What Is the Probability of Coincident Detection Between Two Particle Detectors?

[india]

Coincindence Count Rates !

I have two particle detector,
1. one will counts 13 particle/sec
2. second has 0.138 particle/sec (i.e. 1 particle can be detected in 7.2 sec in second det)
what will be the probability of both particle being detected ? and in how much time ?

 

[Cthugha]

Your question is not well phrased, but maybe one can answer it with a bit more information.

What do you mean by "both particle being detected"? Are you asking for the simultaneous detection rate - how often both detectors click at the same time? Then we need to know the time resolution of the detectors or the binning time of the coincidence counting, that means the duration of the time window which is considered as simultaneous. Also can one assume the particles at both detectors to be statistically independent?

Or are you aiming at something entirely different?

 

[nanosiborg]

I have two particle detector,
1. one will counts 13 particle/sec
2. second has 0.138 particle/sec (i.e. 1 particle can be detected in 7.2 sec in second det)
what will be the probability of both particle being detected ? and in how much time ?

As Cthugha said, the experimental situation isn't clear from your question.

If the particles are, say, polarization entangled photons filtered by polarizers, then the probability of coincidental detection is roughly .058 (assuming a coincidence interval of roughly .076 seconds). From which it can be deduced that the angular difference between the polarizers is roughly 76 degrees.

But, as far as I know, coincidence intervals in polarization entangled photon experiments are many orders of magnitude less than that.

So, as far as I can tell, it really isn't clear what you're asking about.

Unless you specify the particle type and source preparation, then from what you've said I would just say that you've got two independent sources, with one source emitting roughly 94 particles every 7.2 seconds and another source emitting 1 particle every 7.2 seconds. If that's the case, and if the particles aren't entangled or filtered in any way, then I guess that the probability of a coincidental detection within a 7.2 coincidence interval is 1 in 94 or .01063.

 

[india]

Yes, Let's say, single radioactive source is emitting both alphas and x-ray photons. now rate of alpha particle being detected in detector is 13 alpha/sec, and rate of x-ray being detected in xray detector is 0.138 photon/sec. Both detector are different. And Let's say count rates have already included source effect and efficiency of detector.
Now, I know, coincidence means detection of two or more events in some time interval Δt. This Δt will be resolving time of coincidence counter. But this I don't knw, but I want to assume theoretically the rate of coincidence in this system. what will be probability of coincidence ? or rate of coincidence ? and How one can decide the specific Δt for their system ?

 

[india]

As Cthugha said, the experimental situation isn't clear from your question.

If the particles are, say, polarization entangled photons filtered by polarizers, then the probability of coincidental detection is roughly .058 (assuming a coincidence interval of roughly .076 seconds). From which it can be deduced that the angular difference between the polarizers is roughly 76 degrees.

But, as far as I know, coincidence intervals in polarization entangled photon experiments are many orders of magnitude less than that.

So, as far as I can tell, it really isn't clear what you're asking about.

Unless you specify the particle type and source preparation, then from what you've said I would just say that you've got two independent sources, with one source emitting roughly 94 particles every 7.2 seconds and another source emitting 1 particle every 7.2 seconds. If that's the case, and if the particles aren't entangled or filtered in any way, then I guess that the probability of a coincidental detection within a 7.2 coincidence interval is 1 in 94 or .01063.

Yes, Let's say, single radioactive source is emitting both alphas and x-ray photons. now rate of alpha particle being detected in detector is 13 alpha/sec, and rate of x-ray being detected in xray detector is 0.138 photon/sec. Both detector are different. And Let's say count rates have already included source effect and efficiency of detector.
Now, I know, coincidence means detection of two or more events in some time interval Δt. This Δt will be resolving time of coincidence counter. But this I don't knw, but I want to assume theoretically the rate of coincidence in this system. what will be probability of coincidence ? or rate of coincidence ? and How one can decide the specific Δt for their system ?

 

[e.chaniotakis]

The true coincidence probability is defined as: The probability to have a signal in detector 2 when you already have a signal in detector 1.
If there are no correlations, then this probability is : P(1-2)=P(1)*P(2)
Therefore, for a given production rate of particles R, you have that the coincidence rate is R*P(1-2)

For a more quantitative approach see this: http://www.phys.columbia.edu/~w3081/exp_files/coin.pdf , pg.2