Polarizing filters

Anderson, I. S.; Schärpf, O.

doi:10.1107/97809553602060000594

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 4.4, pp. 440-441

Section 4.4.2.6.3. Polarizing filters

I. S. Anderson^a and O. Schärpf^f

4.4.2.6.3. Polarizing filters

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Polarizing filters operate by selectively removing one of the neutron spin states from an incident beam, allowing the other spin state to be transmitted with only moderate attenuation. The spin selection is obtained by preferential absorption or scattering, so the polarizing efficiency usually increases with the thickness of the filter, whereas the transmission decreases. A compromise must therefore be made between polarization, P, and transmission, T. The `quality factor' often used is $[P\sqrt {T}]$ (Tasset & Resouche, 1995).

The total cross sections for a generalized filter may be written as $[ \sigma _{\pm }=\sigma _{0}\pm \sigma _{p}, \eqno (4.4.2.14)]$ where $[\sigma _{0}]$ is a spin-independent cross section and σ_p = (σ₊ + σ₋)/2 is the polarization cross section. It can be shown (Williams, 1988) that the ratio $[\sigma _{p}/\sigma _{0}]$ must be $[\ge]$ 0.65 to achieve |P| $[\gt]$ 0.95 and T $[\gt]$ 0.2.

Magnetized iron was the first polarizing filter to be used (Alvarez & Bloch, 1940). The method relies on the spin-dependent Bragg scattering from a magnetized polycrystalline block, for which $[\sigma _{p}]$ approaches 10 barns near the Fe cut-off at 4 Å (Steinberger & Wick, 1949). Thus, for wavelengths in the range 3.6 to 4 Å, the ratio $[\sigma _{p}/\sigma _{0}\simeq 0.59,]$ resulting in a theoretical polarizing efficiency of 0.8 for a transmittance of $[\sim 0.3]$ . In practice, however, since iron cannot be fully saturated, depolarization occurs, and values of $[P\simeq 0.5]$ with $[T\sim 0.25]$ are more typical.

Resonance absorption polarization filters rely on the spin dependence of the absorption cross section of polarized nuclei at their nuclear resonance energy and can produce efficient polarization over a wide energy range. The nuclear polarization is normally achieved by cooling in a magnetic field, and filters based on ¹⁴⁹Sm (E_r = 0.097 eV) (Freeman & Williams, 1978) and ¹⁵¹Eu (E_r = 0.32 and 0.46 eV) have been successfully tested. The ¹⁴⁹Sm filter has a polarizing efficiency close to 1 within a small wavelength range (0.85 to 1.1 Å), while the transmittance is about 0.15. Furthermore, since the filter must be operated at temperatures of the order of 15 mK, it is very sensitive to heating by γ-rays.

Broad-band polarizing filters, based on spin-dependent scattering or absorption, provide an interesting alternative to polarizing mirrors or monochromators, owing to the wider range of energy and scattering angle that can be accepted. The most promising such filter is polarized ³He, which operates through the huge spin-dependent neutron capture cross section that is totally dominated by the resonance capture of neutrons with antiparallel spin. The polarization efficiency of an ³He neutron spin filter of length l can be written as $[ P_{n}(\lambda)=\tanh [{\cal O}(\lambda) P_{\rm {He}}], \eqno (4.4.2.15)]$ where $[P_{\rm {He}}]$ is the ³He polarization, and $[{\cal O}(\lambda)=[^{3}{\rm He}]l\sigma _{0}(\lambda)]$ is the dimensionless effective absorption coefficient, also called the opacity (Surkau et al., 1997). For gaseous ³He, the opacity can be written in more convenient units as $[ {\cal O}^{\prime }=p[{\rm bar}]\times l\,{[{\rm {}cm}}]\times \lambda[{\rm \AA }], \eqno (4.4.2.16)]$ where p is the ³He pressure (1 bar = 10⁵ Pa) and $[{\cal O}=]$ $[7.33\times 10^{-2}{\cal O}^{\prime }]$ . Similarly, the residual transmission of the spin filter is given by $[ T_{n}(\lambda)=\exp [-{\cal O}(\lambda)]\cosh [{\cal O}(\lambda) P_{\rm {He}}]. \eqno (4.4.2.17)]$ It can be seen that, even at low ³He polarization, full neutron polarization can be achieved in the limit of large absorption at the cost of the transmission.

³ He can be polarized either by spin exchange with optically pumped rubidium (Bouchiat, Carver & Varnum, 1960; Chupp, Coulter, Hwang, Smith & Welsh, 1996; Wagshul & Chupp, 1994) or by pumping of metastable ³He* atoms followed by metastable exchange collisions (Colegrove, Schearer & Walters, 1963). In the former method, the ³He gas is polarized at the required high pressure, whereas ³He* pumping takes place at a pressure of about 1 mbar, followed by a polarization conserving compression by a factor of nearly 10 000. Although the polarization time constant for Rb pumping is of the order of several hours compared with fractions of a second for ³He* pumping, the latter requires several `fills' of the filter cell to achieve the required pressure.

An alternative broad-band spin filter is the polarized proton filter, which utilizes the spin dependence of nuclear scattering. The spin-dependent cross section can be written as (Lushchikov, Taran & Shapiro, 1969) $[\sigma _{\pm }=\sigma _{1}+\sigma _{2}P_{\rm {H}}^{2}\mp \sigma _{3}P_{\rm {H}}, \eqno (4.4.2.18)]$ where $[\sigma _{1}]$ , $[\sigma _{2}]$ , and $[\sigma _{3}]$ are empirical constants. The viability of the method relies on achieving a high nuclear polarization $[P_{\rm {H}}]$ . A polarization P_H = 0.7 gives $[\sigma _{p}/\sigma _{0}\approx 0.56]$ in the cold-neutron region. Proton polarizations of the order of 0.8 are required for a useful filter (Schaerpf & Stuesser, 1989). Polarized proton filters can polarize very high energy neutrons even in the eV range.

References

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International Tables for Crystallography (2006). Vol. C. ch. 4.4, pp. 440-441