Resonance width for a particle-core coupling model with a square-well potential

We derive a simple formula for the width of a multi-channel resonance state. To this end, we use a deformed square-well potential and solve the coupled-channels equations. We obtain the $S$-matrix in the Breit-Wigner form, from which partial widths can be extracted. We apply the resultant formula to a deformed nucleus and discuss the behavior of partial width for an $s$-wave channel.