Abstract. We have discussed positron and ion diffusions in liquids by using the gaugeinvariant effection Lagrange density with the spontaneously broken density (the hedgehog-like density) with the internal non-linear gauge fields (Yaug-Mills gauge fields), and have presented the relation to the Hubbard-Onsager theory.
IntroductionThe Investigation for ion mobility in the liquid phase has been one of the central area of physical chemistry. The electrohydrodynamic theory by Hubbard and Onsager [1,2] and the stochastic theory [3,4] for ionic conductivity in the liquid phase have been proposed.Since fluctuation from the equilibrium medium is preferable in liquid phase, localization of ions such as positrons is highly probable [5,6]. Free energy density functional theories [7,8] provide self-trapping as solution of the ions in a given host liquid. The sensitivity of positrons to changes induced by melting has already been reported by the positron annihilation angular correlation [9][10][11] and lifetime [12,13] studies for liquids. Gramsh et al. [14,15] have observed very different behavior of the diffusion length L + of positrons in liquid and solid metals. That is, on melting, L + decreases remarkably, and in the liquid phase, L + increases with temperature. Kanazawa [16][17][18][19][20] has introduced the effective Lagrangian in the gauge-invariant formula with spontaneous symmetry breaking for liquids and glasses, and has discussed the origin of the boson peak, the glass transition, and the viscosity of the supercooled liquids. Kanazawa and coworkers [21][22][23][24] proposed a qualitative explanation for the increase of the positron diffusion length L + with temperature in the liquid phase, by using the theoretical formula, which is based on the gaugeinvariant effective Lagrangian with spontaneously broken density (the hedgehog like fluctuation) and the massive internal gauge fields. In addition Kanazawa et al. [28] have suggested one origin of the attractive interaction between like ion pairs in liquids, extending the theoretical formula [20][21][22][23]. Recently Yamada et al. [29] have explained the origin of the attractive interaction between the Cl − -Cl − pair in water, which is introduced by the integral equation method [1], by using the theoretical formula [28]. In this study, we have analyzed the positron diffusion in the solid and liquid Pb, and have discussed the relation to the Hubbard-Onsager's dielectric theory for positrons and ions migrations in liquids.