FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton th eory. This sequence is parametrized by the number of zeros, n, of a co mponent of the gauge field potential. It is demonstrated that solution s with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of th ese solutions. The question of instability is critically analyzed.