Theoretical analysis of 2n accidentals rates
Introduction
A given photon pulse may cause multiple neutron-producing reactions, ranging from zero to "infinity" reactions. The number of neutron-producing reactions in a pulse is hereafter denoted by [math]\displaystyle{ N }[/math]. Being the number of neutron-producing reactions actually occurring per pulse, [math]\displaystyle{ N }[/math] is assumed to follow the Poissonian distribution as a limiting case of the binomial distribution. Each neutron-producing interaction is said to produce [math]\displaystyle{ V_{i} }[/math] correlated neutrons, where the random variable [math]\displaystyle{ V_{i} }[/math] is the distribution of the number of neutrons produced in a single neutron-producing reaction. Each of the [math]\displaystyle{ V_i\text{'}s }[/math] are independent and identically distributed random variables, so the purpose of the subscript is to distinguish between several distinct neutron-producing interactions which may occur in a single pulse.
The beam has a Bremsstrahlung end point of 10.5 MeV, which energetically allows for only two possible neutron-producing interactions, 1n-knochout and photofission. Thus, [math]\displaystyle{ V_{i} }[/math] is equal to the photofission neutron multiplicity plus a contribution at [math]\displaystyle{ V_{i}=1 }[/math] from 1n-knockout events. The analysis that follows does not need to distinguish between 1n-knockout events and photofission events that emit a single neutron. In both cases, a single neutron is emitted and is uncorrelated with all and any other neutrons.
Variable reference
| Variable | Description |
|---|---|
| [math]\displaystyle{ N }[/math] | A random variable for the number of neutron producing reactions occurring in a single pulse. |
| [math]\displaystyle{ V_i }[/math] | A random variable for the number of correlated neutrons produced by the [math]\displaystyle{ i\text{th} }[/math] neutron-producing reaction in a given pulse. The index [math]\displaystyle{ i }[/math], ranging from 1 to [math]\displaystyle{ N }[/math], is used to distinguish between each of the distinct and independent reactions in a given pulse, thus all the [math]\displaystyle{ V_i'{s} }[/math] are identical and independently distributed random variables |