R.G. Lovas

Microscopic multicluster description of neutron-halo nuclei with a stochastic variational method

Abstract To test a multicluster approach for halo nuclei, we give a unified description for the ground states of 6 He and 8 He in a model comprising an α-cluster and single-neutron clusters. The intercluster wave function is taken a superposition of terms belonging to different arrangements, each defined by a set of Jacobi coordinates. Each term is then a superposition of products of gaussian functions of the individual Jacobi coordinates with different widths, projected to angular momenta l = 0 or 1. This prescription defines a trial function with linear variational parameters. For 6 He, we were able to use enough terms to produce ground-state energies that are virtully exact within the subspaces defined by the arrangements and l -values, and used this nucleus as a testing ground for stochastic methods to choose trial functions. Trial functions consisting of selectively chosen random terms were found to yield excellent numerical convergence to this “exact” value with significantly fewer terms. For the description of 8 He to be feasible, such a dimensional reduction is indispensable. For 8 He good energy convergence was achieved in a state space comprising three arrangements with all l = 0, and there are indications showing that the contributions of other subspaces are likely to be small. The 6 He and 8 He energies are reproduced by the same effective force very well, and the matter radii obtained are similar to those of other sophisticated calculations.

Cluster-configuration shell model for alpha decay☆

Abstract Combining the shell model with the cluster model, we formulate a linear variational approach to an α-unstable, whose decay leads to a doubly closed-shell residual nucleus, and use this approach in an R-matrix description of the decay of the ground state of 212 Po. All input parameters of the calculations are taken from independent sources or are readjusted to independent data. The low-lying energy levels of the 208 Pb plus one-nucleon and of the 208 Pb plus two-nucleon systems and the ground-state energies of the α-particle and of 212 Po are reproduced satisfactorily. The resulting decay width is in good agreement with experiment, and appears to depend moderately on the input parameters within their inherent uncertainty. By choosing the parameters so as to get exact agreement with the experimental width, the amount of core + α clustering in the parent state and the corresponding (conventional) spectroscopic factor can be assessed precisely, and are found to be 0.30 and 0.025, respectively. These values are substantially higher and their ratio is closer to unity than estimated formerly, and the peak region of clustering has been found to be pushed farther out to the nuclear surface. Our results show the soundness of assuming the existence of performed α-particles with appreciable probability on the nuclear surface in the initial state.

Fragmentation properties of 6Li

Abstract The α+d and t+τ cluster structure of 6Li is described in a microscopic α+d cluster model through quantities that enter into the description of cluster fragmentation processes. The states of the separate clusters α, d, t and τ are described as superpositions of 0s Slater determinants belonging to different potential size parameters. The model state space of 6Li is a tensor product of the α and d cluster state spaces and the state space of zero-orbital-momentum relative motion, restricted by antisymmetrization. To describe both the 6Li and fragment states realistically, we constructed nucleon-nucleon forces optimized for the model state spaces used. The fragmentation properties calculated are the g.s. fragmentation (or reduced-width) amplitudes, their squared Fourier transforms, the corresponding potential overlaps, the spectroscopic factors Sαd, Stτ and the αd asymptotic normalization constant C α d . The forces constructed reproduce the energies and charge radii of 6Li as well as of the fragments excellently. The fragmentation properties predicted by them slightly differ from those calculated with some forces of common use provided the latter are modified so as to reproduce the α, d and 6Li energies. The fragmentation properties change moderately in comparison with simpler versions of the cluster model. The full model yields S α d =0.93, S t τ =0.58 and C α d =3.3 . The results are consistent with phenomenological estimates except for C α d . The shape of our αd fragmentation amplitudes are in accord with α+p+n three-body calculations but our Sαd and C α d are substantially larger. We attribute this discrepancy to the neglect of the Pauli effects in the usual three-body formula for the αd fragmentation amplitude. We give a formula which contains the necessary remedy.

On Fliessbach's approaches to direct reactions

The conventional models of direct cluster reactions treat the nuclear wave-function overlaps or reduced-width amplitudes as single-particle wave functions, which is contrary to the Pauli principle. The motivation of Fliessbachs two approaches reviewed in this paper is to improve on these models by a proper treatment of antisymmetrization. Fliessbachs approaches involve redefined reduced-width amplitudes, which can be regarded as single-particle wave functions. We show, however, that in the approach specialized to transfer reactions the antisymmetrization is in fact treated incorrectly, and the more general approach seems applicable only to processes that involve just two nuclear fragments, like a decay or radiative capture. We outline how single-particle wave functions can be used correctly in approximating reduced-width amplitudes. We show that our approach helps to bring the phenomenological spectroscopic factors into agreement with the nuclear structure models.

Microscopic description of 7Li and 7Be for the DWBA treatment of cluster transfer reactions

Abstract The overlap of the αt interaction times the 7 Li wave function with the product of the α and t wave functions and the analogous quantity for the charge-conjugate system are calculated on microscopic grounds. This quantity contains the structure information on the 7 Li nucleus in the standard finite-range DWBA description of α- and t-stripping from and pick-up to 7 Li. This nucleus is described in the generator-coordinate model assuming the α + t two-cluster structure and schematic nucleon-nucleon forces. The model reproduces the measured g.s. properties reasonably. The microscopic potential overlap is obtained to be very different from those calculated with using local macroscopic αt interactions, but the difference in the 12 C( 7 Li, t) 16 O cross section is only dramatic at backward angles. To facilitate further DWBA analyses, several versions of the potential overlap as well as the overlap without the potential are given in an easily accessible form.

On the self-consistency of the Lane model

Abstract The conditions for the self-consistency of the Lane potential are investigated by fitting the (p, p), (p, n) and (n, n) differential cross sections in pairs. It is concluded that the model is correct only for average potentials to the accuracy of average potentials. The Lane potential can only be found by fitting (p, p) and (p, n) data, and its real and imaginary parts should not be allowed to vary independently.

Cluster correlations, clustering and halo structure

Abstract The performances of uncorrelated single-configuration microscopic models, uncorrelated bases and correlated bases are compared. The correlated bases yield (almost) exact results for A ⩽8 nuclei, which turn out to be very difficult to approximate with uncorrelated bases. Clustering and halo structure are visualized by plots of two-particle correlation functions obtained by nearly exact calculations with correlated Gaussian bases. It is shown that clustering may be present in a single-configuration uncorrelated but antisymmetrized microscopic model state as well, but it is much less pronounced than what is produced by the realistic calculation.

Cluster transfer form factor and intercluster relative motion in the orthogonality-condition model

Abstract The orthogonality-condition model (OCM), as an approximation method for calculating the overlap and potential overlap functions involved in the form factor of transfer reactions, is tested against microscopic cluster calculations for the 7 Li = α + t system. The OCM overlap and potential overlap turn out to depend strongly on the OCM potential although the potentials are chosen so as to produce the same asymptotic phase. Excellent approximations to microscopic overlaps and potential overlaps are, however, obtained by optimizing the OCM potential, so that the OCM may reproduce the microscopic energy surface. In this way the dependence on the OCM potential is traced back to the underlying nucleon-nucleon force.

Strength decoupling from the giant dipole resonance upon diagonalizing a Gaussian force and a δ-force on a particle-hole basis

Abstract The finite-range Gaussian force and δ-force have been diagonalized in a basis of 27 particle-hole states with J π = 1 − in 116 Sn. Depending on the range of the force, 3.9–7.1 % of the total transition rate has been found in the 6–9 MeV excitation energy region, which comprises the unperturbed energies of the basis states containing neutron threshold states.

Improved coupled-channel treatment of the (d, n̄) threshold effect

Abstract Calculations for the 90 Zr(d, p) excitation function in a charge-exchange coupling model suggest that the ( d, n ) threshold effect can be explained with the resonant solution of the Lane equations taken as the proton form factor.