Binding energy for hydrogen-like atoms in the Nelson model without cutoffs

Christian Hainzl, Masao Hirokawa, Herbert Spohn

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge Ze, Z > 0, fixed at the origin and an electron of mass m and charge e. This system forms a bound state with binding energy Ebin =me4Z2/8π2 to leading order in e. We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that Ebin=me4 Z2/8π2 + c0e6 O(e7 ln e) with explicit coefficient c0 and independent of the ultraviolet cutoff. c0 can be computed by perturbation theory, which however is only formal since for the Nelson Hamiltonian the smallest eigenvalue sits exactly at the bottom of the continuous spectrum.

Original languageEnglish
Pages (from-to)424-459
Number of pages36
JournalJournal of Functional Analysis
Volume220
Issue number2
DOIs
Publication statusPublished - Mar 15 2005

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Binding Energy
Hydrogen
Charge
Smallest Eigenvalue
Continuous Spectrum
Bound States
Ultraviolet
Perturbation Theory
Scalar Field
Nucleus
Upper and Lower Bounds
Electron
Imply
Coefficient
Model
Form

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Binding energy for hydrogen-like atoms in the Nelson model without cutoffs. / Hainzl, Christian; Hirokawa, Masao; Spohn, Herbert.

In: Journal of Functional Analysis, Vol. 220, No. 2, 15.03.2005, p. 424-459.

Research output: Contribution to journalArticle

Hainzl, Christian ; Hirokawa, Masao ; Spohn, Herbert. / Binding energy for hydrogen-like atoms in the Nelson model without cutoffs. In: Journal of Functional Analysis. 2005 ; Vol. 220, No. 2. pp. 424-459.
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