Positron induced scattering cross sections for hydrocarbons relevant to plasmaSuvam Singh, and Bobby Antony

Citation: Physics of Plasmas 25, 053503 (2018); doi: 10.1063/1.5024581View online: https://doi.org/10.1063/1.5024581View Table of Contents: http://aip.scitation.org/toc/php/25/5Published by the American Institute of Physics

Positron induced scattering cross sections for hydrocarbons relevantto plasma

Suvam Singh and Bobby Antonya)

Atomic and Molecular Physics Lab, Department of Applied Physics, Indian Institute of Technology(Indian School of Mines), Dhanbad, Jharkhand 826004, India

(Received 2 February 2018; accepted 17 April 2018; published online 4 May 2018)

This article explores positron scattering cross sections by simple hydrocarbons such as ethane,

ethene, ethyne, propane, and propyne. Chemical erosion processes occurring on the surface due to

plasma–wall interactions are an abundant source of hydrocarbon molecules which contaminate the

hydrogenic plasma. These hydrocarbons play an important role in the edge plasma region of

Tokamak and ITER. In addition to this, they are also one of the major components in the planetary

atmospheres and astrophysical mediums. The present work focuses on calculation of different

positron impact interactions with simple hydrocarbons in terms of the total cross section (Qtot), elastic

cross section (Qel), direct ionization cross section (Qion), positronium formation cross section (Qps),

and total ionization cross section (Qtion). Knowing that the positron-plasma study is one of the trend-

ing fields, the calculated data have diverse plasma and astrophysical modeling applications. A com-

prehensive study of Qtot has been provided where the inelastic cross sections have been reported for

the first time. Comparisons are made with those available from the literature, and a good agreement is

obtained with the measurements. Published by AIP Publishing. https://doi.org/10.1063/1.5024581

I. INTRODUCTION

Positrons are not easily obtainable as compared to elec-

trons. However, in recent times, the progress in trapping

methods and their storage has now permitted the accumula-

tion of an adequate number of low-temperature positrons to

form plasmas.1 Due to opposite charge and the same mass,

positrons annihilate electrons and also can combine with

them to form neutral plasmas having dynamical symmetry

between the charged species. Recent years have seen a huge

interest in laboratory experiments on electron-positron plas-

mas such as PAX/APEX experiments.2 Electron-positron

plasmas also known as pair plasmas show odd behavior when

compared with the other four states of matter due to the

absence of Faraday rotation and parametric decay. In addition

to that, they have enhanced nonlinear Landau damping and

solitary wave behavior. Pair plasmas play a fundamental role

in the evolution of extreme astrophysical objects, including

black holes and pulsars.3 They are also associated with the

emission of ultra-bright gamma-ray bursts. Moreover, it is

believed that in the leptonic era that is approximately one sec-

ond after the Big-Bang, the universe consisted mainly of

dense electron-positron plasmas in a hot photon bath.3

Recent works4,5 suggest the production of a large number

of runaway positrons due to pair production caused by the run-

away electrons and background plasma ions and electrons in

tokamak fusion plasma including JET and JT-60U.5 According

to Helander and Ward,5 tokamaks could be the largest reposito-

ries of positrons made by man. This is one of the main reasons

to undertake the present work. This work is devoted to the

study of various cross sections for C2-C3 hydrocarbons via pos-

itron collision. These targets have numerous applications in

various fields especially in plasma and astrophysics. Graphite

(a form of carbon) is one of the vital plasma facing materials in

almost all contemporary operating fusion devices. Thus, due to

chemical erosion of the surface occurring due to plasma-wall

interactions, hydrocarbons become one of the abundant sources

in plasma materials.6 These hydrocarbons become a major con-

tamination source in the hydrogenic plasma as seen in the case

of ITER, where efforts are made to reduce the formation of

hydrocarbon films.7 The composition of the hydrocarbon fluxes

flowing inside the plasma covers a wide spectrum of molecules

from methane to propane.8 The discharge of more complex

C2-C3 hydrocarbons becomes increasingly vital as the impact

energy of plasma ions striking the surface decreases.6 These

hydrocarbons play a significant role in plasma diagnostics

in the Tokamak fusion divertor due to repeated sputtering

of graphite walls.9 In addition to that, they have importance

in edge plasmas of magnetically confined high temperature

hydrogen plasma and also in low temperature plasma process-

ing.10 Apart from their application in plasma science, they are

widely studied in the field of astrophysics where they are

observed as important constituents in the planetary and come-

tary atmospheres.10 Furthermore, the lighter linear hydrocar-

bons are also of interest due to their significant role in chemical

vapor deposition (CVD) reactions.11 To understand the behav-

ior of these molecules in plasma and space physics, reliable

cross sections are needed. Cross sections form an integral part

in studying collision dynamics of any target. The cross section

data have numerous modeling applications ranging from RF

plasma processing to astrophysical and planetary atmospheres.

These data form an integral part of Monte Carlo simulation,

which requires an accurate knowledge of the elastic and inelas-

tic scattering processes12 suffered by positrons to study positron

transport in solids or biological media such as in EPOTRAN.13

The modified form of spherical complex optical poten-

tial (SCOP) formalism14–16 is used in this work to calculatea)Electronic mail: bobby@iitism.ac.in

1070-664X/2018/25(5)/053503/7/$30.00 Published by AIP Publishing.25, 053503-1

PHYSICS OF PLASMAS 25, 053503 (2018)

the positron scattering total cross sections over a wide energy

range from positronium formation threshold to 5000 eV for

the targets ethane, ethane, ethyne, propane, and propyne. To

estimate the direct ionization cross section, the modified

form of the CSP-ic16–18 (complex scattering potential ioniza-

tion contribution) method is used. The total ionization and

positronium formation cross section by the positron impact

are also evaluated.

To the best of our knowledge, no studies on elastic or

inelastic cross sections have been done on the present set of

molecules for positron scattering. However, a few studies

are found in the literature for positron scattering total cross

sections. A complex optical potential approach has been

employed by Raizada and Baluja19 for predicting scattering

cross sections for ethane, ethene, ethyne, and propane, and a

similar approach was used by Baluja and Jain20 to calculate

the total scattering cross section for ethyne. The basic

approach of the present work and the works of Baluja and

Jain20 and Raizada and Baluja20 are similar. The model

potentials used in the work of Baluja and Jain20 and Raizada

and Baluja19 are pretty similar; however, there are several

differences in the interaction potentials that are used in the

present endeavor. We have used a more sophisticated absorp-

tion potential of Reid and Wadehra,21 made exclusively for

positron scattering, where they use modified form of

Staszewska’s model22 potential which was originally devel-

oped for electron scattering. Moreover, the absorption thresh-

old used in the present work efficiently includes the Ps

formation in the inelastic channel which is not seen in previ-

ous studies. Besides, the formalism of the static interaction

and the polarization interaction is also different in the present

case. Some experimental works related to the measurement

of the total cross section have also been carried out. Floeder

et al.23 have used a transmission experiment to measure the

total cross section (Qtot) for ethane, ethene, and propane,

whereas Sueoka and Mori24,25 have used retarding potential-

time of the flight method to measure Qtot for ethane, ethene,

and ethyne. Moreover, Zecca et al.26 have used a linear trans-

mission experiment to measure the Qtot for ethyne, whereas

the lone comparison for Qtot for propyne is available due to

experiments from Makochekanwa et al.27

This paper is organized as follows: In Sec. II, the SCOP

formalism is briefly described with the details of the calcula-

tions. Thereafter (in Sec. III), the present results are reported

and discussed and are compared with the available experi-

mental data. At the end of this work, conclusions are drawn

from the present investigation.

II. THEORETICAL METHODOLOGY

The spherical complex optical potential (SCOP)

approach is employed in this work. The theoretical details are

already explained in the previous articles.14,15,28,29 However,

the essential parts are described in this section. The interac-

tion potential experienced by the projectile due to the target

is given by the following equation:

Voptðr;EiÞ ¼ VstðrÞ þ VpolðrÞ þ i Vabsðr;EiÞ: (1)

In the real part of Eq. (1), Vst is the static potential, which

occurs due to the electronic charge cloud of the target, whereas

Vpol is the polarization potential, which is generated due to the

distortion of the charge distribution of the target by the field

created by the incident projectile (positrons). The complex part

of the above equation gives the absorption potential, which

accounts for the total loss of scattered flux into all allowed

inelastic channels, which includes positronium formation, elec-

tronic excitation, and ionization channels. Due to the restric-

tion of the present model, we have not included the rotational

and vibrational channels in the present calculation. For the for-

mulation of charge density and static potential, the parametric

Roothaan Hartree–Fock (RHF) wavefunctions of Cox and

Bonham30 was used. The correlation polarization potential is

formulated through the work of Zhang et al.,31 whereas Reid

and Wadehra’s21 absorption potential is employed for Vabs.

For detailed explanation, see Refs. 14 and 15.

In the SCOP formalism, it is very important to accurately

evaluate the charge density of the targets since all the interac-

tion potentials are dependent on this property. The parameters

given by Cox and Bonham30 are accurate to estimate the

charge density of atoms. Hence, to precisely evaluate the

charge density of molecules using these atomic parameters,

the multi scattering center (MSC) approach32,33 has been used

in the present work. In this method, various scattering centers

were identified depending on the bond length of the molecule.

The scattering center represent a group of atoms which

depends explicitly on the extent of electronic charge density of

each group in the molecule. This method is justified because

the incident positron sees different groups of the molecule as

an independent unit rather than the molecule as a whole. In the

present set of molecules, the lighter hydrogen atoms attached

to a heavier carbon atom always form one group and are identi-

fied as an independent scattering center. For example, in the

case of propane (CH3-CH2-CH3), three scattering centers were

identified as in two CH3 and one CH2 group. Then, the charge

densities of these scattering centers were added to find the total

charge density of the molecule, which is then used to calculate

various potentials and eventually cross sections. Two scattering

centers were used for ethane, ethene, and ethyne, whereas

for propyne, three scattering centers were identified. However,

such an approximation might overestimate the total inelastic

(Qinel) and total elastic cross section (Qel) due to overlapping of

atoms. In the present case, the carbon atom is partially screened

due to the overlapping of neighboring hydrogen atoms in each

scattering center. This means that the carbon atom in each of

the scattering centers is not exposed to the entire flux of incom-

ing positrons. The quantum mechanical treatment of such a

screening effect using interaction potential is a tedious task.

However, some efforts have been made earlier by Blanco and

Garc�ıa34 and Vinodkumar et al.35 at the cross section level to

account for such an effect. The same idea has been employed

in this work with slight modification to adapt for the MSC

approach. The details are discussed later in this section.

A. Calculation of the total cross section (Qtot)

The interaction potential in Eq. (1) is used in the

Schr€odinger equation, which is solved by the method of

053503-2 S. Singh and B. Antony Phys. Plasmas 25, 053503 (2018)

partial wave analysis using suitable boundary conditions. In

the low energies, a less number of partial waves are used for

the convergence; however, as the incident energy increases,

a more number of partial waves are required for the conver-

gence. In the present calculation, a total of 50 partial waves

are used for the convergence of the solution. The solutions

are obtained in the form of complex phase shifts (dl). These

complex phase shifts are used to calculate the inelasticity

factor (gl), which is then employed in the calculation of elas-

tic and inelastic cross sections, which are added to obtain the

total scattering cross section. Their respective expressions

are given as follows:

QelðEiÞ ¼pk2

X1

l¼0

ð2lþ 1Þjgl exp ð2iRe dlÞ � 1j2; (2)

QinelðkÞ ¼pk2

X1

l¼0

ð2lþ 1Þð1� g2l Þ; (3)

QtotðEiÞ ¼ QelðEiÞ þ QinelðEiÞ: (4)

However, as already mentioned, these cross sections

tend to overestimate due to overlapping of atoms. To over-

come this drawback, screening correction has been used. In

this method, the cross sections arising due to the screening of

the carbon atom because of the surrounding hydrogen atoms

in each of the scattering centers are subtracted from the over-

all cross section. Thus, the cross sections are given by

QinelSCðEiÞ ¼ QinelðEiÞ � nQatomOC ðEiÞ; (5)

QelSCðEiÞ ¼ QelðEiÞ � nQatomOC ðEiÞ: (6)

Here, QinelSC and QelSC are the screening corrected

inelastic and elastic cross sections, respectively, and n is the

number of scattering centers. The screening corrected total

cross section (QtotSC) is given by

QtotSCðEiÞ ¼ QinelSCðEiÞ þ QelSCðEiÞ: (7)

QatomOC represents the average overlap of the surrounding

hydrogen atom to the carbon atom in a scattering center. In

general, it is given by

QatomOC ðEiÞ ¼

Q1Q2

maxð4pr2d;Q1;Q2Þ

; (8)

where Q1 and Q2 are the respective scattering cross sections

for carbon and hydrogen atoms, whereas rd is the C-H bond

length. The approximated form of QatomOC can be given as

QatomOC ðEiÞ ¼

1

NRN

i

Qatomi Qatom

C

maxð4pr2d;Q

atomi Qatom

C Þ : (9)

Here, N is the total number of atoms surrounding the carbon

atom in each of the scattering centers. This screening correc-

tion takes care of the overestimation occurring due to the

MSC approach and gives a better representation in the lower

energy regime. From here onwards, all the cross sections men-

tioned in this article are screening corrected cross sections and

hence bear their regular symbols unless otherwise mentioned.

B. Calculation of different inelastic channels

Positronium (Ps) formation cross section (Qps)

Calculating the Ps formation cross section is one of the

most difficult tasks which one has to deal with while studying

positron scattering. We have adopted a crude method to estimate

Qps. The details of the method can be obtained from our previ-

ous articles.14,15 However, the essential parts are discussed here.

We have used the method proposed by Chiari et al.36 to

determine the threshold parameter. Below this threshold

value, all the inelastic processes are assumed to be prohibited

(considering that we have not included the rotational and

vibrational excitations). Above this value, the inelastic chan-

nels such as Ps formation, electronic excitation, and ioniza-

tion are included in the absorption channel. Although this

method is not accurate, however, it proves to be a very effec-

tive process to determine Qps for large molecules, which is

not possible to calculate using stringent theories due to the

complexity of the problem. The positronium formation cross

section predicted in this work could serve as a benchmark

for further experimental and theoretical studies. The thresh-

old parameter is given as

DðEÞ ¼ De � ðDe � DpÞ exp ð�ðEi � DpÞ=EmÞ; (10)

where Ei is the energy of the incident positron and De and Dp

are the first electronic excitation energy and Ps formation

threshold, respectively. Em is the energy at which the inelastic

cross section attains a maximum value without taking Ps for-

mation into account. Using the above equation, one can cal-

culate the inelastic cross section including the Ps formation.

From this, the inelastic cross section without Ps formation

(calculated using De as threshold) is subtracted to get Qps.

Calculation of the direct ionization cross section

(Qion) and total ionization cross section (Qtion)

Here, we give an overview of the theory employed. The

details have been explained in Refs. 16–18.

As already mentioned, the total inelastic cross section

obtained by using Eq. (10) contains channels such as Ps for-

mation, electronic excitation, and ionization of the target. It

is given as

QinelðEiÞ ¼ QpsðEiÞ þX

QexcðEiÞ þ QionðEiÞ; (11)

where Qps is the Ps formation cross section, whereasPQexcðEiÞ represents the sum over all the discrete excitation

cross sections for all the accessible electronic states and

QionðEiÞ is the total cross sections of all allowed direct ioni-

zation processes. We define a term Qin such that

QinðEiÞ ¼ QinelðEiÞ � QpsðEiÞ ¼X

QexcðEiÞ þ QionðEiÞ:(12)

From this point onwards, the modified form of the

complex scattering potential-ionization contribution (CSP-

ic) method16–18 (please see Refs. 18 and 33 for more details)

can be used in its usual form to determine QionðEiÞ from

QinðEiÞ. From Refs. 18 and 33, it is known that the uncer-

tainty in estimation of the direct ionization cross section is

053503-3 S. Singh and B. Antony Phys. Plasmas 25, 053503 (2018)

around 7% in the present method. Now, the total ionization

cross section is obtained by adding the direct ionization cross

section with the Ps formation cross section being its respec-

tive energies, such that

QtionðEiÞ ¼ QionðEiÞ þ QpsðEiÞ: (13)

The results obtained by employing the above theoretical

methods are discussed in detail in Sec. III. Table I provides

the target properties and the parameters used in the present

calculation where IE is the ionization energy of the target.

III. RESULTS AND DISCUSSION

The positron scattering total cross section for ethane is pro-

vided in Fig. 1 with the energy of the incident positron varying

from near Ps formation threshold to 5 keV. The present data are

compared with all the available works found in the literature.

The general trend of the present curve is as such that it shows a

minimum at a certain point and then rises to a maximum and

then gradually decreases. The minimum is seen at around 5 eV,

which suggests that from this point onwards, positronium forma-

tion starts contributing to the total cross section. As the incident

energy of the positron increases, more inelastic channels such as

electronic excitation and ionization channels start contributing

to the total scattering cross section. The present cross sections

are slightly higher compared to other experimental works in the

low energy region (prior to 20 eV). This could be due to the

crude treatment of the scattering problem in the low energies.

However, in the intermediate and high energy region, it has a

very good agreement with the experimental values of Floeder

et al.23 and Sueoka and Mori.24 The theoretical curve of

Raizada and Baluja19 does not show much of agreement with

neither of the experimental values nor agrees with the present

curve. Although the basic theoretical approach used in the pre-

sent work is similar to that of Raizada and Baluja,19 the present

model shows a much improved result as compared to them.

This adds to the credibility of the present model. Qel is also pro-

vided with the present Qtot since it forms one of the most impor-

tant input parameters for plasma modeling. It is seen that around

the Ps formation threshold mark, Qel coincides with Qtot, which

suggests that below this point, there is no contribution from the

inelastic processes, which complies with the assumption made

in the present theory.

Figure 2 gives the present Qtot values for positron scatter-

ing from ethene along with the comparisons available in the

literature. The present Qel values are also provided in the

graph for the sake of completion of the dataset; however, no

such previous results are available for comparison. The energy

of the positron is taken from near Ps formation threshold to

5 keV. A significant improvement of the present dataset is

seen throughout the energy region when compared with the

theoretical values of Raizada and Baluja.19 There is a good

agreement of the present result with the observed values of

Floeder et al.23 since the present curve lies within the experi-

mental uncertainty as mentioned by them. Likewise, a similar

observation is made when the present values are compared

with the experimental data of Sueoka and Mori24 in the inter-

mediate and high energy region. However, prior to 25 eV,

the present curve does not show much of an agreement with

their data. In the high energies, the present results merge with

all other comparisons as expected from the first Born approxi-

mation where the cross sections do not depend on the interac-

tion potential, but on the kinetic energy of the projectile. Such

a behavior is seen in all the cases discussed in this section.

Figure 3 presents positron scattering Qtot for ethyne

along with its theoretical and experimental comparisons. The

present Qel is also provided; however, it does not have any

comparisons. In the high energies, the present curve and

TABLE I. Target properties.

Target Polarizability (A3)37 IE (eV)37 De (eV) Dp (eV) Em (eV)

Ethane 4.226 11.52 10.00 4.72 40

Ethene 4.188 10.51 9.60 3.71 40

Ethyne 3.487 11.40 9.20 4.60 35

Propane 5.921 10.94 9.49 4.14 40

Propyne 5.550 10.36 9.07 3.56 35

FIG. 1. Positron scattering total cross section for ethane. Solid line: present

data, dashed line: present elastic cross section, dashed dot dot line: Raizada

and Baluja,19 star: Floeder et al.,23 and sphere: Sueoka and Mori.24

FIG. 2. Positron scattering total cross section for ethene. Solid line: present

data, dashed line: present elastic cross section, dashed dot dot line: Raizada

and Baluja,19 star: Floeder et al.,23 and sphere: Sueoka and Mori.24

053503-4 S. Singh and B. Antony Phys. Plasmas 25, 053503 (2018)

the curve of Baluja and Jain20 and Raizada and Baluja19 are

concordant to each other since in this region, the projectile

follows the first Born approximation. However, in the low

energies, these three curves significantly differ from each

other. This could be due to the difference in the interaction

potentials employed in each of the models and also due to the

screening correction employed in the present model which

is expected to improve the results in the low energies. The

present curve shows excellent agreement with the experimen-

tal dataset of Sueoka and Mori25 throughout the compared

energy range. Similarly, the present values have good agree-

ment with the observed values of Zecca et al.26 since the pre-

sent curve lies within the experimental uncertainty as given

by them. It is worth noting that the experimental uncertainties

mentioned by both the experimental groups are quite high in

the low energy regime, and this suggests the complicacy of

the positron scattering problem. In the low energy range, pos-

itron scattering cross sections predicted by different research

groups do not agree well with each other. This suggests that

many studies are necessary for the validation of the findings.

A graphical representation of the positron scattering total

cross section for propane is given in Fig. 4 along with its Qel.

The previous studies available for Qtot are due to the work of

Raizada and Baluja19 and Floeder et al.23 Similar to previous

cases, the present results and the results of Raizada and

Baluja19 do not match well in the low and intermediate ener-

gies. Moreover, the present values agree well with the experi-

mental findings of Floeder et al.23 prior to 55 eV. However,

above this energy, the present cross sections underestimate

their values by about 18%, which gradually decrease and

tend to merge with their values beyond 200 eV.

Figure 5 shows the Qtot for positron scattering from the

propyne molecule along with the present Qel. The only com-

parison available is from the work of Makochekanwa et al.27

The general trend of the present curve follows the same char-

acteristic nature as seen in the previous cases. An increase in

the cross section is observed beyond 4 eV, which suggests

the origin of the Ps formation channel. Beyond this point, as

the energy of the positron increases, more number of inelas-

tic channels (such as electronic excitations and ionizations)

will be open, which results in the rise of cross sections.

Except in the energy range of 9–16 eV, an excellent agree-

ment is found between the present and the experimental

observations of Makochekanwa et al.27 The present cross

section shows a characteristic maximum at around 11 eV,

which is due to the rise of different inelastic channels such

as Ps formation, direct ionization, and electronic excitation.

On the contrary, the results of Makochekanwa et al.27 show

a dip around that energy. As mentioned by them, this feature

occurs due to ionizations. It is noteworthy that if different

ionization channels come into picture at these energies, then

there should be a rise in the magnitude of cross sections

rather than showing such a dip. However, according to our

knowledge, the reason for such a dip is still unexplained.

Since no other comparisons are available according to our

knowledge, it is very difficult to point out the accuracy of

any of the data. More investigations are encouraged for the

FIG. 3. Positron scattering total cross section for ethyne. Solid line: present

data, dashed line: present elastic cross section, dashed dot line: Baluja and

Jain,20 dashed dot dot line: Raizada and Baluja,19 sphere: Sueoka and

Mori,25 and triangle: Zecca et al.26

FIG. 4. Positron scattering total cross section for propane. Solid line: present

data, dashed line: present elastic cross section, dashed dot dot line: Raizada

and Baluja,19 and star: Floeder et al.23

FIG. 5. Positron scattering total cross section for propyne. Solid line: present

data, dashed line: present elastic cross section, and open triangle:

Makochekanwa et al.27

053503-5 S. Singh and B. Antony Phys. Plasmas 25, 053503 (2018)

authentication of the results found in the literature and the

results predicted in the present endeavor.

The positron scattering direct ionization cross section is

graphically shown in Fig. 6. As evident from the graph, Qion

for propane is greater than that of the rest of the molecules,

whereas the cross section of ethyne is the smallest. From

this, it can be concluded that as the number of electrons in

the target increases, Qion increases. Since the number of elec-

trons for propane>propyne>ethane>ethene>ethyne, like-

wise it should be observed for Qion as well. It is correct for

most of the cases as Qion for propane>propyne>ethyne.

However, for ethane and ethene, the situation is reversed

since Qion for ethene is greater than Qion for ethane. A simi-

lar feature is seen for Qtot as well, where Qtot for ethene is

less than Qtot for ethane. This reflects from the fact that the

ionization energy and Ps formation threshold of ethene are

significantly less than those of ethane. Thus, the inelastic

cross sections for ethene should be larger than the respective

cross sections for ethane. Hence, it can be concluded that

the magnitude of the direct ionization cross section mostly

depends on the size of the target (i.e., on the number of elec-

trons); however, the target properties have a significant role

to play as well. Furthermore, it is also observed that all the

curves are pretty steep in the rising end as compared to

the falling end. This suggests that the rate of ionization is

very high in the low energies which gradually attains a maxi-

mum and then decreases as the impact energy increases. At

higher energies, cross sections decrease because the interac-

tion time between the projectile and the target decrease;

hence, the projectile is not able to transfer much of its energy

to the targets which reduces the probability of ionization.

The Ps formation cross section is reported via a graphi-

cal representation in Fig. 7. It is observed that for all the mol-

ecules, the peak for Qps is at around 10 eV. The Ps formation

channel originates from the Ps formation threshold, attains

a maximum value, and then decreases with an increase in

energy. Beyond 100 eV, Qps becomes almost negligible. The

Qps for propyne is maximum, whereas it is minimum for

ethyne. This suggests that the magnitude of Qps not only

depends on the size of the molecule but also depends on the

width of (De-Dp). This is the first attempt to report Qps for

the present set of molecules, and hence, further studies must

be done for the verification of the present calculation.

Figure 8 shows the positron scattering total ionization

cross section for the present set of molecules. Qps and Qion

have been simply added to estimate Qtion. Two peaks are

seen in each of the curves. The first one is due to Ps forma-

tion, whereas the second peak is attributed to Qion. As

expected, prior to 10 eV, the combined effect of the width of

(De-Dp) and molecular size determines the magnitude of the

cross section; however, after this energy, the molecular size

starts dominating the cross section. This is why before the

first peak, Qtion is maximum for propyne. However, beyond

this peak, propane has the maximum Qtion. The total ioniza-

tion cross section for ethyne has the minimum magnitude

throughout the energy region.

FIG. 6. Positron scattering direct ionization cross section. Dashed line: eth-

ane, dotted line: ethene, solid line: ethyne, dashed dot line: propane, and

dashed dot dot line: propyne.

FIG. 7. Positron scattering positronium formation cross section. Dashed

line: ethane, dotted line: ethene, solid line: ethyne, dashed dot line: propane,

and dashed dot dot line: propyne.

FIG. 8. Positron scattering total ionization cross section. Dashed line: eth-

ane, dotted line: ethene, solid line: ethyne, dashed dot line: propane, and

dashed dot dot line: propyne.

053503-6 S. Singh and B. Antony Phys. Plasmas 25, 053503 (2018)

IV. CONCLUSION

This article deals with a comprehensive study of different

elastic and inelastic cross sections by positron scattering from

hydrocarbons. The energy of the positron is taken to be from Ps

formation threshold to 5 keV. The well-known SCOP14,15 for-

malism and CSP-ic16–18 formalism have been employed for the

calculation of different cross sections. A similar attempt has

been made by Baluja and Jain20 and Raizada and Baluja;19 how-

ever their studies were limited to the calculation of the total cross

section. Furthermore, the present method is expected to predict

better cross sections as compared to their previous methods,19,20

as the present method uses a more efficient absorption potential

and inelastic threshold to incorporate Ps formation in the calcula-

tion. In addition to that, the screening correction method used in

the present work ensures some reliability in the low energy

region. It is well known that the present methodology predicts

good cross sections in the intermediate and high energies. The

accountability of the present formalism in the low energy is

questionable as expected. However, the absence of correlation

effects and resonances in positron collision as compared to elec-

trons renders the calculations to be relatively simpler.

Furthermore, the prediction of the Ps formation cross section is

expected to be good. Hence, beyond the Ps formation threshold,

the predicted cross sections are expected to be reliable. This is

one of the reasons to report the present cross sections from the

Ps formation threshold. Even after trying to overcome so many

drawbacks in the low energies, due to the inherent property of

the present model, the cross sections predicted in such an energy

range (i.e., below 10 eV) are not as reliable as compared to the

cross sections predicted in the intermediate and high energies.

The formalism employed here is free from any adjustable

parameters which is not reported in the article and hence

reproducible. Furthermore, with slight modifications, differ-

ent cross sections due to positron scattering can be calculated

with much ease. Moreover, the significance of the present tar-

gets in the field of plasma physics has prompted us to attempt

the present work. In addition to that, the current studies on

pair plasmas are also one of the motivations to undergo the

present investigation. Since positron related studies in the

plasma relevant atmosphere are relatively new, the present

endeavor is expected to be appreciated by the atomic and

molecular physics community. Besides the paucity of studies,

the data reported here would prove to be a benchmark for

future theoretical and experimental studies.

ACKNOWLEDGMENTS

B.A. is pleased to acknowledge the support of this

research from the Department of Space, Government of India,

through the ISRO-RESPOND Project under Grant No. DS-2B-

13012(2)/2/2017.

1R. G. Greaves, M. D. Tinkle, and C. M. Surko, Phys. Plasmas 1, 1439

(1994).2T. S. Pedersen, J. R. Danielson, C. Hugenschmidt, G. Marx, X. Sarasola,

F. Schauer, L. Schweikhard, C. M. Surko, and E. Winkler, New J. Phys.

14, 035010 (2012).3G. Sarri, K. Poder, J. M. Cole, W. Schumaker, A. D. Piazza, B. Reville, T.

Dzelzainis, D. Doria, L. A. Gizzi, G. Grittani, S. Kar, C. Keitel, K.

Krushelnick, S. Kuschel, S. Mangles, Z. Najmudin, N. Shukla, L. Silva, D.

Symes, A. Thomas, M. Vargas, J. Vieira, and M. Zepf, Nature

Communications 6, 6747 (2015).4T. F€ul€op and G. Papp, Phys. Rev. Lett. 108, 225003 (2012).5P. Helander and D. J. Ward, Phys. Rev. Lett. 90, 135004 (2003).6H. Deutsch, K. Becker, R. K. Janev, M. Probst, and T. D. Mrk, J. Phys. B:

At. Mol. Opt. Phys. 33, L865 (2000).7R. E. H. Clark and D. Reiter, Nuclear Fusion Research: UnderstandingPlasma-Surface Interactions (Springer, 2005).

8W. Eckstein, W. Hofer, V. Philipps, and J. Roth, Physical Processes of theInteraction of Fusion Plasmas with Solids (Academic Press, 1996).

9W. L. Morgan, Adv. At. Mol. Opt. Phys. 43, 79 (2000).10Y. Jiang, J. Sun, and L. Wan, Z. Phys. D: At. Mol. Clusters 34, 29

(1995).11T. Makabe, Adv. At. Mol. Opt. Phys. 44, 127 (2001).12A. Bentabet, N. Fenineche, and K. Loucif, Appl. Surf. Sci. 255, 7471 (2009).13C. Champion, C. L. Loirec, and B. Stosic, Int. J. Radiat. Biol. 88, 54

(2012).14S. Singh, S. Dutta, R. Naghma, and B. Antony, J. Phys. Chem. A 120,

5685 (2016).15S. Singh, S. Dutta, R. Naghma, and B. Antony, J. Phys. B: At. Mol. Opt.

Phys. 50, 135202 (2017).16S. Singh, A. Sen, and B. Antony, Chem. Phys. Lett. 692, 242 (2018).17S. Singh and B. Antony, EPL 119, 50006 (2017).18S. Singh and B. Antony, J. Appl. Phys. 121, 244903 (2017).19R. Raizada and K. L. Baluja, Pramana 46, 431 (1996).20K. L. Baluja and A. Jain, Phys. Rev. A 45, 7838 (1992).21D. D. Reid and J. M. Wadehra, J. Phys. B: At. Mol. Opt. Phys. 29, L127

(1996).22G. Staszewska, D. W. Schwenke, D. Thirumalai, and D. G. Truhlar, Phys.

Rev. A 28, 2740 (1983).23K. Floeder, D. Fromme, W. Raith, A. Schwab, and G. Sinapius, J. Phys. B:

At. Mol. Phys. 18, 3347 (1985).24O. Sueoka and S. Mori, J. Phys. B: At. Mol. Phys. 19, 4035 (1986).25O. Sueoka and S. Mori, J. Phys. B: At. Mol. Opt. Phys. 22, 963

(1989).26A. Zecca, L. Chiari, A. Sarkar, and M. J. Brunger, New J. Phys. 13,

115001 (2011).27C. Makochekanwa, H. Kawate, O. Sueoka, M. Kimura, M. Kitajima, M.

Hoshino, and H. Tanaka, Chem. Phys. Lett. 368, 82 (2003).28P. Modak, J. Kaur, and B. Antony, Phys. Plasmas 24, 083514 (2017).29P. Verma, D. Mahato, J. Kaur, and B. Antony, Phys. Plasmas 23, 093512

(2016).30H. L. Cox and R. A. Bonham, J. Chem. Phys. 47, 2599 (1967).31X. Zhang, J. Sun, and Y. Liu, J. Phys. B: At. Mol. Opt. Phys. 25, 1893

(1992).32R. Naghma, D. Gupta, B. Goswami, and B. Antony, Int. J. Mass Spectrom.

360, 39 (2014).33S. Singh, R. Naghma, J. Kaur, and B. Antony, J. Chem. Phys. 145, 034309

(2016).34F. Blanco and G. Garc�ıa, Phys. Lett. A 317, 458 (2003).35M. Vinodkumar, K. Korot, C. Limbachiya, and B. K. Antony, J. Phys. B:

At. Mol. Opt. Phys. 41, 245202 (2008).36L. Chiari, A. Zecca, S. Girardi, E. Trainotti, G. Garc�ıa, F. Blanco, R. P.

McEachran, and M. J. Brunger, J. Phys. B: At. Mol. Opt. Phys. 45, 215206

(2012).37See www.nist.gov/pml/handbook-basic-atomic-spectroscopic data for

cccbdb.

053503-7 S. Singh and B. Antony Phys. Plasmas 25, 053503 (2018)