Quantum-mechanical description of the initial stage of fusion reaction
- PDF / 837,945 Bytes
- 14 Pages / 612 x 792 pts (letter) Page_size
- 32 Downloads / 225 Views
NUCLEI Theory
Quantum-Mechanical Description of the Initial Stage of Fusion Reaction V. V. Sargsyan1)* , А. S. Zubov1) , Z. Kanokov2), G. G. Adamian1), 3)** , and N. V. Antonenko1) Received March 11, 2008; in final form, July 23, 2008
Abstract—Projectile-nucleus capture by a target nucleus at bombarding energies in the vicinity of the Coulomb barrier is treated on the basis of the reduced-density-matrix formalism. The effect of dissipation and fluctuations on the capture process is taken into account self-consistently within this model. Cross sections for evaporation-residue formation in asymmetric-fusion reactions are found by using the calculated capture probabilities averaged over all orientations of the deformed projectile or target nucleus. PACS numbers: 25.70.Jj, 24.10.-i, 24.60.-k DOI: 10.1134/S1063778809030053
1. INTRODUCTION The dynamics of interaction between two heavy ions at bombarding energies in the vicinity of the Coulomb barrier has been the subject of intensive theoretical and experimental investigations [1–11]. In recent years, these investigations have been motivated by successes of the synthesis of new superheavy elements in cold- and hot-fusion reactions [7–9]. The process of projectile-nucleus capture by a target nucleus is an important stage of fusion reactions. The classic deterministic Newton equation for the collective coordinate of the relative distance between the centers of mass of the nuclei involved is usually used to describe the capture process, the force of friction being taken into account in this equation [6]. The diffusion Fokker–Planck equation and the stochastic Langevin equation were also used to describe this process [2, 3, 12]. Many studies based on transport models ignore quantum-mechanical statistical effects, employing a classical description, where the coefficients of friction are related to the diffusion coefficients by the classical fluctuation–dissipation relation. The description of fluctuations and dissipation is usually restricted to the Markov limit even in the case of low temperatures and strong coupling between the collective and internal subsystems for processes as fast as heavy-ion collisions [13]. So far, no model that would take into account all quantum-mechanical effects and non-Markovian effects accompanying the
passage through the potential barrier has been developed. Since the Coulomb barrier frequency is higher than the temperature of a dinuclear system at the instant of its formation, quantum fluctuations about the mean value of the trajectory of colliding nuclei may affect the evaporation-residue cross sections through the capture probability. It should be noted that the passage through the Coulomb barrier was previously studied for the case where this barrier was approximated by a parabola [13–16]. The objective of the present study was to include quantum-mechanical fluctuation and dissipation effects in the description of the capture process within the reduced-density-matrix formalism. The nonMarkov diffusion coefficients in the master equation for the density matr
Data Loading...
