THE ULAM PROBLEM AND THE IONIZATION OF RYDBERG ATOMS BY MICROWAVE-RADIATION

We study the Ulam problem for long limes (several million collisions) by numerical methods. We show that in the diffusion regime, which is v alid or moderate times, this problem is mathematically equivalent to t he problem of the diffusive ionization of atomic Rydberg states by mic rowave radiation. It is concluded that the diffusion regime sets in on ly for a very small number of initial conditions (field phases), It is theorized that the analogy between the two problems can be extrapolat ed to times longer than the diffusion time. We show in the Ulam proble m that after the diffusional buildup of energy has finished, the quasi stationary regime does not continue indefinitely: after several millio n particle-wall collisions the energy rapidly drops to zero. On the ba sis of this extrapolation we examine the possibility that an electron which has reached the continuous spectrum will not fly off to infinity (ionization), but will return to bound Rydberg states of the atoms (i f the field acts for a sufficiently long time). This can make the diff usive ionization probability much lower than the Value given by the kn own estimates. (C) 1998 American Institute of Physics.