No abstract

Rational approximations are presented for the second-order (Uehling) and fourth-order (Kallen-Sabry) vacuum-polarization potentials in configuration space. These approximations may be applied to point-charge or finite-inducing-charge distributions. For the second-order potential, two approximations are given, with nominal accuracies of nine and four figures for the range 0 & r & oo. For the fourth-order potential, one approximation of about three-figure accuracy is given for the range 0 & r &4, .Although the solution for the lowest-order electron-positron vacuum-polarization potential (second-order correction to the photon propagator) around a point charge was reduced to quadrature' in 1935, no entirely satisfactory means of evaluating this result in routine problems has yet been given. This potential is needed for several applications, including the calculation of exotic (and electronic) atom energy levels, and the calculation of some charged-particle scattering cross sections. The best methods of evaluation available to date are two expansions about r= 0 (r is the distance from the point charge). One is a series due to McKinley. ' The other is a different expansion' based on the so-called Glauber technique, ' a technique which is apparently due to Rarita and Sommerfield' and which involves exponential integrals.Both of these methods fail at large r, and they suffer from unnecessary computational effort for the level of accuracy that they yield. In the present note we report two rational approximations to this function. These approximations are valid over the entire range 0( r&~, and they represent considerably improved levels of accuracy and/or efficiency. In addition, we report a somewhat less accurate polynomial fit to the fourth-order vacuum-polarization function.The second-order vacuum-polarization potential around a static point charge Za, acting on a particle of charge -e, is 2 g~g2 2r i', (r) = --K, 3 pr 2 where fd'r'p(r') =Z. If p(r) is spherically symmetric, the angular integrations may be performed to obtain U, (r) =--' dr'r'p(r') K,r r'~-2

No abstract

No abstract

No abstract