  Quasi-bound resonances of H$_2$ are produced via two-photon photolysis of
H$_2$S molecules as reactive intermediates or transition states, and detected
before decay of the parent molecule into three separate atoms. As was
previously reported [K.F. Lai et al., Phys. Rev. Lett. 127, 183001 (2021)] four
centrifugally bound quantum resonances with lifetimes of multiple $\mu$s, lying
energetically above the dissociation limit of the electronic ground state
X$^1\Sigma_g^+$ of H$_2$, were observed as X($v,J$) = (7,21)$^*$, (8,19)$^*$,
(9,17)$^*$, and (10,15)$^*$, while also the short-lived ($\sim 1.5$ ns)
quasi-bound resonance X(11,13)$^*$ was probed. The present paper gives a
detailed account on the identification of the quasi-bound or shape resonances,
based on laser detection via F-X two-photon transitions, and their strongly
enhanced Franck-Condon factors due to the shifting of the wave function density
to large internuclear separation. In addition, the assignment of the rotational
quantum number is verified by subsequent multi-step laser excitation into
autoionization continuum resonances. Existing frameworks of full-fledged ab
initio computations for the bound region in H$_2$, including Born-Oppenheimer,
adiabatic, non-adiabatic, relativistic and quantum-electrodynamic
contributions, are extended into the energetic range above the dissociation
energy. These comprehensive calculations are compared to the accurate
measurements of energies of quasi-bound resonances, finding excellent
agreement. Etc.
