  We improve a nucleon coalescence model to include the coordinate-momentum
correlation in nucleon joint distributions, and apply it to Pb-Pb collisions at
$\sqrt{s_{NN}}=2.76$ TeV to study production properties of deuterons ($d$),
helions ($^3$He) and tritons ($t$). We give formulas of the coalescence factors
$B_2$ and $B_3$, and naturally explain their behaviors as functions of the
collision centrality and the transverse momentum per nucleon $p_T/A$. We
reproduce the transverse momentum spectra, averaged transverse momenta and
yield rapidity densities of $d$, $^3$He and $t$, and find the system effective
radius obtained in the coalescence production of light nuclei behaves similarly
to Hanbury Brown-Twiss interferometry radius. We particularly give expressions
of yield ratios $d/p$, $^3$He$/d$, $t/p$, $^3$He$/p$, $d/p^{2}$, $^3$He$/p^3$,
$t/^3$He and argue their nontrivial behaviors can be used to distinguish
production mechanisms of light nuclei.
