Fusion of the positive $Q$-value system ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$ well below the Coulomb barrier

The fusion excitation function of ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$ has been measured from well above the barrier down to very small cross sections at sub-barrier energies. A steady decrease of the fusion cross sections is observed below the barrier with no pronounced change of slope. The logarithmic derivative saturates and does not reach the value expected for a constant astrophysical S-factor. The S-factor does not show any maximum in the measured energy range. Coupled-channels calculations using a Woods-Saxon potential have been performed.

Figure 1

The top left panel shows the detector setup. Evaporation residues (ER), after beam separation in the electrostatic deflector, were detected by two microchannel plate detectors (MCP1 and MCP2), and finally stopped in a 450 mm${}^2$ silicon detector giving the energy ($E$) and the start signal used for the time-of-flights TOF1, TOF2, and triggering the data acquisition. The total length of the telescope was $\simeq 40$ cm with a geometrical solid angle of 0.076 msr. The E-TOF spectra are discussed in the text. In panels (a), (b), and (c) TOF1 is the ordinate, while (d) and (e) show TOF2 vs. $E$ spectra.

Figure 2

(Top) Fusion excitation function of ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$. Only statistical uncertainties are reported. (Bottom) The same data in a linear scale; here the errors are total uncertainties (statistical plus systematic ones, see text).

Figure 3

(Top) Logarithmic derivative of $E\sigma$ with respect to the energy. The derivative is the incremental ratio for successive pairs of experimental points. (bottom) S-factor vs. energy derived from the present data and from coupled-channels calculations. For the $S$ representation, a ${\eta }_o$ value of 36.05 has been adopted. The quoted errors are purely statistical.

Figure 4

The representation of fusion barrier distribution of ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$, together with the results of CC calculations.

Figure 5

Logarithmic derivatives of ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$ (this work) and ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ [27]. The energy scale for ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ has been shifted down by 9.0 MeV, so to compensate for the different Coulomb barrier.