  The radii of $\alpha$-convexity are deduced for three different kind of
normalized Bessel functions of the first kind and it is shown that these radii
are between the radii of starlikeness and convexity, when $\alpha\in[0,1],$ and
they are decreasing with respect to the parameter $\alpha.$ The results
presented in this paper unify some recent results on the radii of starlikeness
and convexity for normalized Bessel functions of the first kind. The key tools
in the proofs are some interlacing properties of the zeros of some Dini
functions and the zeros of Bessel functions of the first kind.
