J. Rayford Nix

Atomic masses and nuclear ground-state deformations calculated with a new macroscopic-microscopic model

Abstract We tabulate the atomic masses and nuclear ground-state deformations of 4023 nuclides ranging from 16O to 279112, calculated on the basis of a Yukawa-plus-exponential macroscopic model and a folded-Yukawa microscopic model, with new terms included to account for several previously neglected physical effects. With the values of only five constants determined from a least-squares adjustment to ground-state masses, the resulting root-mean-square error in the calculated ground-state masses of 1323 nuclides ranging from 16O to 259No for which experimental values are known with experimental errors less than 1 MeV is 0.835 MeV.

New Calculation of Prompt Fission Neutron Spectra and Average Prompt Neutron Multiplicities

We present a new method for calculating the prompt fission neutron spectrum N(E) and average prompt neutron multiplicity anti nu/sub p/ as functions of the fissioning nucleus and its excitation energy. The method is based on standard nuclear evaporation theory and takes into account (1) the motion of the fission fragments, (2) the distribution of fission-fragment residual nuclear temperature, (3) the energy dependence of the cross section sigma/sub c/ for the inverse process of compound-nucleus formation, and (4) the possibility of multiple-chance fission. We use a triangular distribution in residual nuclear temperature based on the Fermi-gas model. This leads to closed expressions for N(E) and anti nu/sub p/ when sigma/sub c/ is assumed constant and readily computed quadratures when the energy dependence of sigma/sub c/ is determined from an optical model. Neutron spectra and average multiplicities calculated with an energy-dependent cross section agree well with experimental data for the neutron-induced fission of /sup 235/U and the spontaneous fission of /sup 252/Cf. For the latter case, there are some significant inconsistencies between the experimental spectra that need to be resolved. 29 references.

Nuclear mass formula with a Yukawa-plus-exponential macroscopic model and a folded-Yukawa single-particle potential

Abstract We use a Yukawa-plus-exponential macroscopic model and a folded-Yukawa single-particle potential to systematically calculate the ground-state masses of 4023 nuclei ranging from 16 O to {279}112. The method is also used to calculate the fission-barrier heights of 28 nuclei ranging from 109 Cd to 252 Cf. We introduce several previously neglected physical effects, including a smaller nuclear radius constant, a proton form factor, an exact diffuseness correction, an A 0 term, a chargeasymmetry term, and microscopic zero-point energies. The nuclear radius constant is determined from elastic electron scattering and microscopic calculations of nuclear density distributions, the range of the Yukawa-plus-exponential folding function is determined from heavy-ion elastic scattering, the surface-energy constant and surface-asymmetry constant are determined from the fission-barrier heights of the 28 nuclei that are considered, and the remaining constants are determined from the ground-state masses of 1323 nuclei ranging from 16 O to 259 No for which experimental values are known with experimental errors less than 1 MeV. For the final formula, the root-mean-square error in the ground-state masses is 0.835 MeV and the root-mean-square error in the fission-barrier heights is 1.331 MeV. Some of the remaining discrepancies in the groundstate masses can be understood in terms of instabilities with respect to e 3 and e 6 deformations.

New model of the average neutron and proton pairing gaps

Abstract By use of the BCS approximation applied to a distribution of dense, equally spaced levels, we derive new expressions for the average neutron pairing gap \ gDn and average proton pairing gap \ gDp. These expressions, which contain exponential terms, take into account the dependencies of \ gDn and \ gDp upon both the relative neutron excess and shape of the nucleus. The three constants that appear are determined by a least-squares adjustment to experimental pairing gaps obtained by use of fourth-order differences of measured masses. For this purpose we use the 1986 Audi-Wapstra mid-stream mass evaluation and take into account experimental uncertainties. Our new model explains not only the dependencies of \ gDn and \ gDp upon relative neutron excess and nuclear shape, but also the experimental result that for medium and heavy nuclei \ gDn is generally smaller than \ gDp. We also introduce a new expression for the average residual neutron-proton interaction energy \ gd that appears in the masses of odd-odd nuclei, and determine the constant that appears by an analogous least-squares adjustment to experimental mass differences. Our new expressions for \ gDn, \ gDp and \ gd should permit extrapolation of these quantities to heavier nuclei and to nuclei farther removed from the valley of β stability than do previous parameterizations.

Fission dynamics simplified

Abstract By use of Kramers stationary solution of the Folker-Planck equation for the inverted oscillator, we derive analytic expressions as functions of nuclear temperature and dissipation coefficient for several quantities of interest in the dynamics of nuclear fission. These include the mean time from the saddle point to scission, the mean pre-scission fission-fragment kinetic energy and the contribution to the variance in the fission-fragment kinetic energy resulting from fluctuations in the fission degree of freedom.

Extracting Source Parameters from Gaussian Fits to Two-Particle Correlations

Using a quadratic saddle-point approximation we show how information about a particle-emitting source can be extracted from Gaussian fits to two-particle correlation data. Although the formalism is completely general, extraction of the relevant parameters is much simpler for sources within an interesting class of azimuthally symmetric models. After discussing the standard fitting procedure we introduce a new Gaussian fitting procedure which is an azimuthally symmetric generalization of the Yano-Koonin formalism for spherically symmetric sources. This new fitting procedure has the advantage that in addition to being able to measure source parameters in a fixed frame or the longitudinally comoving system, it can also measure these parameters in the local rest frame of the source.

Stability and decay of nuclei at the end of the periodic system

Abstract Recent studies of nuclear mass models show that it is essential to account for the Coulomb redistribution energy when calculating the nuclear potential energy in the heavy-element region. Results obtained by use of a mass model that includes Coulomb redistribution effects are analyzed. Q -values for α- and β-decay are calculated. Half-lives for α-decay are estimated by use of the Viola-Seaborg systematics. For EC, β + decay and β − decay, half-lives are calculated in a microsciopic QRPA model. Calculated single-particle level structures in the heavy-element region are presented. These indicate possible regions of isomers that would be unusually stable with respect to spontaneous fission and α-decay. Finally, we discuss the implications of earlier extensive work on fission properties of nuclei in this region.

Effect of dissipation on ternary fission in very heavy nuclear systems

Abstract On the basis of a macroscopic dynamical model, we explore the effect of two prototype dissipation mechanisms that represent opposite extremes of small and large dissipation on the formation of a third fragment during the fission of very heavy nuclear systems. With five collective coordinates to describe axially symmetric and reflection-symmetric nuclear shapes, we solve the generalized Hamilton equations of motion numerically to determine the time evolution of the system. The nuclear potential energy of deformation is calculated as the sum of a repulsive Coulomb energy and an attractive Yukawa-plus-exponential potential, the inertia tensor is calculated for incompressible, nearly irrotational flow by use of the Werner-Wheeler method and the dissipation tensor is calculated for both two-body viscosity and one-body dissipation. For light nuclei the dynamical evolution leads to compact binary scission shapes, but for sufficiently heavy nuclei it leads to shapes with long necks that subsequently contract at the extremities to form three fragments. This ternary division, whose onset begins at Z 2 A∼35 for two-body viscosity and much later at Z 2 A∼57 for one-body dissipation, is examined in terms of a neck instability that is analogous to the Plateau-Rayleigh hydrodynamic instability of an uncharged, infinite, initially stationary cylinder. For nuclear systems with mass numbers ranging from 200 to 500, we calculate the mass of the third fragment that forms under certain circumstances, the translational kinetic energy of the two end fragments at infinity, and the time required for the system to descend from its saddle point to scission.

The coulomb redistribution energy as revealed by a refined study of nuclear masses

Abstract The macroscopic-microscopic approach to the calculation of nuclear masses has been further refined through the inclusion of e3 and e6 shape degrees of freedom. Most of the systematic discrepancies that previously existed for heavy nuclei have been eliminated. The agreement is so close that the effect of turning on and off the Coulomb redistribution terms in the finite-range droplet model can be clearly discerned, thus confirming the contribution of this physical effect to nuclear stability. Models without the higher-order terms of the finite-range droplet model, such as the finite-range liquid-drop model that we also investigate here, are clearly inferior in the heavy-element region.

Collisions of deformed nuclei: A path to the far side of the superheavy island

Abstract A detailed understanding of complete fusion cross sections in heavy-ion collisions requires a consideration of the effects of the deformation of the projectile and target. Our aim here is to show that deformation and orientation of the colliding nuclei have a very significant effect on the fusion-barrier height and on the compactness of the touching configuration. To facilitate discussions of fusion configurations of deformed nuclei, we develop a classification scheme and introduce a notation convention for these configurations. We discuss particular deformations and orientations that lead to compact touching configurations and to fusion-barrier heights that correspond to fairly low excitation energies of the compound systems. Such configurations should be the most favorable for producing superheavy elements. We analyze a few projectile-target combinations whose deformations allow favorable entrance-channel configurations and whose proton and neutron numbers lead to compound systems in a part of the superheavy region where α half-lives are calculated to be observable, that is, longer than 1 μs.