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WIREs Comput Mol Sci
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Parity violation

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Violation of (space) parity in atomic physics, molecular physics and chemistry is briefly reviewed. The review is structured by frequently asked questions related to the concept of space parity, its violation and the consequences thereof in physics, chemistry and biology. This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy Structure and Mechanism > Molecular Structures Theoretical and Physical Chemistry > Thermochemistry
Equilibrium structure of dichlorodisulfane and plot of the P‐even and P‐odd potentials as a function of the dihedral angle τ. Shown in the left part of the figure is the computed C2‐symmetric equilibrium structure of the P‐enantiomer of ClSSCl, corresponding to the left minimum of the P‐even potential in the right part of the figure. The P‐even torsional potential V (τ) and P‐odd potentials Epv(τ) computed with different basis sets (see Reference for details) are shown as a function of the torsional coordinate τ. τ‐values between 0° and 180° correspond to the P‐enantiomer whereas τ‐values between 180° and 360° correspond to the M‐enantiomer. (Reprinted with permission from Reference . Copyright 2001 John Wiley & Sons, Inc.)
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Schematic diagram for the tunneling situation in chiral molecules. Shown is a one‐dimensional cut through the multi‐dimensional parity‐conserving born–Oppenheimer potential energy hypersurface (, solid curve) along a coordinate q that interconnects the potential energy minima for the left‐handed structure at qL and the right‐handed structure at qR via an achiral arrangement at qA. On the left part of the figure, a cut through the wavefunction Ψ(q) corresponding to the left‐localized state |L〉 (dotted line) and the one corresponding to the right‐localized state |R〉 (dashed line) is sketched. The energy expectation value E is indicated by a horizontal line (dotted and dashed, respectively). In the absence of parity violation, these energy expectation values are identical as shown in the diagram. In the presence of parity violation, these values would become shifted with respect to each other, which gives rise to a parity violating energy difference. On the right part of the figure, cuts through the wavefunction corresponding to parity eigenstates |+〉 (dashed line) and |−〉 (dotted line) are sketched together with the corresponding energy levels (dashed horizontal line and dotted horizontal line, respectively). (Ref. ‐ Reproduced by permission of the PCCP Owner Societies)
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Chiral arrangement of atoms. The two chiral molecules represented by the ball‐and‐stick model in (a) are interconverted by the parity operation and thus are enantiomers. If the individual atoms are chiral as indicated in (b), the two structures are no longer interconverted by the parity operation and thus correspond to diastereoisomers rather than enantiomers
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Helicity of particles. Straight arrows show the direction of linear momentum, curvy arrows indicate the sense of rotation of a spinning classical particle. The resulting angular momentum of the particle in the upper part of the figure is then parallel to the linear momentum (right‐helical particle), whereas for the particle in the lower part of the figure, spin and linear momentum are antiparallel (left‐helical particle)
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A periodic system of elementary particles (PSEP) collects quarks (blue), leptons (green), and the gauge and Higgs bosons (black), with the gauge bosons mediating the interactions of the 12 elementary fermions and the Higgs boson giving rise to masses. The left superscript displays the mass of the respective particle in u, the atomic mass unit (1 u ≈ 1.66 · 10−27 kg). The right superscript is the charge number where the charge is obtained by multiplying the charge number with the elementary charge e of the positron. The right subscript is the corresponding spin of the particle. The gray shaded box describes the coupling of the respective boson to the respective columns of the PSEP. It is not yet known whether or not the Higgs boson couples to the neutrinos listed in column 4. Each column collects particles with the same charge and spin, mass increases from top to bottom
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Scheme of the experimental proof of parity violation reported in Reference . Nuclear spins of the various 60Co nuclei are indicated here for simplicity classically by transparent yellow arrows, the cobalt nuclei are shown as transparent yellow spheres and the cobalt atoms are sketched in blue. Experimentally, nuclear spins are oriented with the help of an external magnetic field that polarizes a paramagnetic cerium magnesium nitrate crystal which then orients the spins of the cobalt sample. The opaque part of the figure illustrates schematically the β‐decay. The electron emitted in the β decay of one of the 60Co nuclei to 60Ni is represented as a red sphere with the motion blur giving an indication of direction of the linear momentum. A corresponding arrow is also shown in red. The nuclear spin of the 60Ni nucleus is indicated classically by a green arrow, the nickel nucleus is shown as a green sphere and the nickel atom is shown in light green. Experimentally the situation in the left part of the figure is found with electrons being ejected in the direction opposite to the nuclear spin, which signals parity violation in the β‐decay. If parity were conserved, the situation on the left should be encountered with equal probability as the parity inverted situation on the right. Pseudo‐vectors, like the nuclear spin, transform even under spatial inversion, whereas vectors, like the linear momentum of the electron, are odd with respect to spatial inversion (see also Figure )
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Decay of the so‐called strange mesons τ+ and θ+, whereas τ+ decays into three pions (superscript indicates charge and subscript parity) with overall P = −1; in contrast, θ+ decays into two pions with overall P = +1. It was anticipated that “both mesons” were different particles because they decay into final states which differ by parity. With increasing experimental accuracy and the discovery of parity violation, τ+ and θ+ were identified as the same particle, called the kaon . It has a mean decay rate constant k ≈ 8.08 · 107 s−1 (mean life τ ≈ 1.24 · 10−8 s), whereas the left mode (hadronic, three particles) contributes about 6% and the right mode (two particles, hadronic mode) contributes about 21%
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Transformation properties with respect to parity (P), time reversal (T), and charge conjugation (C) of the position vector , linear and angular momenta , the spin of the electron and nucleus , as well as electric field strength , magnetic flux density and the electromagnetic field . The transformation properties of the photon field under T has been indicated here as positive to imply overall conservation of CPT
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