  We compute the in-medium partial decay widths of the bottomonium states to
open bottom mesons ($B\bar B$) using a field theoretical model for composite
hadrons with quark constituents. These decay widths are calculated by using the
explicit constructions for the bottomonium states and the open bottom mesons
($B$ and $\bar B$), and, the quark antiquark pair creation term of the free
Dirac Hamiltonian written in terms of the constituent quark field operators.
These decay widths in the hadronic medium are calculated as arising from the
mass modifications of the bottomonium states and the $B$ and $\bar B$ mesons,
obtained in a chiral effective model. The decay amplitude in the present model
is multiplied with a strength parameter for the light quark pair creation,
which is fitted from the observed vacuum partial decay width of the bottomonium
state, $\Upsilon (4S)$ to $B\bar B$. The effects of the isospin asymmetry, the
strangeness fraction of the hadronic matter on the decay widths, arising due to
the mass modifications due to these effects, have also been studied. There is
observed to be appreciable effects from density, and the effects from isospin
asymmetry on the parital decay widths of $\Upsilon \rightarrow B\bar B$ are
observed to be quite pronounced at high densities. These effects should show up
in the asymmetric heavy ion collisions in Compressed baryonic matter (CBM)
experiments planned at the future facility at FAIR. The study of the $\Upsilon$
states will, however, require access to energies higher than the energy regime
planned at the CBM experiment. The density effects on the decay widths of the
bottomonium states should show up in the production of these states, as well
as, in dilepton spectra at the Super Proton Synchrotron (SPS) energies.
