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I have a question, which sounds somewhat silly, but I'm stuck with it. I'm writing some monte carlo code to simulate the effect of multiple hits on neutron detectors, and I'm confronted with the following issue.

Consider a "multiple hit" of a detector. That means, a neutron impact at positions p1, p2, p3, ... pk. I want to study the behaviour of the detector under uniform irradiation with k multiple hits, so I did some simple counting statistics for this case: I counted the different possible cases of k-hit sets {p1, p2...pk}. This gives me a certain distribution of behaviours of the detector.

However, I considered the case of {p1,p2...} and {p2,p1...} as identical: I was considering a set of k neutrons, hitting different positions, without "numbering" them, as neutrons are in principle indistinguishable particles.

Now, you can write the code differently, and say that I draw k times a uniformly distributed neutron, to form my k-hit. But that changes the statistics in the case of identical hits (which is exactly the kind of statistic I'm interested in).

Indeed, consider the simple case of only two "detection outcomes" possible, "left" or "right". Consider that I look at double hits. In my first approach, I'd say, I have 3 possibilities:

{twice "left"},

{twice "right"}

{once "left", once "right"}

Each of these different situations gets equal weight.

However, in the "independent hit" approach, we would have 4 different possibilities:

(first left, second right)

(first left, second left)

(first right, second right)

(first right, second left)

Each of these now has equal weight.

However, the second and the forth correspond to an identical physical situation of two simultaneous hits of a neutron, one left, and one right.

Clearly, these different statistics correspond to two different particle counting statistics: Maxwell-Boltzmann versus Bose Einstein. (it's funny of course to use B-E for neutrons...)

So, quantum-mechanically, I'd opt for the B-E approach, while "standard" neutron detector considerations would usually lead to the M-B approach. Problem is, for what I want to calculate, this differs quite importantly.

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# Detection of multiple hits of neutrons.

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