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 · Catalogue · 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 <psi| z R^(k+1) z |psi> (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Superseded by Puchalski et al.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

{
  "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 review register for the checks and decisions.