We consider a system having decaying states with complex energies E-j
- i Gamma(j)/2, and we define the ''width-weighted spectrum'' as D Gam
ma(E) = Sigma(j) Gamma(j)delta (E - E-j) We derive a semiclassical for
mula for this width-weighted spectrum, a formula which is analogous to
the periodic-orbit representation of the density of states. The formu
la applies if classical motion is regular and if decay occurs by tunne
ling through a barrier. The semiclassical formula involves not periodi
c orbits or closed orbits, but action integrals associated with irredu
cible loops on the ''extremal torus,'' on which the particle climbs up
the barrier and hangs at the top. Calculations confirm the validity o
f the formula. [S0031-9007(98)07690-X].