Evaluation of elastic cross sections for electron scattering from PH₃ molecules

Evaluation of elastic cross sections for electron scattering from PH₃ molecules

2Department of Physics, Punjabi University, Patiala, 147 002, Punjab, (India) 3Department of Chemistry, M.L.N. College, Yamuna Nagar, 135 001, Haryana, (India) E-mail : dr_parjit@hotmail.com

Abstract

A parameter-free spherical optical potential (SOP) model is used to calculate the total cross sections for the elastic

r LH

L,H

(r)

A1 (r)

LH

(1)

scattering of electrons from phosphine molecules at incident energies up to 30 eV. The optical potential is constructed from a near-Hartree-Fock one-center expansion of a phosphine (PH3) wave function. This potential is then treated in a partial-wave analysis to extract total scattering cross sections using spherical approach. The qualitative feature of the scattering parameters (such as a Ramsauer-Townsend (RT) minimum around 1 eV) observed in recent experiments, is very well reproduced in the present model calculation.

1. Introduction

   In matter, energy deposition is due to the interaction of radiation with atoms and molecules. So investigation of electron scattering cross section is an interesting area of

   radiation physics. The total cross sections for electron/positron

   In the spherical approximation, we need only the first term (L = 0, H = 1) of the expansion of equation (1) in order to evaluate all the three potentials. Explicit expression for Vst(r) is given in the literature [5]. We have used modified semi classical exchange (MSCE) form of Vex(r) [6]. Finally, the correlation polarization potential (COP) is calculated from the expression given by Padial and Norcross [7] and Gianturco et a1 [8].

   At larger distances the COP Vp(r) is replaced by the correct asymptotic form -0/2r4 (0 is the dipole polarisability of PH3; we employ the experimental value of 32.67 au for 0). It is now a standard procedure to compute the lth partial-wave phase shift from the solutions of following 2nd order differential equation:

   collisions with a large number of atoms and polyatomic molecules have been measured from low (~ 1 eV) to keV energy region [1, 2]. These cross sections have important applications in space, plasma, laser, biomedical science and the environment. Many approaches ranging from as simple as independent atom models (IAM) [3] to ab initio methods [4]

   d 2

   dr2

   k 2 l l 1

   r2

   V r

   opt.

   fl kr 0

   (2)

   have been proposed. But in case of polyatomic molecules, ab initio calculations are quite difficult to perform. Therefore, our goal here is to apply a simple SOP model approach for calculating the total cross sections for PH3 molecule. In the present paper, phosphine has been chosen because it is a major component in the fabrication of materials for micro- and opto- electronics.

2. Theoretical Methodology

   1

   1

   1

   1

   1

   In the present SOP model, the complicated interaction between the electron molecule system is approximated by an optical potential composed of three local and real terms, namely the static (Vst ), exchange (Vex) and polarization (Vp) potential without involving any adjustable parameter. The PH3 molecule belongs to the C3v symmetry and has an electronic 1A1 ground state with the configuration 1a2 1e4 2a2 3a2 4a2 2e4 5a2 . The central quantity in the calculations of the optical potential is the charge density (r). The quantity (r) is expanded in terms of symmetry-adapted functions belonging to the totally symmetric 1A1 irreducible representation of the molecular point group

   where k2 is the electronic energy. Variable-phase approach (VPA) [9] was employed to find the solutions of equation (2). The total cross sections (t) are then easily obtained from the S matrix at each energy. All our cross sections are converged with respect to number of partial waves up to a value of 0.000 01 rad.

3. Results and Discussion

   We have calculated t cross sections for the e – PH3 system in the energy range of 0.1 30 eV. Calculations have been performed in several combinations of different potentials but in this paper we present results in only SEP model (i.e. static plus MSCE plus correlation polarization potential). In figure 1, t cross sections are presented in the energy range

   0.1 10 eV and compared with the experimental measurements of Szmytkowski et al [10] along with theoretical calculations of Munjal and Baluja [11] as well as Bettega and Lima [12]. It is indeed remarkable that our SEP calculation is able to reproduce the R-T minimum at around 1 eV. Figure 2 presents t cross sections at energies between 10

   – 30 eV. It is clear from the figures that the present results are

   in good agreement with experimental measurements in the entire energy region. Further it has been noticed that above 3 eV, our results are in better agreement with measurements.

   Fig 1: t for e – PH3 system in the energy range 0.1 – 10 eV. Calculations: , Present results in SEP model; – – -, Munjal and Baluja [11]; , Bettega and Lima [12]; Experiment: , Szmytkowski et al [10].

   The main title (on the first page) should begin 1-3/8 inches (3.49 cm) from the top edge of the page, centered, and in Times 14-point, boldface type. Capitalize the first letter of nouns, pronouns, verbs, adjectives, and adverbs; do not capitalize articles, coordinate conjunctions, or prepositions (unless the title begins with such a word). Leave two 12-point blank lines after the title.

4. Conclusion

We reported low-energy e – PH3 total cross sections by using a parameter-free correlation polarization potential along with exact static and approximate exchange model interactions. The R-T minimum position reproduced here is in agreement with measurements and other calculations.

Fig 2: t for e – PH3 system in the energy range 10 – 30 eV. Calculations: , Present results in SEP model; – – -, Munjal and Baluja [11]; , Bettega and Lima [12];

, Limbachiya et al [13]. Experiment: , Szmytkowski et al [10].

Acknowledgement

We gratefully acknowledge the financial support for this research work from Department of Science and Technology (DST), New Delhi, India under the Project No. SR/S2/LOP- 0015/2010(G).

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