aymar_1978#
M. Aymar and M. Coulombe, “Theoretical transition probabilities and lifetimes in Kr I and Xe I spectra”, At. Data Nucl. Data Tables 21, 537-566 (1978)
Source record · Catalogue · Review register
DOI: 10.1016/0092-640X(78)90007-4
Source kind: theory
Recorded technique: Central-field calculation with intermediate coupling and configuration mixing (p. 538): radial functions from Klapisch’s parametric potential (the potentials of Aymar, Physica 57, 178 (1972)); angular expansion coefficients from least-squares fits of the experimental level energies (Kr: Kaufman and Humphreys; Xe: Moore), with the bases Kr 4p5 5s pure, 4p5 (5p + 6p + 7p) and 4p5 (6s + 7s + 4d + 5d + 6d) mixed; Xe 5p5 (6p + 7p) and 5p5 (6s + 7s + 5d + 6d + 7d) (Tables I, II). Line strengths in the length (S_r) and velocity (S_nabla) forms, Eqs. (3a), (3b); A_ki = 2.026e18 S / (g_k lambda^3) and f_ik = 303.7 S / (g_i lambda) with the vacuum wavelength from the experimental energies (Eqs. 1, 2); lifetimes tau_k = 1 / sum_i A_ki over every lower level of the bases (Eq. 4). No uncertainty is stated; the paper says large line strengths (np - ns, np - (n+1)s, np - (n-1)d in the length form) are the better determined, and that the length-velocity difference indicates the accuracy (p. 538).
Materials in structured entries: Kr, Xe
Dataset quantities: radiative_lifetime, transition_probability
Contents: 10 datasets; 0 formulas.
Curation notes#
At. Data Nucl. Data Tables 21(6), 537-566 (June 1978) = PDF pages 1-30 (journal page = PDF page + 536); a scanned (raster) PDF. Identity checked on the first page (title, M. Aymar and M. Coulombe, Laboratoire Aime Cotton, Orsay; footer ‘537’, Atomic Data and Nuclear Data Tables, Vol. 21, No. 6, June 1978, 0092-640X/78/0216-0537) on 2026-10-12. Every taken cell was checked against the rendered pages (PDF pp. 8, 20, 22, 28, 30, native resolution). No argon.
TAKEN (use = check: calculated values without a stated uncertainty, with length-velocity differences of up to a factor 1.6 in the lifetimes and more in weak lines; for comparison with measured lifetimes, NIST and wiese_1989-type compilations, not for fitting). Extraction script tools/extract/aymar_1978.py. - Table VI (p. 564), lifetimes (ns) of Kr 5p, 5p’, 6p, 6p’ (Paschen 2p10-2p1, 3p10-3p1), tau_r and tau_nabla: tau_length_Kr, tau_velocity_Kr (20 levels each). - Table VIII (p. 566), lifetimes (ns) of Xe 6p, 6p’ (2p10-2p1), 7p (3p10-3p5; Table VIII lists no 7p’) and 6d (4d6-4d2): tau_length_Xe, tau_velocity_Xe (24 each). - Table III (p. 544), Kr 4p5 5s - 5p, 5p’ array, AKI (10^6 s^-1), the 30 transitions printed: A_length_Kr_5s5p, A_velocity_Kr_5s5p. - Table IV (p. 556), Xe 5p5 6s - 6p, 6p’ array, the 30 transitions printed (including the far-infrared 6s’[1/2]1 - 6p lines, 34-1189 um): A_length_Xe_6s6p, A_velocity_Xe_6s6p. - Table IV (p. 558), the 19 transitions printed with a 5d lower level and a 6p’ upper level, plus 5d[1/2]1 - 6p[1/2]0 (755.78 um), i.e. every decay of 6p and 6p’ to 5d: A_length_Xe_5d6p, A_velocity_Xe_5d6p. Rows are the paper’s Jl labels (nl, a prime for the 2P1/2 core, [K], J; p. 540), a transition lower-upper as printed; vacuum wavelengths (Angstrom) are in the printed row (LAMBDA is computed from the experimental energies, p. 540).
LEVELS (label = NIST configuration/term/J, held external/nist_asd/<X>_I_levels.tsv; evidence: the printed energies of Tables VI and VIII agree with NIST’s within 0.02-0.11 cm-1 for Kr and 0.4-0.6 cm-1 for Xe (Moore’s energies), and the J of each label gives the printed statistical weights; script check). Kr: nl[K]J = 4s2.4p5.(2P*<3/2>).nl 2[K] J, primed (2P*<1/2>); 2p10-2p1 = 5p[1/2]1, 5p[5/2]3, 5p[5/2]2, 5p[3/2]1, 5p[3/2]2, 5p[1/2]0, 5p’[3/2]1, 5p’[1/2]1, 5p’[3/2]2, 5p’[1/2]0 (91168.5-98855.1 cm-1); 3p10-3p1 the same order with 6p, 6p’ (102887.2-108821.6); 5s[3/2]2, 5s[3/2]1, 5s’[1/2]0, 5s’[1/2]1 = 1s5, 1s4, 1s3, 1s2 (79971.7, 80916.8, 85191.6, 85846.7). Xe: 5p5.(2P*<3/2>).nl 2[K] J (primed 2P*<1/2>); 2p10 6p[1/2]1 (77269.1), 2p9 6p[5/2]2 (78119.8), 2p8 6p[5/2]3 (78403.1), 2p7 6p[3/2]1 (78956.0), 2p6 6p[3/2]2 (79212.5), 2p5 6p[1/2]0 (80119.0), 2p4 6p’[3/2]1 (88379.1), 2p3 6p’[3/2]2 (89162.4), 2p2 6p’[1/2]1 (89278.7), 2p1 6p’[1/2]0 (89860.0); 3p10 7p[1/2]1, 3p9 7p[5/2]2, 3p8 7p[5/2]3, 3p6 7p[3/2]2, 3p7 7p[3/2]1, 3p5 7p[1/2]0 (87927.1-88842.3); 3d6 5d[1/2]0, 3d5 5d[1/2]1, 3d4’ 5d[7/2]4, 3d3 5d[3/2]2, 3d4 5d[7/2]3, 3d1’’ 5d[5/2]2, 3d1’ 5d[5/2]3, 3d2 5d[3/2]1 (79771.3-83890.0); 4d6 6d[1/2]0, 4d5 6d[1/2]1, 4d3 6d[3/2]2, 4d4’ 6d[7/2]4, 4d4 6d[7/2]3, 4d1’’ 6d[5/2]2, 4d1’ 6d[5/2]3, 4d2 6d[3/2]1 (88491.0-90032.2); 1s5-1s2 = 6s[3/2]2, 6s[3/2]1, 6s’[1/2]0, 6s’[1/2]1 (67067.5, 68045.2, 76196.8, 77185.0).
CHECKS (script). Every taken A row: 1e8/LAMBDA = EK - EI within 1 cm-1; A and f from the printed S through Eqs. (1) and (2) within 1 %, both forms. 1 / sum A over every row of Tables III and IV that the library holds for the level reproduces the printed tau_r and tau_nabla within 1 % for Kr 5p, 5p’ and Xe 6p, 6p’ (so the taken arrays plus the 7s, 6d (Xe) and 4d (Kr) rows are all their decays). Not checkable from the library: Kr 6p, 6p’ and Xe 7p, 6d (rows lost, see below). The library’s OCR misreads seven cells of the rows used (corrected in the script, page readings: Table IV p. 556 6s’[1/2]0 - 6p[3/2]1 length AKI .840-02 (OCR .840+02), 6s’[1/2]1 - 6p’[1/2]0 EK 89861. (OCR 69861.), 6s[3/2]2 - 6p[5/2]3 length FIK .641+00; p. 558 three velocity FIK with the exponent sign lost; p. 557 7s[3/2]1 - 6p’[3/2]2 length AKI .843-04; Table III p. 544 one S). None is a misprint of the paper.
NOT TAKEN. Tables I, II (fitted energy parameters: Slater integrals, spin-orbit parameters, rms deviations); the oscillator strengths, line strengths and log gf of Tables III and IV (the same calculation as the A values; oscillator_strength would hold f, not taken to keep one quantity per transition); the other arrays of Tables III and IV (resonance lines 4p6 - 5s, 5s’, 4d, 6s ... and 5p6 - 6s, 6s’, 5d, 7s, ...; np - n’s, n’d for higher n; 7p, 7d), in particular the Xe 6p - 5d, 5d’ rows with 5d as the upper level (PDF p. 21, journal p. 557: the library’s table of that page stops at 6p[5/2]2 - 5d[3/2]2 and lost its last 20 rows, 6p[5/2]2 - 5d[7/2]3 to 6p[3/2]1 - 5d[3/2]1; re-extraction needed before they can be taken); the lifetimes of Kr 7p, 6s, 7s, 4d, 4d’, 5d and Xe 7s, 5d (Tables VI, VIII); the comparison columns of Tables V-VIII (other papers’ measurements and calculations: reproduced).
FINDING (Xe 6p’ lifetimes, TC-1042). NIST’s 1/sum A over its lines (Xe_I_lines.tsv, Xe_I_lines_nir.tsv): 2p4 22.8, 2p3 22.8, 2p2 25.9, 2p1 27.6 ns; measured: 2p3 bruce_1990 32.1 +- 0.8, inoue_1984 37 +- 2; 2p1 bruce_1990 34.1 +- 0.8, inoue_1984 38-40; 2p2 inoue_1984 38; 2p4 inoue_1984 48-50. Aymar and Coulombe: tau_r 37.4, 27.7, 27.2, 28.4 and tau_nabla 48.5, 36.0, 36.0, 36.9 ns; the velocity form agrees with the measurements within 1-4 ns, the length form is 4-11 ns short. The difference from NIST is not missing branches: Aymar’s 6p’ decays include 5d (4.1-8.8e6 s-1 per level, 15-25 % of the total) and 7s (0.7-1.5e6), which NIST lacks, but NIST’s 6s’ - 6p’ lines alone (accuracy C/C+: 820.86 and 893.33 nm 2.0e7 and 2.2e7 s-1; 834.91 nm 4.2e7; 764.41 and 826.88 nm 2.1e7 and 1.62e7; 788.96 nm 3.5e7) are 1.25-2.1 times Aymar’s length A and 1.7-3.5 times the velocity A, and already exceed the measured total decay rates of 2p3 and 2p1 (3.12e7, 2.93e7 s-1). Aymar’s tau_nabla, with those branches, matches the measured lifetimes. NIST’s 6s’ - 6p’ A values are the outliers.
FINDING (Xe 6p and 7p lifetimes). 6p (Aymar r / v; NIST; measured): 2p10 29.7 / 39.5; 30.4; ku_1986 38.2 +- 1.0, inoue_1984 38. 2p9 33.0 / 36.9; 39.4; bruce_1990 36.0 +- 2.8, ku_1986 39.3 +- 1.0, bowering_1986b 30 +- 4 (36 +- 4 low pressure). 2p8 25.5 / 33.7; 33.3; ku_1986 32.3 +- 1.0, inoue_1984 30-31. 2p7 29.9 / 35.0; 37.0; ku_1986 36.7 +- 1.0, inoue_1984 37. 2p6 28.1 / 31.5; 27.2; bruce_1990 31.3 +- 1.8, inoue_1984 31, bowering_1986b 35 +- 3, ku_1986 36.0 +- 3.0. 2p5 22.4 / 33.2; 27.1; bruce_1990 26.8 +- 0.8, bowering_1986b 28 +- 1, ku_1986 32.6 +- 1.0. The velocity form is within the measurements’ spread for all six; the length form is short by 3-10 ns except 2p6. 7p (r / v; bruce_1990; inoue_1984 Ar): 7p[1/2]1 127 / 122; -; 131; 7p[5/2]2 113 / 157; 128.6; 166; 7p[5/2]3 105 / 151; -; 154; 7p[3/2]2 75.0 / 115; 105.3; 115; 7p[3/2]1 59.4 / 72.3; -; 70; 7p[1/2]0 60.1 / 74.6; 69.1; 65: bruce_1990 lies between the forms.
FINDING (A values against NIST, the strong lines, A >= 1e6 s-1). Kr 5s - 5p, 5p’ (16 lines, NIST accuracy AAA-C): A_r / NIST 1.10-1.53 (median 1.24), A_nabla / NIST 0.78-1.20 (median 0.98); Aymar’s velocity form follows NIST, and NIST’s Kr 5p and 5p’ lifetimes (1/sum A: 23.1-38.1 ns) lie near Aymar’s tau_nabla (-6.5 to +5 ns from it; the two shortest, 2p5 and 2p1, decay by one strong line that NIST puts 1.28 and 1.24 times Aymar’s velocity A), above tau_r. Xe 6s - 6p (A+ to C+): A_r / NIST 0.60-1.51, A_nabla / NIST 0.75-1.34; 6s - 6p’ and 6s’ - 6p’ (C, C+): A_r / NIST 0.25-2.3, A_nabla / NIST 0.21-0.80 (above). Whether NIST’s T-references draw on this paper is not checked here; the ratios show they are not copies of it.
FINDING (records quoting Aymar and Coulombe; no edit made). bruce_1990 Table III rows AC (length, footnote k) and AC (velocity): all 18 values (6p[5/2]2 ... 5d[1/2]1) equal Table VIII’s tau_r and tau_nabla. bowering_1986b Table I, Ref. 17 d and e: 2p5 22.4 / 33.2, 2p6 28.1 / 31.5, 2p9 33.0 / 36.9, equal. inoue_1984 Table I’s theoretical tau_r, tau_v: 47 of 48 equal; 4d6 = 6d[1/2]0 tau_v is printed 63.7 in inoue_1984 (table image) against Table VIII’s 63.8 (a transcription slip in Inoue et al.). ku_1986 p. 4308 (PDF p. 6): ‘Xe(3d5) radiatively decays (86-218 ns)’ with Ref. 21 = this paper; Table VIII prints 5d[1/2]1 tau_r 88.9 and tau_nabla 218 ns, so the 86 is not this paper’s (read on the page image). gornik_1980 quotes f_abs = 0.232 for 6p[3/2]2 -> 5d[5/2]3: Table IV p. 558 prints FIK .232+00 in both forms (A 1.14e6 s-1, S 119 au), equal; NIST’s 3107.77 nm line has A 7.3e5 s-1 (f 0.15). bowering_1986 does not cite this paper (its branching ratios are Horiguchi et al.’s).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
aymar_1978/tau_length_Kr#
{
"id": "tau_length_Kr",
"material": "Kr",
"file": "Kr/aymar_1978__tau_length_Kr.csv",
"table": "tbl_b2d644c2e2b3",
"quantity": "radiative_lifetime",
"unit": "ns",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole length form, 1 / sum A (Eq. 4)"
},
"uncertainty": {
"level": "not stated"
}
}
Table VI (p. 564), column tau_r: calculated lifetimes of Kr 5p, 5p’, 6p, 6p’ (2p10-2p1, 3p10-3p1), 19.1-151 ns, length form. Calculated, no stated uncertainty: a check.
aymar_1978/tau_velocity_Kr#
{
"id": "tau_velocity_Kr",
"material": "Kr",
"file": "Kr/aymar_1978__tau_velocity_Kr.csv",
"table": "tbl_b2d644c2e2b3",
"quantity": "radiative_lifetime",
"unit": "ns",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole velocity form, 1 / sum A (Eq. 4)"
},
"uncertainty": {
"level": "not stated"
}
}
Table VI (p. 564), column tau_nabla: calculated lifetimes of Kr 5p, 5p’, 6p, 6p’, 28.8-135 ns, velocity form. Calculated, no stated uncertainty: a check.
aymar_1978/tau_length_Xe#
{
"id": "tau_length_Xe",
"material": "Xe",
"file": "Xe/aymar_1978__tau_length_Xe.csv",
"table": "tbl_fc287c6cfec5",
"quantity": "radiative_lifetime",
"unit": "ns",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole length form, 1 / sum A (Eq. 4)"
},
"uncertainty": {
"level": "not stated"
}
}
Table VIII (p. 566), column tau_r: calculated lifetimes of Xe 6p, 6p’ (2p10-2p1), 7p (3p10-3p5) and 6d (4d6-4d2), 1.3-127 ns, length form. Against measurements and NIST: record notes. Calculated, no stated uncertainty: a check.
aymar_1978/tau_velocity_Xe#
{
"id": "tau_velocity_Xe",
"material": "Xe",
"file": "Xe/aymar_1978__tau_velocity_Xe.csv",
"table": "tbl_fc287c6cfec5",
"quantity": "radiative_lifetime",
"unit": "ns",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole velocity form, 1 / sum A (Eq. 4)"
},
"uncertainty": {
"level": "not stated"
}
}
Table VIII (p. 566), column tau_nabla: calculated lifetimes of Xe 6p, 6p’, 7p and 6d, 1.4-157 ns, velocity form; closer to the measured 6p and 6p’ lifetimes than tau_r (record notes). Calculated, no stated uncertainty: a check.
aymar_1978/A_length_Kr_5s5p#
{
"id": "A_length_Kr_5s5p",
"material": "Kr",
"file": "Kr/aymar_1978__A_length_Kr_5s5p.csv",
"table": "tbl_f7938e7a2c11",
"quantity": "transition_probability",
"unit": "1/s",
"scale": 1000000.0,
"abscissa": "label",
"use": "check",
"parameters": {
"notation": "racah",
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole length form"
},
"uncertainty": {
"level": "not stated"
}
}
Table III (p. 544), AKI length (10^6 s^-1): the 30 transitions of the Kr 5s - 5p, 5p’ array, 0.00143 to 52.4 x 10^6 s^-1; row lower-upper in Jl notation, the vacuum wavelength in the printed row. Calculated, no stated uncertainty: a check.
aymar_1978/A_velocity_Kr_5s5p#
{
"id": "A_velocity_Kr_5s5p",
"material": "Kr",
"file": "Kr/aymar_1978__A_velocity_Kr_5s5p.csv",
"table": "tbl_f7938e7a2c11",
"quantity": "transition_probability",
"unit": "1/s",
"scale": 1000000.0,
"abscissa": "label",
"use": "check",
"parameters": {
"notation": "racah",
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole velocity form"
},
"uncertainty": {
"level": "not stated"
}
}
Table III (p. 544), AKI velocity (10^6 s^-1): the same 30 transitions as A_length_Kr_5s5p. Calculated, no stated uncertainty: a check.
aymar_1978/A_length_Xe_6s6p#
{
"id": "A_length_Xe_6s6p",
"material": "Xe",
"file": "Xe/aymar_1978__A_length_Xe_6s6p.csv",
"table": "tbl_d3ae3ba3383f",
"quantity": "transition_probability",
"unit": "1/s",
"scale": 1000000.0,
"abscissa": "label",
"use": "check",
"parameters": {
"notation": "racah",
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole length form"
},
"uncertainty": {
"level": "not stated"
}
}
Table IV (p. 556), AKI length (10^6 s^-1): the 30 transitions of the Xe 6s - 6p, 6p’ array (4502-1189204 Angstrom); row lower-upper in Jl notation. The 6s’[1/2]0 - 6p[3/2]1 value is printed .840-02 (the library’s OCR reads .840+02; script reading). Calculated, no stated uncertainty: a check.
aymar_1978/A_velocity_Xe_6s6p#
{
"id": "A_velocity_Xe_6s6p",
"material": "Xe",
"file": "Xe/aymar_1978__A_velocity_Xe_6s6p.csv",
"table": "tbl_d3ae3ba3383f",
"quantity": "transition_probability",
"unit": "1/s",
"scale": 1000000.0,
"abscissa": "label",
"use": "check",
"parameters": {
"notation": "racah",
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole velocity form"
},
"uncertainty": {
"level": "not stated"
}
}
Table IV (p. 556), AKI velocity (10^6 s^-1): the same 30 transitions as A_length_Xe_6s6p. Calculated, no stated uncertainty: a check.
aymar_1978/A_length_Xe_5d6p#
{
"id": "A_length_Xe_5d6p",
"material": "Xe",
"file": "Xe/aymar_1978__A_length_Xe_5d6p.csv",
"table": "tbl_a138bdfcb9ef",
"quantity": "transition_probability",
"unit": "1/s",
"scale": 1000000.0,
"abscissa": "label",
"use": "check",
"parameters": {
"notation": "racah",
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole length form"
},
"uncertainty": {
"level": "not stated"
}
}
Table IV (p. 558), AKI length (10^6 s^-1): the 19 decays of 6p’ and 6p[1/2]0 to 5d levels (10128-755781 Angstrom), lines NIST gives no A for; row lower-upper in Jl notation. Calculated, no stated uncertainty: a check.
aymar_1978/A_velocity_Xe_5d6p#
{
"id": "A_velocity_Xe_5d6p",
"material": "Xe",
"file": "Xe/aymar_1978__A_velocity_Xe_5d6p.csv",
"table": "tbl_a138bdfcb9ef",
"quantity": "transition_probability",
"unit": "1/s",
"scale": 1000000.0,
"abscissa": "label",
"use": "check",
"parameters": {
"notation": "racah",
"method": "calculated, intermediate coupling with configuration mixing, parametric central potential, dipole velocity form"
},
"uncertainty": {
"level": "not stated"
}
}
Table IV (p. 558), AKI velocity (10^6 s^-1): the same 19 transitions as A_length_Xe_5d6p. Calculated, no stated uncertainty: a check.
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.