Formation of Superheavy Elements: Study Based on Dynamical Approach
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NUCLEI Theory
Formation of Superheavy Elements: Study Based on Dynamical Approach∗ D. Naderi1)** and S. A. Alavi2) Received October 17, 2017
Abstract—Using multi-dimensional Langevin equations for the probability distribution of the distance between the surfaces of two approaching nuclei, we have studied the formation of superheavy elements via calculation of evaporation and fission cross sections of these elements. Evaporation residue cross sections have been calculated for the 1n, 2n, 3n, 4n, and 5n evaporation channels using one and four dimensional Langevin equations for the 48 Ca+226 Ra, 232 Th, 238 U, 237 Np, 239,240,242,244 Pu, 243 Am, 245,248 Cm, 249 Bk, and 249 Cf reactions. Our results show that with increasing dimension of Langevin equations the evaporation residue cross section is increased. Also, obtained results based on fourdimensional Langevin are in better agreement with experimental data in comparison with one-dimensional model. DOI: 10.1134/S1063778818020138
1. INTRODUCTION The synthesis of superheavy elements is one of the important problems of the recent nuclear physics and has been pursued both theoretically and experimentally. Cold fusion and hot fusion are two main classes of the heavy-ion reactions for production of superheavy nuclei, which are defined based on the type of the projectiles and targets. Cold fusion reactions using Pb or Bi nuclei as target have been used to produce superheavy nuclei with Z = 107–112 [1]. Hot fusion reactions using 48 Ca as projectile and actinide nuclei as target have been used to produce Z = 113–118 [2, 3]. Different theoretical methods have been introduced for analysis of the superheavy nucleus production, such as the dynamical Langevin model [4, 5], the dinuclear system (DNS) model [6– 8], the fluctuation dissipation model [9], the nuclear collectivization concept [10], the macroscopic dynamical model [11], and multidimensional stochastic model [12]. In [13] cold fusion reaction of 238 Pb(58 Fe, n)265 Hs has been analyzed in terms of the coupled Langevin equations in the three-dimensional collective space of neck, radial, and asymmetric degrees of freedom. In [14] the neutron emission in the 48 Ca+238 U and ∗
The text was submitted by the authors in English. Department of Physics, Razi University, Kermanshah, Iran. 2) Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran. ** E-mail: [email protected] 1)
50 Tr+249 Cf
fusion reactions has been investigated based on the one-dimensional Langevin equation. In [15] the mass and energy distributions of fission-like fragments formed in the different reactions were measured. In [16] the influence of entrance channel on the production of hassium isotopes has been studied within the dinuclear system model. In [17] the fission cross sections and fission fragment mass distributions in the reactions of 40 Ca+238 U and 48 Ca+238 U have been measured. Also, they calculated the fusion probabilities based on the fluctuation dissipation model. In this paper, we applied multi-dimensional Langevin equations to
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