Difference between revisions of "Theoretical analysis of 2n accidentals rates"
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[[Production Analysis | go_back]] | [[Production Analysis | go_back]] | ||
| − | + | =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>N</math>. Being the number of neutron-producing reactions ''actually'' occurring per pulse, <math>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>V_{i}</math> correlated neutrons, where the random variable <math>V_{i}</math> is the distribution of the number of neutrons produced in a single neutron-producing reaction. Each of the <math>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. | 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>N</math>. Being the number of neutron-producing reactions ''actually'' occurring per pulse, <math>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>V_{i}</math> correlated neutrons, where the random variable <math>V_{i}</math> is the distribution of the number of neutrons produced in a single neutron-producing reaction. Each of the <math>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>V_{i}</math> is equal to the photofission neutron multiplicity plus a contribution at <math>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. | 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>V_{i}</math> is equal to the photofission neutron multiplicity plus a contribution at <math>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. | ||
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| + | == Variable reference== | ||
| + | |||
| + | {| class="wikitable" | ||
| + | ! Variable !! Description | ||
| + | |- | ||
| + | |<math>V_i</math> | ||
| + | |A random variable equal to the number of correlated neutrons produced by the <math>i\text{th}</math> neutron-producing reaction in a single given pulse. The index <math>i</math> is used to distinguish between any number of distinct and independent reactions in a given pulse, thus <math>V_i'{s}</math> are identical and independently distributed random variables | ||
| + | |- | ||
| + | |} | ||
==Probability of detecting a given pair of neutrons in a single pulse== | ==Probability of detecting a given pair of neutrons in a single pulse== | ||
Revision as of 03:18, 20 January 2018
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 . Being the number of neutron-producing reactions actually occurring per pulse, is assumed to follow the Poissonian distribution as a limiting case of the binomial distribution. Each neutron-producing interaction is said to produce correlated neutrons, where the random variable is the distribution of the number of neutrons produced in a single neutron-producing reaction. Each of the 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, is equal to the photofission neutron multiplicity plus a contribution at 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 |
|---|---|
| A random variable equal to the number of correlated neutrons produced by the neutron-producing reaction in a single given pulse. The index is used to distinguish between any number of distinct and independent reactions in a given pulse, thus are identical and independently distributed random variables |