arXiv subjects

N. Sandulescu

Publications and source records attributed to N. Sandulescu.

At least 19 recordsLinked to original sources

arXiv2026

Anomalous large-angle $\alpha$-scattering in a single-folding model with microscopic densities

We investigate anomalous large-angle scattering (ALAS) of $\alpha$-particles from $N=Z$ nuclei within the framework of the single-folding model. Differential cross sections are calculated by folding the $\alpha$-nucleon interaction with nuclear density distributions obtained from both relativistic and non-relativistic mean-field models. The folding procedure employs a Gaussian-form $\alpha$-nucleon interaction, with its energy dependence and range constrained by previous theoretical studies. Our results show that ALAS in $sd$-shell nuclei is reasonably well reproduced using the microscopic densities together with an $\alpha$-nucleon interaction characterized by a unified parameter set, in which only two parameters vary with the mass number.

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arXiv2026

Charge radii of Sn isotopes in the relativistic mean field approximation

The kink observed in the nuclear charge radius of Sn isotopes around neutron number $N = 82$ is investigated within the relativistic mean-field (RMF) framework using the NL3$^*$ parameter set. It is shown that the small components of the Dirac spinors for the neutron single-particle states near the Fermi level play a crucial role in forming the kink through their contribution to the proton central potential. In particular, the significant differences between the radial parts of the small components of spin-orbit partner states make neutrons with $j = l - 1/2$ more efficient in increasing the nuclear charge radius than those with $j = l + 1/2$. However, the effect induced by the small components alone does not fully account for the magnitude of the kink observed in Sn isotopes.

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arXiv2026

Proton-Neutron Pairing in N=Z Nuclei within the Quark-Meson-Coupling Energy Density Functional

We investigate the impact of isovector and isoscalar proton-neutron pairing correlations on the ground-state properties of even-even N=Z nuclei with mass numbers between A=16 and A=120. Nuclear mean fields are generated using the quark-meson coupling (QMC) energy density functional, while pairing correlations are treated within the quartet condensation model (QCM). Ground-state energies are obtained from axially deformed, self-consistent QMC+QCM calculations employing a zero-range pairing interaction with a density-dependent term derived consistently within the QMC framework. We show that proton-neutron pairing provides a significant contribution to the binding energies of N=Z nuclei, leading to improved agreement with experimental data.

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arXiv2022

Excited states of zero seniority based on a pair condensate

We study the excited states of zero seniority for various like-particle systems interacting by pairing forces and by general two-body interactions. We consider two types of excitations, generated from a ground state described by a pair condensate. One type is obtained by breaking a pair from the ground state condensate and replacing it by "excited" collective pairs built on time-reversed single-particle orbits. The second type of zero seniority excited states is described by a condensate of identical excited pairs. The structure of these excited states is analysed for the picked fence model and for the valence neutrons of $^{108}$Sn. For a state-depending pairing interaction, the first type of excited states agree well with the J=0 states which are known in $^{108}$Sn. At the same time, these states can be also associated unambiguously with those exact states which are the closest in energy to the experimental levels. The states corresponding to the excited pair condensate appear at low energies, around the energy of the second excited state of the first type, and they do not have a simple correspondence with exact eigenstates. However, at a much higher excitation energy there is an exact state which is similar in structure to an EPC state. It is shown that this EPC state has the features of a giant pairing vibration.

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arXiv2022

Coexistence of quartets and pairs in even-even $N>Z$ nuclei

We analyse the structure of the ground states of even-even $N>Z$ nuclei with nucleons moving in the same major shell and interacting via realistic two-body forces of shell-model type. We express the ground states of these nuclei as a product of a quartet term, which represents the $N = Z$ subsystem, and a pair condensate built with the excess neutrons. The accuracy of this approximation is discussed for nuclei with valence nucleons in the $sd$ and $pf$ major shells.

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arXiv2022

Intrinsic states of deformed N=Z nuclei in a quartet formalism

The band structure of N=Z nuclei is constructed from intrinsic states defined in terms of quartets. The simplest of these states is a condensate of collective quartets with isospin T=0. The other intrinsic states are built by promoting one quartet of the condensate to an excited T=0 configuration. From these intrinsic states, by angular momentum projection, band structures are generated that approximate well the experimental ones. The projected states also reproduce to a very good extent the spectra resulting from configuration interaction calculations based on the same quartets forming the intrinsic states. These results show that the quartet-based intrinsic states provide the appropriate framework to understand in a simple and intuitive manner the emergence of band-like structures in N=Z nuclei.

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arXiv2021

Band-like structures and quartets in deformed N=Z nuclei

We provide a description of deformed $N=Z$ nuclei in a formalism of $α$-like quartets. Quartets are constructed variationally by resorting to the use of proper intrinsic states. Various types of intrinsic states are introduced which generate different sets of quartets for a given nucleus. Energy spectra are generated via configuration-iteraction calculations in the spaces built with these quartets. The approach has been applied to $^{24}$Mg and $^{28}$Si in the $sd$ shell and to $^{48}$Cr in the $pf$ shell. In all cases a good description of the low-lying spectra has been achieved. As a peculiarity of the approach, a close correspondence is observed between the various sets of quartets employed and the occurrence of well defined band-like structures in the spectra of the systems under study.

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arXiv2021

Proton-neutron pairing and binding energies of nuclei close to N=Z line

We analyse the contribution of isovector and isoscalar proton-neutron pairing to the binding energies of even-even nuclei with $N-Z=0,2,4$ and atomic mass $20 < A <100$. The binding energies are calculated in the mean-field approach by coupling a Skyrme-type functional to an isovector-isoscalar pairing force of zero range. The latter is treated in the framework of quartet condensation model (QCM), which conserves exactly the particle number and the isospin. The interdependence of pairing and deformation is taken into account by performing self-consistent Skyrme-HF+QCM calculations in the intrinsic system. It is shown that the binding energies are not changing much when the isoscalar pairing is switched on. This fact is related to the off-diagonal matrix elements of the pairing force, which is less attractive for the isoscalar force, and to the competition between the isoscalar and isovector pairing channels.

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arXiv2021

$α$-like quartetting in the excited states of proton-neutron pairing Hamiltonians

Previous studies have shown that the ground state of systems of nucleons composed by an equal number of protons and neutrons interacting via proton-neutron pairing forces can be described accurately by a condensate of $α$-like quartets. Here we extend these studies to the low-lowing excited states of these systems and show that these states can be accurately described by breaking a quartet from the ground state condensate and replacing it with an "excited" quartet. This approach, which is analogous to the one-broken-pair approximation employed for like-particle pairing, is analysed for various isovector and isovector-isoscalar pairing

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arXiv2020

Bridging the quartet and pair pictures of isovector proton-neutron pairing

The formal implications of a quartet coherent state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many body correlation functions. The intrinsic structure of the quartet coherent state is detailed, as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations.

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arXiv2020

Quartet condensation induced by the isovector pairing force

The phenomenon of quartet condensation in the ground state of an isovector pairing Hamiltonian for an even-even $N=Z$ system is investigated. For this purpose we follow the evolution of the ground state from an unperturbed regime up to a strongly interacting one in a formalism of collective pairs. These pairs are those resulting from the diagonalization of the pairing Hamiltonian in a space of two particles coupled to isospin $T=1$. The ground state is found to rapidly evolve from a product of distinct $T=0$ quartets, each one formed by two of the above pairs, to a condensate of identical quartets built only with the pair corresponding to the lowest energy. This finding establishes a link between the complicated structure of the exact ground state and the simple approximation scheme of the Quartet Condensation Model. The mechanism at the basis of this quartet condensation turns out to be the same which is responsible for the development of a pair condensate in the ground state of a like-particle pairing Hamiltonian.

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arXiv2019

Exact T=0 Eigenstates of the Isovector Pairing Hamiltonian

We derive the exact $T=0$ seniority-zero eigenstates of the isovector pairing Hamiltonian for an even number of protons and neutrons. Nucleons are supposed to be distributed over a set of non-degenerate levels and to interact through a pairing force with constant strength. We show that these eigenstates (and among them, in particular, the ground state) are linear superpositions of products of $T=1$ collective pairs arranged into $T=0$ quartets. This grouping of protons and neutrons first into $T=1$ collective pairs and then into $T=0$ quartets represents the distinctive feature of these eigenstates. This work highlights, for the first time on the grounds of the analytic expression of its eigenstates, the key role played by the isovector pairing force in the phenomenon of nuclear quarteting.

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arXiv2018

Quartet structure of $N=Z$ nuclei in a boson formalism: the case of $^{28}$Si

The structure of the $N=Z$ nucleus $^{28}$Si is studied by resorting to an IBM-type formalism with $s$ and $d$ bosons representing isospin $T=0$ and angular momentum $J=0$ and $J=2$ quartets, respectively. $T=0$ quartets are four-body correlated structures formed by two protons and two neutrons. The microscopic nature of the quartet bosons, meant as images of the fermionic quartets, is investigated by making use of a mapping procedure and is supported by the close resemblance between the phenomenological and microscopically derived Hamiltonians. The ground state band and two low-lying side bands, a $β$ and a $γ$ band, together with all known $E2$ transitions and quadrupole moments associated with these states are well reproduced by the model. An analysis of the potential energy surface places $^{28}$Si, only known case so far, at the critical point of the U(5)-$\overline{\rm SU(3)}$ transition of the IBM structural diagram.

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arXiv2018

Isovector and isoscalar proton-neutron pairing in $N>Z$ nuclei

We propose a particle number conserving formalism for the treatment of isovector-isoscalar pairing in nuclei with $N>Z$. The ground state of the pairing Hamiltonian is described by a quartet condensate to which is appended a pair condensate formed by the neutrons in excess. The quartets are built by two isovector pairs coupled to the total isospin $T=0$ and two collective isoscalar proton-neutron pairs. To probe this ansatz for the ground state we performed calculations for $N>Z$ nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. The calculations are done with two pairing interactions, one state-independent and the other of zero range, which are supposed to scatter pairs in time-revered orbits. It is proven that the ground state correlation energies calculated within this approach are very close to the exact results provided by the diagonalization of the pairing Hamiltonian. Based on this formalism we have shown that moving away of N=Z line, both the isoscalar and the isovector proton-neutron pairing correlations remain significant and that they cannot be treated accurately by models based on a proton-neutron pair condensate.

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arXiv2018

Localization of pairing correlations in nuclei within relativistic mean field models

We analyze the localization properties of two-body correlations induced by pairing in the framework of relativistic mean field (RMF) models. The spatial properties of two-body correlations are studied for the pairing tensor in coordinate space and for the Cooper pair wave function. The calculations are performed both with Relativistic-Hatree-Bogoliubov (RHB) and RMF+Projected-BCS (PBCS) models and taking as examples the nuclei $^{66}$Ni, $^{124}$Sn and $^{200}$Pb. It is shown that the coherence length have the same pattern as in previous non-relativistic HFB calculations, i.e., it is maximum in the interior of the nucleus and drops to a minimum in the surface region. In the framework of RMF+PBCS we have also analysed, for the particular case of $^{120}$Sn, the dependence of the coherence length on the intensity of the pairing force. This analysis indicates that pairing is reducing the coherence length by about 25-30 $\%$ compared to the RMF limit.

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arXiv2017

Isovector and isoscalar pairing in odd-odd $N=Z$ nuclei within a quartet approach

The quartet condensation model (QCM) is extended for the treatment of isovector and isoscalar pairing in odd-odd N=Z nuclei. In the extended QCM approach the lowest states of isospin T=1 and T=0 in odd-odd nuclei are described variationally by trial functions composed by a proton-neutron pair appended to a condensate of 4-body operators. The latter are taken as a linear superposition of an isovector quartet, built by two isovector pairs coupled to the total isospin T=0, and two collective isoscalar pairs. In all pairs the nucleons are distributed in time-reversed single-particle states of axial symmetry. The accuracy of the trial functions is tested for realistic pairing Hamiltonians and odd-odd N=Z nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. It is shown that the extended QCM approach is able to predict with high accuracy the energies of the lowest T=0 and T=1 states. The present calculations indicate that in these states the isovector and the isoscalar pairing correlations coexist together, with the former playing a dominant role.

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arXiv2017

Quartet correlations in N=Z nuclei induced by realistic two-body interactions

Two variational quartet models previously employed in a treatment of pairing forces are extended to the case of a general two-body interaction. One model approximates the nuclear states as a condensate of identical quartets with angular momentum $J=0$ and isospin $T=0$ while the other let these quartets to be all different from each other. With these models we investigate the role of alpha-like quartet correlations both in the ground state and in the lowest $J=0$, $T=0$ excited states of even-even $N=Z$ nuclei in the $sd$-shell. We show that the ground state correlations of these nuclei can be described to a good extent in terms of a condensate of alpha-like quartets. This turns out to be especially the case for the nucleus $^{32}$S for which the overlap between this condensate and the shell model wave function is found close to one. In the same nucleus, a similar overlap is found also in the case of the first excited $0^+$ state. No clear correspondence is observed instead between the second excited states of the quartet models and the shell model eigenstates in all the cases examined.

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arXiv2016

Quartetting in odd-odd self-conjugate nuclei

We provide a description of odd-odd self-conjugate nuclei in the sd shell in a formalism of collective quartets and pairs. Quartets are four-body structures carrying isospin T=0 while pairs can have either T=0 or T=1. Both quartets and pairs are labeled by the angular momentum J and they are chosen so as to describe the lowest states of 20Ne (quartets) and the lowest T=0 and T=1 states of 18F (pairs). We carry out configuration interaction calculations in spaces built by one quartet and one pair for 22Na and by two quartets and one pair for 26Al. The spectra that are generated are in good agreement with the shell model and experimental ones. These calculations confirm the relevance of quartetting in the structure of N=Z nuclei that had already emerged in previous studies of the even-even systems and highlight the role of J>0 quartets in the composition of the odd-odd spectra.

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