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Multiphoton excitation and dissociative ionization of SF6
Volume 56, number 1
MULTIPHOTON Ezra
CHEMICAL
EXCJTATION
PHYSICS LE-ITERS
AND DISSOCIATIVE
15 May 1978
IONIZATION OF SF6
BAR-ZLV and Oded KAFRI
Nuclear Research Center-Negev, Beer-SIxeva, Israel Received 5 January 1978
A simple model of multiphoton excitation and dissociative ionization process of SF6 is proposed. The modei is compared with experimental results of Brunner et al. It uas found that a three-photon absorption laid reproduced the experimental results with good agreement. In addition the relative enhancement ratios of dissociative ionization of excited 3-g were evaluated_
1. introduction Numerous experimental studies on the multiphoton excitation and decomposition of SF, with CO, laser radiation have been done in recent years [l-7]. Some understanding of the theoretical aspects of these phenomena has also been achieved [S-l I]. Many of the experiments were performed at high pressure regions where V-V energy transfer processes take place and which cause excitation of molecules to higher vibrational levels. In the collisionless regime and by the use of strong CO, laser radiation, multiphoton decomposition processes of SF6 have proved to give pronounced emichment factors for 34S up to 3000 131. Excitation and decomposition of molecules in a molecular beam machine would enable one to measure changes in beam intensities due to laser excitation in the collisionless regime. Such experiments have been carried out recently by Brunner et al. 1121 and by Coggiola et al. 1131. In both experiments intense CO, laser radiation was directed into a molecular beam of SF6 molecules. While in the first study the detection method was a mass spectrometric analysis for different fluxes of radiation, in the second study the angular and velocity distribution of SF6 fragments were measured at constant radiation flux. Brunner et al. measured the probabilities of the dissociative ionization processes of SF, to its various fragments as a function of CO, laser radiation fluxes. It was found that the probabilities of these processes
varied with the amount of vibrationally excited SF6 molecules. It is indeed the first experimental demonstration that dissociative ionization processes by highly energetic electrons (70 eV) depend on the internal energy of the molecule, which is more than two orders of magnitude less than the electron energy. In this note we would like to suggest a simple model of multiphoton excitation of SF6 which will enable us to evaluate the laser enhancement probabilities of the dissociative ionization processes. The model is able to reproduce the experimental results of Brunner et al. by assuming a three-photon saturation absorption law.
2. The model We assume here that the species produced from the multiphoton decomposition of SF6 molecules are scattered isotropically. Therefore, the concentration of those species which reach the ionization chamber is negligible. Only SF6 molecules in the ground and excited states enter the ionizer. The dissociative ionization processes of SF6 molecules in the ground state to the various fragments are distributed according to the following scheme: SFg+e%SFi+F+e,
,
___, 47
where Cpi] is the set of the fragmentation probabilities. For excited SF6 molecules there is a different set, Cpl} _ Both sets shauld satisfy Zi pi = Xi if = 1. In a first order approximation it is seen that the fragmentation probabrlity for each channel reaches a constant value at high CO, laser energies. This implies that probably the concentration of the vibrationally excited molecules, SF& reaches also a constant value, ISF&/lSF6lr,
=K 5
(1)
where [SFils is the concentration of SF: at saturation, [SF610 is the total concentration of SF6 molecules, and K is a constant to be determined. We wiil assume that the excitation of SF6 is done via a multiphoton process. In the case that the lifetime of the intermediate level is longer than the duration of the laser puke (which is the case in this example) one may see 1141 that the absorption law in such a case Is according to (IfUr namely En and not PAt, as in the simultaneous multiphoton processes (via virtual levels); here E is the energy per unit area and I is the intensity of the laser beam. In our case a first order saturation effect was taken into consideration; therefore, [SF&)]
= [SF6]u K&“/(1
+ uE") ,
(2)
where o is some saturation constant, n is the order of the multiphoton process to be determined. The intuitive meaning of n is the number of photons absorbed in the consecutive absorption process to bring the molecule to the second regime of excitation [8,9,11]. The excited SF6 molecules are distributed among the upper manifold of levels, therefore, K may exceed half. In the ionization chamber the fragment SFf is produced from dissociative ionization reactions of SF6 and SF:. The concentration of this fragment, [SF;], is given by
~S6-@91= Cl=, lo - PF%Ql hi + W&9lp,l(3) Substituting [SF&)] tain: [SF;(E)]=pj[l+K(Zi-
from eq. (2) into (3) we obl)uE”l(l+;uE”)]
[SF610,(4)
(3
[SF:l, = P~C~+~NSF& 9 where Mi=K(Zi-
1) s
(6)
Mi is calculated from the experimental results [6] by:
Mi=
Wilpi-1 >
(7)
where Wi is the fraction of SF: at saturation given by eq_ (3) Substituting (7) into (4) we have an expression for [sF$!i)] as a function of E withtwounknownparameters u andn: [SF;(E)]
=pi[I+(Wi/pikI)
~~“l(l+~~“Il [SF610a (8)
Thus,proper
values for (I and n should reproduce all the results of BNrmeretid.
3. ResuIts and discussion From all fragmentation channels we have chosen only the results for SFf, SF:, and SF: since the concentration changes of the other fragments were smaller than the scattering of the experimental points. We first examined the model by a least square fit of eq. (8) to the experimental points for each fragment. The results for u and n are summarized in table 1. It is seen from table 1 that for ah three cases the values of n are close to three. When n = 3 was introduced into eq. (8) and then simultaneously eq. (8) was fitted to ah results (i = 3,4, S), u = 0.13 was obtained with R2 = 98%, see fig. 1. We conclude, therefore, that the excitation of SF6 molecules is a threephoton absorption process.
Table 1 Fitted valuesof o and II Fragments
o
n
i
where Zi is the probability ratio of the fragment SFf given by Zi = p&i_ At saturation the concentration of the fragment SF;, [SF;], is given by 48
15 May 1978
CHEMICALPHYSICS LETTERS
Volume 56, number 1
5
4 3
R2 aI (53
0.16 0.16 0.13
3.1 29 2.6
99 98 97
a) R3 is the fittingpercentagebetween the experimentalresuns ami the calculated ones.
CHEMICAL PHYSICS LETTERS
Volume 56, number 1
W
tation, it does not mean that this process was inhibited but that the other processes were more enhanced. In our example we may say, therefore, that the rate coefficients for producing SF: and SF: were enhanced at least by factors of 12 and 8 respectively by the laser.
06 04
References
02
0
I5 May 1978
[ 1J VS.
1
2
3
&n4
6
7
f
Fig. 1. The partitionof SF; f?a@nents as a function of Iaser energy: i = S (A), 4 (0). 3 Co) and the sum of ti fragments (m). The solid lines are the model analysis reproductions of the experimental points
fmding confirms other results of Ambartzumian et al. [IS] and of others [7,16,17]. They found that the dkwciation of SF6 under intense CO, Iaser radiation (in the same region of energies as used by Banner et al.) was proportional to the third power of the laser energy. The set &;I can be evaluated from this model since: ‘&is
MI/M4
= (25
-
l&W4
-
0,
M&%
= @4
-
W(z3
-
1) ,
where A = 0.94 is the sum of the fragmentation probabilities (for i = 3,4,5) from the model, at saturation. It was found that 2, = 4.0, Z, = 2.8, and 2s = 0.34, orpi ==0.52,& =O.t9, and& =0.23. From eq. (6) K was determined and was found to approach unity. The physical meaning of K * 1 is that at saturation almost all molecules of SF, are not to be found in the ground state and practically all molecules were excited to the second re@ne of excitation. We would like to emphasize that cpi) is the set of the fragmentation probabilities and not the rate coefficients of the reactions. Thus, if the probably of one of the fragments was decreased by the laser exci-
Letokhov and C.B. Moore, Kvantovaia Elektronika 3 (1976) 485 [English transL Soviet f, Quantum Electron 3 (1976) 2591. [2] XL. Lyman and SD. Rockwood, J. Appl. Phys. 47 (19751 595. [ 31 R.V. Ambartzumian, Yu.A. Gorakbov, VS. Letokhov and G.N. Makarcw, Pis’ma Zh. Eksp. Tear_ Fk 21 (1975) 375; 22 (1975) 96 [English transl JETP Letters 21
(1975) 171; 22 (1975) 43, 141 R-V, Ambartzumian, Yu.A_ Gorokbov, V-S_ Letokbov, and A.A. Pure&k%, Pis’ma Zh. Eksp. Tear. F&z, 22 (1975) 374 [English transl. JETP Letters 22 (1975)
1771.
IS] S.M. Freund and 3.X. Rltter, Chem. Phys. Letters 32 (1975)
255
161 G. Hancock, J.D. Campbell and K.H.
Weise,Opt Commur
16 (1976) 166. 171 J.D. Campbell, G. Hancock and KH.
We&e.
C&m.
Phys.
Letters 43 (1976) 582. E8] N. Bloembergen, Opt. Commum. 15 (1975) 416. [PI D.M. Larsen and N. Bloembergen, Opt. Commun. 17 (1976) 254. [ 101 RV. Ambartzumian, Yu.A. Gorokbov, VS. Letokbov,
C.N. Makarov and A.A. Puretzkii, Pis’ma Zh. Eksp. Tear. Fiz. 23 (1976) 26 ~EngBsh tmnsL JETP Letters 23
(1976) 221. [ 111 S. Mukamel and 3. Jortner, Chem. Phys. Letters 40 (1976) 1.50. 1121 F_ Brunner, T-P. Cotter, M.L. Kompa and D. Proch, 1. Chem. Phys. 67 (1977) 1547.
[13] M.J. Coggiola. P.A. Schulz, Y.T. Lee and Y.R. Shen, Pbys. Rev. Letters 38 (1977) 17. 1141 0, Kafri and S. Khnel. Cbem. Phys. 5 (1974) 488. flSj R.V. Ambartzumian, Yu.A. Gorokhov, VS. Letokhov, G.N. hfakarov and A.A. Puretzkii, JETP Pis’ma 23 (1976) 26. [16] T.P. Cotter and W. Fuss, Ver. D.F.G 2 (1976) 231, paper presented at Friibjahrstagung der Deutschen Physika&cben Ges&s&aft, Harmover, Feb., 1976. [ 171 D. Tal, U-P_ Oppenheim, G, Koren and M. Okon, Chem.
Phys. Letters48 (1977) 67.
49
MULTIPHOTON Ezra
CHEMICAL
EXCJTATION
PHYSICS LE-ITERS
AND DISSOCIATIVE
15 May 1978
IONIZATION OF SF6
BAR-ZLV and Oded KAFRI
Nuclear Research Center-Negev, Beer-SIxeva, Israel Received 5 January 1978
A simple model of multiphoton excitation and dissociative ionization process of SF6 is proposed. The modei is compared with experimental results of Brunner et al. It uas found that a three-photon absorption laid reproduced the experimental results with good agreement. In addition the relative enhancement ratios of dissociative ionization of excited 3-g were evaluated_
1. introduction Numerous experimental studies on the multiphoton excitation and decomposition of SF, with CO, laser radiation have been done in recent years [l-7]. Some understanding of the theoretical aspects of these phenomena has also been achieved [S-l I]. Many of the experiments were performed at high pressure regions where V-V energy transfer processes take place and which cause excitation of molecules to higher vibrational levels. In the collisionless regime and by the use of strong CO, laser radiation, multiphoton decomposition processes of SF6 have proved to give pronounced emichment factors for 34S up to 3000 131. Excitation and decomposition of molecules in a molecular beam machine would enable one to measure changes in beam intensities due to laser excitation in the collisionless regime. Such experiments have been carried out recently by Brunner et al. 1121 and by Coggiola et al. 1131. In both experiments intense CO, laser radiation was directed into a molecular beam of SF6 molecules. While in the first study the detection method was a mass spectrometric analysis for different fluxes of radiation, in the second study the angular and velocity distribution of SF6 fragments were measured at constant radiation flux. Brunner et al. measured the probabilities of the dissociative ionization processes of SF, to its various fragments as a function of CO, laser radiation fluxes. It was found that the probabilities of these processes
varied with the amount of vibrationally excited SF6 molecules. It is indeed the first experimental demonstration that dissociative ionization processes by highly energetic electrons (70 eV) depend on the internal energy of the molecule, which is more than two orders of magnitude less than the electron energy. In this note we would like to suggest a simple model of multiphoton excitation of SF6 which will enable us to evaluate the laser enhancement probabilities of the dissociative ionization processes. The model is able to reproduce the experimental results of Brunner et al. by assuming a three-photon saturation absorption law.
2. The model We assume here that the species produced from the multiphoton decomposition of SF6 molecules are scattered isotropically. Therefore, the concentration of those species which reach the ionization chamber is negligible. Only SF6 molecules in the ground and excited states enter the ionizer. The dissociative ionization processes of SF6 molecules in the ground state to the various fragments are distributed according to the following scheme: SFg+e%SFi+F+e,
,
___, 47
where Cpi] is the set of the fragmentation probabilities. For excited SF6 molecules there is a different set, Cpl} _ Both sets shauld satisfy Zi pi = Xi if = 1. In a first order approximation it is seen that the fragmentation probabrlity for each channel reaches a constant value at high CO, laser energies. This implies that probably the concentration of the vibrationally excited molecules, SF& reaches also a constant value, ISF&/lSF6lr,
=K 5
(1)
where [SFils is the concentration of SF: at saturation, [SF610 is the total concentration of SF6 molecules, and K is a constant to be determined. We wiil assume that the excitation of SF6 is done via a multiphoton process. In the case that the lifetime of the intermediate level is longer than the duration of the laser puke (which is the case in this example) one may see 1141 that the absorption law in such a case Is according to (IfUr namely En and not PAt, as in the simultaneous multiphoton processes (via virtual levels); here E is the energy per unit area and I is the intensity of the laser beam. In our case a first order saturation effect was taken into consideration; therefore, [SF&)]
= [SF6]u K&“/(1
+ uE") ,
(2)
where o is some saturation constant, n is the order of the multiphoton process to be determined. The intuitive meaning of n is the number of photons absorbed in the consecutive absorption process to bring the molecule to the second regime of excitation [8,9,11]. The excited SF6 molecules are distributed among the upper manifold of levels, therefore, K may exceed half. In the ionization chamber the fragment SFf is produced from dissociative ionization reactions of SF6 and SF:. The concentration of this fragment, [SF;], is given by
~S6-@91= Cl=, lo - PF%Ql hi + W&9lp,l(3) Substituting [SF&)] tain: [SF;(E)]=pj[l+K(Zi-
from eq. (2) into (3) we obl)uE”l(l+;uE”)]
[SF610,(4)
(3
[SF:l, = P~C~+~NSF& 9 where Mi=K(Zi-
1) s
(6)
Mi is calculated from the experimental results [6] by:
Mi=
Wilpi-1 >
(7)
where Wi is the fraction of SF: at saturation given by eq_ (3) Substituting (7) into (4) we have an expression for [sF$!i)] as a function of E withtwounknownparameters u andn: [SF;(E)]
=pi[I+(Wi/pikI)
~~“l(l+~~“Il [SF610a (8)
Thus,proper
values for (I and n should reproduce all the results of BNrmeretid.
3. ResuIts and discussion From all fragmentation channels we have chosen only the results for SFf, SF:, and SF: since the concentration changes of the other fragments were smaller than the scattering of the experimental points. We first examined the model by a least square fit of eq. (8) to the experimental points for each fragment. The results for u and n are summarized in table 1. It is seen from table 1 that for ah three cases the values of n are close to three. When n = 3 was introduced into eq. (8) and then simultaneously eq. (8) was fitted to ah results (i = 3,4, S), u = 0.13 was obtained with R2 = 98%, see fig. 1. We conclude, therefore, that the excitation of SF6 molecules is a threephoton absorption process.
Table 1 Fitted valuesof o and II Fragments
o
n
i
where Zi is the probability ratio of the fragment SFf given by Zi = p&i_ At saturation the concentration of the fragment SF;, [SF;], is given by 48
15 May 1978
CHEMICALPHYSICS LETTERS
Volume 56, number 1
5
4 3
R2 aI (53
0.16 0.16 0.13
3.1 29 2.6
99 98 97
a) R3 is the fittingpercentagebetween the experimentalresuns ami the calculated ones.
CHEMICAL PHYSICS LETTERS
Volume 56, number 1
W
tation, it does not mean that this process was inhibited but that the other processes were more enhanced. In our example we may say, therefore, that the rate coefficients for producing SF: and SF: were enhanced at least by factors of 12 and 8 respectively by the laser.
06 04
References
02
0
I5 May 1978
[ 1J VS.
1
2
3
&n4
6
7
f
Fig. 1. The partitionof SF; f?a@nents as a function of Iaser energy: i = S (A), 4 (0). 3 Co) and the sum of ti fragments (m). The solid lines are the model analysis reproductions of the experimental points
fmding confirms other results of Ambartzumian et al. [IS] and of others [7,16,17]. They found that the dkwciation of SF6 under intense CO, Iaser radiation (in the same region of energies as used by Banner et al.) was proportional to the third power of the laser energy. The set &;I can be evaluated from this model since: ‘&is
MI/M4
= (25
-
l&W4
-
0,
M&%
= @4
-
W(z3
-
1) ,
where A = 0.94 is the sum of the fragmentation probabilities (for i = 3,4,5) from the model, at saturation. It was found that 2, = 4.0, Z, = 2.8, and 2s = 0.34, orpi ==0.52,& =O.t9, and& =0.23. From eq. (6) K was determined and was found to approach unity. The physical meaning of K * 1 is that at saturation almost all molecules of SF, are not to be found in the ground state and practically all molecules were excited to the second re@ne of excitation. We would like to emphasize that cpi) is the set of the fragmentation probabilities and not the rate coefficients of the reactions. Thus, if the probably of one of the fragments was decreased by the laser exci-
Letokhov and C.B. Moore, Kvantovaia Elektronika 3 (1976) 485 [English transL Soviet f, Quantum Electron 3 (1976) 2591. [2] XL. Lyman and SD. Rockwood, J. Appl. Phys. 47 (19751 595. [ 31 R.V. Ambartzumian, Yu.A. Gorakbov, VS. Letokhov and G.N. Makarcw, Pis’ma Zh. Eksp. Tear_ Fk 21 (1975) 375; 22 (1975) 96 [English transl JETP Letters 21
(1975) 171; 22 (1975) 43, 141 R-V, Ambartzumian, Yu.A_ Gorokbov, V-S_ Letokbov, and A.A. Pure&k%, Pis’ma Zh. Eksp. Tear. F&z, 22 (1975) 374 [English transl. JETP Letters 22 (1975)
1771.
IS] S.M. Freund and 3.X. Rltter, Chem. Phys. Letters 32 (1975)
255
161 G. Hancock, J.D. Campbell and K.H.
Weise,Opt Commur
16 (1976) 166. 171 J.D. Campbell, G. Hancock and KH.
We&e.
C&m.
Phys.
Letters 43 (1976) 582. E8] N. Bloembergen, Opt. Commum. 15 (1975) 416. [PI D.M. Larsen and N. Bloembergen, Opt. Commun. 17 (1976) 254. [ 101 RV. Ambartzumian, Yu.A. Gorokbov, VS. Letokbov,
C.N. Makarov and A.A. Puretzkii, Pis’ma Zh. Eksp. Tear. Fiz. 23 (1976) 26 ~EngBsh tmnsL JETP Letters 23
(1976) 221. [ 111 S. Mukamel and 3. Jortner, Chem. Phys. Letters 40 (1976) 1.50. 1121 F_ Brunner, T-P. Cotter, M.L. Kompa and D. Proch, 1. Chem. Phys. 67 (1977) 1547.
[13] M.J. Coggiola. P.A. Schulz, Y.T. Lee and Y.R. Shen, Pbys. Rev. Letters 38 (1977) 17. 1141 0, Kafri and S. Khnel. Cbem. Phys. 5 (1974) 488. flSj R.V. Ambartzumian, Yu.A. Gorokhov, VS. Letokhov, G.N. hfakarov and A.A. Puretzkii, JETP Pis’ma 23 (1976) 26. [16] T.P. Cotter and W. Fuss, Ver. D.F.G 2 (1976) 231, paper presented at Friibjahrstagung der Deutschen Physika&cben Ges&s&aft, Harmover, Feb., 1976. [ 171 D. Tal, U-P_ Oppenheim, G, Koren and M. Okon, Chem.
Phys. Letters48 (1977) 67.
49