vinbladh_2022#
J. Vinbladh, J. M. Dahlström and E. Lindroth, “Relativistic Two-Photon Matrix Elements for Attosecond Delays”, Atoms 10, 80 (2022)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Relativistic many-body perturbation theory of one-photon ionisation and two-colour (XUV + IR) two-photon above-threshold ionisation of the outer p (and Xe 4d) subshells, for RABBIT delays. XUV absorption at the level of the relativistic random phase approximation (RRPA, the linear response of time-dependent Dirac-Fock); the IR exchange in the continuum with the static Dirac-Fock ionic potential plus a projected potential (no 2P2C-RRPA). Length gauge only, dipole approximation, Breit interaction neglected. Radial functions on B-splines (orders 7 and 8 for the large and small components) in a box with exterior complex scaling; the continuum-continuum integral continued analytically to infinity with relativistic Coulomb functions. Dirac-Fock orbital energies of the ionised subshell replaced with experimental ionisation energies (Sections 2-5, pp. 4-15).
Materials in structured entries: None recorded.
Dataset quantities: None recorded.
Contents: 0 datasets; 0 formulas.
Curation notes#
Context only, no datasets. Identity checked on the first page (PDF p. 1): Vinbladh, Dahlström and Lindroth, Atoms 10, 80 (2022), received 20 June 2022, published 2 August 2022, 23 pages, CC BY 4.0; PDF page = article page.
WHAT IS PRINTED. Only delays, in vector-drawn figures: the atomic (RABBIT) delay tau_A = (phi_e - phi_a)/(2 omega) (eqs 40-41) and the Wigner delay tau_W (eq 34) of photoelectrons emitted along the common polarisation axis, per fine-structure channel, against ‘Total Absorbed Photon Energy [eV]’ (the sideband’s total, 2 n hbar omega): Ar 3p_1/2^-1 and 3p_3/2^-1 (Fig. 2, about 26-86 eV), Kr 4p_j (Fig. 3, about 22-80 eV), Xe 5p_j (Fig. 4, about 17-61 eV), tau_A - tau_W for Ar, Kr, Xe and Rn with a non-relativistic Ne 2p reference (Fig. 5), the Xe 5p_3/2 - 5p_1/2 delay differences (Fig. 6) and Xe 4d_3/2, 4d_5/2 (Fig. 7). In the text (pp. 17-18): at the 90 eV sideband the computed Xe tau_A(5p_3/2) - tau_A(5p_1/2) is ‘around 2 as’ against Jain et al.’s 14.5 +- 9.3 as, and tau_A(4d_5/2) - tau_A(4d_3/2) is -1.2 as against -4.0 +- 4.1 as. No cross section, no amplitude modulus and no channel-resolved matrix element is printed, and the IR photon energy of the calculations is not stated (the introduction assumes hbar omega = 1.55 eV only to quote the RABBIT time window, p. 2).
THE AMPLITUDE (eq 46, p. 12): M^(2)(q, omega, Omega, b) = lim_{xi -> 0+} sum_p <q|ez|p> <p|ez|b> / (eps_b + hbar Omega - eps_p + i xi) E_omega E_Omega, the fields included, energy-normalised final states (eq 37); it is ‘intrinsically complex for the above threshold ionization, i.e., when hbar Omega exceeds the binding energy, even if correlation effects are neglected’. Only the XUV-first time order is kept: in length gauge the results ‘are completely dominated by the time-order where the XUV photon is absorbed first’ (p. 12, citing Vinbladh et al. 2019), whereas a complete two-photon RPAE treatment is needed for gauge invariance and in velocity gauge both time orders matter (p. 3). The final channels are the ionic core j (2P3/2 or 2P1/2) and the photoelectron’s kappa, summed coherently over kappa and incoherently over its spin m = +-1/2 (eq 41).
THE THRESHOLDS (figure captions, pp. 15-16, 19): Ar 15.76 (3p_3/2) and 15.94 eV (3p_1/2); Kr 14.00 and 14.67 eV; Xe 12.13 and 13.44 eV (Kr and Xe from the NIST ASD, ref. 94); Xe 4d_5/2 67.5 and 4d_3/2 69.5 eV (ref. 99). Each of the p-shell values agrees to its last digit with NIST’s ionisation energy plus the ion’s 2P1/2 level (data/external/nist_asd/ionization_energies.csv and <X>_II_levels.tsv: Ar 15.7596 and 15.9371, Kr 13.9996 and 14.6654, Xe 12.1298 and 13.4363 eV). A misprint: the argon fine-structure splitting is printed ‘Delta E_FS^Ar:3p_j = 0.18 meV’ (p. 15, checked on the rendered page); the paper’s own thresholds differ by 0.18 eV and NIST’s Ar II 2P1/2 level is 1431.58 cm-1 = 0.1775 eV, so it is 0.18 eV. The Kr and Xe splittings, 0.67 and 1.3 eV, are consistent with both.
WHY NOTHING IS TAKEN. No quantity holds a photoionisation delay: NOT TAKEN (awaiting vocabulary): Figs. 2-7, all vector drawings (a candidate quantity, not yet in the vocabulary). The thresholds are NIST’s, rounded, and are held from NIST itself.
FOR OEP 8 (section 4.2, Q6) AND OEP 6 (Q9). The amplitudes behind the delays are nondegenerate, channel-resolved (core j, final kappa) and in length gauge, but only their phases are published, and only for XUV + IR pairs in which the XUV photon alone ionises (Ar above 15.76 eV, Kr above 14.00 eV, Xe above 12.13 eV): far above the first intermediate resonances (Ar 4s[3/2]1 11.62 eV, Kr 5s[3/2]1 10.03 eV, Xe 6s[3/2]1 8.44 eV; NIST <X>_I_levels.tsv), the intermediate state on shell in the continuum; the half-separation (Omega - omega)/2 is about 7-41 eV across the figures for an IR photon near 1.55 eV. Like mccann_1988 and haber_2009, nothing at small splits; and the omitted IR-first time order is part of OEP 8’s symmetrised kernel (its eq. 2).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
No datasets are recorded.
Formulas#
No formulas are recorded.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.