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Isoscaling is a feature typical of statistical processes. As anticipated by theoretical studies about two decades ago [1], this phenomenon was proved by the analysis of selected fission fragment yields available in the public domain [2]. These comprehensive data provide a field of successful studies to the present time [3].
In this regard we analysed fission fragment yields taken from the data library [4], assigned to certain classifications of low-energy fission processes. Fission fragment yields $Y_1$, $Y_2$ within 25 < $Z$ < 70, delivered by the low-energy fission of nuclei in the range from Th to Fm, were analysed according to the relation
$$ Y_2(N,Z)/Y_1(N,Z) = \text{const} \cdot \exp(\alpha N + \beta Z) $$ The processed data showed by the majority an exponential dependence of the ratio of related pairs of fission fragment yields versus their charge $Z$ or neutron numbers $N$. This behavior, denoted as isoscaling,indicates statistcal features in the fission mechanism. Therefore, one expect a dominant role of the symmetry energy of nuclear matter. The isoscaling parameters $α$ and $β$ were derived by fits to the exponential plots. In the framework of statistical models the isoscaling parameters $α$ and $β$ are related to the neutron and proton chemical potentials, i.e the nucleonic compositions of the nuclear systems (s) undergoing fission as well as to the intrinsic nuclear temperature $T$ by the equation including the symmetry energy coefficient $C_{sym}$: $$ α T = 4 C_{\text{sym}} Δ ( Z/A)^2 s $$ This relation was used for a lot of ratio combinations of fission fragments with pronounced isoscaling features, i.e. which are indicated by a regular trend of the isoscaling parameters $α$ on $Z$ or $β$ on $N$. The nuclear temperatures, obtained on such conditions, are in agreement with those evaluated by the isotope thermometry approach [5]. Apart from that, deviations from the regular behavior of the isoscaling parameter $α$ on $Z$ ($β$ on $N$) indicate on appreciable contributions of shape deformations and shell effects in addition to the symmetry energy and require involved corrections.
1. W.A. Friedman, Phys. Rev. C 69, 031601 (2004); A.S. Botvina et al., Phys. Rev. C 65, 044610. (2002).
2. M.B. Tsang et al., Phys. Rev. Lett. 86, 5023 (2001); M. Veselsky et al., Phys. Rev. C 69, 031602 (2004).
3. Y.-J. Chen et al., Chinese Physics C 45, 084101 (2021); S. Kundu et al., // DAE Symp. Nucl. Phys. 67, 681, (2024).
4. https://www-ndc.iaea.org, ENDF/B.
5. M.N. Andronenko et al., //BRAS 2020, 84, 1540.
