- #1

tryingtolearn1

- 58

- 5

- Homework Statement
- Determining if my results are accurate

- Relevant Equations
- ##N(t) = N_0 \exp(- \frac{t}{\tau}) + \text{bg},## where ##bg## is the background counts, ##t## is time interval of the muons in the detector, ##\tau## is the decay time that needs to be determined.

I am trying to understand my results for my muon experiment. I conducted the experiment using a plastic scintillator photomultiplier detector. I have four different data sets, with different discriminator thresholds: 148 mV, 190 mV, 260 mV and 550 mV. I made a histogram of the counts of all four datasets and I fitted a best fit line in order to determine the decay time using ##N(t) = N_0 \exp(- \frac{t}{\tau}) + \text{bg}## as my model function. For the ##148 mV## I got the decay time value of ##1.97\mu s##, for ##190mV## I got ##2.13\mu s##, for ##260mV## I got ##2.05\mu s## and for ##500mV## I got ##2.06\mu s##.

Therefore based on my results it seems like the ##500mV## threshold gave the most accurate results since the mean decay time for muon is around ##2.2\mu s## but how do I confirm that the ##500mV## threshold is actually the best threshold value? I also, took the logarithm of the counts and plotted it and it provided a linear relationship therefore I used a slope equation for the best fit line and it gave me the following results ##3.45\mu s## for ##148mV##, ##2.56\mu s## for ##190mV##, ##2.36\mu s## for ##260mV## and for ##500mV## I got ##2.15\mu s## so again ##500mV## provided the most accurate results.

Should I be confident that ##500mV## is indeed the best threshold value since my data suggests that? Or is there some there missing information that I am not aware of that I can use to determine which threshold value will provide the most accurate results?

Therefore based on my results it seems like the ##500mV## threshold gave the most accurate results since the mean decay time for muon is around ##2.2\mu s## but how do I confirm that the ##500mV## threshold is actually the best threshold value? I also, took the logarithm of the counts and plotted it and it provided a linear relationship therefore I used a slope equation for the best fit line and it gave me the following results ##3.45\mu s## for ##148mV##, ##2.56\mu s## for ##190mV##, ##2.36\mu s## for ##260mV## and for ##500mV## I got ##2.15\mu s## so again ##500mV## provided the most accurate results.

Should I be confident that ##500mV## is indeed the best threshold value since my data suggests that? Or is there some there missing information that I am not aware of that I can use to determine which threshold value will provide the most accurate results?