Associative ionization in laser-excited sodium 3p+3d collisions

29 September 1995

ELSEVIER

CHEMICAL PHYSICS LETTERS Chemical Physics Letters 244 (1995) 121-126

Associative ionization in laser-excited sodium 3p+3d collisions E. Babenko, C. Tapalian 1, W.W. Smith Physics Department, University of Connecticut, Storrs. CT 06269, USA Received 15 June 1995; in final form 25 July 1995

Abstract Collisions of laser-excited Na(3p) and stepwise laser-excited Na(3d) atoms in a single effusive atomic beam have been observed to result in Na+ ion formation: Na(3p)+Na(3d)--~ Na~-+e-. The cross-section for this process is measured to be approximately 15 times larger than the familiar Na(3p) +Na(3p) ~ Na++e - associative ionization reaction, at relative collision velocities of approximately 300 m/s. Theoretical models discussed here are qualitatively consistent with the experimental results.

1. Introduction

J=l/2 5.12

Associative ionization (AI) in thermal energy collisions of excited alkali atoms has been studied by many research groups under various conditions [ 15]. A simple and easily observable example is the Na(3p) + N a ( 3 p ) - - , N a ~ + e - reaction. Ground-state Na(3s) atoms are excited to the Na(3p) electronic energy level by 589 nm light and associative ionization occurs as a result of collisions of two excited atoms. Here we discuss a more complex reaction, where the total excitation energy lies above the Na ionization energy. Stepwise laser excitation provides collisions of two differently excited atoms, using two single-frequency tunable lasers (589 and 819 nm, see Fig. 1). The intensities of the lasers and therefore population densities of the excited states can be adjusted such that ions mainly from the Na(3p)+Na(3d)---~Na~+e- reaction are observed. Na ÷ ions from the direct photoionization process, i.e. the Na(3d) + hv589nm ---~Na+ + e - reaction (which is i Present address: Chemistry Department, Columbia University, New York, NY 10027, USA.

5.

J=3/2

J=l/2

J=5/2,3/2

2_. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

•. - - . - - - . ~

5s

4

--

--

3

--

--

6160.

2

--

--

;3:]0

1.

--

--

O.

--

--

T

4d 682.67

18330

.93

Fig. 1. Electronic levels and dipole-allowed transitions of the sodium atom.

energetically allowed in our experiment), are separated from the desired Na~ signal using time-of-flight (TOF) mass spectrometry. Then two experiments can be performed at the same atomic beam density and characteristic velocity. In one of these there is no infrared (IR) light present and Na~ ions are produced

0009-2614/95/$09.50 @ 1995 Elsevier Science B.V. All rights reserved SSDI 0 0 0 9 - 2 6 1 4 ( 9 5 ) 0 0 8 7 8 - 0

122

E. Babenko et aL / Chemical Physics Letters 244 (1995) 121-126

Linear polarizer 819nm from Ti:sant,hire laser Polarizationrotator Linear polarizer

Fiber-optics coupling

~'] |

Sodium ~ reference c e l l T

Photodiode(819nm)

Lens ~

~

Frequency-Stabilized ~ Ring Dye Laser I /

,~

• 589nm from ring dye laser

Rotating Linear Polarizer

Nonpolarizing beam splitter combinedbeam (coupler) to the interaction chamber

514rim pumpingbeam

Photodiode(589nm)

Spectra Physics 2030 Argon Ion Laser Iodine cell (for tuning only) Fig. 2. Optical set-up for the experiment. A figure showing the Na atomic beam and time-of-flight ion detection apparatus can be found in Ref. [9]. The 819 nm beam from a Ti:sapphire laser is brought in via an optical fiber. The polarizers and polarization rotator are used to attenuate the 819 nm beam for taking the saturation curve in Fig. 4. For the 589 nm beam, Na and I2 reference cells are used in wavelength calibration and the polarizers are used as variable attenuators in taking the data of Fig• 3. The two laser beams are combined on the nonpolarizing beam splitter and fed collinearly to the atomic beam/interaction chamber (not shown). due only to 3 p + 3 p associative ionization 2 , in the other the 589 nm light intensity is kept low enough such that no Na~ is detected from 3 p + 3 p but 3 p + 3 d AI is observed in presence of 819 nm light• Recording Na~ ion yields from both reactions at different laser intensities allows the ratio of cross-sections for these two reactions to be determined.

2. Experimental method Two single-mode narrow-band lasers are used in these experiments (see Fig. 2). A cw frequencystabilized ring dye laser (Spectra-Physics 380D), pumped by an Ar + laser, is tuned to the Na 3s(2S1/2) to Na 3p(2p3/2) transition. Then IR light from a narrow-band stabilized Ti:sapphire laser (Coherent 899), pumped by another Ar + laser, is brought via fiber optics to the same optics table and tuned to the Na 3p(2P3/2) to Na 3d(2Ds/2) transition (819•482 nm). The IR light is collimated and merged with the 2 An important additional process that can occur in the same thermal-energy collisions is energy pooling, see Ref. [6] and also Ref. [71.

589 nm beam and directed to an interaction chamber. Two sets of linear polarizers and a set of neutral density filters are used to vary intensities of both laser beams. In the interaction chamber, atomic and laser beams and TOF spectrometer axis are mutually perpendicular. Ions produced by collisions in the atomic beam are extracted by approximately 40 V / c m , 1 /zs electric field pulses and directed through a flight tube with steering plates to a Channeltron electron multiplier. Standard TOF technique [ 8,9] allows both types of ions Na + and Na~ to be observed either simultaneously or separately. Generally we use the strong Na + signal from photoionization for coarse tuning of the IR laser frequency. We use the Na~ signal for fine tuning of both lasers as follows• First the IR beam is blocked and the 3 p + 3 p AI signal is observed. The signal is maximized by fine-tuning the 589 nm laser and by adjusting a combination o f steering voltage and extraction-plate pulse width. Then the 589 nm intensity is lowered so that no Na~ signal is observed; the 819 nm IR beam is then unblocked and its frequency is scanned across the 2P3/2 to 2D transition in order to locate the frequency which maximizes the Na~ ion yield• In this scan two peaks are detected

E.Babenko et al./Chemical Physics Letters 244 (1995) 121-126 corresponding to 2D5/2 and 2D3/2 states of sodium 3d fine-structure. The Ti:sapphire laser can be set at the frequency of the stronger transition 2p3/2 --+2D5/2. We vary the intensity of each of the laser separately in order to obtain 'saturation' curves: ion yield versus intensity.

3. Analysis of data As in a previous paper [9], a rate-equation analysis of the ion yields provides the rate coefficient ratio k3p+3d/k3p+3p for the reactions under consideration: dNNa~ (3p+3d) dt

( 1)

and

dNNa~ (3p+3p) - k3p+3p f n2p dV, dt

(2)

where NN~(3p+3p,d) is the number of Na~ ions produced in 3p+3p or 3p+3d collisions during a specified time interval, and n3p,3d are population densities of the corresponding species. The population densities can be found approximately by solving laser pumping rate-equations (three-level for 3p+3d and two-level for 3p+3p reactions). Thus for the two-level scheme, we get the population density as a function of the laser intensity, x n3p = no 1 + 2x (3) where x is the 589 nm laser-beam intensity profile including saturation parameter. For our case we assume a Gaussian intensity profile, i.e.

101 e-Zr2/w~. (4) 11sat From the three-level scheme, we have 3p and 3d population densities as follows [ 8] : x =

x(1 + y ) n3p = no (1 + x ) ( 1 + y ) + x(1 + 2 y )

(5)

dNNa~(3p+3d) _ k3p+3dn022"n'Z0( I01 ,~2 ( I02 "~ dt \/lsat ,] \/-~s~t J OC

x

f

xy

e -4r2/w~ e -2r2/w~ r dr

(7)

(102/12sat)e-2r2/w~ '

1+

where 101,2 and ll,2sat are profile maximum and saturation intensities of the 589 and 819 nm laser beams respectively; w1,2 are corresponding spot sizes and z0 = const, is the effective absorption length or size of the interaction region along the laser beam direction. Then, changing variables to u = e -2r2/w~, we get dNNa~(3p+3d) -- k3p+3dn22,n.Z0 dt

x

( lo2 ~

~

u 2(W2/Wl)2du

\Ilsat](/O'--J'-I ~2(-~)2~k/-~t ] S I+('02/Iz.,)U 0

(,o_,]' k 11sat]

(8) Interestingly enough, for some rational values of 2(wz/wl )2 the integral can be calculated analytically and an explicit expression for G(loz/12sat) can be found; however the exact form of this function will depend on the ratio of spot sizes. For the 3p+3p reaction, volume integration over the beam profile gives

dNNa~ (3p+3p) 1 2 2 = k3p+3pnoqTZoWI dt x

In(1

+2Io1/Ilsat)

21ol/llsat "]

1 721~l/llsat]

1 2 2 = ~k3p+3pn0qrZOWl F(lol/llsat),

and

n3d = nO

The experiment can be conducted with the 589 nm intensity much below saturation, i.e. x << 1. Then, expressions for population densities in the three-level scheme can be simplified to n3p = nox and n3d = noxy/( 1 + y). Now analytical integration can be performed for Gaussian beam-profiles and for some specified spot-size ratios. In this case, the ion production rate for the 3p+3p reaction can be written as

o = k3d+3p f n3dn3p dV

123

(6)

(1 + x)(1 + y) + x(1 + 2 y ) '

where y is the 819 nmlaser-beam intensity profile with corresponding saturation parameter.

(9)

where

F( Ioi/Ii sat) --

ln(1

+2101/llsat)

210,/llsat 1 ~satJ"

(10)

124

E. Babenko et al./Chemical Physics Letters 244 (1995) 121-126

The N a f ion-yield versus intensity data from both the 3 p + 3 p and the 3 p + 3 d experiments can be fitted to the theoretically obtained functions using two fitting parameters: the overall constants A and B, plus ll.2sat, i.e.

50.00

--,

. ~ 40,00 e"

J

.o 30.00 _.N .~_

J

2000

dNN.2-~+(3p+3p) = A F ( lol/I1 sat), dt

( 11 )

00o000

and =

B

(12)

G(102/12sat).

dt Then, comparing (11) and (12) with (9) and (8) provides the ratio of rate coefficients and therefore velocity averaged cross-sections (at a specified beam temperature),

O'3p+3d

B (Ilsat'~ 2

(w1 '~2,

(13)

Or3p+3p -- ~- \/'~01-1J3p+3 d \2"-W2j

where I01 is 589 nm laser intensity used during the 3 p + 3 d experiment. Figs. 3 and 4 show the experimental data and fits to the theoretical functions for 3p-l-3p and 3 p ÷ 3 d AI reactions respectively. For the 3 p + 3 d experiment, the condition l o l / l l s a t m, 0.1 << 1 was satisfied. For the spot sizes, we have 2(wl/w2) 2 ..m 2/3 (where wl = 130/xm and w2 = 7 4 / z m ) and the volume integration produced a fitting function

!

40 00

60.00

'

80 00

10000

120.00

'

140.00

160,~0

~000

0.50

0.40

0..) 0.30

0 20

70,10

0.00 0.00

Fig. 4. Na~ ion yield due to 3p+3d AI reaction versus 819 nm laser beam intensity data points and theoretical fit to Eq. (14) are shown. The 589 nm laser beam intensity satisfies condition ll,3p+3d /llsat <'( 1. A small background (<< 1% at maximum) has been subtracted from all the data points. The data have the expected linear behavior at low intensities.

B G(Io2/I2sat) = B 1.5 \/2sat,] - o.6046+

khsa,/

+ 1.1547 arctan

. 5 7 7 3 5 - 1.1547 \i2sat /

[1 + (102/12sat)l/3] 2 } l + j In 1 -- (102/12sat) l /3 + (102/12sat) 2/3 j '

I • 5000

I 10000

I

15000

I 200.00

I 250.00

00.00

589nrn intensity (arb. units) Fig. 3. Naf ion yield due to the 3p+3p AI reaction versus 589 nm laser beam intensity. The experimental data points (+) and theoretical fit to Eq. ( 11) are shown. The data have the expected quadratic behavior at low intensities.

J (14)

where /2sat is the saturation parameter and B is the fitting constant as in (12). Substituting values for the fitting parameters, intensities and spot sizes into (12) yields a cross-section ratio of

O'3p+3d ----15(+5), Or3p+3p

xl0 ~ 060

~)

I

20 00

819nm intensity (arb. units)

d ) N ~%(3p+3d +

• (~

-q+l 1000

z

(15)

where the uncertainty is due to the statistical fluctuations of a number of the experimental factors, such as beam overlap. Approximately the same ratio is obtained using an assumed 819 nm rectangular beam profile, with a Gaussian profile for the broader 589 nm beam. Thus, taking for the numerical value of the 3p-l-3p AI reaction cross-section [ 1,2,4] O'3p+3p = 0.7 X 10 -16 cm 2, we get for the 3 p + 3 d AI reaction a velocity averaged cross-section of

Or3p+3d---- 1.1 x 10 -15 cm 2 at ~rel ~ 300 m/s,

E. Babenko et al./Chemical Physics Letters 244 (1995) 121-126

4. Theoretical discussion Fig. 5 shows the approximate Born-Oppenhiemer molecular potential curves for the ground state and selected excited states of Na~, including asymptotic atomic levels (at R = (x~). On the first consideration of these quasi-molecular potential curves, one might conclude that the large ratio ,,~ 15 between the (velocity averaged) O-3p+3d and O'3p+3p is surprising. The initial N a ( 3 p ) + N a ( 3 d ) state (entrance channel for the AI reaction) lies ~ 0.6 eV above the dissociation limit for Na~ into Na + and Na(3s). Thus, since the 3p+3d potential curves for neutral Na~ are relatively fiat at long range, the initial state in this thermal-energy collision is not expected to couple strongly to the Na~ Rydberg states leading directly to the 2~g+ ground electronic state of Na~ at large internuclear distance R (a putative mechanism for 3p+3p AI) since they lie much lower in energy at large R (see Ref. [4] ). Similarly, the 3p+3d entrance channel states lie well below the lowest 2Eg+ and 2Hu attractive wells corresponding to electronically excited states of Na~, which states are therefore inaccessible at thermal energies. What, then is the mechanism for efficient AI to Na~ from 3p+3d collisions?

4.

3. 2. 1. 0. -1.

Fig. 5. Approximate Bom-Oppenheimermolecular potential curves for Na~, where the energy on the y axis is in eV and the internuclear separation (x axis) is in bohr. Zero energy is chosen at the N a ( 3 s ) + N a + + e - asymptotic level. Curve (a) represents the attractive 1 27-+ and the repulsive 1 2Y,+ potential curves for the lowest electronic states of Na +. Curve (b) is V3 = -C3/R3+const., with C3 = 60 au, and goes to the N a ( 3 p ) + N a ( 3 d ) energy limit at R --, ~ (incident collision channel). Curve (c) represents the Na++Na - * ion-pair interaction and goes approximately to the same energy limit as (d) when R ~ o~. (d) represents the potential curves for the Na~ first excited state, i.e. 2 2~+ u and 2IIg,u states. Curves (a) and (d) are taken from Ref. [14].

125

Fig. 5 also shows the lowest lying accessible longrange curve (b) of the colliding Na~ excited quasimolecular system leading asymptotically to 3p+3d atomic states. Since there is a resonance degeneracy between the two atomic centers with regard to which is excited to 3p and which to 3d, the dominant longrange interaction is the V3 --- - C 3 / R 3 resonant dipole interaction [ 10]. The attractive V3 curve plotted in the figure (with C3 = 60 au, obtained from the known 3p3d atomic-transition line strength) is one of the several such adiabatic curves (some are also repulsive 1/R 3 curves) which lead to the 3p+3d limit at R ~ ~ . Although the asymptotic resonant-dipole shape will not be correct at small R, it seems likely that the attractive (V3) state will still dive into the Na~ X state well at close to R = 14 bohr, as shown. Excitation of one or more of the I/3-type attractive long-range states will then accelerate the two excited atoms toward each other (even orbiting collisions with the 1/R 3 attractive potential are possible). Radial or rotational coupling involving nonadiabatic energy exchange between nuclear and electronic motions can then lead to boundcontinuum coupling [2,4] and efficient Na~ formation near the crossings of the V3 and Na~ X curves. The Rydberg series of Na~ neutral states that converge on the Na~ X state limit may also be excited and subsequently ionized to Na~ during the collision (or even after it, due to small stray electric fields). An interesting test of this picture is that the V3 crossings with the molecular ion X state occur quite high up in the X state potential well and would thus be expected to lead to Na~ production in high vibrational states. Since the total energy in the collision is specified to within thermal energy kT, a measurement of the emitted electron energy distribution from 3p+3d AI collisions will reflect the amount of vibrational excitation of the Na2~ product. We plan to make this experimental test in the near future. Other states of the Na~ quasimolecule which may couple to the asymptotic (3p + 3d) manifold and thus effect the dynamics of the AI process are the states which lead adiabatically to the 3p + 4s separated atom limit and the Na + - N a - * ion-pair states. Fig. 5c shows an example of a long-range ion-pair state (potential - 1 / R + c o n s t . in atomic units) which converges to the N a ( 3 p ) + e - series of resonances. Note the near crossing with the V3 attractive curve which can lead to Landau-Zener radial coupling through avoided cross-

126

E. Babenko et al./Chemical Physics Letters 244 (1995) 121-126

ings between pairs of molecular states with the same symmetry. A detailed close-coupling theory of 3p + 3d AI would have to consider these states as well 3. It is worth noting that, in 3p+3d collisions, a competing process is a kind of Penning ionization, leading to Na(3s)+Na++e - instead of AI to N a ~ + e [ 12]. At thermal energies or below, after escape of the electron, the Na + can polarize the Na(3s) at large R, giving rise to a long-range V(R) o¢ - a ( 3 s ) / 2 R 4 potential and a significant probability of orbiting collisions [ 13]. If some of the rotational kinetic energy could be radiated away (as electric-dipole radiation), this could provide an alternative way to make Na~. A 'back of the envelope' estimate of this radiation rate suggests, however, that it is orders of magnitude too low for significant Na~ production during the orbiting time.

5. Conclusion To our knowledge, this is the first observation of Na(3d) +Na(3p) associative ionization. This basic reaction of two laser-excited alkali atoms has the special feature that it results from a binary collision of Na atoms in two different specified excited states, with the total 3p+3d excitation energy lying in the Na(3s)+Na++e - continuum (by ~ 4700 cm - I ) . Yet, the AI processes involving excitation of autoionizing or Rydberg states of the Na~* collision complex as intermediates in forming bound Na~ ( v ) + e - final states, remain very efficient, leading to a relatively large velocity-averaged cross-section in the 10 -15 cm 2 range. Some unanswered questions bearing on the reaction mechanism that we intend to pursue include: the vibrational energy distribution of the Na~ product ions, alignment effects depending on the polarizations of the two excitation lasers, and the branching ratio to other open channels (such as the ground state ion-pair curve and Penning autoionization during the collision to the atomic channel Na + + N a + e - ) .

3 Dr. R Krstic [ 11 ] is undertaking model calculations for some of these processes.

Acknowledgement We are pleased to acknowledge the support of NSF in initially funding some of the equipment, the support of the University of Connecticut Research Foundation and the generous help of the staff of the University of CT Laser Facility, especially J.-T. Kim, and Dr. He Wang, Dr. Chin-Chun Tsai and Dr. Bing Ji in the use of their Ti:sapphire laser. We acknowledge the help of Dr. P. Krstic and Professor Y. Hahn and his group or, some of the theory.

References [1] J. Huennekens and A. Gallagher, Phys. Rev. A 28 (1983) 1276. [2l R. Bonanno, J. Boulmer and J. Weiner, Comments At. Mol. Phys. 16 (1985) 109. [3] RL. Gould, RD. Lett, P.S. Julienne, W.D, Phillips, H.R. Thorsheim and J. Weiner, Phys. Rev. Letters 60 (1988) 788. [4] J. Weiner, E Masnou-Seeuws and A. Giusti-Suzor, Advan. At. Mol. Opt. Phys. 26 (1989) 209. [5] H.R. Thorsheim, Y. Wang and J. Weiner, Phys. Rev. A 41 (1990) 2873. [6] P. Kowalczyk, J. Phys. B 17 (1984) 817, and references therein. [7l M. Allegrini, R Bicchi and L. Moi, Phys. Rev. A 28 (1983) 1338; G.H. Bearman and J.J. Leventhal, Phys. Rev. Letters 41 (1978) 1227. [8] Ch. Tapalian, Ph.D. Thesis, University of Connecticut (1994), unpublished. [9] C. Tapalian and W.W. Smith, Chem. Phys. Letters 211 (1993) 425. [ 10] J.O. Hirschfelder, Advances in chemical physics, Vol. 12. Intermolecular forces (Interscience, New York, 1967) p. 40. [ 111 R Krstic, private communication (1994). [12] H. Dengel, M.-W. Ruf and H. Hotop, Europhys. Letters 23 (1993) 567. [13] C. Tapalian and W.W. Smith, Phys. Rev. A 49 (1994) 921. [ 14] D.D. Konowalow and M.E. Rosenkrantz, in: Metal bonding and interactions in high temperature systems, ACS Symp. Ser. No. 179, eds. J.L. Gole and W.C. Stwalley (Am. Chem. Sot., Washington, 1982) p. 3.