  Within the framework of a nonrelativistic quark model we evaluate the six
form factors associated to the \Lambda_b^0 \to \Lambda_c^+ l^- \bar{\nu}_l
semileptonic decay. The baryon wave functions were evaluated using a
variational approach applied to a family of trial functions constrained by
Heavy Quark Symmetry (HQS). We use a spectator model with only one-body current
operators. For these operators we keep up to first order terms on the internal
(small) heavy quark momentum, but all orders on the transferred (large)
momentum. Our result for the partially integrated decay width is in good
agreement with lattice calculations. Comparison of our total decay width to
experiment allows us to extract the V_{cb} Cabbibo-Kobayashi-Maskawa matrix
element for which we obtain a value of |V_{cb}|=0.047\pm 0.005 in agreement
with a recent determination by the DELPHI Collaboration. Furthermore, we obtain
the universal Isgur-Wise function with a slope parameter \rho^2=0.98 in
agreement with lattice results.
