Parity-violations

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 

This second point of view can be illustrated by an example from the late 1940 s that will play an important role in this chapter. At that time the Schrodinger equation was well established, and its relativistic generalization, the Dirac equation, appeared to describe the spectrum of hydrogen perfectly, though the question of how to apply the Dirac equation to many-electron systems was still open. However, when more precise experiments were carried out, most notably by Lamb and Retherford [1], a small disagreement with theory was found. The attempt to understand this new physics stimulated theoretical efforts that led to the modern form of the first quantum field theory. Quantum Electrodynamics (QED). This small shift, which removes the Dirac degeneracy between the 2si/2 and states, known as the Lamb shift, is an example of a radiative correction. 

There are two particular aspects of radiative corrections in atomic physics that will be emphasized here. One has to do with the correct implementation of QED to many-electron atoms and ions, a subject also discussed by Labzowsky and Goidenko in Chapter 8 of this book. While QED has been tested quite stringently over the years, and is unlikely to be fundamentally incorrect, to actually carry out bound state calculations is a highly nontrivial task. Even the introduction of relativity has raised serious questions about the stability of atoms, referred to as the Brown-Ravenhall wasting disease [2] or continuum dissolution [3]. While the problem is, in a practical sense, still open for neutral systems, we will show that a particular way of applying QED to atoms, use of the Furry representation [4], allows a consistent and accurate treatment of these questions for highly charged ions. 

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. 

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Crassous, J., Chardonnet, C., Saue, T. and Sdiwerdtfeger, P. (2005) Recent e q)erimental and theoretical developments towards the observation of parity violation (PV) effects in molecules by spectroscopy. Organic and Biomolecular Chemistry, 3, 2218—2224. 

Bast, R. and Sdiwerdtfeger, P. (2003) Parity Violation Effects in ihe C-F Stretching Mode of Heavy Atom Containing Methyl Fluorides. Physical Review Letters, 91, 23001-1—23001-3. 

Zel dovich, Ya.B. (1958) Electromagnetic interaction with parity violation, Sov. Phys. JETP, 6, 1184-1186. 

The influence of the weak interaction on chemical reactions can be calculated since it favours left-handedness, it has an effect on the energy content of molecules and thus on their stability. In the case of the amino acids, the L-form would be more stable than the corresponding D-form to a very small extent. Theoretical calculations (using ab initio methods), in particular by Mason and Tranter (1983), indicated that the energy difference between two enantiomers due to the parity violation is close to 10 14J/mol (Buschmann et al., 2000). More recent evidence suggests that the... 

These experimental results could not be confirmed by Lahav and co-workers they suggest that impurities in the starting materials have a much greater effect on the crystallisation process than the PVED (Parity Violating Energy Difference). Extensive experimental studies indicate the importance of small quantities of impurities, particularly in early phases of crystallisation nucleus formation. Amino acids from various sources were used, and the analyses were carried out using the enan-tioselective gas chromatography technique (M. Lahav et al 2006). 

Bakasov A, Ha T-K, Quack M (1995) Ab initio Calculation of molecular energies including parity violating interactions. In Chela-Flores J, Raulin F (eds) Chemical Evolution Physics of the Origin of Life. Kluwer, Dordrecht Boston London, p 287 Ball P (1994) Designing the Molecular World, Chemistry at the Frontier, Princeton University... 

Kikuchi, O., and H. Wang. 1990b. Parity-Violating Energy Shift of Glycine, Alanine, and Serine in the Zwitterionic Forms Calculation Using HFO-NG Basis Sets. Bull. Chem. Soc. Jpn. 63, 2751-2754. 

Tranter, G. E. 1985a. The Parity Violating Energy Differences Between the Enantiomers of a-amino Acids. Mol. Phys. 56, 825-838. 

Tranter, G. E. 1986. Parity-violating Energy Differences and the Origin of Biomolecular Homochirality. J. Theor. Biol. 119, 467-479. 

Recently, experimental evidence (Achasov,1999) of the G-parity violating (ft W7T0 decay with the partial widths... 

Parity violating electron scattering. Recently it has been proposed to use the (parity violating) weak interaction to probe the neutron distribution. This is probably the least model dependent approach [31]. The weak potential between electron and a nucleus... 

More than forty years ago, Lee and Yang [8] observed anomalies in the decay patterns of theta and tau mesons, which suggested to them that parity was not conserved for certain weak interactions involved in the (3-decay of radioactive nuclei. This Nobel-prize-winning prediction was experimentally validated by Wu et al., [9] who found that the longitudinally polarized electrons emitted during the (3-decay of Co nuclei had a notable (40%) left-handed bias, i.e., their spins were predominantly antiparallel to their directions of motion. These experiments established that parity violation and symmetry breaking occurred at the nuclear level. 

In 1957 Vester and Ulbricht attempted to couple this parity violation on the nuclear level to events at the molecular level. Vester et al. [10,11] suggested that cir-... 

The traditional treatment of molecules relies upon a molecular Hamiltonian that is invariant under inversion of all particle coordinates through the center of mass. For such a molecular Hamiltonian, the energy levels possess a well-defined parity. Time-dependent states conserve their parity in time provided that the parity is well defined initially. Such states cannot be chiral. Nevertheless, chiral states can be defined as time-dependent states that change so slowly, owing to tunneling processes, that they are stationary on the time scale of normal chemical events. [22] The discovery of parity violation in weak nuclear interactions drastically changes this simple picture, [14, 23-28] For a recent review, see Bouchiat and Bouchiat. [29]... 

In the 45 years since its proposal, Frank s autocatalytic mechanism (Section 11.3, above) has spawned numerous theoretical refinements including consideration of such factors as reversibility, racemization, environmental noise, and parity-violating energy differences. [100,101] In contrast to the above examples of stereospecific autocatalysis by the SRURC, however, none of these theoretical refinements is supported by experimental evidence. While earlier attempts to validate the Frank mechanism for the autocatalytic amplification of small e.e.s in other experimental systems have generally been unsuccessful, several recent attempts have shown more promising results. [102,104]... 

The data from microwave spectroscopy have been interpreted with a dihedral angle H—O—O—H = 120.0° for the gas-phase equilibrium structure of H202. The nonplanarity of the peroxide gives rise to a stereogenic 0—0 axis . The computed total parity violating energy shift of —1.9 x 10 kJmoH between the two enantiomers, however, is too small in order to be measured with contemporary devices. ... 

One other reason why many chemists and biologists are skeptical about parity violation and other subtle physical effects, is that the breaking of symmetry can be realized rather simply in the chemistry laboratory. According to Meir Lahav, one of the best known researchers in the field, breaking of symmetry is not the problem. He means by that, that the problem is rather the propagation and amplification of chirality. In sidebox 3.3 he summarizes some of the main concepts in particular, he considers crystals as agents of symmetry breaking (Weissbruch et al, 2003). 

In this chapter the question of homochirality has also been considered according to Meir Lahav breaking of symmetry is not the problem. I do not know how many scientists would agree with him, but it is certainly true that in the laboratory chiral compounds can be obtained starting from racemic mixtures -and this by simple means, without invoking subtle effects of parity violation. Of course we do not know how homochirality really evolved in nature however, it is comforting to know that there is in principle an experimental solution to the problem. 

Mason, S. F. and Tranter, G. E. (1983). The parity violating energy difference between enantiomeric molecules. Chem. Phys. Lett., 94, 34. 

The parity violating energy difference between enantiomeric molecules. Mol Phys., 53, 1091-111. 

Quack, M. and Stohner, J. (2003a). Combined multidimensional anharmonic and parity violating effects in CDBrClF. J. Chem. Phys., 119, 11228 0. 

Titov, A. V. et al. Study of parity violation effects. This issue. 

P,T-PARITY VIOLATION EFFECTS IN POLAR HEAVY-ATOM MOLECULES... 

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