Electron-Atom Collision Cross Sections in Partially Ionized Dense Plasma
T.S. Ramazanov, K.N. Dzhumagulova, Yu.A. Omarbakiyeva, G.Roepke1
IETP, al Farabi Kazakh National University, 96a, Tole bi st., 050012, Almaty, Kazakhstan.
1Institute of Physics, University of Rostock, D-18051, Rostock, Germany
Abstract. The elastic cross sections in a partially ionized plasma are considered on the basis of the effective polarization potential, which takes into account quantum –mechanical and screening effects. The cross sections for the elastic scattering of atomic hydrogen on electron have been studied by the partial wave expansion method.
Keywords: Partially ionized plasma; polarization interaction potential; the elastic cross section
PACS: 52.20.-j, 52.20.Hv, 52.27.Gr
One of the most interesting problems of electron scattering is the elastic scattering of electrons on hydrogen atoms at low energies. The present theoretical work, which considered this problem, based on the wave expansion method. An investigation of scattering processes gives possibility to research interaction of particles, which participate in the scattering. The knowledge of interparticle interaction potential is necessary to adequate description of the thermodynamic and transport properties of partially ionized plasma. In our previous work the effective polarization potential for a partially ionized dense plasma was suggested, it takes into account quantum-mechanical and screening effects. The average distance between particles is3/143⎟⎠⎞⎜⎝⎛=naπ, where. It is well known that the state of the plasma depends greatly on the coupling parameter, which describes the ratio of potential energy of charged particles interaction at the average distance to their thermal energy. The plasma becomes non-ideal at. Furthermore we introduce the density parameter raennn=+ 2/BeakTΓ=1Γ>/SB (a is the Bohr radius), which decreases with increasing of densities.
Most of the potentials that describe interaction between a charge and an atom or ion are model potentials. In  the model of the Buckingham screened potential was taken for hydrogen plasma, that considers polarization of hydrogen atom in external field, it is frequently used in the form: 2222202()exp(1)2()DDerrrrrrα⎛⎞Ψ=−−+⎜⎟+⎝⎠ , (1)
where α is polarizability of atom and is a cutoff radius of hydrogen, (1/40/2Braα= 2(4)DBrkTneπ= is the Debye radius.
In paper  we proposed a pseudopotential for the interaction.
In figurase shifts are presented, they obta
02468100,00,10,20,30,40,50,60,7 δlkaB l=0 l=1 l=2 l=3 l=4 l=5FIGURE 3. The phase shifts as functions of wave number at 0.5,10srΓ== FIGURE 4. The phase shifts as functions of distance at 10.5,10,0.8sBrka−Γ=== 0510150,00,10,20,30,40,5 l=0 l=1 l=2 l=3 δlraB-1
erical solving Calogero’s equation for electron scattering on atomic hydrogen. It is shown that the phase shifts decreased with increasing of incident electrons energy. In the next figure 4 asymptotic behaviors of the phase shifts on large distance are presented. In figure 5 and 6 total and partial cross sections are presented for different coupling parameters. As it is shown from figures the cross sections decrease with increasing of coupling parameter, because with increasing of plasmas non-ideality the effective polarization potential becomes less and therefore there are decreasing effective interaction radius of potential and the cross sections.
3. T. S. Ramazanov,et al., J. Phys. A: Math. Gen
4. T. F. O’ Malley Phys. Rev 130, 1020 (1963). and
5. A. G. Khrapak and I. T. Iakubov, Electrons in Dense Gases60 (2005).
6. W Ebeling et al., Contrib. Plasma Phys. 45, 1
7. L. D. Landau and E. M. Lifshitz, Quantum mechanics III, Moscow:PhysMatGis, 1988 (in Russian). ring, New York: Academic Press, 1967.
8. F. Calogero, Variable Phase Approach to Potential Scatte
9. V. V. Babikov, The Method of Phase Functions in Quantum Mechanics, Moscow: Nauka, 1988 (in R
10. J. F. Willams, J. Phys. B: Atom. Molec. Phys. 8, 1683 (1975).
0246810121410-710-610-510-410-310-210-1100101 l=0 l=1 l=2 l=3 l=4 l=5Qea(k)/aB2kaB FIGURE 7. The absolute differential cross sections,
Опубликовано в рубрике Documents