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Science and Technology of Nuclear Installations
Volume 2011 (2011), Article ID 584256, 8 pages
Research Article

Calculation of the Effective Delayed Neutron Fraction by Deterministic and Monte Carlo Methods

1ENEA, C.R. Casaccia, Via Anguillarese 301, 00123 Roma, Italy
2Dipartimento di Energetica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
3ENEA, C.R.E. E. Clementel, Via Martiri di Monte Sole 4, 40129 Bologna, Italy

Received 7 March 2011; Accepted 5 May 2011

Academic Editor: Antonio Alvim

Copyright © 2011 M. Carta et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The studies on Accelerator-Driven Systems (ADSs) have renewed the interest in the theoretical and computational evaluation of the main integral parameters characterizing subcritical systems (e.g., reactivity, effective delayed neutron fraction 𝛽 e f f , and mean prompt neutron generation time). In particular, some kinetic parameters, as the effective delayed neutron fraction, are evaluated in Monte Carlo codes by formulations which do not require the calculation of the adjoint flux. This paper is focused on a theoretical and computational analysis about how the different 𝛽 e f f definitions are connected and which are the approximations inherent to the Monte Carlo definition with respect to the standard definition involving weighted integrals. By means of a refined transport computational analysis carried out in a coherent and consistent way, that is, using the same deterministic code and neutron data library for the 𝛽 e f f evaluation in different ways, the theoretical analysis is numerically confirmed. Both theoretical and numerical results confirm the effectiveness of the Monte Carlo 𝛽 e f f evaluation, at least in cases where spectral differences between total and prompt fluxes are negligible with respect to the value of the functionals entering the classical 𝛽 e f f formulation.