liu_1997#

W.-C. Liu, Phys. Rev. A 56, 4938 (1997)

Source record · Catalogue · Review register

DOI: 10.1103/physreva.56.4938

Source kind: theory

Recorded technique: Rayleigh-Schrodinger perturbation theory at lowest order for the nonrelativistic, infinite-nuclear-mass helium atom, with mixed Hylleraas and Frankowski basis sets (385 functions per angular block for the polarizability, 307 for Table IV), 128-bit arithmetic; complex rotation (theta trajectories) above the ionisation threshold (pp. 4938-4941).

Materials in structured entries: He

Dataset quantities: photoionization_cross_section, polarizability, polarizability_imaginary

Contents: 5 datasets; 0 formulas.

Curation notes#

Static limit (p. 4941): alpha(0) = 1.383 191 94 a.u., ‘to be compared to ... Bishop and Lam, 1.383 192 a.u., and the very accurate result from Bhatia and Drachman, 1.383 192 179 3 a.u. The agreement is within 2e-7 a.u.’ No uncertainty is stated for the dynamic values; Fig. 2 shows them inside Glover and Weinhold’s rigorous bounds.

Units: atomic units for the infinite-mass, nonrelativistic atom, both for omega and for alpha. For physical 4He, in the reduced-mass approximation, alpha scales by (1 + m_e/M)^3 = 1.000411 and omega by (1 + m_e/M)^-1 (stone_2004 Eqs. 6-7): the physical static value is 1.38376 (Lach et al. 2004, quoted in wang_2021), 4.1e-4 above the printed 1.38319; near the first resonance the frequency scaling changes alpha by a few parts in 1e3 (at omega = 0.75 a.u.). A fit must apply these corrections or treat the values as infinite-mass ones (TC-16).

Above threshold (Table II) the polarizability is complex and its real part is negative (-0.43 to -0.81 a.u.); the format has no quantity for a real part above threshold, so only the imaginary part is extracted. The cross sections follow sigma = (4 pi omega / c) Im alpha (Eq. 17): the printed Im alpha reproduces the printed cross section at all eight energies to the last digit (checked 2026-09-24). Tables III and IV (q >= 3) are nonlinear susceptibilities, outside this extraction.

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

liu_1997/alpha#

{
  "id": "alpha",
  "material": "He",
  "file": "He/liu_1997__alpha.csv",
  "table": "tbl_c824036c5cc9",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "hartree",
  "use": "primary"
}

Table I, omega = 0 to 0.75 a.u.; nonrelativistic, infinite nuclear mass (see the source notes on the mass scaling). The static value is 2e-7 below Bhatia and Drachman’s 1.3831921793 as quoted by the paper.

liu_1997/alpha_imaginary#

{
  "id": "alpha_imaginary",
  "material": "He",
  "file": "He/liu_1997__alpha_imaginary.csv",
  "table": "tbl_936a0db2e146",
  "quantity": "polarizability_imaginary",
  "unit": "au",
  "abscissa_unit": "eV",
  "use": "primary"
}

Table II, imaginary part of the complex polarizability at 27-58 eV (the real parts, -0.57, -0.758, -0.809, -0.739, -0.645, -0.555, -0.473, -0.426, are not extracted).

liu_1997/cross_section#

{
  "id": "cross_section",
  "material": "He",
  "file": "He/liu_1997__cross_section.csv",
  "table": "tbl_936a0db2e146",
  "quantity": "photoionization_cross_section",
  "unit": "Mb",
  "abscissa_unit": "eV",
  "use": "check"
}

Table II, ‘present work’: Eq. (17) applied to alpha_imaginary, so not independent of it.

liu_1997/samson_cross_section#

{
  "id": "samson_cross_section",
  "material": "He",
  "file": "He/liu_1997__samson_cross_section.csv",
  "table": "tbl_936a0db2e146",
  "quantity": "photoionization_cross_section",
  "unit": "Mb",
  "abscissa_unit": "eV",
  "use": "reproduced",
  "reproduced_from": [
    "J. A. R. Samson, Z. X. He, L. Yin and G. N. Haddad, J. Phys. B 27, 887 (1994)"
  ]
}

Table II, ‘Samson et al. [32]’, measured; the original is not in the library.

liu_1997/chi1#

{
  "id": "chi1",
  "material": "He",
  "file": "He/liu_1997__chi1.csv",
  "table": "tbl_5f861154394b",
  "quantity": "polarizability",
  "unit": "cm3",
  "scale": 1e-25,
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check"
}

Table IV, q = 1: |chi_1| in esu (a polarizability volume, cm^3) at 1064, 532, 248 nm and at the ‘low frequency limit’, printed ‘lambda ~ 46 um’ and stored as 46000 nm. The same calculation as Table I with a smaller basis (307 functions); 2.04968e-25 cm^3 is 1.3832 a.u.

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.