Prospects for forbidden-transition spectroscopy and parity violation measurements using a beam of cold stable or radioactive atoms

Abstract

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 M1-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 133 Cs with a statistical precision of 10 −3 and probably also in Fr isotopes for production rates of > ∼ 10 6 Fr atoms s −1 . For APV measurements to become realistic, some practical realization of the collimation of the atomic beam as well as multiple passages of the excitation beam matching the atomic beam looks essential.

Standard model tests with trapped radioactive atoms

“…The group at INFN in Legnaro has trapped ∼ 1000 Fr atoms in a MOT, and is considering atomic physics experiments including atomic parity violation [170,166]. They have pioneered a number of innovative loading techniques [171] in stable Rb and are in the process of applying these to Fr.…”

Spin Dependent Selection Rules for Photonic Transitions in Hydrogen-Like Atoms

“…According to the conventional selection rules ( 1 l    and 0 s   ) which are derived from the Schrödinger equation in the same way as in Section 3, a transition such as 6s 7s  is not allowed ( because this is a transition ( 0 l   0 l  ) in which 0 l   , so it does not meet the condition 1 l    ). But 6s 7s  transition in Cs atom has been already observed [7][8][9]. However, the present spin dependent selection rules allow the transition: 6s   7s  in Cs atom.…”

“…Therefore for the case a) we calculate the matrix elements of the quantity rcos  and for the case b) we calculate the matrix elements of the quantity x  iy= rsin exp(i ). That means for the case a) we will calculate the matrix elements 1 2 3 4 , , , I I I I     given in Equation (18) and for the case b) we will calculate the matrix elements 1 2 3 4 , , , I I I I given in Equation (8). Therefore the selection rules of the magnetic dipole transitions will be the same as the selection rules for the electric dipole transitions.…”

“…By applying the present spin dependent selection rules we can explain the observed (6 s  7 s) transition in Cesium (Cs) atom [7,8]. Because in the (6s  7s) transition in Cesium (Cs) atom we have [ 0 j   while 0 j m   ] which is an allowed transition according to the present selection rules given in Equation (28).…”

“…where B, and C are the normalization constants. Substituting the wave functions from Equation (29) and Equations (30a)-(30b) in Equations (8) and (18) we find:…”