R. J. Liotta

MICROSCOPIC THEORY OF CLUSTER RADIOACTIVITY

Recent developments in the dynamical microscopic theories of cluster decay are reviewed with special emphasis on the nuclear structure aspects and physical interpretation of the models. What we call dynamical microscopic theories are those in which the decay width is derived from the nucleonic structures, of the participating nuclei, which are deduced through the solution of their equations of motion. After a brief review of the various expressions for the decay width, we turn to the nuclear-structure aspects of the problem. We thoroughly discuss the treatment of the Pauli effects in models involving macroscopic elements. We settle the long-standing controversy over the cluster-core norm operator that relates microscopic and macroscopic relative-motion wave functions in the transition amplitude. We conclude that the way the norm operator was originally introduced in the mid-1970s is in principle correct. The main part of the paper is a detailed review, in which the approaches considered are categorized according to the structure models used for the parent nucleus. The approaches discussed are the ordinary shell models, the cluster-like shell models and the Bardeen-Cooper-Schrieffer (BCS) approach. By discussing these diverse calculations, it is concluded that the most essential prerequisite for a realistic model of the mother nucleus is that it should correctly describe the cluster correlation in the surface region. This implies that the proton-neutron interaction is indispensable, and the moderate success of ordinary shell models is accounted for by their failure to include both proton-neutron interaction and large enough bases. For the special case of a doubly-closed-shell residual state, cluster-like models are able to cope with this problem, because their bases are more economical, and, for these cases, they provide a fully satisfactory decay theory. The BCS approach, on the other hand, is widely applicable, and is the only one that has been applied to heavy-cluster decay with reasonable success. We point out, however, that the formation amplitude calculated in this model still contains approximations. We explain the success of the BCS theory by showing that, in spite of appearance, it does include proton-neutron interaction, in an effective manner. In discussing the results for the widths, we address the problem of the preformation probability of a cluster-core pair in the parent nucleus. One can be fairly confident that in the ground state of 212Po the amount of core-α-clustering is as high as 20–30%, but, in respect of other cluster-decaying nuclei, the theory is not yet conclusive. We conclude that a satisfactory understanding of heavy-cluster radioactivity requires the application of both more sophisticated cluster models and improved BCS approaches.

Universal decay law in charged-particle emission and exotic cluster radioactivity.

A linear universal decay formula is presented starting from the microscopic mechanism of the charged-particle emission. It relates the half-lives of monopole radioactive decays with the Q values of the outgoing particles as well as the masses and charges of the nuclei involved in the decay. This relation is found to be a generalization of the Geiger-Nuttall law in alpha radioactivity and explains well all known cluster decays. Predictions on the most likely emissions of various clusters are presented.

Two-Particle Resonant States in a Many-Body Mean Field

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow single-particle resonances. However, they can be significantly affected by the continuum part of the spectrum.

Pairing and continuum effects in nuclei close to the drip line

The Hartree-Fock-Bogoliubov (HFB) equations in coordinate representation are solved exactly, i.e., with correct asymptotic boundary conditions for the continuous spectrum. The calculations are performed with effective Skyrme interactions. The exact HFB solutions are compared with HFB calculations based on box boundary conditions and with resonant continuum Hartree-Fock-BCS (HF-BCS) results. The comparison is done for the neutron-rich Ni isotopes. It is shown that close to the drip line the amount of pairing correlations depends on how the continuum coupling is treated. On the other hand, the resonant continuum HF-BCS results are generally close to those of HFB even in neutron-rich nuclei.

Evidence for a spin-aligned neutron-proton paired phase from the level structure of 92Pd

Shell structure and magic numbers in atomic nuclei were generally explained by pioneering work that introduced a strong spin–orbit interaction to the nuclear shell model potential. However, knowledge of nuclear forces and the mechanisms governing the structure of nuclei, in particular far from stability, is still incomplete. In nuclei with equal neutron and proton numbers (N = Z), enhanced correlations arise between neutrons and protons (two distinct types of fermions) that occupy orbitals with the same quantum numbers. Such correlations have been predicted to favour an unusual type of nuclear superfluidity, termed isoscalar neutron–proton pairing, in addition to normal isovector pairing. Despite many experimental efforts, these predictions have not been confirmed. Here we report the experimental observation of excited states in the N = Z = 46 nucleus 92Pd. Gamma rays emitted following the 58Ni(36Ar,2n)92Pd fusion–evaporation reaction were identified using a combination of state-of-the-art high-resolution γ-ray, charged-particle and neutron detector systems. Our results reveal evidence for a spin-aligned, isoscalar neutron–proton coupling scheme, different from the previous prediction. We suggest that this coupling scheme replaces normal superfluidity (characterized by seniority coupling) in the ground and low-lying excited states of the heaviest N = Z nuclei. Such strong, isoscalar neutron–proton correlations would have a considerable impact on the nuclear level structure and possibly influence the dynamics of rapid proton capture in stellar nucleosynthesis.

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.

Resonant continuum in the Hartree-Fock + BCS approximation

A method for incorporating the effect of the resonant continuum into Hartree-Fock+BCS equations is proposed. The method is applied for the case of a neutron-rich nucleus calculated with a Skyrme-type force plus a zero-range pairing interaction and the results are compared with Hartree-Fock-Bogoliubov calculations. It is shown that the widths of resonant states have an important effect on the pairing properties of nuclei close to the drip line.

SPIN-ALIGNED NEUTRON-PROTON PAIR MODE IN ATOMIC NUCLEI

Shell model calculations reveal that the low-lying spectrum of the N = Z nucleus 92 Pd is generated from a correlated isoscalar spin-aligned neutron-proton pair mode, exhibiting a new form of collectivity different from vibrational and rotational excitations. Already the ground state structure of 92 Pd is mostly built from isoscalar pairs each carrying angular momentum J = 9. This structure is different from all other even-even nuclei studied so far. The energy spectrum generated by the correlated neutron-proton pairs has two distinctive features: i) it is almost equidistant for low-lying energies and ii) the transition probability I ! I − 2 is approximately constant and independent of I. This exotic coupling scheme is predicted to correspond to the yrast structures of the heaviest nuclei approaching the doubly-magic 100 Sn.

Theories of proton emission

A very simple formula is presented that relates the logarithm of the half-life, corrected by the centrifugal barrier, with the Coulomb parameter in proton decay processes. The corresponding experimental data lie on two straight lines which appear as a result of a sudden change in the nuclear shape marking two regions of deformation independently of the angular momentum of the outgoing proton. This feature provides a powerful tool to assign experimentally quantum numbers in proton emitters.

BCS equations in the continuum

Abstract The BCS equations are extended to incorporate the contribution of the resonant part of the continuum single-particle spectrum. The effect of the resonant continuum appears in the new set of equations through the generalized level density. A numerical application is presented for the nucleus 170 Sn.