Can One Bind Three Electrons with a Single Proton?

Of course not for an ideal H – – atom. But with the help of an intense homogeneous magnetic field B , the question deserves to be reconsidered. It is known (see, e.g. Baumgartner et al. in Commun Math Phys 212(3):703–724, 2000; Brummelhuis and Duclos in J Math Phys 47:032103, 2006) that as B → ∞ and...

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Bibliographic Details
Published in:	Few-body systems Vol. 45; no. 2-4; pp. 173 - 177
Main Authors:	Bressanini, D., Brummelhuis, R., Duclos, P., Ruamps, R.
Format:	Journal Article
Language:	English
Published:	Vienna Springer Vienna 01-05-2009 Springer Nature B.V
Subjects:	Atomic Hadrons Heavy Ions Molecular Nuclear Physics Optical and Plasma Physics Particle and Nuclear Physics Physics Physics and Astronomy Single Proton Essential Spectrum Bosonic Statistic Trial Function Bosonic Sector
Online Access:	Get full text
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Summary:	Of course not for an ideal H – – atom. But with the help of an intense homogeneous magnetic field B , the question deserves to be reconsidered. It is known (see, e.g. Baumgartner et al. in Commun Math Phys 212(3):703–724, 2000; Brummelhuis and Duclos in J Math Phys 47:032103, 2006) that as B → ∞ and in the clamped nucleus approximation, this ion is described by a one-dimensional Hamiltonian where N = 3, Z = 1 is the charge of the nucleus, and δ stands for the well known “delta” point interaction. We present an extension of the “skeleton method” (Cornean et al. in Few-Body Syst 38(2–4):125–131, 2006; Proc Symp Pure Math AMS 77:657–672, 2008) to the case of three degree of freedom. This is a tool, that we learn from Rosenthal (J Chem Phys 35(5):2474–2483, 1971) for the case N = 2, which reduces the spectral analysis of (1) to determining the kernel a system of linear integral operators acting on the supports of the delta interactions. As an application of this method we present numerical results which indicates that (1) has a bound state for Z = 1 and N = 3.
ISSN:	0177-7963 1432-5411
DOI:	10.1007/s00601-009-0018-7