On two coincident muon detectors, with scintillators 5 x 5 cm horizontally, and 6cm between detectors what reduction in detection would you expect from geometry alone compared to 1cm between detectors?

For two identical horizontal scintillators of size 5 x 5 cm, the coincidence rate drops as detector spacing increases because the allowed angular acceptance narrows.

A useful estimate is:

tan(theta_max) = 2.5 / d

where:

• 2.5 cm is the half-width of the detector
• d is the detector separation

For d = 1 cm:

tan(theta_max) = 2.5 / 1

theta_max ~= 68 degrees

For d = 6 cm:

tan(theta_max) = 2.5 / 6

theta_max ~= 22.6 degrees

Using the geometric acceptance for two parallel square detectors, the coincidence acceptance ratio is approximately:

G(6 cm) / G(1 cm) ~= 0.23

So from geometry alone, the 6 cm spacing should give:

• about 23% of the coincidence rate compared with 1 cm spacing
• or a reduction by a factor of about 4.4

Assumptions:

• identical 5 x 5 cm scintillators
• perfect detector efficiency
• perfect vertical alignment
• only geometric effects considered