1029
J . Phys. Chem. 1991, 95, 1029-1034
VII. Summary At this time, it may not possible to say which method is preferred for applications for which all are practical. Nor is it passible to assess, in a way that is applicable to most chemical species, the accuracies with which various methods predict bond lengths and energies or other properties. However, there are reasons to recommend some methods over others in specific cases. For example, certain applications require a size-extensive energy (e.g., extended systems that consist of a large or macroscopic number of units or studies of weak intermolecular interactions), so MBPT/MPPT or CC or CAS-based MCSCF are preferred. Moreover, certain chemical reactions (e.g., Woodward-Hoffmann-forbidden reactions) and certain bond-breaking events require two or more "essential" electronic configurations. For them, single-configuration-based methods such as conventional CC and MBTP/MPPT should not be used; MCSCF or CI calculations would be better. Very large molecules, in which thousands of atomic orbital basis functions are required, may be impossible to treat by methods whose effort scales as N4 or higher; density functional methods would be better to use then. For all calculations, the choice of atomic orbital basis set must be made carefully, keeping in mind the N4 scaling of the one- and two-electron integral evaluation step and the scaling of the two-electron integral transformation step. Of course, basis functions that describe the essence of the states to be studied are essential (e.g., Rydberg or anion states require diffuse functions, and strained rings require polarization functions). As larger atomic basis sets are employed, the size of the CSF list used to treat dynamic correlation increases rapidly. For example, most of the above methods use singly and doubly excited
CSFs for this purpose. For large basis sets, the number of such CSFs, Nc, scales as the number of electrons squared n: times the number of basis functions squared IV. Since the effort needed to solve the CI secular problem varies as Ncz or NC),a dependence as strong as N4to M can result. To handle such large CSF spaces, all of the multiconfigurational techniques mentioned in this paper have been developed to the extent that calculations involving of the order of 100-5000 CSFs are routinely performed and calculations using 10000, 100000, and even several million CSFs are practical. A benchmark C1 calculation involving one billion deter~ninants~~ demonstrates the computational tractability of such large CSF expansion methods. Other methods, most of which ?an be viewed as derivatives of the techniques introduced above, have been and are still being developed. This ongoing process has been, in large part, stimulated by the explosive growth in computer power and change in computer architecture that has been realized in recent years. All indications are that this growth pattern will continue, so ab initio quantum chemistry will likely have an even larger impact on future chemistry research and education (through new insights and concepts).
Acknowledgment. This work was supported in part by the Office of Naval Research and by NSF Grant CHE-8814765. I thank my colleagues, W. H. Breckenridge, P. B. Armentrout, and C. A. Wight for insightful feedback and criticism and my Ph.D. students, postdoctoral associates, and collaborators for their many contributions. (49) Olsen, J.; Jmgensen, P.;Simons, J. Chem. fhys. t e f f . 1990, 169,463.
ARTICLES Electron Excitation Energy Transfer from Highly Excited Cs Atoms Forming High Rydberg State Atoms and Molecules Jorgen Lundin and k i f Holmlid* Department of Physical Chemistry GU, University of Goteborg and Chalmers University of Technology, S-412 96 Goteborg, Sweden (Received: November 15, 1989; In Final Form: August 20, 1990) The reactions of excited Cs atoms with various gases have been studied in a quadrupole mass spectrometer ion source. The excited atoms are formed in a thermionic converter (TIC) plasma and are sampled into the ion source as a molecular beam. Direct field ionization of the excited states from the plasma at field strengths up to 600 V/cm in the ion source gives ions The intensity of the doubly ionized Cs is often larger than that of singly ionized Cs, and it is believed Cs+, Cs2+,and Hz+. to be formed from Cs2*. The doubly excited Cs is found to transfer its excitation energy to gas molecules M in the ion source, as Cs2*+ M Cs* (or Cs) + M*. The excited molecules are field ionized to M+ or dissociate to smaller ions. Charge-exchange reactions are excluded, especially due to the low electron affinity of Cs. The variation of the positive current of M+ is studied as a function of gas pressure between IOd and IO4 mbar. During inlet of some gases, e.g. CO,, almost all mass peaks vary linearly with pressure, which is interpreted as excitation transfer from the Rydberg states of CO, to other atoms and molecules. The initial excitation-transfer cross sections are estimated to be 4000-10000 A*, corresponding approximately to n = IO for Cs2*.
-
1. Introduction
Reactions of Rydberg atoms have been studied by a number of research groups. Such processes may have the form of charge tran~ferl-~ A* + X A+ XA* + B A+ B + e -
-- + +
-
or associative i o n i ~ a t i o n ~ , ~ A* + B AB+ + eA*
+ BC
ABC+ + e-
For some processes very large cross sections of the order of IO3-l@
A2 have been reported.2J Since processes with such large cross
0022-3654/91/2095- 1029$02.50/0 0 199 1 American Chemical Society
Lundin and Holmlid
1030 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 100 m m
0 TIC Figure 1. Schematic picture of the experimental equipment. TIC is the thcrmionic converter with its Cs plasma, and QMS is the quadrupole mass spectrometer. Variable voltages are indicated. The shield around the QMS is liquid nitrogen cooled.
sections may be of great importance in many chemical reaction systems, they deserve detailed study. In our group, we have recently reported on the existence of high Rydberg states of cesium and doubly excited cesium atoms at high-temperature surfaces.68 We have also done mass spectrometric studies of the excited states from cesium plasma^.^^^ Studies by static ,field ionization on the flux from such plasmas are more complicated to interpret, however, partly due to the broad distributions of excited states. The present study is a continuation of this work, aimed at studying the reactions of singly and doubly excited atoms of Cs. It also demonstrates once more that the excited states exist in the gas phase and can give energy transfer and reactions not easily understood otherwise. 2. Experimental Section The excited states of cesium are formed in an "open" thermionic energy converter (TIC, TEC) of the type described previously from our group.I0 A cesium plasma is formed between two electrodes, the emitter at 1200-2000 K and the collector at 800 K. The cesium is brought into the interelectrode space through many small laser machined holes in the collector. The cesium pressure in this space is of the order of 1 mbar, and the electrode distance is 0.3-5 mm. Between the electrodes a voltage is usually applied, about 6 V ac at a frequency of 50 Hz. In the chamber surrounding the converter a pressure of mbar is maintained with diffusion pumps. As shown in Figure I , a circular opening leads to a second chamber, with a pressure of the order of IO" mbar. The particles diffusing out from the converter plasma can move through the opening and reach the ion source of the mass spectrometer mounted in this second chamber. In front of this opening, a shielded grid is mounted to enable energy analysis of the charged particles moving into the mass spectrometer chamber. This grid is also used to discriminate between ions and neutral species from the plasma. (This is a change from the apparatus used in ref 6, where a circular opening with no shield in front of it was employed.) The ion source is of the open "grid ion source" type used for ultrahigh-vacuum work (Balzers). It consists of a wire cage with a very small area exposed to the beam from the converter ( I ) Zollars, B. G.; Higgs, C.; Lu, F.; Walter, C. W.; Gray, L. G.; Smith, K. A.; Dunning, F. B.; Stebbings, R. F. Phys. Rev. A 1985, 32, 3330. (2) Kondow, T. In Physics and Chemistry of Small Clusters; Jena, P., Rao, B. K., Khanna. S. N.. Eds.; NATO AS1 Series, Series B: Physics; Plenum: New York, 1987; Vol. 158, p 639. ( 3 ) Barbier, L.: Ch€ret, M. J . Phys. E AI. Mol. Phys. 1987, 20, 1229. Smith, K. A.; Dunning, (4) Kalamarides, A.; Walter, C. W.; Zollars, B. G.;
F. B. J . Chem. Phys. 1987, 87. 4238. (5) Khelifa, N.; Barbe, R.; Desfrancois, C.; Schermann, J . P. Book of Absrracfs, XI1 International Symposium on Molecular Beams, Perugia, 1989; p 362. (6) Lundin, J.; Pettersson, J. B. C.; Moller, K.; Holmlid, L. In Proceedings of the 23rd Intersociety Energy Conversion Engineering Conference; The American Association of Mechanical Engineers: New York, 1988; Vol. I , Paper No. 889222, pp 591-595. (7) Pettersson, J. B. C.; Holmlid, L. Sug. Sci. 1989, 2 l 1 , 263-270. (8) Hansson, T.; Aman, C.; Pettersson, J. B. C.; Holmlid, L. J . Phys. B 1990, 23, 2163-2171. (9) Lundin, J . ; Holmlid, L. In Advances in Mass Spectrometry; Longevialle, P., Ed.; Heyden & Son: London, 1989; Vol. I I A , pp 204-205. (IO) Holmlid, L.; Moller, K. Appl. Phys. A 1984, 33, 199-204.
0
50
100
150
m/z
1 1
I CS"
0
50
100
I1 I
150 mlz
Figure 2. Typical mass spectra with a plasma in the converter at emitter temperature 1400 K, with electron emission at 1.4 mA in (A) and with no electron emission (field ionization) in (B).
and a plate with an exit opening holding the wire cage. Inside the cage, the field strength is very small, and extraction of the ions from the source takes place through penetration of the field outside the exit opening. Between the ion source and the quadrupole rod system, a small circular slit is mounted as an extractor, usually at U, = -120 V voltage. Computer plots have been made to study the field between the cage and the extractor, and the field strength is quite constant over the opening in the slit, which is important for the field ionization process. The quadrupole mass spectrometer has a mass range up to m / z 500 (Balzers QMH 51 1 and QMA I 50). The voltage of the quadrupole field axis UFA is variable. In Figure 1, the apparatus used is shown schematically. The actual voltages used are given in the figure legends of Figures 2-9. The signal is measured directly with an electrometer, and spectra are recorded with a computer. 3. Theory Doubly excited states of Cs have been reported previously from our group.* Not very much is known about them or their reactions. In the present experiments, such excited states originate from a thermal plasma and probably carry relatively high excitation energies. Exciting the two outermost electrons gives a maximum energy of 3.87 25.1 eV = 29.0 eV, which means that they are energetic enough to ionize most atoms and molecules. Since such atoms have two electrons in very highly excited orbitals, they may exhibit special electronic properties with a large correlation between the two excited electrons, as described in the general case in ref 12. This probably means that they may be quite long-lived, and we estimate their time of flight before ionization in the present experiments to be at least 200 ps. The characteristics of singly excited atoms in high Rydberg states are quite ~ell-known.'~Such states can be formed by both
+
( I I ) Deleted in proof. ( I 2) Berry, R. S.; Krause, J. L. In Evolution of Site Effects in Chemical Dynamics; Prigogine, I., Rice, S.A., Eds.; Adv. Chem. Phys. LXX, Part I ; Wiley: New York, 1988; p 35. (13) Stebbings, R. F.; Dunning, F. B. Rydberg Stores of Atoms und Molecules; Cambridge University Press: Cambridge. 1983.
Excitation Energy Transfer from Cs2*
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1031
atoms and molecule^,^^+'^ and they are easily field ionized even at quite low field strengths.I6 4. Results and Discussion Most experiments have been done with the ion source cage voltage U, (see Figure 1 ) at 90 V. The extractor slit voltage UE has usually been 0 or -120 V, and the difference in the results between these two cases is small. The standard value of the field axis potential UFAin the QMS is 0 or 50 V, and it has not been an important parameter in most experiments. The potential of the grid in front of the QMS source U, has been varied more frequently, and the signal changes have often been large. The standard value is 9 V, which means that practically no positive ions from the TIC plasma can pass through the grid. 4.I. Field Ionization and Field-Induced Processes. The difference in the behavior of the signals from the mass spectrometer with and without electron emission (impact ionization) is shown in Figure 2. The Cs+ peak at m / z 133 is the same in both cases. The electron impact ionization normally ionizes a fraction of 10-3-10-4of ground-state atoms and molecules passing the ion source under the conditions used, and it would probably not disturb other ionization mechanisms operating simultaneously in the source, like field ionization. The flux giving rise to the mass peak at m / z 133 is thus ionized by a mechanism that obviously is much more efficient than electron impact. Ionization at surfaces in the ion source with such a high probability seems highly unlikely since the ion source is an open wire cage, with only a small surface area exposed to the beam flux from the TIC. It is likely that the ionization mechanism is field ionization of excited Rydberg states of Cs. This has been concluded before6v9and will also be discussed further in a forthcoming publication. The next highest mass peak in field ionization is Cs2+ at m / z 66.5, which is larger with than without electron impact ionization, in this case even larger than the Cs+ peak with electron impact. The only realistic possibility to form such a doubly ionized state with a large probability with or without electron impact, which requires at least 29 eV, is via a doubly excited Cs state, Csz*. Such states can survive for quite a long time in field-free space, which we have reported on previously in refs 7 and 8. The ionization mechanism may be field ionization or some other so far not well-known mechanism induced by the fields. (The contribution from excited negative ions (Cs*)-may be large for some plasma conditions in the but it can be suppressed by the grid at the chamber wall. Further, it does not appear likely that Cs2+ is formed from (Cs*)- in the ion source.) In field ionization, i.e. without electron emission, also m / z 2, 14, and 28 are apparent. While m / z 28 certainly is formed from N2*, the precursor of m / z 14 is less clear. It might be N*, but also NZ2*,which could give N?+, is possible. However, the most likely process goes via N?*, which may dissociate as
-
NZ2* N
+ N+ + e-
I
-lU 10
+
(14) Schiavone, J . A.; Smyth, K. C.; Freund, R.S . J . Chem. Phys. 1975, 63, 1043. (15) Tarr, S. M.;Schiavone, J . A.; Freund, R. S . J . Chem. Phys. 1981,
Io
Io
m
IO
Cage voltage (V) Figure 3. Variation of intensity of field ionization mass peaks with the voltage of the ion source cage Uc The extractor voltage was -I 20 V. The voltage of the field axis in the quadrupole U,, was 0 V.
- I /
-11
I
-‘
A
PLASMA
I4N//.r”’” -10
I
W
-41.4
,
m
(1)
due to vibrational predis~ociation.~~ (The complete reaction from Cs2* N2 is exothermic by a maximum energy of 4.7 eV.) This agrees with the peak being rather broad. With electron impact, other peaks appear, like m / z 44 (CO,+), 40 (Ar+), and 32 (02?. Both m / z 28 and 14 increase when the electron impact ionization is turned on, which indicates that a large part of the excited molecules of N2 are not in very easily field ionized states. 4.2. Properties ofthe Excited States. The nature of the main species observed by field ionimtion and electron impact ionization was studied in experiments involving variation of the voltage of the ion source cage with no electron emission in Figure 3 and variation of the electron energy in Figure 4. In Figure 3, the ion source cage voltage was varied with the voltage of the equal to 0 V. The signal increased quadrupole field axis ( UFA)
74, 2869. (16) Bekov, G. I.; Letokhov, V. S. Appl. Phys. 19 1983,30, 161.
-101
-
B
NO PLASMA ,
m
70
M
110
Electron energy ( e 9 Figure 4. Variation of some mass peaks with electron energy, at an electron emission current of 1.4 mA. Data in (A) are found with a plasma in the interelectrode space in the converter, while data in (B) are for the case of no plasma with no ac voltage over the converter. Emitter temperature was 1400 K.
for all the masses m / z 14, 28, 66.5, and 133, but the variation with cage voltage was different for each peak. This indicates that the ions are formed in the ion source and also that the processes for formation of the different ions vary. The Cs+ signal in Figure 3 rises smoothly from low voltages of the cage in the ion source. This indicates that the signal is due to a distribution of Cs atoms in Rydberg states extending up to energies close to the ionization limit. At voltages above 60 V, the signal decreases somewhat, which probably indicates that ionization outside the cage starts, giving ions that cannot move into the source or the quadrupole. The peak at m / z 66.5 in Figure 3 is assumed to be formed by field ionization of Cs2*. Its variation with cage voltage is clearly different from that for Cs*, and the Cs2+signal starts to rise with
Lundin and Holmlid
1032 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 A
I
-8d
(a.u.)
I
II
0
50
0
ll
I
100
I
150
50
100
-
200
150
mlz Figure 5. Field ionization mass spectra found with admission of N2 gas at a pressure of I .4 X IOd mbar (A) and with admission of C 0 2gas at 2X mbar (B). The emitter temperature in the converter was 1300 K. A -#
-
-#A
-
n -10
-
-
v
M
-
-11s-12
L/' -6
-4
-8.6
B -#
4.8
c -10 M
2 -10s -11
-1ld
-12
Figure 6. Variation of field ionization mass peak intensities, as collector current in amps, with total pressure in millibar in the QMS chamber, during C 0 2gas inlet. The sloping line indicates a truly linear response. Emitter tcmpcraturc was 1400 K.
1%
(P)
Figure 7. Variation of field ionization mass peak intensities, as collector current in amps, with total pressure in millibar in the QMS chamber,
during N2gas admission. The sloping line indicates a linear variation with pressure. Emitter temperature was 1300 K.
L] -10s -11
-4
4
cage voltage at higher voltages than Cs+. In Figure 4 it is seen that a lower electron energy is required to effect ionization when a plasma exists in the converter. This means that some excitation of the atoms giving Cs2*takes place in the plasma, even if a large part of the excitation .energy probably is transferred to the atom already at the electrode surfaces. The peak m / z 28 is interpreted to correspond to N2+,formed from N2* in a high Rydberg state. In Figure 3, the signal rises rapidly above 30 V, in a way different from Cs+. This indicates that the Rydberg states of N, are not so high in energy as Cs* in this special case. In Figure 4, the signal of N2+increases when a plasma exists in the converter, but it does not change its form and thus not its excitation state significantly. The Rydberg state of N2 is, in most cases studied, probably formed in the ion source and not in the plasma, but exceptions have been observed, as discussed below. The peak at m / z 14 does not change as rapidly as m / z 28 with cage voltage, but they both start to increase above 30 V. The m / z 14 signal is the one which increases most slowly with voltage in Figure 3. As discussed above, this signal may be due to dissociation of N22*,and the present results indicate that the decomposition to N + is initiated by the field. In Figure 4, m / z 14 and 66.5 vary in a similar way when the plasma conditions are changed. This indicates that m / z 14 is due to N + formed by dissociation of highly excited N**, which is formed in collisions between Cs2* and N2. 4.3. Reactions. Reactions between the excited flux from the converter and various gases have been studied by gas inlets into the QMS chamber and also into the converter chamber. Most experiments have employed gas inlets in the QMS chamber. Two field ionization mass spectra with N2 and C 0 2 inlet in the QMS chamber are shown in Figure 5 . The results presented in Figures 6-8, where different gases were admitted and the mass peaks measured as a function of the total
The Journal of Physical Chemistry: Vol. 95, NO. 3, 1991 1033
Excitation Energy Transfer from Cs2*
/
-93
-1l.a
4
/ P*r I
-5
-3
-t
1% (P) Variation of field ionization mass peak intensities, as collector current in amps, with total pressure in millibar in the converter chamber, during N2 gas inlet in that chamber. The sloping line indicates a linear variation with pressure. Emitter temperature was 1400 K. Figure 8.
pressure in the chamber, give some information about the detailed reactions. In Figure 6 , C 0 2 is admitted in the QMS chamber. Mass peaks m / z 2,66.5, and 133 decrease, while all other peaks increase with total pressure, viz. m / z 14, 28, 32,40, and 44. This can only be understood if the amount of ionization in the gas in the ion source is a general effect, mediated by the increased pressure of C02. A possible mechanism to explain this behavior can be found and starts with the reaction Cs2*
+ C02
followed by C02*
-
Cs* (or Cs)
+M
-
C02
+ C02*
+ M*
(2) (3)
M is here a general atom or molecule other than C 0 2 in the ion source, which gives the observed ions. This type of reaction gives a linear variation with C 0 2 pressure of the signal caused by M*. (If M is C 0 2 ,the variation will tend to quadratic in pressure.) Ionization is not necessary or likely in these steps, and the ions result from field ionization of M* in the ion source, after diffusion of the excited Rydberg type atoms to the exit of the source. Reaction 3 should be efficient when the ionization energy of M is somewhat larger than that of C 0 2 , since this makes possible a near-resonant energy transfer to a Rydberg level. If the ionization energy of M is smaller than that of C02, a direct ionization to M+ e- or excitation to M2* will take place. However, the direct ionization process seems less probable, and thus the energy transfer-ionization process is inhibited. In Figure 6, m / z 40 (Ar’) is the only gas peak which does not increase almost linearly with pressure. Since the ionization potential of argon is higher (1 5.7 eV) than for C 0 2 ( I 3.8 eV), it is likely that the excitation level of argon is not high enough for efficient field ionization at the low field strengths used or that some gas quenching is introduced at higher pressures. It is interesting to note that the C 0 2 +signal varies morc rapidly than linearly at low pressures, as remarked above if M in cq 3 is C 0 2 . Experiments with O2 (el = 12.1 eV)
+
instead of CO, give similar results, where almost all mass peaks vary with pressure. In Figure 7, N2 is admitted to the QMS chamber. The ionization potential of N2 is 15.6 eV. In this case, only m / z 14 and 28 increase approximately linearly with total pressure, while m/z 2,66.5, and 133 vary slowly with pressure. The peaks m / z 32, 40, and 44 increase slower than linearly with pressure and tend to level out above mbar. This indicates that N2 is not such a good excitation-energy-transfer agent as C 0 2 and O2 are, perhaps due to quenching of N22*via vibrational predissociation or due to the too large energy carried by such an excited state. (This type of behavior also demonstrates that the ionization processes depend on the gas admitted, with molecular specificity, and thus that other ionization processes, e.g. by UV radiation from the plasma or by ionization on the surfaces in the ion source, are unlikely.) In Figure 8, N2 is admitted to the TIC chamber instead. Also in this case, the m / z 14 and 28 increase approximately linearly with pressure, while the other mass peaks are almost independent of pressure. Peaks m / z 66.5 and 133 decrease with increasing pressure. Thus, excited N2 does form by collision with excited Cs, both in the QMS chamber and in the TIC chamber, but it is not very active in promoting excitation of the other gases in the chamber. This agrees with the observation that m / z 14 and 28 are the dominating gas peaks even without gas inlet, as in Figure 2. 4.4. Excitation Energy Transfer. In Figures 6-8 it is very clear that the total ion current formed is much larger than the Cs+ and Cs2+ion currents. This means either that the excitation energy of the active species is much larger than the ionization energy of the gases used and can be transferred in two or several consecutive excitation-transfer events or that some of the excited flux cannot be field ionized or otherwise avoids detection in the mass spectrometer. One possibility is of course that the active species have higher than thermal velocities and thus that only a fraction of these states, which in fact react in the ion source, are field ionized at the exit of the ion source. Since the excitation energy of Cs* is too low to give excitation close to the ionization limit for almost all other gases, it is anyhow clear that Cs* is not a likely candidate for the active species. ‘Instead, it must be concluded that doubly excited cesium, Cs2*, is the species which initiates the gas-phase reactions. The Csz+ ions are probably formed from a field-ionizable fraction of the doubly excited cesium atoms, as discussed above. However, the intensities of the Cs2+ and Cs’ ions vary almost identically with pressure in Figure 6-8, which could indicate that they have the same origin. It is possible that collisions with gas molecules can lead to inelastic scattering and internal changes in the excitation of Cs2*,and also the excitation-transfer reactions described above will transform cesium atoms from one excited structure to another. As discussed here, the flux of the exciting Cs2* may be larger than the observed Cs2+ current. However, assuming that the measured Cs2+currents correspond to the active flux, approximate cross sections can be calculated from the measurements. A simple derivation gives the cross section for excitation energy transfer from Cs2* to M* u
= (i*/i2*)
Ak2Tgas Tplasma’” Vgp(2 a m k ) I l 2
where i* is the total current formed by field ionization, i2* is the active flux (as current), A the cross-sectional area of the beam of exciting atoms into the QMS, V the ionization volume, g the relative velocity in the collision, p the gas pressure in the ion source, T,,, the gas temperature, and TPIasma the temperature of the Cs atoms from the plasma. Using this formula at mbar gives u =
const.(i*/i2*)
A2
with the constant varying between 400 and 2000 depending on the assumptions about the active dimensions and the plasma temperature. This gives a cross section of 8000-40000 A* for the reaction between Cs2*and N2. The cross section with C 0 2
1034 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 I
I
0
50
100
150
m/z
1
i
0
50
100
150 m/Z
Figure 9. Field ionization mass spectra with voltages U,= U E= UFA= 0 V. The grid voltage U, was 50 V in (A) and -50 V in (B).
seems to be a factor of 2 smaller. We will now assume not only that the measured i2* current corresponds to all the doubly excited flux but also that the cross sections can be converted to radii of the excited states (probability of reaction assumed to be unity up to the radius of the excited state). Then, diameters of the excited states of 70-220 A for Cs2* are found, giving principal quantum numbers n between 8 and 14. This is not unreasonable, compared to the n values that will be field ionized in the source: at 600 V/cm between the cage and the extractor all n values larger than or equal to 28 will be field ionized, while lower n values will survive in the excited state.I6 These cross-section values are of the same size as the largest cross sections reported for Rydberg atom reactions2v3 or larger. 4.5. Other Particles from the Plasma. The results presented here are usually found under conditions that will allow the neutral flux from the converter plasma to interact in the ion source and that minimizes the influence of other particles like ions from the plasma. There exists evidence of other particles like negative Cs
Lundin and Holmlid ions from a Cs plasma of the thermionic but in the present experiments they do not seem to be of importance for the processes observed. However, we have observed negative ions under somewhat different conditions and we cannot totally exclude an influence of negative Cs ions, but to have an influence they must have a very large excitation energy and must not be easily field ionized outside the ion source. To demonstrate the problems met to draw a clear distinction between these particles, we have made some simple experiments. Figure 9 shows two spectra taken under conditions where there is no field ionization in the ion source, since all electrodes there and the field axis are at ground potential. In (A), the grid in front of the QMS is at 50 V, and in (B) it is at -50 V. In (B), there exists a positive ion signal, probably from the plasma. The signal decreases toward larger masses, but the peaks observed do not match any mass that could come from the plasma and are thus caused by the mass-dependent transmission in the quadrupole. In (A), the signal rises with increasing mass, which indicates field ionization in the quadrupole field. In this case, highly excited negative ions as well as neutrals from the plasma can enter the QMS. The continuing studies in our group, concerning the reactions of excited states, have recently been extended to excited-state formation directly from hot surfaces, without a thermal plasma. In that case we have also used pulsed field ionization with very good time resolution coupled to time-of-flight mass spectrometry. Mass spectra resembling the ones presented here have been found, as will be reported in detail e1se~here.I~ 5. Conclusions We have observed excitation energy transfer from excited Cs atoms, probably doubly excited with principal quantum numbers approximately equal to IO. The cross sections are large, probably between 4000 and 10000 A2, and thus comparable to the largest cross-section values reported for Rydberg-state reactions. The excitation energy tranefer gives excited states of the gases used, CO,, N2, and 02,which are easily field ionized at electric field strengths of less than 600 V/cm and thus are in high Rydberg states.
Acknowledgment. This work was supported by the Swedish Natural Science Research Council (NFR) within a project concerned with plasma studies in thermionic converters. Our research on thermionic converters is supported by the Swedish National Energy Agency (STEV). (17) Hansen, L. K.; Woo, H . In Proceedings of the I E E E Infernational Conference on Plasma Science, Madison, WI, 1980; p 45. (18) Kuehn, D. G.;Sutcliff, D. E.; Chanin, L. M. Appl. Phys. Leu. 1978, 33, 906. (1.9) Wallin, E.; Hansson, T.; Holmlid, L. J . Phys. Chem., submitted for publication.
