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Full-Text Articles in Physics
Reducing A Class Of Two-Dimensional Integrals To One-Dimension With An Application To Gaussian Transforms, Jack C. Straton
Reducing A Class Of Two-Dimensional Integrals To One-Dimension With An Application To Gaussian Transforms, Jack C. Straton
Physics Faculty Publications and Presentations
Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/ (x + y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.
Analytical Results For The Three-Body Radiative Attachment Rate Coefficient, With Application To The Positive Antihydrogen Ion H̄+, Jack C. Straton
Analytical Results For The Three-Body Radiative Attachment Rate Coefficient, With Application To The Positive Antihydrogen Ion H̄+, Jack C. Straton
Physics Faculty Publications and Presentations
To overcome the numerical difficulties inherent in the Maxwell–Boltzmann integral of the velocity-weighted cross section that gives the radiative attachment rate coefficient αRA for producing the negative hydrogen ion H− or its antimatter equivalent, the positive antihydrogen ion H¯+ , we found the analytic form for this integral. This procedure is useful for temperatures below 700 K, the region for which the production of H¯+ has potential use as an intermediate stage in the cooling of antihydrogen to ultra-cold (sub-mK) temperatures for spectroscopic studies and probing the gravitational interaction of the anti-atom. Our results, utilizing a 50-term …
On The Production Of The Positive Antihydrogen Ion H̄+ Via Radiative Attachment, Chris M. Keating, M. Charlton, Jack C. Straton
On The Production Of The Positive Antihydrogen Ion H̄+ Via Radiative Attachment, Chris M. Keating, M. Charlton, Jack C. Straton
Physics Faculty Publications and Presentations
We provide an estimate of the cross section for the radiative attachment of a second positron into the state of the ion using Ohmura and Ohmura's (1960 Phys. Rev. 118 154) effective range theory and the principle of detailed balance. The ion can potentially be created using interactions of positrons with trapped antihydrogen, and our analysis includes a discussion in which estimates of production rates are given. Motivations to produce include its potential use as an intermediary to cool antihydrogen to ultra-cold (sub-mK) temperatures for a variety of studies, including spectroscopy and probing the gravitational interaction of the anti-atom.