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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.

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