Fusion and proton transfer in the ${}^{10}\mathrm{B}+{}^{27}\mathrm{Al}$ system at sub-barrier energies

Background: Significant enhancement in sub-barrier fusion cross sections by several orders of magnitude, in the frame of one-dimensional barrier penetration models, is observed for a variety of nuclear systems. To understand this, one needs to find the fundamental degrees of freedom relevant in the sub-barrier fusion region by incorporating nonelastic channels such as coupling of the excited target and/or projectile nuclei, particle transfer channels, threshold variation of nuclear potential, etc.

Purpose: We probe what degrees of freedoms are associated with the ${}^{10}\mathrm{B}+{}^{27}\mathrm{Al}$ reaction at energies $\approx 18\%$ below to $\approx 12\%$ above the Coulomb barrier.

Method: An online $\gamma$-ray spectroscopy technique is used to determine the populated excitation functions in the ${}^{10}\mathrm{B}+{}^{27}\mathrm{Al}$ reaction. The reaction cross sections obtained from these $\gamma$ rays are compared with the statistical model to explore the mechanism of fusion reactions.

Results: At energies near and below the Coulomb barrier, two isotopes of sulfur (${}^{34}\mathrm{S}$ and ${}^{32}\mathrm{S}$) were found to reproduce cross section within the frame of the pace2 model based on Hauser-Feshbach calculations, whereas isotopes of chlorine (${}^{35}\mathrm{Cl}$), sulfur (${}^{35}\mathrm{S}$), and phosphorous (${}^{32}\mathrm{P}$) agree well but at above-barrier energies. Isotopes of Ar, Cl, S, P, and Si show significant enhancement over an entire band of energies. This enhancement (suppression) in the experimental cross section at energies above (below) the barrier points towards the involvement of some nuclear reaction mechanism other than fusion-evaporation. Distorted-wave Born approximation calculations strongly support the population of ${}^{28}\mathrm{Si}$ residue via the one-proton transfer process. The total fusion cross section is found to follow the theory after the inclusion of coupling of low lying excited states of projectile and target. Calculations concerning the astrophysical $S$ factor and the logarithmic derivative factor support the idea of no fusion hindrance at the studied energies. The universal fusion function benchmark shows consistency with previous data for lithium (or Li isotopes) induced systems.

Conclusions: The inclusion of inelastic couplings associated with both target and projectile is important to understand the behavior of total fusion cross section. The formation of ${}^{28}\mathrm{Si}$ via the one-proton transfer reaction supports the present experimental technique to make inclusive transfer measurements. The calculations with the universal fusion function present a slight suppression in the higher energy region, indicating possible breakup effects in this region. The present calculations show that till $18\%$ below the barrier there is no fusion hindrance. On extrapolating the theoretical values we further observed that the present system has no fusion hindrance. No connection of ${}^{10}\mathrm{B}+{}^{27}\mathrm{Al}$ fusion with astrophysics has been made, which raises the question to think of cosmic ray reactions and perhaps reactions in the early solar system, but how the fusion reaction would fit into the picture is not clear at all.

Figure 1

A scheme of the experimental setup; see text for details.

Figure 2

Typical $\gamma$-ray spectrum with beam on target at projectile energy $\approx 15.7$ MeV. $\gamma$ peaks indicate all identified reaction residues in the present work. The initial and final spin-parity of the states involved in the corresponding $\gamma$-ray transition also are shown.

Figure 3

Values of the level density parameter $a$, obtained from the analysis as suggested by [48]. The straight line corresponds to $a=A/7.5$. A zoom in the nuclear mass region $30<A<40$ is shown in the inset where $a=A/9.5$ approximates the average trend in this region, with upper (lower) limit given by $a=A/8.5$ ($a=A/11.1$).

Figure 4

Experimentally measured cross section $\pm$ SE of evaporation residues (a) ${}^{35}\mathrm{Ar}\left(2n\right)$, (b) ${}^{36}\mathrm{Cl}\left(p\right)$, (c) ${}^{35}\mathrm{Cl}\left(pn\right)$, (d) ${}^{34}\mathrm{Cl}\left(p2n\right)$, (e) ${}^{35}\mathrm{S}\left(2p\right)$, (f) ${}^{34}\mathrm{S}\left(2pn\right)$, (g) ${}^{33}\mathrm{S}\left(\alpha \right)$, (h) ${}^{32}\mathrm{S}\left(\alpha n\right)$, (i) ${}^{32}\mathrm{P}\left(\alpha p\right)$, (j) ${}^{31}\mathrm{P}\left(\alpha pn\right)$, (k) ${}^{29}\mathrm{Si}\left(2\alpha \right)$, and (l) ${}^{28}\mathrm{Si}\left(2\alpha n\right)$ are compared with pace2 predictions with different $a$ values. See the text for an explanation.

Figure 5

The measured cross section of ${}^{28}\mathrm{Si}$ evaporation (squares) in comparison with the proton transfer calculations, ${\sigma }_{p\text{−}\mathrm{tr}}^{\mathrm{corr}}$ (red line). The blue line shows the total proton transfer cross section for the ${}^{27}\mathrm{Al}({}^{10}\mathrm{B},{}^9\mathrm{Be}){}^{28}\mathrm{Si}$ reaction calculated within the DWBA.

Figure 6

The experimentally measured excitation function is compared with the 1DBPM, and for different modes of coupling between interacting partners using ccfull. The inclusion of couplings of different inelastic excitations of interacting partners is shown. Lines and curves are self-explanatory. Symbols represent experimental total fusion cross section $\pm$ SE.

Figure 7

Astrophysical $S$ factor derived from experimental total fusion cross sections in the ${}^{10}\mathrm{B}+{}^{27}\mathrm{Al}$ system. In the inset, the logarithmic derivative $L\left(E\right)$ factor is plotted as a function of the center-of-mass energy. The lines and curves are self-explanatory. Symbols represents experimental total fusion cross section $\pm$ SE.

Figure 8

Reduced total fusion cross section as a function of the reduced energy for several nuclear systems. The solid line represent the UFF. The arrow at $E_{\text{red}}$ = 0 corresponds to the barrier height.