1. Introduction

Similar to the electron, its anti-particle (positron) also has important scientific
and technological applications in a large variety of fields. A thorough presentation
of the many applications of positrons can be found, for instance, in the book by
Charlton and Humberston ^{[1]}. This includes
astrophysics, solar physics, bio-medicine (both diagnostics and therapy) and
materials science (defect studies and crystallography). From a more fundamental
perspective, positrons are essential in the formation of antihydrogen, understanding
elementary particle and positronium (Ps) physics, as well as in the investigation of
positron binding to ordinary matter, *i.e.* neutral atoms ^{[1]}. Resonances in electron-impact on atoms and
molecules are well-known; however, the situation with respect to positrons is not as
clear [1]. Positron binding energies have been measured for a large variety of small
targets ^{[1]}, although only a few calculations
are available^{[1]}. Positron scattering in the
gases phase constitutes a sensitive test for atomic interactions. The static
potential between the incoming electron and the fixed charge distribution in an atom
is attractive. Positrons inside an atom experience a repulsive static interaction
from the positive nucleus only partially screened by electrons. The opposite sign of
the static interaction for positrons cause a kind of compensation between the two
parts of the potential (static + polarization) and small adjustments of these parts
cause big differences in cross sections. New scattering measurements are very
important for comparison, setting new standards for both theoreticians and
experimentalists ^{[1,2]}. Indeed one rationale
for the present investigation is to try and shed more light on this state of
affairs. In the last few years, there have been several theoretical activities
concerning the positron-atom scattering at several energies ^{[3]}. Most of the work produced was based on ab initio methods
^{[3]} and also classical collision theory
^{[3]}. However, each of these models works
only on a limited range of targets and these calculations are very time consuming,
limiting the domain of applicability of such models.

In the present work we present a study on the simple scaling of plane wave Born cross
section which was created for positron-impact excitations of targets in general
^{[4]}. The study is based on the traditional
first Born approximation (FBA). The FBA still is used as the starting point in
several studies, because (a) the plane wave is the correct wave function at infinity
for an positron colliding with a target, and (b) it is the simplest collision theory
that uses target wave function explicitly. Validating a scaling method for FBA cross
sections of atoms requires two initial ingredients: (i) the Born integral cross
sections themselves; (ii) reliable experimental or theoretical optical oscillator
strengths. The called BE^{[5]} to convert the FBA to reliable cross sections comparable to accurate
excitation cross sections at all incident electron energies above threshold. The BE^{[5]}
correct the deficiencies of FBA into simple functional forms that depend on a few
atomic properties. Cross sections for positron and electron impact are virtually
identical at high energies and if the basic dynamical ingredients for this evidence
is the FBA, then it is possible extend the analysis developed by Kim ^{[5] }to more complicated systems, as
positron-atom scattering (this is a important consideration and can be significant
for studies using positron as incident particle) ^{[4]}. One of the complications created by the use of positron as incident
particle is the existence of additional positronium channels which are not present
in the case of electron scattering. Thus, we will present a study of the SBP
approach without Ps channel. The goal of the present scaling method is to provide a
simple theoretical method to calculate excitation cross sections comparable not only
to reliable experimental data, but also to more sophisticated theories. To our
knowledge, this study represents the first attempt to establish a theoretical
formulation for positron scattering using the called scaling Born positron (SBP),
*i.e.*, a version for positron of originally BE^{[5]} for
electron scattering.

In Sec. 2 we identify changes necessary to transform the model proposed by Kim ^{[5]} (electron scattering) and the present model
for positron scattering. In Sec. 3 we discuss the application of the method for
excitation of H, He, Hg, and Mg. Conclusions are presented in Sec. 4.

2. Theory

The scaling Born approximation described by Kim ^{[5]} for excitation of neutral atoms is applicable to dipole-allowed
excitations, and use atomic properties as excitation energy, ionization energy, and
the dipole ^{[4},^{5]}

where

where

In Eq. (3), *i.e*., situations where the target wave functions can
be considered frozen. For inelastic scattering, the FBA can be justified only by a
favorable comparison with more elaborate methods. As we will see, the SBP approach
represent a considerable improvement on the FBA, indicant cross sections with the
same order of magnitude as the more sophisticated calculations. The (

where

where

which has the

3. Results and discussion

We present the calculated integral cross sections (ICS) for H, He, Be, Mg, and Hg
atoms by positron scattering and the cross sections are compared to other theories
and experiments (these atoms are chosen because recent experimental data for
electron scattering are described in the literature, and hence well suited as a
benchmark for our method using positron as incident particle). For all targets we
used the theoretical ^{[5]} and the wave
functions for the excited electronic states were all generated with the improved
virtual orbital ^{[4]}.

H-atom

We performed calculations for the Hydrogen atom as our starting point and the ICS
for transition 1s-2s (^{[6]}. We can note
also in Fig. 1 that the SBP approach not
only reduces the cross section magnitude at low energy, but also shifts the peak
to the high energy than the peak of the FBA, while keeping the high energy
validity of the FBA intact.

In Fig. 2, the integral cross sections (ICS)
using the SBP approach for the 1s-2p excitation of H atom are compared to the
MCC ^{[6]} method. Note in Fig. 2 a good level of agreement between the
SBP approach and the MCC method ^{[6]}.

In the high energy region, the polarization interaction, changing with the impact
velocity, becomes relatively weaker. For the static potential, FBA predicts
equal cross sections for positron and electrons ^{[3]}. This convergence (cross sections) for positron and electrons
can be observed using Eq. (2), *i.e*,

Figure 3 shows this effects on the
electronic excitation process of H atom. Cross sections for positron scattering
using the SBP approach (1s-2p, state) close with cross sections for electron
scattering at high energies, without losing its well-known validity at high ^{[5]} and as expected,
predicts equal cross sections for positrons and electrons.

He-atom

Figure 4 shows the integral cross sections
(ICS) for ^{[7]} and experimental data ^{[8]}.

Figure 5 shows the relationship between the
states 2

Figure 6 shows a similar agreement between
the SBP approach and the sophisticated CCC method [10] for the 2^{[8]}. The performance
of the SBP approach for He atom is remarkable, particularly in view of the
simplicity of the scaling.

As in Fig. 3, the Fig. 7 shows the SBP approach compared with BE*i.e.*, the cross sections suggests that the SBP approach
does offer a very useful alternative.

Be atom

Figure 8 presents the SBP approach cross
sections for the Be atom (2s2-2s2p^{[5]}. As noted the SBP again close with BE

Hg atom

Figure 9 shows the SBP approach cross
sections for the Hg atom (6s2-6s6p1P,

Mg atom

The Mg atom has a ground state Ps formation threshold of only 0.8 eV which is
closer to zero energy than any ground or excited state Ps formation thresholds
for the alkali atoms. In addition to this, Mg is a member of the alkaline earth
metals family of elements which has never been investigated in an ^{[9]}. As observed again, the SBP approach does offer a very useful
alternative method.

4.Conclusions

A study of various transitions in positron scattering with ground-state of atoms has
been performed using the scaling Born positron (SBP) approach, without the
Ps-channel. The inelastic cross sections scattering are reported for low,
intermediate and high energies. We observe that the inelastic cross sections using
the SBP approach become relatively well converged with sophisticated methods. The
SBP approach is a simple representation of the Born cross sections and in this
sense, the present approach retains much of the utility of the original Born model
and requires a relatively small amount of computing effort. The SBP described here
will facilitate the calculation of integrated excitation cross sections for many
atoms, making the formulas ideally suited for molecules and other applications where
cross sections for a wide range of incident energies are required. The SBP approach
is relatively simple compared to state-of-the-art *ab initio*
theories.