ХИМИЧЕСКАЯ ФИЗИКА, 2004, том 23, № 2, с. 20-23
ЭЛЕМЕНТАРНЫЕ ФИЗИКО-ХИМИЧЕСКИЕ ПРОЦЕССЫ
y^K 539.184.186
DIFFERENTIAL OPTICAL COLLISIONS IN THE KAr(4s-ty) SYSTEM
© 2004 r. C. Figl*, J. Grosser*, O. Hoffmann*, F. Rebentrost**
*Institut für Atom- und Molekülphysik, Universität Hannover, 30167 Hannover, Germany **Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany Received 16.11. 2002
We report experiments on differential optical collisions in the KAr(4s-4p) system. The observed oscillatory structure is used to test existing potentials with an accuracy of the order 0.1 to 10 wavenumbers. The fraction of K(4p1/2) formed is a direct measure of nonadiabatic transitions in the exit channel of an optical collision.
1. INTRODUCTION
Interatomic potentials have been determined experimentally with an accuracy well below 1 cm-1 by using spectroscopic techniques. However, the standard techniques are applicable to regions where bound states exist. The repulsive parts of potentials can be studied by collision or half collision experiments. Changes in these parts of the potentials of just a few wavenumbers are visible in the interference structures of the differential cross sections of optical collisions [1]. Furthermore, nonadiabatic transition probabilities measured through the observed K(4p1/2) fraction are dependent on the potentials at intermediate to large interatomic distances. A combination of the experimental techniques and the theoretical methods is therefore a promising approach to obtain interatomic potentials that are more reliable over a greated range of interatomic distances.
In the presented work, we study the differential optical collisions
K(4s) + Ar + hv KAr(BE) — K(4p1/2, 3/2) + Ar.(1)
Spectroscopic measurements have already been performed for this system to derive the XL, An and BE potentials [2]. In addition to that, newer quantum chemical calculations for the same potentials have are available [3, 4]. The potential data are shown in Fig. 1.
In the following we discuss the experimental setup and the theoretical methods used to make a comparison with our results. We present data of differential optical collision cross sections obtained over a range of collision velocities and demonstrate the measurement of nonadiabatic transitions in the KAr system.
2. SETUP FOR DIFFERENTIAL OPTICAL COLLISIONS
Since the experimental method of differential optical collisions has been described in detail in [5], only a brief summary is given here. A thermal beam of potassium provided by an oven intersects perpendicularly a supersonic argon beam from a pulsed nozzle (Fig. 2). The scattering volume is illuminated by two laser
beams. One of them, the excitation laser, is detuned by 480 cm-1 from the K(4s) —► K(4p1/2) resonance energy. The detuning specifies the K-Ar distance at which the optical transition can occur (Condon radius), as well as the state that can be excited. A detection scheme has been developed to allow an angular- and time-resolved detection of the outcoming K(4p) atoms. The detection laser is used to transfer the K(4p) atom after the collision to a Rydberg state K(nl) with 20 < n < 40. Depending on the wavelength of the detection laser, K(4p1/2) or K(4p3/2) atoms are excited, allowing a state selective detection of the fine-structure levels. In contrast to a K(4p) state, a Rydberg atom lives long enough to travel
Potential, cm 1
Fig. 1. K-Ar potentials of the XL, An and BL states obtained from spectroscopic measurements by Braune and Zimmermann [2]. Recent abinitio calculations by Jungen [4] (---) and Czuchaj [3] (•••) are shown for the BL state. All potentials are shifted to zero asymptotes. Figl I et al.
DIFFERENTIAL OPTICAL COLLISIONS IN THE KAr(4^-4^) SYSTEM
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Rydberg detector
Pulsed nozzle Detection laser
Excitation laser
Fig. 2. Experimental setup for differential optical collisions. The projectile beam is provided by an oven, the pulsed nozzle together with the skimmer produces a supersonic beam of target atoms. The excitation laser takes part in the optical collision, the detection laser in combination with the detector allows a time and angular resolved detection.
to the rotatable detector. The detector consists of an array of static electric fields which field-ionize Rydberg atoms and guide the ions onto a channeltron where they are detected. The time-delay between the ns laser pulse and the pulse from the channeltron is measured to determine the velocity of the scattered K atom. Thus, the
collision energy of the corresponding collision pair and the scattering angle in the center-of-mass system can be calculated. This is the most striking difference to optical collisions in gas cell experiments where a differential detection is not possible.
The present data of the optical collision experiments are preliminary to some extent. Due to problems in the velocity measurements we expect a certain systematic error of the collision energy in our data. Nevertheless, the results are considered to be qualitatively correct and show that the experimental methods work in principle.
3. DIFFERENTIAL CROSS SECTIONS
Differential cross sections are measured by varying the laboratory scattering angle. Results for different velocities of the scattered potassium are shown in Fig. 3.
The oscillations in the differential cross sections are due to interfering pathways. For a given scattering angle and velocity of the scattered potassium tm there are two possible trajectories for every Condon radius: the optical transition can occur on the incoming or the out-
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Fig. 3. Differential cross sections in the laboratory frame. Each box corresponds to a velocity of the scattered potassium atoms which is indicated at the side of the box. The data has been multiplied by the sine of the scattering angle, units are arbitrary. The lines are spline fits to the measured points. The error bars include the statistical error. Figl I et al.
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Fig. 4. Experimental differential cross section for a velocity of the scattered potassium of 1025 m/s in comparision with theoretical convoluted data using the potentials of Fig. 1: 1 - [2], 2 - [3], 3 - [4].
going part of the collision. The phase difference of the two pathways leads to oscillations in the interference pattern. These phase differences arise due to the motion on either the XL and BL potentials inside the Condon region. In our experiment, the maximal collision energies are around 2000 cm-1 which sets the high energy limit of the potential that can be accessed. In conclusion the interference pattern is determined mainly by the XL and BL potentials for K-Ar distances from the Condon radius to the classical turning point.
When there is more than one Condon radius, the number of trajectories increases and the oscillation structure becomes more complicated. With a detuning of 480 cm-1, there are two Condon radii, one at 8.4 a.u., the other one at 6.3 a.u. Nevertheless, the inner one is accessible only at relatively high collision energies. Furthermore, a smaller impact parameter is needed to reach the inner Condon radius leading to a smaller weight of the corresponding trajectories compared to those with the larger Condon radius.
3.1. Theoretical methods
From a set of potentials, differential cross sections d<5cJdQ are calculated in the center-of-mass frame for both different collision energies and polarization angles of the light with respect to the relative velocity. The calculations are done by the quantum coupledchannels method of optical collisions. A more detailed description can be found in [6].
For a comparison of dacJd Q with the measured differential cross sections, a conversion from the center-of-mass frame to the laboratory frame is performed and the experimental resolutions are taken into account by a convolution procedure. Of the factors controlling the experimental resolution we consider in particular the velocity distribution before the collision both the potassium and the argon beams, the dimensions of the scattering volume as well as of the aperture of the detector and the resolution of the velocity of the scattered atoms. The nozzle of the target beam and the individual openings of the projectile beam source have been assumed as point sources. Furthermore, the different times-of-flight of the ions inside the detector as a function of their point of origin have been corrected for.
In Fig. 4 we give a comparison of the measured differential cross section and the calculated ones using different potential sets. Clearly considerable differences in the oscillatory structures are seen. We have developed a fitting procedure in which the starting potentials can be varied systematically to reproduce the experimental data. In the case of Na-rare-gas collisions, it has been demonstrated that a change in the potentials of several wavenumbers in the corresponding region is visible in the differential cross sections [1, 7].
4. NONADIABATIC TRANSITIONS
In the outer part of the wells of the АП and BL curves, nonadiabatic transitions from a BL to a K(4p1/2) state occur. The transition probability depends on the collision energy and on the details of the potentials in this region. It can be directly measured via a final state analysis of the optical collisions 1. The energy of the photon hv is detuned here from the K(4s) —► K(4p1/2) resonance energy by 480 cm1 so that the collisional complex KAr(XL) is excited to KAr(BL) while the collision energy is well defined. When the two atoms separate, the system passes only once through the transition region.
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