Overlapping gradient sections create bitmapping when exported

Help! I’ve created a gradient colour fill path (outlined/expanded to mesh) in Illustrator (RGB). The path overlaps another path of the same type of fill just a different colour. It’s all crisp and sharp in Illustrator. When I export to PNG or PSD (pixel based apps) the ouline of the section that sits on a transparent background is anti-aliased, but where the paths intersect each other there is sharp satggered bitmapping, no anti-aliasing. Can this be rectified?