  In this paper we extend the arithmetic intersection theory of adelic divisors
on quasiprojective varieties developed by X. Yuan and S. W. Zhang to cover
certain adelic arithmetic divisors that are not nef nor integrable. The key
concept used in this extension is the relative finite energy introduced by T.
Darvas, E. Di Nezza, and C. H. Lu. As an application we compute the arithmetic
self-intersection number of the line bundle of Siegel-Jacobi forms on the
universal abelian variety endowed with its invariant hermitian metric. The
techniques developed in this paper can be applied in many other situations like
mixed Shimura varieties or the moduli space of stable marked curves.
