sanddRydberg series of NO probed by double resonance multiphoton ionization

High-Resolution Continuous-Wave Laser Spectroscopy of Long-Lived Rydberg States in NO

High-resolution continuous-wave (cw) laser spectroscopy of nitric oxide (NO) molecules has been performed to study and characterize the energy-level structure of and effects of electric fields on the high Rydberg states. The experiments were carried out with molecules flowing through a room temperature gas cell. Rydberg-state photoexcitation was implemented using the resonance enhanced ( n l ) X +   Σ + 1 ← H   Σ + 2 ← A   Σ + 2 ← X Π 3 / 2 2 three-color three-photon excitation scheme. Excited molecules were detected by high-sensitivity optogalvanic methods. Detailed measurements were made of Rydberg states with principal quantum numbers n = 22 and 32 in the series converging to the lowest rotational and vibrational state of the NO+ cation. The experimental data were compared with the results of numerical calculations which provided insight into the orbital angular momentum character of the intermediate H 2Σ+ state, improved determinations of the nf and ng quantum defects, a bound on the magnitude of the nh quantum defect, and information on the decay rates of the nf and ng Rydberg states. These measurements represent a step-change in laser spectroscopic studies of high Rydberg states in small atmospheric molecules. They open opportunities for more detailed studies of slow decay processes of Rydberg NO molecules confined in electrostatic traps, the synthesis of ultralong range Rydberg bimolecules, and the development of optical methods for trace gas detection.

Long-range model of vibrational autoionization in core-nonpenetrating Rydberg states of NO

In high orbital angular momentum (ℓ ≥ 3) Rydberg states, the centrifugal barrier hinders the close approach of the Rydberg electron to the ion-core. As a result, these core-nonpenetrating Rydberg states can be well described by a simplified model in which the Rydberg electron is only weakly perturbed by the long-range electric properties (i.e., multipole moments and polarizabilities) of the ion-core. We have used a long-range model to describe the vibrational autoionization dynamics of high-ℓ Rydberg states of nitric oxide (NO). In particular, our model explains the extensive angular momentum exchange between the ion-core and the Rydberg electron that had been previously observed in vibrational autoionization of f (ℓ = 3) Rydberg states. These results shed light on a long-standing mechanistic question around these previous observations and support a direct, vibrational mechanism of autoionization over an indirect, predissociation-mediated mechanism. In addition, our model correctly predicts newly measured total decay rates of g (ℓ = 4) Rydberg states because for ℓ ≥ 4, the non-radiative decay is dominated by autoionization rather than predissociation. We examine the predicted NO⁺ ion rotational state distributions generated by vibrational autoionization of g states and discuss applications of our model to achieve quantum state selection in the production of molecular ions.

Quantum-state-dependent decay rates of electrostatically trapped Rydberg NO molecules

Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been prepared in long-lived Rydberg-Stark states by resonance-enhanced two-colour two-photon excitation from the X 2Π1/2 (v'' = 0, J'' = 3/2) ground state, through the A 2Σ+ (v' = 0, N' = 0, J' = 1/2) intermediate state. These excited molecules were decelerated from 795 ms-1 to rest in the laboratory-fixed frame of reference, in the travelling electric traps of a transmission-line Rydberg-Stark decelerator. The decelerator was operated at 30 K to minimise effects of blackbody radiation on the molecules during deceleration and trapping. The molecules were electrostatically trapped for times of up to 1 ms, and detected in situ by pulsed electric field ionisation. Measurements of the rate of decay from the trap were performed for states with principal quantum numbers between n = 32 and 50, in Rydberg series converging to the N+= 0, 1, and 2 rotational states of NO+. For the range of Rydberg states studied, the measured decay times of between 200 μs and 400 μs were generally observed to reduce as the value of n was increased. For some particular values of n deviations from this trend were seen. These observations are interpreted, with the aid of numerical calculations, to arise as a result of contributions to the decay rates, on the order of 1 kHz, from rotational and vibrational channel interactions. These results shed new light on the role of weak intramolecular interactions on the slow decay of long-lived Rydberg states in NO.

Excitation and characterization of long-lived hydrogenic Rydberg states of nitric oxide

High Rydberg states of nitric oxide (NO) with principal quantum numbers between 40 and 100 and lifetimes in excess of 10 µs have been prepared by resonance enhanced two-color two-photon laser excitation from the X ²Π_1/2 ground state through the A ²Σ⁺ intermediate state. Molecules in these long-lived Rydberg states were detected and characterized 126 µs after laser photoexcitation by state-selective pulsed electric field ionization. The laser excitation and electric field ionization data were combined to construct two-dimensional spectral maps. These maps were used to identify the rotational states of the NO⁺ ion core to which the observed series of long-lived hydrogenic Rydberg states converge. The results presented pave the way for Rydberg-Stark deceleration and electrostatic trapping experiments with NO, which are expected to shed further light on the decay dynamics of these long-lived excited states, and are of interest for studies of ion-molecule reactions at low temperatures.

Determination of the Spin-Rotation Fine Structure of He_{2}^{+}

Measuring spin-rotation intervals in molecular cations is challenging, particularly so when the ions do not have electric-dipole-allowed rovibrational transitions. We present a method, based on an angular-momentum basis transformation, to determine the spin-rotational fine structure of molecular ions from the fine structure of high Rydberg states. The method is illustrated by the determination of the so far unknown spin-rotation fine structure of the fundamentally important He_{2}^{+} ion in the X ^{2}Σ_{u}^{+} state. The fine-structure splittings of the v^{+}=0, N^{+}=1, 3, and 5 levels of He_{2}^{+} are 7.96(14), 17.91(32), and 28.0(6) MHz, respectively. The experiment relies on the use of single-mode cw radiation to record spectra of high Rydberg states of He_{2} from the a ^{3}Σ_{u}^{+} metastable state.

Implementation of Various Modalities of the Optical-Optical Double Resonance Techniques To Simplify the Interpretation of the Spectra of Highly Excited States of Nitric Oxide

We combined various modalities of the optical-optical double resonance (OODR) photoionization technique to simplify the interpretation of crowded molecular spectra. To demonstrate the effectiveness of our method, we applied it to the 64000 to 65200 cm(-1) spectral region of the molecule NO, where exist the following electronic states: B (2)Π (v = 21), D (2)Σ(+) (v = 5), F (2)Δ (v = 1), L (2)Π (v = 3), and K (2)Π (v = 0). This spectral region is complicated because (1) several electronic states are close in energy, (2) some of the rotational energy patterns are irregular, and (3) the relative intensity of the different bands varies markedly. We implemented four modalities of the OODR experimental technique that involved the combined use of two or three lasers. The individual rotational levels up to N' = 20 of the A(2)Σ(+) (v = 0) state were pumped as intermediate states by one-photon excitation from appropriate rotational levels in the X(2)Π (v = 0) ground state. Some of the schemes implemented provided information about line positions and relative band intensities, whereas the ion-dip detection scheme provided insight into the fate of the population in the different states. The term values that we derived are in good agreement with the literature ones. We rotationally resolved the spectra for the K (2)Π (v = 0) and B (2)Π (v = 21) states up to N = 20, and for the D (2)Σ(+) (v = 5) and L (2)Π (v = 3) states up to N = 8 and 7, respectively. Strangely, only in the rotational levels between N = 6 and N = 20 were we able to observe the F (2)Δ state, which is mostly mixed with the B' (2)Δ (v = 4) state and usually notated as F (2)Δ (v = 1) → B' (2)Δ (v = 4). We obtained the rotational constants for the B (2)Π1/2 (v = 21), L (2)Π3/2 (v = 3), and K (2)Π1/2 (v = 0) states, which had not been previously reported.

NO dissociation through ns, np, and nf Rydberg states: angular distributions

Velocity-mapped imaging and theoretical calculations have been used to study the angular distribution of the products of NO predissociation following its excitation to the 11s, 10p, 11p, and 9f Rydberg levels based on the NO(+) (X (2)Σ(+)) core. The Rydberg states were reached from the NO (A (2)Σ(+), v = 0, N = 2, J = 1.5) level prepared with strong alignment by excitation with linear polarization from NO (X (2)Π, v = 0, N = 1, J = 0.5). Ion dip spectra of the Rydberg states were recorded along with velocity-mapped images at the major peaks. The results are compared to calculations based on a previous theoretical approach modified to include transitions to states of Hund's case (d) coupling. The reasonable agreement shows the predictive value of the theory. The theory has also been used to reassess and explain previous results and to understand variations in the rate of photodissociation with components of the 10p and 11p Rydberg states.

Time-energy mapping of photoelectron angular distribution: application to photoionization stereodynamics of nitric oxide

The time-energy mapping of the photoionization integral cross section and laboratory-frame photoelectron angular distribution is used to study photoionization stereodynamics of a diatomic molecule. The general theoretical formalism [Y. Suzuki and T. Suzuki, Mol. Phys., 2007, 105, 1675] is simplified for application to a diatomic molecule, and a high-resolution photoelectron imaging apparatus is used to determine the transition dipole moments and phase shifts of photoelectron partial waves in near-threshold and non-dissociative photoionization of NO from the A(2)Σ(+) state. The transition dipoles and phase shifts thus determined are in reasonable agreement with those by state-to-state photoionization experiment and Schwinger variational calculations. The difference of the phase shifts from those expected from the quantum defects of Rydberg states suggests occurrence of weak hybridization of different l-waves, in addition to the well-known s-d super complex. The circular dichroism in photoelectron angular distribution is also simulated from our results.

AB INITIO R-MATRIX/MULTI-CHANNEL QUANTUM DEFECT THEORY APPROACH TO STUDY MOLECULAR CORE EXCITATION AND IONIZATION: GSCF4R

The ab initio program package named GSCF4R, which is based on the polyatomic R-matrix/MQDT (multi-channel quantum defect theory), has been developed using Gaussian type basis functions for the bound and continuum states to analyze the near edge feature of molecular inner shell excitations. The GSCF4R code is constructed by improvement and extension of the ordinal static exchange (STEX) approach. The R-matrix approach used in GSCF4R is beyond multi-channel multi-reference extensions of STEX, since it is based on the close coupling method augmented with the correlation term solved in the inner part of the R-matrix sphere. Simplification of the input data in GSCF4R has demonstrated that the R-matrix/MQDT method could be widely used in analysis of the molecular inner shell excitation and ionization. The quantum defects of the Rydberg states converging to the lowest valence ionized state NO +(1∑+) and the lowest N1 s ionized state N ⋆ O +(3Π) have been calculated.

A master equation approach to the dynamics of zero electron kinetic energy (ZEKE) states and ZEKE spectroscopy

We have theoretically studied important dynamic processes involved in zero electron kinetic energy (ZEKE) spectroscopy using the density matrix method with the inverse Born-Oppenheimer approximation basis sets. In ZEKE spectroscopy, the ZEKE Rydberg states are populated by laser excitation (either a one- or two-photon process), which is followed by autoionizations and l-mixing due to a stray field. The discrimination field is then applied to ionize loosely bound electrons in the ZEKE states. This is followed by using the extraction field to extract electrons from the ZEKE levels which have a strength comparable to that of the extraction field. These extracted electrons are measured for the relative intensities of the ion states under investigation. The spectral positions are determined by the applied laser wavelength and modified by the extraction electric field. In this paper, all of these processes are conducted within the context of the density matrix method. The density matrix method can provide not only the dynamics of system's population and coherence (or phase) but also the rate constants of the processes involved in the ZEKE spectroscopy. Numerical examples are given to demonstrate the theoretical treatments.

Molecular frame image restoration and partial wave analysis of photoionization dynamics of NO by time-energy mapping of photoelectron angular distribution

The benchmark system of molecular photoionization dynamics, the (1+1{'}) two-photon ionization of NO via the A state, is investigated using the time-energy mapping of the photoelectron angular distribution in a laboratory frame. The molecular frame photoelectron angular distribution and partial wave composition are determined from time-energy maps and compared with those obtained by Schwinger variational calculation (SVC) and state-to-state photoelectron spectroscopy. Good agreement is found with SVC. By comparison of the phase shifts of the scattering waves and the quantum defects of the Rydberg states, the l hybridization of p waves is identified.

Electronic spectroscopy of the E<--X transition of NO-Kr and shielding/penetration effects in Rydberg states of NO-Rg complexes

We report the results of a (2+1) resonance-enhanced multiphoton ionization (REMPI) study of the E2Sigma+(4ssigma) Rydberg state of NO-Kr. We present an assignment of the two-photon spectrum based on a simulation, and discuss it in the context of previously-reported spectra of NO-Ne and NO-Ar. In addition, we report on spectra in the region of the vNO=1 level of the E, F and H' 4s and 3d Rydberg states of NO-Rg (Rg=Ne-Kr). Since the NO vibrational frequency is affected by electron donation from the rare-gas (Rg) atom to the NO+ core, as well as by the penetration of the Rydberg electron, the fundamental NO-stretch frequency reflects the interactions in the complex. The results indicate that the 4s Rydberg state has a strong interaction between the NO+ core and the Kr atom, as was the case for NO-Ar and NO-Ne. For the 3d Rydberg states, although penetration is not as significant as for the 4s Rydberg states, it does play an important role, with subtle angular effects being notable.

Femtosecond time-resolved photoelectron imaging

Femtosecond time-resolved photoelectron imaging (TRPEI) is a variant of time-resolved photoelectron spectroscopy used in the study of gas-phase photoinduced dynamics. A new observable, time-dependent photoionization-differential cross section provides useful information on wave-packet motions, electronic dephasing, and photoionization dynamics. This review describes fundamental issues and the most recent works involving TRPEI.

Quantum defect theory of dipole and vibronic mixing in Rydberg states of CaF

The Rydberg spectra of CaF combine the simplicity of a single electron outside a doubly closed-shell Ca2+F- ion core with the exceptional polarity of the ion core. A global multichannel quantum defect (MQDT) fit to 612 previously assigned levels, 507 from n approximately = 12-18, N=0-14, v+=1, 97 from n approximately = 9-10, N=0-14, v+=2, and 8 from n approximately = 7, N=3-10, v+=3, produces the complete L=0-3 quantum defect matrix mu (with the exception of one element) and 19 of 20 elements of the partial differentialmu/differentialR matrix, as well as the molecular constants of the CaFX 1sigma+ state [omega(e)+=694.58(14), omega(e)x(e+)=2.559(40), B(e+)=0.373 07(16) cm(-1), and the v=0, N=0 to v(+)=0, N(+)=0 ionization energy, 46,996.40(8) cm(-1)]. This experimentally determined mu(R) matrix is unusual in the completeness of its representation of the spectrum of both core-penetrating and nonpenetrating Rydberg series, including both local perturbations and vibrational autoionization rates, as well as all dynamical processes encoded in the spectrum that result from the scattering (at negative energy) of the Rydberg electron off the Ca2+F- ion core. The MQDT theory is presented in a form that clarifies the relationships of the reaction (K) and phase (P) matrices of MQDT to effective Hamiltonian models for local interactions between accidentally near degenerate levels. In particular, a Hund's case (b) like representation of the Hamiltonian is described in which the rovibronic K matrix is diagonalized and the P matrix, which contains information about the v+, N+ eigenstates of the ion, becomes nondiagonal.

RYDBERG WAVEPACKETS IN MOLECULES: From Observation to Control

▪ Abstract  Significant advances in laser technology have led to an increasing interest in the time evolution of Rydberg wavepackets as a means to understanding, and ultimately controlling, quantum phenomena. Rydberg wavepackets in molecules are particularly interesting as they possess many of the dynamical complications of large molecules, such as nonadiabatic coupling between the various degrees of freedom, yet they remain tractable experimentally and theoretically. This review explains in detail how the method of interfering wavepackets can be applied to observe and control Rydberg wavepackets in molecules; it discusses the achievements to date and the possibilities for the future.

Photoelectron kinetic energy dependence in near threshold ionization of NO from A state studied by time-resolved photoelectron imaging

Photoelectron angular distributions in the laboratory frame (LF-PADs) from the A((2)sigma(+)) state of NO molecule were measured by femtosecond time-resolved photoelectron imaging with (1 + 1(')) resonance enhanced multiphoton ionization via the A state. High-precision measurements of the anisotropy parameters of LF-PADs were performed for the photoelectron kinetic energy from 0.03 to 1.05 eV as a function of the pump-probe delay time. The revival feature of the rotational wave packet on the A state was clearly observed in the time dependence of the photoelectron anisotropy parameters. By approximating the phase shifts of the photoelectron partial waves by the quantum defects in the high-lying Rydberg states using the multichannel quantum defect theory, the energy-dependent photoionization transition dipole moments were determined, for the first time, from time-dependent LF-PADs measured by time-resolved photoelectron spectroscopy.

Partial-wave decomposition of the ionization continuum accessed by vibrational autoionization of the NO 14s ( nu = 1, N = 20, N(+)(R) = 20) level

Rotationally resolved photoelectron angular distributions from vibrational autoionization of the NO 14s ( nu = 1, N = 20, N(+)(R) = 20) level are measured by photoelectron spectroscopy, and they are analyzed using a theoretical model based on first-order coupling between the Rydberg level and the ionization continuum. The analysis reveals that lambda-changing collisions and l-changing collisions between the molecular-ion core and the outgoing electron are comparable in magnitude and account for 40% of the partial waves produced in the ionization continuum.