When we tend to focus and become absorbed in something, fixating is the term that comes to mind. However, there are various synonyms for this term that can be used to convey the same meaning. These synonyms include obsessing, becoming fixated, concentrating, preoccupying oneself, getting absorbed, being engrossed, being focused, dwelling on, and being captivated. You could use any of these terms in place of fixating depending on the context and the level of intensity you want to convey. Regardless of the word chosen, they all paint a picture of a deep and prolonged level of attention being paid to something.