On the dynamics of high Rydberg states of large molecules

In this paper we explore the level structure, the optical excitation modes and the dynamics of a mixed Stark manifold of very high Rydberg states (with principal quantum numbers n = 80-250) of large molecules, e.g., 1,4 diaza bicyclo [2,2,2] octane (DABCO) and bis (benzene) chromium (BBC) [U. Even, R. D. Levine, and R. Bersohn, J. Phys. Chem. 98, 3472 (1994)] and of autoionizing Rydbergs of atoms [F. Merkt, J. Chem. Phys. 100, 2623 (1994)], interrogated by time-resolved zero-electron kinetic energy (ZEKE) spectroscopy. We pursue the formal analogy between the level structure, accessibility and decay of very high Rydbergs in an external weak (F≃0.1-1 V cm^-1) electric field and intramolecular (interstate and intrastate) relaxation in a bound molecular level structure. The onset n = n_M of the strong mixing (in an external field F and in the field exerted by static ions) of a doorway state, which is characterized by a low azimuthal quantum number l, a finite quantum defect δ, and a total nonradiative width Γ_s ≃Γ₀/n³, with the inactive high l manifold is specified by n_M≃80.6δ^1/5(F/V cm ^-1)^-1/5. At n≥n_M the level structure and dynamics are characterized by the product γρ, where ρ is the density of states and γ=Γ_sD(n) is the average decay width of the eigenstates, with the dilution factor D(n)≈n^-2 for (lm_l) mixing and D(n) ≃ n^-1 for (l) mixing, whereupon γρ = (Γ₀/4δR)(n_M/n)⁵, being independent of D(n). The sparse level structure is realized for γρ≪1, while the dense level structure prevails for γρ>1, resulting in two limiting situations; (a) a dense limit for n≥n_M and a sparse limit for n≫n_M, and (b) a sparse limit for all n≥n_M. The experimental information currently available on the decay dynamics of molecular (DABCO and BBC) and atomic (Ar) Rydbergs for n≥n_M corresponds to case (b). The time-resolved dynamics was characterized in terms of the excited state total population probability P(t) and the population probability I(t) of the doorway state. P(t), which is interrogated by time-resolved ZEKE spectroscopy, will exhibit for both the sparse and dense level structures and for all excitation conditions a superposition of exponential temporal decay terms with an average lifetime of ∼ℏ/γ. I(t) can be used to interrogate coherence effects, which in case (b) are manifested in quantum beats, while case (a) corresponds to a giant resonance with a molecular time characterized by the reciprocal energetic spread of the Stark manifold. The experimental data for the onset of strong mixing and for the diluted lifetimes [ℏ/Γ_sD(n) with D(n)∼n^-1] of the high Rydbergs (n∼100-200) of BBC and of DABCO are in accord with the predictions of the theory for the limit of strong (l) mixing. While strong mixing is realized for F̄=Fn⁵/3. 4×10⁹δ>1, we expect that for the weak mixing regime (F̄<1) the dynamics of ultrahigh Rydbergs will be characterized by two distinct (∼ns and ∼μs) time scales. Finally, we emphasize the universality of the model, which provides a unified description of the level structure and dynamics of high Rydbergs of molecules and of autoionizing atoms.