Dedicated to Irene Z. CLASSICAL TUNNELING AS THE RESULT OF RETARDATION IN CLASSICAL ELECTRODYNAMICS: NONRELATIVISTIC CASE

The problem of radiation reaction in classical electrodynamics is still discussed in the literature (for ex. see [1]). This problem can be formulated in the following way: it is known that classical charged body moving with acceleration must radiate. Thus there is back reaction of outgoing electromagnetic waves. But what quantity feels this back reaction pure mechanical mass of a charged body or an effective mass, constructed from the mechanical mass and energy of self electromagnetic field? Is this effective mass constant on the trajectory of a moving body or a function of time? In another words, what is the dynamics of a charged body due to radiation reaction? To answer these questions long time ago [2] was proposed by Sommerfeld model of sphere with uniform surface charge Q and mechanical mass m. In nonrelativistic approximation such sphere obeys the equation (see also [3,4,5,6]):