The change in mean-square nuclear charge radii δ⟨r^{2}⟩ along the even-A tin isotopic chain ^{108-134}Sn has been investigated by means of collinear laser spectroscopy at ISOLDE/CERN using the atomic ...transitions 5p^{2} ^{1}S_{0}→5p6 s^{1}P_{1} and 5p^{2} ^{3}P_{0}→5p6s ^{3}P_{1}. With the determination of the charge radius of ^{134}Sn and corrected values for some of the neutron-rich isotopes, the evolution of the charge radii across the N=82 shell closure is established. A clear kink at the doubly magic ^{132}Sn is revealed, similar to what has been observed at N=82 in other isotopic chains with larger proton numbers, and at the N=126 shell closure in doubly magic ^{208}Pb. While most standard nuclear density functional calculations struggle with a consistent explanation of these discontinuities, we demonstrate that a recently developed Fayans energy density functional provides a coherent description of the kinks at both doubly magic nuclei, ^{132}Sn and ^{208}Pb, without sacrificing the overall performance. A multiple correlation analysis leads to the conclusion that both kinks are related to pairing and surface effects.
Measurements of atomic transitions in different isotopes offer key information on the nuclear charge radius. The anticipated high-precision experimental techniques, augmented by atomic cal- ...culations, will soon enable extraction of the higher-order radial moments of the charge density distribution. To assess the value of such measurements for nuclear structure research, we study the information content of the fourth radial moment $\langle r^4\rangle$ by means of nuclear density functional theory and a multiple correlation analysis. We show that $\langle r^4\rangle$ can be directly related to the surface thickness of nuclear density, a fundamental property of the atomic nucleus that is difficult to obtain for radioactive systems. Precise knowledge of these radial moments is essential to establish reliable constraints on the existence of new forces from precision isotope shift measurements.
During the last decade, six new superheavy elements were added into the seventh period of the periodic table, with the approval of their names and symbols. This milestone was followed by proclaiming ...2019 the International Year of the Periodic Table of Chemical Elements by the United Nations General Assembly. According to theory, due to their large atomic numbers, the new arrivals are expected to be qualitatively and quantitatively different from lighter species. The questions pertaining to superheavy atoms and nuclei are in the forefront of research in nuclear and atomic physics and chemistry. This Colloquium offers a broad perspective on the field and outlines future challenges.
The nuclear mean-field model based on Skyrme forces or related density functionals has found widespread application to the description of nuclear ground states, collective vibrational excitations, ...and heavy-ion collisions. The code Sky3D solves the static or dynamic equations on a three-dimensional Cartesian mesh with isolated or periodic boundary conditions and no further symmetry assumptions. Pairing can be included in the BCS approximation for the static case. The code is implemented with a view to allow easy modifications for including additional physics or special analysis of the results.
Program title: Sky3D
Catalogue identifier: AESW_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESW_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 43187
No. of bytes in distributed program, including test data, etc.: 1423973
Distribution format: tar.gz
Programming language: Fortran 90. The OpenMP version requires a relatively recent compiler; it was found to work using gfortran 4.6.2 or later and the Intel compiler version 12 or later.
Computer: All computers with a Fortran compiler supporting at least Fortran 90.
Operating system: All operating systems with such a compiler. Some of the Makefiles and scripts depend on a Unix-like system and need modification under Windows.
Has the code been vectorized or parallelized?: Yes, Runs under OpenMP and MPI, unlimited number of processors can be used.
RAM: 1 GB
Classification: 17.16, 17.22, 17.23.
External routines: LAPACK, FFTW3
Nature of problem:
The time-dependent Hartree–Fock equations can be used to simulate nuclear vibrations and collisions between nuclei for low energies. This code implements the equations based on a Skyrme energy functional and also allows the determination of the ground-state structure of nuclei through the static version of the equations. For the case of vibrations the principal aim is to calculate the excitation spectra by Fourier-analyzing the time dependence of suitable observables. In collisions, the formation of a neck between nuclei, the dissipation of energy from collective motion, processes like charge transfer and the approach to fusion are of principal interest.
Solution method:
The nucleonic wave function spinors are represented on a three-dimensional Cartesian mesh with no further symmetry restrictions. The boundary conditions are always periodic for the wave functions, while the Coulomb potential can also be calculated for an isolated charge distribution. All spatial derivatives are evaluated using the finite Fourier transform method. The code solves the static Hartree–Fock equations with a damped gradient iteration method and the time-dependent Hartree–Fock equations with an expansion of the time-development operator. Any number of initial nuclei can be placed into the mesh in with arbitrary positions and initial velocities.
Restrictions:
The reliability of the mean-field approximation is limited by the absence of hard nucleon–nucleon collisions. This limits the scope of applications to collision energies about a few MeV per nucleon above the Coulomb barrier and to relatively short interaction times. Similarly, some of the missing time-odd terms in the implementation of the Skyrme interaction may restrict the applications to even–even nuclei.
Unusual features:
The possibility of periodic boundary conditions and the highly flexible initialization make the code also suitable for astrophysical nuclear-matter applications.
Running time:
The running time depends strongly on the size of the grid, the number of nucleons, and the duration of the collision. For a single-processor PC-type computer it can vary between a few minutes and weeks.
One of the most important global properties of the atomic nucleus is its size. Experimentally determined nuclear charge radii carry unique information on the nuclear force and complex dynamics of ...protons and neutrons moving inside the nucleus. The intricate behaviour of charge radii along the chain of Ca isotopes, including the unexpectedly large charge radius of neutron-rich 52Ca, poses a daunting challenge for nuclear theory1. Here we present the measurements of the charge radii of proton-rich isotopes 36,37,38Ca, whose properties are impacted by the interplay between nuclear superfluidity and weak binding. Calculations carried out within nuclear density functional theory show that the combination of a novel interaction2 and a state-of-the-art theoretical method can successfully explain the behaviour of charge radii from the lightest to the heaviest Ca isotopes. Through this model, we show how the new data on 36,37,38Ca elucidate the nature of nucleonic pairing in weakly bound proton-rich isotopes.Spectral study on 36,37,38Ca isotopes and calculations based on density functional theory reveal the interplay between charge radii and nucleonic pairing correlations.
Self-consistent mean field models are a powerful tool in the investigation of nuclear structure and low-energy dynamics. They are based on effective energy-density functionals, often formulated in ...terms of effective density-dependent nucleon–nucleon interactions. The free parameters of the functional are adjusted to empirical data. A proper choice of these parameters requires a comprehensive set of constraints covering experimental data on finite nuclei, concerning static as well as dynamical properties, empirical characteristics of nuclear matter, and observational information on nucleosynthesis, neutron stars and supernovae. This work aims at a comprehensive survey of the performance of one of the most successful non-relativistic self-consistent method, the Skyrme–Hartree–Fock model (SHF), with respect to these constraints. A full description of the Skyrme functional is given and its relation to other effective interactions is discussed. The validity of the application of SHF far from stability and in dense environments beyond the nuclear saturation density is critically assessed. The use of SHF in models extended beyond the mean field approximation by including some correlations, is discussed. Finally, future prospects for further development of SHF towards a more consistent application of the existing and promising newly developing constraints are outlined.
The dipole polarizability of stable even-mass tin isotopes 112,114,116,118,120,124Sn was extracted from inelastic proton scattering experiments at 295MeV under very forward angles performed at RCNP. ...Predictions from energy density functionals cannot account for the present data and the polarizability of 208Pb simultaneously. The evolution of the polarizabilities in neighboring isotopes indicates a kink at 120Sn while all model results show a nearly linear increase with mass number after inclusion of pairing corrections.
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