  Size-quantization levels of an exciton in large nanocrystals is studied
theoretically. For the nanocrystal size, $L$, much bigger than the Bohr radius,
$a_B$, the level positions do not depend on $a_B$. The correction to the levels
in a small parameter $a_B/L$ depends on the reflection phase of the exciton
from the boundary. Calculation of this phase constitutes a three-body problem:
electron, hole, and the boundary. This calculation can be performed
analytically in the limit when the hole is much heavier than the electron.
Physically, a slow motion of the hole towards the boundary takes place in the
effective potential created by the fast motion of the electron orbiting the
hole and touching the boundary. As a result, the hole is reflected before
reaching the boundary. The distance of the closest approach of the hole to the
boundary (the dead layer) exceeds $a_B$ parametrically.
