Scattering of intermediate-energy positrons by C, N, O atoms and the corresponding diatomic molecules: elastic and total cross-sections

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1 1 October 1999 Ž. Chemical Physics Letters Scattering of intermediate-energy positrons by C,, O atoms and the corresponding diatomic molecules: elastic and total cross-sections David D. Reid a, J.M. Wadehra b,) a Department of Physics and Astronomy, Eastern Michigan UniÕersity, Ypsilanti, MI 48197, USA b Department of Physics and Astronomy, Wayne State UniÕersity, Detroit, MI 48, USA Received 13 July 1999 Abstract Elastic and total Ž elastic plus absorption. cross-sections for the scattering of positrons by carbon, nitrogen and oxygen atoms and the corresponding diatomic molecules Ž C, C, CO,, O and O. in the energy range from 1 to 5 ev are presented. Parameter-free interaction potentials along with the additivity rule are used in the calculations. Good agreement with the experimental data is obtained wherever such comparisons can be made. q 1999 Elsevier Science B.V. All rights reserved. Positron-atom and positron-molecule scattering are topics of fairly intense current interest in both theoretical as well as experimental studies because they involve interactions of matter with antimatter. Several theoretical techniques are known which provide the positron-atom scattering cross-sections fairly accurately at either low or high impact energy. However, in the intermediate impact energy region, one has to resort to approximate theoretical techniques to obtain the scattering cross-sections. In the case of molecular targets, complications also arise from the non-spherical nature of the interaction. A sensitive test of any approximation technique developed for the scattering of intermediate energy electrons by molecules is provided by its application to the corre- ) Corresponding author. Fax: q ; wadehra@physics.wayne.edu sponding case of intermediate energy positron-molecule scattering. Several recent papers have presented w1 5x calculations of total cross-sections for electron scattering by diatomic and polyatomic molecules using the additivity rule of the independent atom model. In this Letter, we are using this method to present the calculations of both the elastic and total Ž elastic plus absorption. cross-sections for the scattering of positrons by diatomic molecules containing atoms of carbon, nitrogen and oxygen. In particular, the target molecules under present consideration are C, C, CO,, O and O and the range of the positron energy is from 1 to 5 ev. Similar calculations for a different set of molecular targets have been presented by Raizada and Baluja wx 6. In our previous work, we have developed parameter-free model potentials for the polarization and absorption interactions which are quite useful for intermediate to high-energy positron scattering from atomic tar r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž. PII: S

2 386 ( ) D.D. Reid, J.M. WadehrarChemical Physics Letters gets Žnoble gases w7,8x and alkali-metal atoms w9 x.. In the present calculations, we have used these model potentials along with the independent atom model to obtain the various cross-sections. The present positron-molecule scattering crosssections are calculated using a partial wave decomposition of the scattering amplitude for a particular atomic target Ž carbon, nitrogen or oxygen.. The independent atom model is used to approximate the molecular scattering amplitude in terms of atomic scattering amplitudes w1 x. Essentially, the molecule is considered to be a collection of independent scattering centers Ž atoms. located at ri for i s 1to. The molecular amplitude fmol for elastic scatter- ing in terms of atomic amplitudes f i, then, is Ý f Ž u. s f Ž u. expž i kpr., mol i i where " k is the momentum transfer of the projectile, that is, ksk sinž ur.. Here u is the scattering angle and Es" k r m is the energy of the projectile of mass m. Using the optical theorem, the total Ž elastic plus absorption. cross-section for the scattering of positrons by the molecule is 4p stots Im fmolž us. k 4p s Ý Im fiž. k Ý i s s. This is the additivity rule for the total cross-sections which implies that the total cross-section for the molecule is simply the sum of the total cross-sections for the individual atoms. The elastic scattering cross-section is obtained from the molecular scattering amplitude as H p s sp < f Ž u. < sin u du, elas mol which after averaging over all orientations of the molecule becomes p sin k r ) ij selas sph Ý fi fj sin u du, k r i, js1 ij where rij is the separation between the ith and jth atoms in the molecule. ote that the elastic crosssections do not follow any additivity rule similar to the one for total cross-sections. In the present calculations, the positron-atom interaction is taken to be a complex function of the form VintŽ r. svst Ž r. qvcp Ž r. qivabs Ž r.. Here V st, the static part of the interaction, is obtained using the analytical Hartree Fock wave functions of the target atom w11 x. V cp, the parameter-free correla- tion polarization part of the interaction, is obtained from the target electron charge density w1 x. Finally, the absorption part of the interaction, V abs, which takes into account the cumulative effect of all the inelastic processes, is the quasifree model developed by us w7 9 x. These potentials are placed in the radial Schrodinger equation which is integrated, via the umerov technique, out to a radial distance of 6 a.u. Several complex phase shifts Ž up to lsl max. are calculated exactly by comparing the radial wave function at two adjacent points. The value of l max depends upon the energy of the incident positron and in the present energy range lmax is taken to be 6. Phase shifts for the higher partial waves are calculated via the Born approximation and their contribution to the atomic scattering amplitude is taken into account via closed-form expressions for long-range interactions w13 x. The results of our calculations for the total and the integrated elastic cross-sections for positrons scattered from various diatomic molecules are presented in the figures and tables. Fig. 1 shows the present results for the total cross-sections for 1 5 ev positrons scattered from diatomic nitrogen. These results are compared with the experimental measurements of Charlton et al. w14 x, Hoffman et al. w15 x, Sueoka and Mori w16 x, and Dutton et al. w17 x. The present results show quite good agreement with the experimental data throughout the entire range of impact energies. Fig. shows the present results for the total cross-sections for positrons scattered from diatomic oxygen. Again, the range of positron energy is from 1 to 5 ev. These results are compared with the experimental measurements of Charlton et al. w14x and Dababneh et al. w18 x. Here, we observe that our results overestimate the experi-

3 ( ) D.D. Reid, J.M. WadehrarChemical Physics Letters Fig. 1. Total cross-sections for positrons scattered from. The experimental data are as follows: open circles, Charlton et al. w14 x; closed circles, Hoffman et al. w15 x; closed squares, Sueoka and Mori w16 x; open squares, Dutton et al. w17 x. Fig. 3. Total cross-sections for positrons scattered from CO. The experimental data are as follows: closed squares, Sueoka and Mori w16 x; closed circles, Kwan et al. w19 x. Fig.. Total cross-sections for positrons scattered from O. The experimental data are as follows: open circles, Charlton et al. w14 x; closed circles, Dababneh et al. w18 x. Fig. 4. Total cross-sections for positrons scattered from C, C, and O. The dotted curve, solid curve and the dashed curve represent the present theoretical cross-sections for C, C and O, respectively.

4 388 ( ) D.D. Reid, J.M. WadehrarChemical Physics Letters Table 1 Elastic cross-sections Žin units of a. for positron scattering from various atoms and diatomic molecules Ž. E ev C O C C CO O O mental results at 1 ev while showing good agreement at higher impact energies. This good agreement, however, is primarily with the results of Dababneh et al. which are consistently higher than those of Charlton et al. above 1 ev. Since the measured cross-section values only extend up to 6 ev positron energy, the present calculations are, to the best of our knowledge, the only values for positron O scattering cross-sections above 6 ev. Fig. 3 shows the present results for the total crosssections for intermediate energy positrons scattered from carbon monoxide. These results are compared with the experimental results of Sueoka and Mori w x w x 16 and Kwan et al. 19. The present results are in good agreement with the experimental data. The experimental results are available only up to 5 ev; however, we expect our results to be accurate even in the high-energy range where no corresponding experimental cross-sections are available for comparison. For all the target molecules, the experimental values of the total cross-sections show a tendency to deviate from the present results as the positron energy is lowered to 1 ev. This is caused by the neglect of multiple scattering effects as well as by the approximations inherent in the independent atom Table Total cross-sections Žin units of a. for positron scattering from various atoms and diatomic molecules E Ž ev. C O C C CO O O

5 ( ) D.D. Reid, J.M. WadehrarChemical Physics Letters model. As an example, the equilibrium internuclear separations of molecules C, C, CO,, O and O are.48,.3,.13,.7,.17 and.8 a, respectively. The fact that the de Broglie wavelength of the incident positron ranges from.3 a at 1 ev to.38 a at 5 ev suggests that the indepen- dent atom model would certainly not be valid at positron energies below 1 ev. We are also able to use the present approach to calculate positron-molecule scattering data for targets andror at impact energies that have not been or cannot be easily measured experimentally. Fig. 4 displays the present predictions for the total crosssections for positron scattering from C, C and O molecules. We are not aware of any experimental measurements for positrons scattered from these three targets. However, given the success of the present results for molecular nitrogen, oxygen and carbon monoxide, we feel that our predicted total cross-sections for C, C and O molecules are also reason- ably accurate in the intermediate energy range. In Tables 1 and we list the numerical values of the total cross-sections as well as our predictions for the integrated elastic cross-sections for positrons scattered from diatomic molecules consisting of atomic carbon, nitrogen and oxygen. It is obvious from the values of the cross-sections in Table 1 that the elastic cross-sections for molecules cannot be obtained from the corresponding atomic cross-sections by any additivity rule. To summarize, we have found, in this Letter, that total cross-sections for scattering of positrons from diatomic molecules containing C, and O atoms can be calculated with good accuracy above 1 ev using parameter-free model potentials along with the independent atom model. References wx 1 D. Raj, Phys. Lett. A 16 Ž wx J. Sun, Y. Jiang, L. Wan, Phys. Lett. A 195 Ž wx 3 Y. Jiang, J. Sun, L. Wan, Phys. Rev. A 5 Ž wx 4 K.. Joshipura, P.M. Patel, J. Phys. B 9 Ž wx 5 Y. Jiang, J. Sun, L. Wan, J. Phys. B 3 Ž wx 6 R. Raizada, K.L. Baluja, Phys. Rev. A 55 Ž wx 7 D.D. Reid, J.M. Wadehra, J. Phys. B 9 Ž L17. wx 8 D.D. Reid, J.M. Wadehra, J. Phys. B 3 Ž wx 9 D.D. Reid, J.M. Wadehra, Phys. Rev. A 57 Ž w1x.f. Mott, H.S.W. Massey, The Theory of Atomic Collisions, 3rd edn., Oxford Univ. Press, Oxford, 1965, p w11x E. Clementi, C. Roetti, At. Data ucl. Data Tables 14 Ž w1x D.D. Reid, J.M. Wadehra, Phys. Rev. A 5 Ž w13x J.M. Wadehra, S.. ahar, Phys. Rev. A 36 Ž w14x M. Charlton, T.C. Griffith, G.R. Heyland, G.L. Wright, J. Phys. B 13 Ž 198. L353. w15x K.R. Hoffman, M.S. Dababneh, Y.-F. Hsieh, W.E. Kauppila, V. Pol, J.H. Smart, T.S. Stein, Phys. Rev. A 5 Ž w16x O. Sueoka, S. Mori, J. Phys. Soc. Jpn 53 Ž w17x J. Dutton, C.J. Evans, H.L. Mansour, J. Phys. B Ž w18x M.S. Dababneh, Y.-F. Hsieh, W.E. Kauppila, C.K. Kwan, S.J. Smith, T.S. Stein, M.. Uddin, Phys. Rev. A 38 Ž w19x C.K. Kwan, Y.-F. Hsieh, W.E. Kauppila, S.J. Smith, T.S. Stein, M.. Uddin, M.S. Dababneh, Phys. Rev. A 7 Ž