Then on what basis can science deny the reality of the human soul? Mind, some of the intangible soul's effects are themselves intangible: e.g., love, desire, the seemingly in-built sense of justice, the moral sense, et al. These can produce tangible effects, but usually not of the kind studied by the physical sciences.
Thus it seems to me that the soul cannot be a suitable object for scientific study. So science should just leave the matter to the philosophers and theologians, and stick to what it does best.
Sure they can. It's being done all the time. do you not read?
Any phenomenon that has observable manifestations can be studied by the usual and customary methods of science.
Things like subatomic particles are studied, even though they are mathematical constructs based on observation of effects, rather than directly observable entities. We can even study "entities" whose effects indicate they are in two places at the same time.
This goes back a long way. Newton's gravity was criticised because it postulated instantaneous action at a distance. It nevertheless provided a useful generalization and did away with the need for "hypotheses" -- Newton's derisive term for supernatural explanations.