Theoretical Evaluations of the Fission Cross Section of the 77 eV Isomer of 235-U

We have developed models of the fission barrier (barrier heights and transition state spectra) that reproduce reasonably well the measured fission cross section of $^{235}$U from neutron energy of 1 keV to 2 MeV. From these models we have calculated the fission cross section of the 77 eV isomer of $^{235}$U over the same energy range. We find that the ratio of the isomer cross section to that of the ground state lies between about 0.45 and 0.55 at low neutron energies. The cross sections become approximately equal above 1 MeV. The ratio of the neutron capture cross section to the fission cross section for the isomer is predicted to be about a factor of 3 larger for the isomer than for the ground state of $^{235}$U at keV neutron energies. We have also calculated the cross section for the population of the isomer by inelastic neutron scattering form the $^{235}$U ground state. We find that the isomer is strongly populated, and for $E_n = 1 MeV$ the $(n,n'\gamma)$ cross section leading to the population of the isomer is of the order of 0.5 barn. Thus, neutron reaction network calculations involving the uranium isotopes in a high neutron fluence are likely to be affected by the 77 eV isomer of $^{235}$U. With these same models the fission cross sections of $^{233}$U and $^{237}$U can be reproduced approximately using only minor adjustments to the barrier heights. With the significant lowering of the outer barrier that is expected for the outer barrier the general behavior of the fission cross section of $^{239}$Pu can also be reproduced.Comment: 17 pages including 8 figure

Diffusion over a saddle with a Langevin equation

The diffusion problem over a saddle is studied using a multi-dimensional Langevin equation. An analytical solution is derived for a quadratic potential and the probability to pass over the barrier deduced. A very simple solution is given for the one dimension problem and a general scheme is shown for higher dimensions.Comment: 13 pages, use revTeX, to appear in Phys. Rev. E6

Two-Step Model of Fusion for Synthesis of Superheavy Elements

A new model is proposed for fusion mechanisms of massive nuclear systems where so-called fusion hindrance exists. The model describes two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to $^{48}$Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. Combined with the statistical decay theory, residue cross sections for the superheavy elements can be readily calculated. Examples are given.Comment: 4 pages, 4 figure

The interaction of 11Li with 208Pb

Background: 11Li is one of the most studied halo nuclei. The fusion of 11Li with 208Pb has been the subject of a number of theoretical studies with widely differing predictions, ranging over four orders of magnitude, for the fusion excitation function. Purpose: To measure the excitation function for the 11Li + 208Pb reaction. Methods: A stacked foil/degrader assembly of 208Pb targets was irradiated with a 11Li beam producing center of target beam energies from above barrier to near barrier energies (40 to 29 MeV). The intensity of the 11Li beam (chopped) was 1250 p/s and the beam on-target time was 34 hours. The alpha-decay of the stopped evaporation residues was detected in a alpha-detector array at each beam energy in the beam-off period (the beam was on for <= 5 ns and then off for 170 ns). Results: The 215At evaporation residues were associated with the fusion of 11Li with 208Pb. The 213,214At evaporation residues were formed by the breakup of 11Li into 9Li + 2n, with the 9Li fusing with 208Pb. The 214At evaporation residue appears to result from a "quasi-breakup" process. Conclusions: Most of 11Li + 208Pb interactions lead to breakup with a small fraction (<= 11%) leading to complete fusion.Comment: 25 pages, 11 figure

Rate equations for quantum transport in multi-dot systems

Starting with the many-body Schr\"odinger equation we derive new rate equations for resonant transport in quantum dots linked by ballistic channels with high density of states. The charging and the Pauli exclusion principle effects were taken into account. It is shown that the current in such a system displays quantum coherence effects, even if the dots are away one from another. A comparative analysis of quantum coherence effects in coupled and separated dots is presented. The rate equations are extended for description of coherent and incoherent transport in arbitrary multi-dot systems. It is demonstrated that new rate equations constitute a generalization of the well-known optical Bloch equations.Comment: Results are presented in more transparent way. Additional explanations and figures are included. To appear in Phys. Rev.

Classical Analysis of Phenomenological Potentials for Metallic Clusters

The classical trajectories of single particle motion in a Wodds-Saxon and a modified Nilsson potential are studied for axial quadrupole deformation. Both cases give rise to chaotic behaviour when the deformation in the Woods-Saxon and the l**2 term in the modified Nilsson potential are turned on. Important similarities, in particular with regard to the shortest periodic orbits, have been found.Comment: 9 pages LaTex + 4 figures available via e-mail requests from the authors, to appear in Phys.Rev.Let

Analysis of the Fusion Hindrance in Mass-symmetric Heavy Ion Reactions

The fusion hindrance, which is also denominated by the term extra-push, is studied on mass-symmetric systems by the use of the liquid drop model with the two-center parameterization. Following the idea that the fusion hindrance exists only if the liquid drop barrier (saddle point) is located at the inner side of the contact point after overcoming the outer Coulomb barrier, the reactions in which two barriers are overlapped with each other are determined. It is shown that there are many systems where the fusion hindrance does not exist for the atomic number of projectile or target nucleus $Z\leq43$, while for $Z>43$, all of the mass-symmetric reactions are fusion-hindered.Comment: 6 pages, 4 figures. to be published in Sci. in China

Nuclear fission: The "onset of dissipation" from a microscopic point of view

Semi-analytical expressions are suggested for the temperature dependence of those combinations of transport coefficients which govern the fission process. This is based on experience with numerical calculations within the linear response approach and the locally harmonic approximation. A reduced version of the latter is seen to comply with Kramers' simplified picture of fission. It is argued that for variable inertia his formula has to be generalized, as already required by the need that for overdamped motion the inertia must not appear at all. This situation may already occur above T=2 MeV, where the rate is determined by the Smoluchowski equation. Consequently, comparison with experimental results do not give information on the effective damping rate, as often claimed, but on a special combination of local stiffnesses and the friction coefficient calculated at the barrier.Comment: 31 pages, LaTex, 9 postscript figures; final, more concise version, accepted for publication in PRC, with new arguments about the T-dependence of the inertia; e-mail: [email protected]

Observation of Supershell Structure in Alkali Metal Nanowires

Nanowires are formed by indenting and subsequently retracting two pieces of sodium metal. Their cross-section gradually reduces upon retraction and the diameters can be obtained from the conductance. In previous work we have demonstrated that when one constructs a histogram of diameters from large numbers of indentation-retraction cycles, such histograms show a periodic pattern of stable nanowire diameters due to shell structure in the conductance modes. Here, we report the observation of a modulation of this periodic pattern, in agreement with predictions of a supershell structure.Comment: Phys. Rev. Lett., in prin