Angular momentum inelastic collisions

In the classical model the inefficiency of purely disorienting elastic collisions can easily be understood if one takes into account the fact that such disorientation is connected with a turn of the angular momentum J by a tangible angle (collisional randomization of 3(0,rotational level, i.e. the collision becomes an inelastic one. 

The status for inelastic collisions is a little less satisfactory than for elastic collisions. CoIIisional excitation of atoms involves excited states with several magnetic substates. Standard total or differential cross section measurements sum over the magnetic substates, and thus give no information on the shape of the excited state and direction of the angular momentum transferred to the excited atom. These can be determined in... 

Inelastic scattering produces a permanent change in the internal energy and angular momentum state of one or both structured collision partners A and B, which retain their original identity after the collision. For inelastic / = (a, P) (ct, P ) collisional transitions, the energy Efj = yOf relative motion, before (/) and after... 

Figure 18. Angular momentum distributions of the (a) H2O reaction product and the (b) OH and (c) inelastic collision products as the number of data points defining the interpolated surface is iteratively increased from 30 (open circles) to 400 (crosses) as in Fig. 16. The angular momentum distributions obtained from the surface of Schatz and Elgersma are also shown (filled circles) where the error bars represent standard deviations. The HjO distributions were obtained using bin sizes of 4h, whereas the OH and Hj distributions used bin sizes of 2ft.

The decrease at larger angles of the differential cross-section for inelastic scattering can be understood qualitatively in terms of a constructive interference from the many high angular momentum components which are present in a collision of a fast nucleon with a nucleus. Even in a nucleus as light as A1 and at an energy as low as 100 Mev kR 10, and 10 phase shifts need to be considered. 

There is a separate solution corresponding to each possible incoming channel, and the solution is characterized at long range by the S-matrix with elements Sji. The S-matrix is an A open x A open complex symmetric matrix, where A open is the number of open channels. It is unitary, that is, SS = I, where indicates the Hermitian conjugate and / is a unit matrix. If the physical problem is factorized into separate sets of coupled equations for different symmetries (such as total angular momentum or parity), there is a separate S-matrix for each symmetry. All properties that correspond to completed collisions, such as elastic and inelastic integral and differential cross-sections, can be written in terms of S-matrices. 

Processes described by Equation 4.32 are particularly important for inelastic collisions and angular momentum depolarization of molecules trapped in two dimensions at ultracold temperatures. 

When collisions release energy, the energy dependence of the scattering cross-sections near threshold does not depend on the angular momentum in the final collision channel. For example, the cross-section for inelastic energy transfer in three-dimensional collisions is proportional to [52]. For reactive or inelastic... 

When m >0, the energy dependence of the scattering amplitude is determined by the term a so the inelastic scattering cross-section for collisions with angular momentum m is given by... 

The methodology for solving the generalized Born-Oppenheimer equation described above was first applied to the inelastic scattering of H - - 02 v,j) H + 02 v, j ) at low collision energies and zero total angular momentum (i.e. J = The ground state electronic poten-... 

We here outline the coupled-channel approach to inelastic scattering for atom-molecule or molecule-molecule collisions[6]. It is necessary to compute a wavefunction with fixed total angular momentum J and collision energy E. An appropriate e ansion is... 

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