hummer_1998 =========== D\. G\. Hummer and P\. J\. Storey, "Recombination of helium\-like ions \- I\. Photoionization cross\-sections and total recombination and cooling coefficients for atomic helium", Mon\. Not\. R\. Astron\. Soc\. 297, 1073 \(1998\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1046/j\.1365\-8711\.1998\.2970041073\.x `__ **Source kind:** theory **Recorded technique:** Calculated one\-photon photoionisation cross sections of all bound levels of helium with n = 1\-25, l = 0\-5, singlet and triplet, from threshold to a free\-electron energy of 2\.5 Ryd\: the R\-matrix close\-coupling method \(Berrington et al\.; the Opacity Project's STGBF, modified for the outer\-region dipole integral\), extending Fernley, Taylor and Seaton \(1987, the OP\) with a seven\-orbital He\+ target \(Eq\. 5\: 1s, 2s, 2p and the pseudo\-orbitals 1p\-bar', 1d\-bar, 2s\-bar', 2p\-bar' of Calvert and Davison, alpha = 2\.13, beta = 3\.1, Eqs\. 3\-4\), LS coupling, no fine structure\. The energy mesh has at least 40 points within 1/n^2 Ryd of each threshold \(p\. 1075\)\. The threshold cross sections are compared with values extrapolated from Drake's \(1996\) bound\-bound oscillator strengths by Eq\. 1 \(ln\(nu^3 f\) = a \+ b x \+ c x^2, x = ln\(eps\_t/eps\); the threshold cross section is 4\.033643 e^a Mb\), which the paper takes as benchmarks\. **Materials in structured entries:** He **Dataset quantities:** excited\_state\_photoionization\_cross\_section, photoionization\_cross\_section **Contents:** 14 datasets; 0 formulas. Curation notes -------------- Mon\. Not\. R\. Astron\. Soc\. 297, 1073\-1078 \(1998\) = PDF pages 1\-6 \(journal page = PDF page \+ 1072\); the publisher's PDF, text and tables as text, Figs\. 1 and 2 embedded images\. Identity checked against the first page \(journal, volume, pages, year, title, authors\)\. Tables 1 and 2 checked against the table images\. ACCURACY\. 'In all cases, the difference is less than 1 per cent and, excepting the 1S states, less than 0\.5 per cent' \(This Work against Extrapolated, p\. 1075\); the abstract\: 'in error by no more than 1 per cent'\. Table 2\: This Work's 1S quantum defects lie 0\.0013\-0\.0016 below Martin's experimental ones, closer than the OP's\. WHAT IS TAKEN \(tools/extract/hummer\_1998\.py\)\. \(1\) Table 1 \(p\. 1074\), 'Threshold photoionization cross\-sections \(Mb\)', the rows of the levels two photons reach from the ground state and the ground state itself\: 1 1S \(photoionization\_cross\_section\), 2 1S, 3 1S, 4 1S, 3 1D, 4 1D \(excited\_state\_photoionization\_cross\_section\), each in two columns, This Work and Extrapolated \(from Drake's data, with the fitting error as printed, \+\-0\.000 to \+\-0\.053\)\. One point each, at the level's threshold as the calculation places it \(THE THRESHOLDS OF TABLE 1, below\)\. \(2\) Fig\. 1 \(p\. 1076, an embedded image\), log10 sigma \(Mb\) of the 1S levels against the electron energy \(0\-2\.5 Ryd\)\: n = 1 \(the ground state\) and n = 2 \(1s2s 1S\), read from the image at native resolution \(3383 x 2200 pixels; the method in the script's docstring\), from 0\.08 Ryd \(below it the two curves lie within two line widths; they cross at 0\.05 Ryd\) to 2\.45 Ryd, one point every 0\.05 Ryd\. THE PHOTON ENERGY OF FIG\. 1 \(a conversion this record makes\)\: electron energy \(as drawn\) plus the calculation's binding energy of the level, 1/\(n \- delta\)^2 Ryd with This Work's delta \(Table 2\: 0\.2549, 0\.1478\), 1\.801237 and 0\.291490 Ryd, in R\_infinity hc \('rydberg'; the R\-matrix energies are in Ryd; whether the quantum defects refer to R\_infinity or the reduced\-mass Rydberg, 1\.4e\-4 apart, is not said\)\. Nothing is shifted to the experimental thresholds \(24\.5874 and 3\.9716 eV, NIST\)\. The electron energy read is in each point's 'printed'\. THE THRESHOLDS OF TABLE 1 \(corrected 2026\-10\-09; TC\-934 placed them at NIST's\)\. The paper prints no level energies\. The 1S rows' points, in both columns, are placed at the calculation's threshold, 1/\(n \- delta\)^2 Ryd with Table 2's This Work quantum defect \(0\.2549, 0\.1478, 0\.1419, 0\.1401 for n = 1\-4\: 1\.801237, 0\.291490, 0\.122418, 0\.067119 Ryd\), as Fig\. 1's photon energies are, so that the record uses the source's own energies throughout; each point's 'printed' adds the quantum defect used\. These thresholds lie 0\.33 % \(1 1S\), 0\.14 % \(2 1S\), 0\.09 % \(3 1S\) and 0\.07 % \(4 1S\) below NIST's ionisation energies of the levels \(nist\_asd\_2026, data/external/nist\_asd/He\_I\_levels\.tsv\: the He II limit, 198310\.66637 cm\-1, less the level; checked by the script\)\. The Extrapolated values, from Drake's oscillator strengths, refer to the true threshold; they share the calculation's point with This Work\. Table 2 prints no D quantum defects \('the results for the other symmetries are essentially unchanged', p\. 1075\), so the 1D rows' threshold is 'not stated'; NIST puts 3 1D at 12205\.70227 and 4 1D at 6864\.21323 cm\-1 below the limit\. Until the correction the Table 1 points stood at NIST's thresholds, in cm\-1 \(TC\-934, TC\-942\)\. DIGITISING\. Each side of the frame has its own linear scale from its labelled ticks \(residuals within 2 pixels\); every minor tick lies on a dark run within 3 pixels of its predicted place\. 208\.5 pixels per unit of log10 sigma \(one pixel 1\.1 %\), 1133 pixels per Ryd; the lines are 3\-6 pixels wide\. Relative uncertainty 4 %\: the half line width \(2\-3 pixels, 2\.5\-3\.5 %\) and the scale \(1 pixel\)\. The overlay \(the points and the calibrated grid drawn on the image\) was inspected\. CHECKED \(the script\)\. The n = 1 curve carried to threshold by a straight line in log10 sigma fitted from 0\.08 to 0\.3 Ryd gives 0\.996 of Table 1's This Work, 7\.394 Mb\. The n = 2 curve near threshold is not read \(the crossing\), so its 9\.253 Mb is not checked on the figure\. COMPARISONS \(Fig\. 1's 1s2s 1S curve at the photon energies of the citing records, with the calculation's threshold\)\. At 10\.309 eV \(120\.27 nm, 0\.466 Ryd above threshold\) it reads 1\.733 Mb\: kumar\_2026 \(TC\-898\)'s implied 1\.691 Mb is 0\.976 of it and kapralova\_zdanska\_2025 \(TC\-899\)'s 1\.727 Mb \(at 120\.3 nm\) 0\.997\. At 19\.06 eV \(65\.05 nm\) it reads 0\.461 Mb, kumar\_2026's implied 0\.459 \(0\.996\)\. The three calculations agree within the reading \(4 %\)\. NOT TAKEN\. Table 1's other rows \(2\-4 1P, the triplets 2\-4 3S, 3P, 3D\)\: levels two photons from the ground state do not reach \(P odd; triplets spin\-forbidden\), and their thresholds would need a term average of NIST's J levels; for 2 1P, for example, Extrapolated 13\.504 \+\-0\.001, This Work 13\.48 Mb\. The 'Coulomb' column \(the Burgess\-Seaton/Peach method with Martin's energies, 3\.254 Mb for 1 1S, 9\.012 for 2 1S\) and the 'OP' column \(Fernley et al\. 1987, from TOPBASE\: 7\.45 and 9\.42 Mb\), older calculations the paper replaces\. Fig\. 1's n = 5\-25 curves and Fig\. 2 \(the n 1P series\)\: levels outside the two\-photon set; the 2s2p 1P resonance above 2\.5 Ryd and the 2s^2 1S resonance are not read\. Table 2's quantum defects \(no quantity holds them; used for the thresholds\)\. Tables 3\-6 \(recombination and cooling coefficients\)\. The full cross sections of all levels were to be 'deposited in TOPBASE at the CDS in Strasbourg in due course' \(p\. 1076\); no fit coefficients are printed \(Eq\. 1's a, b, c are not given\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- hummer\_1998/table1\_extrapolated\_1s2\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_extrapolated_1s2_1S", "material": "He", "file": "He/hummer_1998__table1_extrapolated_1s2_1S.csv", "table": "tbl_af91b1b8d77f", "quantity": "photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "method": "Drake's (1996) Hylleraas-type oscillator strengths of the series, fitted by Eq. 1 and extrapolated to threshold" } } Table 1 \(p\. 1074\), 'Extrapolated' for 1 1S\: 7\.394 \+\-0\.000 Mb at threshold, from Drake's bound\-bound oscillator strengths extrapolated to the threshold by Eq\. 1 \('benchmark values', p\. 1074\); the \+\- is the error of the fit\. Placed at the calculation's threshold, from Table 2's This Work quantum defect \(the record's notes\)\. hummer\_1998/table1\_1s2\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_1s2_1S", "material": "He", "file": "He/hummer_1998__table1_1s2_1S.csv", "table": "tbl_af91b1b8d77f", "quantity": "photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "parameters": { "method": "R-matrix close coupling, seven-orbital He+ target (Eq. 5), STGBF" } } Table 1 \(p\. 1074\), 'This Work' for 1 1S\: 7\.394 Mb at threshold, the R\-matrix calculation \(within 1 % of the Extrapolated column, 0\.5 % outside the 1S series, p\. 1075\)\. No uncertainty is stated\. Placed at the calculation's threshold, from Table 2's This Work quantum defect \(the record's notes\)\. hummer\_1998/table1\_extrapolated\_1s2s\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_extrapolated_1s2s_1S", "material": "He", "file": "He/hummer_1998__table1_extrapolated_1s2s_1S.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "initial_level": "He 1s2s 1S0 (Table 1's 2 1S)", "method": "Drake's (1996) Hylleraas-type oscillator strengths of the series, fitted by Eq. 1 and extrapolated to threshold" } } Table 1 \(p\. 1074\), 'Extrapolated' for 2 1S\: 9\.219 \+\-0\.001 Mb at threshold, from Drake's bound\-bound oscillator strengths extrapolated to the threshold by Eq\. 1 \('benchmark values', p\. 1074\); the \+\- is the error of the fit\. Placed at the calculation's threshold, from Table 2's This Work quantum defect \(the record's notes\)\. hummer\_1998/table1\_1s2s\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_1s2s_1S", "material": "He", "file": "He/hummer_1998__table1_1s2s_1S.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "parameters": { "initial_level": "He 1s2s 1S0 (Table 1's 2 1S)", "method": "R-matrix close coupling, seven-orbital He+ target (Eq. 5), STGBF" } } Table 1 \(p\. 1074\), 'This Work' for 2 1S\: 9\.253 Mb at threshold, the R\-matrix calculation \(within 1 % of the Extrapolated column, 0\.5 % outside the 1S series, p\. 1075\)\. No uncertainty is stated\. Placed at the calculation's threshold, from Table 2's This Work quantum defect \(the record's notes\)\. hummer\_1998/table1\_extrapolated\_1s3s\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_extrapolated_1s3s_1S", "material": "He", "file": "He/hummer_1998__table1_extrapolated_1s3s_1S.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "initial_level": "He 1s3s 1S0 (Table 1's 3 1S)", "method": "Drake's (1996) Hylleraas-type oscillator strengths of the series, fitted by Eq. 1 and extrapolated to threshold" } } Table 1 \(p\. 1074\), 'Extrapolated' for 3 1S\: 14\.417 \+\-0\.010 Mb at threshold, from Drake's bound\-bound oscillator strengths extrapolated to the threshold by Eq\. 1 \('benchmark values', p\. 1074\); the \+\- is the error of the fit\. Placed at the calculation's threshold, from Table 2's This Work quantum defect \(the record's notes\)\. hummer\_1998/table1\_1s3s\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_1s3s_1S", "material": "He", "file": "He/hummer_1998__table1_1s3s_1S.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "parameters": { "initial_level": "He 1s3s 1S0 (Table 1's 3 1S)", "method": "R-matrix close coupling, seven-orbital He+ target (Eq. 5), STGBF" } } Table 1 \(p\. 1074\), 'This Work' for 3 1S\: 14\.49 Mb at threshold, the R\-matrix calculation \(within 1 % of the Extrapolated column, 0\.5 % outside the 1S series, p\. 1075\)\. No uncertainty is stated\. Placed at the calculation's threshold, from Table 2's This Work quantum defect \(the record's notes\)\. hummer\_1998/table1\_extrapolated\_1s4s\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_extrapolated_1s4s_1S", "material": "He", "file": "He/hummer_1998__table1_extrapolated_1s4s_1S.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "initial_level": "He 1s4s 1S0 (Table 1's 4 1S)", "method": "Drake's (1996) Hylleraas-type oscillator strengths of the series, fitted by Eq. 1 and extrapolated to threshold" } } Table 1 \(p\. 1074\), 'Extrapolated' for 4 1S\: 20\.235 \+\-0\.053 Mb at threshold, from Drake's bound\-bound oscillator strengths extrapolated to the threshold by Eq\. 1 \('benchmark values', p\. 1074\); the \+\- is the error of the fit\. Placed at the calculation's threshold, from Table 2's This Work quantum defect \(the record's notes\)\. hummer\_1998/table1\_1s4s\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_1s4s_1S", "material": "He", "file": "He/hummer_1998__table1_1s4s_1S.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "parameters": { "initial_level": "He 1s4s 1S0 (Table 1's 4 1S)", "method": "R-matrix close coupling, seven-orbital He+ target (Eq. 5), STGBF" } } Table 1 \(p\. 1074\), 'This Work' for 4 1S\: 20\.38 Mb at threshold, the R\-matrix calculation \(within 1 % of the Extrapolated column, 0\.5 % outside the 1S series, p\. 1075\)\. No uncertainty is stated\. Placed at the calculation's threshold, from Table 2's This Work quantum defect \(the record's notes\)\. hummer\_1998/table1\_extrapolated\_1s3d\_1D ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_extrapolated_1s3d_1D", "material": "He", "file": "He/hummer_1998__table1_extrapolated_1s3d_1D.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "initial_level": "He 1s3d 1D2 (Table 1's 3 1D)", "method": "Drake's (1996) Hylleraas-type oscillator strengths of the series, fitted by Eq. 1 and extrapolated to threshold" } } Table 1 \(p\. 1074\), 'Extrapolated' for 3 1D\: 18\.132 \+\-0\.002 Mb at threshold, from Drake's bound\-bound oscillator strengths extrapolated to the threshold by Eq\. 1 \('benchmark values', p\. 1074\); the \+\- is the error of the fit\. The threshold is not stated\: Table 2 prints no D quantum defects \(the record's notes\)\. hummer\_1998/table1\_1s3d\_1D ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_1s3d_1D", "material": "He", "file": "He/hummer_1998__table1_1s3d_1D.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "parameters": { "initial_level": "He 1s3d 1D2 (Table 1's 3 1D)", "method": "R-matrix close coupling, seven-orbital He+ target (Eq. 5), STGBF" } } Table 1 \(p\. 1074\), 'This Work' for 3 1D\: 18\.13 Mb at threshold, the R\-matrix calculation \(within 1 % of the Extrapolated column, 0\.5 % outside the 1S series, p\. 1075\)\. No uncertainty is stated\. The threshold is not stated\: Table 2 prints no D quantum defects \(the record's notes\)\. hummer\_1998/table1\_extrapolated\_1s4d\_1D ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_extrapolated_1s4d_1D", "material": "He", "file": "He/hummer_1998__table1_extrapolated_1s4d_1D.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "initial_level": "He 1s4d 1D2 (Table 1's 4 1D)", "method": "Drake's (1996) Hylleraas-type oscillator strengths of the series, fitted by Eq. 1 and extrapolated to threshold" } } Table 1 \(p\. 1074\), 'Extrapolated' for 4 1D\: 35\.766 \+\-0\.026 Mb at threshold, from Drake's bound\-bound oscillator strengths extrapolated to the threshold by Eq\. 1 \('benchmark values', p\. 1074\); the \+\- is the error of the fit\. The threshold is not stated\: Table 2 prints no D quantum defects \(the record's notes\)\. hummer\_1998/table1\_1s4d\_1D ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_1s4d_1D", "material": "He", "file": "He/hummer_1998__table1_1s4d_1D.csv", "table": "tbl_af91b1b8d77f", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "parameters": { "initial_level": "He 1s4d 1D2 (Table 1's 4 1D)", "method": "R-matrix close coupling, seven-orbital He+ target (Eq. 5), STGBF" } } Table 1 \(p\. 1074\), 'This Work' for 4 1D\: 35\.75 Mb at threshold, the R\-matrix calculation \(within 1 % of the Extrapolated column, 0\.5 % outside the 1S series, p\. 1075\)\. No uncertainty is stated\. The threshold is not stated\: Table 2 prints no D quantum defects \(the record's notes\)\. hummer\_1998/fig1\_1s2\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig1_1s2_1S", "material": "He", "file": "He/hummer_1998__fig1_1s2_1S.csv", "table": "fig_30336517aae5", "digitised": "raster", "quantity": "photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "relative": 0.04, "level": "not stated" }, "parameters": { "method": "R-matrix close coupling, seven-orbital He+ target (Eq. 5), STGBF" } } Fig\. 1 \(p\. 1076\), the n = 1 1S curve \(the ground state\), read from the image from 0\.08 to 2\.45 Ryd above threshold\. Photon energy = electron energy \+ 1\.801237 Ryd \(Table 2's This Work quantum defect; the record's notes\)\. Carried to threshold it gives 0\.996 of Table 1's 7\.394 Mb\. 4 %\: the reading\. hummer\_1998/fig1\_1s2s\_1S ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig1_1s2s_1S", "material": "He", "file": "He/hummer_1998__fig1_1s2s_1S.csv", "table": "fig_30336517aae5", "digitised": "raster", "quantity": "excited_state_photoionization_cross_section", "unit": "Mb", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "relative": 0.04, "level": "not stated" }, "parameters": { "initial_level": "He 1s2s 1S0 (Fig. 1's n = 2)", "method": "R-matrix close coupling, seven-orbital He+ target (Eq. 5), STGBF" } } Fig\. 1 \(p\. 1076\), the n = 2 1S curve \(1s2s 1S\), read from the image from 0\.08 to 2\.45 Ryd above threshold; it turns down into the 2s2p 1P resonance just above 2\.5 Ryd \(p\. 1075\), which is not read\. Photon energy = electron energy \+ 0\.291490 Ryd \(Table 2's This Work quantum defect; the record's notes\)\. 4 %\: the reading\. 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.