Using the different versions of phenomenological proximity potential as well as other parametrizations within the proximity concept, we perform a detailed comparative study of fusion barriers for asymmetric colliding nuclei with asymmetry parameter as high as 0.23. In all, 12 different proximity potentials are robust against the experimental data of 60 reactions. Our detailed study reveals that the surface energy coefficient as well as radius of the colliding nuclei depend significantly on the asymmetry parameter. All models are able to explain the fusion barrier heights within ±10% on the average. The potentials due to Bass 80, AW 95, and Denisov DP explain nicely the fusion cross sections at above-as well as below-barrier energies.

Using the three versions of proximity potentials, namely proximity 1977, proximity 1988, and proximity 2000, we present a pocket formula for fusion barrier heights and positions. This was achieved by analyzing as many as 400 reactions with mass between 15 and 296. Our parametrized formula can reproduced the exact barrier heights and positions within an accuracy of $\pm1%$. A comparison with the experimental data is also in good agreement.Comment: 12 pages, 5 figure

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...

By using 14 different versions and parametrizations of a proximity potential and two new versions of the potential proposed in this paper, we perform a comparative study of fusion barriers by studying 26 symmetric reactions. The mass asymmetry ηA = A 2 −A 1 A 2 +A 1 , however, is very large. Our detailed investigation reveals that most of the proximity potentials reproduce experimental data within ±8% on the average. A comparison of fusion cross sections indicates that Bass 80, AW 95, and Denisov DP potentials have a better edge than other potentials. We also propose new versions of the proximity potential as well as Denisov parametrized potential. These new versions improve the agreement with the data.

We discuss the effect of surface energy coefficients as well as nuclear surface diffuseness in the proximity potential and ultimately in the fusion of heavy-ions. Here we employ different versions of surface energy coefficients. Our analysis reveals that these technical parameters can influence the fusion barriers by a significant amount. A best set of these parameters is also given that explains the experimental data nicely.