MBELL model

Contents 1. Introduction 318 2. Outline of the Models 322 2.1. MBELL model 322 2.2. Outline of the XCVTS model 324 2.3. GKLV model 326 2.4. Outline of the MUIBED Model 328 3. Experimental Data Sources 330 4. Discussion and Conclusions 330 Acknowledgments 375 References 376... 

The relativistic parameters Si, S2, and S3 in Eq. (10), the ionic parameters f and r) in Eq. (11), and the parameters Q and in Eq. (12) have been optimized by minimizing the chi-square, shown in Eq. (8), for fitting the experimental data with the criteria specified earlier. The optimization procedure is similar to that followed for the MBELL model excepting that the repetition over the number of targets is to be done for the same ionizing shell in place of orbit for seeking the convergence of the parameter values. The optimum values thus obtained for all parameters of the XCVTS model are tabulated in Table 6.2. 

The MBELL model combines the Bethe asymptotic form and the low-energy behavior of collision, respectively, through the first and series terms in Eq. (5) and contains nine shell-dependent parameters shown in Table 6.1 excluding the fixed parameter m. 

Bell et al. [33] proposed an analytical formula, widely known in the literature as the Belfast ionization (BELI) formula [34] that contains the dipole interaction term for the electron-impact ionization of atoms and ions. It has been applied to light atomic and ionic targets with species-dependent parameters. Godunov and Ivanov [34] applied the BELI formula to the El ionization of Ne 1 ions. Here also no generality as to parameters of the formula was provided regarding the species-dependent parameters. Moreover, the BELI formula does not make any allowance for relativistic effects. Haque et al. [35-38] have proposed a modification of this BELI model for evaluating the El K-, L-, and M-shell ionization cross sections of atoms. The relativistic and ionic effects are also incorporated in their modified BELI (MBELL) [35-38] model in addition to generalizing the species-independent... 

The calculated EISICS from the MBELL, XCVTS, GKLV, and MUIBED models are compared with available experimental data the K-shell ionization... 

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