Particle-number projection method in time-dependent Hartree-Fock theory: Properties of reaction products

TL;DR

This paper introduces a formalism combining time-dependent Hartree-Fock with particle-number projection to analyze properties of reaction products in low-energy heavy ion collisions, providing insights into nucleon transfer and excitation energies.

Contribution

The work develops a new theoretical framework for calculating properties of reaction fragments in TDHF using particle-number projection, enhancing analysis of collision outcomes.

Findings

Nucleon removal results in small angular momentum and excitation energy.

Nuclei receiving nucleons show increased angular momentum and excitation energy with higher incident energy.

The method effectively analyzes fragment properties in low-energy heavy ion collisions.

Abstract

Background: The time-dependent Hartree-Fock (TDHF) theory has been successful in describing low-energy heavy ion collisions. Recently, we have shown that multinucleon transfer processes can be reasonably described in the TDHF theory combined with the particle-number projection technique. Purpose: In this work, we propose a theoretical framework to analyze properties of reaction products in TDHF calculations. Methods: TDHF calculation in three-dimensional Cartesian grid representation combined with particle number projection method. Results: We develop a theoretical framework to calculate expectation values of operators in the TDHF wave function after collision with the particle-number projection. To show how our method works in practice, the method is applied to $^{24}$O+$^{16}$O collisions for two quantities, angular momentum and excitation energy. The analyses revealed following features of the reaction: The nucleon removal proceeds gently, leaving small values of angular momentum and excitation energy in nucleon removed nuclei. Contrarily, nuclei receiving nucleons show expectation values of angular momentum and excitation energy which increase as the incident energy increases. Conclusions: We have developed a formalism to analyze properties of fragment nuclei in the TDHF theory combined with the particle-number projection technique. The method will be useful for microscopic investigations of reaction mechanisms in low-energy heavy ion collisions as well as for evaluating effects of particle evaporation on multinucleon transfer cross sections.