[Paper Review] Multinucleon transfer reaction in time-dependent Hartree-Fock theory

Kazuyuki Sekizawa, Kazuhiro Yabana|arXiv (Cornell University)|Nov 26, 2015

Nuclear physics research studies4 citations

TL;DR

This paper develops a particle-number projection (PNP) method within time-dependent Hartree-Fock (TDHF) theory to calculate multinucleon transfer (MNT) cross sections in heavy-ion reactions. The method enables accurate computation of transfer probabilities and excitation energies for reaction products, and when combined with a statistical model for particle evaporation, it reproduces experimental MNT cross sections well for small nucleon transfers, though accuracy decreases for large transfers.

ABSTRACT

Time-dependent Hartree-Fock (TDHF) theory has achieved a remarkable success in describing and understanding nuclear many-body dynamics from nucleons' degrees of freedom. We here report our investigation of multinucleon transfer (MNT) processes employing the TDHF theory. To calculate transfer probabilities for channels specified by the number of protons and neutrons included in reaction products, a particle-number projection (PNP) method has been developed. The PNP method is also used to calculate excitation energies of reaction products. Combined use of the PNP method with a statistical model, we can evaluate MNT cross sections taking account of effects of particle evaporation. Using these methods, we evaluate MNT cross sections for $^{40,48}$Ca+$^{124}$Sn, $^{40}$Ca+$^{208}$Pb, and $^{58}$Ni+$^{208}$Pb reactions. From systematic analyses, we find that cross sections for channels with a large reaction probability are in good agreement with experimental data. However, the agreement becomes less accurate as the number of transferred nucleons increases. Possible directions to improve the description are discussed.

Motivation & Objective

• To develop a microscopic, ab initio framework for multinucleon transfer (MNT) reactions beyond empirical models.
• To overcome the computational limitations of traditional TDHF-based transfer probability calculations by introducing an efficient particle-number projection (PNP) method.
• To evaluate MNT cross sections including secondary effects such as particle evaporation using a statistical model.
• To compare theoretical predictions with experimental data for 40,48Ca+124Sn, 40Ca+208Pb, and 58Ni+208Pb reactions.
• To identify limitations of TDHF in describing large nucleon transfers and suggest improvements via TDGCM and TDHFB extensions.

Proposed method

• Applies time-dependent Hartree-Fock (TDHF) theory to simulate nuclear dynamics in low-energy heavy-ion collisions.
• Develops a particle-number projection (PNP) method to extract transfer probabilities for each channel defined by neutron and proton numbers in reaction products.
• Uses PNP to compute excitation energies of reaction fragments from the TDHF wave function after collision.
• Combines PNP results with a statistical model (e.g., evaporation models) to estimate cross sections accounting for particle evaporation from excited fragments.
• Performs TDHF calculations for 40,48Ca+124Sn, 40Ca+208Pb, and 58Ni+208Pb systems at energies near the Coulomb barrier.
• Analyzes the neck formation and rupture dynamics as a precursor to quasifission, particularly in systems with large N/Z asymmetry.

Experimental results

Research questions

• RQ1 Can the PNP method in TDHF theory accurately predict multinucleon transfer cross sections for heavy-ion reactions?
• RQ2 How do the inclusion of particle evaporation effects and excitation energy corrections impact the agreement between theory and experiment?
• RQ3 Why does the accuracy of TDHF-based MNT cross section predictions decrease for large numbers of transferred nucleons?
• RQ4 What role does neck formation and rupture play in initiating large-scale nucleon transfer and quasifission?
• RQ5 What theoretical improvements (e.g., TDGCM, TDHFB) are necessary to enhance the predictive power of TDHF for MNT processes?

Key findings

• The PNP method enables efficient and accurate calculation of transfer probabilities and excitation energies in TDHF, reducing computational cost from 2^N to a few hundred determinants.
• For MNT channels with small numbers of transferred nucleons, the calculated cross sections agree well with experimental data.
• The agreement deteriorates for channels involving large nucleon transfers, indicating a limitation of the current TDHF framework.
• Including particle evaporation effects improves agreement with experiment, but the theory still underestimates cross sections for large transfers.
• Neck formation and rupture are observed as precursors to quasifission, especially in systems with large N/Z asymmetry (e.g., 40Ca+208Pb).
• The method is extendable to include parity and angular momentum projections, enabling future comparison with gamma-ray spectroscopy data.