  The celebrated Smith-Minkowski-Siegel mass formula expresses the mass of a
quadratic lattice (L, Q) as a product of local factors, called the local
densities of (L,Q). This mass formula is an essential tool for the
classification of integral quadratic lattices. In this paper, we will describe
the local density formula explicitly, by constructing a smooth integral group
scheme model for an appropriate orthogonal group. Our method works for any
unramified finite extension of Q_2. Therefore, we give a long awaited proof for
the local density formula of Conway and Sloane and discover its generalization
to unramified finite extensions of Q_2. As an example, we give the mass formula
for the integral quadratic form Q_n(x_1, ..., x_n)=x_1^2 + ... + x_n^2
associated to a number field k which is totally real and such that the ideal
(2) is unramified over k.
