The description of deformed many-body systems, in particular heavy deformed nuclei, in terms of a single particle basis in the laboratory system of coordinates is given. The basic building blocks are given by the coupling of rotational Wigner functions and spherical single particle orbitals to a good angular momentum.The deformed quasiparticle random phase approximation (dQRPA) built on this representation is derived by integrating the equation of motion on Euler angles. It provides a reasonable description of low-lying 2+ excitations in even-even spherical, transitional and well deformed nuclei, by using a common effective charge. Beta and double beta decays are investigated in terms of the proton-neutron dQRPA. The effective value of the axial-vector strength is derived. A similar influence of the nuclear environment on alpha and beta decays is evidenced.