tolstikhina_2014#
I. Yu. Tolstikhina, T. Morishita and O. I. Tolstikhin, “Application of the many-electron weak-field asymptotic theory of tunneling ionization to atoms”, Phys. Rev. A 90, 053413 (2014)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.90.053413
Source kind: theory
Recorded technique: The many-electron weak-field asymptotic theory (ME-WFAT) of tunnelling ionisation (Tolstikhin, Madsen & Morishita, Phys. Rev. A 89, 013421 (2014), ref. 2): in a static field F the rate is Gamma = |g|^2 W(F) [1 + O(F ln F)] (Eq. 1), W(F) the one-electron field factor (Eq. 2), and g the asymptotic coefficient of the Dyson orbital (Eqs. 3-6), ‘an exact asymptotic result, provided the wave functions in Eq. (3) are exact’ (apart from the nonrelativistic approximation; p. 053413-2). Implemented here with Hartree-Fock orbitals of the atom and the ion (Froese Fischer’s program, ref. 15, its 2008 version) in the one-configuration approximation: g = sqrt(p) R_N g_N (Eq. 17), p the occupation factor (2 for a closed-shell atom: ‘for S = 0 there are two electrons in the atom that have equal ionization rates’, p. -3), R_N the relaxation coefficient from the overlaps of the ionic and atomic orbitals (Eq. 14, Appendix), g_N the asymptotic coefficient of the ionising HF orbital (Eqs. 11-12), kappa from its orbital energy (Eq. 10). Leading order in the weak-field limit; valid for F well below F_c ~ kappa^4/8|2 - kappa| (p. -2).
Materials in structured entries: Ar, He, Kr, Ne, Xe
Dataset quantities: ionization_model_parameter, tunnelling_structure_coefficient
Contents: 20 datasets; 0 formulas.
Curation notes#
Journal pp. 053413-1 to -9 = PDF pages 1-9. Identity checked against the first page.
WHAT IS TAKEN. Table I (p. 053413-4, tbl_bb65aa194b35; every taken cell checked against the table image): for He (1s), Ne (2p), Ar (3p), Kr (4p) and Xe (5p), all 1S with p = 2 and M = 0, the orbital exponent kappa, the relaxation coefficient R_N, the orbital’s coefficient g_N and the atom’s g. Not taken: H (g = sqrt 2 by definition), Li, Be, B, Na, Mg, Al (not curated materials), and Tables II-IV (open shells, configuration interaction).
WHAT THEY ARE. Hartree-Fock, nonrelativistic, leading order in the weak-field limit. ‘We also include in the table Kr and Xe, since they are of interest for applications (although relativistic effects in these atoms may be non-negligible)’ (p. -4). kappa is the HF orbital exponent (Koopmans), 0.8 to 3.6 % above sqrt(2 I_p) of the measured ionisation energies (He 1.354958 against 1.3443, Ne 1.304155 against 1.2590, Ar 1.087215 against 1.0762). For helium the accurate two-electron g is 2.932 (ref. 2), ‘much closer’ to Table I’s 2.942 than 2.990 without R_N (p. -5): relaxation is weak (R_N 0.977 to 0.985) and for helium correlation changes g by 0.3 %.
WHAT THEY TEST. With tong_2002’s C_l the same formula is optmat’s one-electron static rate at weak field, so (g/g_TZL)^2, g_TZL = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l, is the atom’s weak-field rate over the model’s one electron: He 1.66, Ar 1.72, Kr 1.78, Xe 1.82, but Ne 0.53, its g_N half of what tong_2002’s C_l implies (TC-852).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
tolstikhina_2014/g_He#
{
"id": "g_He",
"material": "He",
"file": "He/tolstikhina_2014__g_He.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "1s",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "the atom (p = 2 included)"
}
}
Table I (p. 053413-4), column g: the atom’s weak-field coefficient g = sqrt(p) R_N g_N (Eq. 17), p = 2, the ionising 1s orbital with m = 0, Hartree-Fock with relaxation; the rate Gamma = |g|^2 W(F) (Eq. 1). Includes the occupation factor: its square counts both electrons of the orbital.
tolstikhina_2014/g_orbital_He#
{
"id": "g_orbital_He",
"material": "He",
"file": "He/tolstikhina_2014__g_orbital_He.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "1s",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "one electron (the orbital)"
}
}
Table I (p. 053413-4), column g_N: the asymptotic coefficient of the ionising Hartree-Fock 1s orbital (Eqs. 11-12), m = 0, one electron, without relaxation.
tolstikhina_2014/relaxation_He#
{
"id": "relaxation_He",
"material": "He",
"file": "He/tolstikhina_2014__relaxation_He.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "1",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "R_N"
}
}
Table I (p. 053413-4), column R_N: the relaxation coefficient of the ionising 1s orbital (Eq. 14), from the overlaps of the Hartree-Fock orbitals of the ion and the atom (Appendix).
tolstikhina_2014/kappa_He#
{
"id": "kappa_He",
"material": "He",
"file": "He/tolstikhina_2014__kappa_He.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "au",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "kappa"
}
}
Table I (p. 053413-4), column kappa (the CSV’s header ‘x’): the exponent of the ionising Hartree-Fock 1s orbital, kappa = sqrt(-2 epsilon_N) (Eq. 10), printed with its digits grouped by spaces. Not sqrt(2 I_p) of the measured ionisation energy.
tolstikhina_2014/g_Ne#
{
"id": "g_Ne",
"material": "Ne",
"file": "Ne/tolstikhina_2014__g_Ne.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "2p",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "the atom (p = 2 included)"
}
}
Table I (p. 053413-4), column g: the atom’s weak-field coefficient g = sqrt(p) R_N g_N (Eq. 17), p = 2, the ionising 2p orbital with m = 0, Hartree-Fock with relaxation; the rate Gamma = |g|^2 W(F) (Eq. 1). Includes the occupation factor: its square counts both electrons of the orbital.
tolstikhina_2014/g_orbital_Ne#
{
"id": "g_orbital_Ne",
"material": "Ne",
"file": "Ne/tolstikhina_2014__g_orbital_Ne.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "2p",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "one electron (the orbital)"
}
}
Table I (p. 053413-4), column g_N: the asymptotic coefficient of the ionising Hartree-Fock 2p orbital (Eqs. 11-12), m = 0, one electron, without relaxation.
tolstikhina_2014/relaxation_Ne#
{
"id": "relaxation_Ne",
"material": "Ne",
"file": "Ne/tolstikhina_2014__relaxation_Ne.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "1",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "R_N"
}
}
Table I (p. 053413-4), column R_N: the relaxation coefficient of the ionising 2p orbital (Eq. 14), from the overlaps of the Hartree-Fock orbitals of the ion and the atom (Appendix).
tolstikhina_2014/kappa_Ne#
{
"id": "kappa_Ne",
"material": "Ne",
"file": "Ne/tolstikhina_2014__kappa_Ne.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "au",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "kappa"
}
}
Table I (p. 053413-4), column kappa (the CSV’s header ‘x’): the exponent of the ionising Hartree-Fock 2p orbital, kappa = sqrt(-2 epsilon_N) (Eq. 10), printed with its digits grouped by spaces. Not sqrt(2 I_p) of the measured ionisation energy.
tolstikhina_2014/g_Ar#
{
"id": "g_Ar",
"material": "Ar",
"file": "Ar/tolstikhina_2014__g_Ar.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "3p",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "the atom (p = 2 included)"
}
}
Table I (p. 053413-4), column g: the atom’s weak-field coefficient g = sqrt(p) R_N g_N (Eq. 17), p = 2, the ionising 3p orbital with m = 0, Hartree-Fock with relaxation; the rate Gamma = |g|^2 W(F) (Eq. 1). Includes the occupation factor: its square counts both electrons of the orbital.
tolstikhina_2014/g_orbital_Ar#
{
"id": "g_orbital_Ar",
"material": "Ar",
"file": "Ar/tolstikhina_2014__g_orbital_Ar.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "3p",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "one electron (the orbital)"
}
}
Table I (p. 053413-4), column g_N: the asymptotic coefficient of the ionising Hartree-Fock 3p orbital (Eqs. 11-12), m = 0, one electron, without relaxation.
tolstikhina_2014/relaxation_Ar#
{
"id": "relaxation_Ar",
"material": "Ar",
"file": "Ar/tolstikhina_2014__relaxation_Ar.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "1",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "R_N"
}
}
Table I (p. 053413-4), column R_N: the relaxation coefficient of the ionising 3p orbital (Eq. 14), from the overlaps of the Hartree-Fock orbitals of the ion and the atom (Appendix).
tolstikhina_2014/kappa_Ar#
{
"id": "kappa_Ar",
"material": "Ar",
"file": "Ar/tolstikhina_2014__kappa_Ar.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "au",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "kappa"
}
}
Table I (p. 053413-4), column kappa (the CSV’s header ‘x’): the exponent of the ionising Hartree-Fock 3p orbital, kappa = sqrt(-2 epsilon_N) (Eq. 10), printed with its digits grouped by spaces. Not sqrt(2 I_p) of the measured ionisation energy.
tolstikhina_2014/g_Kr#
{
"id": "g_Kr",
"material": "Kr",
"file": "Kr/tolstikhina_2014__g_Kr.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "4p",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "the atom (p = 2 included)"
}
}
Table I (p. 053413-4), column g: the atom’s weak-field coefficient g = sqrt(p) R_N g_N (Eq. 17), p = 2, the ionising 4p orbital with m = 0, Hartree-Fock with relaxation; the rate Gamma = |g|^2 W(F) (Eq. 1). Includes the occupation factor: its square counts both electrons of the orbital.
tolstikhina_2014/g_orbital_Kr#
{
"id": "g_orbital_Kr",
"material": "Kr",
"file": "Kr/tolstikhina_2014__g_orbital_Kr.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "4p",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "one electron (the orbital)"
}
}
Table I (p. 053413-4), column g_N: the asymptotic coefficient of the ionising Hartree-Fock 4p orbital (Eqs. 11-12), m = 0, one electron, without relaxation.
tolstikhina_2014/relaxation_Kr#
{
"id": "relaxation_Kr",
"material": "Kr",
"file": "Kr/tolstikhina_2014__relaxation_Kr.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "1",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "R_N"
}
}
Table I (p. 053413-4), column R_N: the relaxation coefficient of the ionising 4p orbital (Eq. 14), from the overlaps of the Hartree-Fock orbitals of the ion and the atom (Appendix).
tolstikhina_2014/kappa_Kr#
{
"id": "kappa_Kr",
"material": "Kr",
"file": "Kr/tolstikhina_2014__kappa_Kr.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "au",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "kappa"
}
}
Table I (p. 053413-4), column kappa (the CSV’s header ‘x’): the exponent of the ionising Hartree-Fock 4p orbital, kappa = sqrt(-2 epsilon_N) (Eq. 10), printed with its digits grouped by spaces. Not sqrt(2 I_p) of the measured ionisation energy.
tolstikhina_2014/g_Xe#
{
"id": "g_Xe",
"material": "Xe",
"file": "Xe/tolstikhina_2014__g_Xe.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "5p",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "the atom (p = 2 included)"
}
}
Table I (p. 053413-4), column g: the atom’s weak-field coefficient g = sqrt(p) R_N g_N (Eq. 17), p = 2, the ionising 5p orbital with m = 0, Hartree-Fock with relaxation; the rate Gamma = |g|^2 W(F) (Eq. 1). Includes the occupation factor: its square counts both electrons of the orbital.
tolstikhina_2014/g_orbital_Xe#
{
"id": "g_orbital_Xe",
"material": "Xe",
"file": "Xe/tolstikhina_2014__g_orbital_Xe.csv",
"table": "tbl_bb65aa194b35",
"quantity": "tunnelling_structure_coefficient",
"abscissa": "label",
"use": "check",
"parameters": {
"model": "wfat",
"orbital": "5p",
"m": 0,
"normalisation": "Tolstikhina et al. 2014 Eqs. (11)-(12): g_N = lim r->inf sqrt(2(2l+1)/kappa) (2r)^(-1/kappa) e^(kappa r) P_nl(r), P_nl the radial orbital times r, kappa the orbital exponent (Eq. 10); g = sqrt(p) R_N g_N (Eq. 17); the static rate Gamma = |g|^2 (kappa/2) (4 kappa^2/F)^(2/kappa - 1) exp(-2 kappa^3/3F) (Eqs. 1-2), atomic units. Per electron, g_N R_N = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l in Tong, Zhao & Lin's C_l (tong_2002), with which Eqs. (1)-(2) are the static ADK rate",
"electrons": "one electron (the orbital)"
}
}
Table I (p. 053413-4), column g_N: the asymptotic coefficient of the ionising Hartree-Fock 5p orbital (Eqs. 11-12), m = 0, one electron, without relaxation.
tolstikhina_2014/relaxation_Xe#
{
"id": "relaxation_Xe",
"material": "Xe",
"file": "Xe/tolstikhina_2014__relaxation_Xe.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "1",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "R_N"
}
}
Table I (p. 053413-4), column R_N: the relaxation coefficient of the ionising 5p orbital (Eq. 14), from the overlaps of the Hartree-Fock orbitals of the ion and the atom (Appendix).
tolstikhina_2014/kappa_Xe#
{
"id": "kappa_Xe",
"material": "Xe",
"file": "Xe/tolstikhina_2014__kappa_Xe.csv",
"table": "tbl_bb65aa194b35",
"quantity": "ionization_model_parameter",
"unit": "au",
"abscissa": "none",
"use": "check",
"parameters": {
"model": "wfat",
"parameter": "kappa"
}
}
Table I (p. 053413-4), column kappa (the CSV’s header ‘x’): the exponent of the ionising Hartree-Fock 5p orbital, kappa = sqrt(-2 epsilon_N) (Eq. 10), printed with its digits grouped by spaces. Not sqrt(2 I_p) of the measured ionisation energy.
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.