Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-27T00:58:34.176Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 August 2015

M. Rizea  and
N. Carjan
M. Rizea*
Affiliation:
National Institute of Physics and Nuclear Engineering, “Horia Hulubei”, PO Box MG-6, Bucharest, Romania
N. Carjan*
Affiliation:
National Institute of Physics and Nuclear Engineering, “Horia Hulubei”, PO Box MG-6, Bucharest, Romania Centre d’Etudes Nucléaires de Bordeaux-Gradignan, UMR 5797, CNRS/IN2P3-Université Bordeaux 1, BP 120, 33175 Gradignan Cedex, France
*
Corresponding author.Email:[email protected]
Email:[email protected]
Get access

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 Schrödinger 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.

Keywords

65M0681Q0502.60.Lj02.70.Bf25.85.EcScission neutronsfissionbi-dimensional Schrödinger equationstationarytime-dependentnon-standard finite differences
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 4 , April 2011 , pp. 917 - 936
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bowman, H. R., Thompson, S. G., Milton, J. C. D., and Swiatecki, W. J., Velocity and angular distributions of prompt neutrons from spontaneous fission of Cf-252 Phys. Rev., 126 (1962), 2120–2136.Google Scholar
[2]Hwang, J. K., Ramayya, A. V., Hamilton, J. H., Greiner, W., Cole, J. D., Ter-Akopian, G. M.,Oganessian, Yu. Ts., and Daniel, A. V., Search for scission neutrons in the spontaneous fission of Cf-252, Phys. Rev. C., 60 (1999), 044616.Google Scholar
[3]Kornilov, N. V., Kagalenko, A. B., Poupko, S. V., Androsenko, P. A., and Hambsch, F. J., New evidence of an intense scission neutron source in the Cf-252 spontaneous fission, Nucl. Phys. A., 686 (2001), 187–203.Google Scholar
[4]Valsky, G. V., Scission neutrons in the general systematics of the yields of light particles from ternary nuclear fission, Phys. Atom. Nucl., 67(7) (2004), 1264–1276.Google Scholar
[5]Petrov, G. A., Current status of the search for scission neutrons in fission and estimation of their main chracteristics, Nuclear Fission and Fission-Product Spectroscopy, AIP Conference Proceedings, 798 (2005), 205–212.Google Scholar
[6]Danilyan, G. V., Fedorov, A. V., Krakhotin, V. A., Pavlov, V. S., Brakhman, E. V., Karpikhin, I. L., Korobkina, E., Golub, R., Wilpert, T., and Russina, M. V., Search for scission neutrons using specific angular correlations in U-235 fission induced by slow polarized neutrons, Phys. Atom. Nucl., 69 (2006), 1158–1160.Google Scholar
[7]Kornilov, N. V., Hambsch, F. J., and Vorobyev, A. S., Neutron emission in fission, Nucl. Phys. A., 789 (2007), 55–72.Google Scholar
[8]Carjan, N., Talou, P., and Serot, O., Emission of scission neutrons in the sudden approximation, Nucl. Phys. A., 792 (2007), 102–121.Google Scholar
[9]Boneh, Y., and Fraenkel, Z., Dynamic single-particle effects in fission, Phys. Rev. C., 10(2) (1974), 893–900.Google Scholar
[10]Rizea, M., Ledoux, V., Van Daele, M., Vanden Berghe, G., and Carjan, N., Finite difference approach for the two-dimensional Schrodinger equation with application to scission-neutron emission, Comput. Phys. Commun., 179(7) (2008), 466–478.Google Scholar
[11]Stavinsky, V. S., Rabotnov, N. S., and Seregin, A. A., Yad. Fiz., 7 (1968), 1051 [Sov. J. Nucl. Phys., 7 (1968), 631].Google Scholar
[12]Pashkevich, V. V., On the asymmetric deformation of fissioning nuclei, Nucl. Phys. A., 169 (1971), 275–293.Google Scholar
[13]Damgaard, J., Pauli, H. C., Pashkevich, V. V., and Strutinsky, V. M., A method for solving the independent-particle Schrödinger equation with a deformed average field, Nucl. Phys. A., 135 (1969), 432–444.CrossRefGoogle Scholar
[14]Abramowitz, M., and Stegun, I. A., Handbook of Mathematical Functions, 8th ed., Dover, New York, 1972.Google Scholar
[15]Sorensen, D., Lehoucq, R., Yang, C., and Maschhoff, K., ARPACK-An implementation of the implicitly restarted Arnoldi method for computing a few selected eigenvalues and corresponding eigenvectors of a large sparse matrix, www.caam.rice.edu/software/ARPACK.Google Scholar
[16]Brack, M., Damgaard, J., Jensen, A. S., Pauli, H. C., Strutinsky, V. M., and Wong, C. Y., Funny hills: the shell correction approach to nuclear shell effects and its applications to the fission process, Rev. Mod. Phys., 44 (1972), 320–405.Google Scholar
[17]Möller, P., and Nix, J. R., Nucl. Phys. A., 536 (1992), 20.Google Scholar
[18]Sierk, A. J., Koonin, S. E., and Nix, J. R., Modified one-body nuclear dissipation, Phys. Rev. C., 17 (1978), 646–653.Google Scholar
[19]Nishio, K., Nakagome, Y., Yamamoto, H., and Kimura, I., Multiplicity and energy of neutrons from 235U(n th, f) fission fragments, Nucl. Phys. A., 632 (1998), 540–558.Google Scholar
[20]Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in Fortran-The Art of Scientific Computing, Second Edition, Cambridge University Press, 1996.Google Scholar
[21]Golub, G. H., and Van Loan, C. F., Matrix Computations, The Johns Hopkins University Press, 3rd Edition, 1996.Google Scholar
[22]van der Vorst, H. A., Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM Sci, J.. Stat. Comput., 13 (1992), 631–644, www.math.uu.nl/people/vorst/software.html.Google Scholar
[23]Rizea, M., and Carjan, N. , Dynamical study of proton emission from deformed nuclei, Roman. Rep. Phys., 60(1) (2008), 27–44.Google Scholar
[24]Xu, Z. L., Han, H. D., and Wu, X. N., Adaptive absorbing boundary conditions for Schr”odinger-type equations: application to nonlinear and multi-dimensional problems, J. Comput. Phys., 225(2) (2007), 1577–1589.Google Scholar
[25]Antoine, X., Arnold, A., Besse, C., Ehrhardt, M., and Schadle, A., A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations, Commun. Comput. Phys. 4(4) (2008), 729–796.Google Scholar