Journal of Physics B: Atomic, Molecular and Optical Physics
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 095004 (4pp) doi:10.1088/0953-4075/47/9/095004
Magnetic-dipole photo-recombination in
ultracold hydrogen plasma
A S Baltenkov
Institute of Ion-Plasma and Laser Technologies, Uzbek Academy of Sciences 100125, Tashkent,
Uzbekistan
E-mail: arkbalt@mail.ru
Received 21 October 2013, revised 18 December 2013
Accepted for publication 17 January 2014
Published 24 April 2014
Abstract
The cross section for magnetic-dipole photodisintegration of the negative hydrogen ion has
been calculated within the zero-range-potential approximation. The magnetic-dipole cross
section for photodetachment within the very narrow range of energy near the process threshold
is predicted to dominate over the electric-dipole one. It is shown that in ultracold hydrogen
plasma at temperatures below T = 3.29 × 10
−4
K the magnetic-dipole photo-recombination
becomes an important mechanism of electron capture by hydrogen atoms.
Keywords: photodetachment, dipole-electric cross section, dipole-magnetic cross section,
ultracold plasma
(Some figures may appear in colour only in the online journal)
1. Introduction
Photoelectron detachment of negative hydrogen ions has been
theoretically studied in many papers (see, for example, [1–4]
and references therein). In those papers the photodetachment
process was considered as electric-dipole absorption of
photons. Near the process threshold the electric-dipole
photodetachment of s-states of the negative hydrogen ion
does not contribute to the cross section. According to the
Wigner threshold law [5], for systems bound by short-
range forces near the threshold, the photodetachment process
takes place through electron transitions into the continuum
s-state, i.e. these transitions are not allowed in electric-dipole
absorption. They are also absent in the electric-quadrupole
photo-process. According to [5], for a two-particle final state
the near-threshold behaviour of the reaction depends solely
on the asymptotic form of the continuum wave function. The
Wigner threshold law is only the first term of a power series
expansion in the electron momentum, and deviation appears
when higher-order terms become important [6]. The range
of validity of the Wigner law for negative ions is affected
by short-range interactions such as induced polarization,
static multipole moments of the residual atom, and the
existence of nearby Feshbach resonances [7]. This range
varies significantly for different negative ions [8–10], but
up to electron energies of a few meV above threshold the
Wigner law is in good agreement with the experimental results
[10]. Exactly within this range of photoelectron energy the
magnetic-dipole interaction permitting the transitions between
the s-states of the discrete and continuous spectra can be the
main mechanism of negative ion photodetachment.
The need to consider this process was demonstrated, for
the first time, by Fermi in [11], where the recombination of
a neutron and a proton resulting in a deuteron formation and
photon emission was studied. This process is the inverse of
the deuteron photodetachment and the cross sections of these
processes are connected with each other through the principle
of detailed balance. Near the threshold, for small values of the
momentum, p of relative motion of the proton and the neutron
the electric-dipole cross section of radiation capture is directly
proportional to p while the magnetic-dipole cross section is
inversely proportional to this momentum. For this reason, the
probability of slow neutron capture by a proton is independent
of the speed of their relative motion in the magnetic process and
decreases as p
2
in the electric-dipole process. In the diagrams of
the deuteron photo-electric and photo-magnetic detachments,
the latter process manifests itself as a small peak at the deuteron
disintegration energy [12].
Considering all of the above, some questions arise. What
is the role of the magnetic field of the light wave in the process
of photodetachment of negative ions, in particular, hydrogen
ions? The magnetic moment of the electron μ = e/2mc is
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