J Force Constants for Central Forces

This expression must be compared with (3.13), namely 

K) Evaluation of the Coulomb Matrix Using Ewa1d s Method 

The second term in (K.9) is the potential energy of a point charge z e at a 

The first term is the contribution from lying inside a sphere of radius R about the origin, and the second is from that part lying outside the sphere. From the normalization condition 

This quantity decreases rapidly with increasing R and therefore behaves like a short range potential, provided n is suitably chosen. The sum for defined by (K.8) therefore converges rapidly. The situation is different for 

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