29375619482

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Merge 502d76c93 into e783e0147

Pull Request Pull Request #3971: Delta tracking

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94.34

/openmc/data/data.py

from __future__ import annotations

import itertools
import json
import os
import re
from pathlib import Path
from math import sqrt, log
from typing import TYPE_CHECKING, Literal
from warnings import warn

from endf.data import (ATOMIC_NUMBER, ATOMIC_SYMBOL, ELEMENT_SYMBOL,
                       EV_PER_MEV, K_BOLTZMANN, gnds_name, zam)

import openmc
from openmc.checkvalue import PathLike

if TYPE_CHECKING:
    from openmc.deplete import Chain

gnds_name.__module__ = __name__
zam.__module__ = __name__

# Isotopic abundances from Meija J, Coplen T B, et al, "Isotopic compositions
# of the elements 2013 (IUPAC Technical Report)", Pure. Appl. Chem. 88 (3),
# pp. 293-306 (2013). The "representative isotopic abundance" values from
# column 9 are used except where an interval is given, in which case the
# "best measurement" is used.
# Note that the abundances are given as atomic fractions!
NATURAL_ABUNDANCE = {
    'H1': 0.99984426, 'H2': 0.00015574, 'He3': 0.000002,
    'He4': 0.999998, 'Li6': 0.07589, 'Li7': 0.92411,
    'Be9': 1.0, 'B10': 0.1982, 'B11': 0.8018,
    'C12': 0.988922, 'C13': 0.011078, 'N14': 0.996337,
    'N15': 0.003663, 'O16': 0.9976206, 'O17': 0.000379,
    'O18': 0.0020004, 'F19': 1.0, 'Ne20': 0.9048,
    'Ne21': 0.0027, 'Ne22': 0.0925, 'Na23': 1.0,
    'Mg24': 0.78951, 'Mg25': 0.1002, 'Mg26': 0.11029,
    'Al27': 1.0, 'Si28': 0.9222968, 'Si29': 0.0468316,
    'Si30': 0.0308716, 'P31': 1.0, 'S32': 0.9504074,
    'S33': 0.0074869, 'S34': 0.0419599, 'S36': 0.0001458,
    'Cl35': 0.757647, 'Cl37': 0.242353, 'Ar36': 0.003336,
    'Ar38': 0.000629, 'Ar40': 0.996035, 'K39': 0.932581,
    'K40': 0.000117, 'K41': 0.067302, 'Ca40': 0.96941,
    'Ca42': 0.00647, 'Ca43': 0.00135, 'Ca44': 0.02086,
    'Ca46': 0.00004, 'Ca48': 0.00187, 'Sc45': 1.0,
    'Ti46': 0.0825, 'Ti47': 0.0744, 'Ti48': 0.7372,
    'Ti49': 0.0541, 'Ti50': 0.0518, 'V50': 0.0025,
    'V51': 0.9975, 'Cr50': 0.04345, 'Cr52': 0.83789,
    'Cr53': 0.09501, 'Cr54': 0.02365, 'Mn55': 1.0,
    'Fe54': 0.05845, 'Fe56': 0.91754, 'Fe57': 0.02119,
    'Fe58': 0.00282, 'Co59': 1.0, 'Ni58': 0.680769,
    'Ni60': 0.262231, 'Ni61': 0.011399, 'Ni62': 0.036345,
    'Ni64': 0.009256, 'Cu63': 0.6915, 'Cu65': 0.3085,
    'Zn64': 0.4917, 'Zn66': 0.2773, 'Zn67': 0.0404,
    'Zn68': 0.1845, 'Zn70': 0.0061, 'Ga69': 0.60108,
    'Ga71': 0.39892, 'Ge70': 0.2052, 'Ge72': 0.2745,
    'Ge73': 0.0776, 'Ge74': 0.3652, 'Ge76': 0.0775,
    'As75': 1.0, 'Se74': 0.0086, 'Se76': 0.0923,
    'Se77': 0.076, 'Se78': 0.2369, 'Se80': 0.498,
    'Se82': 0.0882, 'Br79': 0.50686, 'Br81': 0.49314,
    'Kr78': 0.00355, 'Kr80': 0.02286, 'Kr82': 0.11593,
    'Kr83': 0.115, 'Kr84': 0.56987, 'Kr86': 0.17279,
    'Rb85': 0.7217, 'Rb87': 0.2783, 'Sr84': 0.0056,
    'Sr86': 0.0986, 'Sr87': 0.07, 'Sr88': 0.8258,
    'Y89': 1.0, 'Zr90': 0.5145, 'Zr91': 0.1122,
    'Zr92': 0.1715, 'Zr94': 0.1738, 'Zr96': 0.028,
    'Nb93': 1.0, 'Mo92': 0.14649, 'Mo94': 0.09187,
    'Mo95': 0.15873, 'Mo96': 0.16673, 'Mo97': 0.09582,
    'Mo98': 0.24292, 'Mo100': 0.09744, 'Ru96': 0.0554,
    'Ru98': 0.0187, 'Ru99': 0.1276, 'Ru100': 0.126,
    'Ru101': 0.1706, 'Ru102': 0.3155, 'Ru104': 0.1862,
    'Rh103': 1.0, 'Pd102': 0.0102, 'Pd104': 0.1114,
    'Pd105': 0.2233, 'Pd106': 0.2733, 'Pd108': 0.2646,
    'Pd110': 0.1172, 'Ag107': 0.51839, 'Ag109': 0.48161,
    'Cd106': 0.01245, 'Cd108': 0.00888, 'Cd110': 0.1247,
    'Cd111': 0.12795, 'Cd112': 0.24109, 'Cd113': 0.12227,
    'Cd114': 0.28754, 'Cd116': 0.07512, 'In113': 0.04281,
    'In115': 0.95719, 'Sn112': 0.0097, 'Sn114': 0.0066,
    'Sn115': 0.0034, 'Sn116': 0.1454, 'Sn117': 0.0768,
    'Sn118': 0.2422, 'Sn119': 0.0859, 'Sn120': 0.3258,
    'Sn122': 0.0463, 'Sn124': 0.0579, 'Sb121': 0.5721,
    'Sb123': 0.4279, 'Te120': 0.0009, 'Te122': 0.0255,
    'Te123': 0.0089, 'Te124': 0.0474, 'Te125': 0.0707,
    'Te126': 0.1884, 'Te128': 0.3174, 'Te130': 0.3408,
    'I127': 1.0, 'Xe124': 0.00095, 'Xe126': 0.00089,
    'Xe128': 0.0191, 'Xe129': 0.26401, 'Xe130': 0.04071,
    'Xe131': 0.21232, 'Xe132': 0.26909, 'Xe134': 0.10436,
    'Xe136': 0.08857, 'Cs133': 1.0, 'Ba130': 0.0011,
    'Ba132': 0.001, 'Ba134': 0.0242, 'Ba135': 0.0659,
    'Ba136': 0.0785, 'Ba137': 0.1123, 'Ba138': 0.717,
    'La138': 0.0008881, 'La139': 0.9991119, 'Ce136': 0.00186,
    'Ce138': 0.00251, 'Ce140': 0.88449, 'Ce142': 0.11114,
    'Pr141': 1.0, 'Nd142': 0.27153, 'Nd143': 0.12173,
    'Nd144': 0.23798, 'Nd145': 0.08293, 'Nd146': 0.17189,
    'Nd148': 0.05756, 'Nd150': 0.05638, 'Sm144': 0.0308,
    'Sm147': 0.15, 'Sm148': 0.1125, 'Sm149': 0.1382,
    'Sm150': 0.0737, 'Sm152': 0.2674, 'Sm154': 0.2274,
    'Eu151': 0.4781, 'Eu153': 0.5219, 'Gd152': 0.002,
    'Gd154': 0.0218, 'Gd155': 0.148, 'Gd156': 0.2047,
    'Gd157': 0.1565, 'Gd158': 0.2484, 'Gd160': 0.2186,
    'Tb159': 1.0, 'Dy156': 0.00056, 'Dy158': 0.00095,
    'Dy160': 0.02329, 'Dy161': 0.18889, 'Dy162': 0.25475,
    'Dy163': 0.24896, 'Dy164': 0.2826, 'Ho165': 1.0,
    'Er162': 0.00139, 'Er164': 0.01601, 'Er166': 0.33503,
    'Er167': 0.22869, 'Er168': 0.26978, 'Er170': 0.1491,
    'Tm169': 1.0, 'Yb168': 0.00123, 'Yb170': 0.02982,
    'Yb171': 0.14086, 'Yb172': 0.21686, 'Yb173': 0.16103,
    'Yb174': 0.32025, 'Yb176': 0.12995, 'Lu175': 0.97401,
    'Lu176': 0.02599, 'Hf174': 0.0016, 'Hf176': 0.0526,
    'Hf177': 0.186, 'Hf178': 0.2728, 'Hf179': 0.1362,
    'Hf180': 0.3508, 'Ta180_m1': 0.0001201, 'Ta181': 0.9998799,
    'W180': 0.0012, 'W182': 0.265, 'W183': 0.1431,
    'W184': 0.3064, 'W186': 0.2843, 'Re185': 0.374,
    'Re187': 0.626, 'Os184': 0.0002, 'Os186': 0.0159,
    'Os187': 0.0196, 'Os188': 0.1324, 'Os189': 0.1615,
    'Os190': 0.2626, 'Os192': 0.4078, 'Ir191': 0.373,
    'Ir193': 0.627, 'Pt190': 0.00012, 'Pt192': 0.00782,
    'Pt194': 0.32864, 'Pt195': 0.33775, 'Pt196': 0.25211,
    'Pt198': 0.07356, 'Au197': 1.0, 'Hg196': 0.0015,
    'Hg198': 0.1004, 'Hg199': 0.1694, 'Hg200': 0.2314,
    'Hg201': 0.1317, 'Hg202': 0.2974, 'Hg204': 0.0682,
    'Tl203': 0.29524, 'Tl205': 0.70476, 'Pb204': 0.014,
    'Pb206': 0.241, 'Pb207': 0.221, 'Pb208': 0.524,
    'Bi209': 1.0, 'Th230': 0.0002, 'Th232': 0.9998,
    'Pa231': 1.0, 'U234': 0.000054, 'U235': 0.007204,
    'U238': 0.992742
}

DADZ = {
    '(n,2nd)': (-3, -1),
    '(n,2n)': (-1, 0),
    '(n,3n)': (-2, 0),
    '(n,na)': (-4, -2),
    '(n,n3a)': (-12, -6),
    '(n,2na)': (-5, -2),
    '(n,3na)': (-6, -2),
    '(n,np)': (-1, -1),
    '(n,n2a)': (-8, -4),
    '(n,2n2a)': (-9, -4),
    '(n,nd)': (-2, -1),
    '(n,nt)': (-3, -1),
    '(n,n3He)': (-3, -2),
    '(n,nd2a)': (-10, -5),
    '(n,nt2a)': (-11, -5),
    '(n,4n)': (-3, 0),
    '(n,2np)': (-2, -1),
    '(n,3np)': (-3, -1),
    '(n,n2p)': (-2, -2),
    '(n,npa)': (-5, -3),
    '(n,gamma)': (1, 0),
    '(n,p)': (0, -1),
    '(n,d)': (-1, -1),
    '(n,t)': (-2, -1),
    '(n,3He)': (-2, -2),
    '(n,a)': (-3, -2),
    '(n,2a)': (-7, -4),
    '(n,3a)': (-11, -6),
    '(n,2p)': (-1, -2),
    '(n,pa)': (-4, -3),
    '(n,t2a)': (-10, -5),
    '(n,d2a)': (-9, -5),
    '(n,pd)': (-2, -2),
    '(n,pt)': (-3, -2),
    '(n,da)': (-5, -3),
    '(n,5n)': (-4, 0),
    '(n,6n)': (-5, 0),
    '(n,2nt)': (-4, -1),
    '(n,ta)': (-6, -3),
    '(n,4np)': (-4, -1),
    '(n,3nd)': (-4, -1),
    '(n,nda)': (-6, -3),
    '(n,2npa)': (-6, -3),
    '(n,7n)': (-6, 0),
    '(n,8n)': (-7, 0),
    '(n,5np)': (-5, -1),
    '(n,6np)': (-6, -1),
    '(n,7np)': (-7, -1),
    '(n,4na)': (-7, -2),
    '(n,5na)': (-8, -2),
    '(n,6na)': (-9, -2),
    '(n,7na)': (-10, -2),
    '(n,4nd)': (-5, -1),
    '(n,5nd)': (-6, -1),
    '(n,6nd)': (-7, -1),
    '(n,3nt)': (-5, -1),
    '(n,4nt)': (-6, -1),
    '(n,5nt)': (-7, -1),
    '(n,6nt)': (-8, -1),
    '(n,2n3He)': (-4, -2),
    '(n,3n3He)': (-5, -2),
    '(n,4n3He)': (-6, -2),
    '(n,3n2p)': (-4, -2),
    '(n,3n2a)': (-10, -4),
    '(n,3npa)': (-7, -3),
    '(n,dt)': (-4, -2),
    '(n,npd)': (-3, -2),
    '(n,npt)': (-4, -2),
    '(n,ndt)': (-5, -2),
    '(n,np3He)': (-4, -3),
    '(n,nd3He)': (-5, -3),
    '(n,nt3He)': (-6, -3),
    '(n,nta)': (-7, -3),
    '(n,2n2p)': (-3, -2),
    '(n,p3He)': (-4, -3),
    '(n,d3He)': (-5, -3),
    '(n,3Hea)': (-6, -4),
    '(n,4n2p)': (-5, -2),
    '(n,4n2a)': (-11, -4),
    '(n,4npa)': (-8, -3),
    '(n,3p)': (-2, -3),
    '(n,n3p)': (-3, -3),
    '(n,3n2pa)': (-8, -4),
    '(n,5n2p)': (-6, -2),
}

# Values here are from the Committee on Data for Science and Technology
# (CODATA) 2018 recommendation (https://physics.nist.gov/cuu/Constants/).

# Unit conversions
JOULE_PER_EV = 1.602176634e-19

# Avogadro's constant
AVOGADRO = 6.02214076e23

# Neutron mass in units of amu
NEUTRON_MASS = 1.00866491595

# Used in atomic_mass function as a cache
_ATOMIC_MASS: dict[str, float] = {}

# Used in half_life function as a cache
_HALF_LIFE: dict[str, float] = {}
_LOG_TWO = log(2.0)

def atomic_mass(isotope):
    """Return atomic mass of isotope in atomic mass units.

    Atomic mass data comes from the `Atomic Mass Evaluation 2020
    <https://doi.org/10.1088/1674-1137/abddaf>`_.

    Parameters
    ----------
    isotope : str
        Name of isotope, e.g., 'Pu239'

    Returns
    -------
    float
        Atomic mass of isotope in [amu]

    """
    if not _ATOMIC_MASS:

        # Load data from AME2020 file
        mass_file = os.path.join(os.path.dirname(__file__), 'mass_1.mas20.txt')
        with open(mass_file, 'r') as ame:
            # Read lines in file starting at line 37
            for line in itertools.islice(ame, 36, None):
                name = f'{line[20:22].strip()}{int(line[16:19])}'
                mass = float(line[106:109]) + 1e-6*float(
                    line[110:116] + '.' + line[117:123])
                _ATOMIC_MASS[name.lower()] = mass

        # For isotopes found in some libraries that represent all natural
        # isotopes of their element (e.g. C0), calculate the atomic mass as
        # the sum of the atomic mass times the natural abundance of the isotopes
        # that make up the element.
        for element in ['C', 'Zn', 'Pt', 'Os', 'Tl', 'V']:
            isotope_zero = element.lower() + '0'
            _ATOMIC_MASS[isotope_zero] = 0.
            for iso, abundance in isotopes(element):
                _ATOMIC_MASS[isotope_zero] += abundance * _ATOMIC_MASS[iso.lower()]

    # Get rid of metastable information
    if '_' in isotope:
        isotope = isotope[:isotope.find('_')]

    return _ATOMIC_MASS[isotope.lower()]


def atomic_weight(element):
    """Return atomic weight of an element in atomic mass units.

    Computes an average of the atomic mass of each of element's naturally
    occurring isotopes weighted by their relative abundance.

    Parameters
    ----------
    element : str
        Element symbol (e.g., 'H') or name (e.g., 'helium')

    Returns
    -------
    float
        Atomic weight of element in [amu]

    """
    weight = 0.
    for nuclide, abundance in isotopes(element):
        weight += atomic_mass(nuclide) * abundance
    if weight > 0.:
        return weight
    else:
        raise ValueError(f"No naturally-occurring isotopes for element '{element}'.")


def half_life(
    isotope: str,
    chain_file: Literal[False] | None | PathLike | Chain = False
) -> float | None:
    """Return half-life of isotope in seconds or None if isotope is stable

    By default, half-life values are from the `ENDF/B-VIII.0 decay sublibrary
    <https://www.nndc.bnl.gov/endf-b8.0/download.html>`_. A depletion chain can
    also be used as the source of half-life values.

    .. versionadded:: 0.13.1

    .. versionchanged:: 0.15.4
        Added the ``chain_file`` argument.

    Parameters
    ----------
    isotope : str
        Name of isotope, e.g., 'Pu239'
    chain_file : False, None, PathLike, or openmc.deplete.Chain, optional
        Source of half-life values. If ``False``, only ENDF/B-VIII.0 data is
        used. If ``None``, the chain specified by
        ``openmc.config['chain_file']`` is used when available. If a path or
        :class:`openmc.deplete.Chain` is given, that chain is used. For ``None``
        or an explicit chain, nuclides absent from the chain fall back to
        ENDF/B-VIII.0 data.

    Returns
    -------
    float or None
        Half-life of isotope in [s], or None if the isotope is stable

    """
    if chain_file is not False:
        if chain_file is not None or openmc.config.get('chain_file') is not None:
            # Local import avoids a circular dependency
            from openmc.deplete.chain import _get_chain
            chain = _get_chain(chain_file)
            if isotope in chain:
                return chain[isotope].half_life

    global _HALF_LIFE
    if not _HALF_LIFE:
        # Load ENDF/B-VIII.0 data from JSON file
        half_life_path = Path(__file__).with_name('half_life.json')
        _HALF_LIFE = json.loads(half_life_path.read_text())

    return _HALF_LIFE.get(isotope.lower())


def decay_constant(
    isotope: str,
    chain_file: Literal[False] | None | PathLike | Chain = False
) -> float:
    """Return decay constant of isotope in [s^-1]

    Decay constants are based on half-life values from the
    :func:`~openmc.data.half_life` function. When the isotope is stable, a decay
    constant of zero is returned.

    .. versionadded:: 0.13.1

    .. versionchanged:: 0.15.4
        Added the ``chain_file`` argument.

    Parameters
    ----------
    isotope : str
        Name of isotope, e.g., 'Pu239'
    chain_file : False, None, PathLike, or openmc.deplete.Chain, optional
        Source of half-life values. If ``False``, only ENDF/B-VIII.0 data is
        used. If ``None``, the chain specified by
        ``openmc.config['chain_file']`` is used when available. If a path or
        :class:`openmc.deplete.Chain` is given, that chain is used. For ``None``
        or an explicit chain, nuclides absent from the chain fall back to
        ENDF/B-VIII.0 data.

    Returns
    -------
    float
        Decay constant of isotope in [s^-1]

    See also
    --------
    openmc.data.half_life

    """
    t = half_life(isotope, chain_file)
    return _LOG_TWO / t if t else 0.0


def water_density(temperature, pressure=0.1013):
    """Return the density of liquid water at a given temperature and pressure.

    The density is calculated from a polynomial fit using equations and values
    from the 2012 version of the IAPWS-IF97 formulation.  Only the equations
    for region 1 are implemented here.  Region 1 is limited to liquid water
    below 100 [MPa] with a temperature above 273.15 [K], below 623.15 [K], and
    below saturation.

    Reference: International Association for the Properties of Water and Steam,
    "Revised Release on the IAPWS Industrial Formulation 1997 for the
    Thermodynamic Properties of Water and Steam", IAPWS R7-97(2012).

    Parameters
    ----------
    temperature : float
        Water temperature in units of [K]
    pressure : float
        Water pressure in units of [MPa]

    Returns
    -------
    float
        Water density in units of [g/cm^3]

    """

    # Make sure the temperature and pressure are inside the min/max region 1
    # bounds.  (Relax the 273.15 bound to 273 in case a user wants 0 deg C data
    # but they only use 3 digits for their conversion to K.)
    if pressure > 100.0:
        warn("Results are not valid for pressures above 100 MPa.")
    elif pressure < 0.0:
        raise ValueError("Pressure must be positive.")
    if temperature < 273:
        warn("Results are not valid for temperatures below 273.15 K.")
    elif temperature > 623.15:
        warn("Results are not valid for temperatures above 623.15 K.")
    elif temperature <= 0.0:
        raise ValueError('Temperature must be positive.')

    # IAPWS region 4 parameters
    n4 = [0.11670521452767e4, -0.72421316703206e6, -0.17073846940092e2,
          0.12020824702470e5, -0.32325550322333e7, 0.14915108613530e2,
          -0.48232657361591e4, 0.40511340542057e6, -0.23855557567849,
          0.65017534844798e3]

    # Compute the saturation temperature at the given pressure.
    beta = pressure**(0.25)
    E = beta**2 + n4[2] * beta + n4[5]
    F = n4[0] * beta**2 + n4[3] * beta + n4[6]
    G = n4[1] * beta**2 + n4[4] * beta + n4[7]
    D = 2.0 * G / (-F - sqrt(F**2 - 4 * E * G))
    T_sat = 0.5 * (n4[9] + D
                   - sqrt((n4[9] + D)**2  - 4.0 * (n4[8] + n4[9] * D)))

    # Make sure we aren't above saturation.  (Relax this bound by .2 degrees
    # for deg C to K conversions.)
    if temperature > T_sat + 0.2:
        warn("Results are not valid for temperatures above saturation "
             "(above the boiling point).")

    # IAPWS region 1 parameters
    R_GAS_CONSTANT = 0.461526  # kJ / kg / K
    ref_p = 16.53  # MPa
    ref_T = 1386  # K
    n1f = [0.14632971213167, -0.84548187169114, -0.37563603672040e1,
           0.33855169168385e1, -0.95791963387872, 0.15772038513228,
           -0.16616417199501e-1, 0.81214629983568e-3, 0.28319080123804e-3,
           -0.60706301565874e-3, -0.18990068218419e-1, -0.32529748770505e-1,
           -0.21841717175414e-1, -0.52838357969930e-4, -0.47184321073267e-3,
           -0.30001780793026e-3, 0.47661393906987e-4, -0.44141845330846e-5,
           -0.72694996297594e-15, -0.31679644845054e-4, -0.28270797985312e-5,
           -0.85205128120103e-9, -0.22425281908000e-5, -0.65171222895601e-6,
           -0.14341729937924e-12, -0.40516996860117e-6, -0.12734301741641e-8,
           -0.17424871230634e-9, -0.68762131295531e-18, 0.14478307828521e-19,
           0.26335781662795e-22, -0.11947622640071e-22, 0.18228094581404e-23,
           -0.93537087292458e-25]
    I1f = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4,
           4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32]
    J1f = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4,
           0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41]

    # Nondimensionalize the pressure and temperature.
    pi = pressure / ref_p
    tau = ref_T / temperature

    # Compute the derivative of gamma (dimensionless Gibbs free energy) with
    # respect to pi.
    gamma1_pi = 0.0
    for n, I, J in zip(n1f, I1f, J1f):
        gamma1_pi -= n * I * (7.1 - pi)**(I - 1) * (tau - 1.222)**J

    # Compute the leading coefficient.  This sets the units at
    #   1 [MPa] * [kg K / kJ] * [1 / K]
    # = 1e6 [N / m^2] * 1e-3 [kg K / N / m] * [1 / K]
    # = 1e3 [kg / m^3]
    # = 1 [g / cm^3]
    coeff = pressure / R_GAS_CONSTANT / temperature

    # Compute and return the density.
    return coeff / pi / gamma1_pi


def _get_element_symbol(element: str) -> str:
    if len(element) > 2:
        symbol = ELEMENT_SYMBOL.get(element.lower())
        if symbol is None:
            raise ValueError(f'Element name "{element}" not recognized')
        return symbol
    else:
        return element


def isotopes(element: str) -> list[tuple[str, float]]:
    """Return naturally occurring isotopes and their abundances

    .. versionadded:: 0.12.1

    Parameters
    ----------
    element : str
        Element symbol (e.g., 'H') or name (e.g., 'helium')

    Returns
    -------
    list
        A list of tuples of (isotope, abundance)

    Raises
    ------
    ValueError
        If the element name is not recognized

    """
    element = _get_element_symbol(element)

    # Get the nuclides present in nature
    result = []
    for kv in NATURAL_ABUNDANCE.items():
        if re.match(r'{}\d+'.format(element), kv[0]):
            result.append(kv)

    return result

1	from __future__ import annotations	11✔
2
3	import itertools	11✔
4	import json	11✔
5	import os	11✔
6	import re	11✔
7	from pathlib import Path	11✔
8	from math import sqrt, log	11✔
9	from typing import TYPE_CHECKING, Literal	11✔
10	from warnings import warn	11✔
11
12	from endf.data import (ATOMIC_NUMBER, ATOMIC_SYMBOL, ELEMENT_SYMBOL,	11✔
13	EV_PER_MEV, K_BOLTZMANN, gnds_name, zam)
14
15	import openmc	11✔
16	from openmc.checkvalue import PathLike	11✔
17
18	if TYPE_CHECKING:
19	from openmc.deplete import Chain
20
21	gnds_name.__module__ = __name__	11✔
22	zam.__module__ = __name__	11✔
23
24	# Isotopic abundances from Meija J, Coplen T B, et al, "Isotopic compositions
25	# of the elements 2013 (IUPAC Technical Report)", Pure. Appl. Chem. 88 (3),
26	# pp. 293-306 (2013). The "representative isotopic abundance" values from
27	# column 9 are used except where an interval is given, in which case the
28	# "best measurement" is used.
29	# Note that the abundances are given as atomic fractions!
30	NATURAL_ABUNDANCE = {	11✔
31	'H1': 0.99984426, 'H2': 0.00015574, 'He3': 0.000002,
32	'He4': 0.999998, 'Li6': 0.07589, 'Li7': 0.92411,
33	'Be9': 1.0, 'B10': 0.1982, 'B11': 0.8018,
34	'C12': 0.988922, 'C13': 0.011078, 'N14': 0.996337,
35	'N15': 0.003663, 'O16': 0.9976206, 'O17': 0.000379,
36	'O18': 0.0020004, 'F19': 1.0, 'Ne20': 0.9048,
37	'Ne21': 0.0027, 'Ne22': 0.0925, 'Na23': 1.0,
38	'Mg24': 0.78951, 'Mg25': 0.1002, 'Mg26': 0.11029,
39	'Al27': 1.0, 'Si28': 0.9222968, 'Si29': 0.0468316,
40	'Si30': 0.0308716, 'P31': 1.0, 'S32': 0.9504074,
41	'S33': 0.0074869, 'S34': 0.0419599, 'S36': 0.0001458,
42	'Cl35': 0.757647, 'Cl37': 0.242353, 'Ar36': 0.003336,
43	'Ar38': 0.000629, 'Ar40': 0.996035, 'K39': 0.932581,
44	'K40': 0.000117, 'K41': 0.067302, 'Ca40': 0.96941,
45	'Ca42': 0.00647, 'Ca43': 0.00135, 'Ca44': 0.02086,
46	'Ca46': 0.00004, 'Ca48': 0.00187, 'Sc45': 1.0,
47	'Ti46': 0.0825, 'Ti47': 0.0744, 'Ti48': 0.7372,
48	'Ti49': 0.0541, 'Ti50': 0.0518, 'V50': 0.0025,
49	'V51': 0.9975, 'Cr50': 0.04345, 'Cr52': 0.83789,
50	'Cr53': 0.09501, 'Cr54': 0.02365, 'Mn55': 1.0,
51	'Fe54': 0.05845, 'Fe56': 0.91754, 'Fe57': 0.02119,
52	'Fe58': 0.00282, 'Co59': 1.0, 'Ni58': 0.680769,
53	'Ni60': 0.262231, 'Ni61': 0.011399, 'Ni62': 0.036345,
54	'Ni64': 0.009256, 'Cu63': 0.6915, 'Cu65': 0.3085,
55	'Zn64': 0.4917, 'Zn66': 0.2773, 'Zn67': 0.0404,
56	'Zn68': 0.1845, 'Zn70': 0.0061, 'Ga69': 0.60108,
57	'Ga71': 0.39892, 'Ge70': 0.2052, 'Ge72': 0.2745,
58	'Ge73': 0.0776, 'Ge74': 0.3652, 'Ge76': 0.0775,
59	'As75': 1.0, 'Se74': 0.0086, 'Se76': 0.0923,
60	'Se77': 0.076, 'Se78': 0.2369, 'Se80': 0.498,
61	'Se82': 0.0882, 'Br79': 0.50686, 'Br81': 0.49314,
62	'Kr78': 0.00355, 'Kr80': 0.02286, 'Kr82': 0.11593,
63	'Kr83': 0.115, 'Kr84': 0.56987, 'Kr86': 0.17279,
64	'Rb85': 0.7217, 'Rb87': 0.2783, 'Sr84': 0.0056,
65	'Sr86': 0.0986, 'Sr87': 0.07, 'Sr88': 0.8258,
66	'Y89': 1.0, 'Zr90': 0.5145, 'Zr91': 0.1122,
67	'Zr92': 0.1715, 'Zr94': 0.1738, 'Zr96': 0.028,
68	'Nb93': 1.0, 'Mo92': 0.14649, 'Mo94': 0.09187,
69	'Mo95': 0.15873, 'Mo96': 0.16673, 'Mo97': 0.09582,
70	'Mo98': 0.24292, 'Mo100': 0.09744, 'Ru96': 0.0554,
71	'Ru98': 0.0187, 'Ru99': 0.1276, 'Ru100': 0.126,
72	'Ru101': 0.1706, 'Ru102': 0.3155, 'Ru104': 0.1862,
73	'Rh103': 1.0, 'Pd102': 0.0102, 'Pd104': 0.1114,
74	'Pd105': 0.2233, 'Pd106': 0.2733, 'Pd108': 0.2646,
75	'Pd110': 0.1172, 'Ag107': 0.51839, 'Ag109': 0.48161,
76	'Cd106': 0.01245, 'Cd108': 0.00888, 'Cd110': 0.1247,
77	'Cd111': 0.12795, 'Cd112': 0.24109, 'Cd113': 0.12227,
78	'Cd114': 0.28754, 'Cd116': 0.07512, 'In113': 0.04281,
79	'In115': 0.95719, 'Sn112': 0.0097, 'Sn114': 0.0066,
80	'Sn115': 0.0034, 'Sn116': 0.1454, 'Sn117': 0.0768,
81	'Sn118': 0.2422, 'Sn119': 0.0859, 'Sn120': 0.3258,
82	'Sn122': 0.0463, 'Sn124': 0.0579, 'Sb121': 0.5721,
83	'Sb123': 0.4279, 'Te120': 0.0009, 'Te122': 0.0255,
84	'Te123': 0.0089, 'Te124': 0.0474, 'Te125': 0.0707,
85	'Te126': 0.1884, 'Te128': 0.3174, 'Te130': 0.3408,
86	'I127': 1.0, 'Xe124': 0.00095, 'Xe126': 0.00089,
87	'Xe128': 0.0191, 'Xe129': 0.26401, 'Xe130': 0.04071,
88	'Xe131': 0.21232, 'Xe132': 0.26909, 'Xe134': 0.10436,
89	'Xe136': 0.08857, 'Cs133': 1.0, 'Ba130': 0.0011,
90	'Ba132': 0.001, 'Ba134': 0.0242, 'Ba135': 0.0659,
91	'Ba136': 0.0785, 'Ba137': 0.1123, 'Ba138': 0.717,
92	'La138': 0.0008881, 'La139': 0.9991119, 'Ce136': 0.00186,
93	'Ce138': 0.00251, 'Ce140': 0.88449, 'Ce142': 0.11114,
94	'Pr141': 1.0, 'Nd142': 0.27153, 'Nd143': 0.12173,
95	'Nd144': 0.23798, 'Nd145': 0.08293, 'Nd146': 0.17189,
96	'Nd148': 0.05756, 'Nd150': 0.05638, 'Sm144': 0.0308,
97	'Sm147': 0.15, 'Sm148': 0.1125, 'Sm149': 0.1382,
98	'Sm150': 0.0737, 'Sm152': 0.2674, 'Sm154': 0.2274,
99	'Eu151': 0.4781, 'Eu153': 0.5219, 'Gd152': 0.002,
100	'Gd154': 0.0218, 'Gd155': 0.148, 'Gd156': 0.2047,
101	'Gd157': 0.1565, 'Gd158': 0.2484, 'Gd160': 0.2186,
102	'Tb159': 1.0, 'Dy156': 0.00056, 'Dy158': 0.00095,
103	'Dy160': 0.02329, 'Dy161': 0.18889, 'Dy162': 0.25475,
104	'Dy163': 0.24896, 'Dy164': 0.2826, 'Ho165': 1.0,
105	'Er162': 0.00139, 'Er164': 0.01601, 'Er166': 0.33503,
106	'Er167': 0.22869, 'Er168': 0.26978, 'Er170': 0.1491,
107	'Tm169': 1.0, 'Yb168': 0.00123, 'Yb170': 0.02982,
108	'Yb171': 0.14086, 'Yb172': 0.21686, 'Yb173': 0.16103,
109	'Yb174': 0.32025, 'Yb176': 0.12995, 'Lu175': 0.97401,
110	'Lu176': 0.02599, 'Hf174': 0.0016, 'Hf176': 0.0526,
111	'Hf177': 0.186, 'Hf178': 0.2728, 'Hf179': 0.1362,
112	'Hf180': 0.3508, 'Ta180_m1': 0.0001201, 'Ta181': 0.9998799,
113	'W180': 0.0012, 'W182': 0.265, 'W183': 0.1431,
114	'W184': 0.3064, 'W186': 0.2843, 'Re185': 0.374,
115	'Re187': 0.626, 'Os184': 0.0002, 'Os186': 0.0159,
116	'Os187': 0.0196, 'Os188': 0.1324, 'Os189': 0.1615,
117	'Os190': 0.2626, 'Os192': 0.4078, 'Ir191': 0.373,
118	'Ir193': 0.627, 'Pt190': 0.00012, 'Pt192': 0.00782,
119	'Pt194': 0.32864, 'Pt195': 0.33775, 'Pt196': 0.25211,
120	'Pt198': 0.07356, 'Au197': 1.0, 'Hg196': 0.0015,
121	'Hg198': 0.1004, 'Hg199': 0.1694, 'Hg200': 0.2314,
122	'Hg201': 0.1317, 'Hg202': 0.2974, 'Hg204': 0.0682,
123	'Tl203': 0.29524, 'Tl205': 0.70476, 'Pb204': 0.014,
124	'Pb206': 0.241, 'Pb207': 0.221, 'Pb208': 0.524,
125	'Bi209': 1.0, 'Th230': 0.0002, 'Th232': 0.9998,
126	'Pa231': 1.0, 'U234': 0.000054, 'U235': 0.007204,
127	'U238': 0.992742
128	}
129
130	DADZ = {	11✔
131	'(n,2nd)': (-3, -1),
132	'(n,2n)': (-1, 0),
133	'(n,3n)': (-2, 0),
134	'(n,na)': (-4, -2),
135	'(n,n3a)': (-12, -6),
136	'(n,2na)': (-5, -2),
137	'(n,3na)': (-6, -2),
138	'(n,np)': (-1, -1),
139	'(n,n2a)': (-8, -4),
140	'(n,2n2a)': (-9, -4),
141	'(n,nd)': (-2, -1),
142	'(n,nt)': (-3, -1),
143	'(n,n3He)': (-3, -2),
144	'(n,nd2a)': (-10, -5),
145	'(n,nt2a)': (-11, -5),
146	'(n,4n)': (-3, 0),
147	'(n,2np)': (-2, -1),
148	'(n,3np)': (-3, -1),
149	'(n,n2p)': (-2, -2),
150	'(n,npa)': (-5, -3),
151	'(n,gamma)': (1, 0),
152	'(n,p)': (0, -1),
153	'(n,d)': (-1, -1),
154	'(n,t)': (-2, -1),
155	'(n,3He)': (-2, -2),
156	'(n,a)': (-3, -2),
157	'(n,2a)': (-7, -4),
158	'(n,3a)': (-11, -6),
159	'(n,2p)': (-1, -2),
160	'(n,pa)': (-4, -3),
161	'(n,t2a)': (-10, -5),
162	'(n,d2a)': (-9, -5),
163	'(n,pd)': (-2, -2),
164	'(n,pt)': (-3, -2),
165	'(n,da)': (-5, -3),
166	'(n,5n)': (-4, 0),
167	'(n,6n)': (-5, 0),
168	'(n,2nt)': (-4, -1),
169	'(n,ta)': (-6, -3),
170	'(n,4np)': (-4, -1),
171	'(n,3nd)': (-4, -1),
172	'(n,nda)': (-6, -3),
173	'(n,2npa)': (-6, -3),
174	'(n,7n)': (-6, 0),
175	'(n,8n)': (-7, 0),
176	'(n,5np)': (-5, -1),
177	'(n,6np)': (-6, -1),
178	'(n,7np)': (-7, -1),
179	'(n,4na)': (-7, -2),
180	'(n,5na)': (-8, -2),
181	'(n,6na)': (-9, -2),
182	'(n,7na)': (-10, -2),
183	'(n,4nd)': (-5, -1),
184	'(n,5nd)': (-6, -1),
185	'(n,6nd)': (-7, -1),
186	'(n,3nt)': (-5, -1),
187	'(n,4nt)': (-6, -1),
188	'(n,5nt)': (-7, -1),
189	'(n,6nt)': (-8, -1),
190	'(n,2n3He)': (-4, -2),
191	'(n,3n3He)': (-5, -2),
192	'(n,4n3He)': (-6, -2),
193	'(n,3n2p)': (-4, -2),
194	'(n,3n2a)': (-10, -4),
195	'(n,3npa)': (-7, -3),
196	'(n,dt)': (-4, -2),
197	'(n,npd)': (-3, -2),
198	'(n,npt)': (-4, -2),
199	'(n,ndt)': (-5, -2),
200	'(n,np3He)': (-4, -3),
201	'(n,nd3He)': (-5, -3),
202	'(n,nt3He)': (-6, -3),
203	'(n,nta)': (-7, -3),
204	'(n,2n2p)': (-3, -2),
205	'(n,p3He)': (-4, -3),
206	'(n,d3He)': (-5, -3),
207	'(n,3Hea)': (-6, -4),
208	'(n,4n2p)': (-5, -2),
209	'(n,4n2a)': (-11, -4),
210	'(n,4npa)': (-8, -3),
211	'(n,3p)': (-2, -3),
212	'(n,n3p)': (-3, -3),
213	'(n,3n2pa)': (-8, -4),
214	'(n,5n2p)': (-6, -2),
215	}
216
217	# Values here are from the Committee on Data for Science and Technology
218	# (CODATA) 2018 recommendation (https://physics.nist.gov/cuu/Constants/).
219
220	# Unit conversions
221	JOULE_PER_EV = 1.602176634e-19	11✔
222
223	# Avogadro's constant
224	AVOGADRO = 6.02214076e23	11✔
225
226	# Neutron mass in units of amu
227	NEUTRON_MASS = 1.00866491595	11✔
228
229	# Used in atomic_mass function as a cache
230	_ATOMIC_MASS: dict[str, float] = {}	11✔
231
232	# Used in half_life function as a cache
233	_HALF_LIFE: dict[str, float] = {}	11✔
234	_LOG_TWO = log(2.0)	11✔
235
236	def atomic_mass(isotope):	11✔
237	"""Return atomic mass of isotope in atomic mass units.
238
239	Atomic mass data comes from the `Atomic Mass Evaluation 2020
240	<https://doi.org/10.1088/1674-1137/abddaf>`_.
241
242	Parameters
243	----------
244	isotope : str
245	Name of isotope, e.g., 'Pu239'
246
247	Returns
248	-------
249	float
250	Atomic mass of isotope in [amu]
251
252	"""
253	if not _ATOMIC_MASS:	11✔
254
255	# Load data from AME2020 file
256	mass_file = os.path.join(os.path.dirname(__file__), 'mass_1.mas20.txt')	11✔
257	with open(mass_file, 'r') as ame:	11✔
258	# Read lines in file starting at line 37
259	for line in itertools.islice(ame, 36, None):	11✔
260	name = f'{line[20:22].strip()}{int(line[16:19])}'	11✔
261	mass = float(line[106:109]) + 1e-6*float(	11✔
262	line[110:116] + '.' + line[117:123])
263	_ATOMIC_MASS[name.lower()] = mass	11✔
264
265	# For isotopes found in some libraries that represent all natural
266	# isotopes of their element (e.g. C0), calculate the atomic mass as
267	# the sum of the atomic mass times the natural abundance of the isotopes
268	# that make up the element.
269	for element in ['C', 'Zn', 'Pt', 'Os', 'Tl', 'V']:	11✔
270	isotope_zero = element.lower() + '0'	11✔
271	_ATOMIC_MASS[isotope_zero] = 0.	11✔
272	for iso, abundance in isotopes(element):	11✔
273	_ATOMIC_MASS[isotope_zero] += abundance * _ATOMIC_MASS[iso.lower()]	11✔
274
275	# Get rid of metastable information
276	if '_' in isotope:	11✔
277	isotope = isotope[:isotope.find('_')]	11✔
278
279	return _ATOMIC_MASS[isotope.lower()]	11✔
280
281
282	def atomic_weight(element):	11✔
283	"""Return atomic weight of an element in atomic mass units.
284
285	Computes an average of the atomic mass of each of element's naturally
286	occurring isotopes weighted by their relative abundance.
287
288	Parameters
289	----------
290	element : str
291	Element symbol (e.g., 'H') or name (e.g., 'helium')
292
293	Returns
294	-------
295	float
296	Atomic weight of element in [amu]
297
298	"""
299	weight = 0.	11✔
300	for nuclide, abundance in isotopes(element):	11✔
301	weight += atomic_mass(nuclide) * abundance	11✔
302	if weight > 0.:	11✔
303	return weight	11✔
304	else:
305	raise ValueError(f"No naturally-occurring isotopes for element '{element}'.")	11✔
306
307
308	def half_life(	11✔
309	isotope: str,
310	chain_file: Literal[False] \| None \| PathLike \| Chain = False
311	) -> float \| None:
312	"""Return half-life of isotope in seconds or None if isotope is stable
313
314	By default, half-life values are from the `ENDF/B-VIII.0 decay sublibrary
315	<https://www.nndc.bnl.gov/endf-b8.0/download.html>`_. A depletion chain can
316	also be used as the source of half-life values.
317
318	.. versionadded:: 0.13.1
319
320	.. versionchanged:: 0.15.4
321	Added the ``chain_file`` argument.
322
323	Parameters
324	----------
325	isotope : str
326	Name of isotope, e.g., 'Pu239'
327	chain_file : False, None, PathLike, or openmc.deplete.Chain, optional
328	Source of half-life values. If ``False``, only ENDF/B-VIII.0 data is
329	used. If ``None``, the chain specified by
330	``openmc.config['chain_file']`` is used when available. If a path or
331	:class:`openmc.deplete.Chain` is given, that chain is used. For ``None``
332	or an explicit chain, nuclides absent from the chain fall back to
333	ENDF/B-VIII.0 data.
334
335	Returns
336	-------
337	float or None
338	Half-life of isotope in [s], or None if the isotope is stable
339
340	"""
341	if chain_file is not False:	11✔
342	if chain_file is not None or openmc.config.get('chain_file') is not None:	11✔
343	# Local import avoids a circular dependency
344	from openmc.deplete.chain import _get_chain	11✔
345	chain = _get_chain(chain_file)	11✔
346	if isotope in chain:	11✔
347	return chain[isotope].half_life	11✔
348
349	global _HALF_LIFE
350	if not _HALF_LIFE:	11✔
351	# Load ENDF/B-VIII.0 data from JSON file
352	half_life_path = Path(__file__).with_name('half_life.json')	11✔
353	_HALF_LIFE = json.loads(half_life_path.read_text())	11✔
354
355	return _HALF_LIFE.get(isotope.lower())	11✔
356
357
358	def decay_constant(	11✔
359	isotope: str,
360	chain_file: Literal[False] \| None \| PathLike \| Chain = False
361	) -> float:
362	"""Return decay constant of isotope in [s^-1]
363
364	Decay constants are based on half-life values from the
365	:func:`~openmc.data.half_life` function. When the isotope is stable, a decay
366	constant of zero is returned.
367
368	.. versionadded:: 0.13.1
369
370	.. versionchanged:: 0.15.4
371	Added the ``chain_file`` argument.
372
373	Parameters
374	----------
375	isotope : str
376	Name of isotope, e.g., 'Pu239'
377	chain_file : False, None, PathLike, or openmc.deplete.Chain, optional
378	Source of half-life values. If ``False``, only ENDF/B-VIII.0 data is
379	used. If ``None``, the chain specified by
380	``openmc.config['chain_file']`` is used when available. If a path or
381	:class:`openmc.deplete.Chain` is given, that chain is used. For ``None``
382	or an explicit chain, nuclides absent from the chain fall back to
383	ENDF/B-VIII.0 data.
384
385	Returns
386	-------
387	float
388	Decay constant of isotope in [s^-1]
389
390	See also
391	--------
392	openmc.data.half_life
393
394	"""
395	t = half_life(isotope, chain_file)	11✔
396	return _LOG_TWO / t if t else 0.0	11✔
397
398
399	def water_density(temperature, pressure=0.1013):	11✔
400	"""Return the density of liquid water at a given temperature and pressure.
401
402	The density is calculated from a polynomial fit using equations and values
403	from the 2012 version of the IAPWS-IF97 formulation. Only the equations
404	for region 1 are implemented here. Region 1 is limited to liquid water
405	below 100 [MPa] with a temperature above 273.15 [K], below 623.15 [K], and
406	below saturation.
407
408	Reference: International Association for the Properties of Water and Steam,
409	"Revised Release on the IAPWS Industrial Formulation 1997 for the
410	Thermodynamic Properties of Water and Steam", IAPWS R7-97(2012).
411
412	Parameters
413	----------
414	temperature : float
415	Water temperature in units of [K]
416	pressure : float
417	Water pressure in units of [MPa]
418
419	Returns
420	-------
421	float
422	Water density in units of [g/cm^3]
423
424	"""
425
426	# Make sure the temperature and pressure are inside the min/max region 1
427	# bounds. (Relax the 273.15 bound to 273 in case a user wants 0 deg C data
428	# but they only use 3 digits for their conversion to K.)
429	if pressure > 100.0:	11✔
UNCOV 430	warn("Results are not valid for pressures above 100 MPa.")	×
431	elif pressure < 0.0:	11✔
UNCOV 432	raise ValueError("Pressure must be positive.")	×
433	if temperature < 273:	11✔
UNCOV 434	warn("Results are not valid for temperatures below 273.15 K.")	×
435	elif temperature > 623.15:	11✔
UNCOV 436	warn("Results are not valid for temperatures above 623.15 K.")	×
437	elif temperature <= 0.0:	11✔
UNCOV 438	raise ValueError('Temperature must be positive.')	×
439
440	# IAPWS region 4 parameters
441	n4 = [0.11670521452767e4, -0.72421316703206e6, -0.17073846940092e2,	11✔
442	0.12020824702470e5, -0.32325550322333e7, 0.14915108613530e2,
443	-0.48232657361591e4, 0.40511340542057e6, -0.23855557567849,
444	0.65017534844798e3]
445
446	# Compute the saturation temperature at the given pressure.
447	beta = pressure**(0.25)	11✔
448	E = beta*2 + n4[2] beta + n4[5]	11✔
449	F = n4[0] * beta*2 + n4[3] beta + n4[6]	11✔
450	G = n4[1] * beta*2 + n4[4] beta + n4[7]	11✔
451	D = 2.0 * G / (-F - sqrt(F*2 - 4 E * G))	11✔
452	T_sat = 0.5 * (n4[9] + D	11✔
453	- sqrt((n4[9] + D)*2 - 4.0 (n4[8] + n4[9] * D)))
454
455	# Make sure we aren't above saturation. (Relax this bound by .2 degrees
456	# for deg C to K conversions.)
457	if temperature > T_sat + 0.2:	11✔
UNCOV 458	warn("Results are not valid for temperatures above saturation "	×
459	"(above the boiling point).")
460
461	# IAPWS region 1 parameters
462	R_GAS_CONSTANT = 0.461526 # kJ / kg / K	11✔
463	ref_p = 16.53 # MPa	11✔
464	ref_T = 1386 # K	11✔
465	n1f = [0.14632971213167, -0.84548187169114, -0.37563603672040e1,	11✔
466	0.33855169168385e1, -0.95791963387872, 0.15772038513228,
467	-0.16616417199501e-1, 0.81214629983568e-3, 0.28319080123804e-3,
468	-0.60706301565874e-3, -0.18990068218419e-1, -0.32529748770505e-1,
469	-0.21841717175414e-1, -0.52838357969930e-4, -0.47184321073267e-3,
470	-0.30001780793026e-3, 0.47661393906987e-4, -0.44141845330846e-5,
471	-0.72694996297594e-15, -0.31679644845054e-4, -0.28270797985312e-5,
472	-0.85205128120103e-9, -0.22425281908000e-5, -0.65171222895601e-6,
473	-0.14341729937924e-12, -0.40516996860117e-6, -0.12734301741641e-8,
474	-0.17424871230634e-9, -0.68762131295531e-18, 0.14478307828521e-19,
475	0.26335781662795e-22, -0.11947622640071e-22, 0.18228094581404e-23,
476	-0.93537087292458e-25]
477	I1f = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4,	11✔
478	4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32]
479	J1f = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4,	11✔
480	0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41]
481
482	# Nondimensionalize the pressure and temperature.
483	pi = pressure / ref_p	11✔
484	tau = ref_T / temperature	11✔
485
486	# Compute the derivative of gamma (dimensionless Gibbs free energy) with
487	# respect to pi.
488	gamma1_pi = 0.0	11✔
489	for n, I, J in zip(n1f, I1f, J1f):	11✔
490	gamma1_pi -= n * I * (7.1 - pi)*(I - 1) (tau - 1.222)**J	11✔
491
492	# Compute the leading coefficient. This sets the units at
493	# 1 [MPa] * [kg K / kJ] * [1 / K]
494	# = 1e6 [N / m^2] * 1e-3 [kg K / N / m] * [1 / K]
495	# = 1e3 [kg / m^3]
496	# = 1 [g / cm^3]
497	coeff = pressure / R_GAS_CONSTANT / temperature	11✔
498
499	# Compute and return the density.
500	return coeff / pi / gamma1_pi	11✔
501
502
503	def _get_element_symbol(element: str) -> str:	11✔
504	if len(element) > 2:	11✔
505	symbol = ELEMENT_SYMBOL.get(element.lower())	11✔
506	if symbol is None:	11✔
507	raise ValueError(f'Element name "{element}" not recognized')	11✔
508	return symbol	11✔
509	else:
510	return element	11✔
511
512
513	def isotopes(element: str) -> list[tuple[str, float]]:	11✔
514	"""Return naturally occurring isotopes and their abundances
515
516	.. versionadded:: 0.12.1
517
518	Parameters
519	----------
520	element : str
521	Element symbol (e.g., 'H') or name (e.g., 'helium')
522
523	Returns
524	-------
525	list
526	A list of tuples of (isotope, abundance)
527
528	Raises
529	------
530	ValueError
531	If the element name is not recognized
532
533	"""
534	element = _get_element_symbol(element)	11✔
535
536	# Get the nuclides present in nature
537	result = []	11✔
538	for kv in NATURAL_ABUNDANCE.items():	11✔
539	if re.match(r'{}\d+'.format(element), kv[0]):	11✔
540	result.append(kv)	11✔
541
542	return result	11✔

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