ОПТИКА И СПЕКТРОСКОПИЯ, 2007, том 103, № 2, с. 335-339
ПРОСТРАНСТВЕННО-ВРЕМЕННАЯ ЭВОЛЮЦИЯ ВОЛНОВЫХ
ФУНКЦИЙ, УПРАВЛЕНИЕ КВАНТОВОЙ ДИНАМИКОЙ ^
С ПОМОЩЬЮ КОГЕРЕНТНЫХ ПРОЦЕССОВ
УДК 535.14
CONTROL OF BRANCHING RATIO IN THE PHOTOFRAGMENTATION OF DCl+ IONS: EFFECT OF INITIAL VIBRATIONAL STATE © 2007 r. M. V. Korolkov*, **, H. G. Breunig**, and K.-M. Weitzel**
* National Academy of Science, Institute of Physics, Minsk, Belarus ** Philipps- Universität Marburg, Fachbereich Chemie, Marburg, Germany Received October 12, 2006
Abstract—Photofragmentation of DCl+ ions alternatively leads to the formation of D+ + Cl or Cl+ + D in competing reaction channels. The branching ratio of the product yields D+/Cl+ has been investigated theoretically by numerically solving coupled time dependent Schrödinger equations and experimentally by femtosecond (fs) dissociative ionization of DCl. The theoretical analysis shows that this branching ratio increases step-like at intensities, which characteristically depend on the initial vibrational state for nonresonant multiphoton excitation. In general the threshold decreases with increasing initial vibrational quantum number. Experimental studies exhibit a similar step-like behavior of the D+/Cl+ branching ratio. Here the intensity at which the step occurs characteristically depends on the chirp of the fs-laser pulses, suggesting that different chirp may lead to intermediate DCl+ ions differing in the effective vibrational quantum number.
PACS: 31.70.Hq, 34.50.Gb, 42.50.Ct, 82.53.Kp
INTRODUCTION
The dissociative ionization of molecules by means of femtosecond laser pulses has received tremendous attention in recent years [1-8]. The process is of fundamental importance with regard to the general interaction of femtosecond laser pulses with molecules. It is one of several competing processes, e.g., rescattering of electrons [9], double ionization [10], generation of attosecond laser pulses [11], localization of electrons [12], control of electronic and nuclear motion [13, 14], etc. For pulses shorter than 100 fs dissociative ioniza-tion implies ionization of the neutral molecule followed by dissociation of the ion. The time required for fragmentation of the neutral molecule and subsequent ion-ization of the fragment is in general longer than this pulse duration. Very recently stimulating results have been reported on the prospect of controlling branching ratios of product intensities by tailored fs laser pulses. For methane strong chirp effects have been reported [15]. For ethanol basically no chirp effects were observed [16]. We have reported the possibility to control the product branching ratio D+/Cl+ in the dissociative ionization of DCl by manipulating the chirp of the laser pulses [17, 18]. In general chirping a fs-laser pulse leads to a longer pulse in the time domain. This is accompanied by a decrease of the pulse intensity, given a constant pulse energy. At first glance it is difficult to distinguish intensity effects from pure chirp effects. In our own study of D+/Cl+, however, we demonstrated that the branching ratio D+/Cl+ can be controlled by a factor 3 by just changing the sign of the chirp [17]. This is a clear manifestation of a pure chirp effect, since
those laser pulses had identical autocorrelation times and thus also intensity. It is clear that we were looking at the dissociation of DCl+ ions in that experiment. The origin of the chirp dependence, however, was not unambiguously resolved. There are two limiting possibilities. Either the chirp effect is coming from the dissociation process itself, i.e., it might be connected to the competition between intra-state excitation and interstate excitation in the molecular ion. Or, on the other hand, the chirp effect could originate from the ioniza-tion process. It appears possible that the properties of the intermediate DCl+ ions, e.g., with respect to the vibrational state, could depend on the chirp of the ionizing laser pulse. In order to shed further light on the origin of the chirp effect we present new experimental and theoretical results on the intensity dependence of the product branching ratio D+/Cl+.
METHODS
Theoretical Calculations
In the first part of this work we have calculated the product branching ratio D+/Cl+ by numerical solution of three coupled time dependent Schrodinger equations in the electromagnetic field of a femtosecond laser pulse. Details of the wavepacket calculations have been described in a previous publication [19]. Only the most important aspects are briefly discussed here. More specifically the lowest three electronic n states (X2 n, 22n, and 32n) of the DCl+ ion are taken into account in this work. The relevant potential energy curves are presented in Fig. 1. One aspect is that there are basically three
Energy, a.u.
Fig. 1. Potential energy curves of DCl+ indicating various initial vibrational states. The vertical arrows indicate a possible multiphoton excitation from the ion ground state at 805 nm. 1 - x2n, 2 - 22n, 3 - 32n.
channels to be considered in this work. The lowest dissociation channel of the ion ground state converges to the formation of Cl+. The first excited electronic 2n state of DCl+ converges to the formation of D+. However, the next higher electronic 2n state again converges to the formation of Cl+. The dipole moments and transition dipole moments are identical to the ones described previously.
All calculations start from DCl+ ions with population put into specific initial vibrational states vin = 0, 8, and 18 as indicated in Fig. 1. Consequently the laser pulse is turned on and the time dependence of the nuclear wavefunctions is calculated, which result in the different fragmentation channels mentioned above. The laser pulse duration applied in the calculations is 45 fs (FWHM). The focus of this work is on the intensity dependence of the product branching ratio. Theoretical intensities refer to peak (maximum) intensities.
Experimental Techniques
All experiments have been performed in the ion source of a time of flight mass spectrometer employing fs-laser pulses with a central wavelength of 805 nm. A description of the experimental setup has been reported in previous publications [17, 18]. Only the most relevant details are briefly discussed at this point. Ions are collected by a double-stage setup with a total acceleration voltage of 2500 V, ensuring very high collection efficiency and negligible discrimination of kinetically hot ions. Experiments have been performed with the laser beam polarized either perpendicular or parallel to
the TOF spectrometer axis. The experimental data shown are for vertical polarization.
Typical pulse duration range from about 50 fs for a chirp free pulse to about 130 fs for a linearly chirped pulse. Typical pulse energies range from 50 pJ to 1 mJ per pulse. The laser pulse is focused by a concave mirror with focal length 75 mm. The effective laser intensity is derived from the measured pulse energy, pulse duration (FWHM) and the focal diameter. The latter was estimated from classical airy discs, which has been found to be in reasonable agreement with values directly measured by the razor edge technique. Experimental intensities correspond to average intensities, since the fluence has been divided by the FWHM duration of the laser pulse. A linear chirp of the laser pulse is introduced by changing the length of a compressor essentially consisting of two gratings.
Deuteriumchloride has been purchased from Sigma Aldrich with 99% purity. Raw data are recorded in the form of averaged time of flight spectra. The integrated ion TOF signals represent the corresponding ion yields. All data with regard to DCl+ and Cl+ discussed in this work include contributions from both Cl isotopes.
RESULTS
In this section we first present results from the numerical wavepacket analysis, followed by experimental results from the fs dissociative ionization.
Numerical Wave Packet Calculations
The main focus of this investigation is on the intensity dependence of the product ion yields for all possible vibrational states of the DCl+ ion. In total there are
39 bound vibrational states within the electronic ground state 2n3/2. For each initial vibrational state the time dependence of the nuclear wavefunctions has been calculated. Ultimately the expectation value of the corresponding wavefunction at the end of the laser pulse gives the final ion yield.
Figure 2 shows the intensity dependence of the product branching ratio D+/Cl+ for three different initial vibrational states, v = 0, 8 and 18. In all spectra shown a pronounced step like behavior is observed, i.e., above a certain intensity the branching ratio increases from below 1 to larger than 1, indicating a channel switching. The effective threshold for switching to the D+ channel is highest for vin = 0, i.e., around 1500 TW/cm2. The threshold is significantly smaller for vin = 8 with 450 TW/cm2. For vin = 18 the threshold even drops to
40 TW/cm2. This trend appears to be in line with the intuitive expectation that the threshold intensity for effective generation of D+ should decrease with increasing vibrational energy in the ion to start with. A closer in-
D+/C1+ 1.8
1.2
0.6
0 1.8
1.2
0.6
(a)
D+/C1+ 6
u_i_i_i......i
(b)
10
1 10 Laser pulse intensity /0/1014, W/cm2
Fig. 2. Calculated intensity dependence of product branching ratio D+/Cl+ for different initial vibrational states: vin = 0 (a), 8 (b), 18 (c).
spection, however, indicates a more complex situation. One aspect is that there are three channels to be considered in this work. The lowest dissociation channel of the ion ground state converges to the formation of Cl+. The first excited electronic state of DCl+ converges to the formation of D+, and the next higher electronic state again converges to the formation of Cl+. We note, that for particular initial vibrational levels excitation by 805 nm photons is in multiphoton resonance
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