Generalized time-dependent generator coordinate method for induced fission dynamics

doi:10.1007/s11467-023-1381-4

Front. Phys.

2024, Vol. 19

Issue (4) : 44201 https://doi.org/10.1007/s11467-023-1381-4

Generalized time-dependent generator coordinate method for induced fission dynamics

B. Li¹, D. Vretenar^2,¹(

), T. Nikšić^2,¹, J. Zhao³, P. W. Zhao¹(

), J. Meng¹(

)

¹. State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
². Physics Department, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
³. Center for Circuits and Systems, Peng Cheng Laboratory, Shenzhen 518055, China

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Abstract

The generalized time-dependent generator coordinate method (TD-GCM) is extended to include pairing correlations. The correlated GCM nuclear wave function is expressed in terms of time-dependent generator states and weight functions. The particle−hole channel of the effective interaction is determined by a Hamiltonian derived from an energy density functional, while pairing is treated dynamically in the standard BCS approximation with time-dependent pairing tensor and single-particle occupation probabilities. With the inclusion of pairing correlations, various time-dependent phenomena in open-shell nuclei can be described more realistically. The model is applied to the description of saddle-to-scission dynamics of induced fission. The generalized TD-GCM charge yields and total kinetic energy distribution for the fission of ²⁴⁰Pu, are compared to those obtained using the standard time-dependent density functional theory (TD-DFT) approach, and with available data.

Keywords nuclear density functional theory generator coordinate method fission dynamics

Corresponding Author(s): D. Vretenar,P. W. Zhao,J. Meng

Issue Date: 25 January 2024

Cite this article:

B. Li,D. Vretenar,T. Nikšić, et al. Generalized time-dependent generator coordinate method for induced fission dynamics[J]. Front. Phys. , 2024, 19(4): 44201.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1381-4
https://academic.hep.com.cn/fop/EN/Y2024/V19/I4/44201

Fig.1 Self-consistent deformation energy surface of ²⁴⁰Pu in the plane of quadrupole-octupole axially-symmetric deformation parameters, calculated with the relativistic density functional PC-PK1 and a monopole pairing interaction. Contours join points on the surface with the same energy, and the open dots correspond to points on the iso-energy curve at 1 MeV below the energy of the equilibrium minimum. In the panel on the right, the normalized probability that the initial TD-GCM wave packet reaches a particular point after 30 zs, is plotted as function of the octupole deformation parameter. The curves correspond to self-consistent TD-DFT fission trajectories from the initial points, to be used as generator states of the generalized TD-GCM.

Fig.2 Fission of ²⁴⁰Pu with the five TD-DFT trajectories that start in region 1. The initial point for the generalized GCM evolution is at

β 20 = 2.91

and

β 30 = 2.08

on the deformation energy surface. The top panel displays the eigenvalues of the overlap kernel, and the square moduli of components of the TD-GCM collective wave function are shown in the second panel. The time evolution of the quadrupole and octupole deformations on the way to scission and beyond, is compared to the single TD-DFT trajectory starting from the same point, in the two lower panels.

Fig.3 Same as in the caption to Fig.2 but for the five TD-DFT trajectories that start in region 3 on Fig.1. The initial point for the generalized GCM evolution is at

β 20 = 2.30

and

β 30 = 1.13

on the deformation energy surface. The vertical dashed line denotes the instant of scission.

Fig.4 Probability distributions of charge yields for the TD-DFT trajectories that start in region 3 on the deformation energy surface in Fig.1. In each panel, from top to bottom, the blue bars denote the charge of the light and heavy fragments calculated for the TD-DFT trajectory that starts from the initial points:

(β 20, β 30) = (2.41, 1.30), (2.33, 1.20), (2.30, 1.13),

(2.36, 1.00)

, and

(2.50, 0.96)

, respectively. The red bars, normalized to 1 for the light and heavy fragments, correspond to the charge yields obtained for the generalized TD-GCM trajectory that starts from the same initial point as the TD-DFT one, but is a superposition of all five basis trajectories.

Fig.5 Charge yields for induced fission of ²⁴⁰Pu. The yields calculated with the generalized TD-GCM (a), and TD-DFT (b) methods, are shown in comparison with the experimental charge distribution. The data are from Ref. [33], and correspond to an average excitation energy of 10.7 MeV.

Fig.6 The calculated total kinetic energies of the nascent fragments for induced fission of ²⁴⁰Pu, as functions of the fragment charge. The generalized TD-GCM and TD-DFT results are shown in comparison to the data [35].

Fig.7 Same as Fig.5, but with equal initial probabilities for each fission trajectory.

Fig.8 Same as the left panel of Fig.1, but the initial points in regions 1 and 2 are here merged into a larger basis 1−2, which includes 10 TD-DFT trajectories.

Fig.9 Probability distributions of charge yields for the TD-DFT trajectories that start in regions 1−2 on the deformation energy surface in Fig.8. In each panel, from (a) to (j), the blue bars denote the charge of the light and heavy fragments calculated for the TD-DFT trajectory that starts from an initial point in decreasing order of

β 30

, respectively. The red bars, normalized to 1 for the light and heavy fragments, correspond to the charge yields obtained for the generalized TD-GCM trajectory that starts from the same initial point as the TD-DFT trajectroy, but is a superposition of all ten basis trajectories.

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