arXiv subjects

M. Grasso

Publications and source records attributed to M. Grasso.

At least 19 recordsLinked to original sources

arXiv2021

Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory

We propose a novel idea to construct an effective interaction under energy-density-functional (EDF) theories which is adaptive to the enlargement of the model space. Guided by effective field theory principles, iterations of interactions as well as enlargements of the model space through particle-hole excitations are carried out for infinite nuclear matter and selected closed-shell nuclei ($^4$He, $^{16}$O, $^{40}$Ca, $^{56}$Ni and $^{100}$Sn) up to next-to-leading order. Our approach provides a new way for handling the nuclear matter and finite nuclei within the same scheme, with advantages from both EDF and ab initio approaches.

nucl-th↗

arXiv2020

Gamow-Teller strength in $^{48}$Ca and $^{78}$Ni with the charge-exchange subtracted second random-phase approximation

We develop a fully self-consistent subtracted second random-phase approximation for charge-exchange processes with Skyrme energy-density functionals. As a first application, we study Gamow-Teller excitations in the doubly-magic nucleus $^{48}$Ca, the lightest double-$\beta$ emitter that could be used in an experiment, and in $^{78}$Ni, the single-beta-decay rate of which is known. The amount of Gamow-Teller strength below 20 or 30 MeV is considerably smaller than in other energy-density-functional calculations and agrees better with experiment in $^{48}$Ca, as does the beta-decay rate in $^{78}$Ni. These important results, obtained without \textit{ad hoc} quenching factors, are due to the presence of two-particle -- two-hole configurations. Their density progressively increases with excitation energy, leading to a long high-energy tail in the spectrum, a fact that may have implications for the computation of nuclear matrix elements for neutrinoless double-$\beta$ decay in the same framework.

nucl-th↗

arXiv2020

Beyond-mean-field effects on the symmetry energy and its slope from the low-lying dipole response of $^{68}$Ni

We study low-energy dipole excitations in the unstable nucleus $^{68}$Ni with the beyond-mean-field (BMF) subtracted second random-phase-approximation (SSRPA) model based on Skyrme interactions. First, strength distributions are compared with available experimental data and transition densities of some selected peaks are analyzed. The so-called isospin splitting is also discussed by studying the isoscalar/isovector character of such excitations. We estimate then in an indirect way BMF effects on the symmetry energy of infinite matter and on its slope starting from the BMF SSRPA low-lying strength distribution. For this, several linear correlations are used, the first one being a correlation existing between the contribution (associated with the low-energy strength) to the total energy-weighted sum rule (EWSR) and the slope of the symmetry energy. BMF estimates for the slope of the symmetry energy can be extracted in this way. Correlations between such a slope and the neutron-skin thickness of $^{68}$Ni and correlations between the neutron-skin thickness of $^{68}$Ni and the electric dipole polarizability times the symmetry energy are then used to deduce BMF effects on the symmetry energy.

nucl-th↗

arXiv2019

Soft breathing modes in neutron--rich nuclei with the subtracted second random--phase approximation

We analyze the isoscalar response related to breathing modes with particular attention being paid to low-lying excitations in neutron--rich nuclei. We use the subtracted second random--phase approximation (SSRPA) to describe microscopically the response. By increasing the neutron excess, we study the evolution of the response in Ca isotopes going from $^{40}$Ca to $^{48}$Ca and to $^{60}$Ca as well as in $N=20$ isotones going from $^{40}$Ca to $^{36}$S and to $^{34}$Si. Finally, the case of $^{68}$Ni is investigated. We predict soft monopole modes in neutron--rich nuclei which are driven by neutron excitations. At variance with dipole pygmy modes, these neutron excitations are not only strongly dominant at the surface of the nucleus but over its entire volume. The effect of the mixing with two particle-two hole configurations induced by the SSRPA model is analyzed. The properties of such soft neutron modes are investigated in terms of their excitation energies, transition densities and wave--function components. Their collectivity is also discussed as a function of the isospin asymmetry and of the mass of the nucleus. The link between such low--energy compression modes and a compressibility modulus introduced for neutron--rich infinite matter is finally studied.

nucl-th↗

arXiv2018

Beyond--mean--field effective masses in the nuclear Fermi liquid from axial breathing modes

Axial breathing modes are studied within the nuclear energy--density--functional theory to discuss the modification of the nucleon effective mass produced beyond the mean--field approximation. This analysis is peformed with the subtracted second random--phase--approximation (SSRPA) model applied to two nuclei, $^{48}$Ca and $^{90}$Zr. Analyzing the centroid energies of axial breathing modes obtained with the mean--field--based random--phase approximation and with the beyond--mean--field SSRPA model, we estimate the modification (enhancement) of the effective mass which is induced beyond the mean field. This is done by employing a relation, obtained with the Landau's Fermi liquid theory, between the excitation frequency of axial modes to $\sqrt{m/m^*}$, where $m$ ($m^*$) is the bare (effective) mass. Such an enhancement of the effective mass is discussed in connection with the renormalization of single--particle excitation energies generated by the energy--dependent SSRPA self-energy correction. We find that the effective beyond--mean--field compression of the single--particle spectrum produced by the self--energy correction is coherent with the increase of the effective mass estimated from the analysis of axial breathing modes.

nucl-th↗

arXiv2017

Toward a systematic strategy for defining power counting in the construction of the energy density functional theory

We propose a new scheme for constructing an effective-field-theory-based interaction to be used in the energy-density-functional (EDF) theory with specific assumptions for defining a power counting. This procedure is developed through the evaluation of the equation of state (EOS) of symmetric and pure neutron matter going beyond the mean-field scheme and using a functional defined up to next-to-leading order (NLO), that we will call NLO EDF. A Skyrme-like interaction is constructed based on the condition of renormalizibility and on a power counting on $k_F/Λ_{hi}$, where $k_F$ is the Fermi momentum and $Λ_{hi}$ is the breakdown scale of our expansion. To absorb the divergences present in beyond mean-field diagrams, counter interactions are introduced for the NLO EDF and determined through renormalization conditions. In particular, three scenarios are explored and all of them lead to satisfactory results. These counter interactions contain also parameters which do not contribute to the EOS of matter and may eventually be determined through future adjustments to properties of some selected finite nuclei. Our work serves as a simple starting point for constructing a well-defined power counting within the EDF framework.

nucl-th↗

arXiv2017

Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field

Phenomenological effective interactions like Skyrme forces are currently used in mean--field calculations in nuclear physics. Mean--field models have strong analogies with the first order of the perturbative many--body problem and the currently used effective interactions are adjusted at the mean--field level. In this work, we analyze the renormalizability of the nuclear many--body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.

nucl-th↗

arXiv2017

A Lee-Yang--inspired functional with a density--dependent neutron-neutron scattering length

Inspired by the low--density Lee-Yang expansion for the energy of a dilute Fermi gas of density $ρ$ and momentum $k_F$, we introduce here a Skyrme--type functional that contains only $s$-wave terms and provides, at the mean--field level, (i) a satisfactory equation of state for neutron matter from extremely low densities up to densities close to the equilibrium point, and (ii) a good--quality equation of state for symmetric matter at density scales around the saturation point. This is achieved by using a density--dependent neutron-neutron scattering length $a(ρ$) which satisfies the low--density limit (for Fermi momenta going to zero) and has a density dependence tuned in such a way that the low--density constraint $|a(ρ) k_F| \le 1$ is satisfied at all density scales.

nucl-th↗

arXiv2016

From dilute matter to the equilibrium point in the energy--density--functional theory

Due to the large value of the scattering length in nuclear systems, standard density--functional theories based on effective interactions usually fail to reproduce the nuclear Fermi liquid behavior both at very low densities and close to equilibrium. Guided on one side by the success of the Skyrme density functional and, on the other side, by resummation techniques used in Effective Field Theories for systems with large scattering lengths, a new energy--density functional is proposed. This functional, adjusted on microscopic calculations, reproduces the nuclear equations of state of neutron and symmetric matter at various densities. Furthermore, it provides reasonable saturation properties as well as an appropriate density dependence for the symmetry energy.

nucl-th↗

arXiv2016

Second--order equation of state with the Skyrme interaction. Cutoff and dimensional regularization with the inclusion of rearrangement terms

We evaluate the second--order (beyond--mean--field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the zero--range character of this interaction. An adjustment of the force parameters is then performed in both cases to remove any double counting generated by the explicit computation of beyond--mean--field corrections with the Skyrme force. In addition, we include at second order the rearrangement terms associated to the density--dependent part of the Skyrme force and discuss their effect. Sets of parameters are proposed to define new effective forces which are specially designed for second--order calculations in nuclear matter.

nucl-th↗

arXiv2015

Neutron $2p$ and $1f$ spin--orbit splittings in $^{40}$Ca, $^{36}$S, and $^{34}$Si $N=20$ isotones: tensor--induced and pure spin--orbit effects

Neutron $2p$ and $1f$ spin--orbit splittings were recently measured in the isotones $^{37}$S and $^{35}$Si by $(d,p)$ transfer reactions. Values were reported by using the major fragments of the states. An important reduction of the $p$ splitting was observed, from $^{37}$S to $^{35}$Si, associated to a strong modification of the spin--orbit potential in the central region of the nucleus $^{35}$Si. We analyze $2p$ and $1f$ neutron spin--orbit splittings in the $N=20$ isotones $^{40}$Ca, $^{36}$S, and $^{34}$Si. We employ several Skyrme and Gogny interactions, to reliably isolate pure spin--orbit and tensor--induced contributions, within the mean--field approximation. We use interactions (i) without the tensor force; (ii) with the tensor force and with tensor parameters adjusted on top of existing parametrizations; (iii) with the tensor force and with tensor and spin--orbit parameters adjusted simultaneously on top of existing parametrizations. We predict in cases (ii) and (iii) a non negligible reduction of both $p$ and $f$ splittings, associated to neutron--proton tensor effects, from $^{40}$Ca to $^{36}$S. The two splittings are further decreased for the three types of interactions, going from $^{36}$S to $^{34}$Si. This reduction is produced by the spin--orbit force and is not affected by tensor--induced contributions. For both reductions, from $^{40}$Ca to $^{36}$S and from $^{36}$S to $^{34}$Si, we predict in all cases that the modification is more pronounced for $p$ than for $f$ splittings. The measurement of the centroids for neutron $2p$ and $1f$ states in the nuclei $^{36}$S and $^{34}$Si would be interesting to validate this prediction experimentally. We show the importance of using interactions of type (iii), because they provide $p$ and $f$ splittings in the nucleus $^{40}$Ca which are in agreement with the corresponding experimental values.

nucl-th↗

arXiv2015

Nuclear excitations as coupled one and two random--phase--approximation modes

We present an extension of the random--phase approximation (RPA) where the RPA phonons are used as building blocks to construct the excited states. In our model, that we call double RPA (DRPA), we include up to two RPA phonons. This is an approximate and simplified way, with respect to the full second random--phase approximation (SRPA), to extend the RPA by including two particle--two hole configurations. Some limitations of the standard SRPA model, related to the violation of the stability condition, are not encountered in the DRPA. We also verify in this work that the energy--weighted sum rules are satisfied. The DRPA is applied to low--energy modes and giant resonances in the nucleus $^{16}$O. We show that the model (i) produces a global downwards shift of the energies with respect to the RPA spectra; (ii) provides a shift that is however strongly reduced compared to that generated by the standard SRPA. This model represents an alternative way of correcting for the SRPA anomalous energy shift, compared to a recently developed extension of the SRPA, where a subtraction procedure is applied. The DRPA provides results in good agreeement with the experimental energies, with the exception of those low--lying states that have a dominant two particle--two hole nature. For describing such states, higher--order calculations are needed.

nucl-th↗

arXiv2015

Subtraction method in the second random--phase approximation: first applications with a Skyrme energy functional

We make use of a subtraction procedure, introduced to overcome double--counting problems in beyond--mean--field theories, in the second random--phase--approximation (SRPA) for the first time. This procedure guarantees the stability of SRPA (so that all excitation energies are real). We show that the method fits perfectly into nuclear density--functional theory. We illustrate applications to the monopole and quadrupole response and to low--lying $0^+$ and $2^+$ states in the nucleus $^{16}$O. We show that the subtraction procedure leads to: (i) results that are weakly cutoff dependent; (ii) a considerable reduction of the SRPA downwards shift with respect to the random--phase approximation (RPA) spectra (systematically found in all previous applications). This implementation of the SRPA model will allow a reliable analysis of the effects of 2 particle--2 hole configurations ($2p2h$) on the excitation spectra of medium--mass and heavy nuclei.

nucl-th↗

arXiv2013

A microscopic model beyond mean-field: from giant resonances properties to the fit of new effective interactions

A completely microscopic beyond mean-field approach has been elaborated to overcome some intrinsic limitations of self-consistent mean-field schemes applied to nuclear systems, such as the incapability to produce some properties of single-particle states (e.g. spectroscopic factors), as well as of collective states (e.g. their damping width and their gamma decay to the ground state or to low lying states). Since commonly used effective interactions are fitted at the mean-field level, one should aim at refitting them including the desired beyond mean-field contributions in the refitting procedure. If zero-range interactions are used, divergences arise. We present some steps towards the refitting of Skyrme interactions, for its application in finite nuclei.

nucl-th↗

arXiv2013

A beyond-mean-field example with zero-range effective interactions in infinite nuclear matter

Zero-range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond- mean-field models, an artificial ultraviolet divergence is generated by the zero-range of the interaction. We analyze this problem in symmetric nuclear matter with the t0-t3 Skyrme model. In this case, the second-order energy correction diverges linearly with the momentum cutoff. After that, we extend the work to the case of nuclear matter with the full Skyrme interaction. A strong divergence related to the velocity-dependent terms of the interaction is obtained. Moreover, a global fit can be simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratios. These results pave the way for applications to finite nuclei in the framework of beyond mean-field theories.

nucl-th↗

arXiv2012

Second random-phase approximation with the Gogny force. First applications

We present the first applications of the second random-phase-approximation model with the finite-range Gogny interaction. We discuss the advantages of using such an interaction in this type of calculations where 2 particle-2 hole configurations are included. The results found in the present work confirm the well known general features of the second random-phase approximation spectra: we find a large shift, several MeV, of the response centroids to lower energies with respect to the corresponding random-phase-approximation values. As known, these results indicate that the effects of the 1 particle-1 hole/2 particle-2 hole and 2 particle-2 hole/2 particle-2 hole couplings are important. It has been found that the changes of the strength distributions with respect to the standard random-phase-approximation results are particularly large in the present case. This important effect is due to some large neutron-proton matrix elements of the interaction and indicates that these matrix elements (which do not contribute in the mean-field calculations employed in the conventional fit procedures of the force parameters) should be carefully constrained to perform calculations

nucl-th↗

arXiv2012

Cosmological constraints from supernova data set with corrected redshift

Observations of distant type Ia supernovae (SNe Ia), used as standard candles, support the notion that the Cosmos is filled with a mysterious form of energy, the dark energy. The constraints on cosmological parameters derived from data of SNe Ia and the measurements of the cosmic microwave background anisotropies indicate that the dark energy amounts to roughly 70% of all the energy contained in the Universe. In the hypothesis of a flat Universe, we investigate if the dark energy is really required in order to explain the SNe Ia experimental data, and, in this case, how much of such unknown energy is actually deduced from the analysis of these data and must be introduced in the LambdaCDM model of cosmology. In particular we are interested in verifying if the Einstein-de Sitter model of the expanding Universe is really to be ruled out. By using a fitting procedure based on the Newton method search for a minimum, we reanalyzed the "Union compilation" reported by Kowalski et al. (2008) formed by 307 SNe, obtaining a very different estimate of the dark energy, that is roughly 60%. Furthermore, in order to balance the correction of the apparent magnitude of SNe Ia, due to the dilation or stretching of the corresponding light curve width, we introduce a suitable modified redsfhit. Taking into account this correction, we refitted the Union compilation dataset after a selection cut. The main result that emerges from our analysis is that the values of Omega_m and Omega_Lambda strongly depend on the fitting procedure and the selected sample. In particular, the constraint we obtain on the mass density, normalized by the critical mass density, is Omega_m = 0.7 for a sample of 252, and Omega_m = 1 for a sample of 242 SNe Ia respectively. The latter case does not imply the existence of any additional form of dark energy.

astro-ph.CO↗

arXiv2012

Pair-transfer probability in open- and closed-shell Sn isotopes

Approximations made to estimate two-nucleon transfer probabilities in ground-state to ground-state transitions and physical interpretation of these probabilities are discussed. Probabilities are often calculated by approximating both ground states, of the initial nucleus A and of the final nucleus A\pm 2 by the same quasiparticle vacuum. We analyze two improvements of this approach. First, the effect of using two different ground states with average numbers of particles A and A\pm2 is quantified. Second, by using projection techniques, the role of particle number restoration is analyzed. Our analysis shows that the improved treatment plays a role close to magicity, leading to an enhancement of the pair-transfer probability. In mid-shell regions, part of the error made by approximating the initial and final ground states by a single vacuum is compensated by projecting onto good particle number. Surface effects are analyzed by using pairing interactions with a different volume-to-surface mixing. Finally, a simple expression of the pair-transfer probability is given in terms of occupation probabilities in the canonical basis. We show that, in the canonical basis formulation, surface effects which are visible in the transfer probability are related to the fragmentation of single-particle occupancies close to the Fermi energy. This provides a complementary interpretation with respect to the standard quasiparticle representation where surface effects are generated by the integrated radial profiles of the contributing wave functions.

nucl-th↗