An atomic linear Stark shift violating P but not T arising from the electroweak nuclear anapole moment

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 of uniaxial symmetry around a direction (n) over cap and a magnetic field. This shift is characterized by the T-even pseudoscalar ((n) over cap (.) B)((n) over cap Lambda E (.) B)/B-2. It involves on the one hand the anisotropy of the hyperfine interaction induced by the quadrupolar interaction anti, on the other, the static electric dipole moment arising from electroweak interactions inside the nucleus. The case of ground state Cs atoms trapped in a uniaxal (hcp) phase of solid He-4 is examined. From an explicit evaluation of both the hyperfine structure anisotropy and the static dipole deduced from recent empirical data about the Cs nuclear anapole moment, we predict the Stark shift. It is three times the experimental upper hound to be set on the T-odd Stalk shift of free Cs atoms: in order to improve the present limit on the electron EDM.