Our studies of heavy-ion reactions include coupled-channels calculations of fusion reactions, elastic and inelastic scattering, and few-nucleon transfer reactions. The calculated fusion cross sections are usually quite sensitive to the structure and the radii of the reacting nuclei, and it is often possible to reproduce the measurements fairly well by including couplings to one- and two-phonon excitations of the low-lying quadrupole and octupole modes. However, it is very challenging to reproduce the high precision fusion data that have become available in recent years. Calculations are also challenging for very heavy systems where couplings to multi-phonon excitations and multi-nucleon transfer channels can influence the fusion.

Another difficulty in the description of heavy-ion fusion reactions occurs at energies far below the Coulomb barrier, where the measured fusion cross sections fall off steeply with decreasing energy. The fall off is so steep in many cases that the S factor for fusion develops a maximum at low energy. This hindrance of the fusion is expected to be an entrance channel phenomenon because it occurs at a rather high excitation energy of the compound nucleus. We have shown that the fusion hindrance can be explained in the coupled-channels approach by using an ion-ion potential that has a shallow pocket in the entrance channel. We have applied this model and analyzed the fusion data for several of the heavy-ion systems that exhibit the fusion hindrance at low energy.

We have tested our three-body models of two-neutron halo nuclei against recent
measurements of the charge radius and dipole response of ^{11}Li.
Both measurements are probes of the core-dineutron distance in ^{11}Li.
The distance we extract from the dipole response is slightly smaller than the
value obtained from the charge radius measurement. The discrepancy is of the
order of 1.5σ. Our interpretation of both measurements is that the s-wave
component in the two-neutron halo ground state must be fairly large.

We are continuing the development of a program for calculating many-body variational wave functions. This approach puts pairing and particle-hole interactions on an equal footing. These wave functions strictly conserve particle-number and parity. Particle number and parity are projected before variation. In studies of nuclides near the N = Z line, we also project states of good Q, the number parity of T = 0 pairs, before variation. This treatment explains many of the unusual features of nuclei having almost equal numbers of protons and neutrons, such as the Wigner energy anomaly, in a simple way. It also explains a similar anomaly for odd-mass nuclides near the N = Z line.

We have developed a code for configuration mixing of the wave functions used
to describe n-p pairing. We have applied these wave functions to explore n-p
pair transfer probabilities in N = Z nuclides. We find that this quantity is
very sensitive to T = 0 and T = 1 correlations in the many-body wave function.
Experimental studies of the pair transfer probability in ^{44}Ti will
establish the magnitude of T = 0 pairing interaction correlations in nuclei
near the N = Z line. Using realistic single-particle energies for nuclei in
this mass region, we have made a refined estimate of the pair transfer
probability to the T = 0 and T = 1 states in ^{44}Ti.

We are developing a method that goes beyond the usual configuration mixing approach. We utilize the power of the variational method in combination with the configuration interaction method. The method determines an optimal improvement to a wave function with a given number of configurations. We have applied the method to the pairing force interaction and to the n-p pairing interaction problem. In both cases, the results are extremely good. In the pairing case, which we studied in detail, this new approach gave well over 99.9% of the total correlation energy. In the past year, we have extended this method to cylindrically symmetric deformed nuclei, described by a Hamiltonian with particle-hole plus pairing interactions. We are finding that it is quite feasible, in terms of computer resources, to extend this variational approach to the more general interaction.

The low-lying states of odd mass nuclei provide a good test of the
parametrizations of single particle potentials. Study of the spectroscopy
of the heavy elements is particularly interesting, as it gives insights
into the potentials that are relevant to the structure of super-heavy elements.
In a collaborative effort with the experimental spectroscopy group at Argonne,
we have analyzed low-lying neutron and proton single particle states in the
mass 250 region. We have studied neutron single-particle states in
^{247}Cm and ^{251}Cf, as well as proton single particle
states in ^{249}Bk, and determined single-particle potentials that
are consistent with these analyses. The study of ^{251}Cf is
particularly important as it has 153 neutrons, giving information on the
neutron single-particle states above the deformed gap at 152 neutrons.
Nine single-particle states have been identified in this nuclide. These
studies constrain potentials that are used to describe superheavy elements.
The same approach should prove useful for constraining potentials used to
describe new regions of nuclides studied with the CARIBU facility.

Nuclear forces and nuclear systems

Theoretical Physics Research

Atomic theory and fundamental quantum mechanics