Particle transfer and fusion cross-section for super-heavy nuclei in dinuclear system

Abstract

Within the dinuclear system (DNS) conception, instead of solving Fokker-Planck Equation (FPE)analytically, the Master equation is solved numerically to calculate the fusion probability of superheavy nuclei, so that the harmonic oscillator approximation to the potential energy of the DNS is avoided. The relative motion concerning the energy, the angular momentum, and the fragment deformation relaxations is explicitly treated to couple with the diffusion process, so that the nucleon transition probabilities, which are derived microscopically, are time-dependent. Comparing with the analytical solution of FPE, our results preserve more dynamical effects. The calculated evaporation residue cross sections for one-neutron emission channel of Pb-based reactions are basically in agreement with the known experimental data within one order of magnitude.

Theoretical study of the synthesis of superheavy nuclei withZ=119and 120 in heavy-ion reactions with trans-uranium targets

“…The dynamical deformations of the projectile and the target in the entrance channel have been included in the DNS models [22][23][24] and they are crucial for calculating the local excitation energy of a DNS during the process of nucleon transfers.…”

“…Then the DNS evolves via nucleon transfer along the mass asymmetry coordinate η instead of in the direction of the relative distance between the projectile and the target R. During the nucleon transfer process, any DNS (A 1 , A 2 ) with A 1 = 0, 1, · · · , A P + A T and A 2 = A P + A T − A 1 may be formed. The evolution of the distribution function of each DNS with time can be described by a master equation [22][23][24],…”

The Harmonic Approximation in Heavy-Ion Reaction Study

“…It should be noted that the derivation of Equation (34) demonstrates that the form of the collective amplitude, ( ) 1 2 3 4 5 6 1 2 3 4 5 6 , , , , , , , , , , , , n n n n n n t t t t t t f x y z satisfy the normalization condition for the total wave function. The collective amplitude is the expansion coefficient of the total wave function ( ) , , , , , , t t t t t t x y z ξ ξ ξ Φ  , and its form can be obtained by using Equations (12), (16), (17), (18) and (22), which then leads to the probability distribution ( ) 1 2 3 4 5 6 1 2 3 4 5 6 2 , , , , , 3 , , , , , 8π , , n n n n n n t t t t t t f x y z as functions of interesting physical parameters for example, energy, intrinsic and collective quantum numbers, etc.…”

Effect of octupole and higher deformations on Coulomb barrier

“…It has been shown both theoretically and experimentally that the sub barrier fusion of spherical and well deformed nuclei is strongly enhanced by deformation [1][2][3][4][5][6][7][8][9][10][11][12][13]. It has long been recognized that the presence of deformation affects the height of Coulomb barrier, its position and its thickness which are especially important quantities for the production of the super-heavy elements [14][15][16]. Recently, particular interest has been paid to the effects of nuclear deformation on the formation and decay of the super-heavy nuclei (SHN) [12,15,17,18].…”

“…It has long been recognized that the presence of deformation affects the height of Coulomb barrier, its position and its thickness which are especially important quantities for the production of the super-heavy elements [14][15][16]. Recently, particular interest has been paid to the effects of nuclear deformation on the formation and decay of the super-heavy nuclei (SHN) [12,15,17,18]. Since reasonable prediction of formation cross section of the super-heavy nuclei requires knowledge of the interaction potential, calculation of potential for spherical-deformed and deformed-deformed pairs of nuclei became essentially important in describing production and decay processes of SHN [19,20] The interaction potential between two nuclei has Coulomb and nuclear contributions.…”