employ, within the framework of Skyrme energy-density functional theory, the subtracted second random-phase approximation, recently developed for charge-exchange excitations, to compute $\beta$-decay half-lives in four nuclei, $^{24}$O, $^{34}$Si, $^{78}$Ni, and $^{132}$Sn. Following our recent results on the description of the Gamow-Teller strength, we proceed coherently in the present work by computing $\beta$-decay half-lives using the bare value of the axial-vector coupling constant $g_A$. Half-lives are thus obtained, within the allowed Gamow-Teller approximation, without the use of any ad hoc quenching factors. A genuine quenching is indeed microscopically introduced in our model owing to the correlations induced by the coupling of one-particle one-hole configurations with two-particle two-hole ones. The role of the so-called $J^2$ terms is also studied. By comparing our results with experimental data, we show a general improvement of $\beta$-decay half-lives with respect to results obtained within the commonly used Random Phase Approximation (RPA). The inclusion of the two-particle two-hole configurations produces a more fragmented and richer spectrum within the $\beta$-window, resulting in lower $\beta$ half-lives with respect to the RPA ones.

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arXiv2021

Quenching of Gamow-Teller strengths and two particle -- two hole configurations

We apply the charge-exchange subtracted second random-phase approximation (SSRPA), based on Skyrme functionals, to investigate Gamow-Teller resonances in several closed-shell and closed-subshell nuclei, located in different regions of the nuclear chart. After having discussed the SSRPA findings obtained within different approximation schemes in $^{48}$Ca, we compare our results with {\it{ab-initio}} coupled-cluster predictions available for C and O isotopes, where two-body currents are included. Our integrated strenghts, obtained by using one-body transition operators, are lower compared to the corresponding {\it{ab-initio}} results. This indicates that, within our model, quenching effects are mainly driven by the inclusion of two particle - two hole configurations and that the role of a two-body contribution in the transition operator is less important than in the coupled-cluster approach. By analyzing heavier nuclei, $^{90}$ Zr and $^{132}$Sn, we confirm the same conclusions that we have recently drawn for $^{48}$Ca: the inclusion of two particle - two hole configurations is very effective in our model for providing strengths which are significantly more quenched than in other theoretical models and, thus, in better agreement with the experimental measurements. This occurs because two particle - two hole configurations have a density which strongly increases with the excitation energy. Their inclusion thus pushes a significant amount of the strength to higher energies, compared to what happens in other theoretical models, reducing in this way the cumulative sum of the strength up to excitation energies around 20-30 MeV.

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arXiv2021

Finite-temperature infinite matter with effective-field-theory-inspired energy-density functionals

Finite-temperature infinite matter is analyzed with the recently introduced effective-fieldtheory(EFT)-inspired YGLO (Yang-Grasso-Lacroix-Orsay) and ELYO (extended Lee-Yang, Orsay) functionals, which are designed to describe very low-density regimes in symmetric (YGLO) and in pure neutron (YGLO and ELYO) matter. The article deals with neutron matter and aims to verify whether the use of these functionals allows us to correctly incorporate finite-temperature effects. We compare our results for some relevant thermodynamical quantities with the corresponding ones computed with a chosen reference ab-initio model, namely the many-body-perturbation-theory scheme. We validate the reliability of both EFT-inspired functionals at least at rather low densities and not too high temperatures and we discuss the effects related to the effective mass. We conclude that, at the present stage, the ELYO functional, having a higher neutron effective mass around saturation (closer to ab-initio values), allows us to describe finite-temperature properties more satisfactorily, in better agreement with ab-initio predictions up to higher densities and temperatures, compared to YGLO.

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arXiv2021

Application of an ab-initio-inspired energy density functional to nuclei: impact of the effective mass and the slope of the symmetry energy on bulk and surface properties

The YGLO (Yang-Grasso-Lacroix-Orsay) functional is applied for the first time to investigate ground-state properties of different isotopic chains, from Oxygen to Lead. Mean-field Hartree-Fock calculations are carried out to analyze global trends for separation energies, binding energies, radii, neutron skins, and density profiles. We have three objectives: i) we study whether this functional leads to a reasonable description of ground-state properties (despite the fact that it was not adjusted on nuclei) and we discuss the associated limitations; ii) we investigate whether the correct description of the low-density nuclear gas, which is the peculiarity of this functional, has any relevant impact on predictions for nuclei; iii) we connect nuclear energies, radii and density profiles with properties of the corresponding equations of state of infinite matter. In particular, we identify a link existing between the isoscalar effective mass and spatial properties in neutron-deficient nuclei, namely proton radii and tails of proton densities. On the other side, we show that the slope of the symmetry energy is connected with spatial properties in neutron-rich nuclei: the slope computed at saturation density is related to neutron skin thicknesses, as already well known, whereas the slope calculated at lower densities is linked to the tails of neutron densities. The YGLO effective mass turns out to be quite low. Directions to improve this aspect are explored and suggested at the end of the manuscript.

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arXiv2020

Towards a power counting in nuclear energy-density-functional theories through a perturbative analysis

We illustrate a step towards the construction of a power counting in energy-density-functional (EDF) theories, by analyzing the equations of state (EOSs) of both symmetric and neutron matter. Within the adopted strategy, next-to-leading order (NLO) EOSs are introduced which contain renormalized first-order-type terms and an explicit second-order finite part. Employing as a guide the asymptotic behavior of the introduced renormalized parameters, we focus our analysis on two aspects: (i) With a minimum number of counterterms introduced at NLO, we show that each energy contribution entering in the EOS has a regular evolution with respect to the momentum cutoff (introduced in the adopted regularization procedure) and is found to converge to a cutoff-independent curve. The convergence features of each term are related to its Fermi-momentum dependence. (ii) We find that the asymptotic evolution of the second-order finite-part coefficients is a strong indication of a perturbative behavior, which in turns confirms that the adopted strategy is coherent with a possible underlying power counting in the chosen Skyrme-inspired EDF framework.

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arXiv2020

Lee-Yang-inspired energy-density functional including contributions from $p$-wave scattering

The ELYO functional proposed in [M. Grasso, D. Lacroix, and C. J. Yang, Phys. Rev. C \textbf{95}, 054327 (2017)] belongs to the family of energy-density functionals (EDFs) inspired by effective-field theories (EFTs) and constrained by \textit{ab--initio} pseudo-data. We present here an extension of this EDF which also accounts for the first $p$-wave term appearing in the low-density expansion from which it derives. It is shown that this enrichment of the ansatz on which the functional is based leads to a significant improvement of the description of neutronic systems, especially in regimes besides the pseudo--data set employed to adjust the parameters. As an illustrative application, the mass-radius relation of neutron stars is considered. In contrast to its initial version, the new functional predicts values which are qualitatively consistent with recent observations.

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arXiv2018

Effective density functionals beyond mean field

I present a review on non relativistic effective energy--density functionals (EDFs). An introductory part is dedicated to traditional phenomenological functionals employed for mean--field--type applications and to several extensions and implementations that have been suggested over the years to generalize such functionals, up to the most recent ideas. The heart of this review is then focused on density functionals designed for beyond--mean--field models. Examples of these studies are discussed. Starting from these investigations, some illustrations of {\it{ab--initio}}--based or {\it{ab--initio}}--inspired functionals are provided. Constructing functionals by building bridges with {\it{ab--initio}} models represents an extremely challenging and timely objective. This will eventually reduce/eliminate the empirical character of EDFs and link them with the underlying theory of QCD. Conclusions are presented in the last part of the review.

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arXiv2018

Energy-density functionals inspired by effective-field theories: Applications to neutron drops

New energy-density functionals (EDFs) inspired by effective-field theories (EFTs) have been recently proposed. The present work focuses on three of such functionals which were developed to produce satisfactory equations of state for nuclear matter. We aim to extend these functionals to treat finite systems including a spin-orbit contribution and pairing correlations. We illustrate here a first step towards this direction, namely a generalization of such functionals tailored to perform applications to neutron gases confined in harmonic traps. Sets of available \textit{ab initio} results are used as benchmark pseudo-data for adjusting the additional parameters (with respect to the nuclear matter case) that have to be introduced for finite-size systems. Several quantities are predicted and compared to \textit{ab initio} and other EDF results such as, for instance, total energies, potentials, and density profiles. The associated effective masses are also analyzed. In cases where \textit{ab initio} results are available, two of these functionals globally provide predictions which are close one to the other as well as to \textit{ab initio} values. It is shown that, in general, this is not the case for several currently used Skyrme functionals. Directions for improving the third functional are discussed.

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arXiv2018

A systematic study of giant quadrupole resonances with the subtracted second random--phase approximation: beyond--mean--field centroids and fragmentation

A systematic analysis of giant quadrupole resonances is performed for several nuclei, from $^{30}$Si to $^{208}$Pb, within the subtracted second random--phase--approximation (SSRPA) model in the framework of the energy--density--functional theory. Centroid energies and widths of the isoscalar giant quadrupole resonances are compared with the corresponding random--phase--approximation (RPA) values. We find lower SSRPA centroid energies compared to the RPA values leading, in general, to a better agreement with the experimental data. As far as the widths are concerned, we observe for both SSRPA and RPA cases a global attenuation of the single--particle Landau damping going from lighter to heavier nuclei and we obtain, systematically, larger widths in the SSRPA model compared to the RPA case. For some selected nuclei for which high--resolution ($p,p'$) experimental data are available, namely $^{40}$Ca, $^{90}$Zr, $^{120}$Sn, and $^{208}$Pb, the theoretical strength distributions are directly compared with the experimental spectra. We observe a significant improvement, with respect to RPA results, in the description of the spreading widths and of the fragmentation of the obtained spectra, due to the coupling between 1 particle-1 hole and 2 particle-2 hole configurations.

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arXiv2017

Electric dipole strength and dipole polarizability in $^{48}$Ca within a fully self-consistent second random-phase approximation

The second random-phase-approximation model corrected by a subtraction procedure designed to cure double counting, instabilities, and ultraviolet divergences, is employed for the first time to analyze the dipole strength and polarizability in $^{48}$Ca. All the terms of the residual interaction are included, leading to a fully self-consistent scheme. Results are illustrated with two Skyrme parametrizations, SGII and SLy4. Those obtained with the SGII interaction are particularly satisfactory. In this case, the low-lying strength below the neutron threshold is extremely well reproduced and the giant dipole resonance is described in a very satisfactory way especially in its spreading and fragmentation. Spreading and fragmentation are produced in a natural way within such a theoretical model by the coupling of 1 particle-1 hole and 2 particle-2 hole configurations. Owing to this feature, we may provide for the electric polarizability as a function of the excitation energy a curve with a similar slope around the centroid energy of the giant resonance compared to the corresponding experimental results. This represents a considerable improvement with respect to previous theoretical predictions obtained with the random-phase approximation or with several ab-initio models. In such cases, the spreading width of the excitation cannot be reproduced and the polarizability as a function of the excitation energy displays a stiff increase around the predicted centroid energy of the giant resonance.

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arXiv2017

From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter

We further progress along the line of Ref. [Phys. Rev. {\bf A 94}, 043614 (2016)] where a functional for Fermi systems with anomalously large $s$-wave scattering length $a_s$ was proposed that has no free parameters. The functional is designed to correctly reproduce the unitary limit in Fermi gases together with the leading-order contributions in the s- and p-wave channels at low density. The functional is shown to be predictive up to densities $\sim0.01$ fm$^{-3}$ that is much higher densities compared to the Lee-Yang functional, valid for $ρ< 10^{-6}$ fm$^{-3}$. The form of the functional retained in this work is further motivated. It is shown that the new functional corresponds to an expansion of the energy in $(a_s k_F)$ and $(r_e k_F)$ to all orders, where $r_e$ is the effective range and $k_F$ is the Fermi momentum. One conclusion from the present work is that, except in the extremely low--density regime, nuclear systems can be treated perturbatively in $-(a_s k_F)^{-1}$ with respect to the unitary limit. Starting from the functional, we introduce density--dependent scales and show that scales associated to the bare interaction are strongly renormalized by medium effects. As a consequence, some of the scales at play around saturation are dominated by the unitary gas properties and not directly to low-energy constants. For instance, we show that the scale in the s-wave channel around saturation is proportional to the so-called Bertsch parameter $ξ_0$ and becomes independent of $a_s$. We also point out that these scales are of the same order of magnitude than those empirically obtained in the Skyrme energy density functional. We finally propose a slight modification of the functional such that it becomes accurate up to the saturation density $ρ\simeq 0.16$ fm$^{-3}$.

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arXiv2014

Magicity of the $^{52}$Ca and $^{54}$Ca isotopes and tensor contribution within a mean--field approach

We investigate the magicity of the isotopes $^{52}$Ca and $^{54}$Ca, that was recently confirmed by two experimental measurements, and relate it to like--particle and neutron--proton tensor effects within a mean--field description. By analyzing Ca isotopes, we show that the like--particle tensor contribution induces shell effects that render these nuclei more magic than they would be predicted by neglecting it. In particular, such induced shell effects are stronger in the nucleus $^{52}$Ca and the single--particle gaps are increased in both isotopes due to the tensor force. By studying $N=32$ and $N=34$ isotones, neutron--proton tensor effects may be isolated and their role analyzed. It is shown that neutron--proton tensor effects lead to increasing $N=32$ and $N=34$ gaps, when going along isotonic chains, from $^{58}$Fe to $^{52}$Ca, and from $^{60}$Fe to $^{54}$Ca, respectively. The mean--field calculations are perfomed by employing one Skyrme parameter set, that was introduced in a previous work by fitting the tensor parameters together with the spin--orbit strength. The signs and the values of the tensor strengths are thus checked within this specific application. The obtained results indicate that the employed parameter set, even if generated with a partial adjustment of the parameters of the force, leads to the correct shell behavior and provides, in particular, a description of the magicity of $^{52}$Ca and $^{54}$Ca within a pure mean--field picture with the effective two--body Skyrme interaction.

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arXiv2013

Tensor parameters in Skyrme and Gogny effective interactions: Trends from a ground-state-focused study

Recent ground--state--focused studies of the tensor effects in the mean--field framework are our starting point. On the basis of phenomenological arguments, we indicate regions for acceptable values of the parameters that are associated with the tensor effective forces within both the Skyrme and the Gogny models. We identify acceptable signs and values of the parameters by making an adjustment on the neutron $1f$ spin--orbit splitting for the nuclei $^{40}$Ca, $^{48}$Ca and $^{56}$Ni. The first nucleus is not used to adjust the tensor parameters because it is spin--saturated, but is employed to tune the spin--orbit strength. One of the main conclusions of this work is that some existing Skyrme parametrizations containing the tensor force should not be employed because the wrong sign of the tensor parameters does not lead to the correct behavior (by comparing with the experimental results). This study also allows us to better constrain the tensor parameters in the Gogny case, where much less work is published and boundaries and signs for the parameters have not been analyzed so far.

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arXiv2013

Two-neutron transfer probabilities and spatial-localization effects at the drip line

We examine Cr isotopes at the drip line, where surface effects related to the existence of a weakly bound $s1/2$ state are known to be important and tightly connected with the pairing phenomenon (anti-halo effect). For these weakly-bound isotopes, we evaluate the ground state to ground state two-neutron transfer probabilities within a mean-field-based approach. An important part of the discussion is devoted to the analysis of several procedures that can be employed to constrain the parameters of a phenomenological pairing interaction. The parameters are first adjusted to reproduce the experimental gaps evaluated with the five-point formula. This choice has however some consequences on the evolution of the pairing correlations along the isotopic chains and, in particular, at shell closures. Other procedures are then followed (adjustment on a theoretical pairing gap at mid-shell and on the two-neutron separation energies). For the transfer probabilities, we discuss the effects associated to different choices of the spatial localization of the pairing interaction. We indicate that the analysis of pair-transfer reactions for such cases (where the last bound state is a low-$l$ state in a weakly bound nucleus) may improve our understanding of two aspects: the spatial distribution of pairing correlations in nuclei and the general problem of the persistence of pairing at the drip lines.

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arXiv2012

Tensor and tensor-isospin terms in the effective Gogny interaction

We discuss the need of including tensor terms in the effective Gogny interaction used in mean-field calculations. We show in one illustrative case that, with the usual tensor term that is employed in the Skyrme interaction (and that allows us to separate the like-nucleon and the neutron-proton tensor contributions), we can describe the evolution of the N=28 neutron gap in calcium isotopes. We propose to include a tensor and a tensor-isospin term in finite-range interactions of Gogny type. The parameters of the two tensor terms allow us to treat separately the like-nucleon and the neutron-proton contributions. Two parameterizations of the tensor terms have been chosen to reproduce different neutron single-particle properties in the 48Ca nucleus and the energy of the first 0- state in the 16O nucleus. By employing these two parameterizations we analyze the evolution of the N=14, 28, and 90 neutron energy gaps in oxygen, calcium and tin isotopes, respectively. We show that the combination of the parameters governing the like-nucleon contribution is crucial to correctly reproduce the experimental (where available) or shell-model trends for the evolution of the three neutron gaps under study.

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arXiv2012

Dimensional regularization applied to nuclear matter with a zero--range interaction

We apply the dimensional regularization procedure to treat an ultraviolet divergence occurring in the framework of the nuclear many-body problem. We consider the second--order correction (beyond the mean-field approximation) to the equation of state of nuclear matter with a zero-range effective interaction. The unphysical ultraviolet divergence that is generated at second order by the zero range of the interaction is removed by the regularization technique and the regularized equation of state (mean-field + second-order contributions) is adjusted to a reference equation of state. The main practical advantage of this procedure, with respect to a cutoff regularization, is to provide a unique set of parameters for the adjusted effective interaction. This occurs because the regularized second-order correction does not contain any cutoff dependence. The encouraging results found in this work indicate that such an elegant technique to generate regularized effective interactions is likely to be applied in future to finite nuclei in the framework of beyond mean-field models.

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arXiv2012

Second-order equation of state with the full Skyrme interaction: toward new effective interactions for beyond mean-field models

In a quantum Fermi system the energy per particle calculated at the second order beyond the mean-field approximation diverges if a zero-range interaction is employed. We have previously analyzed this problem in symmetric nuclear matter by using a simplified nuclear Skyrme interaction, and proposed a strategy to treat such a divergence. In the present work, we extend the same strategy to the case of the full nuclear Skyrme interaction. Moreover we show that, in spite of the strong divergence ($\sim$ $Λ^5$, where $Λ$ is the momentum cutoff) related to the velocity-dependent terms of the interaction, the adopted cutoff regularization can be always simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratio. This paves the way to applications to finite nuclei.

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