Neutron-rich isotope production for $Z\geq 98$ in ^{238} \mathrm{U}+{ }^{248} \mathrm{Cm}$ reaction

Background: Multi-nucleon transfer (MNT) reactions in actinide systems are a promising method to synthesize transuranium neutron-rich elements. Appropriate theoretical approaches are needed to understand the mechanism behind MNT. Purpose: This work aims to produce neutron-rich isotopes in the super-heavy region through the ^{238} \mathrm{U}+{ }^{248} \mathrm{Cm}$ system. We employ a microscopic approach to elucidate reaction mechanisms, and predict new isotope production that expands the known nuclear chart. Methods: The stochastic mean-field (SMF) approach, including fluctuations and correlations, is used to explain the primary cross-sections in MNT reactions based on the quasi-fission and inverse quasi-fission processes, and a statistical de-excitation model with GEMINI++ code to calculate the secondary fragment cross-sections Results: The calculated cross-sections using SMF and GEMINI++ explain available experimental results for the ^{238} \mathrm{U}+{ }^{248} \mathrm{Cm}$ system at $E_\mathrm{c.m.}=898.7$~MeV energy. This shows the effectiveness and applicability of the quantal diffusion approach based on the SMF theory in heavy-ion collisions. Conclusions: Production of transuranium neutron-rich elements with a proton number up to $Z=$101 are obtained with sizable cross-sections. Theoretical results calculated for the Z=102-105 region, for which there are no experimental data, show that the cross-section values would be lower than the microbarn level. SMF theory does not contain any adjustable parameters other than the standard parameters of the energy density functional used in the TDHF theory and is an important approach for the microscopic understanding of reaction mechanisms.