Potential unscreened Coulomb

Figure 13. The screened Coulomb potentials [11c] The Naive Approximation (full curve) is compared with the Debye-Hiickel potential (dashed curve), both at c=50mM. The unscreened potential (wide full curve) is also shown for comparison.

That is, we are interested in y(r) = Y(r, oo) and the corresponding reaction rate, Kq — K(oo). The former satisfies the equation (3.2.39) with the boundary conditions (3.2.40). As it is clear from Chapter 3, the solution of equation (3.2.39) defines uniquely the survival probability u>(l oo) of geminate pairs. In a particular case of the Coulomb interaction, the solution of the steady-state equation (3.2.39) is simplified since for the unscreened Coulomb potential the relation V2C/(r) = 0 holds. Integrating the differential equation... 

Note that Eq. (6.37) (or Eq. (6.38)) does not depend on the particle volume fraction surface potential of a sphere of radius a carrying a total charge Q = 4na (i for the limiting case of k 0, expressed by an unscreened Coulomb potential. That is, the surface potential in this case is the same as if the counterions were absent. 

Equation (6.82) agrees with the unscreened Coulomb potential of a charged cylinder. That is, the surface potential in this case is the same as if the counterions were absent. 

For the dilute case (( < C 1), Eq. (6.147) can be approximated well by an unscreened Coulomb potential of a sphere carrying charge Q, namely. 

When Q < Q (low charge case), the surface potential may be approximated by Eq. (6.155), which is the unscreened Coulomb potential for the case where counterions are absent. The surface potential js is proportional to Q in this case. When 2 >2 (high charge case), the surface potential can be approximated by... 

In Rutherford scattering, the potential is unscreened Coulomb. The power parameter for this potential is m = 1. Derive the Coulomb differential cross-section using the power-law approximation and compare to the Rutherford cross-section given by... 

The calculation is for a uniform beam incident on isolated atoms in a channel (Fig. 8.7). Since we are only interested in scattering angles greater than the critical angle (y/c 1°), the impact parameter is relatively small (rt 10 2 A) thus we use the unscreened Coulomb potential. In this calculation the dechanneling is a result of binary scattering by isolated displaced atoms in an otherwise perfect crystal. 

Equation 15 holds for an unscreened Coulomb potential and hence is justified for sufficiently large projectile energies, i.e., for e > 1. Here the reduced energy e is defined as... 

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