Abstract
In order to find the total collision cross-section a direct method of the effective potential (EPM) in the framework of classical mechanics was proposed. EPM allows to over come both the direct scattering problem (calculation of the total collision cross-section) and the inverse scattering problem (reconstruction of the scattering potential) quickly and effectively. A general analytical expression was proposed for the generalized Lennard-Jones potentials: (6–3), (9–3), (12–3), (6–4), (8–4), (12–4), (8–6), (12–6), (18–6). The values for the scattering potential of the total cross section for pairs such as electron–N\(_{2}\), N–N, and O–O\(_{2}\) were obtained in a good approximation.
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Abbreviations
- \((m-n)\) :
-
The generalized Lennard-Jones potential with the degrees m and \(n (m>n)\): \(U(r)=C_{m,n}\epsilon \left( {\left( {\frac{d}{r}} \right) ^{n}-\left( {\frac{d}{r}} \right) ^{m}} \right) =\frac{A}{r^{m}}-\frac{B}{r^{n}}\), J
- \(C_{m,n}\) :
-
\(\frac{n}{n-m}\left( {\frac{n}{m}} \right) ^{\frac{m}{n-m}}\)
- U(r):
-
The scattering potential, J
- \(\epsilon \) :
-
The function minimum, J
- d :
-
The collision diameter, m
- \(\alpha \) :
-
The polarizability, m\(^{3}\)
- \(\varepsilon \) :
-
The dielectric environment permittivity
- \(\varepsilon _0\) :
-
The electric constant, 8.8541 \(\times \) 10\(^{-12}\) F/m
- e :
-
The elementary electronic charge, 1.6021766208 \(\times \) 10\(^{-19}\) Kl
- \(\mu \) :
-
The reduced mass, \(\mu =\frac{m_1 m_2 }{m_1 +m_2 }\) kg
- \(v_\infty \) :
-
The velocity at infinity, m/s
- \(p_\infty \) :
-
The impulse at infinity, kg m/s
- \(\rho \) :
-
The impact parameter, m
- \(r^{*}\) :
-
The first real root of equation \(U(r)=0\), \(r\ge 0\)
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Tsyganov, D.L. Calculations of Total Classical Cross Sections for a Central Field. Few-Body Syst 59, 74 (2018). https://doi.org/10.1007/s00601-018-1394-7
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DOI: https://doi.org/10.1007/s00601-018-1394-7