Differential cross-section partial

Time-Dependent Theory of the Partial Differential Cross Section... 

The definition of the final quantum state [see Eqs. (4.3) and (4.4)] of the system includes the direction k into which the separating fragments are scattered. If we omit the integrals over all final scattering directions in Eqs. (4.1) and (4.10), we obtain a cross section for scattering into a specific final direction. These are called differential cross sections. Below 1 will briefly outline the definition and properties of the partial differential cross section, which is the probability of producing a specific final quantum state of the system scattered into a well-specified direction. 

The time-independent expression for the partial differential cross section is given in Eq. (4.15) ... 

These partial differential cross section are therefore given bv (see Eqs. (2)) and... 

The partial differential cross-section for magnetic neutron scattering, which measures the probability of scattering per solid angle per unit energy, is... 

Much of the theory of neutron scattering concern the elaboration of expressions (closed formulas) for the partial differential cross section, starting from (model) interaction potentials between the neutron and the nucleus (see, e.g.. Squires 1996 Lovesey 1987). The final result of these calculations for nuclear scattering will be outlined below. 

Taking into account the quantum mechanical probability of the transition of a neutron from a state characterized by wavevector k and energy E to another state characterized by wavevector k and energy E, caused by scattering from a target-system via potential V (taken as the extremely short ranged Fermi-pseudopotential), one arrives at the following expression for the partial differential cross section (see, e.g.. Squires 1996) ... 

Constructing translational states so that p k) = p (k ) = and changing the integration variables to e and fi. the partial differential cross section is... 

Usually, experiments yield the partial differential cross-section per unit volume... 

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