Transition probability from the ground to the first-excited 2+ state of even–even nuclides

Neutron Stars 1: Equation of State and Structure

Nowadays it has become customary in nuclear physics to denote by “tradition” the approach that considers nucleons and mesons as the relevant degrees of freedom. It is the purpose of this chapter to review this “traditional” approach in the area of nuclear forces and their applications to nuclear structure.

The Meson Theory of Nuclear Forces and Nuclear Structure

Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

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.

The shell model as a unified view of nuclear structure

We have measured the deuteron magnetic form factor B(q/sup 2/) for values of the momentum transfer squared between 7 and 28 fm/sup -2/. The data are compared to relativistic and nonrelativistic predictions including meson-exchange--current contributions. Significant disagreement is found for large momentum transfers.

Magnetic form factor of the deuteron.

The $3s$ radial wave function $R(\mathcal{r})$ has been determined by electron scattering from $^{206}\mathrm{Pb}$ and $^{205}\mathrm{Tl}$. The shape of $R(\mathcal{r})$ in the central region of the nucleus is used to test the validity of the independent-particle shell model at large nuclear density.

Is the Shell-Model Concept Relevant for the Nuclear Interior?

https://cds.cern.ch/record/261499/files/P00022619.pdf

3H and 3He electromagnetic form factors

On the radial distribution of the proton orbit

A very-high momentum-transfer (q=780 MeV/c), elastic electron-scattering experiment on $sup 58$Ni has been performed using the 600-MeV linac of Saclay. The charge density, extracted from (e,e) and muonic-x-ray data, exhibits considerably less structure than predicted by Hartree-Fock calculations.

Ph. Leconte

Papers

Magnetic form factor of the deuteron.

Is the Shell-Model Concept Relevant for the Nuclear Interior?

3H and 3He electromagnetic form factors

On the radial distribution of the proton orbit

Shell structure of the $sup 58$Ni charge density