Partial integral cross section

We will be interested not only in the total absorption cross section [Eqs. (4.1) and (4.2)], which gives us a measure of the total probability that the molecule will absorb light and dissociate, but also in the probability that different product quantum states will be formed. This probability is given by a partial cross section cj/( ). From Eq. (4.1) we see that this partial integral cross section may be written as... 

These equations enable us to compute all the possible photofragmentation cross sections, in particular the partial differential cross section given in Eq. (27) and the partial integral cross section below. 

Figure 9 plots the degeneracy averaged partial integral cross sections for H- -H2(v = 0, j = 0) Fl2(v = 1, j = 0 — 3) + FI as a function of energy and include all J < 10. The solid curve and solid squares do not include the geometric phase. The short dashed curve and open squares include the geometric phase and are based on the vector potential approach. For the... 

The partial integral cross section, which is a measure of the probability of absorbing light and breaking up to give a particular final state of the fragments, may be written in the form... 

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 partial-wave integral cross section cr (E) is calculable as... 

The total angular momentum J plays the part of a partial wave quantum number. As for collisions of structureless particles, integral cross-sections involve sums over partial waves and differential cross-sections involve double sums, with interference between different partial waves playing an important role. 

If the integral over the signal spectrum of one particle is proportional to the particle volume, the intrinsic type of property is the volume (r = 3) proportionality to the partial scattering cross section implies that the signal is intrinsically weighted by scattering intensity. 

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

A more extensive calculation at = 0.40 eV, in which all partial waves were calculated in the range J = 0(1)70, has been reported in Ref. [16]. This calculation allowed accurate differential cross sections to be computed, which are very sensitive to the phases of the S matrix elements, in contrast to the integral cross sections, which depend only on the modulus of the S matrix. All the differential cross sections were found to be backward peaked [16], which is typical of a rebound mechanism. 

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