Generalized time-dependent generator coordinate method for induced fission dynamics
B. Li1, D. Vretenar2,1(), T. Nikšić2,1, 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
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.
Corresponding Author(s):
D. Vretenar,P. W. Zhao,J. Meng
引用本文:
. [J]. Frontiers of Physics, 2024, 19(4): 44201.
B. Li, D. Vretenar, T. Nikšić, J. Zhao, P. W. Zhao, J. Meng. Generalized time-dependent generator coordinate method for induced fission dynamics. Front. Phys. , 2024, 19(4): 44201.
Younes W.M. Gogny D.F. Berger J., A Microscopic Theory of Fission Dynamics Based on the Generator Coordinate Method, Springer Cham, 2019
4
Regnier D., Dubray N., Schunck N., Verrière M.. Fission fragment charge and mass distributions in 239Pu(n, f) in the adiabatic nuclear energy density functional theory. Phys. Rev. C, 2016, 93(5): 054611 https://doi.org/10.1103/PhysRevC.93.054611
5
Verriere M., Regnier D.. The time-dependent generator coordinate method in nuclear physics. Front. Phys. (Lausanne), 2020, 8: 233 https://doi.org/10.3389/fphy.2020.00233
6
Tao H., Zhao J., P. Li Z., Nikšić T., Vretenar D.. Microscopic study of induced fission dynamics of 226Th with covariant energy density functionals. Phys. Rev. C, 2017, 96(2): 024319 https://doi.org/10.1103/PhysRevC.96.024319
7
Zhao J., Xiang J., P. Li Z., Nikšić T., Vretenar D., G. Zhou S.. Time-dependent generator-coordinate-method study of mass-asymmetric fission of actinides. Phys. Rev. C, 2019, 99(5): 054613 https://doi.org/10.1103/PhysRevC.99.054613
8
Simenel C., Umar A.. Heavy-ion collisions and fission dynamics with the time-dependent Hartree−Fock theory and its extensions. Prog. Part. Nucl. Phys., 2018, 103: 19 https://doi.org/10.1016/j.ppnp.2018.07.002
9
Nakatsukasa T., Matsuyanagi K., Matsuo M., Yabana K.. Time-dependent density-functional description of nuclear dynamics. Rev. Mod. Phys., 2016, 88(4): 045004 https://doi.org/10.1103/RevModPhys.88.045004
10
Stevenson P., Barton M.. Low-energy heavy-ion reactions and the Skyrme effective interaction. Prog. Part. Nucl. Phys., 2019, 104: 142 https://doi.org/10.1016/j.ppnp.2018.09.002
11
Bulgac A., Magierski P., J. Roche K., Stetcu I.. Induced fission of 240Pu within a real-time microscopic framework. Phys. Rev. Lett., 2016, 116(12): 122504 https://doi.org/10.1103/PhysRevLett.116.122504
12
Magierski P., Sekizawa K., Wlazlowski G.. Novel role of superfluidity in low-energy nuclear reactions. Phys. Rev. Lett., 2017, 119(4): 042501 https://doi.org/10.1103/PhysRevLett.119.042501
13
Scamps G., Simenel C.. Impact of pear-shaped fission fragments on mass-asymmetric fission in actinides. Nature, 2018, 564(7736): 382 https://doi.org/10.1038/s41586-018-0780-0
14
Bulgac A., Jin S., J. Roche K., Schunck N., Stetcu I.. Fission dynamics of 240Pu from saddle to scission and beyond. Phys. Rev. C, 2019, 100(3): 034615 https://doi.org/10.1103/PhysRevC.100.034615
15
Bulgac A., Jin S., Stetcu I.. Nuclear fission dynamics: Past, present, needs, and future. Front. Phys. (Lausanne), 2020, 8: 63 https://doi.org/10.3389/fphy.2020.00063
16
X. Ren Z., Vretenar D., Nikšić T., W. Zhao P., Zhao J., Meng J.. Dynamical synthesis of 4He in the scission phase of nuclear fission. Phys. Rev. Lett., 2022, 128(17): 172501 https://doi.org/10.1103/PhysRevLett.128.172501
17
Li B., Vretenar D., Nikšić T., W. Zhao P., Meng J.. Generalized time-dependent generator coordinate method for small- and large-amplitude collective motion. Phys. Rev. C, 2023, 108(1): 014321 https://doi.org/10.1103/PhysRevC.108.014321
G. Reinhard P., Cusson R., Goeke K.. Time evolution of coherent ground-state correlations and the TDHF approach. Nucl. Phys. A, 1983, 398(1): 141 https://doi.org/10.1016/0375-9474(83)90653-X
20
Regnier D., Lacroix D.. Microscopic description of pair transfer between two superfluid Fermi systems (ii): quantum mixing of time-dependent Hartree−Fock−Bogolyubov trajectories. Phys. Rev. C, 2019, 99(6): 064615 https://doi.org/10.1103/PhysRevC.99.064615
21
X. Ren Z., Zhao J., Vretenar D., Nikšić T., W. Zhao P., Meng J.. Microscopic analysis of induced nuclear fission dynamics. Phys. Rev. C, 2022, 105(4): 044313 https://doi.org/10.1103/PhysRevC.105.044313
22
Ebata S., Nakatsukasa T., Inakura T., Yoshida K., Hashimoto Y., Yabana K.. Canonical-basis time-dependent Hartree−Fock−Bogoliubov theory and linear-response calculations. Phys. Rev. C Nucl. Phys., 2010, 82(3): 034306 https://doi.org/10.1103/PhysRevC.82.034306
23
Scamps G., Lacroix D.. Effect of pairing on one- and two-nucleon transfer below the coulomb barrier: A time-dependent microscopic description. Phys. Rev. C, 2013, 87(1): 014605 https://doi.org/10.1103/PhysRevC.87.014605
24
W. Zhao P., P. Li Z., M. Yao J., Meng J.. New parametrization for the nuclear covariant energy density functional with a point-coupling interaction. Phys. Rev. C, 2010, 82(5): 054319 https://doi.org/10.1103/PhysRevC.82.054319
L. Hu Q., C. Gao Z., Chen Y.. Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states. Phys. Lett. B, 2014, 734: 162 https://doi.org/10.1016/j.physletb.2014.05.045
27
Bonche P., Dobaczewski J., Flocard H., H. Heenen P., Meyer J.. Analysis of the generator coordinate method in a study of shape isomerism in 194Hg. Nucl. Phys. A, 1990, 510(3): 466 https://doi.org/10.1016/0375-9474(90)90062-Q
28
G. Reinhard P., Goeke K.. The generator coordinate method and quantised collective motion in nuclear systems. Rep. Prog. Phys., 1987, 50(1): 1 https://doi.org/10.1088/0034-4885/50/1/001
29
Bender M., Rutz K., G. Reinhard P., A. Maruhn J.. Pairing gaps from nuclear mean field models. Eur. Phys. J. A, 2000, 8(1): 59 https://doi.org/10.1007/s10050-000-4504-z
30
X. Ren Z., Q. Zhang S., Meng J.. Solving Dirac equations on a 3D lattice with inverse hamiltonian and spectral methods. Phys. Rev. C, 2017, 95(2): 024313 https://doi.org/10.1103/PhysRevC.95.024313
31
X. Ren Z., Q. Zhang S., W. Zhao P., Itagaki N., A. Maruhn J., Meng J.. Stability of the linear chain structure for 12C in covariant density functional theory on a 3D lattice. Sci. China Phys. Mech. Astron., 2019, 62(11): 112062 https://doi.org/10.1007/s11433-019-9412-3
32
X. Ren Z., W. Zhao P., Q. Zhang S., Meng J.. Toroidal states in 28Si with covariant density functional theory in 3D lattice space. Nucl. Phys. A, 2020, 996: 121696 https://doi.org/10.1016/j.nuclphysa.2020.121696
33
Ramos D., Caamaño M., Farget F., Rodríguez-Tajes C., Audouin L., Benlliure J., Casarejos E., Clement E., Cortina D., Delaune O., Derkx X., Dijon A., Doré D., Fernańdez-Domínguez B., de France G., Heinz A., Jacquot B., Navin A., Paradela C., Rejmund M., Roger T., D. Salsac M., Schmitt C.. Isotopic fission-fragment distributions of 238U, 239Np, 240Pu, 244Cm, and 250Cf produced through inelastic scattering, transfer, and fusion reactions in inverse kinematics. Phys. Rev. C, 2018, 97(5): 054612 https://doi.org/10.1103/PhysRevC.97.054612
34
Zhao J., Nikšić T., Vretenar D., G. Zhou S.. Microscopic self-consistent description of induced fission dynamics: Finite-temperature effects. Phys. Rev. C, 2019, 99(1): 014618 https://doi.org/10.1103/PhysRevC.99.014618
35
Caamaño M., Farget F., Delaune O., H. Schmidt K., Schmitt C., Audouin L., O. Bacri C., Benlliure J., Casarejos E., Derkx X., Fernańdez-Domínguez B., Gaudefroy L., Golabek C., Jurado B., Lemasson A., Ramos D., Rodríguez-Tajes C., Roger T., Shrivastava A.. Characterization of the scission point from fission-fragment velocities. Phys. Rev. C, 2015, 92(3): 034606 https://doi.org/10.1103/PhysRevC.92.034606
36
Li B., Vretenar D., X. Ren Z., Nikšić T., Zhao J., W. Zhao P., Meng J.. Fission dynamics, dissipation, and clustering at finite temperature. Phys. Rev. C, 2023, 107(1): 014303 https://doi.org/10.1103/PhysRevC.107.014303