Center Shell Model Research Articles

Role of quantum phase transition in spontaneous fission

A systematic study of quantum phase (i.e., nuclear shape) transition has been carried out from the standpoint of spontaneous fission. The quantum phase transition is defined by the ratio of relative excitation energies of IΠ=4+ to IΠ=2+ states between heavier and lighter fission fragments and its extremum value fixes the most probable pair of fission fragments. This ratio provides an effective order parameter which is not only easy to measure, but also distinguishes between first and second order phase transitions and takes on a special value in the critical region. Its (i.e., the energy ratio) variation is mainly controlled by the relative inertia tensors of the correlated pair of fission fragment and is fully supported by our cranking mass parameter calculations based on the asymmetric two center shell model bases.Once the fission fragment pair is governed by the quantum phase transition, its validity is tested by F-spin selection rule that is based on valence nucleons which are responsible for determining the nuclear shape transition. It implies that if a pair of conjugate fission fragments together with appropriate neutron emission have total F-spin equal to 12 with projections F0=±12 then and only then the fission proceeds, provided both the valence shell nucleons in either of the fission fragments are treated as particles like and is valid for the even-even decay modes. The goodness of F-spin selection rule extends further to extract all the allowed pairs of neutron-rich fission fragments. The validity of F-spin selection rule has been tested in various decay modes of spontaneous fission and seems to be a milestone in deciding the appropriate decay channels. These findings have important consequences in the formation and discovery of drip-line exotic nuclei.

Effect of Coriolis Interaction on the Decay of Isotones with N = 149 and N = 153

The quasi-neutron structure of nuclei in two chains of odd isotones with N = 149 and N = 153: 243,247Pu, 245,249Cm, 247,251Cf, 249,253Fm, 251,255No, and is considered. Single-particle energy spectra are calculated using the two center shell model (TCSM). Minimizing the potential energy with respect to the collective coordinates gives the ground state of the studied nucleos, which is subsequently used to describe low-lying quasi-neutron states. The K-mixing of the basis TCSM wave functions is considered by including the Coriolis correction in the total Hamiltonian of the system. The effect of level blocking is also considered in the calculations. The probabilities of the E2 transitions to the ground states and the corresponding lifetimes of the quasi-neutron levels are estimated.

Spontaneous fission, cluster emission and alpha decay of [formula omitted] in a unified description

Three disintegration modes of the parent nucleus 222Ra, namely the fission, the cluster emission and the alpha decay, are treated in a unified manner. The half-lives are calculated by taking into account the penetration probabilities through the potential barrier along disintegration trajectories in the deformation space appropriate to each kind of decay. These trajectories start from the same parent ground state configuration. The disintegration paths are obtained from the least action principle. The deformation energy is calculated within the macroscopic–microscopic procedure based on the Woods–Saxon two center shell model. The effective mass is determined microscopically with the cranking method and the Gaussian Overlap Approximation. The nuclear shape parametrization is characterized by the most important five degrees of freedom encountered in fission, corresponding to the elongation, the mass asymmetry, the necking and the two fragment deformations. Partial half-life results for alpha-decay and cluster emission processes treated as superasymmetric fission agree with the experimental data. The spontaneous fission half-life is predicted. Molecular states are evidenced for the superasymmetric fission process as a result of the large shell effects in the nascent fragments.

Spontaneous fission of the superheavy nucleusFl286

The decimal logarithm of spontaneous fission half-life of the superheavy nucleus $^{286}$Fl experimentally determined is $\log_{10} T_f^{exp} (s) = -0.632$. We present a method to calculate the half-life based on the cranking inertia and the deformation energy, functions of two independent surface coordinates, using the best asymmetric two center shell model. In the first stage we study the statics. At a given mass asymmetry up to about $\eta=0.5$ the potential barrier has a two hump shape, but for larger $\eta$ it has only one hump. The touching point deformation energy versus mass asymmetry shows the three minima, produced by shell effects, corresponding to three decay modes: spontaneous fission, cluster decay and $\alpha$~decay. The least action trajectory is determined in the plane $(R,\eta)$ where $R$ is the separation distance of the fission fragments and $\eta$ is the mass asymmetry. We may find a sequence of several trajectories one of which gives the least action. The parametrization with two deformation coordinates $(R,\eta)$ and the radius of the light fragment, $R_2$, exponentially decreasing with $R$ is compared with the simpler one, in which $R_2$~=constant. The latter is closer to the reality and reminds us about the alpha or cluster preformation at the nuclear surface.

Inversion of the Odd-Even Effect in Cold Fission from the Time-Dependent Pairing Equations

A peculiar phenomenon was observed experimentally in cold fission: the odd partition yields are favored over the even ones for excitations energies of the fragments smaller than 4 MeV. In this contribution, a microscopic model is proposed for the explanation of this odd-even effect in cold fission. This explanation is based on a mixing configuration mechanism that is produced during the fission process. This configuration mixing mechanism is obtained dynamically by solving a the generalized system of time-dependent pairing equations, which include a pair-breaking effect. The time dependent equations of motion for the pair breaking effect were corroborated with a condition that fixes dynamically the number of particles on the two fission fragment. The single particle level scheme was calculated with the Woods-Saxon superasymmetric two center shell model, providing a continuous variation of the single particle energies and of the wave functions from one nucleus up to two separated fragments. A first rule can be extracted from this model. The even-even fission products cannot be obtained at zero excitation energies because of the existence of dynamical excitations produced in the avoided- level-crossing regions when the nuclear system deforms slowly.

Dynamical approach to isotopic-distribution of fission fragments from actinide nuclei

Measurements of the isotope distribution of fission fragments, often denoted as the primary fission yield (pre-neutron yield) or independent fission yield (post-neutron yield) are still challenging at low excitation energies, so that it is important to investigate it within a theory. Such quantities are vital for applications as well. In this study, fragment distributions from the fission of U isotopes at low excitation energies are studied using a dynamical model. The potential energy surface is derived from the two center shell model including the shell and pairing corrections. In order to calculate the charge distribution of fission fragments, we introduce a new parameter η Z as the charge asymmetry, in addition to three parameters describing a nuclear shape, z as the distance between two centers of mass, δ as fragment deformation, and η A as the mass asymmetry. Using this model, we calculated the isotopic distribution of 236 U for the n-induced process 235 U + n → 236 U at low excitation energies. As a result, we found that the current model can well reproduce isotopic fission-fragment distribution which can be compared favorably with major libraries.

Pairing gaps and Fermi energies at scission for 296Lv alpha-decay

The pairing corrections, the single particle occupation numbers, are investigated within density-dependent delta interaction formalism for pairing residual interactions. The potential barrier is computed in the framework of the macroscopic-microscopic model. The microscopic part is based on the Woods-Saxon two center shell model. The alpha-decay of a superheavy element is treated, by paying a special attention to the region of the scission configurations. The sequence of nuclear shapes follows the superasymmetric fission path for alpha decay. It was found that the pairing gaps of the states that reach asymptotically the potential well of the alpha particle have large values at scission but become zero after scission. The 1s1/2 single particle levels of the nascent alpha particle are fully occupied while the superior levels are empties in the scission region and remains in the same states during the penetration of the Coulomb barrier. The projection of the numbers of particle on the two fragments are obtained naturally. At scission, the nascent alpha particle forms a very bound cluster.

Two center shell model description of superheavy element synthesis, fission and cluster decay

A two center shell model provides the possibility to characterize precisely scission configurations. Therefore, low energy disintegration processes could be described within such models. A Woods-Saxon two center shell model, recently elaborated, was used to investigate the cluster decay, the low energy fission and the synthesis of superheavy elements.

Dissipation for Z-channels in fission, alpha-decay and cluster emission

The dissipated energy in fission, cluster and alpha decay was estimated microscopically by using the time dependent pairing equations. The single particle level schemes were determined in the framework of the superasymmetric two center shell model. A strong dependence of the dissipated energy as function of the mass asymmetry is evidenced. The dissipated energy is much lower for alpha decay and cluster emission than for fission.

Predictions for 232U cluster-decays within the macroscopic–microscopic approximation

The decay dynamical path is determined within the macroscopic–microscopic model for the emission of 24Ne from 232U. The nuclear shape parametrization is characterized five degrees of freedom. The single particle energies and the nucleon wave functions are obtained within the superasymmetric Woods–Saxon two center shell model. It turns out that the cluster decay follows a potential magic valley, starting from the ground state of the parent and reaching a configuration of two touching nuclei at scission. A small pocket in the potential barrier is evidenced, as a result of large shell effects in the nascent fragments. The half-life is computed by using several approaches for the effective mass. It is shown that the inertia within by the Gaussian overlap approach gives the closest values to the experimental ones. Half-lives for different cluster decays are predicted. The theoretical values are compared to various phenomenological estimates.

Th and U fission barriers within the Woods-Saxon two center shell model

Abstract Fission barriers of actinides are calculated in the framework of the macroscopic-microscopic method. The single particle energies are obtained within a new version of the Woods-Saxon two-center shell model. A nuclear shape parametrization characterized by five degrees of freedom is used. The barriers are calculated along the minimal action trajectory in the configuration space and the inertia is evaluated within the cranking formalism. The reliability of the model is tested by comparing the theoretical results with values deduced from experimental data.

BINARY AND TERNARY EMISSION FROM SUPERHEAVY NUCLEI

The two center shell model is used to calculate the level scheme transition from the superheavy parent nucleus to the emitted cluster plus the daughter nucleus. The three center shell model is also employed to compute the transition toward eventual three equal fragment partition from the superheavy nuclei. The levels are used to compute the shell corrections within the Strutinsky method. The liquid drop part is calculated using the Yukawa-plus-exponential model. The total deformation energy is then minimized over a multidimensional space of deformation. Dynamics is completed with the Werner-Wheeler tensor calculation, and cluster emission paths for binary and ternary splitting is obtained for Z = 120 isotopes.

HEAVY PARTICLE RADIOACTIVITIES

The potential energy surface for binary decay modes of 228 Th versus the distance between the fragment centers and the mass asymmetry is calculated by using the macroscopic-microscopic model with energy levels obtained within the most advanced asymmetric two center shell model. The valley due to 20 O radioactivity is evidenced as a result of the very strong shell effects due to the doubly magic daughter 208 Pb . For the first time the potential barrier of this decay mode is produced by adding the shell and pairing corrections to the phenomenological deformation energy. The half-lives of cluster emitters predicted by the analytical superasymmetric fission model have been confirmed in all measurements performed until now.

Two center shell model with Woods–Saxon potentials: Adiabatic and diabatic states in fusion

A realistic two-center shell model for fusion is proposed, which is based on two spherical Woods–Saxon potentials and the potential separable expansion method. This model describes the single-particle motion in a fusing system. A technique for calculating stationary diabatic states is suggested which makes use of the formal definition of those states, i.e., they minimize the radial nonadiabatic coupling between the adiabatic states. As an example the system 16O + 40Ca → 56Ni is discussed.

Fine structure in 14C cluster emission from 225Ac

A fine structure in the 14C decay of 225Ac is predicted quantitatively by accounting dynamical aspects during the disintegration process. Transitions to the excited states of the daughter nucleus are considered to be mainly directed by the Landau–Zener promotion mechanism in the region of avoided crossing levels. The level scheme is evaluated with the superasymmetric two–center shell model. The half–lives are computed considering the cluster decay as a superasymmetric fission process.

Quasidynamic propagation in diabatic landscapes for low energy nuclear fission

Successive procedure for evaluating diabatic contributions to the static energy surface is proposed, based on solving collective equation of motion simultaneously with equations for the single-particle occupation probabilities. The method is applied so far to235U(nth,f) in terms of schematic asymmetric two center shell model. Shifts in fragment mass asymmetry due to diabatic dynamics are observed.

Cold valleys: cluster decay, cold fusion, cold fission-a unifying theory of related phenomena

A unified description of cluster decay as spontaneous emission of clusters like 14C, 24Ne, 28Mg and 32Si in which the residual nucleus is close to the spherical double magic 208Pb nucleus, of cold fusion as the inverse process for the synthesis of first superheavy elements with Z=107, 108 and 109 by colliding 208Pb-projectiles with different targets and of cold fission as spontaneous or neutron induced emission of deformed clusters or as a new fission component with high total kinetic energy of the fragments (bimodal fission) of very heavy nuclei close to 264Fm is given in the frame of the two center shell model as cold valleys on potential energy surfaces produced by cold rearrangements of a large number of nucleons.

Mass Distributions and Charge Dispersion for the Nuclear Fission

AbstractThe theory of nuclear fission is reconsidered by introducing the charge asymmetry in the asymmetric two center shell model as a dynamical collective coordinate. The quantum mechanical fluctuations, which are accompanied with the collective motion as a function of the mass asymmetry, are responsible for the mass distributions in nuclear fission. Numerical calculations are carried out for the mass distributions and charge dispersions for the nuclear fission of the 236U and 238U nuclei. The present obtained theoretical calculations are in good agreement with the experimental measurements.

Cranking model mass parameters for the Asymmetrie Two Center Shell Model

We present cranking model calculations of mass parameters for the Asymmetric Two Center Shell Model. It is shown, that terms that are small in a One Center Shell Model and for this reason have been neglected in previous calculations become important in the late stages of the fission process.

Polarization of single particle states in heavy ion induced nuclear reactions within the two center shell model

In “slow” nucleus-nucleus collisions the single particle states will adjust continuously to an instantaneous two center potential. Transfer reactions will occur between polarized rather than between asymptotic states. In order to employ two center states in reaction calculations, an expansion in terms of asymptotic states with good angular momentum is required. This expansion is formulated, and equations for the expansion coefficients are derived. Model calculations for the system 40Ca+ 16O indicate that the polarization of unoccupied proton states in 40Ca is strong, while it is very weak for the tightly bound 1p 1 2 proton in 16O. The dependence of the polarization effect on several relevant parameters is discussed.