Integral cross sections for electronic excitation in KHg collisions

Volume 56, number 1

15 May 1978

CHEMICAL PHYSICS LETTERS

INTEGRAL CROSS SECTIONS FOR ELECTRONIC R. DijREN, U- KRAUSE and G. MORITZ fiir Striimungsforschung, O-3400

MexPianck-lnshlut

EXCITATION IN K-Hg COLLISIONS

Giittingen.

Germany

Received II January 1973

The energy dependence of the integral cross section for the electronic excitation in collisions of K and Hg is investigated for er?ergiesbetween 50 eV and 1500 eV. By the measurement of the spectra of the emitted light the 4*Pjn and the4*Pla states of poQs.siumare found to be dominant. For these the energy dependence of the cross sections is studied in detail. By the measurement of the polarization the contributions to the 4*P3,* state are differentiated with respect to Im$-

1_ Introduction In this communication we want to report about measurements of excitation cross sections and the polarization of the alkali resonance lines in K-Hg collisions for center of mass energies between 20 eV and

1250 eV. This is the first completed set of our measurements in the series of a systematic study of the alkali-mercury interaction_ The main goal of this paper is to present all the experimental information available from integral excitation cross sections for the particular example of K-Hg. Some aspects of this interaction are very similar to the alkali-rare gas interactions for which many experimental * and theoretical studies (calculation of potentials [3]) have been published. In the context of our studies of the alkali-mercury interaction we have performed a pseudopotential calculation of these systems [4] based on the well-known ground-state interaction [.5] _More recently the differential cross section of laser excited Na 32P,,, interacting with Hg has been

given [6,7J _ Finally the differential cross section with energy analysis of the scattered alkali atoms has been measured [8]. The measurements of this report extend measurements given before by ether groups [9, lo] with respect to both the differentiation of the exit channel and the energy range. * For experiments with collisional excitation see ref. [ l] and for experiments with excited states see ref. [21 and references in these papers62

2. Experimental A survey of the experimental fig. 1. It has been described

apparatus

earlier [ 11,121

is given in

so that a brief description will be sufficient here. In this apparatus a neutral atomic beam at energies between 25 and 1500 eV is produced in a charge exchange oven_ The atoms pass through a scattering chamber and are monitored by two detectors. Light produced in the scattering chamber by the excitation process is observed perpendiculariy to the beam by focussing the active volume within the scattering chamber on the entrance slit of a spectrometer_ A polarizer is inserted into the light path. The intensity at the exit slit is measured by counting the pulses from a photomultiplier (Ga-Ascathode, dark current: 2 counts/s)The scattering chamber is a heatable stainless steel chamber with a baffled container for the Hg connected to it- The container can be closed by a valve. By a special design of the valve and an additional magnetic shield inside the scattering chamber the magnetic field in the scattering chamber from the magnet of the valve and the heating of the scattering chamber has been reduced to one fifth of the earth magnetic field. Thus the distortion of the orientation in the measurement of the polarization can be considered negligible_ The temperature of the chamber is stabilized to 20.02 K. The polarizer can be rotated to measure the intensity parallel and perpendicular to the direction of the beam. The additional polarization caused by the opti-

BEAU

15 May 1978

CHEMICAL PHYSICS LETTERS

Volume 56, number 1

UONITOR

II

BEAM

MONITOR I

SOLOMETER

LIGHT-EMISSION

ISLOWI

I FAST)

FILTER FOR POLARIZATION RFTm PLArr LENSE --q

I /

1

I

I I

I

s ,

-

CHARGE EXCHANGE OVEN

/

SPECTROMETER

PHOTO-MULTIPUER

B

Fig. 1. Schematic view of the apparatus cal system has been reduced by a retarding plate. A check of the residual polarization has been performed with a tungsten lamp and confirmed with the unpolarized radiation from the 42P1~2-%2s1~2 transition. In earlier work we have used a calibrated bolometer detector [ 121 which has the advantage of a well-known energy dependence of the efficiency but, at least in our set up, the disadvantage of a long time constant (= 1 min). This disadvantage is severe since it does not allow in practice to renormalize the momentaneous measured intensity of the light with respect to the intensity of the atomic beam. To avoid this a second scattering chamber has been put into the beam and the light from the collisional excitation in this second chamber is used to monitor the beam. This detector in which CO, is used as a target gas is calibrated with the bolometer or at low energies with the excitation cross section measured earlier by Kwan 1131. The experiment is controlled by a small computer for which the program [ 141 scans preselected ranges of the collision energy and of the wavelength of the spectrometer. For a given energy the spectral range is scanned several times until a satisfactory average is obtained. The measurement of the complete spectrum between 3000 A and 8000 A takes typically 24 h. This type of measurements has only been performed for a few energies to establish the general behaviour of the spectra. From these measurements one finds that the resonance states of potassium are predominantly populated.

To measure the energy dependence of the excitation cross se.Aons of these states a repeated scan over the doublet is performed (= 10 min per energy). The intensity of cbe light is reduced by the simultaneously measured intensity of the primary beam (detector I). Thus the cross sections for the specified states are obtained from the intensities at the centers of the lines. Then the program proceeds to the next energy. A final averaging is performed by repeating the energy scan several times.

3. Results

For the proper evaluation of the experimental data of the cross section for a particular state and for the theoretical treatment in a potential calculation [4], first a survey in the observed spectra of the light is needed. Measurements of these spectra have been performed at various collision energies but they are not given here [ 15,161 since they have as the most remarkable result that the excitation of the 42P,,z and the 42Pl,2 states strongly dominate in the spectral range and in the energy range considered here. Quantitatively the ratio of the sum of the cross sections for the two resonance states to the sum of the cross sections referring to all the remaining lines between 3000 A and 8000 A has been determined. For 1250 eV we obtain: F

o&,/(03/2

+ 0’12) G 2 X lO-3

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CHEMICALPHYSICS LETTERS

15 May 1978

where we have labelled with oi specifically the cross sections for the 42P,j2 and 42P1j2 states. This result should hold for the lower energies as well_ Obviously the interesting range of some important Hg-excitation processes decaying with ultraviolet radiation are not covered by our spectral range. But these excitations have been considered in another experiment in our institute [8] by measuring the energy loss of the projectile in a time of flight analysis. There the lOWei limit for the excitation of other states than the resonance lines is given by the noise of the differential cross section which leads to a difference of at ieast two orders of magnitude: Coq(o312 i

f oq

G 10-2

_

From these results two conclusions are drawn: (1) In the experimental evaluation of the resonance lines contributions from higher states due to cascading decays are neghgible. (2) In the calculation of the potentials a comparably small basis of alkali wavefunctions and the treatment of the mercury, as a polarizable target represented by HF densities can be considered sufficient at the present time. The next result to be considered is the energy dependence of the excitation cross sections for the two individual fme structure levels which are displayed in fig. 2 together with their ratio. Together with the measured points (dots) a cubic spline smoothing the data is given. The cross sections are given here in arbitrary but comparable units. From the temperature of the scattering chamber, the vapour pressure of Hg and the measured efficiency of the light detecting system the absolute value of these cross sections has been determined as well with the result that o@*p3,2,

Ec_u,. =837eV)=15A2+25%.

The large error that we give with this particular value is due to the uncertainty in the Hg density and the absolute calibration of the light detecting system. In the energy dependence of the cross sections the one for the P3,2 state is seen to be larger than the one for the Pt/2 state throughout the energy range investigated_ Except for the continuous increase of the Psi2 cross section the cross sections show a common Landau-Zener-type behatiour with maximum around 64

I

250

500

Collision

750

energy

1000

I

1250

ECM CeVl

Fig- 2. Energy dependen- of cross sections and ratio for the excitation of K 4*P,,, and 4*Prj2 in collisions with Hg (open circles from ref. [ 9 1).

140 eV. Together with the threshold measurements [P, lo] this behaviour supports the coincidence of the avoided crossings of all mi = l/2 states at small internuclear distances (4.58 au) which has been found in the pseudopotential calculation (see fig. 3 of ref. [4]). Considering the ratio of the two cross sections one fmds, that it is at high energies with a limiting value of six comparably far from the statistical population of two. At the lower end of our energy range the ratio is accidentally equal to the one for statistical population decreasing further for lower energies [9 1. It is interesting to put this result into relation to the comparable measurements of K interacting with the rare gases [ 11,173. Then it is seen that with increasing number of electrons (and therefore polarizability) of the target the ratio and thus the deviation from the statistical population increases as does the energy at which this deviation still holds. For He as target nearly no deviation from the statistical population is observed, for Xe one fmds a comparably narrow maxi-

15 May 1978

CHEMICAL PHYSICS LEl-fERS

Volume 56, number 1

mum with a vahre of approximately 3.5 at about 70 eV collision energy, while in our case no “fmal” maximum is observed and the value stays at about 6 from 500 eV upward to 1250 eV. By measuring the polarization of the emitted light a further differentiation of the cross sections for the 42PS,2 state is possible namely with respect to the absolute value of the projection quantum number mi (Without polarization of the atoms of the beam before the collision - only au alignment iu the exit channels is produced and observable.) Fig. 3 shows in

the upper panel the measured polarization of the light as a function of the collision energy. The error bars represent the statistical error; the constant displacement of the total function due to the residual polarization of the apparatus is less than 0.002. Together with the experimental points a smoothing fit to these points is given. From this polarization and the total cross section fori = 3/2 (see fig. 2) the individual cross sections for lm$ = 312 and lm,l = l/2 labelled as o{~,, are derived according to the relations given by Fauo and Macek [ 18]_ Appropriate corrections for the not resolved hyperfine structure and the isotopic mixture of K have been taken into account. These cross sec-

I

I

tions are displayed in the central panel (the values given are in the same units as u3j2 and 01j2 in fig. 2). Averaged over the observed oscillations the o$fi, cross section is seen to rise throughout the energy rang{ considered while the 0312 ,1,2, cross section stays nesrly constant after reaching a first maximum at comparably low energies. This general behaviour of the cross section cr$&, and its size (especially at high energies) is seen to be nearly the same as the one for ali2 in fig. 2. Finally we have in the lower panel of fig. 3 the ratio of which shows a very similar pattern in the o%!,G%, energy dependence as the polarization itself. This is easily understood by the fact that the polarizatron can be written as a function of this ratio of cross sections alone. Qualitatively ah these observations are compatible with the calculated potentials (see fig. 4 of ref. [4])_ Starting at very low energies above threshold as measured by Kempter et al. [9 ] only the radial coupling l/2 states is active which leads to connecting the a ratio 03/2/a1/2 = 1 i.e. lower than the statistical population. Accordingly we find in our measurements a tendency toward positive polarization i.e. ratio o$2,/~j$$,, < I. At the lowest energy of our measurements one finds accidentally statistical population with 03/2/0112 = 2. At this energy the polarization measurements show in addition that all three possible channels are opulated with equal weight demonstrated by = l_ This means that compared with the o&e%% lowest energies rotational coupling must have increased enough to populate the ]mil = 3/2 states sufficiently. From the spacing in the oscillatory structure discussed below one is led to the conclusion that this rotational coupling is not a direct one between the excited state and the ground state, but within the excited states. At Mj

lSO-

i/---...

Ino-

I

collisionenergy I& [eVl Fig. 3. Energy dependence of the polarization of the light emitted from K excited to the 4*l& state in collisions with Hg (upper panel), cross sections #,,, , (central panel) and ratio (lower panel) for lmlj = 312 and &z,i = l/2.

=

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Volume 56, number 1

CHEMICAL PHYSICS LE-I-IERS

higher energies this channel increases further while the lmjl= l/2 channels (with radial coupling) have constant cross sections. By this at high energies the negative polarization and the comparably large positive deviation from the statistical population is induced. Upon the coarse structures discussed so far various

15 May 1978

Acknowledgement We want to acknowledge the contributions of H. Pauly in various discussions and of H. Hiibner in establishing most of the computer facilities for the measurements.

Qscillations are superimposed well visible in the ratio 03/2/01/2 (fig_ 2) and better in o$~,/o~/&, (fig. 3)_

For the first case a satisfactory e&&&on has been given before [4] namely that the observed extrema are due to the existence of a second avoided crossing at medium internuciear distances. For the second case the most obvious explanation is that inside the crossing radius at small internuclear distances the interact@ of B 2C,,2 or A2111j2 with A2fi3,2 via rotational coupling yields the oscillations observed. Note that we have used various simplifications in the course of this qualitative discussion. In particular the identification of the fiied frame and collision frame deserves some reservations at low energies but it should hold well in the high energy range.

4. Concluding remarks In summary, the experimental material described in this paper gives a complete account of the data available in such experiments. The spectra yield the amount of states activated in these collisions and the energy dependence of the dominant states is given. By the measurement of the polarization the contributions to the P,,, state with the projection quantum numbers l/2 and 3/2 are resolved. Concerning the mechanism of interaction one fmds most aspects of a calculated set of potentials confirmed. But we want to stress the point that the remarks concerning this agreement are definitely to be understood in a qualitative sense_ Further work in the framework of a close coupling calculation on the basis of the full quantum mechanical treatment are in progress_

66

References [1] J-0. Olsen, N. Andersen and T. Andersen, J. Phys. B 10 (1977) 1723; W. Meckienbrauck, J. S&in. E. Speller and V. Kempter, I. Phys. B 10 (1977) 3217. VI G.M. Carter, D.E. Pritchard, M. Kaplan and T-W. Ducas, Phys. Rev. Letters 35 (1975) 1114; R.E. Smalley, D.A.Auerbach, P-S-H. Fitch, D.H. Levey and L Wharton. J. Chem. Phys. 66 (1977) 3778; W.D. Phillips, CL. Giaser and D. KIeppner, Phys. Rev. Letters 38 (1977) 1018. I31 R. P. Saxon, R.E. Olson and B. Liu, J. Chem. Phys., to be published, and references therein. r41 R. Diiren, J. Phys. B 10 (1977) 3467. 151 U. Buck, M. Kick and H. Pauly, J. Chem. Phys. 56 (1972) 3391. I61 R. Diiren. H-0. Hoppe and H. Pauly, Phys Rev. Letters 37 (1976) 743. 171 R. DBren and H-0. Hoppe, submitted for publication. 181 E. Sch&llich, Doctoral Thesis, Gbttingen (1978). 191 V. Kempter, W. Koch and C. Schmidt, J. Phys. B 7 (1974) 1306. 1101 R-A. Larsen and D-R. Herschbach, to be published (1978). 1111 R. Diiren, M. Kick and H. Pauly, Chem. Phys. Letters 27 (1974) 118. 1121 M. Kick, Report Nr. 126/1974, Max-Planck-Institut fiir Strbmungsforschung, GSttingen (1974). [ 131 K.Ch_ Kwan, Report Nr_ 129/74, Max-Pianck-Institut fiir

StrZimungsforschung, GBttingen(1974). [ 141 H. HClbner,Report Nr. 10/77, Max-PIanck-Institut fir

Str6mungsforschung. Cijttingen (1977). [15] G. Moritz, Doctoral thesis, Giittingen (1978). [ 161 U. Krause, Diplom thesis, Gt%tingen (1978). [17] V. Kempter, B. Kiibler and W. Mecklenbrauck, J. Phys. 7 B (1974) 2375; W. Mecklenbrauck. Doctoral thesis, Freiburg (1976). [ 181 U. Fano and J.H. Macek, Rev. Mod. Phys. 45 (1973) 553.