arXiv subjects

Danilo Gambacurta

Publications and source records attributed to Danilo Gambacurta.

18 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 $β$-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 $β$-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 $β$-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 $β$-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 $β$-window, resulting in lower $β$ half-lives with respect to the RPA ones.

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arXiv2025

Heavy Ion Double Charge Exchange Reactions as Probes for Two-Body Transition Densities

Collisional heavy ion double charge exchange (DCE) reactions, induced by second order nucleon-nucleon interactions, are shown to provide access to the two-body transition densities of the complementary DCE transitions in the interacting nuclei. Corresponding two-body operators are introduced, treating the second order distorted wave reaction amplitude in the s-channel interaction form. The theoretical results are applied to the reaction $^{18}O+{}^{76}Se\to {} ^{18}Ne+{}^{76}Ge$ at $T_{lab}=270$~MeV, being $^{76}Ge$ a candidate for neutrino--less double beta decay.

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arXiv2024

Induced Isotensor Interactions in Heavy-Ion Double-Charge-Exchange Reactions and the Role of Initial and Final State Interactions

The role of initial state (ISI) and final state (FSI) ion-ion interactions in heavy-ion double-charge-exchange (DCE) reactions $A(Z,N)\to A(Z\pm 2,N\mp 2)$ are studied for double single-charge-exchange (DSCE) reactions given by sequential actions of the isovector nucleon-nucleon (NN) T-matrix. In momentum representation, the second-order DSCE reaction amplitude is shown to be given in factorized form by projectile and target nuclear matrix elements and a reaction kernel containing ISI and FSI. Expanding the intermediate propagator in a Taylor series with respect to auxiliary energy allows us to perform the summation in the leading-order term over intermediate nuclear states in closure approximation. %Please ensure meaning has been retained - corrected HL. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the $n^2p^{-2}$ and $p^2n^{-2}$ DCE transitions in the projectile and the target nucleus, respectively. %Please ensure meaning has been retained - corrected HL. A surprising result is that the intermediate propagation induces correlations between the transition vertices, showing that DSCE reactions are a two-nucleon process that resembles a system of interacting spin-isospin dipoles. Transformation of the DSCE NN T-matrix interactions from the reaction theoretical t-channel form to the s-channel operator structure required for spectroscopic purposes is elaborated in detail, showing that, in general, a rich spectrum of spin scalar, spin vector and higher-rank spin tensor multipole transitions will contribute to a DSCE reaction. Similarities (and differences) to two-neutrino double-beta decay (DBD) are discussed. ISI/FSI distortion and absorption effects are illustrated in black sphere approximation and in an illustrative application to data.

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arXiv2024

Theory of Majorana-Type Heavy Ion Double Charge Exchange Reactions by Pion--Nucleon Isotensor Interactions

The theory of heavy ion double charge exchange (DCE) reactions proceeding by effective rank-2 isotensor interactions is presented. Virtual pion--nucleon charge exchange interactions are investigated as the source for induced isotensor interactions, giving rise to the Majorana DCE (MDCE) reaction mechanism. MDCE is of a generic character, proceeding through pairs of complementary ($π^\pm,π^\mp$) reactions in the projectile and target nucleus. The dynamics of the elementary processes is discussed, where the excitation of pion--nucleon resonances are of central importance. Investigations of initial and final state ion--ion interactions show that these effects are acting as vertex renormalizations. In closure approximation, well justified by the finite pion mass, the second-order transition matrix elements reduce to pion potentials and effective two-body isotensor DCE interactions, giving rise also to two-body correlations in either of the participating nuclei. Connections to neutrinoless Majorana double beta decay (MDBD) are elucidated at various levels of the dynamics, from the underlying fundamental electro-weak and QCD scales to the physical scales of nuclear MDBD and MDCE physics. It is pointed out that heavy ion MDCE reactions may also proceed by competing electro-weak charge exchange processes, leading to lepton MDCE by electrons, positrons, and neutrinos.

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arXiv2024

Formal Theory of Heavy Ion Double Charge Exchange Reactions

The theory of heavy ion double charge exchange (DCE) reactions $A(Z,N)\to A(Z\pm 2,N\mp 2)$ is recapitulated emphasizing the role of Double Single Charge Exchange (DSCE) and pion-nucleon Majorana DCE (MDCE) reactions. DSCE reactions are of second--order distorted wave character, mediated by isovector nucleon-nucleon (NN) interactions. The DSCE response functions resemble the nuclear matrix elements (NME) of $2ν2β$ decay. The MDCE process proceeds by a dynamically generated effective rank-2 isotensor interaction, defined by off--shell pion--nucleon DCE scattering. In closure approximation pion potentials and two--nucleon correlations are obtained, similar to the neutrino potentials and the intranuclear exchange of Majorana neutrinos in $0ν2 β$ Majorana double beta decay (MDBD).

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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

Nuclear Matrix Elements for Heavy Ion Sequential Double Charge Exchange Reactions

The theoretical approach to a sequential heavy ion double charge exchange reaction is presented. A brief introduction into the formal theory of second-order nuclear reactions and their application to Double Single Charge Exchange (DSCE) reactions by distorted wave theory is given, thereby completing the theoretical background to our recent work [1]. Formally, the DSCE reaction amplitudes are shown to be separable into superpositions of distortion factors, accounting for initial and final state ion--ion interactions, and nuclear matrix elements. A broad space is given to the construction of nuclear DSCE response functions on the basis of polarization propagator theory. The nuclear response tensors resemble the nuclear matrix elements of $2νββ$ decay in structure but contain in general a considerable more complex multipole and spin structure. The QRPA theory is used to derive explicit expressions for nuclear matrix elements (NMEs). The differences between the NME of the first and the second interaction vertexes in a DSCE reaction is elucidated. Reduction schemes for the transition form factors are discussed by investigating the closure approximation and the momentum structure of form factors. DSCE unit strength cross sections are derived.

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arXiv2020

Isoscalar monopole and quadrupole modes in Mo isotopes: microscopic analysis

The recent RCNP $(α, α')$ data on the Isoscalar Giant Monopole Resonance (ISGMR) and Isoscalar Giant Quadrupole Resonance (ISGQR) in $^{92,94,96,98,100}$Mo are analyzed within a fully self-consistent Quasiparticle Random Phase Approximation (QRPA) approach with Skyrme interactions, in which pairing correlations and possible axial deformations are taken into account. The Skyrme sets SkM*, SLy6, SVbas and SkP$^δ$, that explore a diversity of nuclear matter properties, are used. We discuss the connection between the line shape of the monopole strength ISGMR and the deformation-induced coupling between the ISGMR and the $K=0$ branch of the ISGQR. The ISGMR centroid energy is best described by the force SkP$^δ$, having a low incompressibility $K_{\infty}$ = 202 MeV. The ISGQR data are better reproduced by SVbas, that has large isoscalar effective mass $m^*/m$ = 0.9. The need of describing simultaneously the ISGMR and ISGQR data is stressed, with the requirement of suitable values of $K_\infty$ and $m^*/m$. Possible extensions of the QRPA to deal with soft systems are also envisaged.

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arXiv2019

Nuclear incompressibility from spherical and deformed nuclei

We present an analysis based on the deformed Quasi Particle Random Phase Approximation, on top of a deformed Hartree-Fock-Bogoliubov description of the ground state, aimed at studying the isoscalar monopole and quadrupole response in a deformed nucleus. This analysis is motivated by the need of understanding the coupling between the two modes and how it might affect the extraction of the nuclear incompressibility from the monopole distribution. After discussing this motivation, we present the main ingredients of our theoretical framework, and we show some results obtained with the SLy4 and SkM$^{*}$ interactions for the nucleus ${}^{24}$Mg.

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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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arXiv2013

Pairing and specific heat in hot nuclei

The thermodynamics of pairing phase-transition in nuclei is studied in the canonical ensemble and treating the pairing correlations in a finite-temperature variation after projection BCS approach (FT-VAP). Due to the restoration of particle number conservation, the pairing gap and the specific heat calculated in the FT-VAP approach vary smoothly with the temperature, indicating a gradual transition from the superfluid to the normal phase, as expected in finite systems. We have checked that the predictions of the FT-VAP approach are very accurate when compared to the results obtained by an exact diagonalization of the pairing Hamiltonian. The influence of pairing correlations on specific heat is analysed for the isotopes $^{161,162}$Dy and $^{171,172}$Yb. It is shown that the FT-VAP approach, applied with a level density provided by mean field calculations and supplemented, at high energies, by the level density of the back-shifted Fermi gas model, can approximate reasonably well the main properties of specific heat extracted from experimental data. However, the detailed shape of the calculated specific heat is rather sensitive to the assumption made for the mean field.

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arXiv2013

Quantal corrections to mean-field dynamics including pairing

Extending the stochastic mean-field model by including pairing, an approach is proposed for describing evolutions of complex many-body systems in terms of an ensemble of Time-Dependent Hartree-Fock Bogoliubov trajectories which is determined by incorporating fluctuations in the initial state. Non-linear evolution of the initial fluctuations provides an approximate description of quantal correlations and fluctuations of collective observables. Since the initial-state fluctuations break the particle-number symmetry, the dynamical description in which pairing correlations play a crucial role is greatly improved as compare to the mean-field evolution. The approach is illustrated for a system of particles governed by a pairing Hamiltonian.

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arXiv2012

On the description of two-particle transfer in superfluid systems

Exact results of pair transfer probabilities for the Richardson model with equidistant or random level spacing are presented. The results are then compared either to particle-particle random phase approximation (ppRPA) in the normal phase or quasi-particle random phase approximation (QRPA) in the superfluid phase. We show that both ppRPA and QRPA are globally well reproducing the exact case although some differences are seen in the superfluid case. In particular the QRPA overestimates the pair transfer probabilities to excited states in the vicinity of the normal-superfluid phase transition, which might explain the difficult in detecting collective pairing phenomena as for example the Giant Pairing Vibration. The shortcoming of QRPA can be traced back to the breaking of particle number that is used to incorporate pairing. A method, based on direct diagonalization of the Hamiltonian in the space of two quasi-particle projected onto good particle number is shown to improve the description of pair transfer probabilities in superfluid systems.

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arXiv2012

Projected Quasi-particle Perturbation theory

The BCS and/or HFB theories are extended by treating the effect of four quasi-particle states perturbatively. The approach is tested on the pairing hamiltonian, showing that it combines the advantage of standard perturbation theory valid at low pairing strength and of non-perturbative approaches breaking particle number valid at higher pairing strength. Including the restoration of particle number, further improves the description of pairing correlation. In the presented test, the agreement between the exact solution and the combined perturbative + projection is almost perfect. The proposed method scales friendly when the number of particles increases and provides a simple alternative to other more complicated approaches.

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arXiv2012

Thermodynamics of small superconductors with fixed particle number

The Variation After Projection approach is applied for the first time to the pairing hamiltonian to describe the thermodynamics of small systems with fixed particle number. The minimization of the free energy is made by a direct diagonalization of the entropy. The Variation After Projection applied at finite temperature provides a perfect reproduction of the exact canonical properties of odd or even systems from very low to high temperature.

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arXiv2010

Residual interaction in Second RPA with density-dependent forces. Rearrangement terms

We derive the expression for the residual interaction to be used in the framework of the Second RPA with density-dependent forces. The adopted procedure is based on a variational approach. It is found that the residual interaction to be used in RPA and beyond RPA matrix elements is not the same as far as the rearrangement terms are concerned. A detailed derivation of the matrix elements coupling 1 particle-1 hole with 2 particle-2 hole and 2 particle-2 hole among themselves has been done and the corresponding rearrangement terms are shown here. This formal result indicates that both the currently used prescriptions, namely (i) using the same type of rearrangement terms in RPA and beyond RPA matrix elements or (ii) neglecting the rearrangement terms in beyond RPA matrix elements, are not correct.

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