Coupling Of Relative Motion Research Articles

Systematic study of the effect of individual rotational energy levels on the fusion cross-section of 16 O-based reactions of range 480 ≤ Z P Z T ≤ 592

In heavy-ion fusion reactions, the enhancement in the sub-barrier fusion cross-section has been observed as compared to the 1-Dimensional barrier penetration model due to the coupling of many degrees of freedom to the relative motion. This enhancement can be explained theoretically by including nuclear structure effects like deformation and the coupling of relative motion among two colliding nuclei. The present work aims to investigate the effect of individual rotational energy levels on the fusion cross-sections for 16O-based reaction systems, namely, 16O + 182,184,186W, 16O + 176,180Hf, 16O + 174,176Yb, 16O + 166Er, 16O + 148,152,154Sm, 16O + 150Nd at energies below the fusion barrier. Using the CCFULL code, the effect of low-lying rotational energy levels on the fusion cross-section for 16O induced reactions has been investigated at energies below and around the Coulomb barrier. The calculations are performed by assuming the fixed value of diffuseness parameter a 0 = 0.65 fm in the Woods-Saxon nuclear potential and the other two parameters are optimised by fitting the experimental data at the above barrier. Here we have determined the V 0 and r 0 as a function of Z P Z T , where experimental cross-sections are available. From our calculations, it is observed that the hexadecapole deformation (β 4) with different magnitudes has a significant influence on the fusion cross sections. For the case of the +ve value of β 4, beyond 10+, the rotational levels cease to contribute significantly and also there is a significant difference between the contribution of sequential channels. On the other hand, in the case of -ve β 4, up to 6+ levels contribute significantly. Furthermore, we have established an algebraic systematic of fitting, which one can use to determine the parameters V 0, r 0 of Woods-Saxon nuclear potential within the range of Z P Z T lie in between 480 ≤ Z P Z T ≤ 592.

Comprehensive analysis of heavy-ion fusion reactions around the Coulomb barrier

We have investigated the fusion dynamics of 12C + 92Zr, 16O + 92Zr, 28Si + 92Zr, 35Cl + 92Zr, 16O + 60Ni, 18O + 58Ni, 12C + 194,198Pt, 16O + 144,148,154Sm and 17O + 144Sm reactions in the close vicinity of the Coulomb barrier. For this purpose, we have opted one-dimensional Wong formula, coupled channel approach, and symmetric-asymmetric Gaussian barrier distribution (SAGBD) model to analyze the fusion data for above mentioned reactions. For all studied systems, the theoretical results obtained from the one-dimensional Wong formula are unable to reproduce the fusion data especially at incident energies lying below the nominal barrier. This appeals for the inclusion of intrinsic degrees of freedom which have been originated from the nuclear structure of fusing nuclei, and thus essentially required to explain the experimental data at energies lying in the sub-barrier realm. For the chosen reactions, the coupled channel analysis suggests that the coupling of relative motion with the inelastic surface excitations and/or nucleon transfer channels associated with the reaction partners have produced a remarkable fusion enhancement at energies lying near and below the nominal barrier. It is particularly intriguing that the SAGBD model can replicate the impacts of dominant intrinsic reaction channels such as multi-phonon quantum states and/or nucleon transfer channels via Gaussian type of weight function. The predictions of the SAGBD approach appropriately reproduce the fusion cross-sections data and related barrier distributions data for the selected reactions due the fact that the multi-dimensional nature induces the barrier lowering effects and subsequently reduces the effective fusion barrier between the participants. In the SAGBD approach, the channel coupling effects are quantitively measured in terms of channel coupling parameter and percentage decrement in height of effective fusion barrier with respect to the Coulomb barrier Furthermore, the recovered -values for selected reactions are found to be smaller and hence clearly demonstrate the applicability of the model outcomes to explore the fusion dynamics of the studied systems.

Coupling of relative motion and charge asymmetry coordinates for the fine structure in fission charge distribution yields

A quantum-mechanical model of coupled charge asymmetry and relative coordinates is solved analytically using the parametrised forms of the potentials calculated on the asymmetric two-centre shell model. Newton's classical equation of motion is used to estimate the scission time and the coupling are included numerically in both the quantum-mechanical and classical treatments. The result of coupling the relative motion to charge asymmetry is shown to give rise to fine-structure effects in fission charge distribution yields (the odd-even proton effects), which are in addition to those already known from the shell corrections and the structure in mass parameters. Calculations are made for the fission of 236U.

Dynamical fragmentation process in nuclear fission

Abstract The proton odd-even effect in fission charge distribution yields is shown to be the quantum mechanical fragmentation process, arising due to shell effects in adiabatic potential and structure of adiabatic cranking masses. Additional contribution is shown to come from the coupling of relative motion to charge fragmentation coordinate, that is solved analytically. The dynamics occur near the top of barrier, just past saddle shape.

Theory of energy dissipation in heavy-ion reactions

A formalism for the description of energy dissipation in heavy-ion reactions within the two-centre shell model is proposed. Here dissipation is considered as due to the coupling of relative motion to intrinsic degrees of freedom. First, the formulation is carried out quantum mechanically. The problem reduces to the solution of coupled integrodifferential equations for energy distribution functionsfn(β) and\(\bar f_\varepsilon \)(β), where |\(\bar f_\varepsilon \)(β)|2 de is the probability of finding the intrinsic energy within the intervale andɛ+dɛ. By introducing suitable boundary conditions with incoming and outgoing waves the equations can be solved by iterative methods. The second method is based on the semi-classical approximation and is formulated in the time-dependent picture. Finally, a relationship between the friction coefficient and the distribution functions is given.