berkowitz_1997 ============== J\. Berkowitz, "Sum rules and the oscillator strength distribution in helium", J\. Phys\. B\: At\. Mol\. Opt\. Phys\. 30, 881 \(1997\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` No DOI is recorded. **Source kind:** compilation **Recorded technique:** Evaluation of the oscillator\-strength sums S\(p\), p = \-2\.\.\+2, of helium from calculated discrete oscillator strengths \(Kono and Hattori 1984, Drake 1996\), the measured photoabsorption cross sections of Samson et al\. \(1994\) and Bizeau and Wuilleumier \(1995\), and the calculated cross sections of Hino and collaborators, each region fitted by a power series in y = IP/E \(IP = 24\.5874 eV\) and integrated \(pp\. 881\-888\)\. **Materials in structured entries:** He **Dataset quantities:** cauchy\_moment, oscillator\_strength, polarizability **Contents:** 18 datasets; 9 formulas. Curation notes -------------- Identity unverified by the library; the downloaded pdf's header gives 'J\. Phys\. B\: At\. Mol\. Opt\. Phys\. 30 881' \(1997\), received 15 May 1996\. No DOI recorded\. Pages are counted from 881\. S\(p\) is 'defined with the excitation energy measured in Rydberg units' \(p\. 882\)\: the datasets convert with scale 2^\-p to atomic units\. E/R in Table 1 uses R = 13\.6057 eV \(Table 2's weighted columns check with it\)\. Pekeris's exact values \(p\. 881\-882\)\: S\(\-1\) = 0\.752 497, S\(0\) = 2, S\(\+1\) = 8\.167 45, S\(\+2\) = 121\.336\. The 'exact' S\(\-2\) = 0\.345 778 is derived from Miller's polarizability with a0 = 0\.529 177 249e\-8 cm \(p\. 889\)\. The author's recommended totals \(bold in Table 3\) reach 99\.78 % \(S\(\-2\)\), 99\.40 % \(S\(\-1\)\), 99\.07 % \(S\(0\)\), 98\.6 % \(S\(\+1\)\) and 97\.4 % \(S\(\+2\)\) of the exact values; the older Migneron and Levinger sums \(Table 3 column d\) are in migneron\_1965 and are not extracted again\. Table 3's partial sums are not extracted\. Their merged cells were read on the image; the IP\-120 eV S\(\-1\) of Chan et al\. is printed 0\.4476 in the table but 0\.4776 in the text \(p\. 888\), and the table is probably wrong \(0\.4747 for Samson's data, 'the differences are \< 1%'\)\. Table 4's power\-series fits are recorded as formulas; their integrals reproduce the Table 3 partial sums for the df/d\(E/R\) fits \(checked 2026\-09\-24\), but not for the 3000\-12000 eV \(E/R\)^2 df/d\(E/R\) fit\. Also in the text\: Miller's 'exact' polarizability, printed '0\.020 4956 x 10^\-24 cm^3' \(p\. 889\), a factor 10 too small \(erratum below\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- berkowitz\_1997/f\_kono\_hattori\_1984 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "f_kono_hattori_1984", "material": "He", "file": "He/berkowitz_1997__f_kono_hattori_1984.csv", "table": "tbl_989659e9200e", "quantity": "oscillator_strength", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "A. Kono and S. Hattori, Phys. Rev. A 29, 2981 (1984)" ] } Table 1 column c, 1 1S \-\> n 1P, n = 2\-9 \(the index column is n\)\. The excitation energies E/R \(R = 13\.6057 eV\) are in the printed cells\: the format has no Rydberg energy unit\. berkowitz\_1997/f\_extrapolated ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "f_extrapolated", "material": "He", "file": "He/berkowitz_1997__f_extrapolated.csv", "table": "tbl_989659e9200e", "quantity": "oscillator_strength", "abscissa": "label", "use": "check" } Table 1 column c in parentheses, n = 10\-20\: the author's fit f\_n = a/n\*^3 \+ b/n\*^5 to Kono and Hattori's n = 4\-9, extrapolated \(p\. 886\); energies from a quantum\-defect fit, also in parentheses\. berkowitz\_1997/f\_drake\_1996 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "f_drake_1996", "material": "He", "file": "He/berkowitz_1997__f_drake_1996.csv", "table": "tbl_989659e9200e", "quantity": "oscillator_strength", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "G. W. F. Drake (ed.), Atomic, Molecular and Optical Physics Handbook (AIP, New York, 1996), ch. 11" ] } Table 1 column d, n = 2\-7; the values the author adopts for n = 2\-7\. berkowitz\_1997/f\_schiff\_1971 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "f_schiff_1971", "material": "He", "file": "He/berkowitz_1997__f_schiff_1971.csv", "table": "tbl_989659e9200e", "quantity": "oscillator_strength", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "B. Schiff, C. L. Pekeris and Y. Accad, Phys. Rev. A 4, 885 (1971)" ] } Table 1 column b, n = 2\-5\. berkowitz\_1997/f\_fernley\_1987 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "f_fernley_1987", "material": "He", "file": "He/berkowitz_1997__f_fernley_1987.csv", "table": "tbl_989659e9200e", "quantity": "oscillator_strength", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "J. A. Fernley, K. T. Taylor and M. J. Seaton, J. Phys. B 20, 6457 (1987) (Berkowitz prints 6547)" ] } Table 1 column e, n = 2\-7 \(R\-matrix; about 1 % above the others, p\. 886\)\. berkowitz\_1997/f\_chan\_1991 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "f_chan_1991", "material": "He", "file": "He/berkowitz_1997__f_chan_1991.csv", "table": "tbl_989659e9200e", "quantity": "oscillator_strength", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "N. F. Chan, G. Cooper and C. E. Brion, Phys. Rev. A 44, 186 (1991)" ], "uncertainty": { "column": true, "level": "not stated" } } Table 1 column f, measured by electron energy loss, n = 2\-7, with the printed \+\- errors \(level not stated\)\. berkowitz\_1997/f\_excess ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "f_excess", "material": "He", "file": "He/berkowitz_1997__f_excess.csv", "table": "tbl_2a3db8fd2b0e", "quantity": "oscillator_strength", "scale": 0.0001, "abscissa_unit": "eV", "use": "check" } Table 2\: excess oscillator strength over the continuum of the 2snp \(n = 2\-10\) autoionising series, from Morgan and Ederer's \(1984\) profile parameters \(q about \-2\.5, rho^2 = 1\.0\) and the author's continuum estimates \(p\. 887\); sum 0\.0058\. berkowitz\_1997/sum\_rule\_m2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sum_rule_m2", "material": "He", "file": "He/berkowitz_1997__sum_rule_m2.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 4, "abscissa": "order", "abscissa_unit": "1", "use": "check" } Table 3 'Total sum' \(recommended\), S\(\-2\) in Ry^\-2; scale 2^\(2\) gives atomic units\. berkowitz\_1997/miller\_sum\_rule\_m2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "miller_sum_rule_m2", "material": "He", "file": "He/berkowitz_1997__miller_sum_rule_m2.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 4, "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "T. M. Miller, CRC Handbook of Chemistry and Physics, 76th ed. (CRC, Boca Raton, 1995), pp. 10-192" ] } Table 3 'Exact sum' S\(\-2\) = 0\.345778 \(footnote h\), derived by the author from Miller's polarizability \(p\. 889\); the same information as the miller\_alpha text point\. berkowitz\_1997/sum\_rule\_m1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sum_rule_m1", "material": "He", "file": "He/berkowitz_1997__sum_rule_m1.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 2, "abscissa": "order", "abscissa_unit": "1", "use": "check" } Table 3 'Total sum' \(recommended\), S\(\-1\) in Ry^\-1; scale 2^\(1\) gives atomic units\. berkowitz\_1997/pekeris\_sum\_rule\_m1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pekeris_sum_rule_m1", "material": "He", "file": "He/berkowitz_1997__pekeris_sum_rule_m1.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 2, "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "C. L. Pekeris, Phys. Rev. 115, 1216 (1959)" ] } Table 3 'Exact sum' S\(\-1\) \(footnote i\), from Pekeris's 1078\-term wave function; also migneron\_1965's pekeris\_sum\_rule\_m1 \(fewer digits\)\. berkowitz\_1997/sum\_rule\_0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sum_rule_0", "material": "He", "file": "He/berkowitz_1997__sum_rule_0.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 1, "abscissa": "order", "abscissa_unit": "1", "use": "check" } Table 3 'Total sum' \(recommended\), S\(0\) in Ry^0; scale 2^\(0\) gives atomic units\. berkowitz\_1997/pekeris\_sum\_rule\_0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pekeris_sum_rule_0", "material": "He", "file": "He/berkowitz_1997__pekeris_sum_rule_0.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 1, "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "C. L. Pekeris, Phys. Rev. 115, 1216 (1959)" ] } Table 3 'Exact sum' S\(0\) \(footnote i\), from Pekeris's 1078\-term wave function; also migneron\_1965's pekeris\_sum\_rule\_0 \(fewer digits\)\. berkowitz\_1997/sum\_rule\_1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sum_rule_1", "material": "He", "file": "He/berkowitz_1997__sum_rule_1.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 0.5, "abscissa": "order", "abscissa_unit": "1", "use": "check" } Table 3 'Total sum' \(recommended\), S\(1\) in Ry^1; scale 2^\(\-1\) gives atomic units\. berkowitz\_1997/pekeris\_sum\_rule\_1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pekeris_sum_rule_1", "material": "He", "file": "He/berkowitz_1997__pekeris_sum_rule_1.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 0.5, "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "C. L. Pekeris, Phys. Rev. 115, 1216 (1959)" ] } Table 3 'Exact sum' S\(1\) \(footnote i\), from Pekeris's 1078\-term wave function; also migneron\_1965's pekeris\_sum\_rule\_1 \(fewer digits\)\. berkowitz\_1997/sum\_rule\_2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sum_rule_2", "material": "He", "file": "He/berkowitz_1997__sum_rule_2.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 0.25, "abscissa": "order", "abscissa_unit": "1", "use": "check" } Table 3 'Total sum' \(recommended\), S\(2\) in Ry^2; scale 2^\(\-2\) gives atomic units\. berkowitz\_1997/pekeris\_sum\_rule\_2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pekeris_sum_rule_2", "material": "He", "file": "He/berkowitz_1997__pekeris_sum_rule_2.csv", "table": "tbl_6523ca2ec08b", "quantity": "cauchy_moment", "unit": "au", "scale": 0.25, "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "C. L. Pekeris, Phys. Rev. 115, 1216 (1959)" ] } Table 3 'Exact sum' S\(2\) \(footnote i\), from Pekeris's 1078\-term wave function; also migneron\_1965's pekeris\_sum\_rule\_2 \(fewer digits\)\. berkowitz\_1997/miller\_alpha ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "miller_alpha", "material": "He", "table": "text", "quantity": "polarizability", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "angstrom", "use": "reproduced", "reproduced_from": [ "T. M. Miller, CRC Handbook of Chemistry and Physics, 76th ed. (CRC, Boca Raton, 1995), pp. 10-192" ] } 1 inline points in the source record. 'The polarizability of He tabulated by Miller \(1985\) and labelled exact is alpha = 0\.020 4956 x 10^\-24 cm^3' \(p\. 889\); corrected by the erratum\. The table note says 'Miller \(1985\)', the reference list 'Miller T M 1995'\. Formulas -------- berkowitz\_1997/ip\_120 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ip_120", "material": "He", "equation": "Table 4, p. 889", "printed": "df/d(E/R) = 0.307867 y^2 + 3.025638 y^3 + -3.86086 y^4 + 1.447231 y^5", "variable": "y = IP/E, IP = 24.5874 eV, E the photon energy; E/R with R = 13.6057 eV; df/d(E/R) per Rydberg", "state": "none (per atom)", "density": "none", "range": "IP-120 eV", "coefficients": { "c2": "0.307867", "c3": "3.025638", "c4": "-3.86086", "c5": "1.447231" }, "check": "Integrated over IP-120 eV: S(0) = 1.4085 (the text's 'integrated oscillator strength for the underlying continuum', p. 887); at threshold df/d(E/R) = 0.9199, i.e. 7.42 Mb with the paper's 8.0672845 Mb factor (text: 7.40 Mb from the discrete series). Checked 2026-09-24." } Power\-series fit to J\. A\. R\. Samson, Z\. X\. He, L\. Yin and G\. N\. Haddad, J\. Phys\. B 27, 887 \(1994\) \(Table 4 source column\); the printed coefficients use thin\-space digit groups\. berkowitz\_1997/b\_120\_280 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "b_120_280", "material": "He", "equation": "Table 4, p. 889", "printed": "df/d(E/R) = 0.467252 y^2 + -8.05829 y^3 + 95.45096 y^4 + -242.751 y^5", "variable": "y = IP/E, IP = 24.5874 eV, E the photon energy; E/R with R = 13.6057 eV; df/d(E/R) per Rydberg", "state": "none (per atom)", "density": "none", "range": "120-280 eV", "coefficients": { "c2": "0.467252", "c3": "-8.05829", "c4": "95.45096", "c5": "-242.751" }, "check": "Integrated over 120-280 eV: S(-2..2) = 0.00090, 0.01008, 0.1182, 1.459, 19.06 in Ry units, Table 3 column f (0.0009, 0.0100, 0.1182, 1.459, 19.05). Checked 2026-09-24." } Power\-series fit to J\. Bizeau and F\. J\. Wuilleumier, J\. Electron Spectrosc\. Relat\. Phenom\. 71, 205 \(1995\) \(Table 4 source column\); the printed coefficients use thin\-space digit groups\. berkowitz\_1997/s\_120\_280 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "s_120_280", "material": "He", "equation": "Table 4, p. 889", "printed": "df/d(E/R) = 0.063766 y^2 + 1.389979 y^3 + 22.45416 y^4 + -66.4569 y^5", "variable": "y = IP/E, IP = 24.5874 eV, E the photon energy; E/R with R = 13.6057 eV; df/d(E/R) per Rydberg", "state": "none (per atom)", "density": "none", "range": "120-280 eV", "coefficients": { "c2": "0.063766", "c3": "1.389979", "c4": "22.45416", "c5": "-66.4569" }, "check": "Integrated over 120-280 eV: 0.00085, 0.00959, 0.1126, 1.391, 18.19, Table 3's Samson partial sums (0.0008_5, 0.0096, 0.1126, 1.391, 18.19). Checked 2026-09-24." } Power\-series fit to J\. A\. R\. Samson, Z\. X\. He, L\. Yin and G\. N\. Haddad, J\. Phys\. B 27, 887 \(1994\) \(Table 4 source column\); the printed coefficients use thin\-space digit groups\. berkowitz\_1997/h\_280\_1000 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "h_280_1000", "material": "He", "equation": "Table 4, p. 889", "printed": "df/d(E/R) = -0.014835 y^2 + 3.780229 y^3 + 2.485896 y^4 + -36.52446 y^5", "variable": "y = IP/E, IP = 24.5874 eV, E the photon energy; E/R with R = 13.6057 eV; df/d(E/R) per Rydberg", "state": "none (per atom)", "density": "none", "range": "280-1000 eV", "coefficients": { "c2": "-0.014835", "c3": "3.780229", "c4": "2.485896", "c5": "-36.52446" }, "check": "With the 1000-12000 eV fit, S(0) from 280 eV to 12 keV = 0.0243 against Table 3's 0.0242 (280 eV to infinity, Hino). Checked 2026-09-24." } Power\-series fit to Ishihara et al\. \(1991\), Hino \(1993\), Hino et al\. \(1993\)\: calculated He\+ \+ He2\+ cross sections \(Table 4 source column\); the printed coefficients use thin\-space digit groups\. berkowitz\_1997/h\_1000\_12000 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "h_1000_12000", "material": "He", "equation": "Table 4, p. 889", "printed": "df/d(E/R) = 0.001699 y^2 + 1.977647 y^3 + 88.76041 y^4 + -1458.595 y^5", "variable": "y = IP/E, IP = 24.5874 eV, E the photon energy; E/R with R = 13.6057 eV; df/d(E/R) per Rydberg", "state": "none (per atom)", "density": "none", "range": "1000-12000 eV", "coefficients": { "c2": "0.001699", "c3": "1.977647", "c4": "88.76041", "c5": "-1458.595" }, "check": "See h_280_1000. Evaluated at 12 keV it gives 2.6e-8, about twice Salpeter and Zaidi's asymptotic formula (1.15e-8), so the fit should not be used near its upper end without care. Checked 2026-09-24." } Power\-series fit to Ishihara et al\. \(1991\), Hino \(1993\), Hino et al\. \(1993\)\: calculated He\+ \+ He2\+ cross sections \(Table 4 source column\); the printed coefficients use thin\-space digit groups\. berkowitz\_1997/h2\_280\_3000 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "h2_280_3000", "material": "He", "equation": "Table 4, p. 889", "printed": "(E/R)^2 df/d(E/R) = 6.159374 y + 241.6193 y^2 + -3370.06 y^3 + 14110.29 y^4", "variable": "y = IP/E, IP = 24.5874 eV, E the photon energy; E/R with R = 13.6057 eV; df/d(E/R) per Rydberg", "state": "none (per atom)", "density": "none", "range": "280-3000 eV", "coefficients": { "c1": "6.159374", "c2": "241.6193", "c3": "-3370.06", "c4": "14110.29" }, "check": "Integrated over 280-3000 eV: S(+2) = 43.64; not separately checkable (the text gives 59.22 for 0.28-12 keV). Checked 2026-09-24." } Power\-series fit to Ishihara et al\. \(1991\), Hino \(1993\), Hino et al\. \(1993\)\: calculated He\+ \+ He2\+ cross sections \(Table 4 source column\); the printed coefficients use thin\-space digit groups\. berkowitz\_1997/h2\_3000\_12000 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "h2_3000_12000", "material": "He", "equation": "Table 4, p. 889", "printed": "(E/R)^2 df/d(E/R) = 2856.42 y + 1099.927 y^2 + -81877.5 y^3 + 2670860 y^4", "variable": "y = IP/E, IP = 24.5874 eV, E the photon energy; E/R with R = 13.6057 eV; df/d(E/R) per Rydberg", "state": "none (per atom)", "density": "none", "range": "3000-12000 eV", "coefficients": { "c1": "2856.42", "c2": "1099.927", "c3": "-81877.5", "c4": "2670860" }, "check": "DOES NOT REPRODUCE: as printed (y..y^4) it gives df/d(E/R) = 4.8e-4 at 3 keV, 300 times the neighbouring fits (1.3e-6 to 1.5e-6), and S(+2) = 7164 over 3-12 keV against the text's 59.22 - 43.64 = 15.6. Read as y^2..y^5 it gives 31.8, still twice too large. No single correction found. Checked 2026-09-24." } Power\-series fit to Ishihara et al\. \(1991\), Hino \(1993\), Hino et al\. \(1993\)\: calculated He\+ \+ He2\+ cross sections \(Table 4 source column\); the printed coefficients use thin\-space digit groups\. berkowitz\_1997/salpeter\_zaidi ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "salpeter_zaidi", "material": "He", "equation": "unnumbered, p. 884", "printed": "df/d(E/R) = 287.6 (E/R)^-3.5 - 1807.0 (E/R)^-4.0 + 6836.25 (E/R)^-4.5", "variable": "E/R: photon energy in Rydberg units", "state": "none (per atom)", "density": "none", "range": "asymptotic, above about 13.6 keV ('purports to be satisfactory beyond 13.6 keV')", "coefficients": { "a35": "287.6", "a40": "-1807.0", "a45": "6836.25" }, "check": "Not checkable against printed values here." } Reproduced\: Salpeter and Zaidi's asymptotic photoionisation formula \(E\. E\. Salpeter and M\. H\. Zaidi, Phys\. Rev\. 125, 248 \(1962\)\), in the author's units\. berkowitz\_1997/samson\_asymptotic ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "samson_asymptotic", "material": "He", "equation": "unnumbered, p. 884", "printed": "df/d(E/R) = 173.0 (E/R)^-3.5", "variable": "E/R: photon energy in Rydberg units", "state": "none (per atom)", "density": "none", "range": "3-8 keV (fit to photoelectric data)", "coefficients": { "a35": "173.0" }, "check": "Not checkable here; 60 % of Salpeter and Zaidi's leading term, as the text says." } Reproduced\: Samson et al\. \(1994\)'s analytical fit, in the author's units\. Corrections ----------- .. code-block:: text [ { "dataset": "miller_alpha", "row": "1", "column": "value", "printed": "0.0204956", "corrected": "0.204956", "reason": "The printed polarizability is a factor 10 too small: helium's static polarizability volume is 0.205e-24 cm^3 (1.383 a.u.).", "evidence": "The paper's own derivation from it, S(-2) = alpha/(4 a0^3) with a0 = 0.529177249e-8 cm, gives its printed 'exact' S(-2) = 0.345778 only for 0.204956e-24 cm^3 (0.204956e-24/(4 x 1.48185e-25) = 0.34578; checked 2026-09-24)." } ] 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.