************** Attenuation Effects ************************************

Current	Best answers:  multiple dset 7  pd/pp ratio by = 1.04028 
		       multiple dset 8  pd/pp ratio by = 1.04040
		       multiple dset 11 pd/pp ratio by = 1.04039

***********************************************************************

This document quantifies the effect of beam attenuation on the cross
section ratio of deuterium to hydrogen.

Constants:
=-=-=-=-=-
	LD2 Nuclear interaction length:	54.7 g/cm^2	Physical Review D
	LH2 Nuclear interaction length: 50.8 g/cm^2	Physical Review D

	Densities in gr/cm^3		(from Eric's note pass2.3.txt)
        	       hydrogen target              deuterium target
	data set 7        0.070693                      0.162772
	data set 8        0.070680                      0.162657
	data set 11       0.070669                      0.162632 


	Target length:	50.8 cm

Equation
=-=-=-=-=-

	Since the 'poor' deuterium (data sets 8 and 11) has ~3% hydrogen the 
	interaction length needs to be corrected.  See Web: pass2.3.txt

	Assuming that the nuclear interaction lengths can be calculated from
	a weighted average:

lambda(poor deuterium) = 0.97 * lambda(deuterium) + 0.03 * lambda(hydrogen)
		 
                       = 54.583

L = I * lambda * (1-exp(-t*d/lambda)) / (t*d)

Where

	I = incident intensity
	L = effective luminosity
	lambda = Nuclear interaction length
	d = Density
	t = Target length


So,

  L(deuterium,dset7)    .9280855
  ------------------- = -------- = .9612766 = (1.0402834)^-1
  L(hydrogen, dset7)    .9654719


  L(deuterium,dset8)    .9279874   
  ------------------- = -------- = .9611688 = (1.0404000)^-1
  L(hydrogen, dset8)    .9654781

  L(deuterium,dset11)   .9279979 
  ------------------- = -------- = .9611744 = (1.0403939)^-1
  L(hydrogen, dset11)   .9654834


By:  RST
Date: 17NOV97