Scaling theory: Energy sudden and dynamically modified relations

Abstract

Articles you may be interested inEnergy sudden dissociative collisions: Structure and applications of factorization relations J. Chem. Phys. 82, 1855; 10.1063/1.448369Rotational energy transfer in HF(v=2): Energy corrected sudden approximation scaling relations applied to double resonance measurements A test of the adiabaticity and kinetic energy shift factors in the energy corrected sudden scaling theory An approach is described for dynamically modifying energy sudden (ES) collisional scaling relations. It is based upon a generalized form of perturbation theory (PT), which contains ES dynamics as the zeroth order approximate. The corresponding first order PT scattering matrix is further modified by exponential unitarization (EPT). Our scaling relations take on the following structure: an input column of S-matrix elements (back) projects through first order EPT (and hence in an approximate fashion), onto the corresponding column ofES elements; a set ofES scaling coefficients (forward) projects these elements onto a new column; the new column (forward) projects through again first order EPT, onto the corresponding scaled column. The effectiveness of this approach is illustrated by application to a simple classical path three-state problem. Two slightly different versions of the approach are compared. We also examine how "column based" scaling predictions compare with "single element based" predictions. Finally, a number of avenues for further development and application are discussed.

The use of the energy sudden approximation in them-scaling of rotational cross-sections

“…At the same time, we must recognize that the effectiveness of any cross-section scaling cannot be separated entirely from consideration of the accuracy of the underlying scattering amplitude scaling from which it derives. One may therefore anticipate introducing dynamical extensions to the ES m-scalings along lines which have already been noted in [4][5][6][7][8] for degeneracyaveraged ES-rotational scaling. Table 3.…”

“…Analysis has been dominated by energy sudden (ES) dynamics where it was shown, many years ago now, that a column of degeneracy-or m-averaged rotational cross-sections could be related to the entire cross-section matrix through a set of dynamically invariant quantities [1][2][3]. A variety of dynamical extensions to ES scaling have been developed since [4][5][6][7][8]; these developments have greatly strengthened the role of scaling theory in the analysis of dynamical problems. Scaling theoretical analysis has not, however, been used specifically for the investigation of crossed-beam m-dependencies [9].…”