Importance of higher order coupling effects in sub-barrier fusion

Abstract

Sub-barrier fusion has often been studied by linearizing couplings to nuclear structure for calculational convenience. Using a Green s function technique and the interacting boson model, we are able to include couplings to all orders. After renormalizing the coupling strengths, we find that couplings to all orders lead to improved agreement with data for the fusion cross section and distribution of barriers, compared to the linear couplings.PACS number(s): 25.70.Jj, 24.10.Eq, 21.60.Fw

Systematic study of subbarrier fusion in rare-earth nuclei

“…This result, derived in Ref. [10], is the familiar representation of the subbarrier fusion cross section as a weighted average of cross sections due to tunneling through a set of potential barriers determined by the eigenvalues of the coupling operator. As has been emphasized by many authors [18,19], the validity of this expression depends only on the usual adiabatic and rotating kame approximations which we have discussed previously [9].…”

“…As has been emphasized by many authors [18,19], the validity of this expression depends only on the usual adiabatic and rotating kame approximations which we have discussed previously [9]. Algebraic expressions for the overlaps and (Ori) in (10) are given in Ref. [10].…”

“…(6), i.e. , we do not expand the exponential to only first order as has been done previously, but evaluate its matrix element directly using the Green function technique [10]. In contrast, the Coulomb potential (4) is truncated at the first order.…”

“…We calculate the total fusion cross section using the partial wave expansion in the barrier penetration picture where Tg are the penetration probabilities for the different partial waves which can be evaluated numerically using a uniform WKB approximation, valid for energies both above and below the barrier [17] (10) where rq and r2 are the classical turning points of the motion, and ](n"i, )) refers to the number representation in the interaction basis which diagonalizes the operator 0 with the expectation value (Or)). This result, derived in Ref.…”

“…These calculations employed the usual linear coupling approximation. Most recently, using a Green function technique [13], we were able to include couplings to all orders going beyond the linear coupling approximation [10]. The formalism, in its present form, describes the nuclear structure effects in subbarrier fusion accurately, with all the approximations justified.…”