  The influence of a microsphere having a simultaneously negative permittivity
and permeability (Left-Handed Sphere) on the decay rate of the allowed and
forbidden transitions is considered. It is found, that in contrast to usual
(Right-Handed) materials it is possible to increase the decay rate by several
orders of magnitude even in the case of a sphere of small radii. This
enhancement is due to the fact that there exist a new type of resonance modes
(LH surface modes). The analytical expressions for resonance frequencies and
associated quality factors of the new modes are found.
