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In present research article, modified Khare-BEB model has been employed to calculate the electron impact ionization cross section for oxygen molecule (O2) from ionization threshold to 10 MeV. These are the first calculations for oxygen molecule at relativistic energies. The collisional parameters CRP and M^2 also has been calculated . The calculations are compared with available experimental data and other previous theoretical results. We have found a good agreement among the present results, other previous calculations, and experimental data.

To find suitable formula for calculation of electron impact ionization cross section of Oxygen molicule.

Krishankumar and Srivastava [4] have measured the electron impact cross section by using crossed electron beam molecular beam collision geometry and relative flow technique for oxygen molecule for electron impact energies from ionization threshold to 1000 eV with 13% experimental error. In 1995 Straub et al. [5] reported the experimental data for ionization cross section due to electron impact. They used time of flight mass spectrometer with a position sensitive detector to collect the all energetic fragments ions. They have claimed 3.5% in their experimental studies. Rapp and Englander-Golden [6] have also measured the total ionization cross section of O2 molecule from threshold to 1 keV by using ionization tube from threshold to1 keV. We have only one experimental data at relativistic energies (.1-2.7 MeV) those measured by Reike and Prepejchal [7]. They have measured the cross sections in term of two collisional parameters CRP and Mi2. Recently Sharma and Sharma [8] have calculated the ionization cross section by using Jain Khare semi empirical approach from threshold to 10 KeV.

Theory

The electron impact ionization cross sections of a molecule for j_th molecular orbitalin the modified Khare-BEB method [9] are given by 

(1)

where, Mott term (the ionization cross section due to the hard collision) σ_jM   is given by

kinetic energy of bound electron, the first Bohr  radius, the ionization energy, the occupation number of molecular orbital, the kinetic energy of the incident electron, rest mass of electron, velocity of light and Rydberg energy, respectively. The Bethe cross-section σ_jB is

(3)

where the term X is given by

and the cross section due to the transverse interaction is

 

To evaluate total ionization cross section and collision parameters of molecule, the contributions come from all molecular orbital are added. 

The theoretical methods described in above section are employed to calculate the total ionization cross sections of oxigen molecule.The required molecular parameters binding energies I, kinetic energies of bound electrons U and occupation numbers N are taken from reference [10].

The figure 1 shows present total ionization cross sections along with three experimental data and two theoretical calculations for oxygen molecules due to electron impact from threshold to 10KeV. The present calculations are found in good agreement with experimental results of Rapp and Englander-Golden [6] within 13% for E<100 eV. While for E>100 eV our cross sections underestimate the experimental results. It is evident from figure present rsults are in good agreement with the experimental data those measured by Straub et al. [5] for most of energy range. A fair agreement is also found between our calcultions and experimental results Krishankumar and Srivastava [4] for E>50eV. However, below this energy present results oversetimste the experimental data. Furthermore, we have also found a good agreement among all three theoretical calculations i.e. present results, Kim-BEB calculations [10] and Sharma & Sharma results [8].

Fig.1 Total ionization cross sections (TICS) for oxygen moleculein  10^-16 cm². Solid line, dotted lineand dashed linerepresent present results, Kim-BEB calculations [10] and Sharma & Sharma [8] , respectively. filled circles, opencircles, and filled rectanglesrepresent the experimental results of Krishankumar& Srivastava [4], Rapp & Englander-Golden[6], and Straub et al. [5], respectively.

At relativistic impact energies (.1-10MeV), present cross sections along with experimenta data of Reike and Prepejchal [7] have been depicted in figure (2). Our calculations are in good agreement with experimental results. The values of calculated collisional parameters, C_RP and M_i² are 44.6 and 3.95 at 1 MeV, respectively. The present value of CRP is greater than experimental result (38.85)by 14.83%, however theoretical value of M_i² is lower than experimental value by 5.95%. The value of C_RP does not change with incident energy which is according to expectations.

Fig. 2This figure shows the present total ionization cross sectionsalong with experimental data of Reike and Prepejchal [7]for oxygen molecule in energy range (.1-10MeV) in 10^-16 cm²

In present article, the total ionization cross sections of oxygen molecule due to electron impact have been calculated from ionization threshold to 10MeV and compared previous available data in literature. The agreement between present calculations and experiments is found satisfactory over a wide range of energy.The application of the Khare BEB model to calculate the total ionization cross sections of other molecules is of interest.

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