Experimental evidence for low-temperature (exothermic) atom-exchange chemical reactions was recently reported after starting with an optically trapped nearquantum-degenerate gas of polar (KRb)-K-40-Rb-87 (fermionic) molecules prepared in their absolute ground state. Here we demonstrate the similar fermionic ((HeHe)-He-3-He-3) molecules formation via vacancies in quantum 4He crystal. Aquantum crystal is defined as one in which the energy of the zero-point oscillations of each atom is not small in comparison with the depth of the potential well in which the atom is located (or mathematically Lambda ((h) over bar /a root m E-i) >= 1; m is the mass of an atom, E-i is the characteristic interaction energy of the atoms, and a is the interatomic distance). Our modified Gross-Pitaevskii approach, based on the extention to Anderson's adopting Gross-Pitaevskii equation for treating dilute vacancies, supplies in particular the zero-energy limit of the wave function (and the extra energy caused by the curvature of the wave function) for investigations of possible formation of (He-3)(2) molecules bound by the elastic deformation field around the isotopic impurities as well as bound states (scattering resonances) for a He-3-vacancy system in crystalline He-4.
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