Analytical expression for continuum–continuum transition amplitude of hydrogen-like atoms with angular-momentum dependence
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Date
2024-12-13
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Journal Article
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Abstract
Attosecond chronoscopy typically utilises interfering two-photon transitions to access the phase information. Simulating these two-photon transitions is challenging due to the continuum–continuum transition term. The hydrogenic approximation within second-order perturbation theory has been widely used due to the existence of analytical expressions of the wave functions. So far, only (partially) asymptotic results have been derived, which fail to correctly describe the low-kinetic-energy behaviour, especially for high angular-momentum states. Here, we report an analytical expression that overcomes these limitations. It is based on the Appell’s F1 function and uses the confluent hypergeometric function of the second kind as the intermediate state. We show that the derived formula quantitatively agrees with the numerical simulations using the time-dependent Schrödinger equation for various angular-momentum states, which improves the accuracy compared to the other analytical approaches that were previously reported. Furthermore, we give an angular-momentum-dependent asymptotic form of the outgoing wavefunction and the corresponding continuum–continuum dipole transition amplitudes.
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published
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Volume
57 (23)
Pages / Article No.
235601
Publisher
IOP Publishing
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Subject
attosecond; continuum-continuum transition; Fano’s propensity rule; Wigner time delay; continuum-continuum time delay; confluent hypergeometric function
Organisational unit
03888 - Wörner, Hans Jakob / Wörner, Hans Jakob
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Funding
- Time-resolved measurements of intermolecular Coulombic decay ()
801459 - Fellowship Program of the NCCR MUST (National Competence Center for Research in Molecular Ultrafast Science and Technology) and the Cluster of Excellence RESOLV (EC)
801459 - Fellowship Program of the NCCR MUST (National Competence Center for Research in Molecular Ultrafast Science and Technology) and the Cluster of Excellence RESOLV (EC)