Radioactive decay and decay chains, binding energy, reactor physics basics, radiation shielding and attenuation, and dosimetry.
Nuclear Engineering (nuclear-engineering-ai999x) is an offline Python package for nuclear engineering. It covers radioactive decay and decay chains, binding energy, reactor physics basics, radiation shielding and attenuation, and dosimetry.
It has 83 capabilities — 83 computational procedures — in 10 topics, the largest being Reactor physics, Detectors and counting, Neutron physics, Decay and activity, Shielding and dose and Reactor kinetics. Ask a question in words with ask(), or call a capability by name with typed inputs with solve(). Every answer carries its value and unit, the steps that produced it and the formula in LaTeX.
When a question is not determined — a value is missing, an input is out of range, or the request is outside the package — it says so and names what it needs, instead of guessing. It runs on an ordinary CPU without a network connection (Python >=3.10), and the same question always gets the same answer.
pip install nuclear-engineering-ai999x hf download AI999X/nuclear-engineering-ai999x --local-dir nuclear-engineering-ai999x
Each question below was put to nuclear-engineering-ai999x and the answer shown is the one it returned, with the steps it took.
Specific activity: nuclide = Co-60, m = 1 g
nuclide = Co-60, m = 1 gA = 4.18689443e+13 1/s, A_Ci = 1131.593089 1/s, a = 4.18689443e+16 1/(kg*s), a_Ci_per_g = 1131.593089 1/s, N = 1.004798494e+22 1/sPoint source dose rate: Gamma = 0.351 uSv*m^2/(MBq*h), A = 10 Ci, r = 2 m, mu = 0.0656 1/cm, x = 10 cm, buildup = linear
Gamma = 3.51e-13 (J/kg)*m^2/((1/s)*h), A = 3.7e+11 (1/s), r = 2 m, mu = 0.0656 1/cm, x = 10 cm, buildup = linearH_dot = 7.750139161e-06 J/(kg*s), H_uSv_h = 27900.50098 J/(kg*s), B = 1.656 J/(kg*s), T = 0.8593362895 J/(kg*s)Critical sphere: D = 0.9 cm, Sigma_a = 0.15 1/cm, nuSigma_f = 0.18 1/cm, extrapolation = 2.13D
D = 0.9 cm, Sigma_a = 0.15 1/cm, nuSigma_f = 0.18 1/cm, extrapolation = 2.13DR = 0.1528913163 m, R_ext = 0.1720721163 m, V = 0.01497052629 m^3Xenon after shutdown: Sigma_f = 0.1 1/cm, phi = 3e13 1/(cm^2*s), gamma_I = 0.0639, gamma_X = 0.00237, sigma_X = 2.65e6 b, t = 10 h
Sigma_f = 0.1 1/cm, phi = 3e+13 1/(cm^2*s), gamma_I = 0.0639, gamma_X = 0.00237, sigma_X = 2.65e-22 m^2, t = 10 hX = 3.723382215e+21 1/m^3, ratio = 1.883429887 1/m^3, t_peak = 30167.01507 s, peak_ratio = 1.901549197 1/m^3, I = 2.277591284e+21 1/m^3m.solve("nuc_enrichment_swu", x_p=0.045, x_f=0.00711, x_w=0.0025, P="1 kg") x_p = 0.045, x_f = 0.00711, x_w = 0.0025, P = 1 kgF = 9.219088937 kg, W = 8.219088937 kg, SWU = 6.871112989 kg, F_per_P = 9.219088937 kg, SWU_per_P = 6.871112989 kgCompton edge: E = 662 keV
E = 662 keVT_max = 0.4776504094 MeV, E_bs = 0.1843495906 MeVCommitted dose from a dose coefficient: I = 1 MBq, e = 2.2e-8 Sv/Bq
I = 1000000 (1/s), e = 2.2e-08 (J/kg)/(1/s)E = 0.022 J/kg, E_mSv = 22, I_Bq = 1000000 1/sCollisions to thermalize: A = 12.0, E0 = 2 MeV, Ef = 0.025 eV
A = 12, E0 = 2 MeV, Ef = 0.025 eVn = 115.3429277, xi = 0.1577689898Every snippet was run as shown; the output under it is what it printed.
import nuclear_engineering_ai999x as m
a = m.ask("Specific activity: nuclide = Co-60, m = 1 g")
print(a.outcome)
print(a.values)
for step in a.steps:
print(step["name"])SOLVED
{'A': 41868944303400.0, 'A_Ci': 1131.59308928, 'a': 4.18689443034e+16, 'a_Ci_per_g': 1131.59308928, 'N': 1.00479849416e+22}
Activity and specific activity of a mass of a radionuclide
import nuclear_engineering_ai999x as m
a = m.solve("nuc_enrichment_swu", x_p=0.045, x_f=0.00711, x_w=0.0025, P="1 kg")
print(a.outcome)
print(a.values)SOLVED
{'F': 9.21908893709, 'W': 8.21908893709, 'SWU': 6.87111298932, 'F_per_P': 9.21908893709, 'SWU_per_P': 6.87111298932}
import nuclear_engineering_ai999x as m
# an input is missing: the answer says what it needs instead of guessing
a = m.solve("nuc_enrichment_swu")
print(a.outcome)
print(a.message)NEEDS_INPUT
nuc_enrichment_swu needs x_p, x_f, x_w, P (U-235 assay of the product (weight fraction, e.g. 4.5%); U-235 assay of the feed (0.711% for natural uranium); U-235 assay of the tails (e.g. 0.25%); mass of product). Example: solve('nuc_enrichment_swu', x_p=0.045, x_f=0.00711, x_w=0.0025, P='1 kg').
nuclear-engineering-ai999x "Specific activity: nuclide = Co-60, m = 1 g"
A = 4.18689e+13 1/s, A_Ci = 1131.59, a = 4.18689e+16 1/(kg*s), a_Ci_per_g = 1131.59, N = 1.0048e+22 1. Activity and specific activity of a mass of a radionuclide: N = m N_A / M, A = lambda N with lambda = ln 2 / T_half with nuclide = Co-60, m = 1 g -> A = 4.18689e+13 1/s, A_Ci = 1131.59, a = 4.18689e+16 1/(kg*s), a_Ci_per_g = 1131.59, N = 1.0048e+22 Assumptions: the nuclide is in the table (ICRP-107 half-lives, radioactivedecay 0.6.1); m > 0 …
Every value in these figures was computed by the package, each point a run of solve(); in a notebook, plot() and plot_relation() draw a capability's curves the same way.
12 of its 83 formulas; every one is in the capability browser below.
Search by name, formula, input or topic. Each capability opens to show what it takes, what it returns, when it applies, and a question it answered.
nuc_activation_with_burnupThe product activity when a high flux both depletes the target nuclide and burns up the product by its own absorption, the fraction of target left, and the time and value of the maximum product activity.
N_T0 initial number of target atomssigma_T target capture cross section (barns) [m^2]sigma_P product absorption cross section (barns) [m^2]phi neutron flux [1/(m^2*s)]T_half half-life of the product [s]t irradiation time [s]A_P product activity at t [1/s]f_T fraction of target atoms leftt_max irradiation time of maximum product activity [s]A_max maximum product activity [1/s]nuc_specific_activityThe activity of a stated mass of a named radionuclide, its specific activity (activity per unit mass) and the number of atoms, from its tabulated half-life and atomic mass.
nuclide the radionuclide, written like Co-60, Cs-137, Tc-99m, U-235 choicem mass of the radionuclide (the pure nuclide, not the compound) [kg]A activity (Bq) [1/s]A_Ci activity in curiesa specific activity (Bq/kg) [1/(kg*s)]a_Ci_per_g specific activity in Ci/gN number of atomsnuc_chain_activityStarting from a pure parent of stated activity, the activities of the parent, of its first daughter and of the whole chain (all radioactive progeny) after a time t, with the real branching fractions (Sr-90/Y-90, Mo-99/Tc-99m, Cs-137/Ba-137m, Ge-68/Ga-68, ...).
nuclide the parent nuclide (Sr-90, Cs-137, Mo-99, Ge-68, W-188, Ru-106, Ce-144, Ba-140, Te-132, Sn-113, Sr-82, Zr-95, Sb-125, Pb-212, Te-131m, I-133, Pd-103, Ce-134, Ba-131, Hg-195m, Sr-91) choiceA0 activity of the pure parent at t = 0 [1/s]t decay time [s]A_parent activity of the parent at t [1/s]A_daughter activity of the first daughter at t (Y-90, Ba-137m, Tc-99m, Ga-68, Re-188, Rh-106, Pr-144, La-140, I-132, In-113m, Rb-82, Nb-95, Te-125m, Bi-212, I-131, Xe-133, Rh-103m, La-134, Cs-131, Hg-195, Y-91m) [1/s]A_total total activity of the parent and all radioactive progeny [1/s]ratio daughter-to-parent activity rationuc_irradiation_time_for_saturationHow long a target must be irradiated (constant flux) for the induced activity to reach a stated fraction of its saturation value, in time and in product half-lives.
T_half half-life of the product [s]f fraction of the saturation activity (0 < f < 1)t_irr irradiation time [s]n_half irradiation time in half-livesnuc_mass_for_activityThe mass and the number of atoms of a named radionuclide that has a stated activity (how much material a source of that strength contains).
nuclide the radionuclide, written like Co-60, Cs-137, Tc-99m, U-235 choiceA activity (Bq, or Ci) [1/s]m mass of the nuclide [kg]m_ug mass in microgramsN number of atomsnuc_activation_activityThe activity induced in a target by a neutron flux: at the end of irradiation, after a decay time, at saturation, and the saturation fraction reached (target depletion neglected).
m mass of the target element [kg]M molar mass of the target element [kg/mol]theta isotopic abundance of the target nuclidesigma activation cross section (barns) [m^2]phi neutron flux [1/(m^2*s)]T_half half-life of the product [s]t_irr irradiation time [s]t_d decay time after irradiation (0 when omitted) [s] optionalA_eoi activity at the end of irradiation [1/s]A_d activity after the decay time [1/s]A_sat saturation activity N sigma phi [1/s]S saturation fraction 1 - e^(-lambda t_irr)nuc_generator_daughter_activityThe daughter activity available in a generator (Mo-99/Tc-99m, Ge-68/Ga-68, Sr-82/Rb-82 ...) a time t after the last complete elution, with the branching fraction to the daughter, plus when the daughter activity peaks and its peak value.
A_P0 parent activity at the elution [1/s]T_P half-life of the parent [s]T_D half-life of the daughter [s]b fraction of parent decays that produce the daughter (0 < b <= 1, e.g. 0.8773 for Mo-99 -> Tc-99m)t time since the elution [s]A_D daughter activity at t [1/s]A_P parent activity at t [1/s]ratio A_D / A_Pt_max time of maximum daughter activity [s]A_D_max maximum daughter activity [1/s]nuc_three_member_chainActivities of the three radioactive members of a chain 1 -> 2 -> 3 after a time t, from their half-lives and the initial activity of every member (the daughters need not start at zero).
T1 half-life of member 1 (the parent) [s]T2 half-life of member 2 [s]T3 half-life of member 3 [s]A10 initial activity of member 1 [1/s]A20 initial activity of member 2 (0 if none) [1/s]A30 initial activity of member 3 (0 if none) [1/s]t elapsed time [s]A1 activity of member 1 [1/s]A2 activity of member 2 [1/s]A3 activity of member 3 [1/s]A_total total activity [1/s]nuc_daughter_max_activity_timeWhen the activity of a radioactive daughter, growing from a pure parent, reaches its maximum, and how large it is then (it equals the parent's activity at that moment).
T_P half-life of the parent [s]T_D half-life of the daughter [s]A_P0 initial parent activity (optional: gives the maximum daughter activity) [1/s] optionalt_max time of maximum daughter activity [s]ratio_max maximum daughter activity / initial parent activityt_max_half_lives t_max in daughter half-livesA_D_max maximum daughter activity (when A_P0 is given) [1/s]nuc_equilibrium_ratioThe daughter-to-parent activity and atom ratios once equilibrium is reached (transient; close to 1 in secular equilibrium) and the time after which the activity ratio is within 1 % of it, starting from pure parent.
T_P half-life of the parent [s]T_D half-life of the daughter (shorter than the parent's) [s]ratio_A equilibrium activity ratio A_D/A_P = T_P/(T_P - T_D)ratio_N equilibrium atom ratio N_D/N_Pt_99 time to reach 99 % of the equilibrium activity ratio [s]nuc_compton_edgeWhere a gamma line's Compton edge (maximum electron energy) and backscatter peak (energy of a photon scattered through 180 degrees) appear in a detector's spectrum.
E gamma-ray energy [J]T_max Compton edge: maximum electron recoil energy (MeV) [MeV]E_bs backscatter peak: energy of the photon scattered through 180 degrees (MeV) [MeV]nuc_count_time_for_precisionThe total counting time (optimally split between sample and background) needed for the net count rate to have a stated relative standard deviation, and the two counting times.
Rg gross count rate [1/s]Rb background count rate [1/s]r target relative standard deviation of the net count rate (e.g. 1%)T total counting time [s]tg gross counting time [s]tb background counting time [s]nuc_counts_during_decayThe expected number of counts recorded from a source that decays during the count, the mean activity during the count and the decay-correction factor that converts the mean activity to the activity at the start of counting.
A0 activity at the reference time [1/s]T_half half-life [s]tc counting time [s]eff detection efficiency (fraction of emitted radiations counted)y emission probability per decay (1 when every decay is counted)td delay from the reference time to the start of counting (0 when omitted) [s] optionalN expected countsA_mean mean activity during the count [1/s]F decay-correction factor: activity at the start of counting / mean activitynuc_currie_detection_limitsCurrie's (1968) decision threshold L_C = k sqrt(2B) and detection limit L_D = k^2 + 2 L_C (net counts, paired blank, alpha = beta = 0.05, k = 1.645) from the background counts B, and with the counting time, efficiency and emission yield the minimum detectable activity L_D/(eff y t).
B background counts in the counting timet counting time (optional, for the MDA) [s] optionaleff counting efficiency (optional, with t) optionaly emission yield per decay (default 1) optionalL_C critical level (net counts)L_D detection limit (net counts)MDA minimum detectable activity (Bq) [1/s]nuc_dead_time_nonparalyzableThe true event rate from the observed count rate of a non-paralyzable (non-extendable) detector with a stated dead time, the fraction of events lost and the correction factor.
m observed count rate (cps, cpm) [1/s]tau dead time (e.g. us) [s]n true event rate [1/s]loss fraction of events lostcorr correction factor n/mnuc_dead_time_paralyzableThe true event rate from the observed count rate of a paralyzable (extendable) detector, on the stated branch of the rate curve (below or above the maximum), with the fraction lost and the largest observable count rate.
m observed count rate [1/s]tau dead time [s]branch branch of the rate curve: low (true rate below 1/tau) or high (above it) choicen true event rate [1/s]loss fraction of events lostm_max largest observable count rate 1/(e tau) [1/s]nuc_count_rate_point_sourceThe count rate a detector of stated intrinsic efficiency records from a point source on its axis, from the activity, the emission probability per decay and the geometric efficiency of the detector face.
A source activity [1/s]y emission probability of the counted radiation per decayd source-to-face distance [m]a radius of the detector face [m]eps_int intrinsic efficiency (counts per radiation reaching the face)R expected count rate [1/s]g geometric efficiencyR_cpm expected count rate in counts per minutenuc_decay_curve_fitThe decay constant, half-life, initial count and the standard error of the half-life from counts measured at several times (equal counting intervals), by a Poisson-weighted least-squares fit of ln C against t.
t measurement times, in the unit t_unit vectorC counts recorded at those times (equal counting intervals) vectort_unit unit of the times in the list: s, min, h, d or y choicelambda_ fitted decay constant [1/s]T_half fitted half-life [s]C0 fitted count at t = 0sigma_T standard error of the half-life (Poisson weights) [s]nuc_flux_from_foil_activationThe neutron flux that irradiated an activation foil, from the foil's measured activity a decay time after an irradiation of known length, its mass, molar mass, isotopic abundance and activation cross section; with the saturation activity and the reaction rate per atom.
A_d foil activity measured at the count [1/s]m foil mass (target element) [kg]M molar mass of the target element [kg/mol]theta isotopic abundance of the target nuclidesigma activation cross section (barns) [m^2]T_half half-life of the product [s]t_irr irradiation time [s]t_d time from the end of irradiation to the count [s]phi neutron flux [1/(m^2*s)]A_sat saturation activity [1/s]R_atom reaction rate per target atom sigma phi (1/s) [1/s]nuc_count_time_splitHow to split a fixed total counting time between the sample (gross) count and the background count to minimise the standard deviation of the net count rate, and that minimum standard deviation.
T total counting time available [s]Rg gross count rate (sample plus background) [1/s]Rb background count rate [1/s]tg time for the gross count [s]tb time for the background count [s]sigma minimum standard deviation of the net count rate [1/s]rel relative standard deviation of the net count ratenuc_escape_peaksThe energies of the single- and double-escape peaks (E - m_e c^2 and E - 2 m_e c^2) that pair production by a gamma ray above 1.022 MeV produces in a detector.
E gamma-ray energy (MeV, keV) [J]single_escape_keV single-escape peak in keVdouble_escape_keV double-escape peak in keVannihilation_keV annihilation photon energy in keVE_keV full-energy peak in keVnuc_solid_angle_on_axisThe solid angle subtended by a circular detector face (or aperture) at a point source on its axis and the geometric efficiency (fraction of isotropic emissions that hit it).
d distance from the source to the detector face [m]a radius of the detector face [m]Omega solid angle (sr)g geometric efficiency Omega/(4 pi)nuc_solid_angle_off_axisThe solid angle subtended by a circular detector face at a point source displaced sideways from its axis, and the geometric efficiency.
d distance from the source to the plane of the detector face [m]a radius of the detector face [m]rho0 lateral offset of the source from the detector axis [m]Omega solid angle (sr)g geometric efficiency Omega/(4 pi)nuc_detector_efficiency_point_sourceThe total detection efficiency of a flat detector of given thickness and attenuation coefficient for a point source on its axis (every photon entering the front face crosses the thickness along its slant path), the geometric efficiency and the intrinsic efficiency.
d source-to-face distance [m]a radius of the detector face [m]t detector thickness [m]mu total linear attenuation coefficient of the detector material [1/m]eff total efficiency (interacting photons per emitted photon)g geometric efficiencyintrinsic intrinsic efficiency eff/gnuc_two_component_decay_fitResolve a decay curve that is the sum of two radionuclides of known half-lives into the initial count of each component (Poisson-weighted linear least squares).
t measurement times, in the unit t_unit vectorC counts recorded at those times (equal intervals) vectorT1 half-life of component 1 [s]T2 half-life of component 2 [s]t_unit unit of the times in the list: s, min, h, d or y choiceC1 component 1 count at t = 0C2 component 2 count at t = 0frac1 fraction of the initial count due to component 1nuc_committed_dose_coefficientThe committed effective dose E(50) = e(50) I of an intake I of a radionuclide with the dose coefficient e(50) (Sv/Bq, from ICRP tables for the route and chemical form).
I activity taken in (Bq, kBq, MBq, Ci ...) [1/s]e dose coefficient e(50) (Sv/Bq) [J*s/kg]E committed effective dose (Sv) [J/kg]E_mSv committed effective dose in mSvI_Bq intake in Bq [1/s]nuc_committed_dose_retentionThe number of decays in an organ over the commitment period after an intake retained in exponential compartments, and the committed equivalent dose from the energy absorbed per decay, the radiation weighting factor and the organ mass.
I activity taken into the organ (intake reaching it) [1/s]f fractions of the intake retained in each compartment (sum <= 1) vectorTb biological half-lives of the compartments, in the unit t_unit vectort_unit unit of the times in the list: s, min, h, d or y choiceT_p physical half-life [s]E energy absorbed in the organ per decay (e.g. MeV) [J]w_R radiation weighting factor (1 for photons and electrons, 20 for alpha particles)m organ mass [kg]tau commitment period (50 y for adults) [s]U number of decays in the organ during tauH committed equivalent dose (Sv) [J/kg]H_mSv committed equivalent dose in mSvnuc_effective_doseThe effective dose E = sum w_T H_T from the equivalent doses of the irradiated tissues and their tissue weighting factors (stated; ICRP 103: 0.12 for red marrow, colon, lung, stomach, breast and the remainder, 0.08 gonads, 0.04 bladder, oesophagus, liver, thyroid, 0.01 bone surface, brain, salivary glands, skin).
H equivalent dose of each tissue in mSv vectorw tissue weighting factor of each tissue (as stated) vectorE_mSv effective dose in mSvE effective dose (Sv) [J/kg]w_sum sum of the weighting factors givennuc_effective_half_lifeThe effective half-life of a radionuclide in the body or another system that removes it biologically while it decays, the effective decay constant and (with the initial activity) the total number of decays.
T_p physical half-life [s]T_b biological half-life [s]A0 initial activity in the body (optional) [1/s] optionalT_eff effective half-life [s]lambda_eff effective removal constant [1/s]N_decays total number of decays in the body (cumulated activity, when A0 is given)nuc_radiation_unit_conversionAn activity, absorbed dose or equivalent dose written in any of the SI or traditional units, expressed in both systems (1 Ci = 3.7e10 Bq, 1 rad = 0.01 Gy, 1 rem = 0.01 Sv).
A an activity (Bq, kBq, MBq, Ci, mCi, uCi ...) [1/s] optionalD an absorbed dose (Gy, mGy, rad, mrad) [J/kg] optionalH an equivalent or effective dose (Sv, mSv, rem, mrem) [J/kg] optionalSI_value value in the SI unit (Bq, Gy or Sv)traditional_value value in the traditional unit (Ci, rad or rem)si_unit the SI unittraditional_unit the traditional unitvalue_mCi activity in mCivalue_MBq activity in MBqvalue_mSv_or_mGy dose in mSv or mGyvalue_mrem_or_mrad dose in mrem or mradnuc_enrichment_swuThe natural-uranium feed and tails masses and the separative work (kg SWU) needed to produce a mass of enriched uranium from stated product, feed and tails assays, per kg of product too.
x_p U-235 assay of the product (weight fraction, e.g. 4.5%)x_f U-235 assay of the feed (0.711% for natural uranium)x_w U-235 assay of the tails (e.g. 0.25%)P mass of product [kg]F feed mass [kg]W tails mass [kg]SWU separative work (kg SWU) [kg]F_per_P feed per unit productSWU_per_P kg SWU per kg of productnuc_logarithmic_energy_decrementFor elastic scattering from a nucleus of mass ratio A (isotropic in the centre of mass): the minimum energy ratio alpha, the average logarithmic energy loss per collision xi and the average cosine of the laboratory scattering angle.
A mass of the nucleus in neutron masses (mass number)alpha minimum E'/E, ((A - 1)/(A + 1))^2xi average logarithmic energy decrementmu_bar average cosine of the lab scattering angle, 2/(3A)nuc_collisions_to_thermalizeThe average number of elastic collisions with nuclei of mass ratio A needed to slow a neutron from E0 to Ef (for example from 2 MeV to 0.025 eV), from the lethargy change and xi.
A mass of the moderator nucleus in neutron massesE0 initial neutron energy [J]Ef final neutron energy [J]n average number of collisionsxi average logarithmic energy decrementnuc_exponential_pileThe thermal diffusion length of a moderator from fluxes measured along the axis of an exponential pile (a source at the bottom of a prism of extrapolated sides a and b): least-squares relaxation constant gamma, then L from gamma^2 = 1/L^2 + (pi/a)^2 + (pi/b)^2.
z heights of the measurements along the axis, in cm (far from the source and the top) vectorphi measured fluxes or detector readings at those heights (any consistent unit) vectora first extrapolated transverse side [m]b second extrapolated transverse side [m]gamma fitted relaxation constant [1/m]L diffusion length [m]L2 diffusion area L^2 [m^2]nuc_plane_source_slab_fluxThe one-group thermal flux at a position in a non-multiplying slab of stated (extrapolated) thickness with a plane source of neutrons at its mid-plane, the flux at the source plane and the fraction of neutrons that leak from the two faces.
S source strength per unit area of the plane (neutrons/(m^2 s)) [1/(m^2*s)]D diffusion coefficient [m]Sigma_a absorption cross section [1/m]a extrapolated slab thickness (source at the centre) [m]x distance from the source plane [m]phi flux at x [1/(m^2*s)]phi0 flux at the source plane [1/(m^2*s)]leak fraction of source neutrons leaking from the two facesnuc_point_source_sphere_fluxThe one-group thermal flux at a radius in a non-multiplying sphere (extrapolated radius R) with an isotropic point source at its centre, the fraction of neutrons that leak out, and the flux the same source would give in an infinite medium.
S source strength (neutrons per second) [1/s]D diffusion coefficient [m]Sigma_a absorption cross section [1/m]R extrapolated radius of the sphere [m]r distance from the source [m]phi flux at r [1/(m^2*s)]leak fraction of source neutrons leaking outphi_inf flux at r in an infinite medium [1/(m^2*s)]nuc_maxwellian_average_cross_sectionThe effective thermal cross section of a 1/v absorber averaged over a Maxwellian neutron flux at a stated neutron temperature, from its tabulated 2200 m/s value.
sigma0 cross section at 2200 m/s (barns) [m^2]T neutron temperature [K]sigma_avg flux-averaged cross section [m^2]sigma_avg_b the same in barnsg ratio sigma_avg/sigma0 = (sqrt(pi)/2) sqrt(E0/kT)nuc_moderator_mixtureThe macroscopic scattering and absorption cross sections of a compound moderator (water, heavy water, graphite, beryllium oxide, ...), its average logarithmic energy decrement (weighted by scattering), moderating power and moderating ratio.
n atoms of each element per molecule vectorA mass ratio (mass number) of each element vectorsigma_s scattering cross section of each element, in barns vectorsigma_a absorption cross section of each element, in barns vectorrho density of the moderator [kg/m^3]M molar mass of the molecule [kg/mol]xi average logarithmic energy decrement of the mixtureMP moderating power xi Sigma_s [1/m]MR moderating ratio xi Sigma_s/Sigma_a (when Sigma_a > 0)nuc_elastic_scatteringThe energy of a neutron after elastic scattering from a nucleus of mass ratio A through a stated centre-of-mass angle, the energy ratio, the scattering angle in the laboratory and the lethargy gained.
A mass of the nucleus in neutron masses (mass number; 1 for hydrogen)E neutron energy before the collision [J]theta scattering angle in the centre-of-mass frame (deg or rad) [rad]E_out neutron energy after the collision [J]ratio E'/Epsi scattering angle in the laboratory frame [rad]du lethargy gain ln(E/E')nuc_fuel_cross_sectionsAtom densities of U-235, U-238 and oxygen in uranium dioxide of stated density and enrichment, its macroscopic absorption and fission cross sections, eta (neutrons per absorption in the fuel) and the absorption mean free path.
rho density of the UO2 (e.g. 10.4 g/cm^3) [kg/m^3]w enrichment: mass fraction of U-235 in the uraniumsigma_a5 U-235 absorption cross section (barns) [m^2]sigma_f5 U-235 fission cross section (barns) [m^2]sigma_a8 U-238 absorption cross section (barns) [m^2]sigma_aO oxygen absorption cross section (barns) [m^2]nu neutrons per fission of U-235N5 U-235 atoms per volume [1/m^3]N8 U-238 atoms per volume [1/m^3]NO oxygen atoms per volume [1/m^3]Sigma_a macroscopic absorption cross section [1/m]Sigma_f macroscopic fission cross section [1/m]eta eta = nu Sigma_f/Sigma_a of the fuelmfp_a absorption mean free path 1/Sigma_a [m]nuc_thermal_neutron_speedsThe most probable, mean and root-mean-square speeds and the mean kinetic energy of neutrons in thermal equilibrium (Maxwell-Boltzmann distribution) at a stated temperature.
T neutron (moderator) temperature [K]v_p most probable speed sqrt(2kT/m) [m/s]v_mean mean speed [m/s]v_rms root-mean-square speed [m/s]E_mean mean kinetic energy 3kT/2 [J]E_mean_eV mean kinetic energy in eVnuc_diffusion_lengthThe thermal diffusion length L = sqrt(D/Sigma_a) of a medium and, with the Fermi age tau, the migration area M^2 = L^2 + tau and migration length.
D diffusion coefficient (cm) [m]Sigma_a macroscopic absorption cross section [1/m]tau Fermi age to thermal (cm^2, optional) [m^2] optionalL diffusion length [m]L2 diffusion area L^2 [m^2]L_cm diffusion length in cmM2 migration area L^2 + tau [m^2]M migration length [m]nuc_control_rod_worthThe reactivity worth of a control rod inserted to a depth x in a core of height H with a cosine axial flux (first-order perturbation: worth density ~ sin^2), as a fraction of its total worth, and the differential worth at that depth.
rho_tot total worth of the fully inserted rod (absolute, or in pcm, %, dollars or cents)H core height [m]x insertion depth from the top of the core [m]beta delayed-neutron fraction (optional: converts a worth in dollars and reports dollars) optionalrho worth inserted (absolute)frac fraction of the total worthdrho_dx differential worth at x (reactivity per metre) [1/m]rho_dollars worth in dollars (when beta is given)nuc_power_after_step_one_groupThe relative power P(t)/P0 a time t after a step reactivity change from steady state, from the exact two-mode solution with one delayed group, with the amplitude of the stable period (the exact prompt jump or drop) and the inverse period.
rho step reactivity (absolute, or in pcm, %, dollars or cents)beta delayed-neutron fraction betalam precursor decay constant of the single delayed group (e.g. 0.08 1/s) [1/s]Lambda prompt neutron generation time [s]t time after the step [s]P relative power P(t)/P0A1 amplitude of the stable mode (exact prompt jump or drop)omega inverse stable period [1/s]nuc_power_after_step_six_groupThe relative power P(t)/P0 a time t after a step reactivity change from steady state with six (or any number up to eight) delayed-neutron groups, from all the inhour roots and their residues, and the stable period.
rho step reactivity (absolute, or in pcm, %, dollars or cents)beta delayed-neutron fraction of each group vectorlam decay constant of each group, in 1/s vectorLambda prompt neutron generation time [s]t time after the step [s]P relative power P(t)/P0omega inverse stable period [1/s]T stable period [s]nuc_reactivity_from_periodThe reactivity, in absolute units, dollars and pcm, that produces a measured stable period (or doubling time) with stated delayed-neutron data, from the inhour equation.
beta delayed-neutron fraction of each group vectorlam decay constant of each group, in 1/s vectorLambda prompt neutron generation time [s]T stable period (give this or T_d; negative for falling power) [s] optionalT_d doubling time (give this or T) [s] optionalrho reactivityrho_dollars reactivity in dollarsrho_pcm reactivity in pcmnuc_stable_period_six_groupThe stable reactor period, inverse period and doubling time after a step reactivity change with six (or any number up to eight) delayed groups, and the prompt (most negative) root that sets the prompt jump's time constant.
rho step reactivity (absolute, or in pcm, %, dollars or cents)beta delayed-neutron fraction of each group vectorlam decay constant of each group, in 1/s vectorLambda prompt neutron generation time [s]omega inverse stable period (largest root) [1/s]T stable period [s]T_d doubling time (negative: halving time) [s]omega_p prompt root (most negative) [1/s]nuc_reactor_period_one_groupThe stable (asymptotic) period, inverse period and doubling time of a reactor after a step reactivity change, with one effective delayed-neutron group (the stable root of the inhour equation).
rho step reactivity (absolute, or in pcm, %, dollars or cents)beta delayed-neutron fraction betalam precursor decay constant of the single delayed group (e.g. 0.08 1/s) [1/s]Lambda prompt neutron generation time [s]omega inverse stable period (largest inhour root) [1/s]T stable period (negative: falling power) [s]T_d doubling time T ln 2 (negative: halving time) [s]nuc_inverse_multiplicationPredict the critical loading (fuel elements, kg, rod position) from count rates measured as fuel is added, by extrapolating the inverse multiplication 1/M = C_0/C to zero: least-squares line through all points and the line through the last two.
x loadings (fuel elements, kg or any consistent measure), first = reference vectorC count rates at those loadings (any consistent unit) vectorx_crit predicted critical loading (least-squares line through all points)slope slope of 1/M per unit loadingx_crit_last2 predicted critical loading from the last two pointsinv_M_last 1/M at the last loadingnuc_critical_cylinderThe critical radius of a bare homogeneous cylinder of stated height in one-group diffusion theory, with its extrapolated radius and the physical volume.
D diffusion coefficient (a length, e.g. cm) [m]Sigma_a macroscopic absorption cross section [1/m]nuSigma_f nu times the macroscopic fission cross section [1/m]extrapolation extrapolation distance added at each free surface: none, 2D or 2.13D (= 0.71 transport mean free paths) choiceH physical height of the cylinder [m]R critical physical radius [m]R_ext critical extrapolated radius [m]V critical physical volume [m^3]nuc_critical_sphereThe critical radius (physical and extrapolated) and volume of a bare homogeneous spherical reactor in one-group diffusion theory.
D diffusion coefficient (a length, e.g. cm) [m]Sigma_a macroscopic absorption cross section [1/m]nuSigma_f nu times the macroscopic fission cross section [1/m]extrapolation extrapolation distance added at each free surface: none, 2D or 2.13D (= 0.71 transport mean free paths) choiceR critical physical radius [m]R_ext critical extrapolated radius [m]V critical physical volume [m^3]nuc_critical_slabThe critical thickness of an infinite bare slab of multiplying material in one-group diffusion theory, the extrapolated thickness and the material buckling.
D diffusion coefficient (a length, e.g. cm) [m]Sigma_a macroscopic absorption cross section [1/m]nuSigma_f nu times the macroscopic fission cross section [1/m]extrapolation extrapolation distance added at each free surface: none, 2D or 2.13D (= 0.71 transport mean free paths) choicea critical physical thickness [m]a_ext critical extrapolated thickness [m]nuc_reflected_slab_criticalThe critical core thickness of a slab reactor with a reflector of stated thickness on both faces (one-group diffusion in core and reflector) and the reflector savings compared with the bare core.
D_c core diffusion coefficient [m]Sigma_ac core absorption cross section [1/m]nuSigma_fc core nu Sigma_f [1/m]D_r reflector diffusion coefficient [m]Sigma_ar reflector absorption cross section [1/m]T_r reflector thickness on each face [m]extrapolation extrapolation distance added at each free surface: none, 2D or 2.13D (= 0.71 transport mean free paths) choicea critical core thickness [m]delta reflector savings per face (bare extrapolated half-thickness minus reflected half-thickness) [m]nuc_critical_cuboidThe third side that makes a bare rectangular parallelepiped of two stated sides critical in one-group diffusion theory, its extrapolated value and the physical volume.
D diffusion coefficient (a length, e.g. cm) [m]Sigma_a macroscopic absorption cross section [1/m]nuSigma_f nu times the macroscopic fission cross section [1/m]extrapolation extrapolation distance added at each free surface: none, 2D or 2.13D (= 0.71 transport mean free paths) choicea first physical side [m]b second physical side [m]c critical physical third side [m]c_ext critical extrapolated third side [m]V critical physical volume [m^3]nuc_decay_heat_powerThe fission-product decay power a time t after shutdown of a reactor that ran at constant power for an operating time T, by the Way-Wigner correlation.
P0 thermal power before shutdown [W]T_op operating time at that power [s]t time after shutdown (10 s to about 1e8 s) [s]P_d decay power [W]ratio decay power / operating powernuc_decay_heat_energyThe total fission-product decay energy released between two times after shutdown (the Way-Wigner power integrated), and the mean decay power over that interval.
P0 thermal power before shutdown [W]T_op operating time at that power [s]t1 start of the interval after shutdown [s]t2 end of the interval after shutdown [s]E decay energy released [J]E_MWh the same energy in MWhP_mean mean decay power over the interval [W]nuc_xenon_equilibriumThe equilibrium I-135 and Xe-135 atom densities in fuel operating at a steady flux, the xenon absorptions per fission (its poisoning strength) and the flux at which xenon burn-out equals its decay.
Sigma_f macroscopic fission cross section of the fuel [1/m]phi thermal flux during operation [1/(m^2*s)]gamma_I cumulative fission yield of I-135 (e.g. 0.0639)gamma_X direct fission yield of Xe-135 (e.g. 0.00237)sigma_X Xe-135 absorption cross section (e.g. 2.65e6 b) [m^2]I_eq equilibrium I-135 atoms per volume [1/m^3]X_eq equilibrium Xe-135 atoms per volume [1/m^3]abs_per_fission Xe-135 absorptions per fission at equilibriumnuc_flux_shapeThe neutron flux at a point of a bare slab, sphere or finite cylinder relative to its maximum at the centre (cosine, sin(x)/x, J0 times cosine) and the geometric buckling, for extrapolated dimensions.
geometry shape: slab (a, x), sphere (R, r) or cylinder (R, H, r, z) choicea extrapolated slab thickness [m] optionalR extrapolated radius [m] optionalH extrapolated cylinder height [m] optionalx distance from the slab mid-plane [m] optionalr distance from the centre or axis [m] optionalz height above the cylinder mid-plane [m] optionalratio phi/phi_max at the pointB2 geometric buckling [1/m^2]nuc_bare_reactor_keffThe geometric buckling of a bare homogeneous slab, sphere, cylinder or rectangular reactor of stated size and its effective multiplication factor in one-group diffusion theory, with the non-leakage probability and the reactivity.
D diffusion coefficient (a length, e.g. cm) [m]Sigma_a macroscopic absorption cross section [1/m]nuSigma_f nu times the macroscopic fission cross section [1/m]extrapolation extrapolation distance added at each free surface: none, 2D or 2.13D (= 0.71 transport mean free paths) choicegeometry bare reactor shape: slab (a), sphere (R), cylinder (R, H) or cuboid (a, b, c) choicea slab thickness or first side of a cuboid [m] optionalb second side of a cuboid [m] optionalc third side of a cuboid [m] optionalR radius of a sphere or cylinder [m] optionalH height of a cylinder [m] optionalB2 geometric buckling (extrapolated dimensions) [1/m^2]k_eff effective multiplication factorP_NL non-leakage probability 1/(1 + L^2 B^2)rho reactivity (k - 1)/knuc_two_group_bare_keffThe effective and infinite multiplication factors of a bare homogeneous reactor in two-group (fast and thermal) diffusion theory, with fission in both groups and downscatter from fast to thermal, and the thermal-to-fast flux ratio of the fundamental mode.
geometry bare reactor shape: slab (a), sphere (R), cylinder (R, H) or cuboid (a, b, c) choiceD1 fast-group diffusion coefficient [m]D2 thermal-group diffusion coefficient [m]Sigma_a1 fast-group absorption cross section [1/m]Sigma_12 downscatter (removal) cross section from fast to thermal [1/m]Sigma_a2 thermal-group absorption cross section [1/m]nuSigma_f1 fast-group nu Sigma_f [1/m]nuSigma_f2 thermal-group nu Sigma_f [1/m]a slab thickness or first side of a cuboid (extrapolated) [m] optionalb second side of a cuboid (extrapolated) [m] optionalc third side of a cuboid (extrapolated) [m] optionalR radius of a sphere or cylinder (extrapolated) [m] optionalH height of a cylinder (extrapolated) [m] optionalB2 geometric buckling [1/m^2]k_eff effective multiplication factork_inf infinite multiplication factorflux_ratio thermal/fast flux ratio of the fundamental modenuc_critical_cylinder_minimum_volumeThe radius and height of the bare cylindrical reactor that is critical with the smallest volume (extrapolated height-to-diameter ratio 0.924), and that volume.
D diffusion coefficient (a length, e.g. cm) [m]Sigma_a macroscopic absorption cross section [1/m]nuSigma_f nu times the macroscopic fission cross section [1/m]extrapolation extrapolation distance added at each free surface: none, 2D or 2.13D (= 0.71 transport mean free paths) choiceR physical radius [m]H physical height [m]V_ext minimum critical volume (extrapolated dimensions) [m^3]HD extrapolated height/diameternuc_six_factor_formulak_inf = eta f p eps (four-factor formula) and, with the fast and thermal non-leakage probabilities, k_eff = k_inf P_FNL P_TNL (six-factor formula), with the reactivity (k - 1)/k.
eta reproduction factor etaf thermal utilization fp resonance escape probability peps fast fission factor epsilonP_FNL fast non-leakage probability (optional) optionalP_TNL thermal non-leakage probability (optional) optionalk_inf infinite multiplication factork_eff effective multiplication factor (k_inf without leakage factors)P_NL total non-leakage probabilityrho reactivity (k_eff - 1)/k_effnuc_power_from_reaction_rateThe fission reaction rate density R = N sigma_f phi, the power density q''' = E_f N sigma_f phi and, with a volume, the power, from the fissile number density, the fission cross section, the flux and the energy per fission.
E_f recoverable energy per fission (e.g. 200 MeV) [J]N fissile atoms per unit volume [1/m^3]sigma fission cross section (barns) [m^2]phi neutron flux [1/(m^2*s)]V volume (optional, for the power) [m^3] optionalR fission rate density (1/(m^3 s)) [1/(m^3*s)]q power density [W/m^3]q_MW_m3 power density in MW/m^3P power E_f N sigma phi V [W]P_MW power in MWnuc_core_power_from_fluxThe thermal power of a bare homogeneous sphere, cylinder or rectangular core from its peak thermal flux (or the peak flux from the power), with the average flux, the peak-to-average ratio and the volume, for the fundamental-mode flux shape.
geometry core shape: sphere (R), cylinder (R, H) or cuboid (a, b, c) choiceSigma_f macroscopic fission cross section [1/m]E_f recoverable energy per fission (e.g. 200 MeV) [J]phi_max peak (centre) thermal flux (give this or P) [1/(m^2*s)] optionalP thermal power (give this or phi_max) [W] optionalR extrapolated radius [m] optionalH extrapolated cylinder height [m] optionala first extrapolated side of a cuboid [m] optionalb second side [m] optionalc third side [m] optionalP thermal power [W]phi_max peak flux [1/(m^2*s)]phi_avg volume-average flux [1/(m^2*s)]peaking peak-to-average flux rationuc_samariumThe equilibrium Pm-149 and Sm-149 atom densities during operation (Sm-149 is independent of the flux), the Sm-149 level reached after shutdown when all the promethium has decayed, and (optionally) the level a time t after shutdown.
Sigma_f macroscopic fission cross section [1/m]phi thermal flux during operation [1/(m^2*s)]gamma_Pm fission yield of Pm-149 (e.g. 0.0113)sigma_Sm Sm-149 absorption cross section (e.g. 40800 b) [m^2]t time after shutdown (optional) [s] optionalPm_eq equilibrium Pm-149 [1/m^3]Sm_eq equilibrium Sm-149 [1/m^3]Sm_max Sm-149 after all Pm-149 has decayed [1/m^3]max_ratio Sm_max/Sm_eqSm_t Sm-149 at t after shutdown (when t is given) [1/m^3]nuc_depletion_constant_fluxHow much of an initial mass of U-235 remains after irradiation at a constant flux, the fraction burnt, the fission energy released (J and MWd) and the power at the start and at the end.
m0 initial mass of U-235 [kg]sigma_a U-235 absorption cross section (barns) [m^2]sigma_f U-235 fission cross section (barns) [m^2]phi neutron flux [1/(m^2*s)]t irradiation time [s]E_f recoverable energy per fission (e.g. 200 MeV) [J]m U-235 mass remaining [kg]burnt fraction of U-235 consumedE fission energy released [J]E_MWd energy released in MWdP_t fission power at t [W]nuc_constant_power_depletionHow much of an initial mass of U-235 remains after operation at a constant power (the flux rising as the fuel is consumed), the fraction burnt, the mass consumed and the factor by which the flux has risen.
m0 initial mass of U-235 [kg]P constant thermal power [W]t operating time [s]E_f recoverable energy per fission (e.g. 200 MeV) [J]sigma_a U-235 absorption cross section (barns) [m^2]sigma_f U-235 fission cross section (barns) [m^2]m U-235 mass remaining [kg]burnt fraction of U-235 consumedconsumed U-235 mass consumed [kg]flux_ratio flux at t over the initial flux (N0/N)fissions number of fissions P t/E_fnuc_xenon_after_shutdownThe Xe-135 and I-135 atom densities a time t after shutdown from equilibrium operation, the xenon relative to its equilibrium value, and the time and height of the post-shutdown xenon peak (none at low flux).
Sigma_f macroscopic fission cross section of the fuel [1/m]phi thermal flux during operation [1/(m^2*s)]gamma_I cumulative fission yield of I-135 (e.g. 0.0639)gamma_X direct fission yield of Xe-135 (e.g. 0.00237)sigma_X Xe-135 absorption cross section (e.g. 2.65e6 b) [m^2]t time after shutdown [s]X Xe-135 atoms per volume at t [1/m^3]ratio X(t)/X_eqt_peak time of the xenon peak after shutdown (0 when xenon only falls) [s]peak_ratio peak xenon / equilibrium xenonI I-135 atoms per volume at t [1/m^3]nuc_half_value_layerThe half-value layer ln 2/mu, tenth-value layer ln 10/mu and mean free path 1/mu of a narrow beam in an absorber of linear attenuation coefficient mu, and with a thickness the transmission and number of half-value layers.
mu linear attenuation coefficient [1/m]x absorber thickness (optional) [m] optionalHVL half-value layer [m]TVL tenth-value layer [m]mfp mean free path 1/mu [m]HVL_cm half-value layer in cmTVL_cm tenth-value layer in cmtransmission narrow-beam transmission exp(-mu x)n_HVL thickness in half-value layersnuc_accumulated_dose_decaying_sourceThe dose accumulated over an exposure time when the dose rate falls with the source's half-life, the dose if the exposure lasted until complete decay, and the mean dose rate.
H0 dose rate at the reference time [J/(kg*s)]T_half half-life of the source [s]t exposure time [s]td delay from the reference time to the start (0 when omitted) [s] optionalD dose accumulated [J/kg]D_mSv dose in mSv (or mGy)D_inf dose until complete decay [J/kg]H_mean mean dose rate during the exposure [J/(kg*s)]nuc_point_source_dose_rateThe dose rate at a distance from a point gamma source of stated dose-rate constant, behind a slab shield, with the buildup factor in the stated form (none, linear or Taylor), plus the buildup factor and the transmission.
Gamma dose-rate constant of the nuclide (e.g. uSv*m^2/(MBq*h)) [J*m^2/kg]A source activity [1/s]r source-to-point distance [m]mu linear attenuation coefficient of the shield [1/m]x shield thickness (0 for none) [m]buildup buildup form: none (B = 1), linear (B = 1 + mu x) or taylor choiceA1 Taylor buildup parameter A1 (only with buildup = taylor) optionalalpha1 Taylor buildup parameter alpha1 (only with buildup = taylor) optionalalpha2 Taylor buildup parameter alpha2 (only with buildup = taylor) optionalH_dot dose rate (same quantity as Gamma: Sv/s, Gy/s) [J/(kg*s)]H_uSv_h dose rate in uSv/h (or uGy/h)B buildup factorT transmission B e^(-mu x)nuc_transit_doseThe dose received by a person or detector moving at constant speed along a straight path past an unshielded point source, from the closest distance, the speed and the path length (centred on the closest approach).
Gamma dose-rate constant of the nuclide [J*m^2/kg]A source activity [1/s]d closest distance to the source [m]v speed along the path [m/s]L length of the path, centred on the point of closest approach [m]D dose received (Sv or Gy, as Gamma) [J/kg]D_uSv dose in uSv (or uGy)frac fraction of the dose of an infinitely long pathnuc_klein_nishinaThe total Compton (Klein-Nishina) cross section per electron for a photon energy, the energy-transfer cross section and the mean kinetic energy given to the recoil electron.
E photon energy (10 keV to 100 MeV) [J]sigma Klein-Nishina cross section per electron [m^2]sigma_b the same in barns per electronsigma_tr energy-transfer cross section per electron [m^2]T_mean mean kinetic energy of the Compton electron (MeV) [MeV]nuc_attenuation_coefficient_fitThe linear attenuation coefficient of an absorber from intensities measured behind several thicknesses (least-squares fit of ln I against x), with the half- and tenth-value layers and the fitted unattenuated intensity.
x absorber thicknesses, in cm vectorI measured intensities or count rates (any consistent unit) vectormu fitted linear attenuation coefficient [1/m]HVL half-value layer [m]TVL tenth-value layer [m]I0 fitted intensity with no absorbernuc_multilayer_transmissionThe uncollided (narrow-beam) transmission through several shield layers, the total optical thickness, its value in half-value layers, the attenuation factor and (optionally) the dose rate behind the shield.
mu linear attenuation coefficient of each layer, in 1/cm vectorx thickness of each layer, in cm vectorH0 uncollided dose rate in front of the shield (optional) [J/(kg*s)] optionalT uncollided transmissiontau total optical thickness sum mu_i x_in_hvl thickness in half-value layersattenuation attenuation factor 1/TH uncollided dose rate behind the shield (when H0 is given) [J/(kg*s)]nuc_shield_thickness_for_dose_rateThe slab thickness that brings the dose rate from a point gamma source down to a target value, with no buildup or the linear buildup form B = 1 + mu x (the root of the attenuation equation).
Gamma dose-rate constant of the nuclide [J*m^2/kg]A source activity [1/s]r source-to-point distance [m]mu linear attenuation coefficient of the shield [1/m]H_target target dose rate (e.g. uSv/h) [J/(kg*s)]buildup buildup form: none (B = 1) or linear (B = 1 + mu x) choicex required shield thickness [m]n_mfp thickness in mean free pathsB buildup factor at that thicknessnuc_stay_time_decaying_sourceHow long one can stay at a place where the dose rate decays with the source's half-life before receiving a stated dose, compared with the stay time if the rate were constant.
H0 dose rate at the start of the stay [J/(kg*s)]T_half half-life of the source [s]D_lim dose limit for the stay [J/kg]t_stay allowed stay time [s]frac dose limit as a fraction of the dose until complete decaynuc_line_source_fluxThe uncollided photon flux at a point at perpendicular distance h from a straight line source (a pipe, a wire) running from y1 to y2 along the line, behind a slab shield parallel to the line, with the unshielded flux and the transmission.
S_L source strength per unit length (photons per second per metre) [1/(m*s)]h perpendicular distance from the line to the point [m]y1 position of one end along the line, measured from the foot of the perpendicular (may be negative) [m]y2 position of the other end (y2 > y1) [m]mu linear attenuation coefficient of the shield [1/m]t shield thickness (0 for none) [m]phi uncollided flux at the point [1/(m^2*s)]phi0 flux without the shield [1/(m^2*s)]T transmission phi/phi0nuc_disk_source_fluxThe uncollided flux on the axis of a uniform disk source (a contaminated floor patch, a tank bottom) at distance h, behind a slab shield parallel to the disk, with the unshielded flux and the transmission.
S_A source strength per unit area (photons per second per square metre) [1/(m^2*s)]R disk radius [m]h distance from the disk on its axis [m]mu linear attenuation coefficient of the shield [1/m]t shield thickness (0 for none) [m]phi uncollided flux on the axis [1/(m^2*s)]phi0 flux without the shield [1/(m^2*s)]T transmission phi/phi0nuc_channel_coolant_temperatureThe bulk coolant temperature at a height z (from the core mid-plane) in a heated channel whose linear heat rate follows a chopped cosine, the outlet temperature and the channel's total power.
q0 peak linear heat rate (at the core mid-plane) [W/m]H heated (core) height [m]H_e extrapolated height of the chopped-cosine power shape (H_e >= H) [m]m_dot coolant mass flow rate in the channel [kg/s]c_p coolant specific heat [J/(kg*K)]T_in coolant inlet temperature [K]z height above the core mid-plane (negative below) [m]T coolant temperature at z [K]T_out coolant outlet temperature [K]Q total heat added to the channel [W]nuc_centreline_temperature_variable_kThe centreline temperature of a cylindrical fuel pellet at a stated linear heat rate and surface temperature when its conductivity varies as k = 1/(A + B T) (the usual form for UO2), through the conductivity integral, with the conductivities at the surface and the centre.
q_lin linear heat rate q' [W/m]T_s pellet surface temperature [K]A A in k = 1/(A + B T) (m*K/W) [m*K/W]B B in k = 1/(A + B T) (m/W) [m/W]T_0 centreline temperature [K]dT centre-to-surface temperature rise [K]k_s conductivity at the surface [W/(m*K)]k_0 conductivity at the centre [W/(m*K)]nuc_fuel_rod_temperaturesThe temperatures at the fuel centreline, the pellet surface and the cladding inner and outer surfaces of a cylindrical fuel rod at a stated linear heat rate, from the coolant temperature through the film, cladding, gap and pellet (constant conductivities).
q_lin linear heat rate q' (W/m) [W/m]R_f pellet radius [m]k_f fuel thermal conductivity [W/(m*K)]h_g gap conductance [W/(m^2*K)]t_c cladding thickness [m]k_c cladding thermal conductivity [W/(m*K)]h coolant heat transfer coefficient [W/(m^2*K)]T_cool bulk coolant temperature [K]T_0 fuel centreline temperature [K]T_fs pellet surface temperature [K]T_ci cladding inner surface temperature [K]nuc_max_clad_temperatureWhere along a channel with a chopped-cosine power shape the cladding surface is hottest (above the mid-plane, because the coolant warms up), its temperature there and the coolant outlet temperature.
q0 peak linear heat rate (at the core mid-plane) [W/m]H heated (core) height [m]H_e extrapolated height of the chopped-cosine power shape (H_e >= H) [m]m_dot coolant mass flow rate in the channel [kg/s]c_p coolant specific heat [J/(kg*K)]T_in coolant inlet temperature [K]R_o cladding outer radius [m]h coolant heat transfer coefficient [W/(m^2*K)]z_max height of the maximum cladding temperature above the mid-plane [m]T_max maximum cladding surface temperature [K]T_out coolant outlet temperature [K]15 files, 43.6 MB in total. The largest:
| File | Size |
|---|---|
| model.safetensors | 18.9 MB |
| dist/nuclear_engineering_ai999x-1.0.0-py3-none-any.whl | 14.9 MB |
| onnx/search/encoder.int8.onnx | 4.9 MB |
| docs/nuclear_engineering_ai999x_capabilities.pdf | 3.7 MB |
| onnx/search/index.json | 403.3 KB |
| docs/nuclear_engineering_ai999x_capabilities.html | 319.9 KB |
| docs/nuclear_engineering_ai999x_capabilities.md | 249.6 KB |
| onnx/search/tokenizer.json | 176.4 KB |
| README.md | 25.2 KB |
| LICENSE | 11.4 KB |
| evaluation/release_gate.md | 2.3 KB |
| evaluation/KNOWLEDGE_CARD.md | 1.4 KB |
Nuclear Engineering answers questions in nuclear engineering: radioactive decay and decay chains, binding energy, reactor physics basics, radiation shielding and attenuation, and dosimetry. Each answer gives the value with its unit, the steps and the formula in LaTeX.
With pip: pip install nuclear-engineering-ai999x. The same files are on Hugging Face (hf download AI999X/nuclear-engineering-ai999x --local-dir nuclear-engineering-ai999x) and GitHub.
Yes. It is a Python package that runs on an ordinary CPU without a network connection (Python >=3.10); no GPU and no API key are needed.
83 capabilities in 10 topics, including Reactor physics, Detectors and counting, Neutron physics, Decay and activity, Shielding and dose.
Field: Engineering. Tasks: Question Answering, Token Classification, Text Classification, Sentence Similarity, Feature Extraction.
Asked "Specific activity: nuclide = Co-60, m = 1 g", it answers: A = 4.18689e+13 1/s, A_Ci = 1131.59, a = 4.18689e+16 1/(kg*s), a_Ci_per_g = 1131.59, N = 1.0048e+22.
It says so and names what is missing or out of range, instead of guessing a number.