Piet van Isacker

Nuclear Masses Set Bounds on Quantum Chaos

It has been suggested that chaotic motion inside the nucleus may significantly limit the accuracy with which nuclear masses can be calculated. Using a power spectrum analysis we show that the inclusion of additional physical contributions in mass calculations, through many-body interactions or local information, removes the chaotic signal in the discrepancies between calculated and measured masses. Furthermore, a systematic application of global mass formulas and of a set of relationships among neighboring nuclei to more than 2000 nuclear masses allows one to set an unambiguous upper bound for the average errors in calculated masses, which turn out to be almost an order of magnitude smaller than estimated chaotic components.

Interrelation between the isoscalar octupole phonon and the proton–neutron mixed-symmetry quadrupole phonon in near-spherical nuclei

Abstract The interrelation between the octupole phonon and the low-lying proton–neutron mixed-symmetry quadrupole phonon in near-spherical nuclei is investigated. The one-phonon states decay by collective E3 and E2 transitions to the ground state and by relatively strong E1 and M1 transitions to the isoscalar 2 + 1 state. We apply the proton–neutron version of the interacting boson model including quadrupole and octupole bosons ( sdf -IBM-2). Two F -spin symmetric dynamical symmetry limits of the model, namely the vibrational and the γ -unstable ones, are considered. We derive analytical formulae for excitation energies as well as B( E1 ) , B( M1 ) , B( E2 ) and B( E3 ) values for a number of transitions between low-lying states.

SU(3) realization of the rigid asymmetric rotor within the interacting boson model

It is shown that the spectrum of the asymmetric rotor can be realized quantum mechanically in terms of a system of interacting bosons. This is achieved in the SU(3) limit of the interacting boson model by considering higher-order interactions between the bosons. The spectrum corresponds to that of a rigid asymmetric rotor in the limit of infinite boson number.

THE ART OF PREDICTING NUCLEAR MASSES

A review of recent advances in the theoretical analysis of nuclear mass models and their predictive power is presented. After introducing two tests which probe the ability of nuclear mass models to extrapolate, three models are analyzed in detail: the liquid drop model (LDM), the liquid drop model plus empirical shell corrections (LDMM) and the Duflo–Zuker mass formula (DZ). The DZ model is exhibited as the most predictive model. The Garvey–Kelson mass relations are also discussed. It is shown that their fulfillment probes the consistency of the most commonly used mass formulae, and that they can be used in an iterative process to predict nuclear masses in the neighborhood of nuclei with measured masses, offering a simple and reproducible procedure for short range mass predictions.

PREDICTING NUCLEAR MASSES BY IMAGE RECONSTRUCTION

The differences between measured masses and Liquid Drop Model (LDM) predictions have well known regularities, which can be analyzed as a two-dimensional texture on the N-Z plane. The remaining microscopic effects, obtained after removing the smooth LDM mass contributions, have proved difficult to model. They contain all the information related to shell closures, nuclear deformation and the residual nuclear interactions, and display a well defined pattern. In the present work the more than 2000 known nuclear masses are studied as an array in the N-Z plane viewed through a mask, behind which the approximately 7000 unknown unstable nuclei that can exist between the proton and neutron drip lines are hidden. Employing a Fourier transform deconvolution method these masses can be predicted. Measured masses are reconstructed with and r.m.s. error of less than 100 keV. Potential applications of the present approach are outlined.

An upper limit to ground state energy fluctuations in nuclear masses

Shell model calculations are employed to estimate un upper limit of statistical fluctuations in the nuclear ground state energies. In order to mimic the presence of quantum chaos associated with neutron resonances at energies between 6 to 10 MeV, calculations include random interactions in the upper shells. The upper bound for the energy fluctuations at mid‐shell is shown to have the form σ(A) ≈ 20A−1.34 MeV. This estimate is consistent with the mass errors found in large shell model calculations along the N=126 line, and with local mass error estimated using the Garvey‐Kelson relations, all being smaller than 100 keV.

An upper limit of ground-state energy fluctuations in nuclear masses

Shell model calculations are employed to estimate an upper limit of statistical fluctuations in the nuclear ground-state energies. In order to mimic the presence of quantum chaos associated with neutron resonances at energies between 6 and 10 MeV, calculations include random interactions in the upper shells. The upper bound for the energy fluctuations at mid-shell is shown to have the form σ(A)≈20 A−1.34 MeV. This estimate is consistent with the mass errors found in large-shell model calculations along the N=126 line, and with local mass error estimated using the Garvey–Kelson relations, all being smaller than 100 keV. It agrees in both size and functional form with the fluctuations deduced independently from second-order perturbation theory.

Regularities vs. chaos in nuclear masses

It has been suggested that there might be an inherent limit to the accuracy with which nuclear masses can be calculated, chaotic motion inside the atomic nucleus being responsible for this lack of predictability. However, a thorough application of a set of parameter‐free relationships among neighboring nuclei, known as the Garvey‐Kelson relations, to an up‐to‐date compilation of more than 2500 nuclear masses allows to set an upper bound for the proposed chaotical component, which turns out to be almost an order of magnitude smaller than previously suggested. This is good news for astrophysicists attempting to understand the processes that fuel the stars.