liu_1997
========

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

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/liu_1997.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/physreva\.56\.4938 <https://doi.org/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
~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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 :doc:`review register </register>` for the checks and decisions.