# K-shell width, fluorescence yield, and K *β*/K *α* intensity ratio calculation for Fe in the Dirac-Fock approach

J P Marques, Matteo Guerra, F Parente, J P Santos, P Indelicato, J M

Sampaio

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J P Marques, Matteo Guerra, F Parente, J P Santos, P Indelicato, et al.. K-shell width, fluorescence yield, and K *β*/K *α* intensity ratio calculation for Fe in the Dirac-Fock approach. Journal of Physics: Conference Series, 2015, 635 (9), pp.092094 10.1088/1742-6596/635/9/092094. [hal-01266818](https://hal-fr.sorbonne-universite.fr/hal-01266818)

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K-shell width, fluorescence yield, and $K_β/K_α$ intensity ratio calculation for Fe in the Dirac-Fock approach

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2015 J. Phys.: Conf. Ser. 635 092094

(http://iopscience.iop.org/1742-6596/635/9/092094)

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K-shell width, fluorescence yield, and K<sub>β</sub>/K<sub>α</sub> intensity ratio calculation for Fe in the Dirac-Fock approach

J. P. Marques*<fnref n="1" />, M. Guerra†, F. Parente†, J. P. Santos†, P. Indelicato‡, J. M. Sampaio*

* BioISI - Biosystems & Integrative Sciences Intitute, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, C8, 1749-016 Lisboa, Portugal

† Laboratório de Instrumentação, Engenharia Biomédica e Física da Radiação (LIBPhys-UNL), Departamento de Física, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Monte da Caparica, 2892-516 Caparica, Portugal

‡ Laboratoire Kastler Brossel, École Normale Supérieure, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Case 74; 4, place Jussieu, 75252 Paris CEDEX 05, France

**Synopsis** K-shell fluorescence yield, width, and K<sub>β</sub>/K<sub>α</sub> intensity ratio for Fe are calculated using the Dirac-Fock approach. Results are compared with available data.

The knowledge of accurate values of atomic decay rates and fluorescence yields is fundamental in quantitative analysis in X-ray spectroscopy, plasma physics, nuclear physics, dosimetry, radiation protection, among many other areas [1]. Despite the increasing number of theoretical and experimental work concerning the determination of fluorescence yields for several elements, the available data are still scarce. Iron is one of the most abundant elements in the universe and is of extreme importance in the analysis of stellar objects like stars and galaxies. Iron spectral lines are used in plasma diagnostics and help us to know physical properties such as temperature and electron density as well as for abundance studies [2].

In this work, we present a relativistic calculation of the K-shell width, fluorescence yield and K<sub>β</sub>/K<sub>α</sub> intensity ratio in Fe using the multi-configuration Dirac-Fock (MCDF) code of Desclaux and Indelicato [3, 4]. The code was used in a single-configuration approach, with Breit interaction and the vacuum polarization terms included in the self-consistent field calculations, and other QED effects included as perturbations.

<table><caption>**Table 1.** K-shell fluorescence yield (ω<sub>K</sub>), width (eV), and K<sub>β</sub>/K<sub>α</sub> intensity ratio for iron</caption><thead><tr><th></th><th>ω<sub>K</sub></th><th>width</th><th>K<sub>β</sub>/K<sub>α</sub></th></tr></thead><tbody><tr><td>This work</td><td>0.378</td><td>1.14</td><td>0.134</td></tr><tr><td>McGuire [5]</td><td>0.386</td><td></td><td></td></tr><tr><td>Krause [6]</td><td>0.34</td><td></td><td></td></tr><tr><td>Campbell [7]</td><td></td><td>1.19</td><td></td></tr><tr><td>Carreras et al [8]</td><td></td><td></td><td>0.14</td></tr><tr><td>Scofield [9]</td><td></td><td></td><td>0.139</td></tr><tr><td>Jankowsky et al [10]</td><td></td><td></td><td>0.134</td></tr><tr><td>Bé et al [11]</td><td></td><td></td><td>0.142</td></tr></tbody></table>

Since iron has an open outer shell (3d<sup>6</sup>), electron coupling leads to 348105 possible radiative and radiationless transitions from the initial K hole configuration. Preliminary results for the K-shell fluorescence yield, width and K<sub>β</sub>/K<sub>α</sub> intensity ratio are consistent with the available data (Table 1).

This work was supported by FCT Project PEstOE/FIS/UI0303/2011, Portugal. We also thank the Allianz Program of the Helmholtz Association, contract No. EMMI HA-216 Extremes of Density and Temperature: Cosmic Matter in the Laboratory. BioISI is supported by the centre grant UID/MULTI/04046/2013 from FCT/MCTES/PIDDAC, Portugal.

**References**

[1] J. M. Sampaio *at al* 2014 *Phys. Rev. A* **89** 012512

[2] H. Hartman *at al* 2009 *J. Phys. Conf. Ser.* **130** 012010

[3] J. Descalux 1975 *Comput. Phys. Commun.* **9** 31

[4] P. Indelicato, J. P. Desclaux 1990 *Phys. Rev. A* **42** 5139

[5] E. J. McGuire 1970 *Phys. Rev. A* **2** 273

[6] M. O. Krause 1979 *J. Phys. Chem Ref. Data* **8** 307

[7] J. Campbell, T. Papp 2001 *At. Data Nucl. Data Tables* **77** 1

[8] A. Carreras *et al* 2003 *Rad. Phys. Chem* **67** 703

[9] J. Scofield 1974 *Phys. Rev. A* **9** 1041

[10] K. Jankowski, M. Polasik 1989 *J. Phys. B* **22** 2369

[11] M.-M Bé *et al* 1998 *Appl. Radiat. Isot.* **49** 1367

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<footnote n="1">¹E-mail: jmmarques@fc.ul.pt</footnote>