Parity nonconservation

In Chapter 1, we introduced the concept of parity, the response of the wave function to an operation in which the signs of the spatial coordinates were reversed. As we indicated in our discussion of a decay, parity conservation forms an important selection rule for a decay. Emission of an a particle of orbital angular momentum / carries a parity change (— l/ so that 1+ —0+ or 2 0+ a decays are forbidden. In general, we find that parity is conserved in strong and electromagnetic interactions. 

A number of studies have been undertaken of the interaction of neutrinos with nuclei, to determine the neutrino mass, and to show that neutrinos and antineutrinos are produced in (3+ and (3 decay, respectively. Neutrinos also provide important information about stellar nuclear reactions because they have a very low probability for interacting with matter and come directly out from the stellar interior. 

Starting with the simple equation for the 3 decay of the neutron and the (3+ decay of the proton, we can write two closely related reactions that are induced by neutrinos  

These reactions, called inverse (3 decay, were obtained by adding the antiparticle of the electron in the normal (3 decay equation to both sides of the reaction. When we did this we also canceled (or annihilated) the antiparticle/particle pair. Notice that other neutrino-induced reactions such as ve + n — p+ + e do not conserve lepton number because an antilepton, ve, is converted into a lepton, e. Proving that this reaction does not take place, for example, would show that there is a difference between neutrinos and antineutrinos. One difficulty with studying these reactions is that the cross sections are extremely small, of order 10-19 bams, compared to typical nuclear reaction cross sections, of order 1 barn (10—24 cm2). 

In the second study, Ray Davis and co-workers, irradiated a large volume of liquid CC14 with antineutrinos from a reactor. The putative reaction, ve + 37C1 — 37 Ar + e, could be detected by periodic purging of the liquid, collection of the noble gas, and then detection of the induced activity (37Ar is unstable, of course). The reaction was not observed to occur. Thus, they concluded that the reactor emits antineutrinos and that lepton number is conserved in the reactions. 

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Parity nonconservation (PNC) effects, electric dipole moment search, 242 Parity operator ... 

Abstract. Investigation of P,T-parity nonconservation (PNC) phenomena is of fundamental importance for physics. Experiments to search for PNC effects have been performed on TIE and YbF molecules and are in progress for PbO and PbF molecules. For interpretation of molecular PNC experiments it is necessary to calculate those needed molecular properties which cannot be measured. In particular, electronic densities in heavy-atom cores are required for interpretation of the measured data in terms of the P,T-odd properties of elementary particles or P,T-odd interactions between them. Reliable calculations of the core properties (PNC effect, hyperfine structure etc., which are described by the operators heavily concentrated in atomic cores or on nuclei) usually require accurate accounting for both relativistic and correlation effects in heavy-atom systems. In this paper, some basic aspects of the experimental search for PNC effects in heavy-atom molecules and the computational methods used in their electronic structure calculations are discussed. The latter include the generalized relativistic effective core potential (GRECP) approach and the methods of nonvariational and variational one-center restoration of correct shapes of four-component spinors in atomic cores after a two-component GRECP calculation of a molecule. Their efficiency is illustrated with calculations of parameters of the effective P,T-odd spin-rotational Hamiltonians in the molecules PbF, HgF, YbF, BaF, TIF, and PbO. 

Study of P- and T-parity nonconservation effects in heavy-atom molecules Historical background... 

Nevertheless, calculation of such properties as spin-dependent electronic densities near nuclei, hyperfine constants, P,T-parity nonconservation effects, chemical shifts etc. with the help of the two-component pseudospinors smoothed in cores is impossible. We should notice, however, that the above core properties (and the majority of other properties of practical interest which are described by the operators heavily concentrated within inner cores or on nuclei) are mainly determined by electronic densities of the valence and outer core shells near to, or on, nuclei. The valence shells can be open or easily perturbed by external fields, chemical bonding etc., whereas outer core shells are noticeably polarized (relaxed) in contrast to the inner core shells. Therefore, accurate calculation of electronic structure in the valence and outer core region is of primary interest for such properties. 

The P,T-parity nonconservation parameters and hyperfine constants have been calculated for the particular heavy-atom molecules which are of primary interest for modern experiments to search for PNC effects. It is found that a high level of accounting for electron correlations is necessary for reliable calculation of these properties with the required accuracy. The applied two-step (GRECP/NOCR) scheme of calculation of the properties described by the operators heavily concentrated in atomic cores and on nuclei has proved to be a very efficient way to take account of these correlations with moderate efforts. The results of the two-step calculations for hyperfine constants differ by less than 10% from the corresponding exper-... 

S. F. Mason, From Pasteur to parity nonconservation theories of the origin of molecular chirality , in Circular Dichroism, ed. K. Nakanishi, N. Berova and R. W. Woody, VCH, New York, 1993, pp. 39-57. 

The muon was discovered in cosmic radiation in 1937(19) and muonium was first observed in 1960(20) in a precession experiment based on parity nonconservation in the 7i- i->e decay chain. 

The general method of the experiment to measure ground n=l state energy levels is microwave magnetic resonance spectroscopy as applied to muonium(21,22). It relies on parity nonconservation in the decay to... 

Among several other additional operators, which occur in the complete exact treatment of the parity-nonconserving weak interaction within a four-component relativistic approach, the following nuclear spin-dependent operator [123] is the most important one ... 

R. A. Hegstrom, D. W. Rein, P. G. H. Sandars, Calculation of the parity nonconserving energy difference between mirror-image molecules, J. Chem. Phys. 73 (1980) 2329-2341. 

A description of the theory of parity nonconserving transitions in heavy atoms is presented. Issues of the accurate solution of the many-body problem and the correct incorporation of relativistic and radiative effects are addressed, and the related field of electric dipole moments of atoms is briefly described. 

From this second point of view the many-body problem is simply a nuisance, and in fact hydrogen or hydrogenlike ions are generally considered to be the best places to search for new physics. The new physics that will be treated in this chapter is that of the weak interactions, which lead to parity nonconserving (PNC) transitions in atoms. While this effect has... 

One of the aims of this chapter, then, is to discuss the problem of calculating a property of a many-electron atom with suflicient precision so that the new physics of radiative corrections can be studied. The challenge to many-body theory is quite specific. As will be discussed below, properties of cesium, the atom in which the most accurate PNC measurement has been made [5] must be calculated to the fraction of a percent level to accurately study PNC and radiative corrections to it can this level in fact be reached by modern many-body methods While great progress has been made, the particular nature of this problem, in which relativity has to be incorporated from the start, and a transition between two open-shell states calculated in the presence of a parity-nonconserving interaction, has not permitted solution of the many-body problem to the desired level. It may well be that a reader of this chapter has developed techniques for some other many-electron problem that are of sufficient power to resolve this issue this chapter is meant to clearly lay out the nature of the calculation so that the reader can apply those techniques to what is, after all, a relatively simple system by the standards of quantum chemistry, an isolated cesium atom. 

Parity Nonconservation in Atoms Status of Theory and Experiment, E. N. Fortson and L. Wilets... 

The behavior of wave functions near the nucleus, which is influenced by details of the nuclear charge distribution, is important in calculations of hyperfine constants and amplitudes of parity nonconserving transitions. The basic orbitals in such calculations are obtained from self-consistent field calculations in which Pnnc T) is assumed to be a Fermi (or Woods-Saxon) distribution... 

Molecular parity nonconservation caused by the parity violating property of the elec-troweak force is discussed. Different approaches to the computation of these parity violating influences are outlined and recent predictions for parity violating effects in spectroscopically and biologically relevant molecules are reviewed. 

I note in passing that apart from the effects due to parity nonconservation, also effects that arise from nonconservation of the symmetry with respect to simultaneous spatial and temporal inversion, so-called VT-odd effects, or to simultaneous charge conjugation and spatial inversion, denoted CT -violating effects, received particular attention especially for diatomic molecules. Readers interested in VT- or CP-violating effects in molecular systems are referred to the book of Khriplovich [42] and to the reviews [32,43]. 

We have finally arrived at those effective Hamiltonians, that have been employed in calculations of molecular parity violating effects either within a one-, two- or four-component scheme. In the following section I will outline the various strategies to include these Hamiltonians in perturbative computation of parity nonconservation effects in molecular systems. 

As discussed already in the introduction, the calculations of molecular parity nonconservation effects do at present not reeich the accuracy of the computations of atomic parity violating effects. This can mainly be attributed to additional difficulties due to vibrations and rotations of the molecule — complicating factors which are of course absent in atomic systems. At present, the rovibronic influences on parity violating effects in polyatomic molecules appear to be much more important than for instance radiative corrections and contributions from continuum states, which are vital to achieve the desired accuracy in calculations of parity violation in atoms. 

B. Zel dovich, Parity nonconservation in the first order in the weak-interaction constant in electron scattering and other effects, Sov. Phys. - JETP 9 (1959) 682-683. 

B. Zel dovich, D. Saakyan, I. Sobel man, Energy difference between right-hand and left-hand molecules, due to parity nonconservation in weak interactions of electrons with nuclei, JETP Lett. 25 (1977) 94-97. 

L. Labzowsky, Effects of parity nonconservation in electronic spectra of molecules, Sov. Phys. JETP 46 (1977) 853-858. 

V. Flambaum, I. Khriplovich, On the enhancement of parity nonconserving effects in diatomic molecules, Phys. Lett. A 110 (1985) 121-125. 

Khriplovich, Parity Nonconservation in Atomic Phenomena, Gordon and Breach Science Publ., Philadelphia, 1991. 

A. Barra, J. Robert, L. Wiesenfeld, Possible observation of parity nonconservation by high-resolution NMR, Europhys. Lett. 5 (1988) 217-222. 

C. Daussy, T. Marrel, A. Amy-Klein, C. Nguyen, C. Borde, C. Chardonnet, Limit on the parity nonconserving energy difference between the enantiomers of a chiral molecule by laser spectroscopy, Phys. Rev. Lett. 83 (1999) 1554-1557. 

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