vinbladh_2022 ============= J\. Vinbladh, J\. M\. Dahlström and E\. Lindroth, "Relativistic Two\-Photon Matrix Elements for Attosecond Delays", Atoms 10, 80 \(2022\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.3390/atoms10030080 `__ **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 \ \ / \(eps\_b \+ hbar Omega \- eps\_p \+ i xi\) 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 \(data/external/nist\_asd/ionization\_energies\.csv and \\_II\_levels\.tsv\: Ar 15\.7596 and 15\.9371, Kr 13\.9996 and 14\.6654, Xe 12\.1298 and 13\.4363 eV\)\. 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 \\_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 :doc:`review register ` for the checks and decisions.