  The anomaly in lithium abundance is a well-known unresolved problem in
nuclear astrophysics. A recent revisit to the problem tried the avenue of
resonance enhancement to account for the primordial $^7$Li abundance in
standard big-bang nucleosynthesis (BBN). Prior measurements of the
$^7$Be(d,p)$^8$Be* reaction could not account for the individual contributions
of the different excited states involved, particularly at higher energies close
to the Q-value of the reaction. We carried out an experiment at HIE-ISOLDE,
CERN to study this reaction at E$_{cm}$ = 7.8 MeV, populating excitations up to
22 MeV in $^8$Be for the first time. The angular distributions of the several
excited states have been measured and the contributions of the higher excited
states in the total cross section at the relevant big-bang energies were
obtained by extrapolation to the Gamow window using the TALYS code. The results
show that by including the contribution of the 16.63 MeV state, the maximum
value of the total S-factor inside the Gamow window comes out to be 167 MeV b
as compared to earlier estimate of 100 MeV b. However, this still does not
account for the lithium discrepancy.
