Spectral and Temperature Dependence of Laser Induced Dissociative Attachment in

We consider the influence of resonant laser excitation upon the dissociative reaction between 
SF6 molecules and very low energy electrons. Experimentally, the use of valence electrons 
of atoms in Rydberg states ensures a well-defined energy resolution of the scattering electrons 
in the crossed beam apparatus. A spectroscopic model of the infrared absorption of CO2 laser 
radiation by SF6 gives a fair determination of the energy levels and vibrational transitions 
involved in the dissociative process. This reaction between highly excited atoms and a 
molecule is interpreted as a three step process: attachment of a quasi-free electron, followed 
by the interaction between the atomic ionic core and the negative molecular ion leading to 
a partial stabilization and, finally, the competition between the dissociating and the autodetachment 
channels.


INTRODUCTION
The multiple photon dissociation (MPD) of SF6 into neutral components occurs in two stages, one involving a resonant excitation of the first few discrete vibrational states of the v3 ladder, the other leading to dissociation by absorption of a large number of photons within the vibrational quasi- continuum.
An alternative approach to isotopically selective dissociation of SF6 has been proposed and studied by several authors. 2 In this approach, one takes advantage of a well-known property of SF6: it attaches low energy electrons and, according to its vibrational energy, the negative ion produced 18 R. BARBE ET AL. is either SFor SF-.Thus, the resonant vibrational excitation can strongly modify the branching ratio between the non-dissociative and dissociative channels [Figure 1].The large amount of nonresonant laser energy which is required in the second step of the MPD dissociation into neutral com- ponents is replaced by chemical energy, i.e. the electron affinity of the SFs product.
A modeling of the above processes requires a good knowledge of the collision conditions (for instance, single collision conditions), of the SF6 internal energy and the electron energy distribution.Reciprocally, such a model provides information about the dynamics of low energy electron- SF6 scattering (attachment, autodetachment and dissociation life- times... and parameters of laser excitation.
We report here the spectral and temperature dependence of the following reactions: SF6(E,) + hv--> SF SF6 +e SF + e SFg \ ( / ' S F .+ F (1)   where SF6(Ev) corresponds to SF6 molecules with an internal energy Ev controlled by means of temperature and SF to laser excited molecules.In order to obtain a knowledge of the electron energy distribution as accurately as possible, we use valence electrons of atoms in Rydberg states.Experimentally, this way of producing sub-thermal electrons is somewhat similar to the use of a photoionisation source of quasi monoenergetic electrons, s In comparison with more conventional techniques 6 such as RPD spectrom- eters or swarm experiments in which the electron energy distributions are approximately 100 meV wide with long energy tails, the use of electrons bound to highly excited atoms sets an upper limit to the maximum kinetic energy of the electrons attaching to SF6.As far as attachment alone is concerned, it has been shown by Matsuzawa 7 that these bound electrons behave as if they were free, with momentum distributions governed by the quantum states of the highly excited atoms.The fate of the negative ion parent SF6 molecules, we measured the influence of resonant laser exci- tation upon the reaction (1) for all CO2 laser lines corresponding to the absorption of the isotopic molecule a2SF6.Our results agree reasonably well with those of Chen and Chantry a in respect of the spectral dependence of the process.Their experiment and interpretation concerning the laser excitation and energy threshold were in disagreement with previous mea- surements of the activation energy of the reaction.We attribute this dis- agreement to the problem of electron energy distributions in RPD tech- niques.
By analyzing our results with a spectroscopic model of CO2 laser ab- sorption by SF6, derived from the model of Nowack and Lyman, 9 we interpret the red shift of the dissociative channel with respect to the low temperature small signal absorption curves and we show that single photon excitation is responsible for the laser induced process.From our data, we confirm the accepted value of energy threshold of the reaction (1) and show that, following the suggestion of Nowack and Lyman, one must add to their model the variation of the rotational constant as a function of vibrational energy.We also demonstrate that one has to take into account, for high excitation levels, the competition between the two exit channels of reaction (1), i.e., dissociative attachment and autodetachment.

APPARATUS
A schematic diagram of the experimental arrangement is shown in Figure 2.This cross beam experiment, which satisfies the single collision con- dition, will be described in more detail in a forthcoming paper. 1 A beam of SF6 molecules, emanating from a platinum tube (1 mm i.d. 10 cm long) with variable temperature from 300K to 1000K crosses a beam of argon atoms excited to Rydberg states.These highly excited atoms which act as a source of low energy electrons, are produced by electron bombardment.Their time of flight between their creation and the collision region is approximately 200 Is.The competition between the cross-section for cre- ation of these atoms in the state of a principal quantum number n (low orbital quantum number/) which varies as n-a, and the radiative lifetimes which vary as n" where 4 < ct < 5 (for large values of after redistribution among by collisions undergone after creation) results in an energy dis- tribution of the electrons between 10 and 40 meV (18 < n < 35) as confirmed by field ionization measurements.The SF6 beam with computer controlled temperature (vary- ing between 300K and 1000K), is excited by the CO2 laser beam.The chopping reference drives the up-counting and down-counting in the micro-computer.The laser excited SF6 beam crosses the high Rydberg argon atomic beam and the ionic products are mass-analyzed by a quadrupole-spectrometer.
A CW 4W CO 2 laser, which is grating tuned, is focused at the exit of the platinum tube and a fraction of the SF; beam is excited in the .8mm diameter laser waist.In order to monitor the number of SFions (detected by a quadrupole mass analyzer) produced, due to laser vibrational exci- tation, ON OFF synchronous detection is done by a microcomputer clocked by the laser chopper.Typical 32SF" ion signals due to the laser are 15 counts/sec, with an averaging time of 60 sec.The weakness of these signals, due to the crossing beam intensities, did not allow us to observe 34SF-ion signals, restricting our study to the most abundant isotope 32SF6 (95%).

Experimental results
For several C02 laser lines corresponding to the absorption band of 32SF6, the relative enhancement of the SFg --> SF-+ F dissociative channel, as a function of the SF6 parent molecule temperature, was measured(Figure 3).The qualitative behavior is the same for the different laser lines: the laser induced SFsignal rises around 400K, culminates near 600K and decreases at higher temperatures.At a temperature of 600K at which the laser induced SFsignal is maximum, the dependence of this signal upon the CO2 laser lines is shown in Figure 4.This measurement agrees reasonably well with that of Chen and Chantry 3 obtained with an RPD technique and that of Avrillier and Schermann 2 obtained by an optogalvanic detection in a SF6 discharge.
The power dependence of the laser induced signal is shown in Figure 5.The maximum power available corresponds to a power broadening of about 70 MHz as compared with the 30 MHz Doppler linewidth.In the vibrational excitation region that we consider where Ev 3500 cm-1, there are approximately 102 vibrational levels per cm -1 and, thus, one level every 300 MHz which may absorb.This interval is larger than the laser broad- ening.
The interaction time of the SF6 molecules inside the laser beam waist is 2 Is.With a CO2 laser photon absorption cross-section of 10 -8 cm2, 630K P28 LASER POWER W 0 FIGURE 5 The laser induced signal is plotted, as a function of the CO2 laser power for SF6 temperature of 630K and the P28 CO2 laser line for which this signal is maximum.
saturation is obtained for a few kW/cm2.We thus interpret the power dependence as a linear variation followed by saturation when the probability of excitation of a SF6 molecule reaches unity.

Spectroscopic model
The modeling of the first discrete multiple photon stage of excitation in MPD of SF6 has provided a strong impetus for the determination of the infrared spectrum of this molecule.Till now, a precise interpretation of the very high resolution spectrum has only been made for the v3 funda- mental transition, 11 together with a Doppler limited allalysis 12 of the v3 --21)3 second harmonic and a determination 13 of the v3 vibrational ladder.
Very little information is available about the rovibrational spectrum of the other modes, even at low resolution.We have thus used for our spectral analysis the model of Nowack and Lyman 9 with some modification of the anharmonicity constant, recently determined, t3 and the energy dependence of the rotational constant which was necessary to introduce in order to fit our data to the initial values of Ref. 9. We shall give here only a brief account of this model referring to the original paper.
The vibrational states of SF6 are defined by a set of vibrational quantum numbers [vd corresponding to the 6 normal modes.The only anharmonicity constant which has been precisely measured corresponds to the v3 mode and we adopt the empirical Nowack and Lyman proposal which states that, for each mode, the harmonic shift of a vibrational overtone is proportional to the frequency v of the fundamental.Ignoring rotation energy, the fre- quency of a transition involving a v3 photon, originating from a state [vd is then given by: where vo(O) is the frequency of the 1) 3 transition originating from the ground state.This unique proportionality constant A is related to the anharmonicity constant X33 by the relation X33 ]Av3.We take for X33 the experimental value of Ref. 13 X33 1.74 cm-.
For vibrational energies Ev of states [vi] ranging from 0 to 1650 cm -, we use direct count of these levels.Above this value, the density of states is high enough to consider the vibrational level distribution as quasi con- tinuous.As in Ref. 9, we define as "levels" those which consist of all states with vibrational energy in the range Ev -+ 10 cm-1.These levels are related to a set of mean values of the vibrational quantum numbers [d.The fraction of molecules at energy Ev which have v quanta of mode v is: where D is a degeneracy factor equal to 1 for the non-degenerate mode v, and is equal to v + 1 for the doubly degenerate mode v2 and (v + 1)(v + 2)/2 for the other triply degenerate modes and d the degeneracy of mode v.
The densities g(E,) are computed by means of the Whitten and Rabi- novitch expression. 14For each value of Ev there correspond possible integer values of v from 0 to x integer (Ely,) and the mean value of v is then i .F(vi, E,)vi (4) vi= 0 In Ref. 9, it was assumed that if B' and B" are respectively the rotational constant of the upper and lower states involved in a laser transition, one can neglect the difference B' B" AB as compared to B' and B".We found it necessary to take into account the linear variation 5 of the rotational constant B and the Coriolis coupling as functions of the vibrational energy Eo, thus expressing empirically, the effective rotational constant as" B(E,) Be orEs, with ot Oto + (5) For each level characterized by a vibrational energy Ev and quantum num- bers [v, J] or [, J], there correspond three absorption lines P, Q and R which may coincide with the CO2 laser lines of frequency vL (in crn-1) for certain values of J, solutions of the following numerical equations [-0.0538 + 6.2610 -E,, 0.406et] J aJ 2 Q branch vz Vo[Vi] + od(J + 1) R branch vL Vo[V] + [0.0538 6.2610 -4 E,, 1.594et] J od 2 For a given temperature of SF6, taking into account the vibrational and rotational partition functions, these values of J, corresponding to spectral coincidences, determine, within a constant factor, the absorption coefficient dk(vl.., E,) of the different CO2 laser lines (of frequency vz), by each "vibrational level" (of energy Ev).In this band contour model, our only adjustable constants are the linear ot and quadratic 13 coefficients of the rotational constant B.

Collision model
We use, as a source of thermal electrons, a beam of argon atoms in Rydberg states which ensure a well controlled energy distribution of these electrons.
The collision between the highly excited atoms and the SF6 molecules is a three step process.First, the quasi free electron, with negligible kinetic energy, as compared to the internal energy Ev of the colliding SF6 molecule, attaches with a cross-section independent of Eo. 16 The negative ion thus produced possesses an internal energy E, + EA where EA is the adiabatic electron affinity of SF6.This ionic core of the excited argon atom suffers Coulomb attraction from the SFion and, in a second step, both ions exchange energy, i.e., part of the internal energy of the SFion can be transferred as kinetic energy to the ionic core.This corresponds to the stabilization process of Zembekov 8 where, at the end of the collision, the negative ion is left with an internal energy E, + EA AE.Depending on this energy E,, in a third step, the negative ion can autodetach with an autoionization rate rl[Ev,], be stabilized (an "infinite" lifetime vs autodetachment) or dissociate with a rate "G-[E,,,] (Figure 6).
The dependence of 'i'a, 'T d versus the internal energy E,,, of the negative ion can be estimated by means of RRKM statistical theories 17,18 or by the inverse Laplace transform of the measured values of negative ion produc- tion as a function of temperature.'9'2 The autodetachment lifetime "ra slowly decreases for Ev, between 4000 and 8000 cm with a mean value cc. 10 Is, then drops very small values for E,, above 8000 cm-1.The dissociation lifetime "rd decreases strongly near the threshold energy Ed of the dissociative reaction SF----> SF-+ F, then slowly between 5000 and 8000 cm around a value of 30 Is.
After the absorption by an SF6 molecule with energy Ev of a laser photon of frequency vL, a negative SFion is produced with an internal energy E/, E,, + hvL E, + EA AE + hvL.During its time of flight xp between its creation and its detection this SFion can autodetach or dissociate into SF-.For each "vibrational level", the variation of the number of detected SFions due to the laser is given by: dN(SF-)taser dk(vz,,Eo) 1 exp xaiEi,) "ra(E,,,) Ta(Ev,, -[-'d(Ev,,) 'r,(E,) 'ra(E,,) "r,(Ev,) + 'ra(E,,) where P is the laser power, S the laser beam area and C the proportionality constant.(P/ShvL) dk(vz,E,) is the number of molecules, in the "vibrational level" Eo, excited per second and per unit of volume.
The dissociative channel is open to a SFion (E, > Ea) when its parent molecule internal energy Ev is above the energy threshold Eth Ea + E hv.Thus, the total SFions due to the laser absorption is N(SF-)aer f dN(SF-)t,e If we assume that x and "ra are constant above the energy threshold Eo, Ea + EA and that "ra is infinite for E,, < Ea + EA then the laser has no effect upon molecules with energy E, > Ea + AE since x(E,,,) x(Eo,).We obtain a simple expression: N(SFf) laser In order to take into account the decrease of the branching ratio between dissociation and autodetachment observed in experiments with SFf and SF-,lO the preceeding model can be improved by assuming that the au- todetachment lifetime 'ra(Ev,) is constant up to Ev, EA + Ec, and for Ev, Ec + EA. ('ra(E,/) 0.) This critical value Ec is to be determined.

CONCLUSION
We consider here a reaction between SF6 molecules excited with 3 10 vibrational quanta, and very low energy electrons.This reaction can be thought of as a probe of the spectroscopic properties of this spectral region of SF6, situated between the well-known fundamental transition of v3 and the very highly excited vibrational states.This region is, in fact, the one which was considered, in earlier works on isotope separation, as con- necting the resonant v3 ladder and the quasi-continuum leading to neutral dissociation.
We found that the Nowack and Lyman 9 model correctly describes the absorption of the CO2 laser in this excitation region if we take into account a modification of the anharmonicity constant, recently measured, and if we introduce the variation of the effective rotational constant as a function of the vibrational energy.
Our experimental measurements with a well-defined electron energy distribution together with a spectral analysis, confirm the accepted value of .43eV. for the energy threshold of the dissociative reaction SFg- SFf + F, as opposed to the value of 0.2 eV determined by Chen and N Em 0 Chantry.This discrepancy is most probably due to the high energy tail of the electron energy distribution used in their experiment.We conclude, from our spectral analysis that the absorption process responsible for the laser enhancement of the dissociative channel is a single photon absorption.We also show that this dissociative process is dominated by an autode- tachment channel above a given internal energy of the negative ion that we estimate.This study of the reaction process which occurs in a collision between an atom in a Rydberg state and a molecule is an example of more general kind of reactions between excited atoms and molecules which can be described as three step processes, the first involving the formation of negative ion by means of a shape or Feshbach resonance, 24 the second, a stabilization process and the third, competition between several dissociating processes of the negative ion.

FIGURE 4
FIGURE 4 The laser induced signal is plotted as a function of the CO2 laser lines for several experiments 0 Chen and Chantry (Ref.3) A Avrillier and Schermann (Ref.2) and this experiment.The dotted line corresponds to the spectroscopic model with a new value of the anharmonic constants and variation of the rotation constant.The broken line corresponds to the original model of Ref. 9.
.,E,)The results corresponding to this model are shown in Figure7(broken line Ec 0).

TABLE
Numerical values used in the spectroscopic and collision models.