Hindrance in heavy-ion fusion for lighter systems of astrophysical interest

Abstract

The hindrance in fusion of heavy-ion reactions crops up in the region of extreme sub-barrier energies. This phenomenon can be effectively analyzed using a simple diffused barrier formula derived assuming a Gaussian distribution of fusion barrier heights. Folding the Gaussian barrier distribution with the classical expression for the fusion cross section for a fixed barrier, the fusion cross section is obtained. The energy dependence of the fusion cross section provides good description to the existing data on sub-barrier heavy-ion fusion for lighter systems of astrophysical interest. Using this simple formula, an analysis has been presented from 16 O + 18 O to 12 C + 198 Pt, all of which were measured down to < 10 µb. The agreement of the present analysis with the measured values is better than those calculated even from the sophisticated coupled channels calculations. The relatively smooth variation of the three parameters of this formula implies that it may be exploited to estimate the excitation function or to extrapolate cross sections for pairs of interacting nuclei which are yet to be measured. Possible extensions of the present methodology and its limitations have also been discussed.

Systematic study of the effect of individual rotational energy levels on the fusion cross-section of 16 O-based reactions of range 480 ≤ Z P Z T ≤ 592

“…However, the effects of nucleon transfer on fusion below the barrier have not yet been completely separated [6,[18][19][20][21][22][23][24][25][26][27]. Several works [1,14,[28][29][30][31][32][33][34] have discussed the coupling between the rotational state of the target nuclei.…”