Lim·er·ence

The state of being infatuated or obsessed with another person, typically experienced involuntarily and characterised by a strong desire for reciprocation of one's feelings but not primarily for a sexual relationship.

Three stages of limerence:

I. Infatuation

II. Crystallisation

III. Deterioration

Initially defined in the 1970s by the psychologist Dorothy Tennov: from limer- (apparently an arbitrary syllable) + -ence.