Parity non-conservation

We know from the standard model of elementary particle physics [116] that there is a tiny weak interaction contribution to every Coulomb interaction. For ordinary matter, where particle interconversion can be ignored, weak interactions due to exchange of neutral Z vector bosons are involved. Unlike the Coulomb interaction, the (neutral and charged variants of) weak interactions do not conserve parity. This leads, in consequence, to a very small energy difference between mirror-image molecules (enantiomers), which in turn might prove to be of importance for the development of a homochiral biochemistry on our planet [117]. 

A detailed study of this subject requires the definition of suitable operators which can be included in quantum mechanical electronic structure calculations. These operators should describe the weak neutral interaction between electrons and nucleons (protons and neutrons), as well as the interelectronic contribution (the latter is usually ignored). 

The effective operator used in non-relativistic calculations to describe the electron-nucleon weak interaction in a molecule is [118-120] 

This expression assumes equal distributions for protons and neutrons, or alternatively an averaged nucleon density. The nucleon density, nuc( ) generally representable for every nucleus a as 

In a fully relativistic four-component treatment, the operator from which the effective non-relativistic operator given in Eq. (125) can be derived has the following form [121-124] 

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Extremely accurate calculations of electronic transitions may contribute to explaining parity non-conserving effects in atoms [50, 252-254]. 

Bonner WA (1974) Experiments on the origin of molecular chirality by parity non-conservation during P-decay. J Mol Evol 4 23-39... 

S. Wilson, D. Moncrieff and J. Kobus, European Science Fundation Workshop on Parity Non-Conservation, Oxford, 7-10 April, 1994, Rutherford Appleton Laboratory Report RAL-94-082. 

I85,i87j g74+ j32]. There is thus renewed interest in the analysis of the so-called Bohr-Weisskopf effect [17,18], calling for an improved theoretical description of the nucleus [32], and a suitable way to relate the electronic and nuclear parts of the calculation. The situation is similar to the studies of parity non-conservation, where the unknown neutron distribution would lead to an uncertainty in the interpretation of experiments for chains of isotopes [33,34], larger than the expected experimental uncertainty. 

Atomic spectroscopy is a powerful tool to investigate also nuclear properties, and studies comparing theoretical and experimental results can provide a calibration of nuclear structure calculations, needed e.g., for the interpretation of experiments involving parity non-conservation [63], electric dipole... 

General considerations on symmetry [12,13] lead to the result, that an atomic nucleus in a stationary state with spin quantum number / has electric and magnetic multipole moments only of order 2 with 0 < I <21. For electric multipole moments I must be even, while magnetic multipole moments require I to be odd. These rules are strictly obeyed, as long as very tiny parity non-conservation effects, due to weak interaction between nucleons, axe omitted (as is usually done for the nucleus, but see Sect. 6.3, where these effects are briefly discussed for the electronic structure). Thus,... 

In this last section we mention a few cases, where properties other than the energy of a system are considered, which are influenced in particular by the change from the point-like nucleus case (PNC) to the finite nucleus case (FNC) for the nuclear model. Firstly, we consider the electron-nuclear contact term (Darwin term), and turn then to higher quantum electrodynamic effects. In both cases the nuclear charge density distribution p r) is involved. The next item, parity non-conservation due to neutral weak interaction between electrons and nuclei, involves the nuclear proton and neutron density distributions, i.e., the particle density ditributions n r) and n (r). Finally, higher nuclear electric multipole moments, which involve the charge density distribution p r) again, are mentioned briefly. 

Finally, in Sect. 6, we have briefly given some examples for physical properties or effects, which involve the nuclear charge density distribution or the nucleon distribution in a more direct way, such that the change from a point-like to an extended nucleus is not unimportant. These include the electron-nucleus Darwin term, QED effects like vacuum polarization, and parity non-conservation due to neutral weak interaction. Hyperfine interaction, i.e., the interaction between higher nuclear electric (and magnetic)... 

Another possible somce of non-QED corrections to the energy levels is the parity - conserving weak interaction between the electron and the nucleus. The estimates show that these corrections are too smeill to be considered seriously both in light and heavy atoms and in HCI [9], [16]. The parity non -conserving weak interaction can influence atomic transition probabilities. This leads to the observable asymmetry effects in radiation (see Chapter IV of this book). We should mention that QED effects appear to the observable also in molecules (see the recent publications [17], [18]). 

In conclusion, relativistic atomic structure calculations based on the MBPT and RCI methods are now accurate enough to make precision tests of QED theory in many-electron systems. Tests of parity non-conserving effects in heavy, neutral atoms have also been carried out and this topic is covered in another chapter of this book series. 

Compared to atomic physics, the present situation in molecular physics is by far less comfortable The first detection of molecular parity violating effects is still lacking and calculations of parity non-conservation phenomena in molecules have not yet reached the accuracy of the corresponding atomic computations. Calculations of parity violating effects in chiral molecules, however, play currently more the decisive role of determining suitable molecular candidates for a successful or promising experiment, a task for which computational errors of more than 20 % may be perfectly acceptable. Some of these current uncertainties are due to difficulties in the... 

A. Barra, J. Robert, L. Wiesenfeld, Parity non-conservation and NMR observables. Calculation of T1 resonance frequency differences in enantiomers, Phys. Lett. A 115 (1986) 443-447. 

I. Khriplovich, On the energy difference of optical isomers due to parity non-conservation, Sov. Phys. JETP 52 (1980) 177-183. 

D. Rein, R. Hegstrom, P. Sandars, Parity non-conserving energy differences between mirror image molecules, Phys. Lett. 71A (1979) 499-502. 

IIOS. Mason, G. Tranter, Energy inequivalence of peptide enantiomers from parity non-conservation, J. Chem. Soc. Chem. Commun. (1983) 117-119. 

P. Jungwirth, L. Skala, R. ZahradmTc, The parity non-conserving energy difference between enantiomers and a consequence of the CPT theorem for molecule-antimolecule pairs, Chem. Phys. Lett. 161 (1989) 502-506. 

The presence of a neutral weak current interaction between the electrons and nucleons in an atom gives rise to a parity non-conserving part of the atomic Hamiltonian which can be written as... 

We note that if the electromagnetic and strong interactions conserve flavour, then we should expect associated production of heavy flavours, i.e. that production always occurs with pairs of particles of opposite charm or bottom (this is, of course, not the case for production in neutrino interactions via weak forces). Further, the decay of a heavy particle should be generated by the weak interactions, implying very narrow widths and effects of parity non conservation. 

Actinide elements and their compounds have become the subject of intensive research in recent years (see the reviews [1-3]). In technology, interest is stimulated by the role of these elements in nuclear fuel and waste products, as well as the development of the actinide-organometallic chemical industry. In basic physics, actinide ions are prime candidates for observing parity non-conservation effects, which may reveal possible inconsistencies of the Standard Model [4]. It is interesting to note that actinides may have been involved in the creation of life on our planet [5], In spite of recent progress, many spectroscopic and other physical properties of actinides are still unknown, or known with very low accuracy, due in part to the relative scarcity, toxicity, and radioactivity of these elements. 

This close agreement has further interesting consequences. If a parity non-conserving interaction exists in hydrogenic systems, the wavefunction of the 2S level... 

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