Speaker
Description
Nuclear fission is a phenomenon in which a nucleus splits into two (or more) lighter nuclei. From a theoretical perspective, fission has been studied using macroscopic approaches such as the Langevin method, as well as the microscopic frameworks including the DFT(density functional theory) and GCM(generator coordinate method). A microscopic understanding of nuclear fission at the nucleonic level is essential. Since fission predominantly occurs in the actinide and superheavy region, relativistic effects play an important role, particularly because the spin-orbit interaction is naturally incorporated in relativistic formulations. In this study, nuclei are described within the relativistic mean field (RMF) theory[1], in which the nuclear force is effectively modeled through the exchange of mesons such as $\sigma,\omega,\rho, \text{and} \pi$, between nucleons.
When a nucleus undergoes fission into two fragments, their mass ratio is generally asymmetric due to the quantum shell effects. Therefore, at least two collective deformation parameters are required to describe the fission process: the nuclear elongation (quadrupole deformation, $\beta_{20}$) and the reflection asymmetry (octupole deformation, $\beta_{30}$).
In this research, we focus on spontaneous fission, which proceeds through quantum tunneling in the deformation space $(\beta_{20},\beta_{30})$. The WKB(Wentzel-Kramers-Brillouin) approximation is often used as the simplest method to evaluate this tunneling probability and to determine the fission path. Within this approximation, both the potential energy surface (PES) $V(q)$ and the mass parameters $B(q)$ are required. The PES V(q) represents the nuclear energy as a continuous function of deformation $q=(\beta_{20},\beta_{30})$ and reflects the static properties of fission, while the mass parameters $B(q)$ correspond to the inertia in the deformation space and describe the dynamical aspects of the fission process.
The PES is gained by the constrained RMF with respect to the deformation coordinates $q=(\beta_{20},\beta_{30})$. The mass parameters are evaluated using several approaches, including the cranking approximation[2], the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method[3,4], and the quasiparticle random-phase approximation (QRPA)[5]. While there exist several calculations of mass parameters including octupole deformation within the cranking and ATDHFB approaches, QRPA-based calculations have so far been restricted to quadrupole deformation, with triaxiality taken into account. As a result, the evaluation of the spontaneous-fission lifetime $\tau_\text{SF}$ still suffers from significant uncertainties.
The aim of this research is to evaluate collective mass parameters within the QRPA framework in the two-dimensional deformation space $(\beta_{20},\beta_{30})$ and thereby improve the precision of fission lifetime.
In this talk, we will show the results for the 1-dimensional PES constrained on the quadrupole deformation only and present the current status.
[1] Y.K. Gambhir, P. Ring, and A. Thimet, Annals of Physics 198, 132-179 (1990).
[2] A. Baran, J.A. Sheikh, J. Dobaczewski, and W. Nazarewicz, PRC 84, 054321 (2011).
[3] J. Sadhukhan et al., PRC 88, 064314(2013).
[4] J. Zhao et al., Phys. Rev. C 93, 044315(2016)
[5] K. Washiyama, N. Hinohara, T. Nakatsukasa, PRC 103, 014306 (2021).