  We study bounded pseudoconvex domains in complex Euclidean space. We define
an index associated to the boundary and show this new index is equivalent to
the Diederich-Forn{\ae}ss index defined in 1977. This connects the
Diederich-Forn{\ae}ss index to boundary conditions and refines the Levi
pseudoconvexity. We also prove the $\beta$-worm domain is of index
$\pi/{(2\beta)}$. It is the first time that a precise non-trivial
Diederich-Forn{\ae}ss index in Euclidean spaces is obtained. This finding also
indicates that the Diederich-Forn{\ae}ss index is a continuum in $(0,1]$, not a
discrete set. The ideas of proof involve a new complex geometric analytic
technique on the boundary and detailed estimates on differential equations.
