ammosov_1986
============

M\. V\. Ammosov, N\. B\. Delone and V\. P\. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field", Sov\. Phys\. JETP 64, 1191 \(1986\) \[Zh\. Eksp\. Teor\. Fiz\. 91, 2008 \(1986\)\]

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/ammosov_1986.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

No DOI is recorded.

**Source kind:** theory

**Recorded technique:** The ADK formula\: Perelomov, Popov and Terent'ev's tunnel\-ionisation probability in an alternating field \(Eq\. \(1\)\) with the asymptotic coefficient C\_n\*l\* of a complex atom or ion obtained in the quasiclassical approximation \(n\* \>\> 1, Eq\. \(11\)\) and, for arbitrary l, with the effective l\* = n\*\_0 \- 1 \(Eqs\. \(19\)\-\(21\)\); compared with numerical coefficients \(Radtsig and Smirnov's handbook\) and with measured intensities for noble gases and their ions\.

**Materials in structured entries:** Ar, Ar\+, He, Kr, Kr\+, Ne, Ne\+, Xe, Xe\+

**Dataset quantities:** tunnelling\_structure\_coefficient

**Contents:** 18 datasets; 0 formulas.

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

The English translation, Sov\. Phys\. JETP 64 \(6\), 1191\-1194 \(December 1986\) = PDF pages 1\-4 \(no DOI\)\. The ADK paper\.

EXTRACTED\. Table II \(p\. 1193\)\: for He, Ne, Ne\+, Ar, Ar\+, Kr, Kr\+, Xe and Xe\+ \(all curated\), the numerical coefficient of the handbook converted to Eq\. \(3\) \(reproduced, with its \+\- error\) and this paper's Eq\. \(11\) value, each with the printed n\*\.

THE EQUATIONS \(pp\. 1191\-1193; atomic units, E the binding energy, Z the charge of the atomic residue, script\-E the field amplitude\)\. Eq\. \(1\)\: w = C\_n\*l\*^2 \(3 script\-E/\(pi script\-E\_0\)\)^\(1/2\) E \(2l \+ 1\)\(l \+ \|m\|\)\!/\(2^\|m\| \|m\|\! \(l \- \|m\|\)\!\) \(2 script\-E\_0/script\-E\)^\(2n\* \- \|m\| \- 1\) exp\(\-2 script\-E\_0/\(3 script\-E\)\), linear polarisation, per unit time\. Eq\. \(2\)\: n\* = Z \(2E\)^\(\-1/2\), script\-E\_0 = \(2E\)^\(1/2\)\. Eq\. \(3\)\: Psi\_n\*lm\(r\) = C\_n\*l\* \(Z/n\*\)^\(3/2\) \(Z/n\*\)^\(n\* \- 1\) exp\(\-Z r/n\*\) Y\_lm\(r/r\) as printed \(image checked; the second factor lacks the r that Eq\. \(10\), R\_nl = \(Z/2 pi\)^\(1/2\) \(n\* r\)^\(\-1\) exp\(\-Z r/n\*\) \(2 Z r e/n\*\)^n\*, supplies\)\. Eq\. \(11\)\: C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\)\. Eq\. \(12\)\: w = \(3 script\-E n\*^3/\(pi Z^3\)\)^\(1/2\) \(Z^2/\(2 n\*^2\)\) \(2e/n\*\)^\(2n\*\) \(2 pi n\*\)^\(\-1\) \(2l \+ 1\)\(l \+ \|m\|\)\!/\(2^\|m\| \|m\|\! \(l \- \|m\|\)\!\) \(2 Z^3/\(script\-E n\*^3\)\)^\(2n\* \- \|m\| \- 1\) exp\(\-2 Z^3/\(3 n\*^3 script\-E\)\)\. Eq\. \(13a\), l = 1, m = 0\: w = \(3e/pi\)^\(1/2\) Z^2/n\*^4\.5 \(4e Z^3/\(script\-E n\*^4\)\)^\(2n\* \- 1\.5\) exp\(\-2 Z^3/\(3 n\*^3 script\-E\)\); Eq\. \(13b\), \|m\| = 1\: w = \(3e/pi\)^\(1/2\) 2e Z^2/n\*^3\.5 \(4e Z^3/\(script\-E n\*^4\)\)^\(2n\* \- 2\.5\) exp\(\.\.\.\) \(the library's text renders the first factor as '\(3e/pi\)^4'; the page shows the exponent 1/2\)\. Eq\. \(14\)\: w\_m=0/w\_\|m\|=1 = 2 script\-E\_0/script\-E\. Eq\. \(19\)\: C\_n\*l\*^2 = 2^\(2n\*\)/\(n\* Gamma\(n\* \+ l\* \+ 1\) Gamma\(n\* \- l\*\)\), with Eq\. \(17\) l\* = n\*\_0 \- 1; Eq\. \(20\) its Stirling form, which goes over into Eq\. \(11\) for l\* \<\< n\*; Eq\. \(21\) the rate for arbitrary l\. Eq\. \(25\)\: circular polarisation, w\_circ = w\_stat\. 'A quasiclassical approximation yields results up to values n\* ~ 1, with accuracy up to several percent' \(abstract\); no accuracy is stated for Table II\. The rate is per electron \(no occupation factor appears\)\.

TABLE II's CONVERSION\. The handbook's coefficients A are converted with the factor \(Z/n\*\)^\(n\* \- 0\.5\) 'because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The handbook itself \(Radtsig and Smirnov 1980, in Russian\) is not in the library\.

TABLE I \(p\. 1192, notes only\)\: 'Experimental \(ref\. 7\) and theoretical \[from Eq\. \(13a\)\] values of the laser intensity I for two values of the ionization probability w', w = 0\.01/tau and 0\.1/tau, tau = 1\.1 ns \(the note\: the ionisation rate at signal saturation is taken as the reciprocal pulse duration\), in 10^14 W/cm^2 \(image checked\: the library's header puts 10^15 over the last column; the page prints 10^14 there\)\. I\_exp and I\_theor at w = 0\.01/tau, then at 0\.1/tau\: He 1\.70, 1\.74, 2\.10, 2\.13; Ne 1\.22, 1\.24, 1\.30, 1\.25; Ar 0\.40, 0\.36, 0\.45, 0\.44; Ar\+ 1\.30, 1\.41, 1\.35, 1\.64; Kr 0\.20, 0\.24, 0\.30, 0\.29; Kr\+ 0\.80, 0\.92, 1\.15, 1\.08; Xe 0\.16, 0\.16, 0\.17, 0\.18; Xe\+ 0\.40, 0\.56, 0\.70, 0\.66; Xe\+\+ \-, 1\.59, 1\.50, 1\.81 \(Xe2\+ is not curated\)\. The experiments are Yergeau, Chin and Lavigne, J\. Phys\. B 19 \(1986\) \(ref\. 7\) and Chin, Yergeau and Lavigne, J\. Phys\. B 18, L213 \(1985\) \(ref\. 6\); the laser wavelength is not stated in this paper, and the 'probability' is a rate per pulse length, not a measured yield\: not an ionization\_yield dataset\.

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

Datasets
--------

ammosov\_1986/handbook\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_He",
     "material": "He",
     "file": "He/ammosov_1986__handbook_He.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), He, the neutral atom \(Z = 1\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\.

ammosov\_1986/eq11\_He
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_He",
     "material": "He",
     "file": "He/ammosov_1986__eq11_He.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), He, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* reproduces the value to the printed digits \(checked 2026\-09\-26\)\.

ammosov\_1986/handbook\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_Ne",
     "material": "Ne",
     "file": "Ne/ammosov_1986__handbook_Ne.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), Ne, the neutral atom \(Z = 1\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\.

ammosov\_1986/eq11\_Ne
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_Ne",
     "material": "Ne",
     "file": "Ne/ammosov_1986__eq11_Ne.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), Ne, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* reproduces the value to the printed digits \(checked 2026\-09\-26\)\.

ammosov\_1986/handbook\_Ne\+
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_Ne+",
     "material": "Ne+",
     "file": "Ne+/ammosov_1986__handbook_Ne+.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), Ne\+, the singly charged ion \(Z = 2\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\.

ammosov\_1986/eq11\_Ne\+
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_Ne+",
     "material": "Ne+",
     "file": "Ne+/ammosov_1986__eq11_Ne+.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), Ne\+, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* reproduces the value to the printed digits \(checked 2026\-09\-26\)\.

ammosov\_1986/handbook\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_Ar",
     "material": "Ar",
     "file": "Ar/ammosov_1986__handbook_Ar.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), Ar, the neutral atom \(Z = 1\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\.

ammosov\_1986/eq11\_Ar
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_Ar",
     "material": "Ar",
     "file": "Ar/ammosov_1986__eq11_Ar.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), Ar, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* = 0\.93 gives 2\.137, printed 2\.13 \(checked 2026\-09\-26; the n\* of the calculation may have had more digits\)\.

ammosov\_1986/handbook\_Ar\+
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_Ar+",
     "material": "Ar+",
     "file": "Ar+/ammosov_1986__handbook_Ar+.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), Ar\+, the singly charged ion \(Z = 2\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\.

ammosov\_1986/eq11\_Ar\+
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_Ar+",
     "material": "Ar+",
     "file": "Ar+/ammosov_1986__eq11_Ar+.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), Ar\+, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* reproduces the value to the printed digits \(checked 2026\-09\-26\)\.

ammosov\_1986/handbook\_Kr
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_Kr",
     "material": "Kr",
     "file": "Kr/ammosov_1986__handbook_Kr.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), Kr, the neutral atom \(Z = 1\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\.

ammosov\_1986/eq11\_Kr
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_Kr",
     "material": "Kr",
     "file": "Kr/ammosov_1986__eq11_Kr.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), Kr, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* = 0\.99 gives 2\.165, printed 2\.16 \(checked 2026\-09\-26\)\.

ammosov\_1986/handbook\_Kr\+
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_Kr+",
     "material": "Kr+",
     "file": "Kr+/ammosov_1986__handbook_Kr+.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), Kr\+, the singly charged ion \(Z = 2\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\. The printed cell is '2,30=0,12', '=' standing where the other cells print '\+\-' \(image checked\)\: read as 2\.30 \+\- 0\.12\.

ammosov\_1986/eq11\_Kr\+
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_Kr+",
     "material": "Kr+",
     "file": "Kr+/ammosov_1986__eq11_Kr+.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), Kr\+, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* = 1\.44 gives 2\.252, printed 2\.26; Eq\. \(11\) never exceeds 2\.2528 \(its maximum, at n\* = 1\.40\), so 2\.26 cannot come from it as printed\: probably a misprint for 2\.25, not corrected \(checked 2026\-09\-26\)\.

ammosov\_1986/handbook\_Xe
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_Xe",
     "material": "Xe",
     "file": "Xe/ammosov_1986__handbook_Xe.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), Xe, the neutral atom \(Z = 1\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\.

ammosov\_1986/eq11\_Xe
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_Xe",
     "material": "Xe",
     "file": "Xe/ammosov_1986__eq11_Xe.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), Xe, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* reproduces the value to the printed digits \(checked 2026\-09\-26\)\.

ammosov\_1986/handbook\_Xe\+
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "handbook_Xe+",
     "material": "Xe+",
     "file": "Xe+/ammosov_1986__handbook_Xe+.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. A. Radtsig and B. M. Smirnov, Handbook of Atomic and Molecular Physics [in Russian] (Atomizdat, Moscow, 1980), section 3.3"
     ],
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); converted from the handbook's A by the factor (Z/n*)^(n* - 0.5)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II \(p\. 1193\), Xe\+, the singly charged ion \(Z = 2\) in its ground state\: the coefficient 'obtained by numerical methods' in Radtsig and Smirnov's handbook \(ref\. 4\), printed as A \(Z/n\*\)^\(n\* \- 0\.5\), A the handbook's coefficient\: 'The factor \(Z/n\)^\(n\* \- 0\.5\) was introduced because the definition of the coefficients C\_n\*l\* in Eq\. \(3\) differs from the coefficients of A in the handbook' \(table note\)\. The \+\- error is the handbook's, as printed \(level not stated\); n\* as printed\.

ammosov\_1986/eq11\_Xe\+
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq11_Xe+",
     "material": "Xe+",
     "file": "Xe+/ammosov_1986__eq11_Xe+.csv",
     "table": "tbl_06845899aeaa",
     "quantity": "tunnelling_structure_coefficient",
     "abscissa": "none",
     "columns": {
       "n_star": "1"
     },
     "use": "check",
     "parameters": {
       "model": "adk",
       "orbital": "ground state (not named; the valence shell of the atom or ion)",
       "m": "not stated (the coefficient does not depend on m; Eq. (1))",
       "normalisation": "Ammosov et al. 1986 Eq. (3), p. 1191: Psi_n*lm(r) = C_n*l* (Z/n*)^(3/2) (Z r/n*)^(n* - 1) exp(-Z r/n*) Y_lm(r/r) for r >> (2E)^(-1/2), n* = Z (2E)^(-1/2), atomic units (the printed second factor lacks the r; Eq. (10) has it); Eq. (11): C_n*l* = (2e/n*)^n* (2 pi n*)^(-1/2)"
     }
   }

Table II \(p\. 1193\), Xe\+, 'From Eq\. \(11\)'\: the quasiclassical coefficient C\_n\*l\* = \(2e/n\*\)^n\* \(2 pi n\*\)^\(\-1/2\), independent of l for l \<\< n\*, at the printed n\*\. Eq\. \(11\) at the printed n\* reproduces the value to the printed digits \(checked 2026\-09\-26\)\.

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.