Non-integrability of the anisotropic Stormer problem with angular momentum

We consider the Hamiltonian of the Stormer problem reduced with respect to the rotational symmetry about the magnetic dipole. Considering an anisotropy in the masses, it turns out to be a classical model for the hole-mediated ferromagnetism in Ga1−xMnxAs. We study the anisotropic Stormer problem from the point of view of the existence of a third integral of motion in involution with the angular momentum pφ and the Hamiltonian H, and that is independent of both. For pφ=0 the anisotropic Stormer potential is homogeneous. Almeida et al. [Rev. Bras. Fı́sica 28 (4) (1998)] found that it is non-integrable for all values of the anisotropy parameter outside the interval [0, 2/3]. In this paper, we are able to extend non-integrability to this interval except for two points, viz., 5/12 and 2/3. For these two values, the integrability remains undecided. If pφ≠0, the anisotropic Stormer problem is non-integrable for any value of the anisotropy.