  We will discuss the asymptotic behaviour of the eigenvalues of
Schr\"{o}dinger operator with a matrix potential defined by Neumann boundary
condition in $L_2^m(F)$, where $F$ is $d$-dimensional rectangle and the
potential is a $m \times m$ matrix with $m\geq 2$, $d\geq 2$ , when the
eigenvalues belong to the resonance domain, roughly speaking they lie near
planes of diffraction.
  \textbf{Keywords:} Schr\"{o}dinger operator, Neumann condition, Resonance
eigenvalue, Perturbation theory.
  \textbf{AMS Subject Classifications:} 47F05, 35P15
