travers_2026_pyroraptor#
J. C. Travers, TDSE calculations of helium’s strong-field ionisation with pyroraptor: both electrons active, haCC and one active electron, unpublished (2026)
Source record · Catalogue · Review register
No DOI is recorded.
Source kind: theory
Recorded technique: Numerical solution of the time-dependent Schrodinger equation of helium with J. C. Travers’s code pyroraptor, three ways. (1) Both electrons active: coupled angular channels (l1, l2, L) with total M = 0 and L <= 17, admitted when one electron has l <= 2 (‘inner = 2’, ‘square = 2’), the other capped at l <= 15; multipole order 4 (the space of travers_2026_trecx’s |m| <= 1, Lshape[3;5] basis lies between inner = 1 and inner = 2); finite elements of 4.75 bohr beyond 2 bohr (order 12) to R0 = 40, 59, 78 or 97 bohr, an exterior element of order 20, exterior complex scaling (angle 0.15) from R0, the one-electron spectrum cut at 100 au, RK4 with the step 0.0088 au; the initial state’s energy -2.902737 au. (2) haCC, the hybrid anti-symmetrised coupled channels method (Majety, Zielinski and Scrinzi, New J. Phys. 17, 063002 (2015)): the neutral’s closed-box configuration-interaction states (‘neutral squares’, up to 6) and frozen He+ ion states (1s, ‘haCC(1)’, or the five n <= 2 states, ‘haCC(5)’) times one free electron in finite elements to R0 = 40 bohr (390 nm) or 80 to 140 bohr (800 nm), lMax 40 to 70, mixed gauge (length gauge inside the gauge radius 20 bohr, velocity gauge outside), exterior complex scaling; ground energy -2.9036457 au. (3) One active electron in Tong and Lin’s helium potential (tong_2005 Table 1), m = 0, ionisation energy 0.9038011 au. Populations are read by projecting on the field-free bound states with the ECS transpose (dual) pairing, the principal quantum number of a state n = round(1/sqrt(-2E)) with E its energy above the He+(1s) threshold.
Materials in structured entries: He
Dataset quantities: ionization_yield
Contents: 9 datasets; 0 formulas.
Curation notes#
UNPUBLISHED CALCULATIONS OF J. C. TRAVERS, TIER 3: validators only (use = ‘check’), below published calculations and measurements. Curated 2026-10-16 (TC-1092). The run records and the tables made from them are archived in data/external/pyroraptor (PROVENANCE.md there: pyroraptor’s repository at f9b35142, the records’ sha256, the converter); the data files are written from the tables by tools/extract/travers_2026_pyroraptor.py.
AT 390 NM, in the pulse of travers_2026_trecx’s two-electron helium (A2’s 6 fs Gaussian on the vector potential at 390 nm, 3.684031e14 and 5.68981e14 W/cm2, then 1000 au without field): the population above the bound shells n <= 4 (above4: ionisation plus excitation to n >= 5) and n <= 5 (above5) of each calculation, 1000 au after the pulse. Unlike the norm-loss (travers_2026_trecx’s twoelectron_normloss_*), these are converged in the box: the two-electron above4 changes by 0.03 % (3.684e14) and 0.01 % from R0 = 78 to 97 bohr, while its plain 1 - P(bound) falls by 3.6 % as each larger box binds another Rydberg shell; haCC’s above4 and above5 agree to 0.01 % at R0 = 40, 60 and 80 bohr. At 3.684e14 W/cm2 a resonance fills 1s4f (2.9e-4 at R0 = 78 bohr, about a third of above4), which above4 does not count. The two-electron values are at inner = 2: an inner-arm ladder of the absorbed norm-loss at 3.684e14 W/cm2 (inner 2 -> 3 -> 4: -0.97 % and -0.67 %, extrapolated geometrically) puts the angular limit 3.1 % below them, which is their uncertainty (an excess, not a spread); the ladder was not run at 5.69e14, nor on above4. above5 of the two electrons at R0 = 97 still moves by 0.3 % (3.684e14) from R0 = 78.
AT 800 NM, in Sato et al.’s six-cycle sin^2 pulse (sato_2016, Eq. 27; 4, 8 and 14e14 W/cm2): haCC’s 1 - P(both electrons inside 20 bohr) at the end of the pulse, Sato et al.’s measure, against which sato_2016’s fig6_casscf_He_800nm (MCTDHF) is compared.
The runs’ reports of 10 and 14 October called haCC’s above5 ‘ionisation plus n >= 5’ and compared it with the two-electron and one-electron above4; pyroraptor corrected this on 17 October 2026 (merged at 295a255b), withdrawing the haCC deficit at 390 nm it had reported. Here each measure is compared with its own (TC-1092).
Datasets#
travers_2026_pyroraptor/twoelectron_above4_gauss6_390nm_He#
{
"id": "twoelectron_above4_gauss6_390nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__twoelectron_above4_gauss6_390nm_He.csv",
"table": "data/external/pyroraptor/he_two_electron_390nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"3p68e14": 0.0317,
"5p69e14": 0.0315
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 390,
"pulse_fs": 6,
"pulse_fs_definition": "full width at half maximum of the intensity envelope (the square of the envelope of the vector potential)",
"polarization": "linear",
"pulse_envelope": "gaussian",
"envelope_of": "vector potential",
"cep": 0,
"cep_definition": "A(t) = A0 exp(-2 ln 2 t^2/T^2) sin(omega t): A2's pulse at 390 nm (omega 0.1168291 au, 4.61 cycles in the full width at half maximum), then 1000 au without field; max |A| 0.8734300 and 1.0854638 au",
"measure": "N0 - P(ground) - P(bound states with n <= 4) 1000 au after the pulse: ionisation plus excitation to n >= 5",
"electrons": "two active electrons (the whole atom)",
"basis": "total M = 0, |m| <= 2, inner = 2, l <= 15, multipole 4, R0 = 97 bohr",
"method": "TDSE of two electrons, pyroraptor, ECS",
"model_ionization_energy_au": 0.902737
}
}
Helium with both electrons active (inner = 2, R0 = 97 bohr): N0 - P(ground) - P(bound, n <= 4) 1000 au after the pulse (t = 1744.14 au; records k2b-3p68e14-box97 and k2b-5p69e14-box97): ionisation plus excitation to n >= 5, 8.464e-4 and 7.244e-3. Uncertainty: the angular excess 3.1 % (the values lie above the angular limit by about that) plus the change from R0 = 78 bohr. Set-up in the record’s notes.
travers_2026_pyroraptor/twoelectron_above5_gauss6_390nm_He#
{
"id": "twoelectron_above5_gauss6_390nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__twoelectron_above5_gauss6_390nm_He.csv",
"table": "data/external/pyroraptor/he_two_electron_390nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"3p68e14": 0.0345,
"5p69e14": 0.032
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 390,
"pulse_fs": 6,
"pulse_fs_definition": "full width at half maximum of the intensity envelope (the square of the envelope of the vector potential)",
"polarization": "linear",
"pulse_envelope": "gaussian",
"envelope_of": "vector potential",
"cep": 0,
"cep_definition": "A(t) = A0 exp(-2 ln 2 t^2/T^2) sin(omega t): A2's pulse at 390 nm (omega 0.1168291 au, 4.61 cycles in the full width at half maximum), then 1000 au without field; max |A| 0.8734300 and 1.0854638 au",
"measure": "N0 - P(ground) - P(bound states with n <= 5) 1000 au after the pulse: ionisation plus excitation to n >= 6",
"electrons": "two active electrons (the whole atom)",
"basis": "total M = 0, |m| <= 2, inner = 2, l <= 15, multipole 4, R0 = 97 bohr",
"method": "TDSE of two electrons, pyroraptor, ECS",
"model_ionization_energy_au": 0.902737
}
}
As twoelectron_above4_gauss6_390nm_He, cut above n <= 5: ionisation plus excitation to n >= 6, 7.396e-4 and 6.742e-3. Uncertainty: the angular excess 3.1 % plus the change from R0 = 78 bohr (0.3 % at 3.684e14).
travers_2026_pyroraptor/hacc1_above4_gauss6_390nm_He#
{
"id": "hacc1_above4_gauss6_390nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__hacc1_above4_gauss6_390nm_He.csv",
"table": "data/external/pyroraptor/he_hacc_390nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"3p68e14": 0.00285,
"5p69e14": 0.00285
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 390,
"pulse_fs": 6,
"pulse_fs_definition": "full width at half maximum of the intensity envelope (the square of the envelope of the vector potential)",
"polarization": "linear",
"pulse_envelope": "gaussian",
"envelope_of": "vector potential",
"cep": 0,
"cep_definition": "A(t) = A0 exp(-2 ln 2 t^2/T^2) sin(omega t): A2's pulse at 390 nm (omega 0.1168291 au, 4.61 cycles in the full width at half maximum), then 1000 au without field; max |A| 0.8734300 and 1.0854638 au",
"measure": "N0 - P(ground) - P(bound states with n <= 4) 1000 au after the pulse: ionisation plus excitation to n >= 5",
"electrons": "all, with the ion frozen in its 1s state (one ion channel)",
"method": "haCC(1), pyroraptor, mixed gauge, ECS",
"model_ionization_energy_au": 0.9036457
}
}
haCC with the He+ 1s channel, neutral square 6, R0 = 40 bohr, lMax 40, order 10, cut 200 au, gauge radius 20 bohr, step 0.0088 au (records l_sq6, l_hi_sq6): N0 - P(ground) - P(bound, n <= 4) 1000 au after the pulse, 8.092e-4 and 6.985e-3. Uncertainty: the largest change among the one-channel variations at 3.684e14 W/cm2 (step, order, cut, ECS angle, lMax, rMax 60 and 80, gauge radius) and the last step of the square ladder (5 -> 6).
travers_2026_pyroraptor/hacc5_above4_gauss6_390nm_He#
{
"id": "hacc5_above4_gauss6_390nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__hacc5_above4_gauss6_390nm_He.csv",
"table": "data/external/pyroraptor/he_hacc_390nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"3p68e14": 0.00285,
"5p69e14": 0.00285
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 390,
"pulse_fs": 6,
"pulse_fs_definition": "full width at half maximum of the intensity envelope (the square of the envelope of the vector potential)",
"polarization": "linear",
"pulse_envelope": "gaussian",
"envelope_of": "vector potential",
"cep": 0,
"cep_definition": "A(t) = A0 exp(-2 ln 2 t^2/T^2) sin(omega t): A2's pulse at 390 nm (omega 0.1168291 au, 4.61 cycles in the full width at half maximum), then 1000 au without field; max |A| 0.8734300 and 1.0854638 au",
"measure": "N0 - P(ground) - P(bound states with n <= 4) 1000 au after the pulse: ionisation plus excitation to n >= 5",
"electrons": "all, with the ion frozen in its five n <= 2 states (five ion channels)",
"method": "haCC(5), pyroraptor, mixed gauge, ECS",
"model_ionization_energy_au": 0.9036457
}
}
As hacc1_above4_gauss6_390nm_He with the five He+ n <= 2 channels (records h5_sq6, h5_sq6_hi): 8.277e-4 and 7.150e-3. Uncertainty: haCC(1)’s.
travers_2026_pyroraptor/hacc1_above5_gauss6_390nm_He#
{
"id": "hacc1_above5_gauss6_390nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__hacc1_above5_gauss6_390nm_He.csv",
"table": "data/external/pyroraptor/he_hacc_390nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"3p68e14": 0.00531,
"5p69e14": 0.00531
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 390,
"pulse_fs": 6,
"pulse_fs_definition": "full width at half maximum of the intensity envelope (the square of the envelope of the vector potential)",
"polarization": "linear",
"pulse_envelope": "gaussian",
"envelope_of": "vector potential",
"cep": 0,
"cep_definition": "A(t) = A0 exp(-2 ln 2 t^2/T^2) sin(omega t): A2's pulse at 390 nm (omega 0.1168291 au, 4.61 cycles in the full width at half maximum), then 1000 au without field; max |A| 0.8734300 and 1.0854638 au",
"measure": "N0 - P(ground) - P(bound states with n <= 5) 1000 au after the pulse: ionisation plus excitation to n >= 6",
"electrons": "all, with the ion frozen in its 1s state (one ion channel)",
"method": "haCC(1), pyroraptor, mixed gauge, ECS",
"model_ionization_energy_au": 0.9036457
}
}
As hacc1_above4_gauss6_390nm_He, cut above n <= 5: ionisation plus excitation to n >= 6, 7.113e-4 and 6.513e-3 (the values the runs’ reports called ‘ionisation plus n >= 5’ until pyroraptor’s correction of 17 October 2026).
travers_2026_pyroraptor/hacc5_above5_gauss6_390nm_He#
{
"id": "hacc5_above5_gauss6_390nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__hacc5_above5_gauss6_390nm_He.csv",
"table": "data/external/pyroraptor/he_hacc_390nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"3p68e14": 0.00531,
"5p69e14": 0.00531
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 390,
"pulse_fs": 6,
"pulse_fs_definition": "full width at half maximum of the intensity envelope (the square of the envelope of the vector potential)",
"polarization": "linear",
"pulse_envelope": "gaussian",
"envelope_of": "vector potential",
"cep": 0,
"cep_definition": "A(t) = A0 exp(-2 ln 2 t^2/T^2) sin(omega t): A2's pulse at 390 nm (omega 0.1168291 au, 4.61 cycles in the full width at half maximum), then 1000 au without field; max |A| 0.8734300 and 1.0854638 au",
"measure": "N0 - P(ground) - P(bound states with n <= 5) 1000 au after the pulse: ionisation plus excitation to n >= 6",
"electrons": "all, with the ion frozen in its five n <= 2 states (five ion channels)",
"method": "haCC(5), pyroraptor, mixed gauge, ECS",
"model_ionization_energy_au": 0.9036457
}
}
As hacc5_above4_gauss6_390nm_He, cut above n <= 5: 7.242e-4 and 6.672e-3. Uncertainty: haCC(1)’s.
travers_2026_pyroraptor/sae_above4_gauss6_390nm_He#
{
"id": "sae_above4_gauss6_390nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__sae_above4_gauss6_390nm_He.csv",
"table": "data/external/pyroraptor/he_sae_390nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"3p68e14": 0.00011,
"5p69e14": 6e-05
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 390,
"pulse_fs": 6,
"pulse_fs_definition": "full width at half maximum of the intensity envelope (the square of the envelope of the vector potential)",
"polarization": "linear",
"pulse_envelope": "gaussian",
"envelope_of": "vector potential",
"cep": 0,
"cep_definition": "A(t) = A0 exp(-2 ln 2 t^2/T^2) sin(omega t): A2's pulse at 390 nm (omega 0.1168291 au, 4.61 cycles in the full width at half maximum), then 1000 au without field; max |A| 0.8734300 and 1.0854638 au",
"measure": "N0 - P(ground) - P(bound states with n <= 4) 1000 au after the pulse: ionisation plus excitation to n >= 5",
"orbital": "1s",
"m": 0,
"electrons": "one active electron",
"potential": "Tong and Lin 2005, Table 1, He",
"method": "TDSE of one electron, pyroraptor, ECS",
"model_ionization_energy_au": 0.9038011
}
}
One electron (m = 0) in Tong and Lin’s helium potential, R0 = 75.7 bohr (13 outer elements), lMax 49, order 12, cut 400 au, step 1/192 au (record o13): N0 - P(1s) - P(bound, n <= 4) 1000 au after the pulse, 5.119e-4 and 4.504e-3. Uncertainty: the largest change among the four discretisations (9 and 18 outer elements, lMax 69).
travers_2026_pyroraptor/hacc1_outside20_sin2_800nm_He#
{
"id": "hacc1_outside20_sin2_800nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__hacc1_outside20_sin2_800nm_He.csv",
"table": "data/external/pyroraptor/he_hacc_800nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"I4e14": 0.0112,
"I8e14": 0.0102,
"I14e14": 0.0112
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 800,
"pulse_fs": 16.011,
"pulse_fs_definition": "the total, foot-to-foot duration tau of the sin^2 envelope on the field: 6 cycles",
"pulse_cycles": 6,
"polarization": "linear",
"pulse_envelope": "sin^2",
"envelope_of": "field",
"cep": "sine carrier",
"cep_definition": "E(t) = E0 sin(omega t) sin^2(pi t / tau), 0 <= t <= tau (sato_2016 Eq. 27)",
"intensity_definition": "I = E0^2 in atomic units (3.50945e16 W/cm2 per au^2), as sato_2016",
"measure": "1 - P(both electrons inside r = 20 bohr) at the end of the pulse",
"electrons": "all, with the ion frozen in its 1s state (one ion channel)",
"method": "haCC(1), pyroraptor, mixed gauge, ECS",
"model_ionization_energy_au": 0.9036457
}
}
haCC with the He+ 1s channel, neutral square 6 (records h1/<I>-sq6), in Sato et al.’s pulse: 1 - P(both electrons inside 20 bohr) at the end of the pulse, 2.961e-4, 1.5445e-2 and 0.1536. Uncertainty: per intensity, the largest change among the variations of the square-3 base (step, order, R0, lMax, cut, gauge radius) and the square step 3 -> 6.
travers_2026_pyroraptor/hacc5_outside20_sin2_800nm_He#
{
"id": "hacc5_outside20_sin2_800nm_He",
"material": "He",
"file": "He/travers_2026_pyroraptor__hacc5_outside20_sin2_800nm_He.csv",
"table": "data/external/pyroraptor/he_hacc_800nm.csv",
"quantity": "ionization_yield",
"unit": "1",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"uncertainty": {
"relative_rows": {
"I4e14": 0.0164,
"I8e14": 0.0155,
"I14e14": 0.0164
},
"level": "bound"
},
"parameters": {
"wavelength_nm": 800,
"pulse_fs": 16.011,
"pulse_fs_definition": "the total, foot-to-foot duration tau of the sin^2 envelope on the field: 6 cycles",
"pulse_cycles": 6,
"polarization": "linear",
"pulse_envelope": "sin^2",
"envelope_of": "field",
"cep": "sine carrier",
"cep_definition": "E(t) = E0 sin(omega t) sin^2(pi t / tau), 0 <= t <= tau (sato_2016 Eq. 27)",
"intensity_definition": "I = E0^2 in atomic units (3.50945e16 W/cm2 per au^2), as sato_2016",
"measure": "1 - P(both electrons inside r = 20 bohr) at the end of the pulse",
"electrons": "all, with the ion frozen in its five n <= 2 states (five ion channels)",
"method": "haCC(5), pyroraptor, mixed gauge, ECS",
"model_ionization_energy_au": 0.9036457
}
}
As hacc1_outside20_sin2_800nm_He with the five He+ n <= 2 channels, at haCC(1)’s numerics (records h5/<I>-best): 3.023e-4, 1.5825e-2 and 0.1578. Uncertainty: haCC(1)’s plus haCC(5)’s own lMax step at 8e14 (+0.52 %).
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.