Fusion Hindrance for a Positive-$Q$-Value System ${}^{24}\mathrm{Mg}+{}^{30}\mathrm{Si}$

Measurements of the excitation function for the fusion of ${}^{24}\mathrm{Mg}+{}^{30}\mathrm{Si}$ $(Q=17.89\mathrm{MeV})$have been extended toward lower energies with respect to previous experimental data. The $S$-factor maximum observed in this large, positive-$Q$-value system is the most pronounced among such systems studied thus far. The significance and the systematics of an $S$-factor maximum in systems with positive fusion $Q$ values are discussed. This result would strongly impact the extrapolated cross sections and reaction rates in the carbon and oxygen burnings and, thus, the study of the history of stellar evolution.

Figure 1

Fusion events collected in the measurements at the four lowest energies (green open circles, black open triangles, red stars, and blue circles, respectively) in the spectra of $t_1$, $t_2$, $t_3$ versus $E_R$ (a)–(c) and $\mathrm{\Delta }E$ versus $E_R$ (d).

Figure 2

Excitation functions of ${}^{24}\mathrm{Mg}+{}^{30}\mathrm{Si}$, as measured by Morsad et al. (black open circles) [19] and in the present experiment (green circles). The lines are from calculations (see text for details). The inset shows the radial shape of the potentials.

Figure 3

$S(E)$ factors (a) and logarithmic derivatives $L(E)$ (b) for ${}^{24}\mathrm{Mg}+{}^{30}\mathrm{Si}$. A clear $S$-factor maximum is exhibited.

Figure 4

Plot of the potential pocket values, $V_p$ of the M3Y+Rep potential (black open circles), threshold energy $-Q$ (green triangles) and $E_s$ (red stars) versus entrance parameter $\zeta =Z_1{Z}_2\sqrt{\mu }$.