Chaotization of a supercritical atom
Annotatsiya
Chaotization of supercritical (Z> 137) hydrogenlike atom in the monochromatic field is investigated. A theoretical analysis of chaotic dynamics of the relativistic electron based on Chirikov criterion is given. Critical value of the external field at which chaotization will occur is evaluated analytically. The diffusion coefficient is also calculated. PACS numbers: 32.80.Rm, 05.45+b, 03.20+i Study and synthesis of superheavy elements is becoming one of actual problems of the modern physics [1, 2]. Fast growing interest to the physics and chemistry of actinides and transactinides stimulates extensive study of superheavy elements. One of the main differences which leads to the additional difficulties in the study of superheavy atoms is the fact that the motion of the atomic electrons is described by the relativistic equations of motion due to the large values of the charge of the atomic nucleus. In this Brief Report we will study classical chaotic dynamics of the relativistic hydrogenlike atom with the charge of the nucleus Z> 137, interacting 1 with monochromatic field. Such an atom is called the overcritical atom [5]-[9]. Quantum mechanical properties of such atom was investigated by a number of authors [3, 4, 9]. Quasiclassical dynamics of the supercritical atom was investigated by V.S.Popov and co-workers [5]-[7]. The experimental way of creating the overcritical states are the collision experiments of slow heavy ions with resulting charge Z1+Z2> 137 [10, 11, 12]. To treat chaotic dynamics of the relativistic electron in the supercritical kepler field we need to write the unperturbed Hamiltonian in terms of action-angle variables. As is well known [5], for the relativistic electron moving in the field of charge Z> 137 point charge approximation cannot be applied for describing its motion i.e. there is need in regularizing of the problem. Such a regularizing can be performed by taking into account a finite sizes of the nucleus i.e. by cut off Coulomb potential at small distances: V (r) =