Scattering in the Attractive Yukawa Potential in the Limit of Strong Interaction

Scattering in the attractive screened Coulomb (Yukawa) potential in the limit of strong interaction is investigated. It is shown that the scattering occurs mostly with large angles. The corresponding momentum-transfer cross section is calculated. The results are applied to estimate the ion drag force acting on an isolated micron-sized grain in low-pressure bulk plasmas.

Figure 1

Particle trajectories during collisions for different impact parameters, $\rho$. Interaction is via the attractive Yukawa potential. A unique parameter characterizing the scattering, $\beta$, is equal to 30. Impact parameters are chosen to be below, about, and above the transitional impact parameter, ${\rho }_{*}\simeq 4.24\lambda$.

Figure 2

Scattering angle $\chi$ versus the normalized impact parameter $\rho /{\rho }_{*}$ (${\rho }_{*}$ is the transitional impact parameter). The numerical calculations are for four different scattering parameters $\beta$.

Figure 3

Momentum-transfer cross section, ${\sigma }_{\mathrm{s}}$, normalized to the squared screening length, ${\lambda }^2$, versus the scattering parameter, $\beta$. Our numerical calculation ($+$) and earlier numerical results by Hahn et al. [4] (●) are shown. The analytical expression [Eq. (7), solid line] fits quite well the numerical calculations for $\beta >{\beta }_{\mathrm{c}\mathrm{r}}$. The analytical formula proposed in Ref. 3 agrees well with the numerical results for $\beta \lesssim 5$. The dotted line represents the standard Coulomb scattering theory.

Figure 4

The total momentum-transfer cross section, ${\sigma }_{\Sigma }$, normalized to the squared screening length, ${\lambda }^2$, versus the scattering parameter, $\beta$. The numerical results for different values of $a/\lambda$ are shown to illustrate the role of the finite particle radius, $a$. The dotted line corresponds to ${\sigma }_{\Sigma }=\pi {\rho }_{*}^2+{\sigma }_{\mathrm{s}}^{\mathrm{f}\mathrm{a}\mathrm{r}}$.