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A. P. Zuker

Publications and source records attributed to A. P. Zuker.

At least 19 recordsLinked to original sources
arXiv2020

Quadrupole dominance in the light Sn and in the Cd isotopes

[Background] The BE2 rates of the Sn isotopes for $N\le 64$ exhibit enhancements hitherto unexplained. The same is true for the Cd isotopes. [Purpose] Describe the electromagnetic properties of the Sn and Cd isotopes [Method] Shell model calculations with a minimally renormalized realistic interaction, supplemented by Quasi and Pseudo-SU3 symmetries and Nilsson-SU3 selfconsistent calculations. [Results for $N\le 64$] Shell model calculations with the neutron effective charge as single free parameter describe well the BE2(2>0) and BE2(4>2) rates for $N\le 64$ in the Cd and Sn isotopes. The former exhibit weak permanent deformation corroborating the prediction of a Pseudo-SU3 symmetry, which remains of heuristic value in the latter, where the pairing force erodes the quadrupole dominance. Calculations in $10^7$ and $10^{10}$-dimensional spaces exhibit almost identical patterns: A vindication of the shell model. [Results for $N\ge 64$] Nilsson-SU3 calculations describe BE2 patterns in [112-120]Cd and [116-118]Sn isotopes having sizable quadrupole moment of non-rotational origin denoted as q-vibrations. No calculations are proposed for the heavier species, for which the conventional seniority dscription is assumed for Sn, while in Cd the quadrupole moments change sign. [Conclusion] A radical reexamination of traditional interpretations in the region has been shown to be necessary, in which quadrupole dominance plays a major role. What emerges is a bumpy but coherent view.

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arXiv2020

Quadrupole dominance in light Cd and Sn isotopes

Shell model calculations with the neutron effective charge as single free parameter describe well the \bet and \bef rates for $N\le 64$ in the Cd and Sn isotopes. The former exhibit weak permanent deformation corroborating the prediction of a pseudo SU3 symmetry, which remains of heuristic value in the latter, though the pairing force erodes the quadrupole dominance. Calculations in $10^7$ and $10^{10}$-dimensional spaces exhibit almost identical patterns: A vindication of the shell model. For $N\ge 64$ quadrupole dominance is accentuated in the Cd isotopes and gives way to seniority dominance for the Sn isotopes.

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arXiv2019

Pairing-quadrupole interplay in the neutron-deficient tin nuclei: first lifetime measurements of low-lying states in $^{106,108}$Sn

The lifetimes of the low-lying excited states $2^+$ and $4^+$ have been directly measured in the neutron-deficient $^{106,108}$Sn isotopes. The nuclei were populated via a deep-inelastic reaction and the lifetime measurement was performed employing a differential plunger device. The emitted $γ$ rays were detected by the AGATA array, while the reaction products were uniquely identified by the VAMOS++ magnetic spectrometer. Large-Scale Shell-Model calculations with realistic forces indicate that, independently of the pairing content of the interaction, the quadrupole force is dominant in the $B(E2; 2_1^+ \to 0_{g.s.}^+)$ values and it describes well the experimental pattern for $^{104-114}$Sn; the $B(E2; 4_1^+ \to 2_1^+)$ values, measured here for the first time, depend critically on a delicate pairing-quadrupole balance, disclosed by the very precise results in $^{108}$Sn. This result provides insight in the hitherto unexplained $B(E2; 4_1^+ \to 2_1^+)/B(E2; 2_1^+ \to 0_{g.s.}^+) < 1$ anomaly.

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arXiv2018

Neutron Skins and Halo Orbits in the $sd$ and $pf$ shells

The strong dependence of Coulomb energies on nuclear radii makes it possible to extract the latter from calculations of the former. The resulting estimates of neutron skins indicate that two mechanisms are involved. The first one---isovector monopole polarizability---amounts to noting that when a particle is added to a system it drives the radii of neutrons and protons in different directions, tending to equalize the radii of both fluids independently of the neutron excess. This mechanism is well understood and the Duflo-Zuker (small) neutron skin values derived 14 years ago are consistent with recent measures and estimates. The alternative mechanism involves halo orbits whose huge sizes tend to make the neutron skins larger and have a subtle influence on the radial behavior of $sd$ and $pf$ shell nuclei. In particular, they account for the sudden rise in the isotope shifts of nuclei beyond $N=28$ and the near constancy of radii in the $A=40-56$ region. This mechanism, detected here for the first time, is not well understood and may well go beyond Efimov physics usually associated to halo orbits.

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arXiv2018

Radii in the $sd$ shell and the $s_{1/2}$ "halo" orbit: A game changer

Proton radii of nuclei in the $sd$ shell depart appreciably from the asymptotic law, $ρ_π=ρ_0A^{1/3}$. The departure exhibits systematic trends fairly well described by a single phenomenological term in the Duflo-Zuker formulation, which also happens to explain the sudden increase in slope in the isotope shifts of several chains at neutron number $N=28$. It was recently shown that this term is associated with the abnormally large size of the $s_{1/2}$ and $p$ orbits in the $sd$ and $pf$ shells respectively. Further to explore the problem, we propose to calculate microscopically radii in the former. Since the (square) radius is basically a one body operator, its evolution is dictated by single particle occupancies determined by shell model calculations. Assuming that the departure from the asymptotic form is entirely due to the $s_{1/2}$ orbit, the expectation value $\langle s_{1/2}|r^2|s_{1/2}\rangle$ is determined by demanding that its evolution be such as to describe well nuclear radii. It does, for an orbit that remains very large (about 1.6 fm bigger than its $d$ counterparts) up to $N,\,Z=14$ then drops abruptly but remains some 0.6 fm larger than the $d$ orbits. An unexpected behavior bound to challenge our understanding of shell formation.

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arXiv2015

Nilsson-SU3 selfconsistency in heavy N=Z nuclei

It is argued that there exist natural shell model spaces optimally adapted to the operation of two variants of Elliott' SU3 symmetry that provide accurate predictions of quadrupole moments of deformed states. A selfconsistent Nilsson-like calculation describes the competition between the realistic quadrupole force and the central field, indicating a {\em remarkable stability of the quadruplole moments}---which remain close to their quasi and pseudo SU3 values---as the single particle splittings increase. A detailed study of the $N=Z$ even nuclei from $^{56}$Ni to $^{96}$Cd reveals that the region of prolate deformation is bounded by a pair of transitional nuclei $^{72}$Kr and $^{84}$Mo in which prolate ground state bands are predicted to dominate, though coexisting with oblate ones,

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arXiv2006

Shell-model phenomenology of low-momentum interactions

The first detailed comparison of the low-momentum interaction V_{low k} with G matrices is presented. We use overlaps to measure quantitatively the similarity of shell-model matrix elements for different cutoffs and oscillator frequencies. Over a wide range, all sets of V_{low k} matrix elements can be approximately obtained from a universal set by a simple scaling. In an oscillator mean-field approach, V_{low k} reproduces satisfactorily many features of the single-particle and single-hole spectra on closed-shell nuclei, in particular through remarkably good splittings between spin-orbit partners on top of harmonic oscillator closures. The main deficiencies of pure two-nucleon interactions are associated with binding energies and with the failure to ensure magicity for the extruder-intruder closures. Here, calculations including three-nucleon interactions are most needed. V_{low k} makes it possible to define directly a meaningful unperturbed monopole Hamiltonian, for which the inclusion of three-nucleon forces is tractable.

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arXiv2004

The Shell Model as Unified View of Nuclear Structure

The last decade has witnessed both quantitative and qualitative progresses in Shell Model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Lanczos tridiagonal construction, whose formal and numerical aspects we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the Shell Model to describe simultaneously all the manifestations of the nuclear dynamics either of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.

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arXiv2002

Mirror displacement energies and neutron skins

A gross estimate of the neutron skin [0.80(5)$(N-Z)/A$ fm] is extracted from experimental proton radii, represented by a four parameter fit, and observed mirror displacement energies (CDE). The calculation of the latter relies on an accurately derived Coulomb energy and smooth averages of the charge symmetry breaking potentials constrained to state of the art values. The only free parameter is the neutron skin itself. The Nolen Schiffer anomaly is reduced to small deviations (rms=127 keV) that exhibit a secular trend. It is argued that with state of the art shell model calculations the anomaly should disappear. Highly accurate fits to proton radii emerge as a fringe benefit.

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arXiv2002

A study of randomness, correlations and collectivity in the nuclear shell model

A variable combination of realistic and random two-body interactions allows the study of collective properties, such as the energy spectra and B(E2) transition strengths in 44Ti, 48Cr and 24Mg. It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the B(E2) values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.

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arXiv2002

Isobaric multiplet yrast energies and isospin non-conserving forces

The isovector and isotensor energy differences between yrast states of isobaric multiplets in the lower half of the $pf$ region are quantitatively reproduced in a shell model context. The isospin non-conserving nuclear interactions are found to be at least as important as the Coulomb potential. Their isovector and isotensor channels are dominated by J=2 and J=0 pairing terms, respectively. The results are sensitive to the radii of the states, whose evolution along the yrast band can be accurately followed.

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arXiv2002

Spectroscopy with random and displaced random ensembles

Due to the time reversal invariance of the angular momentum operator J^2, the average energies and variances at fixed J for random two-body Hamiltonians exhibit odd-even-J staggering, that may be especially strong for J=0. It is shown that upon ensemble averaging over random runs, this behaviour is reflected in the yrast states. Displaced (attractive) random ensembles lead to rotational spectra with strongly enhanced BE2 transitions for a certain class of model spaces. It is explained how to generalize these results to other forms of collectivity.

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arXiv2001

Binomial level densities

It is shown that nuclear level densities in a finite space are described by a continuous binomial function, determined by the first three moments of the Hamiltonian, and the dimensionality of the underlying vector space. Experimental values for $^{55}$Mn, $^{56}$Fe, and $^{60}$Ni are very well reproduced by the binomial form, which turns out to be almost perfectly approximated by Bethe's formula with backshift. A proof is given that binomial densities reproduce the low moments of Hamiltonians of any rank: A strong form of the famous central limit result of Mon and French. Conditions under which the proof may be extended to the full spectrum are examined.

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arXiv2001

Canonical form of Hamiltonian matrices

On the basis of shell model simulations, it is conjectured that the Lanczos construction at fixed quantum numbers defines---within fluctuations and behaviour very near the origin---smooth canonical matrices whose forms depend on the rank of the Hamiltonian, dimensionality of the vector space, and second and third moments. A framework emerges that amounts to a general Anderson model capable of dealing with ground state properties and strength functions. The smooth forms imply binomial level densities. A simplified approach to canonical thermodynamics is proposed.

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arXiv2001

Coulomb displacement energies, energy differenced and neutron skins

A Fock space representation of the monopole part of the Coulomb potential is presented. Quantum effects show through a small orbital term in $l(l+1)$. Once it is averaged out, the classical electrostatic energy emerges as an essentially exact expression, which makes it possible to eliminate the Nolen-Schiffer anomaly, and to estimate neutron skins and the evolution of radii along yrast states of mirror nuclei. The energy differences of the latter are quantitatively reproduced by the monopole term and a schematic multipole one.

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arXiv1999

Monopole, quadrupole and pairing: a shell model view

The three main contributions to the nuclear Hamiltonian - monopole, quadrupole and pairing - are analyzed in a shell model context. The first has to be treated phenomenologically, while the other two can be reliably extracted from the realistic interactions. Due to simple scaling properties, the realistic quadrupole and pairing interactions eliminate the tendency to collapse of their conventional counterparts, while retaining their basic simplicity.

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arXiv1998

Shell Model Monte Carlo studies of neutron-rich nuclei in the 1s-0d-1p-0f shells

We demonstrate the feasibility of realistic Shell-Model Monte Carlo (SMMC) calculations spanning multiple major shells, using a realistic interaction whose bad saturation and shell properties have been corrected by a newly developed general prescription. Particular attention is paid to the approximate restoration of translational invariance. The model space consists of the full sd-pf shells. We include in the study some well-known T=0 nuclei and several unstable neutron-rich ones around N=20,28. The results indicate that SMMC can reproduce binding energies, B(E2) transitions, and other observables with an interaction that is practically parameter free. Some interesting insight is gained on the nature of deep correlations. The validity of previous studies is confirmed.

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