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Nuclei undergoing fission can be described by a multi-dimensional potential-energy surface that guides the nuclear shape evolution--from the ground state, through intermediate saddle points and finally to the configurations of separated fission fragments. Until now, calculations have lacked adequate exploration of the shape parameterization of sufficient dimensionality to yield features in the potential-energy surface (such as multiple minima, valleys, saddle points and ridges) that correspond to characteristic observables of the fission process. Here we calculate and analyse five-dimensional potential-energy landscapes based on a grid of 2,610,885 deformation points. We find that observed fission features--such as the distributions of fission fragment mass and kinetic energy, and the different energy thresholds for symmetric and asymmetric fission--are very closely related to topological features in the calculated five-dimensional energy landscapes.

We propose a model based on quantum molecular dynamics (QMD) incorporated with statistical decay model (SDM) to describe various nuclear reactions in an unified way. In this first part of the work, the basic ingredients of the model are defined and the model is applied systematically to the nucleon(N )-induced reactions. It has been found that our model can give a remarkable agreement in the energy-angle double differential cross sections of (N, xN ′ ) type reactions for incident energies from 100 MeV to 3 GeV with a fixed parameter set. An unified description of the major three reaction mechanisms of (N, xN ′ ) reactions, i.e. compound, pre-equilibrium and spallation processes, is given with our model.

A very exotic process of -delayed fission of 180 Tl is studied in detail by using resonant laser ionization with subsequent mass separation at ISOLDE (CERN). In contrast to common expectations, the fissionfragment mass distribution of the post--decay daughter nucleus 180 Hg (N=Z ¼ 1:25) is asymmetric. This asymmetry is more surprising since a mass-symmetric split of this extremely neutron-deficient nucleus would lead to two 90 Zr fragments, with magic N ¼ 50 and semimagic Z ¼ 40. This is a new type of asymmetric fission, not caused by large shell effects related to fragment magic proton and neutron numbers, as observed in the actinide region. The newly measured branching ratio for -delayed fission of 180 Tl is 3:6ð7Þ Â 10 À3 %, approximately 2 orders of magnitude larger than in an earlier study. DOI: 10.1103/PhysRevLett.105.252502 PACS numbers: 24.75.+i, 23.40.Às, 27.70.+q Nuclear fission, discovered more than 70 years ago [1], represents one of the most dramatic examples of a nuclear metamorphosis, whereby the nucleus splits into two fragments releasing a large amount of energy. Initially, the fission process was described within the liquid-drop model [2,3], in which shape-dependent surface and Coulomb energy terms define the potential-energy landscape through which fission occurs. However, this macroscopic approach naturally leads to symmetric fragments and cannot explain observed asymmetric mass splits of actinides. Only by including a microscopic treatment based on shell effects can asymmetric fission be described [4]. Importantly, only in fission below or slightly above the barrier, so-called low-energy fission, can the interplay between the macroscopic liquid-drop contribution and the microscopic single-particle shell corrections be most fully explored.Until recently, such low-energy fission studies were limited to nuclei from around thorium (Th) to fermium (Fm) using spontaneous fission, fission induced by thermal neutrons or -delayed fission. These studies showed the dominance of asymmetric fission over symmetric fission for most isotopes of these elements [5][6][7] and suggested that structure effects due to, specifically, the spherical shell structure of doubly magic 132 Sn dominate the mass split. A decade ago, a new technique, developed at GSI [8]-Coulomb-excited fission of radioactive beamsallowed for a more extensive experimental survey of lowenergy fission in other regions of the nuclidic chart. These studies demonstrated the transition from mostly asymmetric fission in the actinides towards symmetric fission as the dominant mode in the light thorium to astatine region. This is also consistent with earlier studies by Itkis et al. [9], in which fission of stable targets in the mass 185-210 region was induced by bombardment with protons and 3;4 He beams. Itkis et al. found mostly symmetric mass distributions in the region around 208 Pb, with about four systems in the mass A $ 200 region having a slight reduction of PRL 105, 252502 (2010)

Quantum molecular dynamics is applied to study the ground state properties of nuclear matter at subsaturation densities. Clustering effects are observed as to soften the equation of state at these densities. The structure of nuclear matter at subsaturation density shows some exotic shapes with variation of the density. 61.43.Bn,31.15.Qg,21.65.+f,26.20.+c,97.60.Jd,97.60.Bw,05.70.Fh Typeset using REVT E X One of the main interests of heavy-ion physics and astrophysics is the property of nuclear matter in extreme conditions. Its high-density behavior is important for the scenario of supernova explosions, the evolution of neutron stars, the reaction process of high-energy heavy-ion collisions, quark-gluon plasma and so on. Properties of the nuclear matter below saturation density, on the other hand, are essential in describing the multi-fragmentation in the heavy-ion collisions, the collapsing stages in supernova explosions and the structure of neutron star crusts. Here the saturation density is the density of the energy-minimum state of the nuclear matter at a fixed proton ratio. For symmetric nuclear matter, the saturation density is the normal nuclear density ρ 0 = 0.165 fm −3 . Since the matter is unstable below the saturation density, an inhomogeneous state is expected to appear below the saturation density.Besides, supernova matter (SNM) and neutron star matter (NSM) are also interesting from the viewpoint of the nuclear shape. At low densities, nuclei in these matters are expected to be crystalized so as to minimize the long range Coulomb energies. They melt into uniform matter at a certain density close to the saturation density. Then what happens in between? About a decade ago, three groups [1-3] suggested that nuclei have exotic structures in the SNM and/or NSM. They showed that the stable nuclear shape changes from sphere to cylinder, slab, cylindrical hole, and to spherical hole with increase of the matter density. The favorable nuclear shape is determined by a balance between the surface and Coulomb energies. In the liquid drop model, a simple geometrical argument demonstrates that the favorable shape changes as a function of the volume fraction of the nucleus in the cell, independently of specific nuclear interactions [2,4]. ¿From recent studies in the liquid drop model [5] and the Thomas Fermi calculations [6,7], the non-spherical shapes of nuclei are expected in a density range at about half the saturation density although the range depends on the choice of nuclear interaction. Furthermore these shapes are expected to survive even if the shell effects are taken into account [8].

We re-examine the effort to constrain the time-variability of the coupling constants of the fundamental interactions by studying the anomalous isotopic abundance of Sm observed at the remnants of the natural reactors which were in operation at Oklo about 2 billion years ago, in terms of a possible deviation of the resonance energy from the value observed today. We rely on new samples that were carefully collected to minimize natural contamination and also on a careful temperature estimate of the reactors. We obtain the upper bound $(-0.2\pm 0.8)\times 10^{-17}$ ${\rm y}^{-1}$ on the fractional rate of change of the electromagnetic as well as the strong interaction coupling constants. Our result basically agrees with and even suggests some improvement of the result due recently to Damour and Dyson. Strictly speaking, however, we find another range of the resonance energy shift indicating a nonzero time variation of the constants. We find a rather strong but still tentative indication that this range can be ruled out by including the Gd data, for which it is essential to take the effect of contamination into account.Comment: 20 pages LaTex including 6 figures. Theoretical interpretation changed. More detailed discussions on the temperature estimate also adde

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We present calculated fission-barrier heights for 5239 nuclides, for all nuclei between the proton and neutron drip lines with 171 ≤ A ≤ 330. The barriers are calculated in the macroscopicmicroscopic finite-range liquid-drop model (FRLDM) with a 2002 set of macroscopic-model parameters. The saddle-point energies are determined from potential-energy surfaces based on more than five million different shapes, defined by five deformation parameters in the threequadratic-surface shape parameterization: elongation, neck diameter, left-fragment spheroidal deformation, right-fragment spheroidal deformation, and nascent-fragment mass asymmetry. The energy of the ground state is determined by calculating the lowest-energy configuration in both the Nilsson perturbed-spheroid (ǫ) and in the spherical-harmonic (β) parameterizations, including axially asymmetric deformations. The lower of the two results (correcting for zero-point motion) is defined as the ground-state energy. The effect of axial asymmetry on the inner barrier peak is calculated in the (ǫ, γ) parameterization. We have earlier benchmarked our calculated barrier heights to experimentally extracted barrier parameters and found average agreement to about one MeV for known data across the nuclear chart. Here we do additional benchmarks and investigate the qualitative, and when possible, quantitative agreement and/or consistency with data on β-delayed fission, isotope generation along prompt-neutron-capture chains in nuclear-weapons tests, and superheavy-element stability. These studies all indicate that the model is realistic at considerable distances in Z and N from the region of nuclei where its parameters were determined.