PHYSICAL REVIEW A 95, 052502 (2017)
Resonances in positronic lithium in hot and dense plasmas
Arijit Ghoshal
1 , *
and Yew Kam Ho
2
1
Department of Mathematics, Burdwan University, Golapbag, Burdwan 713 104, West Bengal, India
2
Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 106, Taiwan
(Received 3 March 2017; published 2 May 2017)
Low-lying S -wave resonances in positronic lithium (e
+
Li) under hot and dense plasmas are investigated by
the stabilization method. The screened interaction in plasma is represented by the Debye-Hückel model. Two
resonances are located lying below the Ps(n = 2) excitation threshold. It is found that resonance positions are
lifted with increasing plasma screening strength. For the free atomic system, our reported results are in agreement
with the results of other reliable calculations.
DOI: 10.1103/PhysRevA.95.052502
I. INTRODUCTION
Theoretical calculations show that a positron can bind itself
to the ground state of a lithium atom to form a positronic
lithium atom (e
+
Li) [1–8]. In fact, positronic lithium is the
first atom that showed that a positron is able to bind itself
to the ground state of a neutral atom [1]. The ground state
of positronic lithium has a binding energy of 0.002 484 a.u.
and is electronically stable against decay into both the Li-e
+
and Li
+
-Ps channels [6]; however, it is not stable against
electron-positron annihilation. Besides the ground state of
lithium, the positron can also attach itself to a number of
excited states of the lithium atom [1]. Such states can be
viewed as excited states of e
+
Li and would open the possibility
of spectroscopic detection of this system [1]. There is also cal-
culational evidence that positrons can form bound states with
a variety of atoms such as positronic sodium and positronic
calcium [9–14]. The existence of positron bound states with
neutral atoms and molecules has important implications for
positron and positronium (Ps) chemistry [15]. One possible
signature for positron-atom binding is the existence of resonant
structures associated with atomic excited states in the positron
scattering spectrum. The bound or quasibound (resonance) of
positron and Ps to atoms and molecules has been a subject
of extensive study (see [2–26] and references therein). Large
Feshbach resonances have been observed in annihilation cross
sections corresponding to the formation of positron-molecule
bound states, providing strong evidence that such states also
exist for molecules [27]. However, experimental evidence of
positron-atom bound states has proven to be evasive [9]. In
the case of the positron-lithium system, experimental results
relating to cross sections have been found [28,29], but their
energy resolution is not adequate to map out the resonance
structure.
In this paper we look for S -wave resonances lying below
the Ps(n = 2) excitation threshold in positronic lithium under
hot and dense plasmas. The existence of such low-lying S
resonances, as a rule, leads to a resonant radiative recombi-
nation (RRR) process, which is bound to take place in dense
plasma. The RRR process is likely to dominate recombination
rates in the low-energy regimes where the wavelength of
the electron is much larger than the range of the potential.
*
arijit98@yahoo.com
Moreover, the observational evidence of the existence
of positrons in several astrophysical plasma environments
[30–33] suggests that we examine positron scattering phenom-
ena in plasma environments. In astrophysical environments,
such as of compact objects and inertial confinements, plasma
remains hot and dense. The ranges of density N
e
and
temperature T
e
are around 10
20
–10
23
cm
−3
and 10
7
–10
8
K,
respectively [34,35], whereas the Debye length λ
D
for such
plasmas is known to be λ
D
10a
0
, where a
0
is the first
Bohr radius of the hydrogen atom. These plasmas can be
classified as Debye plasmas or weakly coupled plasmas.
For these plasmas, the coupling parameter Ŵ (ratio of the
potential energy to the average kinetic energy) is much less
than unity. These conditions are also fulfilled in a wide class
of laboratory plasmas. In a Debye-type plasma, it is known that
the short-range potential around a unit test charge scales as the
Debye-Hückel potential or static screened Coulomb potential
(SSCP) [36] (in a.u.)
V (r ) = e
−r/λ
D
/r. (1)
Here μ = 1/λ
D
is called the plasma screening parameter.
The Debye length is related to the thermal velocity v
T
and
plasma frequency ω
P
by the formula λ
D
= v
T
/ω
P
. In a Debye
plasma the interaction screening is the collective effect of
the correlated many-particle interactions and in the lowest
particle correlation order it reduces to a SSCP of the form (1).
This paper aims at looking for S -wave resonances lying
below the Ps(n = 2) excitation threshold in the e
+
-Li system
under Debye-type plasmas by applying a stabilization method.
Atomic units will be used in the rest of the paper unless
explicitly stated otherwise.
II. THEORY AND CALCULATIONS
Carrying out calculations on resonances by applying the
stabilization method in a multibody system such as the
positron-lithium system requires enormous computational
effort. In order to reduce computational effort, here we resort
to the model potential method to treat the positron-lithium
system as a three-body system. In the model potential method,
the lithium atom is treated as a two-body system consisting of
a positive ionic core (Li
+
) together with an electron (active).
The interaction between the electron and the ionic core is then
represented by a model potential, whereas the core includes
the average effect of all other electrons (passive). Considering
2469-9926/2017/95(5)/052502(6) 052502-1 ©2017 American Physical Society