  We propose a direct method of detection of the nuclear anapole moment. It is
based on the existence of a linear Stark shift for alkali atoms in their ground
state perturbed by a quadrupolar interaction potential and a magnetic field.
This shift is proportional to the T-even pseudoscalar built from the
quadrupolar potential symmetry axis, the directions of the applied electric and
magnetic fields.It involves on the one hand the anisotropy of the hyperfine
interaction induced by the quadrupolar interaction and, on the other,the static
electric dipole moment arising from electroweak interactions inside the
nucleus. The case of ground state cesium atoms trapped in a uniaxial (hcp)
phase of solid helium-4 is examined. From an explicit evaluation of both the
hyperfine structure anisotropy and the static P-odd T-even dipole deduced from
recent empirical data about the cesium nuclear anapole moment, we predict the
Stark shift. It is three times the experimental upper bound to be set on the
T-odd Stark shift of free cesium atoms in order to improve the present limit on
the electron EDM.
