vinbladh_2019 ============= J\. Vinbladh, J\. M\. Dahlström and E\. Lindroth, "Many\-body calculations of two\-photon, two\-color matrix elements for attosecond delays", Phys\. Rev\. A 100, 043424 \(2019\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.100\.043424 `__ **Source kind:** theory **Recorded technique:** Two\-colour two\-photon random\-phase approximation with exchange \(two\-photon RPAE, i\.e\. second\-order time\-dependent Hartree\-Fock\) for one XUV harmonic plus or minus one 800 nm photon \(hbar omega = 1\.55 eV\), linear parallel polarisations, in both the length and the velocity gauge, with all time orders\: the XUV\-first diagram \(Fig\. 2\(a\)\), the IR\-first diagram \(2\(b\)\), the hole\-field couplings \(2\(c\), 2\(d\)\) and the correlated diagrams \(2\(e\)\-2\(l\)\), with exchange \(Secs\. III A\-C, eqs\. 15\-43\)\. One\-particle basis from B splines in a box with a nonlocal Hartree\-Fock potential plus a projected monopole potential \(eqs\. 15, 31\); exterior complex scaling for the outgoing boundary condition \(eq\. 22\); the continuum\-continuum integral of Fig\. 2\(a\) completed with analytical Coulomb waves along the imaginary r axis, its stability judged from the spread of 'break points' \(Sec\. III C\)\. Hartree\-Fock orbital energies throughout except for Ar 3s \(Figs\. 7\-9\), where experimental ionisation energies replace them at the cost of gauge invariance \(p\. 043424\-9\)\. **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, Phys\. Rev\. A 100, 043424 \(2019\), received 1 July 2019, published 31 October 2019, 13 pages; PDF page n = article page 043424\-n\. WHAT IS PRINTED\. Only atomic \(RABBIT\) delays, tau\_A = \(phi\_e \- phi\_a\)/\(2 omega\) \(eq\. 12\), and tau\_A \- tau\_W, for photoelectrons along the common polarisation axis \(and angle\-integrated in Fig\. 8\), all in vector\-drawn figures against 'Photon Energy \[eV\]', the total absorbed by the photoelectron \(XUV plus or minus IR, p\. 043424\-8\), or against electron energy \(Fig\. 9\)\: Ne 2p, length gauge \(Fig\. 3, 28\-34 eV\) and velocity gauge \(Fig\. 4, 28\-42 eV\), each diagram class added in turn; Ar 3p, velocity gauge \(Fig\. 5\) and both gauges with five or two orbitals in the RPAE \(Fig\. 6\), 40\-62 eV; Ar 3s, length gauge with experimental energies \(Fig\. 7, 34\-48 eV\); Ar tau\_A\(3s\) \- tau\_A\(3p\) \(Fig\. 8, 34\-56 eV\); tau\_A \- tau\_W for Ar 3s and 3p against the analytical continuum\-continuum delay \(Fig\. 9, electron energies about 4\-25 and 20\-48 eV\)\. The figures' raster in the PDF holds only the diagrams of Figs\. 1\-2 \(pp\. 5\-6\)\. In the text\: the Ne 2p length\-gauge corrections beyond Fig\. 2\(a\) are 'less than an attosecond' \(pp\. 8\-9\); in velocity gauge Fig\. 2\(a\) alone misses the Ar 3p delay by 'around 40 as' below and 'more than 50 as' above the Cooper minimum \(p\. 9\); Ar 3s Koopmans binding energy '~34\.8 eV' against the true '~29\.2 eV' \(p\. 9\); Cooper minima near 40 eV \(3s\) and 50 eV \(3p\) \(p\. 10\); and the one\-photon Ar 3s partial cross section '~0\.003 Mb' near 40 eV \(RPAE, all orbitals, experimental energies, length gauge\) against '~0\.02 Mb' for the 3p^\-2\(1D\)3d satellite from Wijesundera and Kelly \(p\. 12\)\. No two\-photon cross section, no amplitude modulus and no channel\-resolved matrix element is printed\. THE AMPLITUDE AND THE TIME ORDERS\. M^\(2\)\(q, omega, Omega, a\) = lim\_{xi \-\> 0\+} sum\_p \\ / \(eps\_a \+ hbar Omega \- eps\_p \+ i xi\) E\_omega E\_Omega in length gauge \(eq\. 10; e p\_z/m and A\_omega A\_Omega in velocity gauge\), the fields included, the final state normalised through the asymptotic form of eq\. 3 \(the factor \-pi sqrt\(2m/\(pi k hbar^2\)\)\)\. The full element is M = M^TO\:1 \+ M^TO\:2 \+ delta M \(eq\. 43\)\: TO\:1 XUV first \(eq\. 39\), TO\:2 IR first \(eq\. 40\), each with its hole\-field term, and delta M the correlated rest\. The summed second\-order correction with both time orders is eq\. 25, the symmetrisation over the two photons that OEP 8's kernel \(its eq\. 2\) writes\. Findings \(Secs\. IV A\-B, V A\)\: in length gauge the delay is 'completely dominated' by Fig\. 2\(a\); in velocity gauge the IR\-first order matters and dropping it 'leads to wrong results' \(p\. 2\); only the complete set of diagrams is gauge invariant \(Figs\. 4\-6\)\. Eqs\. 48\-50\: for one off\-shell intermediate state i, the velocity\-gauge term is the length\-gauge term times \(eps\_i \- eps\_0\)\(eps\_0 \+ hbar Omega\_1 \+ hbar Omega\_2 \- eps\_i\)/\(hbar^2 Omega\_1 Omega\_2\), at most \(\(Omega\_1 \+ Omega\_2\)/2\)^2/\(Omega\_1 Omega\_2\), about Omega\_\>/\(4 Omega\_\<\) for Omega\_\>/Omega\_\< \>\> 2\. For equal photons this maximum is 1\: the gauge disparity of single terms is a large\-split effect\. WHY NOTHING IS TAKEN\. The delays have no quantity \(photoionisation delays declined, TC\-1011\)\: NOT TAKEN \(no quantity; declined, TC\-1011\), Figs\. 3\-9\. The Ar 3s value '~0\.003 Mb' is a subshell partial cross section printed as an approximation, not the total per\-atom photoionization\_cross\_section\: NOT TAKEN\. The 1\.55 eV and the binding energies are context\. FOR OEP 8 \(Q6\) AND OEP 6 \(Q9\)\. The method computes exactly the nondegenerate, both\-time\-order, gauge\-invariant amplitude OEP 8 needs, but only for XUV \+ IR pairs whose XUV photon alone ionises \(Ne 2p above 21\.6 eV, Ar 3p above 15\.8 eV; Figs\. 3\-9 start at 28 and 34 eV total\), far above the first intermediate resonance \(Ar 4s\[3/2\]1 11\.62 eV, NIST\) and at half\-separations \(Omega \- omega\)/2 of about 12\-33 eV\. Nothing is below the first resonance and nothing is at small splits; only phases are published\. The paper notes \(p\. 2\) that the RPAE two\-photon studies of the 1980s\-1990s treated equal\-energy photons below threshold\: L'Huillier, Jönsson and Wendin, Phys\. Rev\. A 33, 3938 \(1986\) \(record lhuillier\_1986, TC\-947\) and Pan, Gao and Starace, Phys\. Rev\. A 41, 6271 \(1990\) \(record pan\_1990b, TC\-908\)\. The group's lowest\-order XUV\-first amplitudes are in Dahlström, Carette and Lindroth, Phys\. Rev\. A 86, 061402\(R\) \(2012\), Dahlström and Lindroth, J\. Phys\. B 47, 124012 \(2014\) and Lindroth and Dahlström, Phys\. Rev\. A 96, 013420 \(2017\), none in the library; vinbladh\_2022 \(TC\-1009\) is its relativistic successor\. **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.