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JOURNAL OF CHEMICAL PHYSICS

LETTERS TO THE EDITOR

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VOLUME 110, NUMBER I I JANUARY 1999

The Letters to the Editor section is divided into three categories entitled Notes, Comments, and Errata. Letters to the Editor arelimited to one and three-fourlhs journal pages as described in the Announcement in the 1 January 1999 issue.

NOTES

Total electron scattering cross section for CI2G. D. Cooper, J. E. Sanabia, and J. H. MooreDepartmentof Chemistry,Universityof Maryland,CollegePark,Maryland20742

J. K. Olthoff') and L. G. ChristophorouElectricityDivision,ElectronicsandElectricalEngineeringLaboratory,NationalInstituteof Standardsand Technology,Gaithersburg,Maryland20899

(Received 17 August 1998; accepted 25 September 1998)

[S0021-9606(99)02001-2]

Chlorine is used in a number of technologies such asrare-gas halide lasers and plasma processing. For this reasonattempts have been made to model its behavior in gas dis-charges and plasma reactors. In these efforts, electron colli-sion data are crucial and yet not sufficient.1 A significantcross section for which measurements are needed over a

wide range of energies is the total electron scattering crosssection, (J'scie ). At the time that we undertook to perform ameasurement of (J'scie) for Cl2 there were no measurementsof (J'sc,t<e), except one unacceptably large cross section(-6ooXlO-2om2 near 8 eV) made in 1937.2 As we werepreparing our data for publication, a new measurement3 of(J'scie) for Cl2 was published for electron energies rangingfrom 20 meV to 9.5 eV.

In this note we report absolute measurements of (J'scie )for Cl2 between 0.3 and 23 eV. The present measurementsgenerally agree (within combined uncertainties) with the re-cent measurements of Gulley et at} thus confirming theirmeasurements, and extend the range of electron energies to23 eV. The present measurements are also compared withpreviously reported measurements4 and calculations5 of thetotal rotational excitation cross section, (J'rot,t(e), of Cl2 toprovide the first assessment of the contribution of vibrationalexcitation to (J'sc.t(e) for Cl2.

Figure 1 shows the present measurements of (J'scie ) .The measurements were made using a total scattering appa-ratus described earlier.6The apparatus consists of an electrongun followed by a trochoidal monochrometer and a collisioncell filled with the gas of interest. The cross section is deter-mined by measuring the unscattered portion of the electronbeam with and without the gas in the collision cell. Theelectron beam energy resolution was -100 meV. The totalestimated 1(J'uncertainty for the cross-section measurements(:t20%) is derived from the estimated uncertainties of thepressure measurement (:t 15%), the uncertainties in the ef-fective length of the collision cell immersed in the magneticfield «:t1O% above I eV),6 and possible errors (:t5%)

0021-9606/99/110(1 )/682/2/$15.00

caused by the finite acceptance angle of the detector (2°).Relative uncertainties, based upon the scatter in the mea-sured signal, are -2%.

The recently published total scattering cross sections3are also shown in Fig. 1 as small open circles (0). The twomeasurements of (J'scie) exhibit the same general shape,with our data falling below the previous data at all but thelowest energies. Agreement between the two measurementsis within the combined uncertainties for energies above 0.5eV. For comparison, previously measured4values of (J'rot,t(e)are also shown in Fig. 1, along with the calculated5values of(J'rot,t(e) and (J'rot,e(e ), the cross section for rotational elasticscattering.7While our present measurements of (J'sc,t(e) areobserved to fall below the measurements4 of (J'rotie) at

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FIG. L Electron scattering cross sections for C12: (x) present measure-

ments of total electron scattering cross section, U"'..( e ); (0) previous mea-surements of u",.,(e) by Gulley et al. (Ref. 3); (-0-) measurements ofGote and Ehrhardt (Ref. 4) of total rotational scattering cross section,

urot.,(e); (- -) calculation of Kutz and Meyer (Ref. 5) of the total rota-tional scattering cross section, U ro~'( e); (- - -) calculation of Kutz andMeyer (Ref. 5) of the total elastic rotational scattering cross section,

urot..(e).

682 @ 1999 American Institute of Physics

J. Chern. Phys., Vol. 110, No.1, 1 January 1999

some energies (a physical impossibility), these data are notinconsistent with each other within the combined estimateduncertainties of the two measurements. The lower values of

our measurements of (Tsc.t(e ), compared to the other data inFig. 1, may result in part from the fact that electrons scat-tered forward into small angles (~2°) with little energy lossare detected as "unscattered" in our measurements due tothe presence of the magnetic field. This may be a significantfactor in the present experiment, as previous measurements4have shown that forward electron scattering is appreciable atall energies for Clz.

As can be seen in Fig. 1, the (Tsc.t<e) data exhibit peaks(or bumps) that can be attributed to resonance-enhancedelectron scattering. The peaks at low energies observed byGulley et ai. and the bump in our data near 2.5 eV corre-spond to the negative ion states identified by electron attach-ment studies1,8-10near 0.3 and 2.5 eV. The large peak in the(Tsc.t<e)data near 8 eV corresponds to the negative ionstate1,8-10at 5.5 eV overlapping with the lowest electron-excited Feshbach resonance of Clz at 7.50 eV, identified byan electron transmission study.u The minimum near 0.4 eVis a distinctive feature common to all the cross sections inFig. 1.

The comparable magnitude of the measured values of(Tsc.t<e) and (Trot,le) implies a significant role for rotationalscattering over most of this electron energy range; however,the fact that (Tsc.t(e ) exceeds (Trot.t<e ) in certain energyranges indicates that there exists a vibrational excitation con-tribution to the total scattering cross section. Chlorine is ahomopolar molecule, and measurements on other homopolarmolecules, such as Nz, Oz, and Hz, have shown that directvibrational excitation is much smaller than indirect (or reso-nance enhanced) vibrational excitation.1Z,13Thus, the contri-bution to (Tsc.t<e) from direct vibrational excitation should besmall, so the large magnitude of (Tsc.t<e ) compared to(Trot,t(e) for electron energies below 1 eV implies the pres-ence of significant indirect vibrational excitation, most prob-ably via scattering through the low-lying (-0.03 eV) nega-tive ion state of Clz. The vibrational excitation energy of Clzis only 0.07 eV,14and the spacing of the peaks and inflec-tions in the data of Gulley et a1.3at 0.089, 0.14, and 0.2 eVare not inconsistent with expected excitations of progres-sively higher vibrational levels with decreasing probability.Similarly, the higher values of (Tsc.t<e) around 8 eV suggesta contribution from indirect vibrational scattering via thenegative ion states of Clz in this energy range. In this energyrange, electronic excitation is also possible, but calculationsby Rescigno15indicate that the cross section for this pro-cesses would be only about 1X lO-zo mZ at 8 eV. The de-gree to which the total scattering cross section exceeds therotational excitation cross section in this region suggests that

~

Letters to the Editor 683

the magnitude of the vibrational excitation cross sectioncould be lOX lO-zomz or larger. This is significantly higherthan the values attributed to vibrational excitation cross sec-tions derived by Boltzmann-based models.16 Some vibra-tional excitation would also be expected at energies near thenegative ion state at 2.5 eV. This conclusion is contrary tothe general statement of Gulley et ai.3 that there is relativelylittle contribution to (Tsc.t<e) from inelastic events in the en-ergy range between 200 meV and 9.5 eV. In fact, rotationaland vibrational excitation appear to account for the majorityof (Tsc.t<e) in this energy range.

In conclusion, the data in Fig. 1 indicate that: (i) Thescattering cross sections exhibit a minimum around 0.4 eV,(ii) the largest contribution to the total scattering cross sec-tion of Clz comes from rotational scattering, except for elec-tron energies near the minimum, (iii) the total cross sectionhas a significant contribution from indirect vibrational exci-tation at energies near the minimum, presumably via thelowest negative ion state of Clz, and (iv) in the energy rangearound 8 eV there is a significant contribution to (Tsc.t<e )from indirect vibrational scattering, in addition to the largerotational inelastic scattering (rainbow scattering).4.5

Work supported by NSF Grant No. CHE-95-03348.

a)Electronic mail: james.olthoff@nist.gov1L. G. Christophorou and J. K. Olthoff, J. Phys. Chern. Ref. Data (to be

published).21. B. Fisk, Phys. Rev. 51, 25 (1937).

3R. 1. Gulley, T. A. Field, W. A. Steer, N. J. Mason, S. L. Lunt, J.-P.Ziesel, and D. Field, J. Phys. B 31, 2971 (1998).

4M. Gote and H. Ehrhardt, J. Phys. B 28, 3957 (1995).

5H. Kutz and H.-D. Meyer, Phys. Rev. A 51, 3819 (1995).6H.-X. Wan, J. H. Moore, and J. A. Tossell, 1. Chern. Phys. 91, 7340

(1989).

7The term "rotational elastic scattering cross section, Urot.e(e ) " is used by

the authors of Ref. 5 to designate j = 0-+0 scattering. The total rotational

cross section, Urot.,(e), is the sum of Urot,e(e) and the cross section for

rotational excitation to higher rotational levels, j.

8M. V. Kurepa and D. S. Balic, J. Phys. B 11, 3719 (1978).9W._C. Tam and S. F. Wong, J. Chern. Phys. 68, 5626 (1978).

lOR. Azira, R. Abouaf, and D. Teillet-Billy, J. Phys. B IS, L569 (1982).

11D. Spence, Phys. Rev. A 10, 1045 (1974).12L. G. Christophorou, Atomic and Molecular Radiation Physics (Wiley-

Interscience, New York, 1971), p. 328.13H. Ehrhardt, L. Langhans, F. Linder, and H. S. Taylor, Phys. Rev. 173,

222 (1968).

14K. P. Huber and G. Herzberg, Molecular Spectra and Molecular StructureN: Constants of Diatomic Molecules (Van Nostrand Reinhold, New York,1979).

15T. N. Rescigno, Phys. Rev. A SO, 1382 (1994).

16G. L. Rogoff, J. M. Kramer, R. B. Piejak, IEEE Trans. Plasma Sci. PS-14,103 (1986); N. Pinhao and A. Chouki, Proceedings XXII Int. Conf. onPhenomena in Ionized Gases, Hoboken, USA, July 31-August 4, 1995,

edited by K. H. Becker, W. E. Carr, and E. E. Kunhardt, ContributedPapers 2, 1995, p. 5.