) Verschur, J. W.; van Linden van den Heuvell, H. B. Chcm. Phys. 1989. 129,l. Chupka, W. A. J. Chcm. Phys. 1987

Abstract

8103 the methyl iodide molecule as quasi-diatomic, the cytindrical symmetry of the problem allows us to place the perpendicular transition dipole vector anywhere in the x-y plane. Lao et al. define their perpendicular transition dipole as being in the (l,l,O) direction, but the algebra is somewhat less cumbersome if the dipole is chosen along either the x or y molecule-fixed axes. The electric vectors for the incident and scattered radiation are given in our coordinate system by 8, = 2 cos 7 + 2 sin 7 8, = 2 cos 8 + P sin 8 (A.4) The scalar products of transition dipoles with polarization vectors produce 81-& = cos 7 dZx + sin 7 q5zz 4+i2 = cos 7 dXx + sin 7 q5xz 8s.fil = cos 8 Ozx + sin 8 &y < T I I T I I > = <T22T22> = (1/15)(2 cos2 7 cos2 B + 1) <TI2Tl2> = <T2'TZ1> = (1/15)(sin2 7 COS' 0 + sin2 0 + 1) <TIIT22> = <T12TZI> = <T2lTl2> = <T22Tll> = (1/30)(3 cos2 7 cos2 B -1) (A.6) Equations A.6 apply to experiments in which both the incident and scattered polarization are determined. However, we determine the polarization only for the incident photon, collecting scattered photons of all polarizations. To obtain the orientation averaged geometric factors for this case, eq A.6 is integrated from 0 to r over the scattered light polarization direction angle 8. This averaging over 0 reduces eq A.6 to <TIITII> = <T22T22> = (*/15)(cO~' 7 + 1) <TI2Tl2> = <T2,T2,> = (*/30)(sin2 7 + 3) <TIIT22> = <Tl2T21> = <T2lT12> = <T22Tll> (*/60)(3 cos2 7 -2) (A.7) The geometric factors for our experiment are summarized in Introduction Multiphoton ionization of diatomic molecules has been studied in recent years by a variety of techniques and is generally well understood.' The ionization is predominantly due to resonance-enhanced multiphoton ionization (REMPI) processes, whereas nonresonant multiphoton processes only play a minor role. Dynamical aspects of the interaction of laser radiation with molecules have been studied by several groups using conventional and zero kinetic energy (ZEKE) photoelectron spectroscopy* as well as ion detection techniques. However, detailed studies of the excitation processes and the different decay channels of highly excited states, which are embedded in the ionization and in the fragmentation continuum, are very rare up to now. The under- studies of molecular Rydberg states of H2, Liz, and Na2 have shown how complex direct photoionization can be! Only recently we have reported on the interaction of a particular bound doubly excited molecular state with different continua and the competition between the various decay channel^.^ In that study we used femtosecond laser pulses as an experimental tool to distinguish between the dissociative ionization of the molecule and the neutral fragmentation with subsequent excited-fragment photoionization. Both processes, which may lead to formation of the same fragment ion, are difficult to distinguish when using nanosecond or even picosecond laser pulses. This distinction is of particular importance in multiphoton ionization studies of metal cluster systems. The multiphoton ionization and fragmentation of alkali-metal dimers and, in particular, of Naz has attracted considerable current interest. In many experiments it has been found that, in conjunction with the formation of Na: ions, the atomic ions Na' are also formed. REMPI processes via A'Z: or the B'n, states are responsible for this observationn6 Ionization and fragmentation studies of Na2 Rydberg states involving vibrational-rotational autoionization have also been reported recently.' However, the final continuum states have been analyzed only in very few experiments. Examples of such detailed studies include the twophoton ionization and dissociation of Na2 resonantly enhanced by the intermediate 2'2: double-minimum state where the kinetic energy of the ionic fragments is measured* and the fragmentation of the neutral molecule Na2** into Na*(3p) + Na*(3p) where Doppler spectroscopy is applied to measure the angular and energy distributions of the neutral fragment^.^ Time-resolved measurements often open up new directions and provide a more comprehensive view of the physical and chemical processes. Due to recent developments in the generation and amplification of ultrashort light pulses, direct measurements of transient ionization and fragmentation spectra with femtosecond resolution are now possible. This allows a closer look at the dynamical aspects of molecular multiphoton ionization. In a series of beautiful experiments in the gas phase and in molecular beams, Zewail and co-workersI0 have demonstrated the enormous advantage of applying femtosecond lasers to the study of molecular dynamics. Their pioneering work in the field of femtosecond photochemistry and transient molecular fluorescence spectroscopy has initiated several other time-resolved ultrafast laser studies.'' The observation of transient molecular fluorescence spectra in Zewail's femtosecond pumpprobe experiments and the analysis using Heller's wave packet methodI2 show that detailed information about different processes is obtained from the real-time motion of wave packets in potential energy surfaces. Therefore, by probing ultrafast molecular dynamics with femtosecond lasers, the transient characteristics of processes like molecular ionization and fragmentation can also be studied in great detail. In this paper we present and discuss experimental results of time-resolved studies of molecular multiphoton ionization of the diatomic sodium molecule in molecular beam experiments applying femtosecond pump-probe techniques and ion and electron spectroscopy. Experiment In our femtosecond laser-molecular beam studies of multiphoton ionization processes, we have used a combination of experimental techniques. Femtosecond laser pulses are used to induce and probe the molecular transitions. A supersonic molecular beam provides the Na2 molecules in a collision-free environment and restricts the set of initial states to u" = 0, J". Time-of-flight (TOF) spectroscopy is used to determine the masses of the ions, the released kinetic energy of the ionic fragments, and the energy distribution of the ejected electrons. Because the ion and electron collection angles are fixed, the ion and electron angular distributions can be studied by rotating the laser polarization. The laser system and the schematic experimental arrangement of the molecular beam and the ion and electron TOF spectrometers are shown in The resulting pulse broadening, mainly due to GVD in the dye amplifiers was reduced in the pulse compression unit. The amplified and recompressed 70-fs laser pulses of 100 A spectral width are nearly transform limited. The Fourier transform limit of 70-fs laser pulses assuming 'sech2 pulse shapes is 60 A. Experimentally it is difficult to reach that limit because of nonlinear chirp contributions in the amplification process. At an earlier stage of the experiments we had amplified the CPM output (1 SO-MHz pulse train) in a onastage N2-laser-pumped rhodamine 6G to produce pulses of 10-nJ energy and 120-fs time duration. For the pump-probe experiment we used a Michelson arrangement to delay the probe laser relative to the pump laser. A stepper-motor-driven linear precision actuator with 0.05-pm feed in one arm of the interferometer sets the time delay. Both the pump and the probe laser beams enter the interaction region collinearly with the same polarization and perpendicular to the molecular beam. We used recompressed laser pulses of 70-fs duration, about 100-A spectral width, and 0.2-pJ (I = 50 GW/cm2) for both the pump and the probe. The laser pulse energy was kept this low in the pumpprobe experiment to simplify the study of the basic physical processes. Results and Discussion The ion TOF spectrum displayed in The results of that paper are shortly summarized here. The ionization-enhancing intermediate electronic state 2'II (3s,3d) is populated by a two-photon absorption process. The i l l l state is then photoionized by absorption of a third photon leacfing to Considering the 120-fs time duration of the laser pulses, the observed "slow" and "fast" Na+ ionic fragments have to originate from processes occurring at small internuclear distances. Therefore, predissociation of Naz* and photoionization of Na* as the origin of the ionic fragments can be ruled out. Absorption of one more photon from still the same femtosecond laser pulse induces the bound-free transition 22:-z2: in the molecular ion Na: leading to recoil energies Wof the ionic fragments Na+ that agree with the value W = 10 500 f 500 cm-I obtained from the analysis of the ion TOF spectrum. On the basis of both the measured electron spectrum and the distribution of recoil energies W = 900 f 400 cm-' obtained from the analysis of the "slow" ionic fragments Na+, the excitation and the decay of doubly excited molecular states of Naz is found to be a second multiphoton ionization channel for diatomic sodium. The electronic autoionization of a bound state of Naz** into the two continua zZ+ and '2: as well as the autoionization-induced fragmentation fia2** -Na+ + Na + e-(&,,) + W are very important processes with regard to the dynamics of highly excited molecules. A very interesting question is, what happens with the molecule during the multiphoton ionization and fragmentation when we look at it on a femtosecond time scale? What are the dynamics of these processes, and does the molecule absorb one photon after another or all at once? Our interest is focused on the dynamics of molecular multiphoton ionization on a femtosecond time scale and on the coherence or incoherence of the contributions to the ionization step. The first time-resolved studies of molecular multiphoton ionization in a molecular beam using femtosecond pumpprobe techniques" revealed unexpected features of the dynamics of the absorption of many photons by a diatomic molecule. The observed femtosecond ump-probe delay spectrum, corresponding to the experimental parameters of the measurement were 70-fs laser pulse duration, 0.24 pulse energy, and A-= 627 nm. The spectrum shows a beat structure superimposed on a strong modulation of transient Na, P ionization spectrum is shown in This is easy to understand from the superposition of two oscillations. For two oscillations in phase at zero delay time the envelope intensity is at its maximum value for At = 0. However, the superposition of two oscillations with a phase shift of 180° at Af = 0 leads to an envelope variation showing its minimum value at At = 0 and increasing values for increasing delay times At. The strong modulation of the signal decreases for longer delay times. With the given experimental parameters, the observed dynamics can best be understood in terms of the motion of wave packets in bound molecular potentials. A Fourier analysis of the pump-probe delay spectrum ( For higher laser intensity and A-= 618 nm, additional lower frequency components appear, which are attributed to wave packet motion in the 4'2: shelf state and will be discussed elsewhere.ls From the transient Na: ionization spectrum ion zZl, u+ = 0 is 0.976, and 0.906 for the transition u' = 20 to u+ = 20. Thus, ionizing transitions, leading to electron energies of about 7050 cm-I for the applied laser wavelengths, may occur with equal probability for all internuclear distances between the inner and outer turning points. Analysis based on the difference potentials 2'n -AiZ: (displayed in The relevant RKR potential curves and the preparation and probing of the A-state wave packet motion are shown in The Fourier analysis ( An interesting question is now, are these two contributions to the observed oscillating Na: ionization signal just two different intramolecular ionization pathways, whose amplitudes have to be added coherently to account for the observation, or do these contributions come from two independent multiphoton ionization processes resulting in distinguishable final states, to require incoherent addition of intensities? If we apply only Franck-Condon arguments, there is no reason why direct photoionization of the Rydberg electron should take place only at the outer turning point for the given vibrational levels v*. Moreover, the difference potential analysis a plied to the probe recently performed wave packet calculations by Enge122 show that transition Na:(2lIIg, u* = 11-18) -Na:(2Z,, P u+) and also the In order to gain more insight into the anticipated ionization process, we have performed another time-resolved experiment where we now measured the variation of the "slow" Na+ ionic fragment signal as a function of the delay time between the femtosecond pump and probe laser pulses. The experiment showed a striking result. The observed transient Na+ photofragment signal is shown in the lower part of The excitation of the inner electron of the Na2*(3s,3d) Rydberg state by the probe laser into a higher orbital n'l', to form a neutral electronically doubly excited Na2 molecule, is such a process. A doubly excited molecule Naz**(nl,n'l') may electronically autoionize, to form Na: as well as the fragments Na+ + Na + ein a three-particle breakup, to give the observed electron and Na+ ionic fragment kinetic energy distributions shown in Reasons why such a "core" excitation occurs in this case only at the outer turning point of the 2Ing state could be the relative location of the two potentials involved and a strong R dependence of their electronic transition moment. Note that no calculations have yet been reported for molecular doubly excited states in this energy range.24 The two-photon-pump and one-photon-probe ionization process, which involves excitation and decay of a doubly excited state, is illustrated in (24) Only potential energy curves for excited states of Na2** up to the (3p molecules. From the observed ion and electron spectra, these molecules have different ionization and fragmentation channels compared to direct photoionization and bound-free fragmentation. This second autoionization decay leads to the observation of the "slow" ionic fragments Na+. The actual kinetic energy of the electron and the Na+ fragment in this three-particle breakup is determined by the internuclear distance R where the autoionization takes place. The energy released in this process is E = E(Na2**) -E(Na* + Na), and it is shared between the ejected electron and the ionic and neutral fragments Na+ and Na, respectively, Conclusion In conclusion, we report here on the first study in a molecular beam experiment where femtosecond pumpprobe techniques have been used in combination with ion and photoelectron spectroscopy to study the dynamics of molecular multiphoton ionization. For the study we have chosen the spectroscopically well-known diatomic sodium molecule as a prototype. Our results reveal unexpected features of the dynamics of the absorption of many photons by a diatomic molecule. The measured pump-probe ionization and photofragmentation spectra show oscillatory structures and the Fourier analysis of the spectra indicate that under our experimental conditions two major contributions to the spectra exist. The detailed analysis of the transient Na: ionization spectra measured with 70-fs pum and probe pulses shows that Three arguments led us to the conclusion that, for Na:, two different multiphoton ionization processes exist, requiring incoherent addition of the intensities to account for the measured signal: the observation of two different oscillation periods and their 180° phase shift, the time structure of the transient 'slow" Na+ photofragmentation signal, and the difference potential analysis. wave packet oscillations in the A'Z, P and the 2lI4 potentials occur. The direct photoionization of an excited electronic state, where one pump photon creates a wave packet in the A'Z: state and two probe photons transfer that motion via the 2'll state into the Na:(*Z;) ionization continuum is one process, +he second involves excitation of two electrons and subsequent electronic autoionization. Here two pump photons create a wave packet in the 2lII, state and one probe photon transfers its motion into the ionization continuum, but this happens only at the outer turning point of the 2'II, state. This particular process involves a bound doubly excited state of diatomic sodium, which through electronic autoionization forms Na: molecular ions and by autoionizationinduced fragmentation Na+ ionic fragments. In this second multiphoton ionization process the probe photon is absorbcd the first time about 180 fs after the pump photons have been absorbed and then periodically after each round trip of the wave packet, but only at the outer turning point. The timeresolved motion of the wave packets in two molecular potentials clearly shows there are two different multiphoton ionization processes rather than two intramolecular pathways. An interesting problem, which will be addressed in a forthcoming publication,2' is the relative strengths of the two multiphoton ionization processes for higher and higher laser field intensities. A method based on maximum entropy is developed in order to calculate the impact parameter distribution fib) for dissociation of a parent compound into two fragments. The method provides the least biased P(b) distribution based on (1) whatever dynamical data are available and (2) the prior statistical information, which includes conservation of energy, linear momentum, and angular momentum. This information can often be used to decide whether a dissociation producing two fragments is concerted or stepwise. The data used to determine f i b ) can include, for example, the vibrational and/or rotational distribution of the fragment(s), the recoil velocity distribution, and vector correlations. The method is illustrated by use of recent data on the photodissociation of formaldehyde. Acknowledgmen