Non-Poisson counting statistics of a hybrid G–M counter dead time model Sang Hoon Lee a,b, * , Moosung Jae b , Robin P. Gardner c a Physics Department, Kyungpook National University, Daegu 702-701, Republic of Korea b Innovative Technology Center for Radiation Safety (iTRS), Nuclear Engineering Department, Hanyang University, Seoul 133-791, Republic of Korea c Center for Engineering Applications of Radioisotopes (CEAR), Nuclear Engineering Department, North Carolina State University, Raleigh, NC 27695-7909, USA Available online 11 April 2007 Abstract The counting statistics of a G–M counter with a considerable dead time event rate deviates from Poisson statistics. Important char- acteristics such as observed counting rates as a function true counting rates, variances and interval distributions were analyzed for three dead time models, non-paralyzable, paralyzable and hybrid, with the help of GMSIM, a Monte Carlo dead time effect simulator. The simulation results showed good agreements with the models in observed counting rates and variances. It was found through GMSIM simulations that the interval distribution for the hybrid model showed three distinctive regions, a complete cutoff region for the duration of the total dead time, a degraded exponential and an enhanced exponential regions. By measuring the cutoff and the duration of degraded exponential from the pulse interval distribution, it is possible to evaluate the two dead times in the hybrid model. Ó 2007 Elsevier B.V. All rights reserved. PACS: 29.40.Cs; 29.85.+c; 29.90.+4 Keywords: G–M counter; Dead time; Hybrid model 1. Introduction The G–M counter is an excellent radiation detector since it is rugged, stable in operation, inexpensive and versatile in detecting radiation. It only lacks the capabilities of spec- trometry and high counting rate measurement. While the first disadvantage cannot be modified, it is possible that the accurate useful counting rate range of G–M counter systems can be extended if the high counting rate behavior due to dead time effects can be accurately described. A hybrid dead time model has been developed and is used in many applications along with two idealized models, non-paralyzable and paralyzable [1,2]. However, the count- ing statistics of the hybrid model are not fully known. In this paper, GMSIM, a dead time effect simulator, has been developed to analyze the counting statistics of G–M coun- ters using a Monte Carlo method. Important characteris- tics, observed counting rates as a function true counting rates, variances and interval distributions were simulated and analyzed for three dead time models, the non-paralyz- able, paralyzable and hybrid. 2. Poisson statistics and dead time models When a G–M counter is perfect in detecting incoming radiation events without any dead time loss, it is theoreti- cally clear that the observed events follow Poisson statistics [3]. According to theory, an observed counting rate, m, is equal to the counting rate, n, and the distribution of inter- vals between two successive events is given by the exponen- tial distribution. The variance of measured counts during t, 0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.04.041 * Corresponding author. Address: Physics Department, Kyungpook National University, Daegu 702-701, Republic of Korea. Tel.: +82 53 950 7355; fax: +82 53 952 1739. E-mail address: lee@knu.ac.kr (S.H. Lee). www.elsevier.com/locate/nimb Nuclear Instruments and Methods in Physics Research B 263 (2007) 46–49 NIM B Beam Interactions with Materials & Atoms