PHYSICAL REVIE%' A VOLUME 48, NUMBER 1 JULY 1993 Role of potential structure in the collisional excitation of metastable O('D) atoms D. A. Padmavathi and Manoj K. Mishra Department of Chemistry, Indian Institute of Technology, Powai, Bombay 400076, India Herschel Rabitz Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (Received 22 February 1993) This paper considers the collisional excitation of 0('D) modeled by the crossing of two valence 1 IIg curves dissociating to 0{'P)+0{'P) [ V»{R)] and 0('P)+0('D) [ V22{R}] which in turn are further crossed by the C 'Ils Rydberg curve dissociating to 0('P )+0{ 'S ) [ V33(R ) ]. The role of structure in the potential curves and coupling matrix elements is quantitatively probed by the first-order functional- sensitivity densities 5lncr»(E)/51nVJ(R) of the excitation cross section o. l2(E) obtained from close- coupling calculations. The results reveal that, in spite of the well-separated nature of the crossing be- tween the two valence curves from their crossings with the Rydberg potential curve, the excitation cross section 0. » displays considerable sensitivity to the Rydberg curve V33(R) at all energies in the range 3. 0 — 9. 0 eV. For relative collisional energies corresponding to the higher closely spaced vibrational ener- gy levels of the Rydberg state, the excitation cross section is found to be much more sensitive to the Ryd- berg state than to the two valence states themselves. At all energies, the sensitivity of the excitation cross section o. » to the coupling V»(R) between the valence states is much larger than the sensitivity to the couplings V»(R) or V»(R) with the Rydberg state. At higher energies, the large increase in the sen- sitivity of the cross section to the Rydberg potential is mirrored by a similar increase in sensitivity to its coupling V»(R) with the upper valence state. Due to the weak coupling between the three curves, a qualitative similarity exists between the sensitivity profiles and those predicted by the Landau-Zener- Stueckelberg (LZS) theory. Quantitative departures witnessed in earlier work are, however, more pro- nounced for the multilevel curve crossings investigated here. Implications of the results for attempts to extend the LZS-type treatment to multilevel curve crossings and for functional-sensitivity-based algo- rithms for the inversion of cross-section data are discussed. PACS number(s): 34.20. — b, 31. 20. — d I. INTRODUCTION The interaction of the C II Rydberg state of 02 with its two 1 II valence states dissociating to 0( P)+0( P)[V»(R)] and 0( P)+0('D)[V22(R)], re- spectively, has received extensive theoretical [1 — 3] and experimental [1 — 6] attention. The collisional excitation 0( P)+0( P)~O( P)+0('D) is believed to be a significant source of red line emission in the outer atmo- sphere and has been modeled [1] by the crossing of the valence curves V»(R) and V2z(R) with each other and the C Ils Rydberg curve V»(R). Even though the crossing between the valence curves V»(R) and Vzz(R) is weH removed from their crossings with the Rydberg curve V»(R ), the effect of the closed Rydberg channel on the excitation cross section o, 2(E) is clearly seen [1] as resonances in the profile of the iS', 2i as a function of the nuclear angular momentum l. Since these resonances occur for small l values, the effect of the Rydberg curve on excitation cross sections has been taken to be insignificant [1]. While the qualitative reasoning employed above is plausible, the dynamical dependence of collision cross sections on the functional form of the underlying potential-energy curve(s) or surface(s) V(R) may be ex- amined through a first-order functional expansion of the collision cross section o ( [ V] ), o5. = r(t[ V+5]V) — 0([V])= f dR 5V(R), 5V(R) where R denotes generic coordinate space variables. Those regions of R where 5cr/5V(R) is large (small) imply regions of importance (unimportance) for the cross section. Additionally, the sign dependence of the sensi- tivities tells the sense of how cr will respond to an in- crease or decrease in V(R). While such an investigation may also be considered using the brute force method of varying V(R) and repeating the calculations for the cross section many times, direct calculation of the functional sensitivities 5o /5V(R) requires only a minor extension and expense beyond the cross-section calculation [10] alone. This approach has been applied to determine re- gions of potential curves critical to diverse dynamical processes [7 — 11]. In our earlier analyses using functional-sensitivity den- sities from close-coupling calculations [7,8] a qualitative similarity to the idealized 5(R — R )-type behavior for 5cr, 2(E)/5V, 2(R) and the +d5(R — R*)/dR type- behavior for 5cr, 2(E) /5 V» (R ) and 5o, 2(E)/5 V22(R ) pointing to the critical importance of the curve crossing point (R ) conformed to the predictions of the weak- coupling Landau-Zener-Stueckelberg (LZS) theory [12]. 1050-2947/93/48(1)/286(6)/$06. 00 OO1993 The American Physical Society