Description of the multinucleon transfer mechanism for $^{48}\mathrm{Ca}+^{244}\mathrm{Pu}$ and $^{86}\mathrm{Kr}+^{198}\mathrm{Pt}$ reactions in a quantal transport approach

Description of the multinucleon transfer mechanism for ${}^{48}{Ca} + {}^{244}{Pu}$ and ${}^{86}{Kr} + {}^{198}{Pt}$ reactions in a quantal transport approach

M. Arik, S. Ayik, O. Yilmaz, and A. S. Umar

Phys. Rev. C 108, 064604 – Published 12 December 2023

Abstract

Background: Multinucleon transfer (MNT) reactions involving heavy projectile and target combinations stand as a promising method for synthesizing new neutron-rich exotic nuclei, which may not be possible using hot or cold fusion reactions or fragmentation. Exploring the mechanisms behind MNT reactions is essential and it requires a comprehensive theoretical framework that can explain the physical observables in these reactions.

Purpose: This work aims to show that the quantal diffusion approach based on the stochastic mean-field (SMF) theory is capable of explaining the reaction dynamics observed in MNT reactions. Primary product mass distributions in ${}^{48}{Ca} + {}^{244}{Pu}$ reaction at $E_{c.m.} = 203.2 MeV$ and ${}^{86}{Kr} + {}^{198}{Pt}$ reaction at $E_{c.m.} = 324.2 MeV$ are calculated and compared with the available experimental data.

Methods: In this work, we utilize the time-dependent Hartree-Fock (TDHF) calculations to analyze the mean-field reaction dynamics computationally in the reactions ${}^{48}{Ca} + {}^{244}{Pu}$ and ${}^{86}{Kr} + {}^{198}{Pt}$ for a broad range of initial angular momenta. Quantal transport description based on the SMF approach is used to calculate quantal diffusion coefficients and mass variances in ${}^{48}{Ca} + {}^{244}{Pu}$ and ${}^{86}{Kr} + {}^{198}{Pt}$ systems. The primary products arising from quasifission reactions are described by joint probability distribution in the SMF approach and those arising from fusion-fission are estimated by using the statistical deexcitation code gemini $+ +$ .

Results: Mean values of charge and mass numbers, scattering angles of the primary reaction products, and the total kinetic energies after the collision are calculated within the TDHF framework for a broad range of initial angular momenta. Throughout all the collisions, drift toward the mass symmetry and large mass dispersion associated with this drift are observed. The calculated primary fragment and mass distributions using the SMF approach successfully explain experimental observations for the ${}^{48}{Ca} + {}^{244}{Pu}$ and ${}^{86}{Kr} + {}^{198}{Pt}$ systems.

Conclusions: The primary mass distributions, mean values of binary products, and mass dispersions are determined and results are compared with the available experimental data. The observed agreement between the experimental data and SMF results highlights the effectiveness of the quantal diffusion mechanism based on the SMF approach, which does not include any adjustable parameters other than standard parameters of Skyrme energy density functional.

Received 30 August 2023
Accepted 9 November 2023

DOI:https://doi.org/10.1103/PhysRevC.108.064604

Physics Subject Headings (PhySH)

Models & methods for nuclear reactions Nuclear reactions Transfer reactions

Nuclear Physics

Authors & Affiliations

M. Arik ¹, S. Ayik ^2,*, O. Yilmaz ¹, and A. S. Umar ³

¹Physics Department, Middle East Technical University, 06800 Ankara, Turkey
²Physics Department, Tennessee Technological University, Cookeville, Tennessee 38505, USA
³Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA

^*ayik@tntech.edu

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Vol. 108, Iss. 6 — December 2023

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Figure 1
Mass-energy distributions of fragments obtained by TDHF calculations for the ${}^{48}{Ca} + {}^{244}{Pu}$ system at $E_{c.m.} = 203.2 MeV$ and the ${}^{86}{Kr} + {}^{198}{Pt}$ system at $E_{c.m.} = 324.2 MeV$ . Red continuous contours represent the gates used in the experiments in Refs. [27, 54, 55].
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Figure 2
Mean values of neutron and proton numbers of targetlike fragments at initial angular momentum $ℓ_{i} = 40 ℏ$ for ${}^{48}{Ca} + {}^{244}{Pu}$ system at $E_{c.m.} = 203.2 MeV$ and $ℓ_{i} = 60 ℏ$ for ${}^{86}{Kr} + {}^{198}{Pt}$ system at $E_{c.m.} = 324.2 MeV$ are shown as a function of time. Solid blue lines denote the neutron numbers and dashed red lines denote the proton numbers of targetlike fragments. The labels $t_{A}$ , $t_{B}$ , and $t_{C}$ indicate the projection of the time intervals used to determine the curvature parameters.
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Figure 3
Mean drift path in the $N − Z$ plane for the targetlike fragments are given at initial angular momentum $ℓ_{i} = 40 ℏ$ for ${}^{48}{Ca} + {}^{244}{Pu}$ system at $E_{c.m.} = 203.2 MeV$ and $ℓ_{i} = 60 ℏ$ for ${}^{86}{Kr} + {}^{198}{Pt}$ system at $E_{c.m.} = 324.2 MeV$ . Solid blue lines denote the mean drift path and dashed black lines denote the isoscalar lines. The labels A, B, and C indicate the projection of the time intervals used to determine the curvature parameters.
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Figure 4
Diffusion coefficient for neutron and proton transfers at initial angular momentum $ℓ = 40 ℏ$ for ${}^{48}{Ca} + {}^{244}{Pu}$ system at $E_{c.m.} = 203.2 MeV$ , and $ℓ = 60 ℏ$ for ${}^{86}{Kr} + {}^{198}{Pt}$ system at $E_{c.m.} = 324.2 MeV$ are shown as a function of time. Solid blue lines denote the diffusion coefficients of neutron transfer, $D_{N N} (t)$ ; dashed red lines denote the diffusion coefficients of proton transfer, $D_{Z Z} (t)$ .
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Figure 5
Neutron, proton, and mixed variances as a function of time at initial angular momentum $ℓ = 40 ℏ$ for ${}^{48}{Ca} + {}^{244}{Pu}$ system at $E_{c.m.} = 203.2 MeV$ , and $ℓ = 60 ℏ$ for ${}^{86}{Kr} + {}^{198}{Pt}$ system at $E_{c.m.} = 324.2 MeV$ . Solid blue lines denote the neutron variances, $σ_{N N}$ ; dashed red lines denote the proton variances, $σ_{Z Z}$ ; and dotted green lines denote the mixed variances, $σ_{N Z}$ .
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Figure 6
Primary fragment yield in the ${}^{48}{Ca} + {}^{244}{Pu}$ system at $E_{c.m.} = 203.2 MeV$ and ${}^{86}{Kr} + {}^{198}{Pt}$ system at $E_{c.m.} = 324.2 MeV$ in tip orientation of targetlike nuclei. The experimental data obtained from Refs. [27, 54] are indicated by the closed black circles. Dashed blue lines indicate the primary product mass distributions calculated within the SMF framework. The fusion-fission fragment distribution indicated by the green filled area was calculated using the gemini $+ +$ code [76]. The summation of yield distribution calculated by the SMF approach and gemini $+ +$ are indicated by solid red lines.
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Description of the multinucleon transfer mechanism for ${}^{48}{Ca} + {}^{244}{Pu}$ and ${}^{86}{Kr} + {}^{198}{Pt}$ reactions in a quantal transport approach

M. Arik, S. Ayik, O. Yilmaz, and A. S. Umar

Phys. Rev. C 108, 064604 – Published 12 December 2023

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Description of the multinucleon transfer mechanism for Ca48+Pu244 and Kr86+Pt198 reactions in a quantal transport approach

M. Arik, S. Ayik, O. Yilmaz, and A. S. Umar

Phys. Rev. C 108, 064604 – Published 12 December 2023

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Description of the multinucleon transfer mechanism for ${}^{48}{Ca} + {}^{244}{Pu}$ and ${}^{86}{Kr} + {}^{198}{Pt}$ reactions in a quantal transport approach