The dynamical cluster-decay model (DCM), a nonstatistical description developed by Gupta and collaborators to account for the decay studies of excited compound nuclei formed in low-energy reactions has been applied to study various reactions. One of the main ingredient of the model is the use of temperature-dependent binding energies. In the present work, the effect of temperature-dependent binding energies in the model is analyzed. In earlier works on the DCM, the temperature-dependent liquid drop energy from Davidson et al.'s work [N. J. Davidson, S. S. Hsiao, J. Markram, H. G. Miller, and Y. Tzeng, Nucl. Phys. A 570, 61 (1994)], with two of its constants refitted for each isotopic chain to reproduce ground-state experimental binding energies, is used. In this work, the temperature-dependent binding energy formulas of Krappe [H. J. Krappe, Phys. Rev. C 59, 2640 (1999)] and Guet et al. [C. Guet, E. Strumberger, and M. Brack, Phys. Lett. B 205, 427 (1988)] are used in the DCM without any refitting of the coefficient of the liquid drop needed to study the decay of the hot and rotating 56 Ni * system formed in the 32 S + 24 Mg reaction at two incident energies, E c.m. = 51.6 and 60.5 MeV. The use of Krappe's formula results in the explicit preference of a four-nucleon transfer, indicating a strong minima in the potential energies corresponding to α-structured nuclei as well as exhibiting structural effects in the preformation calculations favoring α-structured nuclei. The overall cross sections for the light particles and intermediate mass fragments are nicely reproduced by the use of Krappe's formula. However, the individual channel cross-sections exhibit a strong distribution only for α nuclei, and for other fragments the results are lower by a factor of 2 to 3. The use of Guet et al.'s formula though does not show any explicit structure effects in the potential energy calculations or the preformation calculations; the overall cross sections calculated for light particles and intermediate mass fragments compare well with the experimental data. The results of individual channel cross-sections, however, do not exhibit any explicit preference for the α-structured nuclei; rather, the individual channel cross sections decreases with an increase in the mass number of the fragments. The calculated average kinetic energies using both formulas for the favored α fragments compares well with experimental values. Without any refitting of the coefficients of the temperature-dependent binding energies, the DCM works out well and the explicit preference of α structure depends mainly on the choice of formula used.

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Empirical relations for the preformation probability of cluster decay process in terms of the Q-value, mass asymmetry (η), mass number of the emitted cluster A2 is analyzed based on the discrepancy between the calculated and experimental half-lives of the cluster emitters. For the different empirical expressions considered corresponding to different physical quantities the preformation probability for the complete binary breakup of 226 Ra is calculated and the obtained results are compared with the preformed cluster model calculation (P0( PCM )) and another calculation in which the overlapping penetration probability is treated as the preformation probability (P0(μ)). Our empirical results for the use of Q-value compare well with P0(μ). Results due to the use of Q and its powers along with the combination of mass number A2 of the cluster emitted, and mass asymmetry η, reveal that preformation factor depends strongly on Q-value rather than A2 and η. Calculated half-lives of different cluster decays for the use of empirical P0 values are found to be in good agreement with the experimental values.

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