Fission modes of mercury isotopes

Background: Recent experiments on beta-delayed fission in the mercury-lead region and the discovery of asym- metric fission in 180 Hg [1] have stimulated theoretical interest in the mechanism of fission in heavy nuclei. Purpose: We study fission modes and fusion valleys in 180 Hg and 198 Hg to reveal the role of shell effects in pre-scission region and explain the experimentally observed fragment mass asymmetry and its variation with A. Methods: We use the self-consistent nuclear density functional theory employing Skyrme and Gogny energy density functionals. Results: The potential energy surfaces in multi-dimensional space of collective coordinates, including elongation, triaxiality, reflection-asymmetry, and necking, are calculated for 180 Hg and 198 Hg. The asymmetric fission valleys - well separated from fusion valleys associated with nearly spherical fragments - are found in in both cases. The density distributions at scission configurations are studied and related to the experimentally observed mass splits. Conclusions: The energy density functionals SkM\ast and D1S give a very consistent description of the fission process in 180 Hg and 198 Hg. We predict a transition from asymmetric fission in 180 Hg towards more symmetric distribution of fission fragments in 198 Hg. For 180 Hg, both models yield 100 Ru/80 Kr as the most probable split. For 198 Hg, the most likely split is 108 Ru/90 Kr in HFB-D1S and 110 Ru/88 Kr in HFB-SkM\ast.Comment: 6 pages, 5 figures, to be published in Physical Review

Theoretical X-Ray Absorption Debye-Waller Factors

An approach is presented for theoretical calculations of the Debye-Waller factors in x-ray absorption spectra. These factors are represented in terms of the cumulant expansion up to third order. They account respectively for the net thermal expansion $\sigma^{(1)}(T)$, the mean-square relative displacements $\sigma^2(T)$, and the asymmetry of the pair distribution function $\sigma^{(3)}(T)$. Similarly, we obtain Debye-Waller factors for x-ray and neutron scattering in terms of the mean-square vibrational amplitudes $u^2(T)$. Our method is based on density functional theory calculations of the dynamical matrix, together with an efficient Lanczos algorithm for projected phonon spectra within the quasi-harmonic approximation. Due to anharmonicity in the interatomic forces, the results are highly sensitive to variations in the equilibrium lattice constants, and hence to the choice of exchange-correlation potential. In order to treat this sensitivity, we introduce two prescriptions: one based on the local density approximation, and a second based on a modified generalized gradient approximation. Illustrative results for the leading cumulants are presented for several materials and compared with experiment and with correlated Einstein and Debye models. We also obtain Born-von Karman parameters and corrections due to perpendicular vibrations.Comment: 11 pages, 8 figure

Spontaneous fission modes and lifetimes of super-heavy elements in the nuclear density functional theory

Lifetimes of super-heavy (SH) nuclei are primarily governed by alpha decay and spontaneous fission (SF). Here we study the competing decay modes of even-even SH isotopes with 108 <= Z <= 126 and 148 <= N <= 188 using the state-of-the-art self-consistent nuclear density functional theory framework capable of describing the competition between nuclear attraction and electrostatic repulsion. The collective mass tensor of the fissioning superfluid nucleus is computed by means of the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov approach. Along the path to fission, our calculations allow for the simultaneous breaking of axial and space inversion symmetries; this may result in lowering SF lifetimes by more than seven orders of magnitude in some cases. We predict two competing SF modes: reflection-symmetric and reflection-asymmetric.The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow corridor formed by $^{280}$Hs, $^{284}$Fl, and $^{284}_{118}$Uuo that separates the regions of SH nuclei synthesized in "cold fusion" and "hot fusion" reactions. The region of long-lived SH nuclei is expected to be centered on $^{294}$Ds with a total half-life of ?1.5 days.Comment: 6 pages, 4 figure

One-particle exchange in the double folded potential in a semiclassical approximation

The one-particle exchange in the double folded model is analyzed. To this aim the Extended Thomas-Fermi approach to the one-body density matrix is used. The nucleon- nucleon force with Yukawa, Gauss and Coulomb-type form factors are considered. The energy dependence of the exchange part of the double folded potential is investigated and a comparison of the present approach with former ones is carried out.Comment: 22 pages, LateX, and 6 PostScript figures, (submitted to J.of Phys.G

The T=0 neutron-proton pairing correlations in the superdeformed rotational bands around 60Zn

The superdeformed bands in 58Cu, 59Cu, 60Zn, and 61Zn are analyzed within the frameworks of the Skyrme-Hartree-Fock as well as Strutinsky-Woods-Saxon total routhian surface methods with and without the T=1 pairing correlations. It is shown that a consistent description within these standard approaches cannot be achieved. A T=0 neutron-proton pairing configuration mixing of signature-separated bands in 60Zn is suggested as a possible solution to the problem.Comment: 9 ReVTex pages, 10 figures, submitted to Phys. Rev.

Relations between fusion cross sections and average angular momenta

We study the relations between moments of fusion cross sections and averages of angular momentum. The role of the centrifugal barrier and the target deformation in determining the effective barrier radius are clarified. A simple method for extracting average angular momentum from fusion cross sections is demonstrated using numerical examples as well as actual data.Comment: 16 REVTeX pages plus 8 included Postscript figures (uses the epsf macro); submitted to Phys. Rev. C; also available at http://nucth.physics.wisc.edu/preprint

Extended Hauser-Feshbach Method for Statistical Binary-Decay of Light-Mass Systems

An Extended Hauser-Feshbach Method (EHFM) is developed for light heavy-ion fusion reactions in order to provide a detailed analysis of all the possible decay channels by including explicitly the fusion-fission phase-space in the description of the cascade chain. The mass-asymmetric fission component is considered as a complex-fragment binary-decay which can be treated in the same way as the light-particle evaporation from the compound nucleus in statistical-model calculations. The method of the phase-space integrations for the binary-decay is an extension of the usual Hauser-Feshbach formalism to be applied to the mass-symmetric fission part. The EHFM calculations include ground-state binding energies and discrete levels in the low excitation-energy regions which are essential for an accurate evaluation of the phase-space integrations of the complex-fragment emission (fission). In the present calculations, EHFM is applied to the first-chance binary-decay by assuming that the second-chance fission decay is negligible. In a similar manner to the description of the fusion-evaporation process, the usual cascade calculation of light-particle emission from the highly excited complex fragments is applied. This complete calculation is then defined as EHFM+CASCADE. Calculated quantities such as charge-, mass- and kinetic-energy distributions are compared with inclusive and/or exclusive data for the $^{32}$S+$^{24}$Mg and $^{35}$Cl+$^{12}$C reactions which have been selected as typical examples. Finally, the missing charge distributions extracted from exclusive measurements are also successfully compared with the EHFM+CASCADE predictions.Comment: 34 pages, 6 Figures available upon request, Phys. Rev. C (to be published

Quantum Tunneling in Nuclear Fusion

Recent theoretical advances in the study of heavy ion fusion reactions below the Coulomb barrier are reviewed. Particular emphasis is given to new ways of analyzing data, such as studying barrier distributions; new approaches to channel coupling, such as the path integral and Green function formalisms; and alternative methods to describe nuclear structure effects, such as those using the Interacting Boson Model. The roles of nucleon transfer, asymmetry effects, higher-order couplings, and shape-phase transitions are elucidated. The current status of the fusion of unstable nuclei and very massive systems are briefly discussed.Comment: To appear in the January 1998 issue of Reviews of Modern Physics. 13 Figures (postscript file for Figure 6 is not available; a hard copy can be requested from the authors). Full text and figures are also available at http://nucth.physics.wisc.edu/preprints

Staggering effects in nuclear and molecular spectra

It is shown that the recently observed Delta J = 2 staggering effect (i.e. the relative displacement of the levels with angular momenta J, J+4, J+8, ..., relatively to the levels with angular momenta J+2, J+6, J+10, ...) seen in superdeformed nuclear bands is also occurring in certain electronically excited rotational bands of diatomic molecules (YD, CrD, CrH, CoH), in which it is attributed to interband interactions (bandcrossings). In addition, the Delta J = 1 staggering effect (i.e. the relative displacement of the levels with even angular momentum J with respect to the levels of the same band with odd J) is studied in molecular bands free from Delta J = 2 staggering (i.e. free from interband interactions/bandcrossings). Bands of YD offer evidence for the absence of any Delta J = 1 staggering effect due to the disparity of nuclear masses, while bands of sextet electronic states of CrD demonstrate that Delta J = 1 staggering is a sensitive probe of deviations from rotational behaviour, due in this particular case to the spin-rotation and spin-spin interactions.Comment: LaTeX, 16 pages plus 30 figures given in separate .ps files. To appear in the proceedings of the 4th European Workshop on Quantum Systems in Chemistry and Physics (Marly-le-Roi, France, 1999), ed. J. Maruani et al. (Kluwer, Dordrecht