NORMALIZATION key Nh - # of hydrogen target events Nd - # of deuterium target events I - beam intensity atth, attd - beam attenuation in hydrogen and deuterium t - target thickness Rh - hydrogen mass density R'd, R'h - deuterium and hydrogen mass density in the deuterium target #H/g, #D/g - # of hydrogen and deuterium atoms per gram sigH - proton hydrogen Drell Yan cross section sigD - proton deuterium Drell Yan cross section fh - fraction of hydrogen atoms in deuterium target fd - fraction of deuterium atoms in deuterium target some units are shown in [] Nh = I * atth * t[cm] * Rh[g/cm**3] * #H/g * sigH Nd = I * attd * t[cm] * {(fh * R'h[g/cm**3] * #H/g * sigH) + (fd * R'd[g/cm**3] * #D/g * sigD) } From these we get.... sigD/sigH = Nd/Nh * (Rh * #H/g * atth)/(fd * R'd * #D/g * attd) - (fh * R'h * #H/g)/(fd * R'd * #D/g) where Nd/Nh is empty subtracted and sem6sb normalized From the E866 Notes page on the web, there is a note by Vassili on the molar densities of H2, D2, and HD. H2: P = 14.9 psi => T = 20.315 K => rho(H2) = 0.03509 mol/cm3 D2: P = 15.1 psi => T = 23.615 K => rho(D2) = 0.04034 mol/cm3 rho(HD) = 0.03684 mol/cm3 rho(H2) = 0.03302 mol/cm3 And in the target densites page, on the E866 Notes page, has our best estimate of the "bad" deuterium. Poor Deuterium (Data Sets 1,8-11) ========================================================== percent uncertainty ------- ----------- D2 94.9 Notes: - Percent is by Volume. HD 1.94 .02 - This is from DS1 LD2. H2 3.12 .06 - P. 82 of Log 2. H2O .014 .005 N2 .014 .002 O2 .0015 .0005 Ar .0002 .0001 CO2 .0016 .0008 When I use these numbers, I get for data sets 8 and 11.... sigD/2*sigH = Nd/Nh * 1.0387 * 0.45406 - 0.01795 where the factor of 1.0387 accounts for different beam attenuation in the two targets. The last two numbers will change slightly when we get the official assay of the deuterium back from Argonne.