We present a theory whose goal is to account for the recent exciting h
ysteresis experiments on the spin cluster crystal Mn-12-acetate that i
ndicate the occurrence of spin tunneling. We have found the tunneling
probability P For the tunneling of spin from one spin state into anoth
er at a spin level crossing in response to a swept applied magnetic fi
eld H. It is shown that P is a function of only one parameter, the dim
ensionless sweep rate rho given by rho = 2<(tau)over bar>(h) over bar/
Delta(0)(2), where 2<(tau)over bar> is the rate at which the two energ
y levels approach each other as the field is swept (being proportional
to the sweep rate dH/dt). Delta(0) is the minimum energy gap at the a
nti-crossing, Delta(0)/(h) over bar being the tunneling rate thereat.
Numerical integration leads to P(rho) = 1 - exp[-tau/2 rho]. We find t
hat, contrary to widespread belief, the experiments cannot be understo
od in terms of tunneling of individual spin clusters in the presence o
f a static applied transverse field. Rather, the required transverse f
ield must have dynamic nuclear spins and other dynamic spin clusters a
s its source.