Exploring Zeptosecond Quantum Equilibration Dynamics: From Deep-Inelastic to Fusion-Fission Outcomes in Ni58+Ni60

Abstract

Energy dissipative processes play a key role in how quantum many-body systems dynamically evolve towards equilibrium. In closed quantum systems, such processes are attributed to the transfer of energy from collective motion to single-particle degrees of freedom; however, the quantum manybody dynamics of this evolutionary process are poorly understood. To explore energy dissipative phenomena and equilibration dynamics in one such system, an experimental investigation of deepinelastic and fusion-fission outcomes in the 58 Ni+ 60 Ni reaction has been carried out. Experimental outcomes have been compared to theoretical predictions using Time Dependent Hartree Fock and Time Dependent Random Phase Approximation approaches, which respectively incorporate onebody energy dissipation and fluctuations. Excellent quantitative agreement has been found between experiment and calculations, indicating that microscopic models incorporating one-body dissipation and fluctuations provide a potential tool for exploring dissipation in low-energy heavy ion collisions.The dynamic evolution of perturbed quantum manybody systems towards equilibrium is a topic of great interest in many fields, including quantum information [1], condensed matter [2-5], and nuclear physics [6][7][8][9][10]. Energy dissipation-the transfer of energy from collective motion to internal or external degrees of freedomshapes this dynamic evolution, playing a significant role in whether and how such complex systems achieve full equilibration. To date, a great deal of effort has focused on quantum systems in which energy dissipation is brought about via contact with an external environment (e.g., gas, photons, etc.) [11,12]. Much less is known about energy dissipation that arises from internal degrees of freedom [2, 5,13].One testing ground for the exploration of energy dissipation due to internal degrees of freedom can be found in heavy ion collisions. The nuclear collision process results in a closed composite quantum system that is isolated from external environments during the time of the collision (a timescale of several zeptoseconds, prior to particle emission), rapidly evolves towards equilibration in many degrees of freedom, and undergoes significant excitation and internal rearrangement throughout the equilibration process. Through the manipulation of collision entrance channel parameters (projectile-target combinations and energies), a range of factors with the potential to affect energy dissipation can be explored. Typical timescales for energy dissipation in such systems could in principle vary from isospin and mass equilibration times on the order of 0.3-0.5 zs [14,15] and ∼5 zs [16,17], respectively.In nuclear reactions, the observation of the total kinetic energy of the reaction products (TKE) offers a direct measure of energy dissipation. The observation of the masses of reaction products via direct or indirect methods offers a measure of system equilibration in a key degree of freedom, and can be used to explore fluctuations in reaction product mas...

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

“…In Ref. [171], the SMF approach was also applied to the Ni+Ni reaction, showing quantitative agreement with experimental data [156], comparable to TDRPA. Recently, Bulgac et al [172] proposed another way to introduce stochasticity by means of external potentials which are random in both space and time.…”

“…By extending the variational space for fluctuations of a one-body observable, one obtains a formula that includes effects of one-body fluctuations on top of the TDHF mean-field trajectory, which may be regarded as time-dependent RPA (TDRPA). It has recently been shown that the description of the width of fragment mass distributions in deepinelastic collisions, which is severely underestimated in TDHF [20,21,153], is substantially improved [154,155], or even quantitatively agrees with experimental data [156], in TDRPA. It implies that one-body dissipation and fluctuations described by TDHF and TDRPA, respectively, are the predominant mechanisms in deep-inelastic collisions.…”

“…It implies that one-body dissipation and fluctuations described by TDHF and TDRPA, respectively, are the predominant mechanisms in deep-inelastic collisions. Here, a caution is required: the TDRPA formula in the present form can only be applied to symmetric reactions [156]. To overcome this difficulty, one may extend the derivation based on the Balian-Vénéroni variational principle to include higher-order corrections, or derive a formula generalized for asymmetric reactions from, e.g., the stochastic mean-field (SMF) theory [157,158], from which one can derive the TDRPA formula in the small fluctuation limit [157].…”

Quasifission Dynamics in Microscopic Theories

“…Various extensions have been developed to study the fluctuations of one-body observables. These include the time-dependent random phase approximation (TDRPA) approach of Balian and Vénéroni [68,69,70,71,72], the time-dependent generator coordinate method [73], or the stochastic mean-field (SMF) method [74,75]. The effects of two-body dissipation on reactions of heavy systems using the time-dependent density matrix (TDDM) [76,77] approach have also been recently reported [78,79].…”

Quantal diffusion approach for multinucleon transfers in Xe + Pb collisions

“…The time-dependent random phase approximation (TDRPA) approach of Balian and Vénéroni [21][22][23][24][25] provides a possible approach for calculating dispersion of fragment mass distributions. However, this approach has severe technical difficulties in applications to the collisions of asymmetric systems [26]. Here, we employ the stochastic meanfield (SMF) approach [27,28] to calculate the mass distribution of the primary fragments in 136 Xe + 208 Pb system.…”