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The technique of H(D) atom photofragment translation spectroscopy has been used to investigate the dissociation of jet-cooled HOD molecules following excitation to individual rovibrational levels of its [image omitted](1B1) Rydberg state near 124 nm. Spectra have been recorded for both the D + OH and H + OD dissociation channels. The branching ratios between OH/OD(X [image omitted], high v, low N), OH/OD(X [image omitted], low v, high N), and OH/OD(A [image omitted]) channels vary between different parent rotational levels, and between the OH and OD products. The variation between the OH and OD channels can be attributed to an isotopic mass effect on the rotational axes which influences non-adiabatic coupling strengths. In addition, there is a population alternation with product rotational quantum number N for the OH/OD(X, high v, low N) product, most striking for the OH case, the sense of which is correlated with the value of the parent pseudo-quantum number [image omitted]. It is shown that this is a consequence of recoil forces which lead to a closing of the HOD angle to near 90° accompanying non-adiabatic transfer from the [image omitted] state to the [image omitted](1B1) state. The oscillation in population then derives from the symmetry properties around this angle of the product rotational wavefunctions. This suggests that the symmetry-induced population oscillation can only occur for a narrowly defined angular dissociation path. Model calculations also explain the different structure of the spin-orbit doubled low N band heads for each v(OH/OD) which also alternates for even and odd [image omitted]. The necessary conditions to observe these phenomena are discussed. [ABSTRACT FROM AUTHOR]