A Modified Proximity Approach in the Fusion of Heavy Ions

Abstract

By using a suitable set of the surface energy coefficient, nuclear radius, and universal function, the original proximity potential 1977 is modified. The overestimate of the data by 4% reported in the literature is significantly reduced. Our modified proximity potential reproduces the experimental data nicely compared to its older versions. PACS numbers: 25.70.Jj, 24.10.-i. I. INTRODUCTIONRecently, great theoretical and experimental efforts are taken to studying the fusion of heavy nuclei leading to several new phenomena including the understanding of the formation of neutron -rich and super heavy elements [1,2]. The precise knowledge of the interaction potential between two nuclei is a difficult task and continuing efforts are needed in this direction. This problem has been of very active research over the last three decades and remains one of the most widely studied subject in low-energy heavy-ion physics [1-10].The total interaction potential is sum of the long range Coulomb repulsive force and short range nuclear attractive force. The Coulomb part of the interaction potential is well-known, whereas nuclear part is not clearly understood. A large number of efforts have been made to giving simple and accurate forms of the nuclear interaction potentials [1-10]. Among such efforts, proximity potential is well known for its simplicity and numerous applications. Based upon the proximity force theorem [4,5], a simple formula for ion-ion interaction potential as a function of the separation between the surfaces of two approaching nuclei was presented [4,5].As pointed out by many authors [7], original form of the proximity potential 1977 overestimates the experimental data by 4% for fusion barrier heights. In a recent study involving the comparison of 16 proximity potentials, one of us and collaborators pointed out that proximity potential 1977 overestimates the experimental data by 6.7% for symmetric colliding nuclei [1]. Similar results were obtained for asymmetric colliding nuclei [1].With the passage of time, several improvement/ modifications were made over the original proximity potential 1977 to remove the gray part of the potential. It includes either the better form of the surface energy coefficient [6] or the universal function and/or nuclear radius [7]. A careful look reveals that these modifications/improvements are not able to explain the experimental data [1,8]. A deep survey also pointed out that these technical parameters (i.e. surface energy coefficient, nuclear radius, and universal function) were chosen quite arbitrarily in the literature. Among them, the surface energy coefficient is available in a large variety of forms from time to time [1,2]. It affects the fusion barrier heights and cross sections significantly [1,2]. Also, nuclear radius is available in large variety of forms [1,2]. These forms varies either in terms of its coefficients or either different mass or isospin dependence. The third technical parameter i.e, the universal function, is also parametrized in different forms [1,4,5,7]. U...

Towards the fusion of weakly bound projectiles with heavy targets with proximity based potentials

“…As noted above, a careful analysis of [11,12] has shown that the potentials due to AW 95, Bass 80, Denisov DP and Proximity 2010 yield close agreement with experimental data. All these potentials were parameterized in terms of the proximity concept [12,[14][15][16].…”

“…Though the proximity 1977 potential has been the benchmark for all the calculations, the recent form and value of γ, radius as well as Φ have lead to proximity 2010 [12]. Based on the liquid drop model, Bass had suggested a potential that can be parameterized in terms of the proximity concept [14].…”

“…For the details of all potentials, the reader is referred to Refs. [11][12][13]. By adding the Coulomb potential to the nuclear potential, one can compute the total potential V T (R) and hence barrier positions and heights.…”

“…There, the potentials due to AW 95, Bass 80 and Denisov DP were found to reproduce barrier heights and positions far better than others in the class [11]. In addition to many extensions of the original proximity potential, Dutt and Bansal [12] also proposed a new form of proximity potential (labelled as Prox. 2010).…”

A new technique to determine fusion barrier heights using proximity potentials

“…This version [30] was introduced by replacing the form of nuclear charge radius in Prox 2000 with the form given by Royer and Rousseau [29]. The values of surface energy constant γ 0 and surface asymmetry constant k s were taken to be 1.25284 MeV/fm 2 and 2.345 respectively.…”