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 · Catalogue · Review 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#
{
"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#
{
"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#
{
"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#
{
"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+#
{
"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+#
{
"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#
{
"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#
{
"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+#
{
"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+#
{
"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#
{
"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#
{
"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+#
{
"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+#
{
"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#
{
"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#
{
"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+#
{
"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+#
{
"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 review register for the checks and decisions.