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.
Similar content being viewed by others
References
M.J. Puska, R.M. Nieminen, Phys. Rev. A 47, 1181 (1993)
A.S. Baltenkov, J. Phys. B: At. Mol. Opt. Phys. 32, 2745 (1999)
M.Y. Amusia, A.S. Baltenkov, U. Becker, Phys. Rev. A 62, 012701 (2000)
M.A. McCune, E.M. Mohamed, H.S. Chakraborty, Phys. Rev. A 80, 011201(R) (2009)
V.K. Dolmatov, P. Brewer, S.T. Manson, Phys. Rev. A 78, 013415 (2008)
D.S. Bethune, R.D. Johnson, J.R. Salem, M.S. de Vries, C.S. Yannoni, Nature 366, 123 (1993)
A.S. Baltenkov, V.K. Dolmatov, S.T. Manson, Phys. Rev. A 66, 023201 (2002)
M. Aichinger et al., J. Mod. Opt. 50, 2691 (2003)
Z. Chen, A.Z. Msezane, J. Phys. B: At. Mol. Opt. Phys. 42, 165206 (2009)
A.L. Kilcoyne et al., Phys. Rev. Lett. 105, 213001 (2010)
R.A. Phaneuf et al., Phys. Rev. A 88, 053402 (2013)
L. Jacak, O. Hawrylak, A. Wojs, Quantum Dots (Springer), Berlin, 1998)
A. Zrenner, J. Chem. Phys. 112, 7790 (2000)
F.V. Prudente, L.S. Costa, J.D.M. Vianna, J. Chem. Phys. 123, 224701 (2005)
S. Saha, A. Thuppilakkadan, H.R. Varma, J. Jose, J. Phys. B: At. Mol. Opt. Phys. 52, 145001 (2019)
P.C. Deshmukh, A. Mandal, S. Saha, A.S. Kheifets, V.K. Dolmatov, S.T. Manson, Phys. Rev. A 89, 053424 (2014)
D.A. Keating et al., J. Phys. B: At. Mol. Opt. Phys. 50, 175001 (2017)
A. Mandal, P.C. Deshmukh, A.S. Kheifets, V.K. Dolmatov, S.T. Manson, Phys. Rev. A 96, 053407 (2017)
A.W. Bray, F. Naseem, A.S. Kheifets, Phys. Rev. A 98, 043427 (2018)
A. Kumar et al., Phys. Rev. A 94, 043401 (2016)
C.J. Joachain, Quantum Collision Theory (North-Holland Publishing, New York, 1975)
F. Calogero, Variable Phase Approach to Potential Scattering (Academic Press Inc, London, 1967)
V.D. Viterbo, N.H.T. Lemes, J.P. Braga, Revista Brasileira de Ensino de Fisica 36, 1310 (2014)
P.M. Morse, W.P. Allis, Phys. Rev. 44, 269 (1933)
Z. Chen, A.Z. Msezane, Eur. Phys. J. D 69, 88 (2015)
E.P. Wigner, Phys. Rev. 98, 145 (1955)
X.M. Tong, C.D. Lin, J. Phys. B: At. Mol. Opt. Phys. 38, 2593–2600 (2005)
H.G. Muller, Phys. Rev. A 60, 1341 (1999)
A.T. Le, R.R. Lucchese, S. Tonzani, T. Morishita, C.D. Lin, Phys. Rev. A 80, 013401 (2009)
J.P. Connerade, V.K. Dolmatov, P.A. Lakshmi, S.T. Manson, J. Phys. B: At. Mol. Opt. Phys. 32, L239 (1999)
V.K. Dolmatov, J.L. King, J.C. Oglesby, J. Phys. B: At. Mol. Opt. Phys. 45, 105102 (2012)
A.B. Patel, H.S. Chakraborty, J. Phys. B: At. Mol. Opt. Phys. 44, 191001 (2011)
R.D. Woods, D.S. Saxon, Phys. Rev. 95, 577–578 (1954)
A.S. Baltenkov, S.T. Manson, A.Z. Msezane, J. Phys. B: At. Mol. Opt. Phys. 48, 185103 (2015)
C.Y. Lin, Y.K. Ho, J. Phys. B: At. Mol. Opt. Phys. 45, 145001 (2012)
E.M. Nascimento, F.V. Prudente, M.N. Guimarães, A.M. Maniero, J. Phys. B: At. Mol. Opt. Phys. 44, 015003 (2011)
W.R. Johnson, C.D. Lin, Phys. Rev. A 20, 964 (1979)
J.M. Thijssen, Computational Physics (Cambridge University Press, Cambridge, 2007)
Q. Zhang, P. Lan, P. Lu, Phys. Rev. A 90, 43410 (2014)
H. Friedrich, Theoretical Atomic Physics (Springer, Berlin, 2005)
B.H. Bransden, C.J. Joachain, Physics of Atoms and Molecules (Pearson Education, Noida, 2003)
P. Swan, Nuclear Phys. 18, 245–270 (1960)
A.K. Ghatak, S. Lokanathan, Quantum Mechanics: Theory and Applications (Macmillan, Noida, 2004)
J.P. Connerade, V.K. Dolmatov, S.T. Manson, J. Phys. B: At. Mol. Opt. Phys. 32, L395 (1999)
H.R. Varma, P.C. Deshmukh, V.K. Dolmatov, S.T. Manson, Phys. Rev. A 76, 012711 (2007)
J. George et al., J. Phys. B: At. Mol. Opt. Phys. 45, 185001 (2012)
W.R. Johnson, K.T. Cheng, Phys. Rev. A 20, 978 (1979)
A.S. Kheifets, Phys. Rev. A 87, 063404 (2013)
S. Saha, A. Mandal, J. Jose, H.R. Varma, P.C. Deshmukh, A.S. Kheifets, V.K. Dolmatov, S.T. Manson, Phys. Rev. A 90, 053406 (2014)
J.M. Dahlstrӧm, T. Carette, E. Lindroth, Phys. Rev. A 86, 061402 (2012)
K. Klϋnder et al., Phys. Rev. Lett. 106, 143002 (2011)
D. Guénot et al., Phys. Rev. A 85, 053424 (2012)
Acknowledgements
J J acknowledges the support provided by DST-SERB through Project No. ECR/2016/001564, and HRV is supported by the DST-SERB through Project with Grant No. EMR/2016/002695.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Saha, S., Thuppilakkadan, A., Varma, H.R. et al. Photoionization phase shift and Wigner time delay of endohedrally confined atoms using transient phase methods. Eur. Phys. J. Plus 135, 753 (2020). https://doi.org/10.1140/epjp/s13360-020-00762-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-020-00762-5