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 · Catalogue · 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 <q|ez|p><p|ez|a> / (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

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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.