arXiv subjects

M. Sambataro

Publications and source records attributed to M. Sambataro.

At least 19 recordsLinked to original sources

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

$α$-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

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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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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arXiv2016

Isoscalar-isovector proton-neutron pairing and quartet condensation in N=Z nuclei

We show that the correlations generated in the ground state of $N=Z$ nuclei by the isovector and isoscalar pairing forces can be treated with high precision as a condensate of alpha-like quartets. To treat these correlations, the quartet condensation model (QCM) is extended to the treatment of spherically symmetric isovector $(T=1,J=0)$ and isoscalar $(T=0,J=1)$ pairing forces . Within QCM we discuss the competition between $T=1$ and $T=0$ pairing correlations in the case of a two-level model and for $N=Z$ nuclei with nucleons moving in the open shells above $^{16}$O, $^{40}$Ca and $^{100}$Sn. We show that in $N=Z$ systems isovector and isoscalar proton-neutron pairing correlations always coexist.

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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.

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arXiv2015

Quarteting and spin-aligned proton-neutron pairs in heavy N=Z nuclei

We analyze the role of maximally aligned isoscalar pairs in heavy $N=Z$ nuclei by employing a formalism of quartets. Quartets are superpositions of two neutrons and two protons coupled to total isospin $T=0$ and given $J$. The study is focused on the contribution of spin-aligned pairs carrying the angular momentum $J=9$ to the structure of $^{96}$Cd and $^{92}$Pd. We show that the role played by the $J=9$ pairs is quite sensitive to the model space and, in particular, it decreases considerably by passing from the simple $0g_{9/2}$ space to the more complete $1p_{1/2}$,$1p_{3/2}$,$0f_{5/2}$,$0g_{9/2}$ space. In the latter case the description of these nuclei in terms of only spin-aligned $J=9$ pairs turns out to be unsatisfactory while an important contribution, particularly in the ground state, is seen to arise from isovector $J=0$ and isoscalar $J=1$ pairs. Thus, contrary to previous studies, we find no compelling evidence of a spin-aligned pairing phase in $^{92}$Pd.

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arXiv2015

Four-body correlations in nuclei

Low-energy spectra of 4$n$ nuclei are described with high accuracy in terms of four-body correlated structures ("quartets"). The states of all $N\geq Z$ nuclei belonging to the $A=24$ isobaric chain are represented as a superposition of two-quartet states, with quartets being characterized by isospin $T$ and angular momentum $J$. These quartets are assumed to be those describing the lowest states in $^{20}$Ne ($T_z$=0), $^{20}$F ($T_z$=1) and $^{20}$O ($T_z$=2). We find that the spectrum of the self-conjugate nucleus $^{24}$Mg can be well reproduced in terms of $T$=0 quartets only and that, among these, the $J$=0 quartet plays by far the leading role in the structure of the ground state. The same conclusion is drawn in the case of the three-quartet $N=Z$ nucleus $^{28}$Si. As an application of the quartet formalism to nuclei not confined to the $sd$ shell, we provide a description of the low-lying spectrum of the proton-rich $^{92}$Pd. The results achieved indicate that, in 4$n$ nuclei, four-body degrees of freedom are more important and more general than usually expected.

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arXiv2014

Isoscalar and isovector pairing in a formalism of quartets

Isoscalar (T=0,J=1) and isovector (T=1,J=0) pairing correlations in the ground state of self-conjugate nuclei are treated in terms of alpha-like quartets built by two protons and two neutrons coupled to total isospin T=0 and total angular momentum J=0. Quartets are constructed dynamically via an iterative variational procedure and the ground state is represented as a product of such quartets. It is shown that the quartet formalism describes accurately the ground state energies of realistic isovector plus isoscalar pairing Hamiltonians in nuclei with valence particles outside the 16O, 40Ca and 100Sn cores. Within the quartet formalism we analyse the competition between isovector and isoscalar pairing correlations and find that for nuclei with the valence nucleons above the cores 40Ca and 100Sn the isovector correlations account for the largest fraction of the total pairing correlations. This is not the case for sd-shell nuclei for which isoscalar correlations prevail. Contrary to many mean-field studies, isovector and isoscalar pairing correlations mix significantly in the quartet approach.

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arXiv2013

Isovector pairing in a formalism of quartets for N=Z nuclei

We describe the ground state of the isovector pairing Hamiltonian in self-conjugate nuclei by a product of collective quartets of different structure built from two neutrons and two protons coupled to total isospin T=0. The structure of the collective quartets is determined by an iterative variational procedure based on a sequence of diagonalizations of the pairing Hamiltonian in spaces of reduced size. The accuracy of the quartet model is tested for N=Z nuclei carrying valence nucleons outside the $^{16}$O, $^{40}$Ca, and $^{100}$Sn cores. The comparison with the exact solutions of the pairing Hamiltonian, obtained by shell model diagonalization, shows that the quartet model is able to describe the isovector pairing energy with very high precision. The predictions of the quartet model are also compared to those of the simpler quartet condensation model in which all the collective quartets are assumed to be identical.

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arXiv2013

Treatment of like-particle pairing with quartets

The ground state correlations induced by a general pairing Hamiltonian in a finite system of like fermions are described in terms of four-body correlated structures (quartets). These are real superpositions of products of two pairs of particles in time-reversed states. Quartets are determined variationally through an iterative sequence of diagonalizations of the Hamiltonian in restricted model spaces and are, in principle, all distinct from one another. The ground state is represented as a product of quartets to which, depending on the number of particles (supposed to be even, in any case), an extra collective pair is added. The extra pair is also determined variationally. In case of pairing in a spherically symmetric mean field, both the quartets and the extra pair (if any) are characterized by a total angular momentum J=0. Realistic applications of the quartet formalism are carried out for the Sn isotopes with the valence neutrons in the 50-82 neutron shell. Exact ground state correlation energies, occupation numbers and pair transfer matrix elements are reproduced to a very high degree of precision. The formalism also lends itself to a straightforward and accurate description of the lowest seniority 0 and 2 excited states of the pairing Hamiltonian. A simplified representation of the ground state as a product of identical quartets is eventually discussed and found to improve considerably upon the more traditional particle-number projected-BCS approach.

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arXiv2012

Multipair approach to pairing in nuclei

The ground state of a general pairing Hamiltonian for a finite nuclear system is constructed as a product of collective, real, distinct pairs. These are determined sequentially via an iterative variational procedure that resorts to diagonalizations of the Hamiltonian in restricted model spaces. Different applications of the method are provided that include comparisons with exact and projected BCS results. The quantities that are examined are correlation energies, occupation numbers and pair transfer matrix elements. In a first application within the picket-fence model, the method is seen to generate the exact ground state for pairing strengths confined in a given range. Further applications of the method concern pairing in spherically symmetric mean fields and include simple exactly solvable models as well as some realistic calculations for middle-shell Sn isotopes. In the latter applications, two different ways of defining the pairs are examined: either with J=0 or with no well-defined angular momentum. The second choice reveals to be more effective leading, under some circumstances, to solutions that are basically exact.

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