Radiation Detection Question

Regarding radiation a radiation detection system for gamma rays, following
is a quote from a paper I read:

"Halving the distance between source and detector would increase the
sensitivity by a factor of four; quadrupling the counting time would
increase the sensitivity by a factor of two."

I understand the first part -- i.e. source strength goes as the inverse
square of the distance, therefore half distance implies four times
sensitivity. I also understand the geometrical reasons for this.

I don't understand why quadrupling counting time only increases the
sensitivity by 2. In my ignorance, I cannot imagine why quadrupling the
counting time would not result in four times the sensitivity or detection
capability. Can someone please enlighten me on this? Perhaps someone could
point me to an Internet source that explains this phenomenon.

Thanks in advance.

Matt


.

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