Scattering with spin-flip

The contribution of protons (spin 1/2) to neutron diffraction by organic molecules is important and complex. To study it, we consider the scattering produced by the potential 

When there is a neutron-nucleus spin interaction, several collision channels are open. It is then possible to introduce operators t( ) which depend in a characteristic way on the operator s S and on the spin state i. In this way, we can consider all the possible channels together. 

When this operator is applied to a state with total spin J = S 1/2, it is diagonal and we may simply write 

Consequently, the collision amplitude of the neutron with initial spin state i and final spin state j is 

This amplitude is a complex number, but when k0 0, it becomes real 

---

The spin-incoherent scattering (prominent for protons) involves a change of the spin-state of the scattered neutrons (spin-flip scattering) with a probability of%. 

Incident polarized beam and analysis of the polarization of the scattered beam. Cross-section with spin-flip... 

There is then a net scattering amplitude (Z-fl) /+ -fZ/ associated with l = li scattering where the neutron spin is not changed, and an amplitude (/ — /+) associated with spin flip. The non spin flip part has a factor (cos ) (surface spherical harmonic for Z = Z, m = 0) while the spin flip amplitude is multiplied by the surface spherical harmonic for Z = Zj, w==F 1 to give a factor sin times a function of cos. For 74=0 it is necessary to state more fully how Jq is composed from Ja> a> 1. The specification of the angular dependence of... 

Measurements of the self-correlation function with neutrons are normally performed on protonated materials since incoherent scattering is particularly strong there. This is a consequence of the spin-dependent scattering lengths of hydrogen. Due to spin-flip scattering, which leads to a loss of polarization, this... 

For nuclear incoherent scattering from a non-magnetic system with randomly oriented nuclear spins, the cross-sections per atom are independent of the neutron polarization direction and the spin-flip scattering cross section is twice that for non spin-flip scattering ... 

As tj is increased, so i.s the phase space available for spin-flip scattering and hence tire linewidth. The most important processes involve interchain scattering with q 23c... A rough calculation, taking account of the pnase-space cutoffs imposed by conservation of energy, yields in the high-temperature limit ... 

Coherent and isotopic-incoherent scattering involve no spin-flip, whereas spin incoherent scattering (i.e., for hydrogenated molecules) inverts the neutron spin with a probability of 2/3. Since spin-polarized neutrons are used in the neutron spin-echo technique, the polarization of the neutron beam, after spin-incoherent scattering woifld be reversed and three times less intense. 

A second example is that of O2, in which a magnetic electron spin-flip transition occurs at 59.501 GHz. That line is surrounded by a scatter of others due to rotational transitions with their peak intensity occurring at 60.306 GHz. This peak occurs at a higher value of J — 5 because O2 possesses a somewhat lower rotational constant than NH3. 

For systems containing localized magnetic moments, the thermopower has not been theoretically investigated in such detail as the resistivity. An expression for the thermopower of ferromagnetic materials with localized moments has been obtained by Kasuya (1959) in both the molecular field approximation and the spin wave approximation. In the former case, Kasuya used a molecular field approximation to obtain the energy spectrum of the conduction electrons and the localized magnetic moments. In addition he assumed that the spin-flip transition probabilities for scattering of electrons by local moments dominate the non-spin-flip transition probabilities. 

Fig. 31. Temperature-dependent conductance data from a Y123/Cu tunnel junction. Voltage is defined to be the voltage of Cu with respect to Y123. The ZBCP is observed to split in zero magnetic field at 1.5 K. Inset zero-bias conductance, G(0), versus temperature for the same junction, also in zero field. The downfami in G(0) below 10 K is in contrast to the G(0) In(T ) behavior expected from spin-flip scattering proposed by Lesueur et al. (1992), which is indicated by the dotted line. After Covington et al. (1997, fig. 1).

---