The dynamical cluster-decay model (DCM), an extended version of the preformed cluster model (PCM) for ground-state ($T=0$) decays, is applied to study the decay of the proton-rich compound nucleus ${}^{124}\mathrm{Ce}$${}^{*}$ formed in the ${}^{32}\mathrm{S}$ + ${}^{92}\mathrm{Mo}$ reaction at an above-barrier beam energy of 150 MeV. Application of the statistical code pace4 to experimental data shows large deviations in all cases of proton clusters' (2$p$, 3$p$, and 4$p$) evaporation residue (ER) and the non-$\alpha$ nucleus ${}^6\mathrm{Be}$ intermediate mass fragment (IMF). Furthermore, the $\alpha$-nucleus ${}^8\mathrm{Be}$ decay is not observed in this experiment (not even the upper limit is given). Using the DCM, with effects of deformations up to hexadecapole and “compact” orientations included, for the best-fitted cross sections of 2$p$ and 3$p$ ERs and of ${}^5\mathrm{Li}$ and ${}^6\mathrm{Be}$ IMFs, the relative cross section of ${}^8\mathrm{Be}$ is found to be more than that of ${}^6\mathrm{Be}$, possibly due to the $\alpha$-nucleus structure of ${}^8\mathrm{Be}$. The same is shown to be true for ${}^{12}\mathrm{C}$ versus ${}^{10}\mathrm{C}$, i.e., $\alpha$-nuclei clusters are populated strongly relative to non-$\alpha$ clusters, similar to what was predicted by one of us (R.K.G.) et al. [S. Kumar, D. Bir, and R. K. Gupta, Phys. Rev. C 51, 1762 (1995)] for ground-state decays of such nuclei and the decay of ${}^{116}\mathrm{Ba}$${}^{*}$ formed in the ${}^{58}\mathrm{Ni}$ + ${}^{58}\mathrm{Ni}$ reaction at various compound nucleus excitation energies [R. K. Gupta et al., J. Phys. G: Nucl. Part. Phys. 32, 345 (2006)]. The only parameter of the DCM is the neck-length $\Delta R$, related to the “barrier-lowering” parameter. The compound nucleus formation probability and “barrier-lowering/-modification” effects are analyzed, and the role of varying the deformations of ${}^6\mathrm{Be}$ and/or ${}^8\mathrm{Be}$ nuclei on relative cross sections is studied, since the measured deformations are not available. The ones used here are from relativistic mean-field calculations [${\beta }_2{(}^6\mathrm{Be})=-0.087$ and ${\beta }_2{(}^8\mathrm{Be})=-0.094$]. Calculations are also presented for a beam energy of 140 MeV, supporting the above result.

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