Two-photon ionisation: source coverage and comparisons#

Start with Two-photon ionisation and absorption for the cross-section convention and model interface. This chapter describes the recorded evidence and its limits; source details are in the Source catalogue catalogue.

The curated two-photon ionisation cross sections#

Every curve read from a figure is use = "check" (data rule 8): those read from a vector drawing by their script, those read from a scanned image (raster) by theirs. The tables list every two-photon ionisation dataset of each gas, with the photon energies it covers inside the window \([I_p/2, E_1)\). The comparisons give the total cross section, the sum of the partials where a source draws only those, at photon energies off resonance. Each value is followed by its ratio to the first row.

Helium#

Dataset	Form	Use	Polarisation	Channel	Photon energies in the window (eV)
`bachau_1990/fig1a_W2_L2`	raster	check	linear	total	12.339 to 14.962
`bachau_1990/tbl1_sigma2_L2`	table	check	linear	total	13.606
`bachau_1990/tbl1_sigma2_qd`	table	check	linear	total	13.606
`kulander_1987/tbl1b_sigma2_tdhf`	table	check	linear	total	13.600 to 17.700
`lhuillier_1986/fig11_one_electron`	raster	check	linear	total	12.406 to 21.143
`lhuillier_1986/fig11_rpa`	raster	check	linear	total	12.406 to 21.206
`mihelic_2021/fig3a_sigma2_L0`	vector	check	linear	total	12.300 to 21.192
`mihelic_2021/fig3a_sigma2_L2`	vector	check	linear	total	12.300 to 21.204
`mihelic_2021/fig3b_sigma2_L0`	vector	check	linear	total	outside
`mihelic_2021/fig3b_sigma2_L2`	vector	check	linear	total	outside
`mihelic_2021/fig5_sigma2_L0_1ses`	vector	check	linear	1s eps s	outside
`mihelic_2021/fig5_sigma2_L0_2pep`	vector	check	linear	2p eps p	outside
`mihelic_2021/fig5_sigma2_L0_2ses`	vector	check	linear	2s eps s	outside
`mihelic_2021/fig5_sigma2_L0`	vector	check	linear	total	outside
`mihelic_2021/fig5_sigma2_L2_1sed`	vector	check	linear	1s eps d	outside
`mihelic_2021/fig5_sigma2_L2_2pef`	vector	check	linear	2p eps f	outside
`mihelic_2021/fig5_sigma2_L2_2pep`	vector	check	linear	2p eps p	outside
`mihelic_2021/fig5_sigma2_L2_2sed`	vector	check	linear	2s eps d	outside
`mihelic_2021/fig5_sigma2_L2`	vector	check	linear	total	outside
`nikolopoulos_2001/fig3_sigma2_D`	vector	check	linear	total	12.748 to 21.200
`nikolopoulos_2001/fig4_sigma2_D`	vector	check	linear	total	12.350 to 21.067
`nikolopoulos_2001/fig4_sigma2_S`	vector	check	linear	total	12.350 to 21.167
`nikolopoulos_2001/fig5_sigma2_double`	vector	check	linear	total	outside
`nikolopoulos_2001/fig5_sigma2_single`	vector	check	linear	total	outside
`nikolopoulos_2001/text_sigma2_single_45eV`	text	check	linear	total	outside
`proulx_1993/tbl1_rate2`	table	check	linear	total	14.327 to 20.449
`proulx_1993/tbl2_sigma2`	table	check	linear	total	outside
`ritchie_1977/tbl1_E_nonorth`	table	check	linear	total	12.408 to 21.198
`ritchie_1977/tbl1_E`	table	check	linear	total	12.408 to 21.198
`ritchie_1977/tbl1_NE_nonorth`	table	check	linear	total	12.408 to 21.198
`ritchie_1977/tbl1_NE`	table	check	linear	total	12.408 to 21.198
`ritchie_1977/tbl2_E_nonorth`	table	check	linear	total	12.408 to 20.762
`ritchie_1977/tbl2_E`	table	check	linear	total	12.408 to 20.762
`ritchie_1977/tbl2_NE_nonorth`	table	check	linear	total	12.408 to 20.762
`ritchie_1977/tbl2_NE`	table	check	linear	total	12.408 to 20.762
`ritchie_1977/text_length_1000A`	text	check	linear	total	12.408
`saenz_1999/fig1a_sigma2_1S`	vector	check	linear	total	12.651 to 21.214
`saenz_1999/fig1b_sigma2_1D`	vector	check	linear	total	12.650 to 21.217
`saenz_1999/fig4_sigma2_1D_length`	vector	check	linear	total	12.650 to 21.212
`saenz_1999/fig4_sigma2_1D_velocity`	vector	check	linear	total	12.650 to 21.217
`saenz_1999/text_sigma2_1D_complex_scaling`	text	check	linear	total	13.500
`saenz_1999/text_sigma2_1D_length`	text	check	linear	total	13.500
`saenz_1999/text_sigma2_1D_velocity`	text	check	linear	total	13.500
`saenz_1999/text_sigma2_1S_complex_scaling`	text	check	linear	total	13.500
`saenz_1999/text_sigma2_1S_length`	text	check	linear	total	13.500
`saenz_1999/text_sigma2_1S_velocity`	text	check	linear	total	13.500
`sato_2011/tbl2_lopt`	table	check	linear	total	20.193
`sato_2011/tbl2_obs`	table	check	linear	total	20.193
`sato_2011/tbl2_rmf`	table	check	linear	total	20.193
`sato_2011/text_1e10`	text	check	linear	total	20.193
`travers_2026_trecx_two_photon/sigma2_hacc_He`	table	check	linear	total	13.000 to 20.000
`travers_2026_trecx_two_photon/sigma2_sae_He`	table	check	linear	total	13.000 to 20.000
`vanderhart_2005/fig2_sigma2_rmf`	vector	check	linear	total	12.324 to 21.215
`vanderhart_2005/fig2_sigma2_saenz`	vector	check	linear	total	12.651 to 21.215

\(\sigma^{(2)}\) (cm⁴ s) at	13 eV	14 eV	16 eV	18 eV	20 eV
Saenz & Lambropoulos 1999, ¹S + ¹D (velocity)	1.48e-51	1.43e-51	1.09e-51	8.24e-52	7.75e-52
Mihelič & Horvat 2021, L = 0 + 2	1.32e-51 (0.90)	1.27e-51 (0.89)	1.04e-51 (0.96)	8.55e-52 (1.04)	8.74e-52 (1.13)
Nikolopoulos & Lambropoulos 2001, S + D (Fig. 4)	1.49e-51 (1.01)	1.31e-51 (0.92)	9.83e-52 (0.90)	6.97e-52 (0.85)	6.98e-52 (0.90)
van der Hart & Bingham 2005, R-matrix Floquet (1e13 W/cm²)	1.37e-51 (0.93)	1.31e-51 (0.92)	1.07e-51 (0.98)	8.51e-52 (1.03)	8.28e-52 (1.07)

The three calculations agree within about 15 % from threshold to 20 eV. Mihelič and Horvat’s own curves and Saenz and Lambropoulos’s differ the most near threshold; there Saenz’s scaled axis matters (TC-873, TC-874). Sato et al.’s FEL measurement (TC-876) has one point in the window, 2.6(6)×10⁻⁵² cm⁴ s at 61.4 nm (20.19 eV, 1e13 W cm⁻²), three times below the calculations. Its other points lie above \(E_1\), one on the 1s2p resonance. Sato’s LOPT column is Nikolopoulos and Lambropoulos’s D wave alone (their Fig. 3), not the S + D total (TC-875, TC-876). Van der Hart and Bingham’s R-matrix Floquet calculation at 1e13 W cm⁻² (TC-904), which Sato quotes, is 0.92 to 1.07 of Saenz’s. Bachau et al.’s and Proulx and Shakeshaft’s tables (TC-905, TC-906) lie above the window.

Neon#

Dataset	Form	Use	Polarisation	Channel	Photon energies in the window (eV)
`mcguire_1981/fig1_sigma2_Ne`	raster	check	circular	total	11.069 to 16.553
`mckenna_2004/fig1_sigma2_Ne`	vector	check	linear	total	10.800 to 16.667
`mckenna_2004/fig2_sigma2_Ne`	vector	check	linear	total	outside
`moccia_1983/fig1_sigma2_L_Ne`	raster	check	linear	total	11.976 to 15.777
`moccia_1983/fig1_sigma2_V_Ne`	raster	check	linear	total	11.157 to 16.193

\(\sigma^{(2)}\) (cm⁴ s) at	11 eV	12 eV	14 eV	16 eV
McKenna & van der Hart 2004	1.82e-51	1.71e-51	1.56e-51	1.6e-51
Moccia, Rahman & Rizzo 1983, velocity (raster)	—	1.05e-51 (0.62)	5.69e-52 (0.37)	2.21e-52 (0.14)
Moccia, Rahman & Rizzo 1983, length (raster)	—	3.28e-52 (0.19)	1.23e-52 (0.08)	3.27e-53 (0.02)
McGuire 1981, circular (raster)	—	1.01e-51 (0.59)	1.16e-51 (0.75)	1.53e-51 (0.96)

One calculation from a vector drawing, McKenna and van der Hart’s. The only independent one is Moccia, Rahman and Rizzo’s perturbative calculation (raster; TC-910). It is strongly gauge dependent: its velocity form is 0.62 to 0.14 of McKenna’s from 12 to 16 eV, its length form 0.19 to 0.02. McGuire’s is for circular polarisation, read from a scan with a piecewise axis.

Argon#

Dataset	Form	Use	Polarisation	Channel	Photon energies in the window (eV)
`fink_1990/fig3_circular`	raster	check	circular	total	7.997 to 11.578
`fink_1990/fig3_linear`	raster	check	linear	total	8.006 to 11.581
`mcguire_1981/fig2_sigma2_Ar`	raster	check	circular	total	8.919 to 11.373
`mckenna_2004/fig5_sigma2_Ar`	vector	check	linear	total	7.912 to 11.623
`mckenna_2004/fig7_sigma2_Ar`	vector	check	linear	total	outside
`moccia_1983/fig2_sigma2_L_Ar`	raster	check	linear	total	8.027 to 11.562
`moccia_1983/fig2_sigma2_V_Ar`	raster	check	linear	total	7.894 to 11.562
`pan_1990b/fig1b_all_L_p1S_Ar`	raster	check	linear	3p5(2P) epsilon-p 1S	8.101 to 10.899
`pan_1990b/fig1b_all_V_p1S_Ar`	raster	check	linear	3p5(2P) epsilon-p 1S	8.199 to 11.002
`pan_1990b/fig1b_noshakeup_L_p1S_Ar`	raster	check	linear	3p5(2P) epsilon-p 1S	8.301 to 11.299
`pan_1990b/fig1b_noshakeup_V_p1S_Ar`	raster	check	linear	3p5(2P) epsilon-p 1S	8.098 to 9.299
`pan_1990b/fig2_all_L_p1D_Ar`	raster	check	linear	3p5(2P) epsilon-p 1D	8.102 to 9.601
`pan_1990b/fig3_all_L_f1D_Ar`	raster	check	linear	3p5(2P) epsilon-f 1D	8.199 to 11.600
`pan_1990b/fig4a_hf_L_Ar`	raster	check	linear	total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)	8.101 to 11.198
`pan_1990b/fig4a_hf_V_Ar`	raster	check	linear	total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)	8.099 to 11.602
`pan_1990b/fig4b_noshakeup_L_Ar`	raster	check	linear	total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)	8.098 to 11.301
`pan_1990b/fig4b_noshakeup_V_Ar`	raster	check	linear	total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)	8.101 to 11.500
`pan_1990b/fig4c_all_L_Ar`	raster	check	linear	total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)	8.401 to 11.098
`pan_1990b/fig4c_all_V_Ar`	raster	check	linear	total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)	8.098 to 11.098
`pan_1990b/fig5_all_L_circular_Ar`	raster	check	circular	total (3p5 epsilon-p 1D + epsilon-f 1D; no 1S for circular)	8.099 to 10.002
`pan_1990b/fig5_all_V_circular_Ar`	raster	check	circular	total (3p5 epsilon-p 1D + epsilon-f 1D; no 1S for circular)	9.701 to 11.199
`pan_1990b/fig5_hf_L_circular_Ar`	raster	check	circular	total (3p5 epsilon-p 1D + epsilon-f 1D; no 1S for circular)	8.299 to 11.500
`pan_1990b/fig5_hf_V_circular_Ar`	raster	check	circular	total (3p5 epsilon-p 1D + epsilon-f 1D; no 1S for circular)	9.601 to 10.002
`petrov_2016/fig10_corr_L`	vector	check	linear	total	8.000 to 11.617
`petrov_2016/fig10_corr_V`	vector	check	linear	total	8.000 to 11.617
`petrov_2016/fig10_corrcp_L`	vector	check	linear	total	8.000 to 11.619
`petrov_2016/fig10_corrcp_V`	vector	check	linear	total	8.000 to 11.623
`petrov_2016/fig6_corr_L_ep1S`	vector	check	linear	3p5 ep (1S)	8.000 to 11.619
`petrov_2016/fig6_corr_V_ep1S`	vector	check	linear	3p5 ep (1S)	8.000 to 11.621
`petrov_2016/fig6_corrcp_L_ep1S`	vector	check	linear	3p5 ep (1S)	8.000 to 11.430
`petrov_2016/fig6_corrcp_V_ep1S`	vector	check	linear	3p5 ep (1S)	8.000 to 11.466
`petrov_2016/fig7_corr_L_ep1D`	vector	check	linear	3p5 ep (1D)	8.000 to 11.623
`petrov_2016/fig7_corrcp_L_ep1D`	vector	check	linear	3p5 ep (1D)	8.000 to 11.319
`petrov_2016/fig8_corr_L_ef1D`	vector	check	linear	3p5 ef (1D)	8.000 to 11.617
`petrov_2016/fig8_corrcp_L_ef1D`	vector	check	linear	3p5 ef (1D)	8.000 to 11.619
`pindzola_1975/fig2_L_p1D_Ar`	raster	check	linear	3p5 kp 1D	8.000 to 9.001
`pindzola_1975/fig2_V_p1D_Ar`	raster	check	linear	3p5 kp 1D	8.001 to 9.001
`pindzola_1975/fig3_L_p1S_Ar`	raster	check	linear	3p5 kp 1S	7.998 to 11.002
`pindzola_1975/fig3_V_p1S_Ar`	raster	check	linear	3p5 kp 1S	7.997 to 10.500
`pindzola_1975/fig4_L_f1D_Ar`	raster	check	linear	3p5 kf 1D	8.001 to 11.502
`pindzola_1975/fig4_V_f1D_Ar`	raster	check	linear	3p5 kf 1D	7.998 to 11.502
`pindzola_1975/fig6_LGI_f1D_Ar`	raster	check	linear	3p5 kf 1D	9.498 to 10.998
`pindzola_1975/fig6_VGI_f1D_Ar`	raster	check	linear	3p5 kf 1D	9.498 to 11.502
`starace_1987/fig2_esi_f1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-f 1D	8.498 to 11.501
`starace_1987/fig2_gsc_f1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-f 1D	8.498 to 11.599
`starace_1987/fig2_hf_f1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-f 1D	8.499 to 11.602
`starace_1987/fig2_iic_f1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-f 1D	8.601 to 11.498
`starace_1987/fig3_esi_p1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-p 1D	8.399 to 9.702
`starace_1987/fig3_hf_p1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-p 1D	8.202 to 10.398
`starace_1987/fig3_iic_p1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-p 1D	8.401 to 10.301
`starace_1987/fig4_esi_p1S_linear_Ar`	raster	check	linear	3p5(2P) epsilon-p 1S	8.398 to 11.101
`starace_1987/fig4_gsc_p1S_linear_Ar`	raster	check	linear	3p5(2P) epsilon-p 1S	8.402 to 10.700
`starace_1987/fig4_hf_p1S_linear_Ar`	raster	check	linear	3p5(2P) epsilon-p 1S	8.202 to 10.702
`starace_1987/fig4_iic_p1S_linear_Ar`	raster	check	linear	3p5(2P) epsilon-p 1S	8.402 to 10.798
`starace_1987/fig5_esi_shifted_f1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-f 1D	8.401 to 11.402
`starace_1987/fig5_iic_shifted_f1D_linear_Ar`	raster	check	linear	3p5(2P) epsilon-f 1D	8.799 to 9.902
`starace_1987/fig6_esi_circular_Ar`	raster	check	circular	total	8.100 to 11.100
`starace_1987/fig6_iic_circular_Ar`	raster	check	circular	total	8.100 to 11.003
`starace_1987/fig7_esi_linear_Ar`	raster	check	linear	total	8.098 to 9.400
`starace_1987/fig7_iic_linear_Ar`	raster	check	linear	total	8.399 to 10.799
`travers_2026_trecx_two_photon/sigma2_sae_Ar`	table	check	linear	total	8.000 to 11.000

\(\sigma^{(2)}\) (cm⁴ s) at	8 eV	9 eV	10 eV	11 eV
McKenna & van der Hart 2004	1.27e-50	1.24e-50	1.17e-50	1.13e-50
Petrov et al. 2016, corr + CP, length	1.15e-50 (0.91)	1.14e-50 (0.92)	1.07e-50 (0.92)	1.18e-50 (1.05)
Petrov et al. 2016, corr + CP, velocity	1.26e-50 (0.99)	1.19e-50 (0.95)	1.09e-50 (0.93)	1.06e-50 (0.94)
Petrov et al. 2016, corr, length	1.02e-50 (0.81)	9.83e-51 (0.79)	8.83e-51 (0.75)	8.02e-51 (0.71)
Starace & Jiang 1987, IIC, length (raster)	—	1.3e-50 (1.04)	1.32e-50 (1.13)	1.43e-50 (1.27)
Starace & Jiang 1987, ESI, length (raster)	—	1.04e-50 (0.84)	9.26e-51 (0.79)	8.14e-51 (0.72)
Pan, Gao & Starace 1990, length (raster)	—	9.21e-51 (0.74)	8.09e-51 (0.69)	7.06e-51 (0.63)
Pan, Gao & Starace 1990, velocity (raster)	—	8.77e-51 (0.71)	8.31e-51 (0.71)	7.53e-51 (0.67)
Pindzola & Kelly 1975, second order, length (raster)	—	1.17e-50 (0.94)	1.19e-50 (1.01)	1.15e-50 (1.02)
Moccia, Rahman & Rizzo 1983, velocity (raster)	7.77e-51 (0.61)	8.57e-51 (0.69)	9.04e-51 (0.77)	9.16e-51 (0.81)
Moccia, Rahman & Rizzo 1983, length (raster)	—	1.09e-50 (0.87)	9.34e-51 (0.80)	8.49e-51 (0.75)
Fink & Johnson 1990, linear (raster)	—	1.03e-50 (0.83)	8.77e-51 (0.75)	7.42e-51 (0.66)
McGuire 1981, circular (raster)	—	1.53e-50 (1.23)	1.72e-50 (1.47)	2.1e-50 (1.87)

The two all-electron calculations agree within 10 % from 8 to 11 eV: Petrov et al. with core polarisation (both gauges), and McKenna and van der Hart. Without core polarisation, Petrov et al.’s is 0.71 to 0.81 of it (TC-877). Starace and Jiang’s two transition-matrix approximations (raster) bracket them, 0.72 to 1.27 (TC-878). McGuire’s circular cross section is 1.2 to 1.9 times the linear calculations, more than his own ratio \(R\) allows (at most 3/2; TC-879).

Three effects together are therefore about ±10 % in argon below 11 eV:

independent calculation;
gauge;
core polarisation.

Without core polarisation, or in the simpler approximations, the spread is about ±30 %. The older many-body calculations, all raster, lie mostly below the two all-electron ones:

Pan, Gao and Starace (0.63 to 0.74; TC-908);
Moccia, Rahman and Rizzo (0.61 to 0.87; TC-910);
Fink and Johnson’s relativistic calculation (0.66 to 0.83; TC-912);
Pindzola and Kelly’s second order (0.94 to 1.02; TC-909).

No measured argon two-photon ionisation cross section was found. Xenakis et al. observed argon two-photon ionisation at 82.9 nm but measured no cross section (TC-911).

Krypton#

Dataset	Form	Use	Polarisation	Channel	Photon energies in the window (eV)
`fink_1990/fig4_circular`	raster	check	circular	total	7.347 to 9.943
`fink_1990/fig4_linear`	raster	check	linear	total	7.616 to 9.946
`lhuillier_1989/fig10_total_Kr`	raster	check	linear	total	7.470 to 8.648
`lhuillier_1989/fig6_J0_Kr`	raster	check	linear	J = 0 final states (partial)	7.130 to 7.208
`lhuillier_1989/fig6_total_Kr`	raster	check	linear	total (J = 0 and J = 2 final states)	7.130 to 7.221
`mcguire_1981/fig3_sigma2_Kr`	raster	check	circular	total	7.749 to 9.918

\(\sigma^{(2)}\) (cm⁴ s) at	7.2 eV	7.5 eV	8 eV	8.5 eV	9.5 eV
L’Huillier, Tang & Lambropoulos 1989, MQDT (raster)	3.11e-50	—	—	—	—
L’Huillier, Tang & Lambropoulos 1989, above ²P₁/₂ (raster)	—	1.14e-50	3.13e-51	1.83e-51	—
Fink & Johnson 1990, linear (raster)	—	—	1.9e-50	1.68e-50	1.24e-50
Fink & Johnson 1990, circular (raster)	—	1.56e-50	1.58e-50	1.49e-50	1.21e-50
McGuire 1981, circular (raster)	—	—	4.25e-50	4.86e-50	5.63e-50

Krypton has no vector-drawn or tabulated two-photon ionisation cross section and no measurement. Its only curves are read from scans:

L’Huillier, Tang and Lambropoulos’s MQDT, between the thresholds and above ²P₁/₂;
Fink and Johnson’s relativistic calculation, linear and circular, from the ²P₁/₂ threshold (TC-912);
McGuire’s, circular polarisation.

Above ²P₁/₂ the MQDT and relativistic calculations differ by up to a factor of 6 at 8 eV. McGuire’s circular values are 2.7 to 4.7 times Fink and Johnson’s from 8 to 9.5 eV.

The data do not support a model of krypton.

Xenon#

Dataset	Form	Use	Polarisation	Channel	Photon energies in the window (eV)
`bischel_1979/alpha_Xe`	table	check	not stated	total	6.424
`fink_1990/fig5_circular`	raster	check	circular	total	6.803 to 8.378
`fink_1990/fig5_linear`	raster	check	linear	total	6.803 to 8.381
`fink_1990/fig6_circular_p12`	raster	check	circular	Xe+ 5p5 2P1/2 core	6.803 to 7.894
`fink_1990/fig6_circular_p32`	raster	check	circular	Xe+ 5p5 2P3/2 core	6.966 to 8.003
`fink_1990/fig6_linear_p12`	raster	check	linear	Xe+ 5p5 2P1/2 core	6.966 to 7.891
`fink_1990/fig6_linear_p32`	raster	check	linear	Xe+ 5p5 2P3/2 core	6.963 to 8.000
`gangopadhyay_1986/fig1`	raster	check	linear	Xe+ 2P3/2 (the only open core between the thresholds)	6.103 to 6.598
`gangopadhyay_1986/tab1_jc12`	table	check	linear	Xe+ 2P1/2 (residual core J = 1/2)	7.000 to 8.435
`gangopadhyay_1986/tab1_jc32`	table	check	linear	Xe+ 2P3/2 (residual core J = 3/2)	7.000 to 8.435
`hodges_1981/alpha_Xe`	text	check	not stated	total	6.424
`karamatskou_2017/fig1_interchannel`	vector	check	linear	total	outside
`karamatskou_2017/fig1_intrachannel`	vector	check	linear	total	outside
`karamatskou_2017/fig2_interchannel`	vector	check	linear	total	outside
`karamatskou_2017/fig3_interchannel_shifted`	vector	check	linear	total	outside
`kligler_1978/sigma_over_I_Xe`	table	check	not stated	total	6.424
`kulander_1988/text_sigma2_Xe`	text	check	linear	total	6.424
`lagutin_2017/fig3a_hf`	vector	check	linear	total	7.037 to 8.417
`lagutin_2017/fig3a_pf`	vector	check	linear	total	7.020 to 8.405
`lagutin_2017/fig3a_pfcp`	vector	check	linear	total	7.075 to 8.435
`lagutin_2017/fig3b_hf`	vector	check	linear	total	outside
`lagutin_2017/fig3b_pf`	vector	check	linear	total	outside
`lagutin_2017/fig3b_pfcp`	vector	check	linear	total	outside
`lagutin_2017/fig4_cipfcp_length`	vector	check	linear	total	6.722 to 8.436
`lagutin_2017/fig4_cipfcp_velocity`	vector	check	linear	total	6.721 to 8.436
`lagutin_2017/fig4_pf_length`	vector	check	linear	total	6.722 to 8.426
`lagutin_2017/fig4_pf_velocity`	vector	check	linear	total	6.722 to 8.393
`lagutin_2017/fig6_present_w`	vector	check	linear	total	6.722 to 8.436
`lagutin_2017/fig6_present_wo`	vector	check	linear	total	6.722 to 8.436
`lagutin_2017/fig7_cipf_length`	vector	check	linear	5p3/2^5 ep3/2 (J = 0)	6.803 to 8.435
`lagutin_2017/fig7_cipf_velocity`	vector	check	linear	5p3/2^5 ep3/2 (J = 0)	6.823 to 8.435
`lagutin_2017/fig7_noshakeup_length`	vector	check	linear	5p3/2^5 ep3/2 (J = 0)	6.815 to 8.437
`lagutin_2017/fig7_noshakeup_velocity`	vector	check	linear	5p3/2^5 ep3/2 (J = 0)	6.804 to 8.428
`lagutin_2017/fig8_cipfcp_circular`	vector	check	circular	total	6.721 to 8.436
`lagutin_2017/fig8_cipfcp_linear`	vector	check	linear	total	6.721 to 8.436
`lhuillier_1987/fig6_hf_Xe`	raster	check	linear	5p shell (5p -> eps p, eps f)	6.286 to 8.434
`lhuillier_1987/fig6_ldrpa_Xe`	raster	check	linear	5p shell (5p -> eps p, eps f)	6.313 to 8.436
`lhuillier_1987/fig6_rpae_Xe`	raster	check	linear	5p shell (5p -> eps p, eps f)	6.286 to 8.436
`lhuillier_1987/fig7_hf_Xe`	raster	check	linear	5p shell (5p -> eps p, eps f)	outside
`lhuillier_1987/fig7_ldrpa_Xe`	raster	check	linear	5p shell (5p -> eps p, eps f)	outside
`lhuillier_1987/fig7_rpae_Xe`	raster	check	linear	5p shell (5p -> eps p, eps f)	outside
`lhuillier_1987b/fig2_lda`	raster	check	linear	5p shell	6.346 to 8.002
`lhuillier_1987b/fig2_ldrpa_first`	raster	check	linear	5p shell	6.089 to 8.348
`lhuillier_1987b/fig2_ldrpa`	raster	check	linear	5p shell	6.102 to 8.414
`lhuillier_1987b/fig3_rpae_first`	raster	check	linear	5p shell	6.316 to 8.436
`lhuillier_1987b/fig4_ldrpa`	raster	check	linear	5p shell	6.074 to 8.411
`lhuillier_1987b/fig4_rpae`	raster	check	linear	5p shell	6.289 to 8.411
`lhuillier_1989/fig10_total_Xe`	raster	check	linear	total	6.850 to 8.028
`lhuillier_1989/fig6_J0_Xe`	raster	check	linear	J = 0 final states (partial)	6.386 to 6.558
`lhuillier_1989/fig6_total_Xe`	raster	check	linear	total (J = 0 and J = 2 final states)	6.386 to 6.570
`mccann_1988/sigma2_Xe_118_355`	text	check	linear	total	outside
`mccown_1982/alpha_Xe`	table	primary	natural	total	6.424
`mccown_1982/bischel_Xe`	table	check	not stated	total	6.424
`mccown_1982/hodges_Xe`	table	check	not stated	total	6.424
`mccown_1982/mcguire_Xe`	table	check	circular	total	6.424
`mcguire_1981/fig4_sigma2_Xe`	raster	check	circular	total	6.390 to 8.211
`santra_2004/sigma2_Xe`	text	check	linear	total	6.420

\(\sigma^{(2)}\) (cm⁴ s) at	6.42 eV	7 eV	7.5 eV	8 eV
Lagutin et al. 2017, CIPFCP, linear	—	4.27e-50	3.7e-50	3.44e-50
Lagutin et al. 2017, CIPFCP, circular	—	4.46e-50 (1.05)	3.99e-50 (1.08)	3.15e-50 (0.92)
Karamatskou & Santra 2017, TDCIS (Fig. 1)	—	—	—	—
Fink & Johnson 1990, linear (raster)	—	3.59e-50 (0.84)	2.77e-50 (0.75)	3.41e-50 (0.99)
Gangopadhyay et al. 1986, MQDT, Table I (sum of cores)	—	1.98e-50 (0.46)	1.38e-50 (0.37)	2.36e-50 (0.69)
Gangopadhyay et al. 1986, MQDT, between the thresholds (raster)	4.77e-51	—	—	—
L’Huillier & Wendin 1987 (J. Phys. B), RPAE (raster)	2.61e-50	2.02e-50 (0.47)	1.35e-50 (0.36)	9.35e-51 (0.27)
L’Huillier & Wendin 1987, RPAE (raster)	2.59e-50	2.05e-50 (0.48)	1.46e-50 (0.39)	9.39e-51 (0.27)
L’Huillier, Tang & Lambropoulos 1989, MQDT (raster)	5.71e-50	—	—	—
L’Huillier, Tang & Lambropoulos 1989, above ²P₁/₂ (raster)	—	2.51e-50 (0.59)	1.71e-50 (0.46)	2.09e-50 (0.61)
McCown, Ediger & Eden 1982, measured	4.12e-50	—	—	—
Bischel et al. 1979, estimate	1.03e-52	—	—	—
Hodges, Lee & Moseley 1981, lower limit	5.15e-52	—	—	—
Santra & Greene 2004	6.2e-50	—	—	—
McGuire 1981, circular (raster)	8.35e-50	1.19e-49 (2.80)	1.29e-49 (3.50)	1.37e-49 (3.99)

Above the upper threshold the calculations disagree by factors of 2 to 4:

Lagutin et al.’s relativistic, correlated calculation (TC-880) begins at the ²P₁/₂ threshold (6.72 eV) and has nothing between the thresholds.
L’Huillier and Wendin’s RPAE and L’Huillier, Tang and Lambropoulos’s MQDT (raster) are 0.3 to 0.6 times it.
Fink and Johnson’s relativistic calculation (raster; TC-912) is 0.75 to 0.99 of it, and Lagutin et al. redraw it.
Gangopadhyay et al.’s MQDT Table I (TC-914) is 0.37 to 0.69 of it. Every later drawing of “Gangopadhyay et al.” is this table, above the ²P₁/₂ threshold.
Karamatskou and Santra’s TDCIS (TC-881) starts above the window, at 9 eV. There it is 20 to 200 times Lagutin et al.’s off resonance.
The only measurement, McCown et al.’s at 193 nm (4.1×10⁻⁵⁰ cm⁴ s; TC-884), lies between the thresholds, where only the raster MQDT curve and Santra and Greene’s single-threshold calculation reach. It is drawn by L’Huillier, Tang and Lambropoulos 1.39 times higher than its printed value, and by Lagutin et al. and L’Huillier and Wendin at it (TC-882, TC-883). Gangopadhyay et al.’s raster curve between the thresholds (TC-914) reads 0.11 of it at the line centre. Bischel et al.’s estimate and Hodges et al.’s lower limit at 193 nm, both with McCown’s definition, are 400 and 80 times below it (TC-917, TC-918).

Circular polarisation: in the window, Lagutin et al.’s circular cross section is 0.92 to 1.08 times their linear one; McGuire’s circular values are 2.8 to 4 times Lagutin’s linear ones.

See OEP 6 — Two-photon ionisation and absorption of the noble gases for the completed proposal and its phase reports.