Neck Degree Of Freedom Research Articles

Fission fragment mass and total kinetic energy distributions of spontaneously fissioning plutonium isotopes

The fission-fragment mass and total kinetic energy (TKE) distributions are evaluated in a quantum mechanical framework using elongation, mass asymmetry, neck degree of freedom as the relevant collective parameters in the Fourier shape parametrization recently developed by us. The potential energy surfaces (PES) are calculated within the macroscopic-microscopic model based on the Lublin-Strasbourg Drop (LSD), the Yukawa-folded (YF) single-particle potential and a monopole pairing force. The PES are presented and analysed in detail for even-even Plutonium isotopes with A = 236–246. They reveal deep asymmetric valleys. The fission-fragment mass and TKE distributions are obtained from the ground state of a collective Hamiltonian computed within the Born-Oppenheimer approximation, in the WKB approach by introducing a neck-dependent fission probability. The calculated mass and total kinetic energy distributions are found in good agreement with the data.

Mass distribution of fission fragments within the Born-Oppenheimer approximation

.The fission fragments mass-yield of 236 U is obtained by an approximate solution of the eigenvalue problem of the collective Hamiltonian that describes the dynamics of the fission process whose degrees of freedom are: the fission (elongation), the neck and mass-asymmetry modes. The macroscopic-microscopic method is used to evaluate the potential energy surface. The macroscopic energy part is calculated using the liquid drop model and the microscopic corrections are obtained using a Woods-Saxon single-particle levels. The four-dimensional modified Cassini ovals shape parametrization is used to describe the shape of the fissioning nucleus. The mass tensor is taken within a cranking-type approximation. The final fragment mass distribution is obtained by weighting the adiabatic density distribution in the collective space with the neck-dependent fission probability. The neck degree of freedom is found to play a significant role in determining the final fragment mass distribution.

Dynamical effects in the fusion hindrance

It is well known that there is a hindrance to fusion in collisions with heavy nuclei that plays a decisive role in synthesis of the super-heavy elements (SHE). The origin of the fusion hindrance is nowadays qualitatively understood but there are still quantitative ambiguities on the dynamics of the fusion mechanism and the predictions need to be assessed. In this communication, we stress the fact that dynamical effects play a crucial role in the amplitude of the reduction of the fusion probability. We found that the fast evolution of the neck degree of freedom affects the slow radial motion, i.e., the fusioning motion, through a dynamical coupling. We showed that we could do a so-called adiabatic elimination of the fast variable in the coupled equation, resulting in an effective one-dimensional equation for the radial motion with a shift of the starting point. This treatment of the dynamical coupling leads to a larger hindrance.

Quantum propagator approach to heavy-ion fusion

The real-time path-integral propagator approach is used to study the fusion probability of massive nuclei including of quantum effect. An analytical expression of the probability to pass over barrier of an inverted harmonic potential is obtained, in which both height and curvature of the barrier are controlled by the neck degree of freedom. The fusion probabilities of three systems in central collision as functions of the center-of-mass energy are calculated and in agreement with the experimental results. It is shown that the quantum fluctuation enhances the fusion probability at low energies, and the neck fluctuation makes the slope of the fusion probability curve become flatter.

Classical versus quantum chaos in strongly deformed nuclear potentials

The correspondence of classical dynamical chaos and statistical properties of the energy spectrum has been investigated for the single-particle motion in strongly deformed nuclear potentials with axial symmetry. The properties of the classical and of the quantized system were analyzed for two potentials: the two-center well potential of finite depth and the two-center oscillator shell model. It has been found that in such mean fields the occurrence of fully developed random matrix statistics is a generic feature corresponding to a global instability of classical trajectories. But due to the absence of scaling invariance, for the general case with a mixed phase space a significant energy dependence of the chaotic phase-space volume has been obtained so that the over-all level-spacing distribution cannot be specified by the chaotic volume as a single parameter. The reason for the appearance of chaoticity turns out to be rather complex. Besides the expected important role of large deformations of high multipolarity, including the neck degree of freedom, the spin-orbit part of the nuclear interaction can also be responsible for the occurrence of dynamical chaos.

Multi-dimensional tunneling description of subbarrier fusion including neck degree of freedom

Subbarrier fusion of heavy ions is treated as a multidimensional tunneling problem on a potential energy surface spanned by the relevant degrees of freedom in the fusion process. In addition to the radial separation these are taken to be the deformation of the two nuclei and the formation of noses or a neck between them. An initial wave packet is constructed on this surface and is then propagated in time by the Hamiltonian of the system. Thus the dynamical evolution is treated in a fully quantum-mechanical way using degrees of freedom which are adapted to the fusion process. In this way one can clearly ascertain the effects of the spreading of the wave packet (zero point motion and internal excitation), the role of barriers and saddle points, and the tunneling process. We have applied the model to the fusion of the symmetric system58Ni+58Ni where we can reasonably limit the number of coordinates. Neck formation is found to be very important for the fusion enhancement and we even obtain a quantitative description of the data. In addition the time dependent wave packet method provides a very intuitive picture of the fusion process which helps to discuss the different approaches to subbarrier fusion in a unified way.

Fusion, deep-inelastic collisions, and neck formation.

We use the liquid drop model to calculate the cross section for neck formation in a heavy-ion collision and show that for the recently measured /sup 58/Ni+/sup 124/Sn case this cross section is strongly related to the sum of the fusion and deep-inelastic cross sections. We note that the observation of deep-inelastic collisions at sub-Coulomb barrier energies may be classically understood by the effective barrier lowering obtained when the neck degree of freedom is considered.

Description of nuclear molecular resonances in 24Mg+ 24Mg with the two-center shell model and the neck degree of freedom

A new ansatz for the description of nuclear reactions revealing molecular-like resonances is presented. The hamiltonian of the model contains an extra potential for the pole-to-pole orientation of deformed nuclei. Calculations for the system 24Mg+ 24Mg show that this potential has a minimum for energies and angular momenta where resonances have been found.

BIMODAL FISSION IN 258FM

Within the 2-center shell model we present an explanation for the mass and total-kinetic-energy distributions of fission products of very heavy nuclei called “bimodal fission.” For the case of 258 FM we show that the symmetric fission can be described by a 2-dimensional treatment of the elongation and neck degree of freedom. Owing to shell corrections the system fissions via two decay channels that have distinct kinetic energies.

Influence of neck formation on heavy ion subbarrier fusion.

We calculate the effect of the neck degree of freedom on subbarrier fusion reaction cross sections. The potential energy and mass tensor are calculated on the basis of a two-dimensional representation of the liquid drop model. The WKB and Hill-Wheeler approximations are used to calculate the tunneling amplitudes for motion along the direction of the neck size degree of freedom. The resulting cross section for collisions between two identical Ni isotopes show a marked enhancement at low energies compared with the standard one-dimensional radial penetration calculations.

Symmetrical fusion of heavy ions around the Coulomb barrier energy

Using the liquid-drop model, the authors have performed a systematic study of symmetrical fusion with a neck degree of freedom and tunnelling effects, the nuclear potential being calculated with the proximity approach. Barrier heights and positions are in very good agreement with experimental data when they are known (light-medium systems); the recent experimental data for the reactions 58Ni+58Ni and 64Ni+64Ni are investigated particularly. For heavier systems double-humped fusion barriers and isomeric states are predicted which strongly limit the complete fusion probability.