skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Time-dependent Schrödinger equation for molecular core-hole dynamics

Abstract

X-ray spectroscopy is an important tool for the investigation of matter. X rays primarily interact with inner-shell electrons, creating core (inner-shell) holes that will decay on the time scale of attoseconds to a few femtoseconds through electron relaxations involving the emission of a photon or an electron. Furthermore, the advent of femtosecond x-ray pulses expands x-ray spectroscopy to the time domain and will eventually allow the control of core-hole population on time scales comparable to core-vacancy lifetimes. For both cases, a theoretical approach that accounts for the x-ray interaction while the electron relaxations occur is required. We describe a time-dependent framework, based on solving the time-dependent Schrödinger equation, that is suitable for describing the induced electron and nuclear dynamics.

Authors:
 [1]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1393932
Alternate Identifier(s):
OSTI ID: 1342438
Grant/Contract Number:
AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 95; Journal Issue: 2; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Picón, A. Time-dependent Schrödinger equation for molecular core-hole dynamics. United States: N. p., 2017. Web. doi:10.1103/PhysRevA.95.023401.
Picón, A. Time-dependent Schrödinger equation for molecular core-hole dynamics. United States. doi:10.1103/PhysRevA.95.023401.
Picón, A. Wed . "Time-dependent Schrödinger equation for molecular core-hole dynamics". United States. doi:10.1103/PhysRevA.95.023401. https://www.osti.gov/servlets/purl/1393932.
@article{osti_1393932,
title = {Time-dependent Schrödinger equation for molecular core-hole dynamics},
author = {Picón, A.},
abstractNote = {X-ray spectroscopy is an important tool for the investigation of matter. X rays primarily interact with inner-shell electrons, creating core (inner-shell) holes that will decay on the time scale of attoseconds to a few femtoseconds through electron relaxations involving the emission of a photon or an electron. Furthermore, the advent of femtosecond x-ray pulses expands x-ray spectroscopy to the time domain and will eventually allow the control of core-hole population on time scales comparable to core-vacancy lifetimes. For both cases, a theoretical approach that accounts for the x-ray interaction while the electron relaxations occur is required. We describe a time-dependent framework, based on solving the time-dependent Schrödinger equation, that is suitable for describing the induced electron and nuclear dynamics.},
doi = {10.1103/PhysRevA.95.023401},
journal = {Physical Review A},
number = 2,
volume = 95,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1work
Citation information provided by
Web of Science

Save / Share:
  • Cited by 1
  • In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. This was the starting point of the popular “black hole (BH) information paradox”. In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model,more » a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking’s claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect ’t Hooft’s assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.« less
  • We present a novel approach, the iterative solution of the time-dependent Schrödinger equation (iTDSE model), for the investigation of atomic systems interacting with external laser fields. This model is the extension of the momentum-space strong-field approximation (MSSFA) [1], in which the Coulomb potential was considered only as a first order perturbation. In the iTDSE approach higher order terms were gradually introduced until convergence was achieved. Benchmark calculations were done on the hydrogen atom, and the obtained results were compared to the direct numerical solution [2].
  • One-dimensional model systems have a particular role in strong-field physics when gaining physical insight by computing data over a large range of parameters, or when performing numerous time propagations within, e.g., optimal control theory. Here we derive a scheme that removes a singularity in the one-dimensional Schrödinger equation in momentum space for a particle in the commonly used soft-core Coulomb potential. By using this scheme we develop two numerical approaches to the time-dependent Schrödinger equation in momentum space. The first approach employs the expansion of the momentum-space wave function over the eigenstates of the field-free Hamiltonian, and it is shownmore » to be more efficient for laser parameters usual in strong field physics. The second approach employs the Crank–Nicolson scheme or the method of lines for time-propagation. The both methods are readily applicable for large-scale numerical simulations in one-dimensional model systems.« less
  • Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H{sub 3}{sup +}, for which a global adiabatic potential energy surface accurate to better than 0.1 cm{sup −1} exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon themore » choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D{sub 3h} point-group symmetry is employed. The vibrational mass of the proton in H{sub 3}{sup +} is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m{sub opt,p}{sup (v)}=m{sub nuc,p}+0.31224 m{sub e}. This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.« less