I'd use fadings instead of shadings for that.
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{fadings}
\tikzfading[name=fade out,
inner color=transparent!0,
outer color=transparent!100]
\begin{document}
\begin{tikzpicture}
\fill [blue,path fading=fade out] (3,0) circle (1);
\draw[fill=white] (3,0) circle [radius=0.7];
\fill [blue,path fading=fade out] (4.8,0) circle (1);
\draw[fill=white] (4.8,0) circle [radius=0.7];
\end{tikzpicture}
\end{document}

EDIT: It might be advantageous to construct the ring in a slightly different fashion that avoids drawing a white disk.
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{fadings}
\tikzfading[name=fade out,
inner color=transparent!0,
outer color=transparent!100]
\begin{document}
\begin{tikzpicture}
\fill [blue,path fading=fade out] (4,0) arc(0:360:1) -- (3.7,0) arc(360:0:0.7);
\fill [blue,path fading=fade out] (5.8,0) arc(0:360:1) -- (5.5,0) arc(360:0:0.7);
\end{tikzpicture}
\end{document}