The neutron sector calculation (/neutron) left the photon sector with a sharpened list of what its keystone must supply: gain, level restoration, and a signal controlled inhibition. The theory's Section 2 had already named the level restoration search as a computable problem, pairs of isomers whose cascade lines and gateway lines are mutually resonant, and Open Problem 1 had put it first. This directory runs that search against the adopted level schemes of every nuclide that carries an isomer holding a bit for at least a second, adds the inhibition search the neutron result made necessary, and writes down what the chart contains.
| file | what it is |
|---|---|
ensdf.py |
fetches the adopted levels and gammas of every isomer bearing nuclide from the IAEA Live Chart (ENSDF), caches them, and packs them into levels.json.gz |
census.py |
the three searches, the physics, results.md, the three tables, and figure 16; needs only numpy and matplotlib and the packed file |
levels.json.gz |
the packed level schemes the census reads, committed so that it reproduces offline |
gateways.csv |
every gateway of every isomer with its release cascade, width, cross section, and the areal density it demands |
pairs.csv.gz |
every release line landing on a gateway absorption within three standard deviations of the data, with the mismatch, its uncertainty, the velocity that would close it, and the areal density wall (compressed: tens of thousands of rows) |
inhibitors.csv |
every isomer with a signal gateway and a veto gateway |
results.md |
the census, regenerated by census.py |
A gateway is a level above an isomer that the isomer can be lifted into by absorbing a photon of the level difference, or, in the NEEC picture, by capturing an electron whose kinetic energy plus binding supplies it. Two classes are kept, and the distinction matters. In the observed class ENSDF lists the gamma from gateway to isomer, so the absorption is the time reverse of a measured transition and its partial width follows from the level's lifetime and branching. In the allowed class the spins and parities permit an E1, M1 or E2 and the line is simply unobserved; the 4.85 keV gateway of ⁹³ᵐMo, the most studied triggering candidate in the literature, is in this class, because a 4.85 keV transition is almost entirely converted and has never been seen as a photon. A search that used only observed lines would miss it, so the census carries both, with the width of the allowed class taken from the Weisskopf single particle estimate and labelled as such wherever it is used.
The release cascade from each gateway is followed through the adopted gammas, with conversion coefficients turning photon intensities into transition probabilities, until every branch has reached the ground state, a long lived isomer, or a level whose decay ENSDF does not give. The population that returns to the original isomer is the fraction of triggers that do nothing; the rest is the release, with its photons per trigger and the energy it lets go.
A pair is a release line of one isomer landing on a gateway absorption of another. A photon emitted by a free nucleus leaves short of the transition energy by the recoil E²/2Mc², and the absorber needs it to arrive above its own transition by the same amount, so at 1 MeV on a mass 180 nucleus the two recoils open a 6 eV gap that thermal Doppler broadening, about 1 eV wide at room temperature, does not close. Moon closed exactly this gap in 1951 with a 700 m/s rotor, since a velocity v shifts a line by Ev/c, and the census allows a rotor of up to 1 km/s: a match is any coincidence that a rotor can bring within the two thermal widths. Low energy lines in solids can be recoilless, but for two different nuclides that only narrows the tolerance to a natural linewidth, which no accident satisfies, so the same rule is applied throughout.
The areal density wall is theory Section 1.1 with the chart's own numbers in it. A gateway's integrated photoabsorption cross section is 2π²(ħc/E)² g Γ₀ with g the spin factor and Γ₀ the partial width back to the isomer; broadened over the thermal width it is a peak cross section of order barns at 1 MeV for a millielectronvolt width. For one release of A to trigger at least one release of B, the line's yield y times the areal density of inverted B nuclei times that cross section must exceed one, and the table reports the areal density and the thickness of a solid made entirely of the isomer that it amounts to.
Inhibition is the operation the neutron sector could not perform, because every neutron coupling adds fissions. An isomer with two releasing gateways whose cascades differ can perform it: a control that opens the second gateway spends the stored energy down a path that does not emit the signal line, emptying the register without producing the signal. The census counts isomers with a signal gateway and a veto gateway, the veto's cascade carrying less than a tenth of the signal line.
| what | number | what it means |
|---|---|---|
| isomers holding a bit for a second, matched to an adopted level | 415 | the register class of the README |
| gateways, observed class | 2451 | absorptions that are time reversed measured lines |
| gateways, allowed class | 2747 | E1, M1 or E2 permitted, line unobserved; ⁹³ᵐMo's is here |
| gateways that release | 1802 | the cascade leaves rather than returning |
| isomers with a releasing gateway | 259 | states that can be triggered at all |
| NEEC class, releasing, within 30 keV | 34 | the Phase B1 target list |
| release lines compatible with a gateway absorption, within the data's uncertainty | 12470 | the convertible class, as candidates |
| of which heterogeneous | 12402 | different nuclides, the pairs the theory asked for |
| closed loops | 3775 | A triggers B and B triggers A |
| candidates the data can call resonant within rotor reach | 0 | ENSDF is 475× too coarse for the rest |
| releasing gateways with a measured width | 58 | the rest lean on Weisskopf estimates |
| least demanding candidate, measured width | ¹²⁷Ba → ⁵²Mn: 1×10²⁴ cm⁻², 23 cm of pure isomer | the areal density wall, chart's best case |
| isomers with a signal gateway and a veto gateway | 214 of 220 with two releasing gateways | the inhibition the neutron sector lacked |
The convertible class the theory asked for exists as a list of candidates that the adopted data are too coarse to confirm, and fails as a list of gates, every member by orders of magnitude, on the areal density that a barns wide resonance demands of an inverted solid. The veto exists. The NEEC class is where the sector's one remaining experimental number applies, and it is now a list.
python3 ensdf.py # about ten minutes the first time; cached afterwards
python3 census.py # seconds
census.py reads only levels.json.gz, so it runs anywhere with numpy and matplotlib and needs no network; ensdf.py regenerates that file from the IAEA service and keeps its raw CSVs in photon/cache/, which git ignores.
The theory asked whether its convertible class exists. It exists as a list of energy coincidences and fails as a list of amplifiers, by the areal density wall, and the search that showed this also found the veto the neutron sector lacked and wrote down every state the one remaining experimental number will apply to.