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# Near-threshold Cooper minimum in the photoionisation of the 2p subshell of sodium atom and its impact on the angular distribution parameter

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The present work reports the photoionisation studies of 2p subshell of Na atom, just above the threshold region. The calculations are performed in the framework of multiconﬁguration Dirac-Hartree-Fock method (MCDHF). It unravels the eﬀect of 3d orbital on the ﬁnal state leading to the appearance of Cooper minimum (CM) in the region close to the threshold. Further, the impact of this CM on the angular distribution parameter is studied. It is found that CM not only modiﬁes the cross section proﬁle but also makes dramatic changes in the angular distribution.
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Journal of Physics B: Atomic, Molecular and Optical Physics
J. Phys. B: At. Mol. Opt. Phys. 55 (2022) 135001 (10pp) https://doi.org/10.1088/1361-6455/ac6553
Near-threshold Cooper minimum
in the photoionisation of the 2p
subshell of sodium atom and its impact
on the angular distribution parameter
Nishita M Hosea1, Jobin Jose2and Hari R Varma1,
1School of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175075, Himachal Pradesh, India
2Department of Physics, Indian Institute of Technology Patna, Bihta 801103, Bihar, India
E-mail: hari@iitmandi.ac.in
Received 20 December 2021, revised 7 March 2022
Accepted for publication 29 March 2022
Published 31 May 2022
Abstract
The present work reports the photoionisation studies of 2psubshell of Na atom, just above the
threshold region. The calculations are performed in the framework of multiconguration
Dirac–Hartree–Fock method (MCDHF). It unravels the effect of 3d orbital on the nal state
leading to the appearance of Cooper minimum (CM) in the region close to the threshold.
Further, the impact of this CM on the angular distribution parameter is studied. It is found that
CM not only modies the cross section prole but also makes dramatic changes in the angular
distribution.
Keywords: photoionization, cross section, angular distribution, correlation effects, Cooper
minimum
(Some gures may appear in colour only in the online journal)
1. Introduction
Atomic photoionisation is a fundamental process in nature
involving the interaction between light and atom. The ejected
electrons, known as photoelectrons, carry information about
the target’s electronic structure, electron-electron correlation
and relativistic interactions. These features can be extracted
using parameters such as cross section and angular distribu-
tion parameters. The study of these parameters as a func-
tion of energy plays an important role in understanding the
ionisation dynamics. Accurate photoionisation data nds
important applications in various elds of physics including
stellar physics [1], radiation physics [2], solid state physics
[3,4], plasma modelling [5] etc. Apart from these tradi-
tional areas, it also provides important impetus to elds like
nanoscience and uv and x-ray lithographies. For example, pho-
toionisation data in the vicinity of 6.5–6.9 nm provides an
Author to whom any correspondence should be addressed.
important role in designing the next generation extreme ultra-
violet lithography [6]. Recent developments in the eld of
attosecond science have opened up new avenues in the eld
of photoionisation that can unravel the dynamics at extremely
short time scales [79]. All of these developments underpin
the need of photoionisation data.
The photoionisation studies of alkali atoms have attracted
considerable attention because they are the simplest of open-
shell systems having just a single electron outside the closed
shell structure. Among the alkali group of atoms, Na is the
rst atom having closed p-subshell conguration. Its atomic
spectra contain rich information due to the contributions from
various congurations present in the system. Due to this, Na is
an ideal system to test various many-body theoretical meth-
ods. Theoretical studies have employed both ab initio and
semi-empirical models to simulate such systems [1013]. For
the reason mentioned above, many experimental work have
also been reported in the past covering various aspects of the
ground and excited states of Na [1417].
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In this work, we present level-resolved photoionisation cross sections for neutral iron across a wide energy range from a 262 level Dirac R-matrix calculation. Comparisons with existing experimental measurements reveal good agreement in the positions of the various low-energy resonance features. However, additional comparisons with theoretical data sets highlight wide variations. Significant resonance structures at high photon energies are explored by employing an additional series of 262 level and 896 level Dirac R-matrix calculations with a smaller six configuration target. The resulting photoionisation cross sections reproduce the main features from existing experimental observations. The results presented throughout will be useful to those requiring an extensive set of level-resolved photoionisation cross sections for astrophysical applications. 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In order to probe bulk electronic states of correlated electron systems near the Fermi level, high resolution photoemission spectroscopy by excitation in the soft X-ray region above several hundred eV is a very powerful tool. The best combination of the light source, analyzer, samples and miscellaneous experimental conditions is required. Photon resolution down to 50 meV and photoelectron total energy resolution down to 80 meV is realized near 1 keV as a breakthrough of bulk sensitive high resolution photoemission spectroscopy (BHPES), in which surface 4f electronic states are found to be significantly depressed. The BHPES spectra are very much different from the result of surface sensitive spectra measured slightly above 100 eV or by use of He II and I. Some BHPES results are demonstrated for Yb and Ce Kondo and valence fluctuating compounds. © 2001 Elsevier Science B. V. All rights reserved.
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Photoionization cross sections, branching ratios, and photoelectron angular distributions have been calculated for Ra (Z=88) 7s, 6p, 6s, 5d, and 5p, and Rn (Z=86) 6p, 6s, 5d, and 5p subshells within the framework of the relativistic random-phase approximation, including coupling between all of the relativistic channels arising from these subshells, in an effort to elucidate the interplay between relativistic and interchannel interactions at high Z where no experiments are extant. The results show that, aside from inducing structure in subshell cross sections, relativistic plus interchannel effects dominate the photoelectron angular-distribution asymmetry parameter and the branching ratio between spin-orbit doublets largely through the relativistic splitting of Cooper minima. This qualitatively confirms effects predicted by simple central-field calculations. Detailed explanations of the reasons for each of the structures are presented.