Fusion cross sections for 46,50Ti+90Zr,93Nb and some systematics of heavy-ion fusion at barrier and subbarrier energies.

Abstract

Measurements of the fusion cross sections in the barrier and subbarrier regions are presented for the four heavy-ion systems $^{46,50}\mathrm{Ti}$${+}^{90}$Zr${,}^{93}$Nb. The measured cross sections varied from 0.04 to 400 mb. The evaporation residues were detected by the use of a velocity filter. Procedures are described for extracting fusion cross sections from such measurements. The observed differences in the subbarrier fusion cross sections for the $^{90}\mathrm{Zr}$ and $^{93}\mathrm{Nb}$ nuclei, both of which have small collectivity, have led us to question the view that excursions of the strong nuclear force due to collective motions of the colliding nuclei are the primary enhancement mechanisms for the observed heavy-ion subbarrier fusion cross sections.A simple formula is presented, based on a flat distribution of barriers, which is applied to the near-barrier region (10--200 mb). This formula states that the quantity (\ensuremath{\sigma}E${)}^{1/2}$ vs E is linear in the near-barrier region with a zero intercept defining a threshold energy for fusion. These threshold values reflect variations in the binding energies of the valence neutrons. We also point out that the far-subbarrier region (10 mb) shows large variations in fusion cross sections and that these variations reflect differences in the collectivities of the colliding nuclei (especially noticeable differences are seen between permanently deformed nuclei and ``vibrational'' nuclei). These systematics of heavy-ion subbarier fusion suggest that neck formation is playing an important role. The barrier for neutron transfer vanishes at distances typically 1.5 fm beyond the typical barrier distance and this distance could vary with the binding energy of the valence neutrons. The presence of neutrons in the region between the nuclei could promote neck formation which provides a force strong enough to overcome the Coulomb force. The collective properties of the colliding nuclei are then interpreted as a modulation of the threshold for neck formation and thereby reflect the large observed differences in the far-subbarrier cross sections. Formulas are presented for ${\mathrm{\ensuremath{\sigma}}}_{\mathit{L}}$ which result from a flat distribution of barriers. These formulas predict a broad bell-shaped spin distribution and are compared to the measured distribution in the subbarrier region for the system $^{64}\mathrm{Ni}$${+}^{100}$Mo.