Anapole Moment

During the p decay process, there exists anapole moment along the spin axis of the parent nuclei [1]. The anapole moment presents a new kind of dipole moment which is invariant under time reversal and odd under parity. A pseudoscalar p( V x H. ct) exists between the anapole moment and the spin of the emitted electrons, where p is the interaction strength. This interaction breaks parity conservation. 

In recent years, some anapole structures have been discussed [2,3], but most of them are impossible to distinguish from other existing electro-weak processes. In this paper, it is shown that the anapole moment in crystal [3] can be easily distinguished from other mechanisms since its magnitude is adjustable. 

Crystal anapole moment and its coupling to electro-weak process... 

Crystal anapole moment is composed of the atomic magnetic moments which array in anapole structure [3]. It has the same intrinsic structure as Majorana neutrino [2], If we plant a p decay atom into this anapole lattice, the crystal anapole moment will couple to the nuclear anapole moment of the decaying nuclei. So the emitted electron will be given an additional pseudoscalar interaction by the presence of the crystal anapole moment. Then the emission probability will be increased. This is a similar process to that assumed by Zel dovich [1], The variation of the decay rate may be measured to tell whether the crystal anapole moment has an effect on the p decay or not. 

For example, let us consider a typical crystal anapole moment of MrnNiN [4], Its anapole moment can be adjusted by temperature. The p source 3H may be permeated into this lattice without destroying the crystal structure. When the temperature is higher than 266K, the atomic magnetic moments of Mn do not array in anapole structure. Then the crystal anapole moment is zero. The p emission probability of 3H is normal. Contributions from other electro-weak processes may be measured at this temperature. When the temperature is lower than 184 K, the atomic magnetic moments of Mn array in the anapole structure and the crystal present anapole moment to the 3H nuclei. Then the electron s emission rate of 3H will be increased. 

As the anapole interaction is the candidate which directly breaks parity conservation in electromagnetic interaction [1], it is very desirable to test whether the anapole moment could couple to the p decay or not. This experiment can be performed by solid state detectors as well asby a magnetic spectrometer. There are also other choices for the crystal samples [3] and p sources. Since the anapole moment has the same intrinsic structure as for Majorana neutrinos, its coupling is valid to both p decay and p+ decay. 

A new experimental method has been introduced to measure the effect of the crystal anapole moment on p decay. The basic hypothesis is very similar to that assumed by Zel dovich. The special idea is to introduce the description of solid-state physics (crystallography) into the process of weak interaction. The p decay rate will be modified due to the presence of crystal anapole moment. If this modification could be detected, the hypothesis for the anapole moment and its coupling to weak interaction will be verified for the first time if this modification could not be detected by this method, an upper limit of up to 1(T6 for the coupling of anapole moment to weak process should be given. This experiment will give direct verification to Zel dovich s assumption. 

Rekalo, M.P. (1978) Scattering of polarized leptons by hadrons and the anapole moment of leptons and... 

The first line in this expression describes the rotational structure with color spin-doubling and the hyperflne interaction of the effective electron spin S with the nuclear spin I. B is the rotational constant, J is the electron-rotational angular momentum, A is the o -doubling constant. The second line describes the interaction of the molecule with the external fields B and E, (A is the unit vector directed from the heavy nucleus to the light one). The last line corresponds to the P-odd electromagnetic interaction of the electrons with the anapole moment of the nucleus described by the constant /ca [40], P,T-odd interaction of the electron EDM de with the interamolecular field, and P,T-odd scalar interactions of the electrons with the heavy nucleus [90]. 

Here, k = 4, 7 = 7/2 and K2 = —0.05 for the valence proton of Cs. Additionally, parity violation in the nucleus leads to to a parity-violating nuclear moment, the anapole moment mentioned above, that couples elec-tromagnetically to the atomic electrons. The anapole-electron interaction is described by a Hamiltonian similar to (103),... 

Indeed, around 1980, first experimental results on atomic parity violation have been reported, in particular measurements of the optical activity of bismuth, thallium and lead vapours as well as measurements of an induced electric dipole (El) amplitude to a highly forbidden magnetic dipole transition (Ml) in caesium. These experiments have nowadays reached very high resolution so that even effects from the nuclear anapole moment, which results from weak interactions within the nucleus, have been observed in caesium. The electronic structure calculations for caesium are progressing to a sub-percent accuracy for atomic parity violating effects and the reader is referred to chapter 9 of the first part of this book [12]. 

S. Kulkarni, C. Warke, Y. Gambhir, Relativistic mean-field approach to anapole moment Atomic parity-violating hyperfine transitions, Phys. Rev. C 52 (1995) 1047-1060. 

V. Flambaum, I. Khriplovich, Nuclear anapole moments, Phys. Lett. B 146 (1984) 367-369. 

W. Haxton, E. Henley, M. Musolf, Nucleon and nuclear anapole moments, Phys. Rev. Lett. 63 (1989) 949-952. 

C. Bouchiat, C. Piketty, Nuclear spin dependent parity violating electron-nucleus interaction in heavy atoms. The anapole moment and the perturbation of the hadronic vector neutral current by the hyperfine interaction, Phys. Lett. B 269 (1991) 195-200. 

V. Dmitriev, I. Khriplovich, V. Telitsin, Nuclear anapole moments in single-particle approximation, Nucl. Phys. A 577 (1994) 691-708. 

There is also nuclear physics interest in parity violation because it plays a role in nuclear structure. A particularly interesting possibility is that weak interactions in nuclei can induce an anapole moment, a P-odd multipole that produces no external field and corresponds in lowest order to a toroidal flow of current within the nucleus. An experiment is under way at Yale University to measure the anapole moment of the Ba nucleus using BaF molecules [36],... 

W. C. Haxton, C.E. Wieman Atomic parity nonconservation and nuclear anapole moments. Ann. Rev. Nucl. Part. Sci. Annual Reviews 2001, 261 (2001)... 

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