Recent studies in heavy ion induced fission reactions

Nuclear fission process involves large scale shape changes of the nucleus, while it evolves from a nearly spherical configuration to two separated fission fragments. The dynamics of these shape changes in the nuclear many body system is governed by a strong interplay of the collective and single particle degrees of freedom. With the availability of heavy ion accelerators, there has been an impetus to study the nuclear dynamics through the investigations of nucleus-nucleus collisions involving fusion and fission process. From the various investigations carried out in the past years, it is now well recognized that there is large scale damping of collective modes in heavy ion induced fission reactions, which in other words implies that nuclear motion is highly viscous. In recent years, there have been many experimental observations in heavy ion induced fission reactions at medium bombarding energies, which suggest possible occurrence of various non-equilibrium modes of fission such as quasi-fission, fast fission and pre-equilibrium fission, where some of the internal degrees of freedom of the nucleus is not fully equilibrated. We have carried out extensive investigations on the fission fragment angular distributions at near barrier bombarding energies using heavy fissile targets. The measured fragment anisotropies when compared with the standard saddle point model (SSPM) calculations show that for projectile-target systems having zero or low ground state spins, the angular anisotropy exhibits a peak-like behaviour at the sub barrier energies, which cannot be explained by the SSPM calculations. For projectiles or targets with large ground state spins, the anomalous peaking gets washed out due to smearing of the K-distribution by the intrinsic entrance channel spins. Recently studies have been carried out on the spin distributions of fission fragments through the gamma ray multiplicity measurements. The fission fragments acquire spin mainly from two sources: (i) due to rigid rotation of the nascent fragments at scission and (ii) due to statistical excitation of the spin bearing collective modes in the fissioning nucleus. One of the collective modes — the tilting mode depends on the K quantum number and is responsible for the emission angle dependence of fragment spin. In our studies, we have shown conclusively that the collective statistical spin modes get strongly suppressed for high K values corresponding to large rotational frequencies along the fission axis. These results bring out the importance of the dynamical effects in the heavy ion induced fusion-fission reactions. The present article will review the work carried out on the above aspects in heavy ion fission reactions as well as on the fission time scales, and some of the recent studies on the mass-energy correlations of fission fragments at near-barrier bombarding energies.     

Geometrical and dynamical state of the 252Cf nucleus at the scission point as determined from the experimental results of ternary fission

Resuits on the geometrical and dynamical states of fission fragments and α-particles are presented for the most probable mode of ternary fission, at the instant of release of the light particle. The distributions of the relevant physical quantities are obtained by means of a program calculating the trajectories of three point charges. A total of about 2 × 10⁵ combinations of the parameters, derived by subdividing the quantities into physically significant intervals, are used. The computed values are compared with experimental results and the distributions of the parameters are weighted by the spectrum of the α-parlicles. The dynamics of the system undergoing fission at scission point are characterized by the following quantities: (i) The total kinetic energy of fragments. (ii) The kinetic energy of the α-particle. (iii) The distance between the centres of charge of the fragments, (iv) The abscissa and Ordinate of the α-particle emission point, (v) The emission angle of the α-parlicle with respect to the line of flight of the light fragment. The distributions of above quantities are presented for the most probable model of spontaneous ternary fission of ²⁵²Cf The results obtained are discussed and relevant information on the dynamical properties of the last fission stage is presented.     

The effect of angular momentum coupling on the angular distribution of fission fragments

We examine what information can be obtained from fission angular distributions through precise measurements and an analysis in terms of the simple statistical model of Ericson. We report on the systematics of the decoupling angle and present the role of the angular momentum coupling between the entrance and the exit channel. The results indicate that the directional coupling of the angular momentum in the entrance and the exit channel is always strong for heavy-ion induced fission, and the angular momentum coupling plays a decisive role on the angular distribution of fission fragments. The average channel spins of fission fragments 〈I_f〉 are deduced through the decoupling angles determined experimentally. They agree well with γ-multiplicity measurements.     

Angular distributions of fragments originating from the spontaneous fission of oriented nuclei and problem of the conservation of the spin projection onto the symmetry axis of a fissile nucleus

The concept of transition fission states, which was successfully used to describe the angular distributions of fragments for the spontaneous and low-energy induced fission of axisymmetric nuclei, proves to be correct if the spin projection onto the symmetry axis of a fissile nucleus is an integral of the motion for the external region from the descent of the fissile nucleus from the external fission barrier to the scission point. Upon heating a fissile nucleus in this region to temperatures of T ≈ 1 MeV (this is predicted by many theoretical models of the fission process), the Coriolis interaction uniformly mixes the possible projections of the fissile-nucleus spin for the case of low spin values, this leading to the loss of memory about transition fission states in the asymptotic region where the angular distributions of fragments are formed. Within quantum-mechanical fission theory, which takes into account deviations from A. Bohr’s formula, the angular distributions of fragments are calculated for spontaneously fissile nuclei aligned by an external magnetic field at ultralow temperatures, and it is shown that an analysis of experimental angular distributions of fragments would make it possible to solve the problem of spin-projection conservation for fissile nuclei in the external region.     

Angular momentum transfer and spin dealignment mechanisms in damped nuclear reactions Ar+Bi and Ni+Pb

The angular momentum transferred to fragment spins has been studied in the damped nuclear reactions Ar+Bi at 255 MeV and 295 MeV and Ni+Pb at 435 MeV from measurement of the angular distribution of the fission fragments of the heavy-recoil nucleus in coincidence with the projectile-like fragment. The heavy-fragment spin is strongly aligned along the normal to the reaction plane and the rigid-rotation limit of the dinuclear system is attained. The dealignment mechanisms produce spin components mainly located in a plane approximately perpendicular to the heavy-recoil lab direction. They are well described by a dynamical model based on the nucleon exchange between the two ions during the collision. The spin-component fluctuations reach high values. In the heavy-recoil direction, these fluctuations are increasing with the total kinetic energy loss and the charge transfer from the projectile to the target. The spin values extracted from both the angular distributions and the fission probabilities are seen to be compatible.     

Post-scission dynamics in fission

A dynamical model for fission from the classical turning point to scission and beyond is presented. We consider the fissioning nucleus as well as the fission fragments as incompressible irrotational deformable charged liquid drops. We focus on the post-scission time evolution of the neck, stretching of the fragments, kinetic energy and excitation energy.     

Dynamical mean-field theory for pairing and spin gap in the attractive hubbard model

We solve the attractive Hubbard model for arbitrary interaction strengths within dynamical mean-field theory. We compute the transition temperature for superconductivity and analyze electron pairing in the normal phase. The normal state is a Fermi liquid at weak coupling and a non-Fermi-liquid state with a spin gap at strong coupling. Away from half filling, the quasiparticle weight vanishes discontinuously at the transition between the two normal states.     

Investigation of the reaction 208Pb(18O, f): Fragment spins and phenomenological analysis of the angular anisotropy of fission fragments

The average multiplicity of gamma rays emitted by fragments originating from the fission of ²²⁶Th nuclei formed via a complete fusion of ¹⁸O and ²⁰⁸Pb nuclei at laboratory energies of ¹⁸O projectile ions in the range E _lab = 78–198.5 MeV is measured and analyzed. The total spins of fission fragments are found and used in an empirical analysis of the energy dependence of the anisotropy of these fragments under the assumption that their angular distributions are formed in the vicinity of the scission point. The average temperature of compound nuclei at the scission point and their average angular momenta in the entrance channel are found for this analysis. Also, the moments of inertia are calculated for this purpose for the chain of fissile thorium nuclei at the scission point. All of these parameters are determined at the scission point by means of three-dimensional dynamical calculations based on Langevin equations. A strong alignment of fragment spins is assumed in analyzing the anisotropy in question. In that case, the energy dependence of the anisotropy of fission fragments is faithfully reproduced at energies in excess of the Coulomb barrier (E _c.m. ? E _B ≥ 30 MeV). It is assumed that, as the excitation energy and the angular momentum of a fissile nucleus are increased, the region where the angular distributions of fragments are formed is gradually shifted from the region of nuclear deformations in the vicinity of the saddle point to the region of nuclear deformations in the vicinity of the scission point, the total angular momentum of the nucleus undergoing fission being split into the orbital component, which is responsible for the anisotropy of fragments, and the spin component. This conclusion can be qualitatively explained on the basis of linear-response theory.     

Deformation parameter changes in fission mass yields within the systematic statistical scission-point model

The fission fragment mass-yields are evaluated for pre-actinide and actinide isotopes using a systematic statistical scission point model. The total potential energy of the fissioning systems at the scission point is presented in approximate relations as functions of mass numbers,deformation parameters and the temperature of complementary fission fragments. The collective temperature, Tcoll, and the temperature of fission fragments, Ti, are separated and the effect of collective temperature on mass yields results is investigated. The fragment temperature has been calculated with the generalized superfluid model. The sum of deformation parameters of complementary fission fragments has been obtained by fitting the calculated results with the experimental data. To investigate the transitions between symmetric and asymmetric modes mass yields for pre-actinide and heavy actinides are calculated with this model. The transition from asymmetric to symmetric fission is well reproduced using this systematic statistical scission point model. The calculated results are in good agreement with the experimental data with Tcoll= 2 Me V at intermediate excitation energy and with T_(coll)= 1MeV for spontaneous fission.Despite the Langevin model, in the scission point model, a constraint on the deformation parameters of fission fragments has little effect on the results of the mass yield.     

Bi—dimension Position Sensitive Detector Used in the Study of Fusion Fission of Heavy Ions at the Sub—Coulomb Barrier Energy Region

The structure,operation principle and performance of the bi—dimension position sensitive avalanche chamber (BPAC) used in the study of fusion fission induced by heavy ions at the near and sub-Coulomb barrier energy region are describerd.
The fold angle distribution of fragments in different angle region for 84MeV(E_cm)¹⁶O+²³²Th reaction system was obtained by using BPAC,from which the angle distribution of transfer—fission fragments has been distinguished from that of compound mucleus fission fragments.It is thereby certified that transfer—fission is not the reason of anomalous anisotropies of fragment angle distribution.Meanwhile experimental results supported the preequilibrium fission model,in frame of which the anomalous anisotropies of fragment distribution was explained.     

Driving potential and fission-fragment charge distributions

We propose an efficient approach to describe the fission-fragment charge yields for actinides based on the driving potential of the fissioning system. Considering the properties of primary fission fragments at their ground states, the driving potential, which represents the potential energies of the system around scission configuration and closely relates to the yields of fragments, can be unambiguously and quickly obtained from the Skyrme energy-density functional together with the Weizsäcker–Skyrme mass model. The fission-fragment charge distributions for thermal-neutron-induced fission and spontaneous fission of a series of actinides, especially the odd–even staggering in the charge distributions, can be well reproduced. Nuclear dynamical deformations and pairing corrections of fragments play an important role in the charge distributions.     

Exotic and excited-state meson spectroscopy and radiative transitions from lattice QCD

We discuss recent progress in extracting the excited meson spectrum and radiative transition form factors from lattice QCD.We mention results in the charmonium sector,including the first lattice QCD calculation of radiative transition rates involving excited charmonium states,highlighting results for high spin and exotic states.We present recent results on a highly excited isovector meson spectrum from dynamical anisotropic lattices.Using carefully constructed operators we show how the continuum spin of extracted states can be reliably identified and confidently extract excited states,states with exotic quantum numbers and states of high spin.This spectrum includes the first spin-four state extracted from lattice QCD.We conclude with some comments on future prospects.     

Ferromagnetic Heisenberg spin chain in a resonator

We investigate the properties of a generalized Rabi model by replacing the two-level atom in Rabi model with a ferromagnetic Heisenberg spin chain. We find that the dynamical behavior of the system can be divided into four categories.The energy spectrum of the ground state and some low excited states are obtained. When the magnons and the photon are in resonance, the model is exactly solvable and the rigorous solution is obtained. Near the resonance point where the detuning is small, the system is studied with the help of perturbation theory. This model has a spontaneously breaking of parity symmetry, suggesting the existence of a quantum phase transition. The critical exponent from the normal phase is computed.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Nonuniform character of the population of spin projections K for a fissile nucleus at the scission point and anisotropies in the angular distributions of fragments originating from the induced fission of nuclei

It is shown that the emergence of anisotropies in the angular distributions of fragments originating from the spontaneous and induced fission of oriented actinide nuclei is possible only if nonuniformities in the population of the projectionsM (K) of the fissile-nucleus spin onto the z axis of the laboratory frame (fissile-nucleus symmetry axis) appear simultaneously in the vicinity of the scission point but not in the vicinity of the outer saddle point of the deformation potential. The possibilities for creating the orientation of fissile nuclei for spontaneous and induced fission and the effect of these orientations on the anisotropies under analysis are considered. The role of Coriolis interaction as a unique source of the mixing of different-K fissile-nucleus states at all stages of the fission process is studied with allowance for the dynamical enhancement of this interaction for excited thermalized states of the nucleus involved that is characterized by a high energy density. It is shown that the absence of thermalization of excited states of the fissile nucleus that appear because of the effect of nonadiabaticity of its collective deformation motion in the vicinity of the scission point is a condition of conservation of the influence that transition fission states formed at the inner and outer fission barriers exerts on the distribution of the spin projections K for lowenergy spontaneous nuclear fission. It is confirmed that anisotropies observed in the angular distributions of fragments originating from the fission of nuclei that is induced by fast light particles (multiply charged ions) are due to the appearance of strongly excited equilibrium(nonequilibrium) states of the fissile nucleus in the vicinity of its scission point that have a Gibbs (non-Gibbs) distribution of projections K.     

Defining a reaction plane in particle-fission correlation measurements

A simple model is developed to describe the spin misalignment in particle-fission correlation measurements. Analytical expressions are derived for the spin fluctuations as a function of fission fragment emission angle. Some recent experimental results onα-fission correlations are interpreted within the framework of the model.     

Possible Mechanisms of Ternary Fission in the 197Au+197Au System at 15 A MeV

Ternary fission in ^197Au＋^197Au collisions at 15 A MeV is investigated by using the improved quantum molecular dynamical （ImQMD） model. The experimental mass distributions for each of the three fragments are reproduced for the first time without any freely adjusting parameters. The mechanisms of ternary fission in central and semicentral collisions are dynamically studied. In direct prolate ternary fission, two necks are found to be formed almost simultaneously and rupture sequentially in a very short time interval. Direct oblate ternary fission is a very rare fission event, in which three necks are formed and rupture simultaneously, forming three equally sized fragments along space-symmetric directions in the reaction plane. In sequential ternary fission a binary division is followed by another binary fission event after hundreds of fm/c.     

Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle

We analytically and numerically study the local dynamical characteristics of the Bessel beams reflected from an airglass interface near the Brewster angle.A Taylor series expansion based on the angular spectrum component is applied to correct the reflection coefficients near the Brewster angle.Using a hybrid angular spectrum representation and vector potential method,the explicit expressions for the electric and magnetic field components of the reflected Bessel beams are derived analytically under paraxial approximation.The local energy,momentum,spin,and orbital angular momentum of the Bessel beams upon reflection near the Brewster angle are examined numerically by utilizing a canonical approach.Numerical simulation results show that the properties of these dynamical quantities for the Bessel beams near Brewster angle incidence change abruptly,and are significantly affected by their topological charge,half-cone angle,and polarization state.The present study has its importance in understanding the dynamical aspects of optical beams with vortex structure and diffraction-free nature during the reflection process.     

Angular momentum of fission fragments

We continue the discussion on the respective roles of individual and collective motion in the angular momentum distribution in fission fragments. As in our prior publications on the subject, the role of individual nucleon motion in fragments in the postscission configuration is underlined, and the central part in the discussion concerns phenomena observed in the spontaneous fission of even-even nuclei. A formalism is prepared to study the spin distribution of fragments in induced fission from high-spin states.     

Two-dimensional atom-phonon coupling model for spin conversion: role of metastable states

Spin conversion, (SC), compounds are composed of molecules organized around a transition metal ion. The ion spin value is smaller for the ion fundamental level than for its first excited one. So, increasing the temperature changes the spin mean value. This spin conversion can be continuous or can display a first order phase transition called spin transition. The atom phonon coupling model, introduced recently, allows to describe at least qualitatively different experimental results. Up to now, this model has been applied on a linear chain of atoms. In this paper we apply it on a square lattice. We study the thermal variations of different thermodynamic parameters and the metastable states which are present around the transition. In this study, it is expected that the critical point of some (SC) compounds can be reached by applying on them a small hydrostatic pressure; it is also expected that ultrasound pulses can induce, at a very low temperature, a conversion between the stable low spin state and the metastable high spin state and it is also predicted that the crystal sound velocity can display a discontinuity at the first order phase transition.