  We investigate quantum phase transitions for the $s=1/2$ antiferromagnetic
Heisenberg model on a pyrochlore lattice. By means of a series expansion
starting from isolated tetrahedra, the ground-state phase diagram is
determined. When the ratio of the two competing exchange couplings is varied,
the first-order (second-order) quantum phase transition occurs between the two
spin gap phases (the spin-gap and the antiferromagnetic phases). We also
discuss some properties expected for the s=1 pyrochlore spin system.
