Background: The fluctuation-dissipation mechanism underlying nonequilibrium transport in low-energy heavy-ion reactions remains unclear. Although the time-dependent Hartree-Fock (TDHF) method provides a reasonable description of average reaction outcomes and one-body dissipation, it is known to significantly underestimate fluctuations of observables.

Purpose: The purpose of this work is to investigate deep-inelastic collisions of ${}^{144}\mathrm{Sm}+{}^{144}\mathrm{Sm}$ and ${}^{154}\mathrm{Sm}+{}^{154}\mathrm{Sm}$ with microscopic mean-field approaches and to show a predominant role of one-body dissipation as well as one-body fluctuations and correlation in low-energy heavy-ion reactions.

Methods: Three-dimensional TDHF calculations are carried out for ${}^{144}\mathrm{Sm}+{}^{144}\mathrm{Sm}$ at $E_{\text{c.m.}}=500\mathrm{MeV}$ and ${}^{154}\mathrm{Sm}+{}^{154}\mathrm{Sm}$ at $E_{\text{c.m.}}=485\mathrm{MeV}$ for a range of impact parameters with the Skyrme SLy5 energy density functional. Backward time evolutions are performed as well to evaluate fluctuations and correlation in nucleon numbers within time-dependent random phase approximation (TDRPA).

Results: As results of TDHF calculations we obtain total kinetic energy loss (TKEL), scattering angles, and contact time, for a wide range of impact parameters. TKEL takes almost constant values in an impact parameter range of $0\le b\lesssim 6\mathrm{fm}$, indicating a fully damped character of the reactions. We find a systematically lower TKEL for ${}^{144}\mathrm{Sm}+{}^{144}\mathrm{Sm}$ collisions as compared with the other, presumably because of the shell effects of $N=82$. With TDRPA we calculate mass- and charge-number fluctuations, ${\sigma }_{AA}$ and ${\sigma }_{ZZ}$, as well as the correlation between neutron and proton transfers, ${\sigma }_{NZ}$, for each impact parameter. By combining these results, we make a comparison of the ${\sigma }^2$-TKEL plot with available experimental data. We demonstrate that TDRPA quantitatively reproduces the experimental ${\sigma }_{AA}^2$-TKEL distributions, whereas it systematically underestimates the charge fluctuation, ${\sigma }_{ZZ}$. The double-differential cross sections of reaction products are calculated, showing good agreement with the experimental data. We demonstrate a long sought-after characteristic property that the closed-shell structure limits nucleon transfer at small energy losses, based on our microscopic TDHF and TDRPA calculations.

Conclusions: It has been shown that one-body fluctuations and correlation in TDRPA, built on top of TDHF mean-field dynamics, are the predominant mechanisms in deep-inelastic collisions. TDRPA systematically overestimates proton-number fluctuations ${\sigma }_{ZZ}$ in both ${}^{144}\mathrm{Sm}+{}^{144}\mathrm{Sm}$ and ${}^{154}\mathrm{Sm}+{}^{154}\mathrm{Sm}$ reactions, which offers room for refining our understanding of reaction mechanisms in low-energy heavy-ion reactions.

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• Low & intermediate energy heavy-ion reactions
• Models & methods for nuclear reactions
• Nuclear density functional theory