Feynman-α Analysis Using BGO Gamma-Ray Detector in a University Training and Research Reactor

Abstract

Feynman-α analyses for a critical state and several subcritical states of the UTR-KINKI reactor have been carried out using two Bi₁₄Ge₃O₁₂ (BGO) gamma-ray detectors free from radioactivation of the scintillator. As a statistical index of the analyses, the covariance-to-mean ratio of gamma counts between these detectors instead of the variance-to-mean ratio of each of the detectors is employed to get rid of a large negative correlation originating from the counting loss of a signal processing circuit. In the gate width dependence of the covariance-to-mean ratio measured at each reactor state, not only a familiar neutron-correlation component but also another small positive correlation between prompt gammas can clearly be observed. The prompt-neutron decay constant α determined considering the positive gamma correlation agrees very well with that obtained from a conventional Feynman-α analysis based on neutron detection. Neglecting the gamma correlation term, the decay constant is much overestimated with an increase in subcriticality, and the maximum overestimation reaches about 24% at a shutdown state with a subcriticality of 1.49%Δk/k.

Keywords:

• Feynman-α
• reactor noise
• gamma
• photon
• BGO

Nomenclature

$A_k$	=	= residues of zero-power reactor transfer function
$G\left(s\right)$	=	= zero-power reactor transfer function
$R$	=	= counting rate of a neutron counter (1/s)
$s_{\hspace{0.17em}}$	=	= poles of zero-power reactor transfer function (1/s) $\left({\alpha }_k=-s_k\right)$
$T$	=	= gate width (s)
$v$	=	= velocity of gamma (cm/s)
$Y_k$	=	= correlation amplitude defined by Eq. (8)(8) $Y_k=2\frac{\overline{\nu \left(\nu -1\right)}}{{\bar{\nu }}^2}{A}_k\frac{G\left({\alpha }_k\right)}{{\alpha }_k}.$(8)

Greek

$\alpha$	=	= prompt-neutron decay constant (1/s) $\left(\alpha ={\alpha }_7=-s_7\right)$
${\beta }_{eff,k}$	=	= effective fraction of k’th delayed-neutron group
${\epsilon }_n$	=	= detection efficiency of a neutron counter (counts per fission)
${\epsilon }_{\gamma }$	=	= detection efficiency of a gamma counter (counts per fission)
${\lambda }_k$	=	= decay constant of precursor of k’th delayed-neutron group (1/s)
$\bar{\eta }$	=	= first factorial moment of number of prompt gammas released from a fission
$\overline{\eta \left(\eta -1\right)}$	=	= second factorial moment of number of prompt gammas released from a fission
$\mathrm{\Lambda }$	=	= generation time (s)
$\bar{\nu }$	=	=  first factorial moment of number of neutrons released from a fission
$\overline{\nu \left(\nu -1\right)}$	=	= second factorial moment of number of neutrons released from a fission
$\rho$	=	= reactivity
$\mathrm{\Sigma }$	=	= macroscopic gamma-absorption cross section (1/cm)
$\tau$	=	= dead time of a neutron counter

Disclosure Statement

No potential conflict of interest was reported by the authors.