Scattering cross section partial differential

The distinct intramolecular and intermolecular contributions of the differential cross-section (5) are related to the sum of all partial structure factors, which is essentially proportional to the differential scattering cross-section, weighted by the respective coherent neutron scattering lengths (6). 

In inelastic scattering the scattered intensity needs to be determined as a function of both the scattering angle Q and the magnitude of energy exchange fico. This function, called the double (or partial) differential scattering cross section d2o/dQ dco, is a... 

The quantity measured in such an experiment is the differential neutron scattering cross section da/dQ, of which the interference part (or total structure factor) can be expressed as a linear sum of the partial structure factors, S(Q). The structure factor describes the spatial distribution of scattering centres (the atomic nuclei) of the sample in question. Thus, in the total structure factor, all distances between all scatterers are present, weighted according to the concentration of each particular type of atom, c, and their scattering length, b. The differential neutron scattering cross section can be written as ... 

Since this potential competes with the centrifugal potential , i i H- l)/2mr, which is contained in the kinetic energy operator and which determines the asymptotic forms involving Bessel functions we used above, the boundary conditions themselves must be revised. The potential in equation (23) couples all partial waves asymptotically. In fact, for a dipole fixed in space the differential cross section for electron scattering is infinite in the forward direction, and the total elastic scattering cross section diverges as well. These problems have been discussed at some length in the literature. The way... 

Eq. (8.45) shows that for an ordinary Raman experiment the absolute differential Raman scattering cross sections can be expressed in terms of derivatives of the molecular polarizability invariants a and y with respect to normal coordinates. These derivatives contain valuable information about the variation of molecular polarizability with vibrational motion. Gas-phase Raman scattering cross sections are most suited for intensity analysis since at low partial pressure of the sampling gas these quantities are not influenced by effects of intermolecular interactions, thus reflecting properties of individual molecules. 

D. Partial Cross Sections, Product State Distributions, and Differential Cross Sections III. Reactive Scattering Theory... 

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. 

Figure 33. Experimental scattering geometry for observation of polarization effects in differential quenching process F may be varied to determine ratio of maximum (/raax) to minimum (/mirL) partial quenching cross section.

If k is in atomic units ap1. the differential cross section is in units per steradian. Differential and total cross sections for multichannel scattering by an atomic target can be derived from general formulas [27, 184], The partial cross section for scattering from channel q to channel p is... 

The differential cross section for elastic scattering of a charged particle by a nucleus is given in terms of the asymptotic phase shifts di of the partial wave of angular momentum 1% by the formula (Schiff )... 

Elastic scattering of neutrons. The absence of Coulomb scattering simplifies formula (16.1) in which fc d) and may be put equal to zero. The differential cross section for scattering near a resonance formed by the partial wave of orbital momentum 1% reduces to... 

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

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