Your $sig calculation is conditional, but you push the same variable with either condition. Might as well push it once, after the if-else:

    $sig = ($r>20)
         ? $twopi*($rad**2)
         : $pi*($rad**2)*$a0*(1-exp((-$c0)*$rad));
    push (@rads, $rad);
    push (@sigs, $sig);
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