  We perform photometric measurements on a large HST snapshot imaging survey
sample of 97 ultraluminous infrared galaxies (ULIRGs). We select putative
nuclei from bright clumps in all the sample targets, mainly based on a
quantitative criterion of I-band luminosity as well as the global and local
morphological information. All the sources are then classified into three
categories with multiple, double and single nucleus/nuclei. The resultant
fractions of multiple, double and single nucleus/nuclei ULIRGs are 18%, 39% and
43%, respectively. This supports the multiple merger scenario as a possible
origin of ULIRGs, in addition to the commonly-accepted pair merger model.
Further statistical studies indicate that the AGN fraction increases from
multiple (36%) to double (65%) and then to single (80%) nucleus/nuclei ULIRGs.
For the single nucleus category, there is a high luminosity tail in the
luminosity distribution, which corresponds to a Seyfert 1/QSO excess. This
indicates that active galactic nuclei tend to appear at final merging stage.
For multiple/double nuclei galaxies, we also find a high fraction of very close
nucleus pairs (e.g., 3/4 for those separated by less than 5 kpc). This
strengthens the conclusion that systems at late merging phase preferentially
host ULIRGs.
