  Let $A=\{x\in \R^{2N+2} : 0< a< |x| <b\}$ be an annulus. Consider the
following singularly perturbed elliptic problem on $A$
  \begin{equation}
  \begin{array}{lll}
  -\eps^2{\De u} + |x|^{\alpha}u = |x|^{\alpha}u^p, &\mbox{\qquad in} A \notag
u>0 &\mbox{\qquad in} A
  \frac{\partial u}{\partial\nu} = 0 &\mbox{\qquad on} \partial A
  \end{array} %\label{a1}
  \end{equation} $1<p<2^*-1$. We shall show that there exists a positive
solution $u_\eps$ concentrating on an $S^1$ orbit as $\eps\to 0$. We prove this
by reducing the problem to a lower dimensional one and analyzing a single point
concentrating solution in the lower dimensional space. We make precise how the
single peak concentration depends on the parameter $\alpha$.
