A.M. Gaspar, M.S. Appavou, S. Busch, W. Doster
Physics Department E13, Technische Universitaet Muenchen

In this experiment we intended to use the possibility to perform polarization analysis at MIRA to obtain quantitative information on the fraction of coherent to spin-incoherent nuclear scattering from a representative set of protein samples, over the widest Q range possible (from small to wide angles). Such a method had so far limited application in the study of amorphous materials [1-3], despite of its potential. Its use in spectroscopic measurements would allow experimentally separating the self and the collective terms of the dynamic structure factor, while in a diffractometer it would also allow obtaining structure factors uncontaminated by incoherent scattering from the non-exchangeable hydrogens of the proteins.
In this experiment the method was first tested at MIRA in measurements of the static structure factors of different protein samples investigated before by us at the time-of-flight instrument TOFTOF [4]. In addition to the usual small-angle scattering information, we were particularly interested in quantifying the coherent and incoherent components of the signal in the region of the inter-side-chain correlations, appearing at Q~0.4-0.8 Å^-1.
Two alternative possible instrument configurations with regards to the polarization analyzer + detection system were explored in order to maximize the signal to noise ratio over the angular range of interest. These are shown in Figure 1.

In both cases a π-spin flipper (of efficiency determined to be ~1) was introduced before the sample to reverse the polarization of the incident neutron beam for spin-flip and non-spin-flip measurements. Setup 1 involved the use of a super mirror analyzer, diverting the neutrons with the right polarization into a finger detector (He³ gas filled) of 2.54 cm circular section while setup 2 involved the use of a quartz cell filled in with polarized He³ gas, as analyzer (absorbing the neutrons with the wrong polarization), and a 2D position sensitive detector. For setup 1, the total neutron transmission through the analyzer was determined to be ~40%, with a flipping ratio of R~11.5 (A_eff~0.84), while in the case of setup 2 the total transmission as well as the flipping ratio were decreasing in time, due to the on going depolarization of the He³ gas (T~23→17%, R~12→6 and A_eff~0.85→0.70, over a 24h period). Setup 1 was found to be the best option to explore the wide-angle region (Q>0.045 Å^-1), while setup 2 was used to explore the small-angle region, with the 2D-detector placed in the forward direction.

The experiment performed relied on the principle that if we can polarize the incident beam and we can count separately neutrons scattered with and without spin-flip with regards to the incident beam polarization, we can then separate coherent from spin-incoherent nuclear scattering processes. This is because only 1/3 of the spin-incoherent scattering events are without spin flip (the other 2/3 being with spin flip), while all the coherent nuclear scattering events correspond to scattering without spin flip. Hence from I_NSF=I_coh+1/3I_inc and I_SF=2/3I_inc one directly obtains I_coh=I_NSF -1/2 I_SF and I_inc=3/2 I_SF. In practice, the scattered intensities have to be corrected for a finite flipping ratio R [2]: I_NSFc= I_NSFm+(1-R)-1( I_NSFm -I_SFm) and I_SFc= I_SFm+(1-R)-1( I_SFm –I_NSFm). Figures 2 and 3 illustrate how this separation was successfully achieved at MIRA for several protein D₂O solutions and figure 4 displays the fraction coherent and spin-incoherent scattering events determined from the wide-angle data.

References
[1] J.C. Dore et al., Nucl. Instr. & Methods 138 (1976) 317-319.
[2] B.J. Gabrys, Physica B 267-268 (1999) 122-130
[3] T.R. Gentile et al., J. Appl. Cryt. 33 (2000) 771-7
[4] A.M. Gaspar et al., report on exp 668