  We present a new variation of Young's double-slit formula for
polarization-averaged molecular-frame photoelectron angular distributions
(PA-MFPADs) of hetero-diatomic molecules, which may be used to extract the bond
length. So far, empirical analysis of the PA-MFPADs has often been carried out
employing Young's formula in which each of the two atomic centers emits a
$s$-photoelectron wave. The PA-MFPADs, on the other hand, can consist of an
interference between the $p$-wave from the X-ray absorbing atom emitted along
the molecular axis and the $s$-wave scattered by neighboring atom, within the
framework of Multiple Scattering theory. The difference of this $p$-$s$ wave
interference from the commonly used $s$-$s$ wave interference causes a dramatic
change in the interference pattern, especially near the angles perpendicular to
the molecular axis. This change involves an additional fringe, urging us to
caution when using the conventional Young's formula for retrieving the bond
length. We have derived a new formula analogous to Young's formula but for the
$p$-$s$ wave interference. The bond lengths retrieved from the PA-MFPADs via
the new formula reproduce the original C-O bond lengths used in the reference
$ab$-$initio$ PA-MFPADs within the relative error of 5 %. In the high energy
regime, this new formula for $p$-$s$ wave interference converges to the
ordinary Young's formula for the $s$-$s$ wave interference. We expect it to be
used to retrieve the bond length for time-resolved PA-MFPADs instead of the
conventional Young's formula.
