D. Kelvin

On the distribution of shell-model eigenvector components

Abstract We present results that show that the components of shell-model eigenvectors are not distributed like those of a randomly oriented vector. An argument based on the invariance properties of the ensemble of random matrices arising from two-body hamiltonians is used to suggest the correct form of the distribution. The agreement with distributions obtained in actual shell-model calculations is found to be excellent.

High-spin rotational states in 24Mg

Abstract The states of T = 0, J = 8, 9, 10, 11 and 12 in 24 Mg, calculated using the Preedom-Wildenthal interaction, have been studied with a view to assigning some of them to rotational bands. With the possible exception of a J = 9 member of the K = 2 excited band, there is no evidence that band structure persists beyond J = 8. The lowest J = 8 state has a very peculiar structure corresponding to a condensation of particles into the d 5 2 shell.

Shell-model calculations in the sd shell. IX. Masses, spectra and beta decays of the mass-24 nuclei

For pt.VIII see ibid., vol.3, no.7, p.919 (1977). The authors present the results of a shell-model investigation of the masses, spectra, Coulomb energies and beta decays of the mass-24 nuclei. They have used the effective interaction of Chung and Wildenthal together with an empirically-determined Coulomb interaction. The ab initio use of a reasonably good Coulomb interaction reveals the presence of quite large errors in the calculated energies of certain states and hence of serious imperfections in the nuclear effective interaction. The calculated Coulomb energy differences in the mass-24 system have been used to improve the empirical Coulomb matrix elements.

Electromagnetic properties of the 01+, 21+, 41+ states in 20Ne, 24Mg, 28Si, 32S☆

Abstract The 0 + , 2 + , 4 + sequence in the 4 N nuclei in the 1s-0d shell has been examined by comparing the results of a large-basis shell-model calculation with electron scattering data. While the ground state is well described by the shell-model wave function there is evidence that extra s-d space configurations play an important role in defining the radial shapes of inelastic transition densities. For 0 + → 4 + transitions, mixing of the Og shell is important. The Chung-Wildenthal interaction shows erroneous behaviour in the description of some of the electromagnetic properties of these states.

Configurational analysis of rotational states in the SD shell

Abstract It is shown that the shell-model states belonging to a given rotational band in 23 Na and 24 Mg have very similar subshell occupancies, different bands being characterised by different occupancies. On the one hand this establishes a connection, somewhat different from that provided by the SU (3) scheme, between the spherical shell model and the idea of an intrinsic state, and on the other hand helps discriminate between possible candidates for membership of a band and imposes limits on the lengths of the bands.

Shell-model calculation of strength functions

Abstract We show how shell-model calculations that use the Lanczos method may be extended to provide information about the distribution of the initial vector among the eigenstates of the system, without actually calculating these eigenstates. By choosing the initial state appropriately this allows, for example, the calculation of the distribution of particle strengths or the extent to which some particular approximate symmetry is spread among the eigenstates.

Shell-model calculations in the sd shell. X. Termination of rotational bands

For pt.IX see Phys. Lett., vol.63B, p.385 (1976). It is shown that the shell-model states belonging to a given rotational band have very similar subshell occupancies which are interpreted as indicating similar intrinsic structures. Subshell occupancies can be used to help decide whether or not a state belongs to a given band and hence to determine the upper limits of rotational bands. In the sd shell, the prediction that no rotational bands extend beyond J=10 is made, and in many cases when one might expect them, rotational features are absent.

Elastic electron scattering as a test of effective interactions in the 1s-0d shell

Abstract Wave functions obtained from untruncated shell-model calculations for various effective interactions have been used to calculate the elastic electron scattering form factors for 24Mg and 32S. Chung-Wildenthal matrix elements best reproduce the form factors and the experimental excitation spectra for these nuclei. It is also shown that the use of harmonic oscillator wave functions and/or Born approximation can lead to a misjudgement of the actual situation.

Empirical Coulomb matrix elements and the mass of 22Al

Abstract We have attempted to obtain a set of Coulomb matrix elements which fit the known Coulomb energy shifts in the nuclei of mass 18 to 22. The interaction obtained fits the data well with only a few exceptions, one of these being the Coulomb shift of the notorious third 0 + state in 18 Ne. These Coulomb matrix elements are used together with the Chung-Wildenthal interaction to obtain a new prediction for the mass excess of 22 Al. The results indicate that 22 A should be bound against proton emission.

Quadrupole transitions in 20Ne

Abstract Untruncated shell model calculations in the 1s-0d shell using Chung-Wildenthal effective interactions have been performed for 20 Ne and the electron scattering form factors for elastic scattering and for the excitation of 2 1 + , 2 1 + and 2 3 + states have been examined. Saxon-Woods wave functions and a phase-shift analysis have been used. It is shown that within the limited space of the 1s-0d shell, it is possible to obtain vastly different momentum transfer dependence for the electro-excitation of ΔJ π = 2 + transitions. The 2 1 + and 2 2 + states are seen to be adequately described by the wave functions obtained in this calculation, but 2 3 + is not described well.