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

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.

arXiv comment10 pages, 6 figures; v2 - Version accepted for publication in PRC

References in corpus (10)

• Nuclear Quantum Many-Body Dynamics: From Collective Vibrations to Heavy-Ion Collisions
• Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique
• Time-dependent Hartree-Fock calculations for multinucleon transfer processes in ${}^{40,48}$Ca+${}^{124}$Sn, ${}^{40}$Ca+${}^{208}$Pb, and ${}^{58}$Ni+${}^{208}$Pb reactions
• 3-D unrestricted TDHF fusion calculations using the full Skyrme interaction
• Effect of pairing on one- and two-nucleon transfer below the Coulomb barrier: a time-dependent microscopic description
• Novel insights into transfer processes in the reaction 16O+208Pb at sub-barrier energies
• Neutron Transfer Dynamics and Doorway to Fusion in Time-Dependent Hartree-Fock Theory
• Quadrupole resonances in unstable oxygen isotopes in time-dependent density-matrix formalism
• New parameterization of Skyrme's interaction for regularized multi-reference energy density functional calculations
• Configuration mixing calculation for complete low-lying spectra with the mean-field Hamiltonian

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