Systematics of humidity captures

[Claude Petitjean <claude.petitjean@psi.ch>]

Dear friends,

I reevalulated the systematics of muon captures on
water (in fact, oxygen) in our tpc as follows:

Our humidity sensors measured 35 ppb in eqilibrium
state (c_O = 3.5 10^-8). The normalized density
in 10 bar protium is phi = 0.0116 and the reduced
transfer rate to O is lambda_Tr_O = 0.85 10^11/s
(Schellenberg et al.).

The effective muon transfer rate to Oxygen is then:
lambda_tr_O * phi * c_O =
0.85 10^11/s * 0.0116 * 3.5 10^-8  = 34.5/s

and the transfer probability per muon ~34.5/l_mu
= 34.5 / 455700 = 7.6 10^-5

The muon capture rate in Oxygen is l_c_O = 97400/s
(Eckhause), the probability l_c_O/(l_c_O + l_o) =
= 0.176.

We expect thus in 35 ppb H2O 0.176 * 7.6 10^-5 =
= 1.34 10^-05 Oxygen captures per muon.

In reality we saw (background deducted)
~ 1.1 10^-05. Thus if we assume an overall
detection efficiency epsilon_O = 0.82 for
observing in the tpc the mu-O captures, then our
impurity measurements agree exactly with the
theoretical expectation from the humidity measurement!

Question to Peter, Francoise and other experts:

- Do you see anything wrong with my numbers?

- Where is the factor 2 of too many impurity captures
   which was repeatedly claimed during the last run?

- Is my conclusion correct, that the impurity events
   of our last 2 runs were clearly dominated by the
   humidity?

Lets discuss this on tomorrows teleconf.

With best regards

Claude