Mesoscopic Difference of Hydrogen Double Minimum Well in Proton Irradiated Ferroelectric System*

We investigate the microscopic structure of hydrogen double-well potentials in a hydrogen-bonded ferroelectric system exposed to radioactive particles of

hydrogen-ion beams. The hydrogen-bonded system is ubiquitous, forming the base of organic-inorganic materials and the double-helix structure of DNA

inside biological materials. In order to determine the difference of microscopic environments, an atomic-scale level analysis of solid-state ¹H high-resolution

nuclear magnetic resonance (NMR) spectra were performed. The hydrogen environments of inorganic systems represent the Morse potentials and wave

function of the eigen-state and eigen-state energy derived from the Schrodinger equation. The wave functions for the real space of the localized

hydrogen derived from the approximated solutions in view of the atomic scale by using quantum mechanics are manifested by a difference in the charge-density

distribution.