  We study the asymptotic behavior, as $\lambda \rightarrow 0$, of least energy
radial sign-changing solutions $u_\lambda$, of the Brezis-Nirenberg problem
  \begin{equation*} \begin{cases} -\Delta u = \lambda u + |u|^{2^* -2}u &
\hbox{in}\ B_1\\ u=0 & \hbox{on}\ \partial B_1, \end{cases} \end{equation*}
where $\lambda >0$, $2^*=\frac{2n}{n-2}$ and $B_1$ is the unit ball of $\R^n$,
$n\geq 7$.
  We prove that both the positive and negative part $u_\lambda^+$ and
$u_\lambda^-$ concentrate at the same point (which is the center) of the ball
with different concentration speeds. Moreover we show that suitable rescalings
of $u_\lambda^+$ and $u_\lambda^-$ converge to the unique positive regular
solution of the critical exponent problem in $\R^n$.
  Precise estimates of the blow-up rate of $\|u_\lambda^\pm\|_{\infty}$ are
given, as well as asymptotic relations between $\|u_\lambda^\pm\|_{\infty}$ and
the nodal radius $r_\lambda$.
  Finally we prove that, up to constant, $\lambda^{-\frac{n-2}{2n-8}}
u_\lambda$ converges in $C_{loc}^1(B_1-\{0\})$ to $G(x,0)$, where $G(x,y)$ is
the Green function of the Laplacian in the unit ball.
