WEAK NEUTRAL CURRENTS IN ATOMIC PHYSICS

Abstract Possible ways of detecting weak neutral currents in atomic physics through parity-violating effects in heavy atoms are analysed from a theoretical point of view.

Here we would like to discuss a totally different approach, based on atomic physics measurements, i.e. involving energy transfers of only a few electron volts. We shall try to convince you that such an idea is, perhaps, not as stupid as it may look,for the following reasons i) very accurate measurements are usually po·ssible in ·, aiomic physics, so, tin~ effects are often detectable ; ii) the atomic physics effects, associated with neutral currents, exhibit a very strong enhancement in heavy atoms (they go roughlf like z. 3) iii) recent progress in laser technology (dye lasers) allows the study of highly forbidden radiative transitions where a weak electron-nucleus interaction has the best chance to show up.

Ve (~) A~CX)= IC-x)op..Os eCx) ( I )
We exclude from our discussion the currents which involve field derivatives, like the vector current associated with Pauli magnetic moment or an electric dipole moment ("second class currents").
The Dirac matrices currents have been defined in such a way that the five ~ ( X-) ... are hermitian operators.
If we require the hadronic neutral currents to conserve st!angeness (and eventually charm and color), we are led to the following currents "diagonal" in the quark field ::: l a.s,i, 9~ (x.J 9~oc) QVJ~ 9/XJ 'tl'-9/:x) ect .. . ( 2) We shall restrict our attention to the part of the weak neutral current hamiltonian density 'Jef-.v (:x.)which violates parity. It · wiil be written as a sum of terms involving the products of the currents defined above : For the partial hamilt~nian de~sities 'Jf:,S p J c}gP5 , ~VA, dLAV the first index is relative to the electron, the second to the hadrons : Vi" (4) For the tensor interaction, we have only one partial harniltonian density 'JeTT = ;J-eTT where ~V is obtained from Qh, is the "charge" operator associated with the vector For a nucleus of mass A and charge Z it is convenient to express the "charge'' of the nucleus in terms of the "charges" Z: (., avt 9l (x) 'tr-9 t < a:.) is conserved if one neglects weak and electromagnetic interactions.
One can write the "charge" of the nucleus as = (8) It is also possible to express the constants CVf' and C Vf\. Salam of (9a) (9 -b) For our discussion it is convenient to work in first quantized scheme for the electron. Going to the non relativistic limit, one can replace the hamiltonian by a non relativistic poiential (In the above expression mass, position, momentum and spin of the electron,respectively), A similar analysis can be performed for the partial hamiltonian e,(.x)/ )(

:.t=o
The additivity relation which gives the "scalar" charge of a nucleus in terms of the scalar "charge" of the nucleons and , is only approximate but should hold as long as the nucleus can be described as a system of non relativistic nucleons.    When used to compute hyperfine separation of atoms and ions with one~ electron, the formula appears rather accurate, provided relativistic corrections a re included properly (6]: In the above expression Approximate expressions in terms of the nuclear radius are given in ref (5) As an e xample let us quote the results obtained in the case of Cesium The being the atomic shielding factor computed by Sandars. We Unless the ratio between the c~upling constants and C 5 tt. appears to be accidentally equal to -78  In all the above cases the contribution of an eventual tensor interaction is expected to give a contribution smaller by (25) ( 2 6) ( 2 7) two orders of magnitude than a scalar interaction of similar strength.
In order to get information on tensor -pseudo tensor interactions~one has to reanalyze experiments originally performed in order to detect a proton electric dipole. Only one such experiment exists up to now; it involves the polar molecule (The ground state proton configuration of ). is We have estimated the ratio tc. 1 between the contrjbution coming from a proton electric dipole moment given by a renormalizable model of scalar currents · pseudoscalarVinvolving an intermediate neutral scalar _boson and that associated with a tensor pseudotensor interacticnof similar strength.
The ratio is app~oximately independent of the molecular wave function and has been found to be of the order of· So it appears legitim. ate to analyse the T£- 1£ -F being a rather complex object a reliable evaluation of the molecular wave function near the origin is not a simple affair. In order to get an order of magnitude, we shall describe t:he valence electron of the TI atom in the TR. -F molecule assumed to be completely oriented in a static electric field along the ~ axis by the simple "hybrid orbital"

( t l~)
Gs + being the wave functions of the free atom.
The matrix element of the electron spin -independent tensor potential, using the method of ref [~ or  r2; )' l..

-rn 2,05
If one takes for < Sf) )one half of the ratio of JJc, magnetic moment to that of the free proton, one gets the final result : that their value of the matrix is at least ten times larger than our simple minded estimate.
In conclusion, we can say that the existing measurements of electric dipole moment of heavy atoms exclude weak electronnucleon interaction involving scalar-pseudoscalar and tensor -pseudo tensor products of neutral currents with a coupling constant larger -3 than 10 (,r , the limits on the scalar being on much firmer grounds than that of the tensor.  rotates of an angle <j as the beam is transmitted through matter.

The rotation angle
'j' is given by (38) where is the wavelength and the length of the traversed matter. It will receive a contribution both from the parity violating   it implies that goes to a constant.
) rough estimate of shows that equality r.P is obtained for a pressure of the order of 10 torr.
So n~thing is gained by going to a pressure much higher than 10 torr •.
In fact, it does not seem much easier to measure such a small rotation rather than to look for a circular polarisation