The relations for the quantity 
indicate that the R uncertainty in increases sharply at larger values of -t. The I dependence is of the
order of I itself which is clear from direct inspection of 
.
Numerical integrations of [22] suggest milder variation of with I in the region of 
than for itself, indicating the curvature of 
in the region of the maximum decreasing with I. The analytical expression for 
bears this out but the effect is only
mild with the I dependence of the -t interval 0.002-0.004 only
about 8% less than that of .
The maximum of the Quality value, positionally independent of 
,
has double the I and 
uncertainties of . 
contributes a significant uncertainty to the location of the maximum. The
influence of 
on the Quality value increases dramatically at larger -t.
This tends to underline the problem hadronic spin flip presents to the
achievement of a 5% beam polarization uncertainty. appears to be
nearly as uncertain as without the advantage of a fully maximized analysing power. Spin-flip uncertainties in the Quality are also significant.
With our present knowledge of the 
amplitude it would not be possible to guarantee 5% accuracy in beam polarization measurements by CNI, but there is considerable circumstancial evidence to suggest that CNI will in future be able to provide an efficient and effective polarimeter. Typifying
the symbiosis of theory and experiment, it is encouraging that the construction of the polarized beam facility at RHIC will serve to improve our knowledge
of hadronic spin flip, providing a better basis for CNI polarimetry.
}
Appendix 1
Pauli and Gamma Matrices
The familiar 
Pauli Spin Matrices are denoted,
1-4mu l 1-4mu l 1-4.5mu l 1-5mu l =(
) _1=(
)
_2=(
) _3=(
)
The Dirac Gamma Matrices 
, for 
may then be represented as,
^0=(
) ^i=(
)
where in addition 
.
Appendix 2
Calculation of EM Proton Currents and Helicity Amplitudes
For the general current in Eqn 3.18 the first term in 
becomes
Factorizing the 4-spinors in terms of 2-spinors, and representing the rotation by
a 
,
The choice of the CMS system simplifies the momenta to 
for particles A and B and for particle B the value -k is ascribed.
For the simplest case of 
and so explicitly,
using
And for the magnetic term in 
,
Giving,
= 2 e F_2^p k^3( 
/2)
j_B^4(+,-)^F_2=-e4m F_2^p (E + m) (( 2),( 2),-( 2)pE + m,-( 2)pE + m)
(
) (
)
= 2m eF_2^p E k^2( /2)( /2)
j_B^(+,+)= j_A(+,+)= 2eF_1^p(q^2)[E( /2),-k( /2),- ik( /2),
-k( /2)]
2eF_2^p(q^2)[0,k(( /2))^3,ik( /2),
k(( /2))^2( /2)]
j_B^(+,-)= 2eF_1^p(q^2)[-m( /2),0,0,0] - 2meF_2^p(q^2)[k^2( /2),
-Ek(( /2))^2( /2),0,-Ek(( /2))^2( /2)].
_1=1q^2 j_B^(+,+).j_A(+,+)
=1q^2(4 e^2 F_1^p^2(E^2 + k^2) -4 e^2 F_2^p^2 k^2^2( /2)
(1 - ^2( /2)^2( /2)-^4( /2)))
_5= 1q^2 j_B^(+,-).j_A(+,+)
=1q^2 ( 4e^2EF_1^p^2m( /2)( /2)
+8e^2EF_1^pF_2^pmk^2( /2)( /2)
+ 4 e^2EF_2^p^2mk^2( /2)^3( /2) )
(,',')=_^P_^P_'^P _'^P(,',')
_0^P=_N^P=1,_S^P=_L^P=-1.
(,',')=___'^* _'^*(_P,_P_P',_P')
_0=_N=1,-_S=_L=i.
(,',') =(_T',_T'_T,_T)
O_T^A=O^A,N_T^A=N^A
S_T^A=-_CS^A+_CL^A,L_T^A=_CS^A+_CL^A
O_T^B=O^B,N_T^B=N^B
S_T^B= _RS^B+ _RL^B,L_T^B= _RS^B- _RL^B
D^A_LL=(LO LO)=^2_C D_SS^A + 122_CD^A_LS+122_CD^A_SL+ ^2_CD^A_AA
_0^T=_Y^T=_Z^T=1,_X^T=-1.
( ' ')=_^S_^S_'^S_'^S(' ')
_X^S=_Y^S=-1,_0^S=_Z^S=1.
_z(v))= (
)
D(w)= (
)
where 
is defined in equations 2.17 and 2.18.