  An extensive analysis was performed on 8.0 pb-1 of dimuon data produced in
pi- - A collisions at 515 GeV/c to search for Lambda_b events in the decay
channel Lambda_b --> J/psi Lambda^0, with J/psi --> mu^+ mu^- and Lambda^0 -->
p pi^- (and for the conjugate reactions). The data was collected by the
Fermilab fixed target experiments E672 and E706. Several cuts were applied to
the Lambda^0 (and anti-Lambda^0) to make a clean Lambda^0 (and anti-Lambda^0)
data sample. Among the cuts there was a K^0_s mass cut, in which if the
Lambda^0 --> p pi^- (or conjugate reaction) had the mass of the K^0_s under the
hypothesis of both tracks being pi^+ pi^-, the Lambda^0 (or anti-Lambda^0)
candidates were rejected. The results show 2 events in the Lambda_b mass
region. Using the E672/E706 measurement of the bb_bar cross-section, and
considering the 2 Lambda_b event candidates as signal with zero background, an
upper limit to F(Lambda_b) * Br(Lambda_b --> J/psi Lambda^0) was found to be
less than 6.2x10^-2 at 90 % C. L. An upper limit was also calculate without
using the K^0_s mass cut for the Lambda^0 s (and anti-Lambda^0 s), and again,
requiring that the J/psi s originate from secondary vertices, giving that
F(Lambda_b) * Br(Lambda_b --> J/psi Lambda^0) < 3.1x10^-2 at 90 % C. L. and
F(Lambda_b) * Br(Lambda_b --> J/psi Lambda^0) < 3.2x10$^-2 at 90 % C.L.,
respectively.
