In this study, we surveyed a total of 245 people about unidentified anomalous phenomena (UAP), 93 who directly witnessed UAP. Paying special attention to the psychological impact of UAP, our study survey covered different aspects, including opinions on official UAP releases, the scientific approach to the phenomena and the search for extra-terrestrial intelligence. This study found that UAP had a clear psychological impact on witnesses, with a transformative effect, and a benign form of a non-pathological obsessive-like interest in the topic we defined as the UAP deep psychological engagement triad. This deep psychological engagement triad is characterized by UAP topic being present in a witness's mind daily, with a self-recognized interest and appreciation for the topic and a need to talk about UAP topic, not necessarily the event they experienced. UAP appear to have a very specific impact focused on extra-terrestrial aspects and the phenomena itself, which is experienced as a life-changing event by direct witnesses. These psychological aspects are quantitatively and qualitatively objectifiable, and further research is needed in this direction since all research efforts appear currently focused on the physical aspects of these phenomena.