High-energy tail of the linear momentum distribution in the ground state of hydrogen atoms or hydrogen-like ions
Year: 2001
Type: article
Abstract: A long-standing dispute concerning the high-energy tail of the linear momentum distribution (HTMD) in the ground state of hydrogen atoms/hydrogen-like ions (GSHA) has been unresolved up to now. A possible resolution of the above dispute might be connected to the problem of the role of singular solutions of quantal equations, which is a fundamental problem in its own right . The paradigm is that, even allowing for finite nuclear sizes, singular solutions of the Dirac equation for the Coulomb problem should be rejected for nuclear charges Z < 1/α≈137. In this paper we break this paradigm. First, we derive a general condition for matching a regular interior solution with a singular exterior solution of the Dirac equation for arbitrary interior and exterior potentials. Then we find explicit forms of several classes of potentials that allow such a match. Finally, we show that, as an outcome, the HTMD for the GSHA acquires terms falling off much slower than the 1/ p 6 -law prescribed by the previously adopted quantal result. Our results open up a unique way to test intimate details of the nuclear structure by performing atomic (rather than nuclear) experiments and calculations.
Author: E Oks
Institution: Auburn University
Language: English
Topic: Atomic and Molecular Physics
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1973252995