Rydberg States Of NO Research Articles

Laser-induced amplified spontaneous emission from the 3d and nf Rydberg states of NO

Amplified spontaneous emission (ASE) from single rotational levels of 3dσ, πH 2Σ +, H ′ 2Π and nf ( n=4–6) Rydberg states of NO has been investigated through optical–optical double resonance excitation via the A 2Σ + state. The H, H ′→3pσ, πD 2Σ +, C 2Π (0,0) systems were rotationally resolved. The mixing of the C 2Π ( v=0) state with the valence B 2Π ( v=7) state explained the rotational pattern successfully. The degree of polarization of ASE for these transitions was measured and compared with the theoretical values of the corresponding resonant fluorescence. As the major ASE relaxation channels from the 4f and 5f ( v=0) states, transitions down to the 3d and 4d ( v=0) Rydberg series were identified, respectively. A new ASE relaxation pathway, 6f→5g, was found in addition to the 6f→5d band. The ASE from the 7f ( v=1) state located above the ionization threshold was observed for the first time. The spectral profiles were discussed briefly in connection with the lifetimes of the upper levels.

Rydberg states in the condensed phase studied by fluorescence depletion spectroscopy

Higher Rydberg states of NO trapped in rare gas matrices have been studied by inducing Rydberg-Rydberg transitions from the lowest \(\)\(\) Rydberg state and detecting its fluorescence depletion. This technique unravels Rydberg states, which cannot be accessed by ground state absorption. However, no clear cut Rydberg series show up. The data show a compression of the n-(n + 1) splittings between Rydberg states, as well as of the \(\) splittings. The results are rationalised in terms of the quantum defect model and the lack of extended Rydberg series is due to the compression of high-n Rydberg states in a tiny energy region below the ionisation potential. Finally, fluorescence depletion data of NO trapped in amorphous sites (the so-called red sites) of solid Ar can be interpreted in terms of the gas phase NO-Ar van der Waals data. A general discussion on the fate of Rydberg states in van der Waals complexes, in liquids, and in solids is presented in an attempt to relate the data in these different media.

Dynamics of electronic “bubble” formation in solid hydrogen

Excitation of the A(3s σ) Rydberg state of NO trapped in an H 2 crystal leads to the electronic “bubble” formation around the NO impurity, resulting in an increase of 0.9 Å of the ground state cage radius. Its dynamics has been followed in real-time by femtosecond pump–probe spectroscopy. The results show that “bubble” formation is completed in about 1.5 ps without recurrences of the cage motion. A model based on classical hydrodynamics provides quantitative agreement with experimental data, suggesting that solid hydrogen can be described like a liquid on ultrashort time scales.

Dynamics of Electronic “Bubble” Formation in Solid Hydrogen: A Classical Model Calculation based on Fluid Dynamics

A model based on fluid dynamics is proposed, which describes the dynamics of a photoinduced spherical deformation in solid hydrogen. The dynamics is driven by femtosecond excitation of the lowest $A(3s\ensuremath{\sigma})$ Rydberg state of NO trapped in an ${\mathrm{H}}_{2}$ crystal, leading to electronic ``bubble'' formation. The model is based on a continuum approximation and considers the medium as incompressible. Energy dissipation due to friction is also taken into account. The model provides quantitative agreement with experimental data, suggesting that solid ${\mathrm{H}}_{2}$ can be described as a liquid on ultrashort time scales.

Autoionizing Rydberg states of NO in strong electric fields

We report on an investigation on autoionization of Rydberg electrons of the nitric oxide molecule in strong, static electric fields. The excitation was done via various rotational states of the A 2Σ+ intermediate state (v′=0) and with polarization parallel or perpendicular to the electric field. The splitting of the autoionizing Rydberg states into overlapping Stark manifolds is resolved for excitation above the saddlepoint created by the field. We observe that the competing decay between photoionization and predissociation can lead to an incorrect interpretation of threshold energy. The photoionization spectrum of NO Rydberg series attached to various rotational thresholds is very similar owing to weak rotational coupling. The experimental results are accurately simulated by quantum calculations based on multichannel quantum defect theory (MQDT). A more intuitive formulation of the average behavior of the photoionization cross section is developed that accounts for the suppression of ionization near the threshold due to competing predissociating channels.

Mechanism of the parametric four-wave mixing processes involving the C [formula omitted] and D [formula omitted] Rydberg states of NO

When the 3pπ C 2 Π and 3pσ D 2 Σ + states of the NO molecule were populated through the two-photon resonant excitation, highly directional emission was generated in IR and UV regions along the laser propagation. It was concluded that amplified spontaneous emission (ASE) was mainly responsible for the IR wave corresponding to the C 2 Π , D 2 Σ + →3sσ A 2 Σ + (0, 0) bands because the IR emission was detected in the backward direction as well as forward. The UV radiation composed only of the A 2 Σ + →X 2 Π (0, 0) band evidenced the existence of the parametric four-wave mixing (PFWM) process. The analyses of emission properties revealed that the interaction of the forward propagating ASE with a two-photon field of the input laser produced the UV wave as the fourth wave in the PFWM process.

Decay Dynamics of the Predissociating High Rydberg States of NO

The dynamics of predissociating high molecular Rydberg states of NO below the lowest ionization threshold is computed in the presence of a weak external dc field using a quantum theory based on an effective Hamiltonian formalism. The core−electron interaction affecting the low l states (l ≤ 2) is taken into account by molecular quantum defect theory, while for the high l states (l ≥ 2), a long range multipolar expansion is used to describe the effect of the anisotropy of the molecular core. Time- and frequency-resolved ZEKE spectra are computed. In the energy range investigated, the decay kinetics of the ZEKE intensity is found to exhibit two time scales, which differ by more than an order of magnitude. The short decay constant typically falls in the submicrosecond range and is in agreement with previous experimental results and computations. In addition, our computations predict a long-time component, which decays in the tens of microseconds range. The two decay times are discussed in terms of the short and long range interseries dynamics, in terms of the strength of the external dc field, and in terms of the nature of the bottlenecks in phase space for a predissociating molecular core with a rather large rotational constant (BNO+ = 1.9842 cm-1). It is found that for this particular case where all series are coupled to the fragmentation channels through a low l bottleneck, the predissociation process does not quench the long time component in the decay kinetics. The reason is that the interplay between the interseries coupling and the external dc field leads to a shift of the decay constants to larger values together with an enhancement of the weight of the long time component in the decay kinetics. Special attention is devoted to the role of the dipolar interaction and its synergy with the external dc field.

Radiative decay processes in the 6s and 7s Rydberg states of NO studied by three-color laser-induced amplified spontaneous emission spectroscopy

A novel spectroscopic technique involving amplified spontaneous emission (ASE) is presented to excite single rotational levels of the 6sσT 2Σ+ and 7sσZ 2Σ+ Rydberg states of the NO molecule. In this excitation regime, the 3pπD 2Σ+ state, which is populated by the ASE deexcitation process from the 4sσE 2Σ+ Rydberg state, serves as the intermediate state. As the initial radiative decay channels form the T 2Σ+ and Z 2Σ+ states, the dipole allowed ASE transitions down to the nearest Rydberg states, i.e., T 2Σ+→5pσR 2Σ+ and Z 2Σ+→6pσY 2Σ+, are identified. The anomalous intensity distributions both in the excitation and emission spectra are well explained by s–d mixing and l uncoupling in the upper Rydberg states.

Parametric four-wave mixing in the 3d and 4d Rydberg states of NO

Σ+,H′ 2Π±(v′=2), and 4dσ,πO2Σ+,O′ 2Π±(v′=0) Rydberg states of NO molecules are described. The analyses of the two-photon excitation functions and infrared emission spectra revealed that only the 2Π- component was involved in PFWM. This is in good accordance with the absence of amplified spontaneous emission (ASE) in the 2Σ+ and 2Π+ components due to their predissociative character. Results provide some support for the mechanism that the generation of the vacuum ultraviolet radiation was brought by PFWM in which ASE served as a third driving wave.

A, C, and D electronic states of the Ar–NO van der Waals molecule revisited: Experiment and theory

The A–X transition of ArNO has been reinvestigated by laser induced fluorescence (LIF) both in the bound–free and bound–bound region. The discrete part of the spectrum is at least two orders of magnitude weaker than the continuum part, indicative of a large change in geometry from the ground state. This very different configuration, both from the ground state and from the C and D states, can only be explained by strong interactions, induced by the perturbing argon atom, between the excited states of the van der Waals complex converging to the 3sσ,A, 3pπ,C, and 3pσ,D Rydberg states of NO. In order to quantitatively understand the observed structure of the A–X, C–X, and D–X excitation spectra, a global theoretical approach is proposed, based on ab initio calculations of the potential energy surfaces in the planar A′ and A″ symmetries, including a configuration interaction between the states of same symmetry. Small adjustments of the diabatic energy surfaces lead to a satisfactory agreement between the observed and calculated spectra. In contrast to the ground state, the Renner–Teller splitting of the 3pπ,C state into two A′ and A″ components is very large, of the order of 4000 cm−1. This effect is complicated by further mixing between the states of A′ symmetry induced by the argon atom. The A state is anisotropic and weakly bound with a small potential well at the linear configuration (the argon atom being on the side of the oxygen). The C(A″) and the bound electronic component of the strongly mixed C+D(A′) states exhibit a vibrational structure close to that of the ion and, consequently, present some Rydberg character even if the Coulomb field central symmetry (s-p) is broken by the perturbing argon atom.

Two-photon spectroscopy of the low lying Rydberg states of NO. II. Application to the NO–Ar complex

The rotational structure of two-photon spectra of van der Waals complexes involving an open shell diatomic molecule is analyzed in terms of the spherical tensor components of the two-photon absorption operator of the uncomplexed diatom. The formalism is used to explain the rotational structure of several band systems of the NO–Ar complex correlating with Rydberg states of the bare NO molecule. All spectra recorded suggest an N–O bond distance typical for a Rydberg state. For the C 2Π state, the vibrationally averaged structure is T shaped. Within the effective experimental resolution no P-type doubling could be identified. For the bands correlating with the state E 2Σ, a significant deviation from the T-shaped structure is found. Once the rotational contour can be simulated, a complete analysis of the vibrational structure due to the intermolecular vibrations can be performed. For the Ar–NO E state, the bending and stretching frequencies suggest a close resemblance to the cationic complex Ar–NO+.

Two-photon spectroscopy of the low lying Rydberg states of NO. I. The 3p and 3d complexes

The rotational structure and polarization dependence of two-photon spectra of aligned ensembles of open shell diatomics is investigated in terms of the spherical tensor components of the two-photon absorption operator. The formalism allows the straightforward incorporation of state interactions and perturbations. It is applied to the two-photon spectroscopy of NO, in particular to the excitation of the Rydberg states derived from the 3p and 3d complexes. All states investigated show a nearly quadratic power dependence indicating the saturation of the ionization step. Transitions dominated by a zeroth rank tensor component (e.g., C 2Π–X 2Π or H 2Σ, H′ 2Π–X 2Π) are insensitive to a possible angular momentum alignment in the ensemble. These transitions are ideally suited to determine degeneracy averaged observables, e.g., collision cross sections in a molecular beam scattering experiment or product velocity anisotropies in a single color photodissociation experiment. Rotational alignment data must be determined using two-photon transitions which are carried by a second rank tensor component (e.g., D 2Σ–X 2Π or F 2Δ–X 2Π).

Ab initio potential energy curves of Rydberg, valence and continuum states of NO

Bound states and quasibound Rydberg states of NO are studied as a function of internuclear distances in the range . R-matrix calculations which include 12 configuration interaction target states in the close-coupling expansion are performed. Rydberg states of up to n = 10 are studied for the , and symmetries of NO. Intruder states, of both valence and Rydberg character, are followed both above and below the ionization threshold. Where possible these states are classified as Rydberg states of an excited state of the ion. Away from avoided crossings, it is found that the quantum defects of the Rydberg series converging on the state of show little sensitivity to bondlength but show considerable dependence on the number of states included in the close-coupled expansion.

Rotationally resolved photoelectron spectra from vibrational autoionization of NO Rydberg levels

Rotationally resolved photoelectron spectra from vibrational autoionization of individual rotational levels of the nlR (v=1, 11⩽n⩽15, 0⩽lR⩽3) Rydberg states of NO are measured by combining two-color double-resonance excitation via the NO A 2∑+ (vi=1, Ni=19) state with time-of-flight photoelectron spectroscopy. The photoelectron spectra show that both even-l and odd-l continuum partial waves are generated by the autoionization events, and thus provide evidence for angular momentum exchange between the outgoing electron and the molecular-ion core. We interpret these observations as caused by the multipolar interactions between the outgoing electron and the vibrating nuclear core, which appear to be brought about both by the dependence on internuclear distance of the electron-ion-core electronic interaction and by Rydberg-valence state couplings.

Rydberg states in quantum crystals NO in solid H2

Fluorescence, excitation and fluorescence depletion spectra of the lowest Rydberg states of NO trapped in H2 matrices are reported. The absorption bands are shifted by about 0.58 eV to the blue of the gas phase energy. They are strongly broadened and exhibit an asymmetry by a blue wing. The fluorescence bands are significantly narrower, with a red wing, and lie very close to the gas phase energy. The absorption lineshape can be accounted for by the large extension of the ground state wavefunction, due to the strong contribution of the zero point motion in the H2 lattice. The absorption–emission Stokes shift is interpreted in terms of ‘bubble’ formation around the Rydberg excited molecule. A moment analysis of the absorption and emission bands in the harmonic approximation shows that most of the absorption–emission Stokes shift is used up as energy to create the ‘bubble’ around the excited molecule. The fluorescence depletion spectrum yields Rydberg–Rydberg transitions very close to the gas phase energy. This, together with the fluorescence spectra, indicates that the molecule is in a quasi-free, gas-phase-like state in the expanded cage. The excitation spectra and the fluorescence depletion spectra indicate a severe compression of the Rydberg series of NO in H2 matrices, which can be accounted for by a large negative electron affinity of solid H2. Concerning the intramolecular energy relaxation in NO, it is found that the Rydberg↔valence relaxation processes follow much the same pattern as observed in rare gas matrices for the lower valence states. For the higher valence states, a photochemical route is suggested. For the vibrational relaxation by Δv=2 in the A state and for the C–A electronic relaxation, intermolecular energy transfer processes between NO molecules are invoked, which occur in the sub-ns timescale.

Intramolecular coupling between non-penetrating high molecular Rydberg states

We address a central question in the realm of the dynamics of high-n (= 40- 250) Rydberg states of diatomics and large molecules. What is the coupling responsible for the 'global' l mixing, which results in the breakdown of the n 3 scaling law for the non-radiative lifetimes and for the lifetime lengthening (by two to four orders of magnitude) of these states? To explore the implications of intramolecular interactions on l mixing and on electronic-rotational energy exchange we analysed the intramolecular couplings of the ion core dipole, quadrupole and (anisotropic) polarizability with a non-penetrating (l⩾ 3) Rydberg electron, in conjunction with the energy gaps between proximal pairs of energy levels. Calculations of the energy gaps and the couplings were performed for the high-n non-penetrating Rydberg states of NO and for model 'light' (B = 19 cm-1) and 'heavy' (B = 0⋅05 cm-1) polar molecules. All the intramolecular interactions are of the form of a power law proportional to l -η, with η being determined by the nature of the long-range coupling, by the l dependence of the quantum defects for multipole couplings and by the l dependence of angular integrals. We established a bottleneck effect for the intramolecular couplings between non-penetrating (l⩾3) states. For n- and N+-changing dipole, quadrupole and polarizability interactions the energetics ofthe proximalpairs of levels, in conjunction with the bottleneck effect,prohibit the |n, l, N +, N> - |n', l', N +', N>, l (⩾ 3) couplings (with n ╪ n') and the electronic-rotational energy exchange. For n- and N +-conserving quadrupole and polarizability interactions, the l (⩾ 3) mixing (which prevails only for l N ++ N) is also prohibited by the bottleneck effect. 'Global' intramolecular l mixing (with both n ╪ n' and n = n') in diatomics and in large molecules is precluded, implying that the dramatic lengthening of the non-radiative lifetimes of high-n Rydberg states can be induced only by exterior electric field coupling.

The dynamics of predissociating high Rydberg states of NO

In this paper we present a theoretical study of the predissociation dynamics of the nf(N+=2) (with the principal quantum numbers n=40–95) and the np(N+=0) (n=70–125) Rydberg series of NO, which exhibit a marked lifetime dilution (lengthening) at n≳65 for the f series and at n≳116 for the p series [M.J.J. Vrakking and Y. T. Lee, J. Chem. Phys. 102, 8818 (1995)]. The multichannel effective Hamiltonian with several doorway (for excitation) and escape (for decay) states was constructed using experimental information on the quantum defects and on the decay width constants incorporating both intramolecular coupling and exterior electric field coupling between high Rydbergs. The analysis of the intramolecular Rydberg electron–core dipole long range coupling (HR-D) in conjunction with the energy gaps between proximal pairs of energy levels, which are subjected to appropriate selection rules, reveals that (i) for low l(≤3) core-penetrating Rydbergs only a small number of accidental near-resonances are exhibited, and (ii) for high l(≳3) nonpenetrating Rydbergs the electron-core dipole coupling decreases fast with increasing l, i.e., (HR-D)∝l−7. The general characteristics of the high l(≳3) manifold establish a bottleneck effect, which precludes intramolecular l mixing, implying that high Rydberg lifetime dilution effects can be induced only by exterior electric field coupling (HSTARK). Parameter-free multichannel effective Hamiltonian calculations were conducted under narrow-band excitation conditions, which interrogate the electric field induced mixing in the energetic vicinity of the doorway state. The electric field induced l mixing model accounts semiquantitatively for the electric field dependence of the energy-resolved line shapes of the nf(N+=2) series and for the n and electric field dependence of the lifetimes of the nf(N+=2) and the np(N+=0) series. Accidental near-resonant simultaneous intramolecular and electric field coupling np(N+=0)↔HR-Dn′d(N+=1)↔HSTARKn′ l(≥3)(N+=1) for two sets of proximal states n=92, n′=80 and n=95, n′=82, result in mediated-sequential mixing, which is manifested by slow decay times below the onset of effective electric field mixing by weak (F0≂0.04–0.08 V/cm) stray electric fields.

Rydberg series in condensed matter: a fluorescence depletion experiment

Rydberg-Rydberg transitions are induced by absorption from the lowest Rydberg state of NO A 2Σ + (3 sσ) in Ar matrices, which is excited by an ArF laser at 193.3 nm. The depopulation of the A( ν = 0) level to higher Rydberg states is probed by depletion of its fluorescence. Absorption bands are observed in the 1.0–2.0 eV region which are attributed to transitions to the 3p, 3d, 4s and 4p members of the Rydberg series. At higher energies, a continuous absorption structure appears. It is attributed to transitions to the n > 4 members of the Rydberg series which are compressed in a tiny energy range below the ionization potential. A quantum defect model is applied and accounts well for the observations.

Three-color triple resonance spectroscopy of highly excited ng Rydberg states of NO: Decay dynamics of high-l Rydberg states

With three-color triple resonance excitation, rotational-state-resolved laser multiphonon ionization spectra of highly excited ng Rydberg states (n=11–67, v=0 and 1) of NO have been observed. Determining the term values of the observed states, we have found that those values are in good agreement with the theoretical values calculated on the basis of the long range force model. Through detailed analysis of the spectral intensity distributions, we have proved, for the first time, the theoretical prediction that even in g Rydberg states there are efficient vibrational and rotational autoionization processes much faster than the radiative decay. In addition, we have also found the presence of non-negligible predissociation processes competing with the autoionization processes, roughly estimating both predissociation and autoionization rates.

Predissociative linewidths of (4pσ) M 2Σ+ (v=1) and (3dσ,π) H 2Σ+, H′ 2Π (v=2) Rydberg states of NO studied by the two-color laser-induced grating technique

The two-color laser-induced grating (TC-LIG) technique has been employed to probe the predissociative Rydberg states (4pσ) M 2Σ+ (v=1) and (3dσ,π) H 2Σ+, H′ 2Π± (v=2) and the non-Rydberg B 2Π (v=26) state of nitric oxide. The ultraviolet pump laser frequency is fixed to a specific rotational line of the A 2Σ+ (v′=1 and 2)←X 2Π3/2 (v″=0) transition of NO. Interference of two pump laser beams crossing at a small angle in the gas sample forms a population grating. Then, the visible probe laser beam is diffracted off the grating as the signal beam when the probe laser frequency is resonant to a transition from the rotational level excited by the pump laser. Term values and rotational assignments of the H 2Σ+, H′ 2Π± (v=2)–B 2Π3/2 (v=26) states have been established for the first time, resulting in the value of ∼1.77 cm−1 for the l-uncoupling constant. Line broadenings due to predissociation are observed in the TC-LIG spectra for the M 2Σ+ (v=1) and H 2Σ+, H′ 2Π+ (v=2) states. The linewidths of the M 2Σ+ (v=1) state show no marked rotational dependence except for the N=4 level which is locally perturbed. On the other hand, the predissociative lifetimes of the H 2Σ+ and H′ 2Π+ (v=2) states exhibit a significant rotational dependence: The linewidth of the former state decreases with N, while the reverse tendency is seen for the latter. The mixing between the H 2Σ+ and H′ 2Π+ states caused by l-uncoupling explains the observed rotational dependence successfully.