, where

is the repulsive Coulomb potential energy between the

-particle (charge

) and the daughter nucleus (charge

). The energy of the emitted

-particle is given by

, where

is the distance from the center of the nucleus at which the

becomes a free particle, while

is the approximate radius of the nuclear potential well in which the

is originally bound. The integral

can be done exactly to give

. For

, a sufficiently good approximation is

, so that

. The transition probability per unit time approximates the reciprocal of the half-life for

-decay, thus

. The Geiger–Nuttall formula introduces two empirical constants to fudge for the various approximations and is commonly written in the form

, where

, measured in MeV, is often used in nuclear physics in place of

.