J.P. Elliott

Matrix elements of the nucleon-nucleon potential for use in nuclear-structure calculations

Abstract The experimental nucleon-nucleon phase shifts are used to deduce matrix elements of the nucleon-nucleon potential in a basis of harmonic oscillator wave functions of the interparticle distance. Extensive tables are given for each partial wave. The method is essentially a distorted wave Born approximation.

A soluble γ-unstable hamiltonian

Abstract A simple five-dimensional hamiltonian for the nuclear shape is solved analytically for any value of a parameter whose variation describes vibration about a spherical equilibrium at one extreme and a rigid non-spherical but γ -unstable nucleus at the other. Spectra and E2 transition rates are compared with results from the interacting boson model.

An IBM analysis of a single j-shell of neutrons and protons

Abstract A subset of states of a single j -shell of neutrons and protons with good isospin is mapped into those of a system of isovector s- and d-bosons (IBM-3). The shell-model analogue of the boson U(6) and U(5) labels is established and a shell-model calculation for nuclei in the f 7 2 shell with a realistic effective interaction confirms the physical significance of these labels.

Intermediate coupling in the nuclear ds-shell

Energy levels diagrams are calculated for almost all nuclei in the mass region 18 < A < 38 using an intermediate coupling approach. An interpolation method is used to pass between the U3 scheme in LS coupling and the jj coupling extreme. The results are compared with the known energy levels.

First-order binding energies and spectra with a potential matrix deduced from phase shifts

Abstract The matrix elements deduced from phase shifts in an earlier paper are used in first-order perturbation-theory calculations for closed-shell nuclei and for nuclei with one or two particles or holes. Nuclear matter is also studied in the same approximation

An application of the interacting boson model to the first half of the sd shell

A version of the interacting boson model which includes np bosons with both T = 0, S = 1 and T = 1, S = 0 is used to describe the even-even nuclei in the first half of the sd shell, 16 < A < 28. The model is found to be consistent with the observed spectra, E2 transitions and binding energies relative to 16O. The more usual version (IBM 2) of the model which has only nn and pp bosons leads to significant disagreement.

Second order binding energies and spectra with an interaction matrix deduced from phase shifts

Abstract The matrix elements deduced from phase shifts in an earlier paper are modified to incorporate the effects of a hard core and then used in second order perturbation theory to calculate binding energies and spectra for some light nuclei near closed shells.

Coherent-state theory for the proton-neutron quasispin group

Abstract An extended coherent-state theory 1, 2 ) is used to give a simple construction for the matrix elements of the proton-neutron sp(4) quasispin algebra. A very simple analytical expression is given for the matrix elements of the sp(4) generators valid for all cases where initial and final states are multiplicity-free with respect to the U(1) × SU(2) n , T subalgebra. In the more general case, involving multiplicity, the most natural orthonormal basis constructed by the coherent-state method leads to many-nucleon states in the seniority scheme which are approximately labelled by T p , the isospin of the p nucleon pairs coupled to J = 0, T = 1.

An IBM-3 analysis of the nuclei just beyond the magic numbers N = Z = 28

Abstract The isospin-invariant form IBM-3 of the interacting boson model has been used to study energies and electromagnetic properties of the isotopes of nickel, zinc, germanium and selenium in the first half of the 1p 3 2 , 0f 5 2 and 1p 1 2 shell. The hamiltonian and electromagnetic operators vary with boson number and isospin in a manner determined by a mapping into the shell-model based on seniority and reduced isospin.

A shared mixed-symmetry state in 56Fe

Abstract Analysis of the γ-decay data suggests that the lowest mixed-symmetry 2 + state in 56 Fe is shared almost equally between the two 2 + levels at 2.658 MeV and 2.960 MeV.