  This work is a continuation of our previos paper \cite{Zel1}, where for the
the Schr\"odinger operator $H=-\Delta+ V(\e)\cdot$ $(V(\e)\ge 0)$, acting in
the space $L_2(\R^d)\,(d\ge 3)$, some constructive sufficient conditions for
discreteness of its spectrum have been obtained on the base of well known Mazya
-Shubin criterion and an optimization problem for a set function. Using a {\it
capacitary strong type inequality} of David Adams, the concept of {\it base
polyhedron} for the harmonic capacity and some properties of Choquet integral
by this capacity, we obtain more general sufficient conditions for discreteness
of the spectrum of $H$ in terms of a repeated nonincreasing rearrangement of
the function $Y(\e,\bt)=\sqrt{V(\e)}\frac{1}{|\e-\bt|^{d-2}}\sqrt{V(\bt)}$ on
cubes that are going to infinity.
