Vector Particle with Anomalous Magnetic Moment and Electric Quadruple Moment in the Presence of Uniform Electric and Magnetic Fields

Abstract

In the paper, a spin 1 particle with anomalous magnetic and electric quadruple moments has been examined in presence of the external uniform electric and magnetic fields. A generalized 10-dimensional Duffin–Kemmer–Petiau equation is specified in cylindrical coordinates (t, r, φ, z) and corresponding tetrad. Solutions with cylindric symmetry are searched. On constructed solutions we diagonalize the operators of the energy and third projection of the total angular momentum. First, after separating the variables we derive the system of 10 first order differential equations for functions FA(r, z) = FA(r)FA(z), A = 1, . . . , 10. The use of the Fedorov–Gronskiy method permits to express 10 variables FA(r) through only three different functions f1(r), f2(r), f3(r). After that we derive the system of 10 differential equations for functions FA(z) dependent on the coordinate z. This system is solved by means of the method which generalized the known approach applied when solving a similar problem in Cartesian coordinates. In this way we derive the system of three second order differential equations for three primary functions. After diaginalizing the mixing matrix, the last system is transformed to separate equations for three new functions. All three equations are solved in terms of confluent hypergeometric functions.