piszczatowski_2015 ================== K\. Piszczatowski, M\. Puchalski, J\. Komasa, B\. Jeziorski and K\. Szalewicz, "Frequency\-Dependent Polarizability of Helium Including Relativistic Effects with Nuclear Recoil Terms", Phys\. Rev\. Lett\. 114, 173004 \(2015\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevLett\.114\.173004 `__ **Source kind:** theory **Recorded technique:** Ab initio frequency\-dependent polarizability of the helium atom as the series alpha\(omega\) = alpha\_0 \+ alpha\_2 omega^2 \+ \.\.\., alpha\_k^\(0\) = 2 \ \(Eq\. 5\), with fully and stochastically optimized Slater\-geminal bases \(up to 600 and 800 terms\); relativistic \(Breit\-Pauli\) corrections alpha\_k^\(20\) and the recoil terms alpha\_0^\(21\), alpha\_2^\(21\); static QED terms from Lach et al\. \(2004\) with a recomputed field derivative of the Bethe logarithm \(pp\. 1\-3\)\. The abridged account of puchalski\_2016, by the same authors\. **Materials in structured entries:** He **Dataset quantities:** polarizability **Contents:** 1 dataset; 0 formulas. Curation notes -------------- Superseded by Puchalski et al\. \(2016\) \(puchalski\_2016\), which gives the details and adds the QED correction to the dispersion, alpha\_2^\(30\) omega^2 = 0\.32 u a0^3 at 632\.9908 nm, which this Letter neglected \('slightly outside the uncertainty range given in Ref\. \[13\]', puchalski\_2016 p\. 2\)\. Both values are kept here as a check only\. Units \(p\. 1\)\: atomic units, 'we never use reduced atomic units'; 4He, 1/M = 1/7294\.2995361, c = 137\.0359991; A\_k = f^k alpha\_k with f = 2 pi c a0/nm = 45\.56335253 \(lambda in nm, a0 = 0\.05291772109 nm\), vacuum wavelengths \(the He\-Ne line 632\.9908 nm\)\. Table I components\: static nonrelativistic 1\.383 809 98641\(1\), 1/c^2 \-0\.000 080 4534\(1\) \(including the recoil \-0\.000 000 0935\(1\)\), 1/c^3 0\.000 030 655\(1\) \(Lach et al\. 2004 except the field derivative of the Bethe logarithm, 0\.000 000 182\(1\)\), 1/c^4 0\.000 000 56\(14\), finite nuclear size 0\.000 000 0217\(1\), total 1\.383 760 77\(14\); lambda^\-2 nonrelativistic 0\.007 995 7979\(1\), relativistic \-0\.000 000 1721\(1\) \(recoil \-0\.000 000 00075\(1\)\), total 0\.007 995 6258\(1\); lambda^\-4 0\.000 054 8363\(1\), 0\.000 000 00014\(1\), 0\.000 054 8364\(1\); lambda^\-6 0\.000 000 4076\(1\); lambda^\-8 0\.000 000 0032\(1\); alpha\(lambda\) \- alpha\(0\) 0\.008 050 8730\(1\) \(BD 0\.008 050 871\); total 1\.391 811 64\(14\) \(BD 1\.391 780 800\)\. The static total equals puchalski\_2016's to all printed digits\. alpha\_8^\(0\)\.\.alpha\_14^\(0\) \(p\. 3\) are the values printed in puchalski\_2016\. The abstract prints alpha\(632\.9908 nm\) = '1\.39181141 a\.u\.' \(checked on the pdf text\), Table I 1\.391 811 64\(14\); puchalski\_2016 \(Table VII note e\) confirms that the abstract 'contains a typographical error'\. The table value is extracted\. Table II \(virial expansion of n; not extracted\: a\_r = \(2/3\) a\_n = A\_eps \+ A\_mu includes the magnetizability, and b\_n, c\_n are coefficients of n, not the Lorentz\-Lorenz B\_R; see puchalski\_2016's notes\)\: a\_r\(0\) present 0\.517 246 21\(6\), experimental \(Schmidt et al\. 2007\) 0\.517 245 5\(47\); a\_r\(632\.9908\) present 0\.520 255 64\(6\), experimental \[19,20\] \(Achtermann et al\. 1991, 1993\) 0\.521 3\(1\), \[21\] \(Birch 1991\) 0\.522 0\(3\); a\_r\(546\.2268\) present 0\.521 297 25\(6\), experimental \[22\] \(Leonard 1974\) 0\.521 57\(15\); b\_n\(0\) 273\.16 K 0\.0245\(2\); b\_n\(632\.9908\) 273\.16 K 0\.0238\(2\), 302 K 0\.0184\(2\), 323 K 0\.0151\(2\), experimental \[20\] 0\.000\(15\); c\_n\(0\) 273\.16 K \-0\.93\(25\)\. Notes\: a\_n = 8\.694 292 2\(9\) a0^3 = 0\.775 869 31\(8\)\(4\) cm^3/mol \(static\) and 8\.744 8758\(9\) a0^3 = 0\.780 383 35\(8\)\(4\) cm^3/mol \(632\.9908 nm\); chi = \-0\.000 021 194\(1\) a0^3 \(Bruch and Weinhold\); 1 cm^3/mol = 11\.205 8721 a0^3 \(the factor 1/\(N\_A a0^3\) between a molar and a per\-atom volume; 8\.6942922/0\.77586931 = 11\.20587\); b\_eps = \-0\.0978\(2\) cm^3/mol and c\_eps = \-1\.34\(36\) cm^6/mol^2 at 273\.16 K, b\_eps\(303\) = \-0\.1065\(2\), b\_eps\(323\) = \-0\.1107\(2\) \(Rizzo et al\. 2002\); the b\_n row says 302 K where the note says 303 K\. puchalski\_2016 revises b\_n\(0\) to 0\.0244\(3\), b\_n\(323 K\) to 0\.0150\(3\) and c\_n to \-0\.96\(25\)\. The 546\.2268 nm 'experimental' a\_r is 'inferred from measured value of n \- 1 = 34\.895\(10\) x 10^\-4 at T = 273\.16 K' \(note e\)\: the exponent should be 10^\-6, and puchalski\_2016 \(p\. 12\) says this value was 'mistakenly' taken from Leonard as a measurement when it is a theoretical value cited by him\. The a\_r\(546\.2268\) 'present' value, converted to A\_eps by adding 0\.0000079224 cm^3/mol, is a second theoretical wavelength \(without alpha\_2^\(30\)\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- piszczatowski\_2015/alpha ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha", "material": "He", "file": "He/piszczatowski_2015__alpha.csv", "table": "tbl_df068b216aa3", "quantity": "polarizability", "unit": "au", "abscissa_unit": "nm", "wavelength_medium": "vacuum", "use": "check", "uncertainty": { "column": true, "level": "not stated" } } Table I totals for 4He\: static 1\.383 760 77\(14\) and alpha\(632\.9908 nm\) = 1\.391 811 64\(14\) \(relativistic with recoil, static QED, one\-loop 1/c^4, finite nuclear size; no QED in the dispersion\)\. A check\: superseded by puchalski\_2016 \(static identical, dynamic 1\.39181197\(14\) with the dispersion QED term\)\. The uncertainty 0\.14 u a0^3 is dominated by the 25 % allowance on the 1/c^4 term \(p\. 2\), level not stated\. 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.