Instrument simulations and neutron polarisation

[PASeeger at aol.com]

Kristian,

Thank you for sending the web-page information.  In the meantime, here are 
some notes I made on the way home:

<<
Polarization is represented by a 3-vector P, with magnitude P <= 1.  The 
probability of the spin of the neutron being in direction P is (1 + P)/2, and 
the probability of the opposite spin is (1 - P)/2.  The probabilities in an 
arbitrary direction given by a unit vector A usey the dot product AoP in 
place of P.  Thus P = 0 is an unpolarized beam, with probability in any 
direction being 50%.  This notation is completely equivalent to tracking 
separate spin-up and spin-down neutrons with appropriate statistical weights. 
 For instance, consider a longitudinal polarizer from which 90% of the 
emerging neutrons have spin in the +Z direction.  This may be represented 
either by two histories
       (wt, P) = (0.9, 0, 0, 1)  +  (0.1, 0, 0, -1)
or by a single history
                      (1.0, 0, 0, 0.80)
that is simply the weighted average of the two.  Any operation that is 
symmetric with respect to spin, such as precession or spin-flip, can be 
applied either to the combined or to the separated histories.  For algorithms 
that act differently on the two spin states, the single history must be 
decomposed; after the interaction, the two histories may either be recombined 
by weighted average, or may remain separated.  For instance, if the above 
history passes through a filter which transmits 90% of the + spin and 2% of 
the - spin, the result is either
                   (0.810, 0, 0, 1)  +  (0.002, 0, 0, -1)
or (only if both neutrons have the same trajectory!)
                   (0.812, 0, 0, 0.995).
If it is desired also to track the non-transmitted neutrons (perhaps 
reflected out of the beam, contributing to backgrounds), they would be 
represented by
                  (0.090, 0, 0, 1)  +  (0.098, 0, 0, -1)
or (again, only if the trajectories are identical) by
                   (0.188, 0, 0, -0.04255).
In practice, an interaction in NISP may only result in two histories, so the 
combined form is necessary if the background neutron is also to be tracked.  
No information is lost because the partially polarized history can always be 
reconstituted into two spin states with respect to any analyzer direction.
>>

For most cases of multiple scattering, I do it within the sample region so 
propagation between regions would not be an issue.  The first scatter is 
forced, with adjustment of statistical weight.  Further scatters are Russian 
roulette.  If you look in my OPERATE subroutine, cases which include multiple 
scattering are 30, 34, and 36.

It was nice talking with you at PSI.

Cheers,
   Phil Seeger