Asymmetric Two-center Shell Model Research Articles

Analysis of neutron multiplicity and fission fragment mass distribution within the asymmetric two-center shell model

The fission fragment mass distribution followed by neutron emission is studied for the 238U(18O,f) reaction using the asymmetric two-center shell model. Within the thermodynamic approach, excitation energy carried by the compound nucleus is dissipated in the emission of a pair of neutrons in several consecutive steps. Therefore, we have considered 2–12 (in step of 2) neutron emission channels in our formalism. The mass distribution corresponding to 8-neutron emission channel compares reasonably well with the experimental data. The observed fine structure dips corresponding to shell closure (Z = 50 and N = 82 of individual fission fragment arise mainly due to shell structure in the mass parameters. However, an exact location and magnitude of the dip at A = 124 in the mass distribution depends on how the temperature modifies masses and, also, on the precise information of pre- and post-neutron emission data. This suggests a possible importance of extending these calculations to get new insight into an understanding of the dynamical behaviour of fragment formation in the fission process.

Potential energy surfaces for cluster emitting nuclei

Potential energy surfaces are calculated by using the most advanced asymmetric two-center shell model allowing to obtain shell and pairing corrections which are added to the Yukawa-plus-exponential model deformation energy. Shell effects are of crucial importance for experimental observation of spontaneous disintegration by heavy ion emission. Results for 222Ra, 232U, 236Pu and 242Cm illustrate the main ideas and show for the first time for a cluster emitter a potential barrier obtained by using the macroscopic-microscopic method.

Entrance and Exit Channels for the Heaviest Elements

The potential barriers governing the entrance and α decay channels of the heaviest elements have been determined within a Generalized Liquid Drop Model including the asymmetry, the proximity effects, an adjustment to reproduce the Q value and within the asymmetric two-center shell model and the Strutinsky method. In cold fusion reactions double-hump barriers stand and incomplete fusion may occur. Warm fusion paths lead to one-hump potential barriers but also to very excited systems cooling down by neutron or even α particle evaporation. Partial half-lives for α decay have been calculated and compared with the new available experimental data.

On the formation and alpha decay of superheavy elements

The potential energy governing the entrance and α-decay channels for superheavy elements has been determined within a Generalized Liquid Drop Model including the proximity effects, the asymmetry, an accurate nuclear radius, an adjustment to reproduce the experimental Q value and within the asymmetric two-center shell model and the Strutinsky method. In cold fusion paths double-hump fusion barriers stand and incomplete fusion events may occur. Warm fusion reactions lead to one hump potential barriers and to very excited systems cooling down by neutron or even α-particle evaporation. α-decay half-lives of superheavy elements have been calculated and compared with the new available experimental data.

Single Particle Potential and Collective Coordinates in Fission

The theory of nuclear fission is considered. The relation between the single particle potential of the asymmetric two-center shell model and the collective coordinates in the fission theory is studied. Theoretical expressions are developed to show the dependence of the coordinates of the centers of the two centers oscillator on the various collective parameters. Numerical calculations are carried out using the present obtained theoretical expressions. From these calculations, the dependences of the different oscillator frequencies on the collective coordinates are investigated. The present study shows the great importance of that dependence in the nuclear fission process.

Molecular single-particle effects in the 12C

We have used the asymmetric two-center shell model to calculate the single-neutron energies in the $^{12}$C${+\mathrm{}}^{17}$,18O and $^{13}$C${+\mathrm{}}^{17}$O collisions as a function of the internuclear distance. The periodic resonancelike structures observed in the angle-integrated inelastic cross sections for these systems can be understood in terms of the nuclear Landau-Zener promotion of a loosely bound valence neutron from the 1${d}_{5/2}$ (\ensuremath{\Omega}=(1/2) state to the 2${s}_{1/2}$ state of the oxygen isotopes. Inclusion of the effects of a turning point in the Landau-Zener formula is found to give marked improvements in accounting for the observed angle-integrated inelastic cross sections for these systems. Intermediate structures in the cross sections are found to arise due to the energy-dependent oscillatory behavior of the partial cross sections. While some resonancelike peaks can be attributed to a single orbital angular momentum, many others arise due to the combined contributions of two or more angular momenta.

Model for fusion and cool compound nucleus formation based on the fragmentation theory.

Collective potential energy surfaces are calculated in both the adiabatic and sudden approximations by using the asymmetric two-center shell model in the Strutinsky method. It is shown that fusion of two colliding heavy ions occurs by their crossing over of the adiabatic interaction barrier. The adiabatic scattering potentials present two barriers, whereas no barrier is shown to occur in sudden scattering potentials. The first barrier is obtained just past the saddle shape but is too low, such that a deep inelastic process is expected. The other, inner, barrier is high enough to let the system fall into the fusion well, whose excitation energy then determines whether a cool compound nucleus is produced or the fusion-fission process occurs. For a given compound nucleus, the excitation energy is found to be small for only a few target-projectile combinations, which increase as their mass asymmetry increases. Such target-projectile combinations which refer to a cool compound nucleus can be identified by a simple calculation of the fragmentation potential based on the ground state binding energies with Coulomb and proximity effects calculated at a constant relative separation of the two nuclei. Our calculations are made for the composite systems with 102\ensuremath{\le}Z\ensuremath{\le}114.

Analytically solvable model of charge dispersion in nuclear fission

Using the asymmetric two-center shell model potentials in parametrized forms, the time-dependent Schr\"odinger equation is solved analytically for the charge dispersion yields. We obtain a Gaussian function, characterized by a most probable charge and the width of the distribution. The hypothesis of an unchanged charge density and a minimum potential energy are given as limiting cases. Calculations are made for $^{236}\mathrm{U}$ and $^{252}\mathrm{Cf}$.NUCLEAR REACTIONS Nuclear fission, fragmentation theory, two-center shell model, time-dependent Schr\"odinger equation, analytical solution, Gaussian charge distribution, most-probable charge, unchanged charge density and minimum potential energy postulates, $^{236}\mathrm{U}$, $^{252}\mathrm{Cf}$.

Signatures of molecular single-particle states by level crossings in heavy ion collisions

In heavy ion collisions, the molecular single-particle motion may cause specific structures in the energy dependence of the cross sections which arise by the promotion of nucleons at level crossings according to the Landau-Zener excitation mechanism. In order to examine this effect in asymmetric heavy ion collisions, we have calculated level diagrams of the two-center shell model for the target projectile combinations $^{13}\mathrm{C}$ + $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$ + $^{17}\mathrm{O}$ and analyzed with respect to inelastic excitation and neutron transfer. We select certain reactions as possible candidates for showing enhanced cross sections for nucleon excitation and transfer due to real and avoided level crossings near the Fermi level.NUCLEAR REACTIONS Heavy ion scattering, molecular theory of nucleon transfer, asymmetric two-center shell model; $^{13}\mathrm{C}$($^{16}\mathrm{O}$, $^{17}\mathrm{O}$), calculated level diagrams.

Theory of nucleon transfer in the dynamical two-center shell model

The theory of nucleon transfer in heavy ion reactions is formulated on the basis of the molecular particlecore model for a system consisting of two cores and one extracore nucleon. The extracore nucleon is described by the molecular wave functions of the asymmetric two-center shell model. The cores, which are assumed to be collectively excitable, are treated with vibrator-rotator models. Potentials for shape polarization are contained in the asymmetric two-center shell model and the interaction between the cores. The excitation and transfer of the extracore nucleon is induced by the radial and rotational couplings. The coupled channel equations, which include the recoil effects in first approximation, are derived in a form suitable for numerical calculations of cross sections.NUCLEAR REACTIONS Heavy ion scattering, theory of nucleon transfer, molecular wave functions, two-center shell model, collective and single-particle excitation.

Theory of Charge Dispersion in Nuclear Fission

By introducing charge asymmetry as a new dynamical collective coordinate in the asymmetric two-center shell model, the nuclear charge dispersion in the fission of $^{236}\mathrm{U}$ is calculated without using any free parameter. The agreement between theory and experiment is quite good.

Transition from mass asymmetry to symmetry in the spontaneous fission of Fm isotopes

The observed transition in the spontaneous fission mass distribution from asymmetry in the lighter Fm isotopes to symmetry in the heavier Fm isotopes is studied on the basis of the potential energy surfaces (PES) and fragment shell effects in the two-center shell model. To that end, we have calculated the PES for $^{256}\mathrm{Fm}$ and compared them with our previous PES results for other Fm isotopes. Our calculations show that the lighter Fm isotopes (up to $^{256}\mathrm{Fm}$) should fission asymmetrically, while $^{258}\mathrm{Fm}$ and other heavier Fm isotopes should fission symmetrically. This is due to the fact that the shell corrections in these nuclei are found to increase with increasing mass number and decreasing neck radius, particularly in the region beyond the second barrier. This, in turn, is a consequence of strong shell effects in fragment nuclei near the doubly closed-shell $_{50}^{132}\mathrm{Sn}_{82}$. The results supporting these conclusions are shown.NUCLEAR STRUCTURE Spontaneous fission $^{252,256,258,264}\mathrm{Fm}$; calculated shell corrections and potential energy surfaces; asymmetric two-center shell model; transition from mass asymmetry to symmetry.

Theory of fragmentation dynamics in nucleus-nucleus collisions

The fragmentation of a nuclear system is described by a dynamical coordinate, the fragmentation coordinate η=A1−A2/A1+A2 The total Hamiltonian describing a binary heavy ion encounter includes a part H(R, α,η) which describes the fragmentation and its coupling to other degrees of freedom. It is a collective Hamiltonian which is calculated from the microscopic Asymmetric Two-Center Shell Model (ATCSM). The properties of this Hamiltonian are extensively discussed and methods for its solution are described. Formulae for cross sections of specific nuclear fragmentations including fusion are derived.

Asymmetric fission in the shell-correction method with the asymmetric two-center shell model

The asymmetry of the fragment mass distribution of fissioning nuclei is described by suitable parametrization of an asymmetric two-center shell model (ATCSM). The deformation energy surface is calculated by applying a modified shell-correction prescription due to Strutinsky. It is shown that the ATCSM is specially suited for the description of the scission asymmetry which turns out to be strongly dependent on the shell structure of the fragments. It is demonstrated that the mass asymmetry at scission is unaffected by whether or not the Strutinsky renormalization for the shell corrections is employed for the calculation of the deformation energy surface.

Theory of Fission-Mass Distributions Demonstrated forRa226,U236,Fm258

With the mass asymmetry described by the dynamical collective fragmentation coordinate $\ensuremath{\xi}$, and with use of the asymmetric two-center shell model, the fission mass distributions for $^{226}\mathrm{Ra}$, $^{236}\mathrm{U}$, and $^{258}\mathrm{Fm}$ (which are typical representatives for triple-, double-, and single-humped distributions) are explained.