All Figures

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig1.ps}\end{figure}$ Figure 1: The normalized function $G_n(\xi )/G_n(0)$ defined by Eq. (15) as function of the normalized drift velocity $\xi=\vert{\vec u}_s-{\vec u}_{s^\prime}\vert/a_{ss^\prime}$ with n=0, 1, 2, 3, and 4 ( solid curves). The dashed curves show the approximations given by Draine & Salpeter (1979) for the cases n=0 and n=4.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig2.ps}\end{figure}$ Figure 2: The momentum transfer cross section for collisions HCO⁺-H₂ as a function of $E_{\rm cm}$ computed by Flower (2000) ( dots and solid curve). The dashed curve shows the Langevin cross section.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig3.ps}\end{figure}$ Figure 3: The rate coefficient for HCO⁺-H₂ collisions as a function of the temperature T for $v_{\rm d}=0$ ( thick solid curve); and $v_{\rm d}=1$ km s^-1; $v_{\rm d}=2$ km s^-1 ( thin solid curves, bottom to top), compared with the Langevin rate ( dashed line).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig4.ps}\end{figure}$ Figure 4: Momentum transfer cross section for H₃⁺-H₂ collisions as a function of the energy in the center-of-mass system according to Phelps (1990) ( solid curve). The dotted line shows our extrapolation at low energies, whereas the dashed line shows the Langevin crosssection.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig5.ps}\end{figure}$ Figure 5: The momentum transfer rate coefficient for H₃⁺-H₂ collisions as function of the temperature T computed with the cross section shown in Fig. 4 for $v_{\rm d}=0$ ( thick solid curve); $v_{\rm d}=1$ km s^-1 ( dotted curve); $v_{\rm d}=5$ km s^-1 ( short-dash dotted curve); and $v_{\rm d}=10$ km s^-1 ( long-dash dotted curve). The dashed line shows the Langevin rate.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig6.ps}\end{figure}$ Figure 6: The momentum transfer cross section for H⁺-H₂collisions as a function of $E_{\rm cm}$ : fully-quantal calculation by Krstic & Schultz (1999a,c) ( solid curve), with our extrapolation to low energies ( dotted line); classical calculation by Bachmann & Reiter (1995) ( long-dashed curve); semi-empirical recommendations by Phelps (1990) ( dot-dashed curve); Langevin cross section ( dashed curve).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig7.ps}\end{figure}$ Figure 7: The collision rate coefficient for H⁺-H₂ collisions as a function of the temperature, computed with the momentum transfer cross section of Krstic & Schultz (1999a,c) for $v_{\rm d}=0$ ( thick solid curve); and $v_{\rm d}=2$ km s^-1; $v_{\rm d}=4$ km s^-1; $v_{\rm d}=10$ km s^-1 ( thin solid curves, bottom to top). The dashed line shows the Langevin rate.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig8.ps}\end{figure}$ Figure 8: The momentum transfer cross section for e-H₂ collisions as a function of the electron kinetic energy. Experimental values: England et al. (1988) ( empty triangles), Schmidt et al. (1994) ( empty squares), Shyn & Sharp (1981) ( empty circles), Nishimura et al. (1985) ( filled triangles), Khakoo & Trajmar (1986) ( filled squares), Brunger et al. (1990, 1991) ( filled circles). The dashed and dotted curves show the Langevin cross section and the quantum-mechanical theoretical results of Henry & Lane (1969), respectively. The solid curve shows the cross section adopted in this work.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig9.ps}\end{figure}$ Figure 9: The momentum transfer rate coefficient for e-H₂collisions computed with the cross section shown in Fig. 8 as a function of the temperature T for $v_{\rm d}=0$ ( thick solid curve); and $v_{\rm d}=50$ km s^-1; $v_{\rm d}=100$ km s^-1 ( thin solid curves, top to bottom), compared with the values computed with Eq. (14) of Draine (1983) for the same values of the drift velocity ( dotted curve). The dashed line shows the Langevin rate.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig10.ps}\end{figure}$ Figure 10: The momentum transfer cross section for collisions C⁺-H computed by Flower & Pineau-des-Fôrets (1995) as a function of the collision energy in the center-of-mass frame (original data, triangles; our interpolation, solid curve). The dashed curve shows the Langevin cross section.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig11.ps}\end{figure}$ Figure 11: The collision rate coefficient for collisions C⁺-H as a function of the temperature for $v_{\rm d}=0$ ( thick solid curve); and $v_{\rm d}=5$ ; $v_{\rm d}=10$ ; and $v_{\rm d}=15$ km s^-1 ( thin solid curves, bottom to top), compared with the Langevin rate ( dashed line).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig12.ps}\end{figure}$ Figure 12: The momentum transfer cross section for collisions H⁺-H computed by GKS as a function of the collision energy in the center-of-mass frame ( solid curve), compared to the Langevin cross section ( dashed curve). The empty circle is the measurement by Brennan & Morrow (1971) at $E_{\rm cm}\approx 5$ eV. The filled triangles are the values of the charge exchange cross section for the same interacting particles, measured by Newman et al. (1982), multiplied by 2.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig13.ps}\end{figure}$ Figure 13: The collision rate coefficient for collisions H⁺-H as a function of the temperature for $v_{\rm d}=0$ ( thick, solid curve); $v_{\rm d}=10$ ; $v_{\rm d}=50$ km s^-1; and $v_{\rm d}=100$ km s^-1 ( thin, solid curves, bottom to top); compared with the fitting formula of GKS for the same values of the drift velocity ( dotted curves), the fitting formula of Geiss & Bürgi (1986) for $v_{\rm d}=0$ ( long-dashed curve) and the Langevin value ( short-dashed curves).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig14.ps}\end{figure}$ Figure 14: Momentum transfer cross section for e-H collisions. Experimental values: Shyn & Cho (1989) ( filled circles); Williams (1975a,b) ( filled triangles); Shyn & Grafe (1992) ( filled squares); Callaway & Williams (1975) ( empty circles). The solid curve is the theoretical calculation of Dalgarno et al. (1999).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig15.ps}\end{figure}$ Figure 15: Collision rate coefficient for e-H collisions as a function of temperature, for $v_{\rm d}=0$ km s^-1 ( thick curve); $v_{\rm d}=50$ km s^-1; and $v_{\rm d}=100$ km s^-1 ( thin curves, bottom to top). The dashed line shows the Langevin rate.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig16.ps}\end{figure}$ Figure 16: The momentum transfer cross section for collisions H⁺-He, according to the fully-quantal calculations of Krstic & Schultz (1999a,b), as a function of the collision energy in the center-of-mass frame ( solid curve), compared to the Langevin cross section ( dashed line).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig17.ps}\end{figure}$ Figure 17: The collisional rate coefficient for H⁺-He collisions as a function of the temperature for $v_{\rm d}=0$ ( thick, solid curve); $v_{\rm d}=10$ km s^-1; $v_{\rm d}=20$ km s^-1; and $v_{\rm d}=30$ km s^-1( thin, solid curves, top to bottom) compared with the fitting formula of Geiss & Bürgi (1986) for $v_{\rm d}=0$ ( long-dashed curve) and the Langevin value ( short-dashed curves).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig18.ps}\end{figure}$ Figure 18: The momentum transfer cross section for e-He collisions as a function of the electron kinetic energy. Experimental values: Crompton et al. (1970) ( filled triangles); Milloy & Crompton (1977) ( filled squares). The dotted curve shows the experimental results of Ramanan & Freeman (1990), with uncertainty $\sim$ 3%. The dashed curve shows the Langevin cross section, whereas the solid curve is the cross section adopted in this work.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig19.ps}\end{figure}$ Figure 19: The momentum transfer rate coefficient for e-He collisions computed with the cross section shown in Fig. 18 as a function of the temperature T for $v_{\rm d}=0$ ( thick, solid curve); and $v_{\rm d}=50$ km s^-1; $v_{\rm d}=100$ km s^-1 ( thin, solid curves, bottom to top). The dashed line shows the Langevin rate.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig20.ps}\end{figure}$ Figure 20: Momentum transfer rate coefficient for collisions grain-neutral as a function of the relative drift velocity, from Eq. (15) with n=0 ( solid curve), compared with the expressions from Draine & Salpeter (1979) ( dotted curve); Nakano (1984) ( dashed curve); and Mouschovias & Ciolek ( dot-dashed curve).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig21.ps}\end{figure}$ Figure 21: Argument of the Coulomb logarithm $\Lambda _{\rm g i}$ for grain-ions interactions normalized to $\Lambda _{{\rm e}i}$ for pointlike particles, and ratio $r_{\rm g}/{\overline r_{\rm C}}$ as a function of the reduced temperature of the ions $\tau _{i}=r_{\rm g} kT_{i}/(Z_{i}e)^2$ . The solid and dashed curves are for ``light ions'' with effective atomic weight 1 and ``heavy ions'' with effective atomic weight 25.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig1.ps}\end{figure}$	Figure 1: The normalized function $G_n(\xi )/G_n(0)$ defined by Eq. (15) as function of the normalized drift velocity $\xi=\vert{\vec u}_s-{\vec u}_{s^\prime}\vert/a_{ss^\prime}$ with n=0, 1, 2, 3, and 4 ( solid curves). The dashed curves show the approximations given by Draine & Salpeter (1979) for the cases n=0 and n=4.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig2.ps}\end{figure}$	Figure 2: The momentum transfer cross section for collisions HCO⁺-H₂ as a function of $E_{\rm cm}$ computed by Flower (2000) ( dots and solid curve). The dashed curve shows the Langevin cross section.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig3.ps}\end{figure}$	Figure 3: The rate coefficient for HCO⁺-H₂ collisions as a function of the temperature T for $v_{\rm d}=0$ ( thick solid curve); and $v_{\rm d}=1$ km s^-1; $v_{\rm d}=2$ km s^-1 ( thin solid curves, bottom to top), compared with the Langevin rate ( dashed line).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig4.ps}\end{figure}$	Figure 4: Momentum transfer cross section for H₃⁺-H₂ collisions as a function of the energy in the center-of-mass system according to Phelps (1990) ( solid curve). The dotted line shows our extrapolation at low energies, whereas the dashed line shows the Langevin crosssection.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig5.ps}\end{figure}$	Figure 5: The momentum transfer rate coefficient for H₃⁺-H₂ collisions as function of the temperature T computed with the cross section shown in Fig. 4 for $v_{\rm d}=0$ ( thick solid curve); $v_{\rm d}=1$ km s^-1 ( dotted curve); $v_{\rm d}=5$ km s^-1 ( short-dash dotted curve); and $v_{\rm d}=10$ km s^-1 ( long-dash dotted curve). The dashed line shows the Langevin rate.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig7.ps}\end{figure}$	Figure 7: The collision rate coefficient for H⁺-H₂ collisions as a function of the temperature, computed with the momentum transfer cross section of Krstic & Schultz (1999a,c) for $v_{\rm d}=0$ ( thick solid curve); and $v_{\rm d}=2$ km s^-1; $v_{\rm d}=4$ km s^-1; $v_{\rm d}=10$ km s^-1 ( thin solid curves, bottom to top). The dashed line shows the Langevin rate.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig10.ps}\end{figure}$	Figure 10: The momentum transfer cross section for collisions C⁺-H computed by Flower & Pineau-des-Fôrets (1995) as a function of the collision energy in the center-of-mass frame (original data, triangles; our interpolation, solid curve). The dashed curve shows the Langevin cross section.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig11.ps}\end{figure}$	Figure 11: The collision rate coefficient for collisions C⁺-H as a function of the temperature for $v_{\rm d}=0$ ( thick solid curve); and $v_{\rm d}=5$ ; $v_{\rm d}=10$ ; and $v_{\rm d}=15$ km s^-1 ( thin solid curves, bottom to top), compared with the Langevin rate ( dashed line).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig14.ps}\end{figure}$	Figure 14: Momentum transfer cross section for e-H collisions. Experimental values: Shyn & Cho (1989) ( filled circles); Williams (1975a,b) ( filled triangles); Shyn & Grafe (1992) ( filled squares); Callaway & Williams (1975) ( empty circles). The solid curve is the theoretical calculation of Dalgarno et al. (1999).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig15.ps}\end{figure}$	Figure 15: Collision rate coefficient for e-H collisions as a function of temperature, for $v_{\rm d}=0$ km s^-1 ( thick curve); $v_{\rm d}=50$ km s^-1; and $v_{\rm d}=100$ km s^-1 ( thin curves, bottom to top). The dashed line shows the Langevin rate.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig16.ps}\end{figure}$	Figure 16: The momentum transfer cross section for collisions H⁺-He, according to the fully-quantal calculations of Krstic & Schultz (1999a,b), as a function of the collision energy in the center-of-mass frame ( solid curve), compared to the Langevin cross section ( dashed line).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig19.ps}\end{figure}$	Figure 19: The momentum transfer rate coefficient for e-He collisions computed with the cross section shown in Fig. 18 as a function of the temperature T for $v_{\rm d}=0$ ( thick, solid curve); and $v_{\rm d}=50$ km s^-1; $v_{\rm d}=100$ km s^-1 ( thin, solid curves, bottom to top). The dashed line shows the Langevin rate.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8819fig20.ps}\end{figure}$	Figure 20: Momentum transfer rate coefficient for collisions grain-neutral as a function of the relative drift velocity, from Eq. (15) with n=0 ( solid curve), compared with the expressions from Draine & Salpeter (1979) ( dotted curve); Nakano (1984) ( dashed curve); and Mouschovias & Ciolek ( dot-dashed curve).
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