TDHF Theory and Its Extensions for the Multinucleon Transfer Reaction: A Mini Review

Abstract

Time-dependent Hartree-Fock (TDHF) theory has been a powerful tool in describing a variety of complex nuclear dynamics microscopically without empirical parameters. In this contribution, recent advances in nuclear dynamics studies with TDHF and its extensions are briefly reviewed, along the line with the study of multinucleon transfer (MNT) reactions. The latter lies at the core of this Research Topic, whose application for production of extremely neutron-rich nuclei has been extensively discussed in recent years. Having in mind the ongoing theoretical developments, it is envisaged how microscopic theories may contribute to the future MNT study. 1 Here a local EDF (like Skyrme) has been assumed, which makes the TDHF equations (1) local in space, as it is currently used in most of practical applications. In general, E = E(r)dr is composed of various local densities, ξ ≡ {ρ, τ, . . . }, and the TDHF equations (1)In such a case, the single-particle Hamiltonian can have spin dependence as well as differential operators (for the explicit form, see, e.g., Refs. [27][28][29]).

Quasifission Dynamics in Microscopic Theories

“…It is also possible to compute the probability to form a fragment with a given number of nucleons [80,81,82,83], but the resulting fragment mass and charge distributions are often underestimated in dissipative collisions [84,71]. Recent reviews [61,47] succinctly summarize the current state of TDHF (and its extensions) as it has been applied to various MNT reactions.…”

“…Returning to the inference of shell effects influencing fragment production, this phenomenon can also be seen through thorough TDHF studies of a particular system and systematically analyzing the fragments produced for different impact parameters and deformation orientations. TDHF studies of quasifission dynamics have taught us that the dynamics of a system may be dominated by shell effects [61,47]. An interesting finding of these TDHF studies is the prediction of the role of shell effects which favor the formation of magic fragments, in particular in the Z = 82 region in reactions involving an actinide collision partner [31].…”

“…The final phase of the dynamics is also impacted by the fissility of the composite system [26,29], its neutron richness [32], and by shell effects in the exit channel [12,13,20,23,38,39,40,24,31]. A number of theoretical approaches have been developed that describe the quasifission in terms of multi-nucleon transfer (MNT) processes [41,42,43,44,45,46,47]. Recently, time-dependent Hartree-Fock (TDHF) theory have proven to be an excellent tool for studying QF dynamics, and in particular mass-angle distributions and final fragment total kinetic energies (TKE) [48,31,37,49,32,50,51,52,34,53,45,54,55,56].…”

“…Recently, time-dependent Hartree-Fock (TDHF) theory have proven to be an excellent tool for studying QF dynamics, and in particular mass-angle distributions and final fragment total kinetic energies (TKE) [48,31,37,49,32,50,51,52,34,53,45,54,55,56]. While the fragments produced in TDHF studies are the excited primary fragments [57] a number of extensions based on the use of Langevin dynamics have been successfully applied to de-excite these fragments [55,58,59,56,60] Theoretical studies of quasifission dynamics have taught us that dynamics themselves may be dominated by shell effects [61,47]. Despite the apparent strong differences between fission and quasifission, it is interesting to note that similar shell effects are found in both mechanisms [54].…”

TDHF and a Macroscopic Aspect of Low-Energy Nuclear Reactions

“…In this Mini Review, however, we do not discuss the development of TDHF itself (see recent review articles on the development of TDHF in Refs. [35,36,37,38,39,40]). Instead, we focus on a macroscopic aspect of low-energy nuclear reactions described by TDHF.…”