Sudden- or Frozen-density approximation in Semi-classical extended Thomas Fermi model for Wong formula used in 64Ni+64Ni reaction

TL;DR

This paper demonstrates that using the frozen-density approximation within the semiclassical extended Thomas Fermi model with the {}-summed Wong formula provides an almost exact fit to 64Ni+64Ni reaction data, explaining hindrance phenomena.

Contribution

It shows that the frozen-density approximation yields significantly better fits to reaction data than the sudden approximation in the ETF model with Wong formula.

Findings

Frozen-density approximation achieves near-perfect data fit.

Sudden approximation requires barrier modifications.

Hindrance phenomena can be explained by the {}-summed Wong expression.

Abstract

The {\ell}-summed Wong expression is applied in the semiclassical extended Thomas Fermi (ETF) method of Skyrme energy density formalism (SEDF), using both the sudden and frozen-density approximations, to the case of 64Ni+64Ni reaction data. We find that a very much improved fit (almost exact, point to point) to the data is obtained for the frozen-density approximation with {\ell}max (Ec.m.) varying smoothly. On the other hand, the same could not be achieved in the sudden case, still requiring a modification of the barrier at both the below- and above-barrier energies. This result means to say that the phenomenon of hindrance, observed in coupled channel calculations for 64Ni+64Ni reaction, could be explained simply on the basis of the {\ell}-summed Wong expression, at least for the frozen-density approximation in ETF method of SEDF.