Molecular picture of excited states and fragmentation paths of the Na 5 F 4 cluster

The stability against fragmentation and possible relaxation of the lowest excited states of the Na₅F₄ cluster (representative of cubic non stoechiometric clusters with an excess sodium atom, also called sodium-tail) is investigated by means of one-electron pseudopotential calculations with particular reference to photoabsorption processes from the ground state. Whereas the equilibrium configuration of the ground state has C_3v symmetry, the doubly degenerate 1²E excited state is affected by a conical intersection and a Jahn-Teller effect associated with the rotation of the sodium tail around the C₃-axis. This yields a “Mexican hat" topology for the lowest sheet with three equivalent C_s minima. Alternatively the 2²A₁ state has a minimum retaining the C_3v symmetry. The dissociation paths of the cluster along the C₃-axis into respectively Na₄F_{4 +} Na and Na₄F_{3 +} NaF are also investigated. Among the former paths, the excited states are found adiabatically stable with respect to the products. However in the A₁ symmetry, fragmentation into NaF exhibits an interesting avoided crossing between configurations correlated respectively with Na₄F₃ ^{+ +} NaF^- and Na₄F_{3 +} NaF. Such interaction, similar to the well-known charge exchange processes in elementary molecules might induce non adiabatic predissociation of the 2²A₁ state. This mechanism is invoked to explain the differences between R2PI and depletion spectra, correlated with the dissociation or relaxation of the excited states. Received 24 March 2000 and Received in final form 11 July 2000     

Theoretical exploration of ultrafast spectroscopy of small clusters

We present the ultrafast multistate nuclear dynamics involving adiabatic and nonadiabatic excited states of non-stoichiometric halide deficient clusters (Na_nF_n-1) characterized by strong ionic bonding and one-excess electron for which the “frozen ionic bonds” approximation has been justified allowing to consider the optical response of the single excess electron in the effective field of the other electrons. We combined the Wigner-Moyal representation of the vibronic density matrix with the ab initio multi state molecular dynamics in the ground and excited electronic states including the nonadiabatic couplings calculated “on the fly” at low computational demand. This method allows the simulation of femtosecond pump-probe and pump-dump signals based on an analytical formulation, which utilizes temperature dependent ground state initial conditions, an ensemble of trajectories carried out on the electronic excited state as well as on the ground state after the passage through the conical intersection in the case of nonadiabatic dynamics and for probing either in the cationic state or in the ground state. The choice of the systems we presented has been made in order to determine the timescales of the fast geometric relaxation leaving the bonding frame intact as during the dynamics in the first excited state of Na₄F₃, and of the bond breaking processes leading to conical intersection between the first excited state and the ground state as in Na₃F₂. The former is the smallest finite system prototype for an surface F-center of bulk color centers. The latter allows to study the photo isomerization in full complexity taking into account all degrees of freedom. In the case of Na₄F₃ after the fast geometric relaxation in the excited state leading to deformed cuboidal structure without breaking of bonds, different types of internal vibrational redistribution (IVR) processes have been identified in pump-dump signals by tuning the dump laser. In contrast, from the analysis of the pump-probe signals of Na₃F₂ cluster, the timescales for the metallic and the ionic bond breaking, as well as for the passage through conical intersection have been determined. Finally the conditions under which these processes can be experimentally observed have been identified. Received 22 December 2000     

Femtosecond pump-probe experiments on non-stoichiometric sodium-fluoride clusters

In this paper we present two-color pump and probe spectroscopy on Na₂F, the smallest of the non-stoichiometric sodium-fluoride clusters (Na_nF_n-1), in molecular beams by employing femtosecond laser pulses. The molecules were pumped into the first excited state by one photonic transition and consecutively ionized from there by the second photon. We resolved the wavepacket oscillatory motion involving periodical structural rearrangements in the first excited state of Na₂F with a period of 185 fs. The time-resolved experiments show that sodium fluoride clusters provide interesting features which can be manipulated in optimal control experiments.     

Optical losses in YVO4: RE (RE = Nd3+, Er3+, Tm3+) laser crystals

The relevance of processes contributing to depletion of pump and upper laser levels has been assessed based on experimental data obtained during measurement of excited state absorption, steady state emission and dynamics of excited states as a function of excitation power and activator concentration. It has been concluded that the excited state absorption in YVO₄: Nd and YVO₄: Er is not significant except for that from the ⁴ I _11/2 level of Er³⁺. In these systems, the interionic processes are dominant. In particular, the reported decrease of the YVO₄: Er laser slope efficiency when the Er³⁺ concentration increased from 0.5 to 1 at % is due mainly to the up-conversion by energy transfer from the pump level and upper laser level. Excited state absorption cannot contribute to depletion of excited states involved in the ³ F ₄-³ H ₆ laser operation near 1800 nm in the YVO₄: Tm crystal. However, the heavy doping required to enhance the cross-relaxation process which feeds the upper laser level brings about the migration-accelerated energy transfer to energy sinks.     

Hindered Coulomb explosion of embedded Na clusters — stopping,shape dynamics and energy transport

We investigate the dynamical evolution of a Na₈ cluster embedded in Ar matrices of various sizes from N=30 to 1048. The system is excited by an intense short laser pulse leading to high ionization stages.We analyze the subsequent highly non-linear motion of cluster and Ar environment in terms of trajectories, shapes, and energy flow. The most prominent effects are: temporary stabilization of high charge states for several ps, sudden stopping of the Coulomb explosion of the embedded Na₈ clusters associated with an extremely fast energy transfer to the Ar matrix, fast distribution of energy throughout the Ar layers by a sound wave. Other ionic-atomic transfer and relaxation processes proceed at slower scale of few ps. The electron cloud is almost thermally decoupled from ions and thermalizes far beyond the ps scale.     

Influence of covalence and anion symmetry on the structure of small metal hydroxide clusters: Sodium versus silver hydroxide

An ab initio study of the Na_n(OH)_n, Na_n(OH)_n-1 ⁺, Ag_n(OH)_n, and Ag_n(OH)_n-1 ⁺ clusters with n up to four is presented. The results of this study show that, in accordance with experimental observations, the sodium hydroxide clusters are almost purely ionic, while the Ag-O bond exhibits a significant covalent character. The perturbation caused by the non-spherical OH^- group relatively to an atomic anion, as well as the influence on structures and energies of the covalent character of the metal-oxygen bond are determined. The appearance of metal-metal bonds in the silver hydroxide clusters is also discussed. Finally, the theoretical results obtained on the Na-OH clusters are compared to experimental results available on the dissociation of the Na_n(OH)_n-1 ⁺ clusters. Received 9 August 1999 and Received in final form 1st December 1999     

F+ laser performance and interaction of Cu,Ag and Au at the reduced oxygen coordination of MgO surface: first principles calculations

F⁺ laser performance and interaction of the title group IB transition metals at the reduced oxygen coordination of MgO surface were investigated using the TD and DFT methods of ab initio molecular electronic structure calculations. The considered ion clusters were embedded in simulated Coulomb fields that closely approximate the Madelung fields of the host surfaces and the nearest neighbor ions to the F⁺ site were allowed to relax to equilibrium in each case. The F⁺ laser performance fades quickly as the reduced oxygen coordination decreases from 5 to 4 to 3. The relaxed excited states (RESs) of the defect containing surfaces are compact and deep below the conduction bands of the perfect MgO surface. The probability of orientational destruction of the center in laser experiment is expected to follow the order flat>corner>edge. The excited state at the edge has higher energy than that at the flat or at the corner. F⁺ is easily formed at the lower oxygen coordination and the disappearance of anisotropy and 2p splitting observed in absorption of F⁺ at the surface follow the order corner>flat>edge. The Glasner–Tompkins relation is generalized to include the F⁺ bands at the reduced oxygen coordination of a metal oxide surface. As far as the adsorbate–substrate interactions are concerned, the F⁺ center enhances the adsorptivity of Ag, Cu and Au by ca. 1.91–3.33 eV and changes the nature of adsorption from physical adsorption to chemical adsorption. The adsorption energies follow the order Cu>Au>Ag and are explainable in terms of electrostatic potential curves, energy gaps and spin pairing. Cu and Ag act as electron donors while Au acts as electron acceptor and the MgO surface cannot be made semiconducting by F⁺ imperfection.     

Control of wavepacket dynamics in mixed alkali metal clusters by optimally shaped fs pulses

We have performed adaptive feedback optimization of phase-shaped femtosecond laser pulses to control the wavepacket dynamics of small mixed alkali-metal clusters. An optimization algorithm based on Evolutionary Strategies was used to maximize the ion intensities. The optimized pulses for NaK and Na₂K converged to pulse trains consisting of numerous peaks. The timing of the elements of the pulse trains corresponds to integer and half integer numbers of the vibrational periods of the molecules, reflecting the wavepacket dynamics in their excited states. Received 4 December 2001     

De-excitation process and hot luminescence in the FA(type I) center in KCl:Na

The de-excitation process of F_A(type I) centers in KCl:Na has been investigated by measuring the hot luminescence spectrum from optically excited F_A centers with time-resolved spectroscopy. The experimental results are analyzed by using a model that describes a time evolution of the phonon wave packet during the vibronic relaxation process from the Franck-Condon state to a relaxed excited state. From the analysis of the experimental data, information on the vibronic mixing between 2p and 2s states, whose magnitude varies during the relaxation process, and the adiabatic potential energy curves of 2s and 2p states are extracted. The present results are compared with the already known ones of the F_A(type II) centers.     

Multiple-Photon Dynamics in Molecules: A New Approach to High Resolution Spectroscopy of Highly Excited Vibrational States

Multi-photon transitions with two simultaneously interacting IR laser fields lead to final excited states with frequenciesnν = n₁ν₁+ n₂ν₂, withnthe total number of photons absorbed and (n,n₁,n₂) = (2, 1, 1), (3, 2, 1), (4, 1, 3), etc. The nature of the actual transition is determined by shift measurements, where the lasers are frequency-tuned by δν_iin opposite directions keeping the sum frequency,nν, resonant with the molecular transition. This technique opens a new spectral range for multi-photon transitions and a unique identification of the observed features. Forn₁andn₂both positive the excitation will lead to a “normal” up–up multi-photon transition. Many three- and four-photon transitions in the ν₃vibrational ladder of SF₆could be resolved with a resolution of 1 MHz, as well as four new two-photon transitions. As long asn₁+ n₂≥ 0, one of the twon_imay be negative resulting in an, e.g., up–down excitation pathway with its particular selection rules. The up–down excitations are demonstrated both for one- and two-photon transitions using the frequency shift technique. The different possible excitation schemes which meet the resonance condition for these transitions lead to interference effects and local couplings to highly excited states. Changes in resonance frequency for a one-photon transition (n= 1), due to these effects, are demonstrated. Evidently, the radiative coupling of participating levels to high-lying or quasi-continuum states may drastically change for different δν_ileading both to ac Stark shift and transition probability variations.     

Energy levels,luminescence and electronic structure of ZnS:Tm3+

Energy levels, densities of states, electronic densities, electrostatic interaction integral parameters F_k and spin-orbit coupling parameters ζ_4f for ZnS: Tm³⁺ are calculated self-consistently, using both one-electron local density discrete variational non-relativistic Hartree-Fock-Slater (HFS) and relativistic Dirac-Slater (DS) cluster models. In these calculations, both spin-restricted and spin-polarized models are considered. The finite clusters calculated include TmS₄ and TmS₄Zn₁₂ clusters for cubic ZnS, which are embedded in the crystal environment. The spin-orbit coupling parameter ζ_4f derived from DS cluster calculations is equal to 2689 cm^-1, rather near the result of the relativistic Hartree-Fock free ion model. The parameters F_k and ζ_4f are further calculated from the 4f radial wave function obtained by solving the HFS and the DS atomic equations. It is shown that by decreasing the effective exchange-correlation potential, these parameters can be reduced to approximately match empirical values. A comparison of the excited energy level scheme of ZnS:Tm derived from the calculated parameters and the experimental spectra is presented.     

Electron dynamics in Na and Pt clusters from time-dependent Hartree-Fock theory

We present a method for the numerical investigation of the electron dynamics in small metallic clusters in intense laser fields. We obtain information about collective excitations and relaxation processes in the Na ₉ ⁺ and Pt₃ clusters analyzing the power spectrum of the dipole moment within a mean-field approach. The power spectrum is computed for various laser pulse parameters as well as for the limit of an infinitely short laser pulse. Due to the basis set expansion of the wave function our method is capable to follow the dynamics not only of the whole electron cloud, but of any particular molecular orbital. Received 28 March 2002 / Received in final form 31 May 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: pavlyukh@mpi-halle.de     

Upconversion-pumped population kinetics for4I13/2 and4I11/2 laser states of Er3+ ion in several host crystals

Population kinetics of the upper⁴I_11/2 and lower⁴I_13/2 laser states of the Er³⁺ ion were studied experimentally and theoretically in (Er)BaY₂F₈, (Er)YLF, (Er)YSGG, (Er)CaF₂ and (Er)YALO. Fluorescence from these states to the⁴I_15/2 ground state was excited through upconversion simultaneously with the⁴I_11/2 →⁴I_13/2 lasing using 1.53 µm radiation from an erbium : glass laser for optical pumping. Lifetimes of both states are altered during lasing by co-operative energy transfer processes: the lifetime of the lower state τ₁ is shortened and that of the upper state τ₂ increased with the resultant ratio τ₂/τ₁>1. After lasing the lifetime ratio returns to the ‘normal’ value τ₂/τ₁ <1; that is, one obtained under weak ultraviolet excitation. Kinetic rate equations for the population density functions for both laser states were set up and solved by approximation in three time domains. It was assumed that only one co-operative energy transfer process operates in the laser crystals and determines the population inversion kinetics. Consistency relationships for comparison of the theoretical results with the experiment were developed. Only (Er)BaY₂F₈ spectral features showed close agreement with theory, resulting in a high score of 94% for the overall correlation in the consistency test, whereas all other crystals scored <50%. As a result of this high correlation, a close match between theoretical and experimental population decay curves was shown for (Er)BaY₂F₈. Most probably, more than one energy transfer process shapes the decay curves and determines the population inversion kinetics for the other laser crystals. (Er)YALO showed little lifetime change for the laser states, apparently due to inefficient co-operative energy transfer processes. As a result it probably lased in a self-terminating short-pulse mode.     

Time behaviour of diffuse band emission in Na2 and K2

The C states of sodium and potassium dimers were excited with short laser pulses (about 500 ps) and time evolution of the diffuse bands in Na₂ (413–456 nm) and K₂ (550–583 nm) was observed in fluorescence. The measured decay times were interpreted as lifetimes of unidentified triplet states giving origin to the diffuse bands. Our results contradict the values reported before.     

超低温高电场下GaAs的电子太赫兹功耗谱的研究

利用自由空间太赫兹电光取样方法,测量了在高电场下,GaAs中受飞秒激光脉冲激发的电子所辐射出的太赫兹电磁波,发现从样品中辐射出的和电子加速度成正比的太赫兹电磁波电场强度E_THz（t）,表现出双极特性.通过分析GaAs中辐射出的太赫兹电磁波的傅里叶变换谱,首次实验上得到在阶跃电场下的GaAs的电子太赫兹功耗谱.研究发现,当电场小于50 kV/cm时,由电子谷间散射引起的负功耗（即增益）的截止频率ν_c,随着电场的增大而增大;当电场大于50 kV/cm时,负功耗的截止频率ν_c开始在750 GHz（10 K）附近饱和. 关键词： 太赫兹 非平衡载流子 功耗谱 谷间散射     

Lifetime-measurements of alkali-molecules excited by different laserlines

Absorbing different lines of acw-argon ion laser or a He-Ne-laser the alkali molecules Na₂, K₂, Rb₂ and Cs₂ can be pumped into different rotational-vibrational levels of an excited electronic state. The lifetimes of these states have been measured using the phase shift technique at a modulation frequency of 18 Mc/sec. Because of collisions with the always present alkali atoms the excited molecules may undergo collision-induced transitions to other states and their lifetimes are dependent on the atomic pressure. This dependence was measured and the spontaneous lifetimes were obtained by extrapolation against zero pressure. Different collision processes are discussed which compete with the unperturbed fluorescence.     

Small-x behavior of the structure function and its slope for “frozen” and analytic strong-coupling constants

Using the leading-twist approximation of the Wilson operator product expansion with “frozen” and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F₂ and its slope ∂lnF₂/∂ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA.     

Electron impact ionization of atomic clusters in ultraintense laser fields

In this paper we report on inner ionization of Xe_n clusters (n = 55- 2171) in ultraintense Gaussian laser fields (peak intensity I = 10¹⁵- 10²⁰ Wcm^-2, pulse width τ= 25 fs, frequency 0.35 fs^-1). The cluster inner ionization process is induced by the barrier suppression ionization (BSI) mechanism and by electron impact ionization (EII), which occurs sequentially with the BSI. We address electron impact ionization of clusters, which pertains to inelastic reactive processes of the high-energy (100 eV–1 keV per electron) nanoplasma. We utilized experimental data for the energy dependence of the electron impact ionization cross-sections of Xe^j+ (j = 1-10) ions, which were fit by an empirical three-parameter Lotz-type equation, to explore EII in clusters by molecular dynamics simulations. Information was obtained on the yields and time-resolved dynamics of the EII levels (i.e., number n_imp of electrons per cluster atom) in the Xe_n clusters and their dependence on the laser intensity and cluster size. The relative long-time (t = 90 fs) yields for EII, n_imp/n_ii (where n_ii is the total inner ionization yield) are rather low and increase with decreasing the laser intensity. In the intensity range I = 10¹⁵-10¹⁶ Wcm^-2, n_imp/n_ii = 0.21 for n = 2171 and n_imp/n_ii = 0.09-0.14 for n = 459, while for I = 10¹⁸-10²⁰ Wcm^-2, n_imp/n_ii = 0.01-0.05. The difference Δn_imp between the EII yield at long time and at the termination of the laser pulse reflects on ionization dynamics by the nanoplasma when the laser pulse is switched off. For Xe₂₁₇₁ in the lower intensity domain, Δ n_imp = 0.9 at I = 10¹⁵ Wcm^-2 and Δn_imp = 0.4 at 10¹⁶ Wcm^-2, reflecting on EII by the persistent nanoplasma under “laser free” conditions, while in the higher intensity domain of I = 10¹⁷ - 10¹⁸ Wcm^-2, Δn_imp is negligibly small due to the depletion of the transient nanoplasma.