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First Born triple differential cross sections (TDCS) for ionization of metastable 3P-state hydrogen atoms by electrons are calculated for various kinematic conditions in the asymmetric coplanar geometry. A multiple scattering theory is used in this study. The present results are compared with other existing related theoretical results for ionizations of hydrogen atoms from metastable 2S-state and 2P-state, showing a good qualitative agreement. There is no available theoretical study for ionization of metastable 3P-state hydrogen atoms by electrons. We are expecting that the present results provide a wide scope for further study of such ionization problems.

Hydrogen atom is one of the most abundant elements in the universe and is one of the simplest elements. Under some conditions, hydrogen atom occurs as ion, where its unusual properties make it of particular interest to chemists, physicists and astronomers as well as applied mathematicians.

Atoms in metastable states possess certain characteristic properties, such as long lifetimes, capability of transferring large amounts of energy [

Total differential cross section for the ionization of atoms and molecules by electron impact is one of the essential sets of data needed in a wide range of various applications. Electron impact ionization of hydrogen atoms by electrons was investigated first by Bethe [

Ionization of hydrogen atoms by electrons have been successfully used during the last five decades to investigate the details of the ionization process both in the ground state [

Presently we have quantum mechanically discussed the TDCS of the metastable 3P-state hydrogen atom by electrons considering at intermediate and high energies due to the multiple scattering theory of Das [

Ionization cross sections are obtained by taking the ratio of the number of ionization events per unit time and per unit target to the incident electron flux. The most detailed information presently available is about the single ionization processes of the following type:

where the symbol 3P denotes the hydrogenic metastable state and has been obtained in the coplanar geometry by analyzing TDCS measured in (e, 2e) coincidence experiments. The TDCS is a measure of the probability that in an (e, 2e) reaction an incident electron of momentum _{1} and E_{2} and momenta

the symbol

For unpolarized incident electrons and targets, it is a function of the quantities

It is useful when studying (e, 2e) coincidence experiments to distinguish between several kinematical arrangements, since these have important implications for the theoretical analysis of the collision as we shall see later. A first distinction can be made between coplanar geometries-such that the momenta

The multiple scattering theory of ionization of hydrogen atoms by electrons is described in detail [

The direct T-matrix element for ionization of hydrogen atoms by electrons [

where the perturbation potential

and

where

Here

Here the approximate wave function

Here

and

Now applying Equations ((3) and (4)) in Equation (2), we get

where

For first Born approximation Equation (6) may be written as

where

For First Born approximation, we have calculated the terms of Equation (10).

After analytical calculation by using the Lewis integral [

The first Born TDCS are presented here for some varied kinematic conditions. In this study, the incident energy

In all figures, the present First Born results in the metastable 3P-state hydrogen atoms exhibit two sharp peak structures in recoil region and loaded peaks in binary region.

In

In

In

Finally, we notice that in our present results and the 2P-metastable state results [

A table (please see

In the present calculation, we have computed the TDCS for ionization of metastable 3P-state hydrogen atoms by incident electron energy 250 eV electron impact using the multiple scattering theory of Das & Seal [

Ejected angle( | 2S | 2P | 3P |
---|---|---|---|

0 | 1.1501 | 5.1354 | 7.2001 |

36 | 0.4791 | 0.0841 | 0.1179 |

72 | 0.3101 | 4.8045 | 6.7357 |

108 | 0.3275 | 0.7241 | 1.0154 |

144 | 0.3665 | 3.8972 | 5.4639 |

180 | 0.5391 | 1.8393 | 2.5787 |

216 | 2.1587 | 2.6473 | 3.7109 |

252 | 2.3911 | 3.1421 | 4.4046 |

288 | 110.00 | 1.3769 | 1.9305 |

324 | 2.9969 | 4.2969 | 6.0240 |

360 | 1.2911 | 0.4133 | 0.5794 |

scattering theories. In the future calculations, other kinematic conditions or other atomic species will also be interesting and significant.

The computational works were performed in the Simulation Lab of the Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong-4349, Bangladesh.

SunilDhar,ShahrinaAkter,NurunNahar, (2016) The First Born Triple Differential Cross-Section for Ionization of H(3P) by Electron Impact in the Asymmetric Coplanar Geometry. Open Journal of Microphysics,06,15-23. doi: 10.4236/ojm.2016.61002