Binding Energy of Muonium Hydride

Abstract

Binding energy of muonium hydride is calculated variationally with wave function dependent exponentially on three interparticle distances. The lower bound for the dissociation energy into the hydrogen atom and muonium is obtained as 3.853 eV. Expectation values of the interparticle distances are also calculated.PACS numbers: 36.10. Gv, 71.35.+z The muonium hydride, a system consisting of the muonium atom and a hydrogen atom is, after the positronium hydride, an example of a four-particle neutral system. Its ground state has the same quantum numbers as the positronium hydride [1,2]. The difference between the two systems is in the mass of the positron and that of the positive muon. The proton-positron mass ratio is mp/me = 1836.152701, the proton-muon mass ratio mp /mμ = 8.8802444 [3].The muon spin precession in magnetic field is well measured in solids and in liquids [4][5][6][7][8][9][10]. Muonium is observed by means of its triplet state precession [5]. Muonium may become incorporated in a variety of molecules and chemical consequences of replacement of hydrogen by muonium in a molecule can be observed [6]. Therefore, consideration of muonium bound to a neutral atom with immobile nucleus can be investigated also as a system of considerable interest. We calculated the ground state of muonium hydride with a variational wave function, symmetrized in the coordinates of the two electrons of the molecule, as described previously [11][12][13]. The wave function was a linear combination of monomials in four interparticle distances with an overall exponential factor dependent on the three lepton distances from the most massive particle. The most massive particle was a proton in muonium hydride, HMu, a deuteron with mass and = 3670.483014me in DMu [3], a triton with mass m t = 5496.918me in TMu [14,15], and an immobile proton in Ho.Mu. We used the corresponding reduced masses μr of the muon as shown in Table I. For the triton mass we used the larger of the two quoted [14][15][16][17] (157)

Variational calculation of muonium hydride

“…However, since the mass ratio of proton and muon is m p /m µ ∼ 9, which is much smaller than the mass ratio of proton and electron m p /m e ∼ 1836, the system is basically a nonadiabatic one. To our knowledge, MuH and its isotopes were first studied by Suffczyński and Wolniewicz [4] a decade ago, who determined the binding energies for the ground states variationally and calculated expectation values of the interparticle distances. A similar paper [5] was published recently.…”

C60 Topological Isomers: Other Carbon Allotropes

“…However, other carbyne topological isomers of C 60 buckminsterfullerene (structure 1e in Figure ) are also possible. Till now various topological (carbon) isomers were described in terms of mathematical chemistry. −

1 Space filling model of 2 2 1 (C 30 C 30 ) catecarbyne ( 1a ), 6 3 2 (C 20 C 20 C 20 ) catecarbyne ( 1b ), 3 1 C 60 knocarbyne (trefoil) ( 1c ), C 60 cycarbyne ( 1d ), C 60 fullerene ( 1e ), and 4 1 C 60 knocarbyne (figure-eight structure) ( 1f ).

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