Commun. Comput. Phys., 9 (2011), pp. 917-936.


Computational Study of Scission Neutrons in Low-Energy Fission: Stationary and Time-Dependent Approaches

M. Rizea 1*, N. Carjan 2

1 National Institute of Physics and Nuclear Engineering, "Horia Hulubei", PO Box MG-6, Bucharest, Romania.
2 National Institute of Physics and Nuclear Engineering, "Horia Hulubei", PO Box MG-6, Bucharest, Romania; and Centre d'Etudes Nucleaires de Bordeaux-Gradignan, UMR 5797, CNRS/IN2P3-Universite Bordeaux 1, BP 120, 33175 Gradignan Cedex, France.

Received 4 February 2010; Accepted (in revised version) 27 August 2010
Available online 14 October 2010
doi:10.4208/cicp.040210.270810a

Abstract

The emission of scission neutrons from fissioning nuclei is of high practical interest. To study this process we have used the sudden approximation and also a more realistic approach that takes into account the scission dynamics. Numerically, this implies the solution of the bi-dimensional Schrodinger equation, both stationary and time-dependent. To describe axially symmetric extremely deformed nuclear shapes, we have used the Cassini parametrization. The Hamiltonian is discretized by using finite difference approximations of the derivatives. The main computational challenges are the solution of algebraic eigenvalue problems and of linear systems with large sparse matrices. We have employed appropriate procedures (Arnoldi and bi-conjugate gradients). The numerical solutions have been used to evaluate physical quantities, like the number of emitted neutrons per scission event, the primary fragments' excitation energy and the distribution of the emission points.

AMS subject classifications: 65M06, 81Q05
PACS: 02.60.Lj, 02.70.Bf, 25.85.Ec
Key words: Scission neutrons, fission, bi-dimensional Schrodinger equation, stationary, time-dependent, non-standard finite differences.

*Corresponding author.
Email: rizea@theory.nipne.ro (M. Rizea), carjan@cenbg.in2p3.fr (N. Carjan)
 

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