  We use early-time observations of He I 10830 \AA to measure the extent of
upward mixing of radioactive material in SN 1987A. This work develops and
extends the work of Graham (1988), and places constraints on actual explosion
models. The presence of the He I 10830 \AA (2s^{3}S--2p^{3}P) line at $\geq 10$
days post-explosion implies re-ionisation by $\gamma$-rays from upwardly-mixed
radioactive material produced during the explosion. Using the unmixed explosion
model 10H (Woosley 1988) as well as mixed versions of it, we estimated the
$\gamma$-ray energy deposition by applying a purely absorptive radiative
transfer calculation. The deposition energy was used to find the ionisation
balance as a function of radius, and hence the 2s$^{3}$S population density
profile. This was then applied to a spectral synthesis model and the synthetic
spectra were compared with the observations. Neither model 10H nor the mixed
version, 10HMM, succeeded in reproducing the observed He I 10830 \AA line. The
discrepancy with the data found for 10HMM is particularly significant, as this
model has successfully reproduced the X-ray and $\gamma$-ray observations and
the UVOIR light curve. We find that a match to the He I line profile is
achieved by reducing the extent of mixing in 10HMM. Our reduced-mixing models
also reproduce the observed $\gamma$-ray line light curves and the iron-group
velocities deduced from late-time infrared line profiles. We suggest that the
He I line method provides a more sensitive measure of the extent of mixing in a
type II supernova explosion.

Astrophysics