By the way, I have derived a very general expression for the ratio of dilution
factors when the proton cross section is changed by some scale factor:

Initial dilution: f = proton/all =  proton/(proton + others)

so others = all - proton, and all = proton/f

New dilution: f' = scale*proton/(scale*proton + others)
                  = scale*proton/(scale*proton + all - proton)
                  = scale*proton/(proton*(scale - 1) + proton/f)
                  = scale*f/(f*(scale - 1) + 1)

so f'/f = scale/(f*(scale - 1) + 1).

With scale = 1.1 this predicts f'/f = 1.1/(0.146*0.1 + 1) = 1.0842 for our
bottom parallel target with average f = 0.146. In this calculation the pf does
not change. Shige's result includes the effect of the change in pf required to
match the data for the increased proton sigma, but he could easily check if
the formula is right by looking just at the MC output when only the proton
sigma
changes.

A similar formula for packing fraction changes is

f'/f = 1/(scale + (He/(pf*proton))*(1-scale)*f), 

where scale is now pf' = scale*pf, but it is model dependent on the cross
sections He/proton = (rho_He*sigma_He/M_He)/(rho_proton*3*sigma_proton/M_NH3) ~
0.95, if sigma_He = 4*sigma_p.

Cheers,

Oscar