PHYSICAL REVIE% A VOLUME 30, NUMBER 2 AUGUST 1984

Rotational excitation of CH4 molecules by low-energy positrons

Ashok Jain' and D. G. ThompsonDepartment of Applied Mathematics and Theoretical Physics, Queen 's University Belfast,

Belfast BT71NN, Northern Ireland(Received 16 January 1984)

Cross sections for rotationally elastic and inelastic scattering of low-energy positrons by methanemolecules are reported in the adiabatic-nuclei-rotation approximation. A model-potential approach is em-

ployed, in which an accurate static potential is appended with an ab initio nonparametric polarization poten-tial. The present positron results are compared with the corresponding electron cross sections, There areremarkable differences between the two sets of results for both elastic and inelastic processes.

The subject of positron-atom (and molecule) scattering isnow a field of intense activity from both experimental andtheoretical points of view; Morrison, Gibson, and Austinhave given references of the review articles published todate on the positron scattering. In most of these references,discussion of the excitation of vibrational and/or rotationallevels of the molecules is almost negligible. In this paper,we are concerned only with the rotational transitions in apolyatomic molecule due to incoming slow positrons (belowthe positronium threshold).

From the experimental point of view, it has now becomepossible to resolve small energy spacings (such as the rota-tional energy levels; the vibrational energy spectrum is rela-tively easier to resolve) in a molecule due to scattering by aparticle; for example, rotational excitation of molecules byelectron impact has recently been measured in severalmolecular targets like CO, N2, and H20 (Jung er al. ; seealso Tanaka3 for CH4). Although there have been no mea-surements on rotational excitation of molecules by positronimpact, its investigation is of some importance. Masseyhas recently pointed out that the rotational excitation crosssections for electrons and positrons are likely to be quitedifferent, and much larger differences are to be expected forvibrational excitation.

There have been a few calculations on rotational excita-tion of molecules by positron impact: Hara' has reportedcross sections for rotational transitions in H2, N2, and 02 inthe distorted-wave approximation; in the fixed-nuclei modelwith a one-center formalism, Bailie and Darewych andBailie, Darewych, and Lodge have studied vibrational androtational excitation of H2. Very recently, Morrison, Gib-son, and Austin have calculated rotational excitation crosssections of H2 by positron impact using laboratory-frameclose-coupLing theory.

We have, therefore, two objectives in mind: (i) to reporttotal, momentum transfer, and differential cross sections forrotationally elastic and inelastic scattering of positrons byCH4 below the positronium threshold; and (ii) to comparethese results with the corresponding electron data. In doingso, our main emphasis will be on the understanding of thedifference between the two types of processes.

The main approximations and the method of solving cou-pled differential equations have already been discussed indetail in our earlier publications regarding positron ' andelectron"' scattering by CH4. Since the present theory ofpositron scattering is a counterpart of our electron-moleculescattering model (the possibility of positronium formation, ,

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virtual or real, is neglected altogether in this investigation),the cross-section formulas, various approximations, and thedetails of the calculations are exactly the same as, for exam-ple, discussed for the electron case. ' We will not repeatthat analysis and discussion here (for more details seeJain'3).

In Fig. I we show our results for the total elastic (0 0)and inelastic (0 3 and 0 4) cross sections for both thepositron and the electron cases. The correspondingmomentum-transfer cross sections are shown in Fig. 2. Inthe elastic case there is a considerable difference betweenthe two sets of cross sections: positron scattering exhibitsno minimum at low energy as compared with the well-

30 1098 1984 The American Physical Society

30 BRIEF REPORTS 1099

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FIG. 3. Same as in Fig. 1, but for the differential cross sectionsat 60'.

known Ramsauer-Townsend (RT) minimum for the elec-tron case. We also note that a.;(E) & a.;(P) for E & 1 eVbut that a.;(E) & o.;(P) for E & 1 eV. A similar situationoccurs in the case of the elastic momentum-transfer (a. )cross sections (Fig. 2). Here, o. (E) & o. (P) for E & 0.5eV, but a. (E) & o. (P) for E & 0.5 eV. In addition, theo. (P) curve has a wide minimum around 0.8 eV as com-pared with the sharp Ramsauer-Townsend minimum around0.2 eV for the electron case. However, the presence or ab-sence of an RT rninimurn in the integrated total positron-molecule cross section is very sensitive to the treatment ofpolarization. Since in the present second-order treatment,the polarization potential is independent of the charge of theparticle, a true positron-CH4 polarization potential maychange the above features in the total cross section.

We now consider inelastic cases for both the o-; and o-

cross sections. For the positron case, we see thato-;(0 3) » o.;(0 4) at all energies. However, in theelectron case the 0 4 transition is stronger than the 0 3

transition except in the energy range 1.5—5 eV. A similarsituation exists for the o. cross sections (Fig. 2).

For positron-molecule scattering, there has so far been nomeasurement of a differential cross section (DCS), which isa very sensitive test of the validity of a theoretical model orthe accuracy of experimental observations. We also present,therefore, some theoretical data on the DCS. Figure 3displays our rotationally elastic and inelastic DCS for elec-trons and positrons at 60' only. Here also the 0 4 transi-tion is very weak as compared with the 0 3 transition inthe positron case; again this is just the reverse of electronscattering. Finally, in Fig. 4, the positron-CH4 DCS aredisplayed at 3, 5, and 7.5 eV for all three transitions. There

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1100 BRIEF REPORTS 30

is a deep minimum around 50' at 3 eV in the elastic case;these minima shift towards lower angles as the energy in-creases (around 40' at 5 eV and around 30' at 7.5 eV). Weconclude that the rotational excitation mechanisms in CH4due to incoming positrons or electrons are quite different.We do not yet know how the present predictions may bechanged if one takes into account the formation of virtualpositronium in this energy range.

Another point of interest is the investigation of thepositron-molecule scattering phenomenon using differentpolarization potentials for electrons and positrons. In thepresent perturbative treatment (up to second order) the pos-itron and electron polarization potentials are identical. Onlya third-order treatment will introduce any differencebetween the two. Carrying out such a third-order perturba-tion theory is a very difficult task and has not yet been ac-complished for any molecule.

Morrison et al. ' have recently studied positron-H2 polari-zation potentials. The approach of Morrison et al. is quitedifferent from the present one: they calculated a self-consistent-field variationally determined polarized energy bycalculating the distortion of the target orbitals due to theelectric field of the scattering particle (different for electrons

and positrons). They modified these polarization potentialsby a multiplicative cut-off function with an adjustableparameter and showed that the results were sensitive to thecharge of the projectile. They obtained a third, and againdifferent, set of results using an ab initio electron polariza-tion potential.

Morrison et al. ' concluded this study of H2 by stating that"it is important to determine if the sensitivity of the polari-zation potential (and calculated cross sections) to the sign ofthe charge of the scattering particle seen in the presentstudy of positron-H2 collisions holds for other positron-molecule systems. " In the present work, we provide someresults against which future work on this problem may becompared.

One of the authors (A.J.) is grateful to the Queen' sUniversity of Belfast for financial support and to Dr. D. W.Norcross for critically reading the manuscript. He alsothanks D. F. J. da Paixao for useful discussions. Thisresearch problem was suggested to one of the authors (A.J.)by the late Professor H. S. W. Massey in order to see thedifference between the rotational excitation mechanism inmolecules due to electrons and positrons.

Present address: Joint Institute for Laboratory Astrophysics,University of Colorado, and National Bureau of Standards,Boulder, CO 80309.

~M. A. Morrison, T. L. Gibson, and D. Austin, J. Phys. B (to bepublished). This article summarizes earlier reviews on positronscattering.

K. Jung, Th. Antoni, R. Muller, K. M. Kochen, and H. Ehrhardt,J. Phys. B 15, 3535 (1982).

H. Tanaka, in Symposium on Electron-Molecule Collisions: .Invited Pa-pers, edited by I. Shirnamura and M. Matsuzawa (University ofTokyo, Tokyo, 1979).

4H. S. W. Massey, Can. J. Phys. 60, 461 (1982); (private communi-cation).

5S. Hara, J. Phys. B 5, 589 (1972).P. Bailie and J. W. Darewych, J, Phys. Paris Lett. 35, L243 (1974).P, Bailie, J. W. Darewych, and J. G. Lodge, Can. J. Phys. 52, 667

(1974).M. A. Morrison, T. L. Gibson, and D. Austin, Bull. Am. Phys.

Soc. 28, 810 (1983).A. Jain, J. Chem. Phys. 78, 6579 (1983).A. Jain and D. G. Thompson, J. Phys. B 16, 1113 (1983),A. Jain and D. G. Thompson, J. Phys. B 15, L631 (1982).A, Jain and D. G. Thompson, J. Phys. B 16, 3077 (1983).A. Jain, Ph. D. thesis, The Queen's University of Belfast, 1983.