Relative acceptance

In our stopping fraction measurements, most or all of the hydrogen was placed on the upstream target, while the muon can stop in gold at both upstream and downstream targets. The relative geometrical acceptance for the electrons from hydrogen and gold is expected to be similar for the counters at the sides (Ege, En1), but can be different for the downstream counters (En2). Taking this into account, the expression for the stopping fraction Eq. 6.5 should read:

where F_u, F_d are relative fractions of muons which stops in the upstream and downstream gold foil, respectively ( F_u + F_d = 1), and is the acceptance ratio. Obviously, when or , the expression reduces to Eq. 6.5.

If the beam momentum width is larger than the corresponding thickness of gold foils and the hydrogen layer, one would very roughly expect for the beam momentum optimized for the maximum stopping in hydrogen. can be roughly estimated to be about 1.3 for En2 from the fact that target spacing between the upstream and the downstream layers is some 12% of the detector distance. Assuming a point source, this would make about a 10% upward correction to S^AR_H (from 25% to 27.4%) for the downstream counter pair En2.