# Potential electron scattering by the phosphorous systems Pn (n = 1÷3)

S. Demes, V Kelemen, E Yu Remeta

► To cite this version:

S. Demes, V Kelemen, E Yu Remeta. Potential electron scattering by the phosphorous systems Pn (n = 1÷3). XXIX International Conference on Photonic, Electronic, and Atomic Collisions (ICPEAC2015), Jul 2015, Toledo, Spain. 635 (7), pp.072020, 2015, Journal of Physics: Conference Series. 10.1088/1742-6596/635/7/072020. hal-03038755

HAL Id: hal-03038755

https://hal.science/hal-03038755

Submitted on 21 Oct 2021

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>
Potential electron scattering by the phosphorous systems $P_n$ ($n = 1 \div 3$)

This content has been downloaded from IOPscience. Please scroll down to see the full text.

2015 J. Phys.: Conf. Ser. 635 072020

(http://iopscience.iop.org/1742-6596/635/7/072020)

View the table of contents for this issue, or go to the journal homepage for more

Download details:

IP Address: 193.6.168.240

This content was downloaded on 15/09/2015 at 06:28

Please note that terms and conditions apply.
# Potential electron scattering by the phosphorous systems $P_n$ ($n=1 \div 3$)

Sh.Sh. Demesh<fnref n="1" />, V.I. Kelemen, E.Yu. Remeta<fnref n="2" />

Universitetska str. 21, Institute of Electron Physics of NAS of Ukraine, Uzhgorod 88017, Ukraine

**Synopsis** Independent atom model and the optical potential approach are used in order to calculate the differential and integral cross sections for the electron scattering by single-, two- and three-atom compounds of phosphorus. The potentials and atomic characteristics are determined in the local approach of the stationary and time-dependent density functional theory with account of some relativistic effects for the corresponding study of electron scattering process on the atoms from the molecules.

We have used the optical potential approach [1,2] for the $e+P_n$ ($n=1 \div 3$) elastic scattering in the independent atom model (IAM) [3,4] for the cross section calculations. The static-exchange approximation in the SMC method were used with pseudopotentials in [5] for the calculation of integral (ICSs) and differential cross sections (DCSs) of electron scattering by $X_2$ and $XH_3$ molecules (X=N, P, As).

The DCSs of potential electron scattering by an N-atomic molecule in the IAM is given [3,4]

$$ \frac{d\sigma_{el}}{d\Omega} = \sum_{m=1}^{N} \sum_{n=1}^{N} [f_m(\theta, k) f_n^*(\theta, k) + g_m(\theta, k) g_n^*(\theta, k)] \frac{\sin(st_{nm})}{sr_{nm}} $$

Here, $f_m, g_m$ are the scattering angle, the direct and spin-flip amplitudes due to the m-th atom of the molecule; $s = 2k \sin(\theta/2)$, where $E$ is the electron energy; $r_{nm}$ is the distance between the n-th and m-th atoms (calculated by the GAMESS code). Elastic, momentum transfer and viscosity ICSs are calculated from the DCSs by integration along the scattering angle.

We have used the local relativistic parameter-free real optical potential approximation (RSEP LA). It contains static, local exchange, polarization (local correlation-polarization), scalar-relativistic and spin-orbit potentials [1,2].

Polarization potential at large distances has an asymptotic form $-\alpha_d(0)/2r^4$, where $\alpha_d(0)$ – dipole static polarizability of the n-th atom calculated in the local approximation of time-dependent density functional theory (for the P atom it is 30.65 $a_0^3$).

The cross sections are calculated in the 0.5÷30 eV energy region. On the Fig.1, as an example, we present the DCSs at 10 eV of impact energy. At all other impact energies E atomic and molecular DCSs have a similar special form. At small (<60°) and large (>150°) angles the DCSs [5] are close to our calculated atomic DCS while at intermediate angles they are between our DCSs for e+P and e+P₂. On the Fig.2 the elastic ICSs are presented. A similar behavior of the momentum transfer and viscosity ICSs was obtained.

<figure><img src="image_2.png" /><figcaption>Figure 1. Differential cross sections at 10 eV.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2. Elastic integral cross sections.</figcaption></figure>

## References

[1] Sh. Demesh et al 2014 *Contributed papers of the 6th CEPAS* (Bratislava, Slovakia) 65.

[2] V. Kelemen et al 2014 *Ukr. J. Phys.* **59** 569.

[3] D. Raj 1991 *Phys. Lett. A* **169** 571.

[4] P. Mozejko et al 2002 *Nucl. Instr. Meth. B.* **196** 245.

[5] M.H.F Bettega et al 1998 *J. Phys. B.* **31** 2091.

<footnote n="1">¹ E-mail: shandor.demesh@iep.org.ua</footnote>

<footnote n="2">² E-mail: remetov@inbox.ru</footnote>