Photoionization phase shift and Wigner time delay of endohedrally confined atoms using transient phase methods
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Photoionization phase shift and Wigner time delay of endohedrally confined atoms using transient phase methods Subhasish Saha1, Afsal Thuppilakkadan2 , Hari R. Varma2 , Jobin Jose1,a 1 Department of Physics, IIT Patna, Bihta, Bihar 801103, India 2 School of Basic Sciences, IIT Mandi, Mandi, Himachal Pradesh 175005, India
Received: 24 March 2020 / Accepted: 7 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In contrast to the conventional finite difference methods, two transient phase methods have been effectively used in the present work to directly compute the photoionization phase shift and Wigner time delay of confined atoms (A@C60 ) in the single-active electron (SAE) approximation. The different phase methods: (A) employing logarithmic derivatives at shell boundaries, and (B) Born approximation are verified with the help of well-established finite difference methods in SAE approximation and sophisticated many-electron techniques. In this work, confinement oscillations on the dipole phase and photoelectron group delay following ionization from 1s subshell of H@C60 , 3p subshell of Ar@C60 and 5p subshell of Xe@C60 are analyzed. The comparison with many-body calculation shows that the features in the time delay of a confined system are governed mainly by the effects of screening apart from that due to the external potential. A systematic study and comparison of the results from phase methods and many-electron techniques indicate that these techniques can be effectively used in the analysis of photoionization phase shift and time delay in confined atoms.
1 Introduction Photoionization parameters of atoms trapped in fullerenes exhibit confinement oscillations aka confinement resonances [1–5]. To date, many theoretical and experimental investigations have been reported on the confinement oscillations in several endohedral systems. It is important to understand the nature of these oscillations as it is necessary to study the dynamical properties of trapped atoms and molecules and their solid-state characteristics [6]. The oscillations were studied for noble gas [1–3], and metal [7–9] atoms encaged in C60 . The Ar atom encapsulated in larger fullerenes C240 and C540 was also studied [5]. These resonances have been observed experimentally in the 4d photoionization cross section of Xe@C+60 [10, 11]. Applications of these systems are, in particular, in mesoscopic-scale semiconductor structures such as quantum dots [12–14]. It is not only the dipole matrix elements and cross section but also the dipole phase shift and time delay display confinement oscillations [15]. Of particular importance is the finding that confinement oscillations are more prominent in the dipole phase shift and time delay
a e-mail: [email protected] (corresponding author)
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than in the cross section as shown in the case of Xe@C60 [16]. Moreover, the pattern of oscillation is not the same in cro
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