Neutron-scattering experiments have been performed to study the dynami
c spin properties of La1.85Sr0.15CuO4 (T(c)=33 K) in the temperature r
ange 1.9 K less-than-or-equal-to T less-than-or-equal-to 150 K and ene
rgy range 1.5 meV less-than-or-equal-to omega less-than-or-equal-to 20
meV; these span, respectively, T(c) and the weak-coupling BCS gap ene
rgy 2DELTA approximately 10 meV. The width of S(q,omega) in momentum s
pace decreases with decreasing temperature at fixed energy as well as
with decreasing energy at fixed T(c) becoming very sharp at both low o
mega and low temperature. It is found that both in the normal state at
T = 35 K and in the superconducting state at T = 10 K the integrated
generalized susceptibility chi''(omega)= integral (pi,pi) dq2Dchi''(q,
omega) is constant above omega approximately 10 meV with an amplitude
about three times that in La1.98Sr0.02CuO4 and begins to decrease with
decreasing omega at omega approximately 10 meV, which corresponds to
the BCS superconducting gap energy 2DELTA. However, we observe nonzero
magnetic scattering well below the pseudogap energy at temperatures a
s low as 2 K. These results are compared with those in La1.98Sr0.02CuO
4 and YBa2Cu3O6.6.