Neutron Spin Echo - NSE and Spin-incoherent Scattering (from Protons)

NSE and Spin-incoherent Scattering (from Protons)

Many inelastic studies that use normal time-of-flight (TOF) or backscattering spectrometers rely on the huge incoherent neutron scattering cross section of protons. The scattering signal is dominated by the corresponding contribution, which represents the (average) self-correlation function (in time) of the protons.

For NSE spin incoherent scattering has the disadvantage that it flips the neutron spins during scattering with a probability of 2/3. Thus converting 2/3 of the scattering intensity into "non-polarized" background and putting a factor of -1/3 in front of the cos-Fourier integral contribution pertaining the incoherent intensity. This signal subtracts from the coherent echo signal. The result may be a complicated combination which cannot be decomposed if only NSE is employed. However, in pure cases, i.e. when there is an overwhelming intensity contribution due to protons, NSE can be used to measure their incoherent spectrum.

The intensity situation of NSE—for e.g. soft-matter samples—is the same as in small angle scattering (SANS). Which means that molecular objects with coherent scattering contrast at low Q (momentum transfer) show a much larger intensity as the incoherent contribution (which is the background level). But at larger Q usually somewhere around Q=0.3 A−1 the incoherent scattering becomes stronger than the coherent part. At least for hydrogen containing systems contrast requires the presence of some protons and even pure deuterated samples show spin-incoherent scattering from deuterons, however, 40 times weaker than the proton scattering.

Fully protonated samples allow successful measurements but at intensities of the order of the SANS background level. This requires correspondingly long counting times.

Note: This interference with the spin manipulation of the NSE technique occurs only with spin-incoherent scattering. Isotopic incoherent scattering yields a "normal" NSE signal.