  Laser cooling and trapping offers the possibility of confining a sample of
radioactive atoms in free space. Here, we address the question of how best to
take advantage of cold atom properties to perform the observation of as highly
forbidden a line as the 6S-7S Cs transition for achieving, in the longer term,
Atomic Parity Violation measurements in radioactive alkali isotopes. Another
point at issue is whether one might do better with stable, cold atoms than with
thermal atoms. To compensate for the large drawback of the small number of
atoms available in a trap, one must take advantage of their low velocity. To
lengthen the time of interaction with the excitation laser, we suggest choosing
a geometry where the laser beam exciting the transition is colinear to a slow,
cold atomic beam, either extracted from a trap or prepared by Zeeman slowing.
We also suggest a new observable physical quantity manifesting APV, which
presents several advantages:specificity, efficiency of detection, possibility
of direct calibration by a parity conserving quantity of a similar nature. It
is well adapted to a configuration where the cold atomic beam passes through
two regions of transverse, crossed electric fields, leading both to
differential measurements and to strong reduction of the contributions from the
M_1-Stark interference signals, potential sources of systematics in APV
measurements. Our evaluation of signal to noise ratios shows that with
available techniques, measurements of transition amplitudes, important as
required tests of Atomic Theory should be possible in cesium 133 with a
statistical precision of 1/1000 and probably also in Fr isotopes for production
rates of 10^6 Fr atoms/s.
