musulin_1964
============

B\. Musulin and S\. T\. Epstein, Phys\. Rev\. 136, A966 \(1964\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/musulin_1964.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/physrev\.136\.a966 <https://doi.org/10.1103/physrev.136.a966>`__

**Source kind:** theory

**Recorded technique:** Shielding approximation \(Dalgarno and Stewart\) extended to the dynamic polarizability\: first\-order corrections to two independent hydrogenic electrons of effective charge zeta, zeta fixed by making the first\-order correction vanish; the result is a power series in omega through omega^4 \(pp\. A966\-A967\)\.

**Materials in structured entries:** He

**Dataset quantities:** None recorded.

**Contents:** 0 datasets; 1 formula.

Curation notes
--------------

No tabulated values\: the paper gives one formula \(below\) and a figure comparing it with Cuthbertson and Cuthbertson \(1932\), Wheeler \(1933\) and Karplus and Kolker \(1963\)\. Stated accuracy 'about 10%' \(abstract\)\. Hartree atomic units, with lambda \(A\) = 456/omega \(footnote 11\); zeta runs from 1\.641 at omega = 0 to 1\.629 at omega = 0\.456\. No dataset is extracted\. mansfield\_peck\_1969 \(Table IV\) quotes 2\.983e\-5 for this theory at 5462 A, but the formula gives 3\.130e\-5 there \(checked 2026\-09\-24\)\: the quoted value does not come from this formula as printed\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

No datasets are recorded.

Formulas
--------

musulin\_1964/shielding
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "shielding",
     "material": "He",
     "equation": "unnumbered, p. A967",
     "printed": "(n^2 - 1) x 10^4 = 0.50064 {zeta^-4 (9 + b0/zeta) + omega^2 zeta^-8 (319/6 + b2/zeta) + omega^4 zeta^-12 (297541/864 + b4/zeta)}, b0 = 207/16 + 36 (zeta - Z), b2 = 3983/24 + (1276/3)(zeta - Z), b4 = 4673097941/2764800 + (297541/72)(zeta - Z); zeta from b0 + omega^2 b2/zeta^4 + omega^4 b4/zeta^8 = 0 (solved through omega^4)",
     "variable": "omega: photon energy in hartree (lambda in A = 456/omega); Z = 2 for helium",
     "state": "1atm_0C",
     "density": "ideal",
     "range": "low frequencies, well below the first resonance ('it seemed reasonable to confine our attention to low frequencies', p. A967)",
     "coefficients": {
       "prefactor": "0.50064",
       "c0": "9",
       "c2": "319/6",
       "c4": "297541/864",
       "b0": "207/16 + 36 (zeta - Z)",
       "b2": "3983/24 + (1276/3)(zeta - Z)",
       "b4": "4673097941/2764800 + (297541/72)(zeta - Z)"
     },
     "check": "At omega = 0 the zeta equation gives zeta = 1.640625, the printed 1.641; n - 1 = 3.110e-5 static and 3.130e-5 at 5462 A, 10 % below experiment, as the paper says. The prefactor 0.50064e-4 is 4 pi N0 a0^3 with N0 = 2.689e19 cm^-3 (Loschmidt's number, 0 degrees C, 1 atm). Checked 2026-09-24."
   }

The check solved the zeta equation numerically in full, not truncated at omega^4 as the paper did; at 5462 A the difference is far below the method's 10 %\.

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.