A new effective fusion barrier transmission model is developed. This gives a good description of the measured fusion cross sections both below and above the Coulomb barrier for a number of pairs of nuclei. The model uses only the surface region (r> RF-RB) of the heavy-ion optical potential describing the scattering data. The correlation of this approach with the direct reaction description of fusion is established. A physical interpretation for rF is indicated in terms of nucleon flux and neutron transfer time across the two nuclei.
Abstract:This paper proves that for N attractive delta function potentials the number of bound states (N ) satisfies, and is 0 ≤ N ≤ N in three dimensions (3D). Algebraic equations are obtained to evaluate the bound states generated by N attractive delta potentials. In particular, in the case of N attractive delta function potentials having same separation between adjacent wells and having the same strength λV, the parameter g=λVa governs the number of bound states. For a given N in the range 1-7, both in 1D and 3D cases the numerical values of g , where n=1,2,..N are obtained. When g=g , N ≤ n where N includes one threshold energy bound state. Furthermore, g are the roots of the Nth order polynomial equations with integer coefficients. Based on our numerical calculations up to N=40, even when N becomes large, 0 ≤ ≤ 4 and Σ N 2 and this result is expected to be generally valid. Thus, for g > 4 there will be no threshold or zero energy bound state, and if g≈ 2 for a given large N, the number of bound states will be approximately N/2. The empirical formula g = 4/[1 + ((N 0 − )/β)] gives a good description of the variation of g as a function of n . This formula is useful in estimating the number of bound states for any N and g both in 1D and 3D cases.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.