# Covariance, Bicovariance of the Stochastic Neutron Field -

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Noise and Nonlinear Phenomenain Nuclear Systems,” Proceedingsof a NATO Advanced ResearchWorkshop’on Noise and Nonlinear Phenomenain Nuclear Systems,May 23-27,1988, Valencia, Spain. Edited by J. L. Munoz-Cobo and F. C. Difilippo, p. 59. 12. Difilippo, F. Sci. , 90, 13-18 (1985). 13. Spencer,R. , Nucl. Sci. , 80,603 (1982). l 31 This page intentionally 32 left blank. ’ APPENDIX 6 A Start from . 21 . 2) into (A. 6) and perform the indicated integrals to get . @A(@1 w,)=(2~)-2vp(vp-1)(vp- 2) (c& 10, (0, + 33 02) 0; (OJ 0; (wz)kA*7) Consider next the term CDB([email protected])=(27r)-~ Tdzl dz2 + 013 02 +-;23 exp {i (WI ~1+~2 0,) ~2)) 7 -m dt (

K. Mattingly D. W. McDonald J. T. Mihalczo R. B. Oberer R. B. Perez V . Protopopescu T. E. Valentine J. D. White M. C. NL Laboratory Records (RC) ?

VIII. SUMMARY AND DISCUSSION On the basis of the general stochasticneutron field theory developedby Munoz-Cobo et al,5results on the covarianceand bicovariance of the neutron field have been presented. These two statistical quantities are obtained from the counts observedin detectors operating during a period of time (gate length), A+. A classical example is the so called Feynmann Y-function that is defined as the varianceto mean ratio of the neutron field (see for instance reference 5). Upon taking the limit of the covarianceand bicovariance function for Aqc + o , one obtains the two and three detector crosscorrelation functions ,.