Time-Dependent Description of Incomplete Fusion of Nuclei and Cluster and Nucleon-Transfer Reactions
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CLEI Theory
Time-Dependent Description of Incomplete Fusion of Nuclei and Cluster and Nucleon-Transfer Reactions V. V. Samarin1), 2)* Received January 11, 2018
¨ Abstract—A numerical solution of the time-dependent Schrodinger equation is applied in studying the dynamics of incomplete fusion of nuclei and cluster- and nucleon-transfer reactions at energies near the Coulomb barrier. The evolution of wave functions for all nucleons is used to describe multineutron- and multiproton-transfer reactions in 40 Ca+124 Sn collisions. The results of the calculations are in satisfactory agreement with experimental data. The evolution of the alpha-cluster wave function in the 12 C nucleus is used to calculate the incomplete-fusion cross section for the 12 C+51 V reaction. Agreement with experimental data for the (12 C, α) and (12 C, 2α) channels is attained. DOI: 10.1134/S1063778818040178
1. INTRODUCTION Grazing inelastic collisions of atomic nuclei are accompanied by nucleon transfer and the deformation of the nuclear surface. This entails the excitation of collective degrees of freedom. In this case, the relative motion of heavy nuclei may be analyzed on the basis of classical mechanics by employing the concepts of the trajectory and scattering angle, which depend on the impact parameter. A quantum-mechanical treatment should be applied in dealing with intrinsic degrees of freedom, such as single-particle states, low-lying (quadrupole, octupole, etc.) vibrations of nuclear surfaces, and high-lying oscillations (giant resonances). In those cases, the minimum distance Rmin between the centers of colliding nuclei may serve as a characteristic parameter. At rather large Rmin , the probabilities for nucleon transfer and collective excitations are low, which permits employing approximate approaches, including perturbation theory, linear terms of power-series expansions, and empirical models. At small impact parameters, a projectile nucleus is captured by a target nucleus after overcoming the Coulomb barrier, and this may be followed by an incomplete or a complete fusion of nuclei. Touching and a partial intersection of nuclear surfaces entail deep-inelastic reactions and multinucleon transfers, in which case substantial changes in nucleon wave functions prevent the application of perturbation theory, so that it becomes necessary to 1)
Joint Institute for Nuclear Research, ul. Joliot-Curie 6, Dubna, Moscow oblast, 141980 Russia. 2) Dubna State University, Universitetskaya ul. 19, Dubna, Moscow oblast, 141982 Russia. * E-mail: [email protected]
¨ solve the time-dependent Schrodinger equation. In the present study, this time-dependent approach is applied both to individual nucleons of colliding nuclei and to their strongly bound alpha-particle clusters. 2. TIME-DEPENDENT APPROACH TO DESCRIBING TRANSFER REACTIONS AND INCOMPLETE FUSION OF NUCLEI ¨ Via numerically solving the time-dependent Schrodinger equation [1, 2], one can perform a straightforward study of the dynamics of incomplete fusion and cluster- and nucleon-transfer reaction
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