Analytical calculation of the nucleation rate for first order phase transitions beyond the thin wall approximation

First order phase transitions in general proceed via nucleation of bubbles. A theoretical basis for the calculation of the nucleation rate is given by the homogeneous nucleation theory of Langer and its field theoretical vers ion of Callan and Coleman. We have calculated the nucleation rate beyond th e thin wall approximation by expanding the bubble solution and the fluctuat ion determinant in powers of the asymmetry parameter. The result is express ed in terms of physical model parameters.