python3-periodictable 1.5.0-3 / usr / lib / python3 / dist-packages / periodictable / nsf.py

# -*- coding: utf-8 -*-
# This program is public domain
# Author: Paul Kienzle
r"""

Neutron scattering factors for the elements and isotopes.

For details of neutron scattering factor values, see :class:`Neutron`.
The property is set to *None* if there is no neutron scattering information
for the element. Individual isotopes may have their own scattering
information.

Example
=======

Print a table of coherent scattering length densities for isotopes
of a particular element:

.. doctest::

    >>> import periodictable
    >>> for iso in periodictable.Ni:
    ...     if iso.neutron.has_sld():
    ...         print("%s %7.4f"%(iso,iso.neutron.sld()[0]))
    58-Ni 13.1526
    60-Ni  2.5575
    61-Ni  6.9417
    62-Ni -7.9464
    64-Ni -0.3379


Details
=======

There are a number of functions available in periodictable.nsf

    :func:`neutron_energy`
        Return neutron energy given wavelength.

    :func:`neutron_wavelength`
        Return wavelength given neutron energy.

    :func:`neutron_wavelength_from_velocity`
        Return wavelength given neutron velocity.

    :func:`neutron_scattering`
        Computes scattering length density, cross sections and
        penetration depth for a compound.

    :func:`neutron_sld`
        Computes scattering length density for a compound.

    :func:`neutron_composite_sld`
        Returns a scattering length density for a compound whose composition
        is variable.

    :func:`energy_dependent_table`
        Lists isotopes with energy dependence.

    :func:`sld_table`
        Lists scattering length densitys for all elements in natural abundance.

    :func:`absorption_comparison_table`
        Compares the imaginary bound coherent scattering length to the
        absorption cross section.

    :func:`coherent_comparison_table`
        Compares the bound coherent scattering length to the
        coherent scattering cross section.

    :func:`total_comparison_table`
        Compares the total scattering cross section to the sum of the
        coherent and incoherent scattering cross sections.

For private tables use :func:`init` to set the data.

The neutron scattering information table is reproduced from the Atomic
Institute for Austrian Universities\ [#Rauch2003]_  (retrieve March 2008):

http://www.ati.ac.at/~neutropt/scattering/table.html

The above site has references to the published values for every entry in
the table.  We have included these in the documentation directory
associated with the periodictable package.

.. Note:

   Enteries in the table have been measured independently, so the values
   measured for the scattering length of an element or isotope may be
   inconsistent with the values measured for the corresponding cross section.

.. [#Rauch2003] Rauch, H. and Waschkowski, W. (2003)
    Neutron Scattering Lengths in ILL
    Neutron Data Booklet (second edition), A.-J. Dianoux, G. Lander, Eds.
    Old City Publishing, Philidelphia, PA. pp 1.1-1 to 1.1-17.

.. [#Rauch2000] Rauch, H. and Waschkowski, W. (2000)
    Neutron scattering lengths. Schopper, H. (ed.).
    SpringerMaterials - The Landolt-Börnstein Database (http://www.springermaterials.com).
    doi: 10.1007/10499706_6

.. [#Koester1991] Koester, L., Rauch, H., Seymann. E. (1991)
    Atomic Data Nuclear Data Tables 49, 65

.. [#Lynn1990] Lynn, J.E. and Seeger, P.A. (1990)
    Resonance effects in neutron scattering lengths of rare-earth nuclides.
    Atomic Data and Nuclear Data Tables 44, 191-207.

.. [#Sears1999] Sears, V. F. (1999)
    4.4.4 Scattering lengths for neutrons.
    In Wilson & Prince eds. Intl. Tables for Crystallography C
    Kluwer Academic Publishers. pp 383.

.. [#Sears1992] Sears, V.F. (1992)
    Neutron scattering lengths and cross sections.
    Neutron News 3, No. 3, 26-37.

.. [#May1982] May, R.P.,  Ibel, K. and Haas, J. (1982)
    The forward scattering of cold neutrons by mixtures of light and heavy water.
    J. Appl. Cryst. 15, 15-19.

.. [#Smith2006] Smith, G.S. and Majkrzak, C.M. (2006)
    2.9 Neutron reflectometry.
    In E. Prince ed. Intl. Tables for Crystallography C
    Wiley InterScience. pp 126-146.
    doi: 10.1107/97809553602060000584

.. [#Glinka2011] Glinka, C.J. (2011)
    Incoherent Neutron Scattering from Multi-element Materials.
    J. Appl. Cryst. 44, 618-624.
    doi: 10.1107/S0021889811008223
"""
from __future__ import print_function

import numpy
from numpy import sqrt, pi, asarray, inf
from .core import Element, Isotope, default_table
from .constants import (avogadro_number, plancks_constant, electron_volt,
                        neutron_mass, atomic_mass_constant)
from .util import require_keywords

__all__ = ['init', 'Neutron',
           'neutron_energy', 'neutron_wavelength',
           'neutron_wavelength_from_velocity',
           'neutron_scattering', 'neutron_sld', 'neutron_composite_sld',
           'sld_plot',
           'absorption_comparison_table', 'coherent_comparison_table',
           'incoherent_comparison_table', 'total_comparison_table',
           'energy_dependent_table', 'sld_table',
           'neutron_sld_from_atoms',
           #'scattering_potential',
          ]

ABSORPTION_WAVELENGTH = 1.798


# Velocity (m/s) <=> wavelength (A)
#   lambda = h / p = h (eV) (J/eV) / ( m_n (kg) v (m/s) ) (10^10 A/m)
#
# Since plancks constant is in eV
#   lambda = (1e10 * h*electron_volt/(neutron_mass/N_A)) / velocity

# Energy (eV) <=> wavelength (A)
#   h^2/(2 m_n kg lambda A) (10^20 A/m) (1000 meV/eV) / (electron_volt J/eV)
# Since plancks constant is in eV
#   (h J)^2/electron_volt = ((h eV)(electron_volt J/eV))^2/electron_volt
#                         = (h eV)^2 * electron_volt
ENERGY_FACTOR = (plancks_constant**2*electron_volt
                 / (2 * neutron_mass * atomic_mass_constant)) * 1e23
VELOCITY_FACTOR = (plancks_constant*electron_volt
                   / (neutron_mass * atomic_mass_constant)) * 1e10
def neutron_wavelength(energy):
    r"""
    Convert neutron energy to wavelength.

    :Parameters:
        *energy* : float or vector | meV

    :Returns:
        *wavelength* : float or vector | |Ang|

    Energy is converted to wavelength using

    .. math::

        E = 1/2 m_n v^2 = h^2 / (2 m_n \lambda^2)
        \Rightarrow \lambda = \sqrt{h^2 / (2 m_n E)}

    where

        $h$ = planck's constant in |Js|

        $m_n$ = neutron mass in kg

    """
    return sqrt(ENERGY_FACTOR / asarray(energy))

def neutron_wavelength_from_velocity(velocity):
    r"""
    Convert neutron velocity to wavelength.

    :Parameters:
        *velocity* : float or vector | m/s

    :Returns:
        *wavelength* : float or vector | |Ang|

    Velocity is converted to wavelength using

    .. math::

        \lambda = h/p = h/(m_n v)

    where

        $h$ = planck's constant in |Js|

        $m_n$ = neutron mass in kg
    """
    return VELOCITY_FACTOR / velocity

def neutron_energy(wavelength):
    r"""
    Convert neutron wavelength to energy.

    :Parameters:
        *wavelength* : float or vector | |Ang|

    :Returns:
        *energy* : float or vector | meV

    Wavelength is converted to energy using

    .. math::

        E = 1/2 m_n v^2 = h^2 / (2 m_n \lambda^2)

    where:

        $h$ = planck's constant in |Js|

        $m_n$ = neutron mass in kg
    """
    return ENERGY_FACTOR / asarray(wavelength)**2

def _CHECK_scattering_potential(sld):
    r"""
    Convert neutron scattering length density to energy potential.

    :Parameters:
        *sld* : float or vector | |1e-6/Ang^2|

            Scattering length density.

    :Returns:
        *energy* : float or vector | $10^{-6}$ eV

            Scattering potential.

    Computes:[#Smith2006]_

    .. math::

        V = 2 \pi \hbar^2 N_b / m_n

    where:

        $\hbar = h / (2 \pi)$

        $h$ = planck's constant in |Js|

        $N_b = \sum{ n_i b_i } / V$

        $m_n$ = neutron mass in kg
    """
    return (ENERGY_FACTOR/pi) * asarray(sld)

class Neutron(object):
    r"""
    Neutron scattering factors are attached to each element in the periodic
    table for which values are available.  If no information is available,
    then the neutron field of the element will be *None*. Even when neutron
    information is available, it may not be complete, so individual fields
    may be *None*.

    The following fields are defined:

    * b_c (fm)
        Bounds coherent scattering length.

    * total (barn)
        Total scattering cross section $\sigma_s$.  This does not include the
        absorption cross section.  To compute the total collision cross
        section use $\sigma_t = \sigma_s + \sigma_a$

    * absorption (barn)
        Absorption cross section $\sigma_a$ at 1.798 |Ang|.  Scale to your beam
        by dividing by periodictable.nsf.ABSORPTION_WAVELENGTH and multiplying
        by your wavelength.


    Additional fields not used for calculation include:

    * b_c_i (fm)
        Imaginary bound coherent scattering length.  This is
        related to absorption cross section by $\sigma_a = 4 \pi b_i/k$ where
        $k = 2 \pi/\lambda$ and an additional factor of 1000 for converting
        between |Ang|\ |cdot|\ fm and barns.  b_c_i is not available
        for all isotopes for which absorption cross sections have been measured.

    * bp, bm (fm)
        Spin-dependent scattering for I+1/2 and I-1/2 (not always available).
        Incoherent scattering arises from the spin-dependent scattering b+
        and b-. The Neutron Data Booklet\ [#Rauch2003]_ gives formulas for
        calculating coherent and incoherent scattering from b+ and b- alone.

    * bp_i, bm_i (fm)
        Imaginary portion of bp and bm.

    * is_energy_dependent (boolean)
        Do not use this data if scattering is energy dependent.

    * coherent (barn)
        Coherent scattering cross section.  This is tabulated but not used.
        In theory coherent scattering is related to bound coherent scattering
        by $\sigma_s = 4 \pi b_c^2/100$. In practice, these values are
        different, with the following table showing the largest relative
        difference:

        ========  ========  ========  ========  ========
        Sc   3%   Ti   4%   V   34%   Mn   1%   Cd   4%
        Te   4%   Xe   9%   Sm 100%   Eu  46%   Gd 61%
        Tb   1%   Ho  11%   W    4%   Au   7%   Hg  2%
        ========  ========  ========  ========  ========

    * incoherent (barn)
        Incoherent scattering cross section $\sigma_i$.  This is tabulated but
        not used. Instead, the incoherent cross section is computed from the
        total cross section minus the coherent cross section even for single
        atoms so that results from compounds are consistent with results from
        single atoms.

    For elements, the scattering cross-sections are based on the natural
    abundance of the individual isotopes. Individual isotopes may have
    the following additional fields

    * abundance (%)
        Isotope abundance used to compute the properties of the element in
        natural abundance.

    * nuclear_spin (string)
        Spin on the nucleus: '0', '1/2', '3/2', etc.

    Each field ``T`` above has a corresponding ``T_units`` attribute with
    the name of the units. For scattering calculations, the scattering
    length density is the value of interest. This is computed from the
    *number_density* of the individual elements, as derived from the element
    density and atomic mass.

    .. Note:: 1 barn = 100 |fm^2|
    """
    b_c = None
    b_c_i = None
    b_c_units = "fm"
    bp = None
    bp_i = None
    bp_units = "fm"
    bm = None
    bm_i = None
    bm_units = "fm"
    coherent = None
    coherent_units = "barn"
    incoherent = None
    incoherent_units = "barn"
    total = None
    total_units = "barn"
    absorption = None
    absorption_units = "barn"
    abundance = 0.
    abundance_units = "%"
    is_energy_dependent = False
    def __init__(self):
        self._number_density = None
    def __str__(self):
        return ("b_c=%.3g coh=%.3g inc=%.3g abs=%.3g"
                % (self.b_c, self.coherent, self.incoherent, self.absorption))
    def has_sld(self):
        """Returns *True* if sld is defined for this element/isotope."""
        return None not in [self.b_c, self._number_density]
    @require_keywords
    def sld(self, wavelength=ABSORPTION_WAVELENGTH):
        """
        Returns scattering length density for the element at natural
        abundance and density.

        :Parameters:
            *wavelength* : float | |Ang|

        :Returns:
            *sld* : (float, float, float) | |1e-6/Ang^2|
                (*real*, -*imaginary*, *incoherent*) scattering length density.

        .. Note:

           Values may not be correct when the element or isotope has
           *is_energy_dependent=True*

        See :func:`neutron_scattering` for details.
        """

        # Compute number and absorption density assuming isotope has
        # same structure as the bulk element
        if not self.has_sld():
            return None, None, None

        b_c = self.b_c
        sigma_s = self.total
        sigma_a = self.absorption/ABSORPTION_WAVELENGTH*wavelength

        number_density = self._number_density*1e-24

        # PAK 2017-04-21: compute incoherent cross section from total cross section
        sigma_c = 4*pi/100 * b_c**2
        sigma_i = max(sigma_s - sigma_c, 0.)

        # Compute SLD
        sld_re = number_density * b_c * 10
        sld_im = number_density * sigma_a / (2 * wavelength) * 0.01
        sld_inc = number_density * sqrt(sigma_i / (4*pi/100)) * 10

        return sld_re, sld_im, sld_inc

    @require_keywords
    def scattering(self, wavelength=ABSORPTION_WAVELENGTH):
        r"""
        Returns neutron scattering information for the element at natural
        abundance and density.

        :Parameters:
            *wavelength* : float | |Ang|

        :Returns:
            *sld* : (float, float, float) | |1e-6/Ang^2|
                (*real*, -*imaginary*, *incoherent*) scattering length density
            *xs* : (float, float, float) | |1/cm|
                (*coherent*, *absorption*, *incoherent*) cross sections.
            *penetration* : float | cm
                1/e penetration length.

        .. Note:

           Values may not be correct when the element or isotope has
           *is_energy_dependent=True*

        See :func:`neutron_scattering` for details.
        """

        # Compute number and absorption density assuming isotope has
        # same structure as the bulk element
        if not self.has_sld():
            return None, None, None

        b_c = self.b_c
        sigma_s = self.total
        sigma_a = self.absorption*wavelength/ABSORPTION_WAVELENGTH

        number_density = self._number_density*1e-24

        # PAK 2017-04-21: compute incoherent cross section from total cross section
        sigma_c = 4*pi/100 * b_c**2
        sigma_i = max(sigma_s - sigma_c, 0.)

        # Compute SLD
        sld_re = number_density * b_c * 10
        sld_im = number_density * sigma_a / (2 * wavelength) * 0.01
        sld_inc = number_density * sqrt(sigma_i / (4*pi/100)) * 10

        # Compute scattering cross section per unit volume
        total_xs = number_density * sigma_s
        coh_xs = number_density * sigma_c
        abs_xs = number_density * sigma_a
        inc_xs = number_density * sigma_i

        # Compute 1/e length
        penetration = 1/(abs_xs + total_xs)

        return (sld_re, sld_im, sld_inc), (coh_xs, abs_xs, inc_xs), penetration


def init(table, reload=False):
    """
    Loads the Rauch table from the neutron data book.
    """
    if 'neutron' in table.properties and not reload:
        return
    table.properties.append('neutron')
    assert ('density' in table.properties and 'mass' in table.properties), \
        "Neutron table requires mass and density properties"

    # Defaults for missing neutron information
    missing = Neutron()
    Isotope.neutron = missing
    Element.neutron = missing

    for line in nsftable.split('\n'):
        columns = line.split(',')

        nsf = Neutron()
        p = columns[1]
        spin = columns[2]
        nsf.b_c, nsf.bp, nsf.bm = [fix_number(a) for a in columns[3:6]]
        nsf.is_energy_dependent = (columns[6] == 'E')
        nsf.coherent, nsf.incoherent, nsf.total, nsf.absorption \
            = [fix_number(a) for a in columns[7:]]

        parts = columns[0].split('-')
        Z = int(parts[0])
        symbol = parts[1]
        isotope_number = int(parts[2]) if len(parts) == 3 else 0

        # Fetch element from the table and check that the symbol matches
        element = table[Z]
        assert element.symbol == symbol, \
            "Symbol %s does not match %s" % (symbol, element.symbol)

        # Plug the default number density for the element into the nsf so
        # it can calculate sld.
        nsf._number_density = element.number_density


        # For new elements, clear out 'neutron' attribute for isotopes
        # This protects against isotope using the element data when
        # they don't have any specific neutron data.
        #if isotope_number == 0 or not hasattr(element,'neutron'):
        #    for iso in element: iso.neutron = None

        if isotope_number == 0:
            # Bulk values using laboratory abundances of isotopes
            element.neutron = nsf
        else:
            # Values for the individual isotope
            isotope = element.add_isotope(isotope_number)
            isotope.neutron = nsf
            isotope.nuclear_spin = spin
            # p column contains either abundance(uncertainty) or "half-life Y"
            isotope.neutron.abundance = fix_number(p) if ' ' not in p else 0

            # If the element is not yet initialized, copy info into the atom.
            # This serves to set the element info for elements with only
            # one isotope.
            if element.neutron is missing:
                element.neutron = nsf

    for line in nsftableI.split('\n'):
        columns = line.split(',')

        # Fetch the nsf record
        parts = columns[0].split('-')
        Z = int(parts[0])
        symbol = parts[1]
        isotope_number = int(parts[2]) if len(parts) == 3 else 0
        element = table[Z]
        if isotope_number == 0:
            nsf = element.neutron
        else:
            nsf = element[isotope_number].neutron

        # Read imaginary values
        nsf.b_c_i, nsf.bp_i, nsf.bm_i = [fix_number(a) for a in columns[1:]]

    # Xe total cross section is missing from the table
    # put it in even though it has not been independently measured
    if table.Xe.neutron.total is None:
        table.Xe.neutron.total = table.Xe.neutron.coherent + table.Xe.neutron.incoherent


# Note: docs and function prototype are reproduced in __init__
@require_keywords
def neutron_scattering(compound, density=None,
                       wavelength=ABSORPTION_WAVELENGTH, energy=None,
                       natural_density=None):
    r"""
    Computes neutron scattering cross sections for molecules.

    :Parameters:
        *compound* : Formula initializer
            Chemical formula
        *density* : float | |g/cm^3|
            Mass density
        *natural_density* : float | |g/cm^3|
            Mass density of formula with naturally occuring abundances
        *wavelength* 1.798 : float | |Ang|
            Neutron wavelength.
        *energy* : float | meV
            Neutron energy.  If energy is specified then wavelength is ignored.

    :Returns:
        *sld* : (float, float, float) | |1e-6/Ang^2|
            (*real*, -*imaginary*, *incoherent*) scattering length density.
        *xs* : (float, float, float) | |1/cm|
            (*coherent*, *absorption*, *incoherent*) cross sections.
        *penetration* : float | cm
            1/e penetration depth of the beam

    :Raises:
        *AssertionError* : density is missing.


    .. Note:

        Values may not correct if any element or isotope has
        *is_energy_dependent=True*

    The coherent and incoherent cross sections are calculated from the
    bound scattering lengths for nuclei. The actual cross sections depend
    on the incoming neutron energy and sample temperature, especially for
    light elements. For low energy neutrons (cold neutrons), the tabulated
    cross sections are generally a lower limit. The measured incoherent
    scattering from hydrogen, for example, can be considerably larger
    (by more than 20%) than its bound value. For example, the incoherent
    scattering cross section of H2O is 5.621/cm as computed from these tables
    compared to ~7.0/cm as measured with 5 meV neutrons at 290K. [#May1982]_

    The scattering factor tables are not self consistent.  The following
    functions show discrepencies between the various measurements of the
    scattering potential:

        :func:`absorption_comparison_table`

        :func:`coherent_comparison_table`

        :func:`total_comparison_table`

    To compute the neutron cross sections we first need to average
    quantities for the unit cell of the molecule.

    Molar mass *m* (g/mol) is the sum of the masses of each component:

    .. math::

        m = \sum{n_i m_i}\ {\rm for\ each\ atom}\ i=1,2,\ldots

    Cell volume $V$ (|Ang^3|/molecule) is molar mass $m$ over density
    $rho$, with a correction based on Avogadro's number $N_A$ (atoms/mol)
    and the length conversion $10^8$ |Ang|/cm:

    .. math::

        V = m/\rho \cdot 1/N_A \cdot (10^8)^3

    Number density $N$ is the number of scatterers per unit volume:

    .. math::

        N = \left.\sum{n_i} \right/ V

    Coherent scattering cross section $\sigma_c$ of the molecule is computed
    from the average scattering length of its constituent atoms, weighted by
    their frequency.

    .. math::

        b_c = \left.\sum n_i b_c \right/ \sum n_i

    This is converted to a scattering cross section and scaled
    by 1 barn = 100 |fm^2|:

    .. math::

        \sigma_c = \left. 4 \pi b_c^2 \right/ 100

    Similarly, the absorption cross section $\sigma_a$, the incoherent cross
    section $\sigma_i$, and the total cross section $\sigma_s$ can be computed
    from the corresponding cross sections of the constituent elements,\ [#Sears1999]_
    already expressed in barns:

    .. math::

        \sigma_a &= \left. \sum n_j \sigma_{aj} \right/ \sum n_j \\
        \sigma_i &= \left. \sum n_j \sigma_{ij} \right/ \sum n_j \\
        \sigma_s &= \left. \sum n_j \sigma_{sj} \right/ \sum n_j

    The neutron cross sections are tabulated at wavelength 1.798 |Ang|.
    In the thermal neutron energy range most absorption cross sections
    scale linearly with wavelength,\ [#Lynn1990]_ and can be adjusted
    with a simple multiplication:

    .. math::

        \sigma_a = \sigma_a \lambda / \lambda_o = \sigma_a \lambda / 1.798

    If *isotope.neutron.is_energy_dependent()* is true for any part of
    the material, then this relation may not hold, and the returned values
    are only valid for 1.798 |Ang|.

    From the scattering cross sections, the scattering length for a material
    $b = b' - i b''$ can be computed using the following relations:[#Sears1999]_

    .. math::

        \sigma_c &= 4 \pi |b_c|^2 \\
        \sigma_a &= \left. 4 \pi \left< b'' \right> \right/k \ {\rm for} \ k=2\pi / \lambda \\
        \sigma_i &= 4 \pi |b_i|^2 \\
        \sigma_s &= 4 \pi \left< |b|^2 \right>

    Transforming we get:

    .. math::

        b'' &= \left. \sigma_a \right/ (2 \lambda) \\
        b_i &= \sqrt{ \sigma_i / (4 \pi) }

    The incoherent scattering length $b_i$ can be treated primarily
    as an absorption length in large scale structure calculations, with the
    complex scattering length approximated by $b = b_c - i (b'' + b_i)$.

    The scattering potential is often expressed as a scattering length
    density (SLD).  This is just the number density of the scatterers times
    their scattering lengths, with a correction for units.

    .. math::

        \rho_{\rm re}  &= 10 N b_c \\
        \rho_{\rm im}  &= -N b'' / 100 \\
        \rho_{\rm inc} &= 10 N b_i

    with the factors of 10 chosen to give SLD in units of $\AA^{-2}$.  The
    resulting $\rho = \rho_{\rm re} + i \rho_{\rm im}$ can be used in the
    scattering equations.  Treatment of the incoherent scattering $\rho_{\rm inc}$
    will depend on the equation.  For example, it can be treated as an absorption
    in specular reflectivity calculations since the incoherently scattered neutrons
    are removed from the multilayer recurrence calculation.

    Similarly, scattering cross section includes number density:

    .. math::

        \Sigma_{\rm coh} &= N \sigma_c \\
        \Sigma_{\rm inc} &= N \sigma_i \\
        \Sigma_{\rm abs} &= N \sigma_a \\
        \Sigma_{\rm s} &= N \sigma_s


    The 1/e penetration depth *t_u* represents the the depth into the sample at
    which the unscattered intensity is reduced by a factor of $e$:

    .. math::

        t_u = \left. 1 \right/ (\Sigma_{\rm s} + \Sigma_{\rm abs})

    Note that the calculated penetration depth includes the effects of both
    absorption and incoherent scattering (which spreads the beam in the
    full $4\pi$ spherical surface, and so it looks like absorption with
    respect to the beam), as well as the coherent scattering from the sample.
    If you instead want to calculate the effective shielding of the sample,
    you should recalculate penetration depth without the coherent scattering.

    Transmission rate can be computed from $e^{-d/t_u}$ for penetration i
    depth $t_u$ and sample thickness $d$.

    In general, the total scattering cross section is not the sum of the
    coherent and incoherent cross sections,
    $\Sigma_{\rm s} \ne \Sigma_{\rm coh}+\Sigma_{\rm inc}$.\ [#Glinka2011]_
    Instead, we compute $\Sigma_{\rm inc} = \Sigma_{\rm s} - \Sigma_{\rm coh}$
    in accordance with Sect. 4.4.4 of the Internation Tables for Crystallography
    Volume C.

    Including unit conversion with $\mu=10^{-6}$ the full scattering equations
    are:

    .. math::

        \rho_{\rm re}\,(\mu/\AA^2) &= (N/\AA^3)
            \, (b_c\,{\rm fm})
            \, (10^{-5} \AA/{\rm\,fm})
            \, (10^6\,\mu) \\
        \rho_{\rm im}\,(\mu/\AA^2) &= (N/\AA^3)
            \, (\sigma_a\,{\rm barn})
            \, (10^{-8}\,\AA^2/{\rm barn}) / (2 \lambda\, \AA)
            \, (10^6\,\mu) \\
        \rho_{\rm inc}\,(\mu/\AA^2) &= (N/\AA^3)
            \, \sqrt{(\sigma_i\, {\rm barn})/(4 \pi)
                \, (100\, {\rm fm}^2/{\rm barn})}
            \, (10^{-5}\, \AA/{\rm fm})
            \, (10^6\, \mu) \\
        \Sigma_{\rm coh}\,(1/{\rm cm}) &= (N/\AA^3)
            \, (\sigma_c\, {\rm barn})
            \, (10^{-8}\, \AA^2/{\rm barn})
            \, (10^8\, \AA/{\rm cm}) \\
        \Sigma_{\rm inc}\,(1/{\rm cm}) &= (N/\AA^3)
            \,(\sigma_i\, {\rm barn})
            \, (10^{-8}\, \AA^2/{\rm barn})
            \, (10^8\, \AA/{\rm cm}) \\
        \Sigma_{\rm abs}\,(1/{\rm cm}) &= (N/\AA^3)
            \,(\sigma_a\,{\rm barn})
            \, (10^{-8}\, \AA^2/{\rm barn})
            \, (10^8\, \AA/{\rm cm}) \\
        \Sigma_{\rm s}\,(1/{\rm cm}) &= (N/\AA^3)
            \,(\sigma_s\,{\rm barn})
            \, (10^{-8}\, \AA^2/{\rm barn})
            \, (10^8\, \AA/{\rm cm}) \\
        t_u\,({\rm cm}) &= 1/(\Sigma_{\rm s}\, 1/{\rm cm}
            \,+\, \Sigma_{\rm abs}\, 1/{\rm cm})
    """
    from . import formulas
    compound = formulas.formula(compound, density=density,
                                natural_density=natural_density)
    assert compound.density is not None, "scattering calculation needs density"
    if energy is not None:
        wavelength = neutron_wavelength(energy)
    assert wavelength is not None, "scattering calculation needs energy or wavelength"

    # Sum over the quantities
    molar_mass = num_atoms = 0
    sigma_s = sigma_a = b_c = 0
    is_energy_dependent = False
    for element, quantity in compound.atoms.items():
        if not element.neutron.has_sld():
            return None, None, None
        #print element,quantity,element.neutron.b_c,element.neutron.absorption,element.neutron.total
        molar_mass += element.mass*quantity
        num_atoms += quantity
        sigma_a += quantity * element.neutron.absorption
        sigma_s += quantity * element.neutron.total
        b_c += quantity * element.neutron.b_c
        is_energy_dependent |= element.neutron.is_energy_dependent

    # If nothing to sum, return values for a vacuum.  This might be because
    # the material has no atoms or it might be because the density is zero.
    if molar_mass*compound.density == 0:
        return (0, 0, 0), (0, 0, 0), inf

    # Turn sums into scattering factors
    b_c /= num_atoms
    sigma_s /= num_atoms
    sigma_a *= wavelength/ABSORPTION_WAVELENGTH/num_atoms

    # Compute number density
    cell_volume = (molar_mass/compound.density)/avogadro_number*1e24 # (10^8 A/cm)^3
    number_density = num_atoms / cell_volume

    # PAK 2017-04-21: compute incoherent cross section from total cross section
    sigma_c = 4*pi/100 * b_c**2  # = 4 pi |b_c/10|^2
    sigma_i = max(sigma_s - sigma_c, 0.0)

    # Compute SLD
    sld_re = number_density * b_c * 10
    sld_im = number_density * sigma_a / (2 * wavelength) * 0.01
    sld_inc = number_density * sqrt(sigma_i / (4*pi/100)) * 10

    # Compute scattering cross section per unit volume
    total_xs = number_density * sigma_s
    coh_xs = number_density * sigma_c
    abs_xs = number_density * sigma_a
    inc_xs = number_density * sigma_i

    # Compute 1/e length
    penetration = 1/(abs_xs + total_xs)

    return (sld_re, sld_im, sld_inc), (coh_xs, abs_xs, inc_xs), penetration


def neutron_sld(*args, **kw):
    """
    Computes neutron scattering length densities for molecules.

    :Parameters:
        *compound* : Formula initializer
            Chemical formula
        *density* : float | |g/cm^3|
            Mass density
        *natural_density* : float | |g/cm^3|
            Mass density of formula with naturally occuring abundances
        *wavelength* : float | |Ang|
            Neutron wavelength.
        *energy* : float | meV
            Neutron energy.  If energy is specified then wavelength is ignored.

    :Returns:
        *sld* : (float, float, float) | |1e-6/Ang^2|
            (*real*, -*imaginary*, *incoherent*) scattering length density.

    :Raises:
        *AssertionError* : density is missing.

    Returns the scattering length density of the compound.
    See :func:`neutron_scattering` for details.
    """
    return neutron_scattering(*args, **kw)[0]

def neutron_sld_from_atoms(*args, **kw):
    r"""
    .. deprecated:: 0.91

        :func:`neutron_sld` now accepts dictionaries of \{atom\: count\} directly.

    """
    return neutron_scattering(*args, **kw)[0]


def _sum_piece(wavelength, compound):
    """
    Helper for neutron_composite_sld which precomputes quantities of interest
    for material fragments in a composite formula.
    """
    # Sum over the quantities
    molar_mass = num_atoms = 0
    sigma_a = sigma_s = b_c = 0
    is_energy_dependent = False
    for element, quantity in compound.atoms.items():
        #print element,quantity,element.neutron.b_c,element.neutron.absorption,element.neutron.total
        molar_mass += element.mass*quantity
        num_atoms += quantity
        sigma_a += quantity * element.neutron.absorption
        sigma_s += quantity * element.neutron.total
        b_c += quantity * element.neutron.b_c
        is_energy_dependent |= element.neutron.is_energy_dependent

    return num_atoms, molar_mass, b_c, sigma_s, sigma_a

def neutron_composite_sld(materials, wavelength=ABSORPTION_WAVELENGTH):
    """
    Create a composite SLD calculator.

    :Parameters:
        *materials* : [Formula]
            List of materials
        *wavelength* = 1.798: float OR [float] | |Ang|
            Probe wavelength(s).

    :Returns:
        *calculator* : f(w, density=1) -> (*real*, -*imaginary*, *incoherent*)

    The composite calculator takes a vector of weights and returns the
    scattering length density of the composite.  This is useful for operations
    on large molecules, such as calculating a set of contrasts or fitting
    a material composition.

    Table lookups and partial sums and constants are precomputed so that
    the calculation consists of a few simple array operations regardless
    of the size of the material fragments.
    """
    parts = [_sum_piece(wavelength, m) for m in materials]
    V = [numpy.array(v) for v in zip(*parts)]
    num_atoms_parts, molar_mass_parts, b_c_parts, sigma_s_parts, sigma_a_parts = V

    def _compute(weights, density=1):
        # Sum over the quantities
        molar_mass = numpy.sum(weights*molar_mass_parts)
        num_atoms = numpy.sum(weights*num_atoms_parts)
        sigma_a = numpy.sum(weights*sigma_a_parts)
        sigma_s = numpy.sum(weights*sigma_s_parts)
        b_c = numpy.sum(weights*b_c_parts)

        # If nothing to sum, return values for a vacuum.  This might be because
        # the material has no atoms or it might be because the density is zero.
        if molar_mass*density == 0:
            return 0, 0, 0

        # Turn sums into scattering factors
        b_c /= num_atoms
        sigma_a *= wavelength/ABSORPTION_WAVELENGTH/num_atoms # at tabulated wavelength
        sigma_s /= num_atoms

        # Compute number density
        cell_volume = (molar_mass/density)/avogadro_number*1e24
        number_density = num_atoms / cell_volume

        # PAK 2017-04-21: compute incoherent cross section from total cross section
        sigma_c = 4*pi/100 * b_c**2
        sigma_i = max(sigma_s - sigma_c, 0.0)

        # Compute SLD
        sld_re = number_density * b_c * 10
        sld_im = number_density * sigma_a / (2 * wavelength) * 0.01
        sld_inc = number_density * sqrt(sigma_i / (4*pi/100)) * 10

        return sld_re, sld_im, sld_inc

    return _compute


def sld_plot(table=None):
    """
    Plots SLD as a function of element number.

    :Parameters:
        *table* : PeriodicTable
            The default periodictable unless a specific table has been requested.

    :Returns: None
    """
    from .plot import table_plot

    table = default_table(table)

    SLDs = dict((el, el.neutron.sld()[0])
                for el in table
                if el.neutron.has_sld())
    SLDs[table.D] = table.D.neutron.sld()[0]

    table_plot(SLDs, label='Scattering length density ($10^{-6}$ Nb)',
               title='Neutron SLD for elements in natural abundance')


# We are including the complete original table here in case somebody in
# future wants to extract uncertainties or other information.
#
# Z-Symbol-A
#   This is the atomic number, the symbol and the isotope.
#   If Z-Symbol only, the line represents an element with scattering determined
#   by the natural abundance of the isotopes in laboratory samples.  If there
#   is only one isotope, then there is no corresponding element definition.
# concentration/half-life
#   This is the natural abundance of the isotope expressed as a percentage, or
#   it is the half-life in years (number Y) or seconds (number S).
# spin I
#   For isotopes, the nuclear spin.
# b_c, bp, bm
#   Bound coherent scattering length in fm
#   b+/b- if present are spin dependent scattering for I+1/2 and I-1/2
#   respectively
# c
#   'E' if there is a strong energy dependency.
#   '+/-' if separate b+/b- values are available [doesn't seem true -PAK]
# coherent, incoherent, total
#   The coherent and incoherent scattering cross-sections in barns.
# absorption
#   The thermal absorption cross section in barns at 1.798 Angstroms/25.30 meV.
#
# Numbers in parenthesis represents uncertainty.
# Numbers followed by '*' are estimated.
# Numbers may be given as limit, e.g., <1.0e-6
#
# Formatting corrections by Paul Kienzle

nsftable = """\
0-n-1,618 S,1/2,-37.0(6),0,-37.0(6),,43.01(2),,43.01(2),0
1-H,,,-3.7409(11),,,,1.7568(10),80.26(6),82.02(6),0.3326(7)
1-H-1,99.985,1/2,-3.7423(12),10.817(5),-47.420(14),+/-,1.7583(10),80.27(6),82.03(6),0.3326(7)
1-H-2,0.0149,1,6.674(6),9.53(3),0.975(60),,5.592(7),2.05(3),7.64(3),0.000519(7)
1-H-3,12.26 Y,1/2,4.792(27),4.18(15),6.56(37),,2.89(3),0.14(4),3.03(5),<6.0E-6
2-He,,,3.26(3),,,,1.34(2),0,1.34(2),0.00747(1)
2-He-3,0.013,1/2,5.74(7),4.7(5),8.8(1.4),E,4.42(10),1.6(4),6.0(4),5333.0(7.0)
2-He-4,99.987,0,3.26(3),,,,1.34(2),0,1.34(2),0
3-Li,,,-1.90(3),,,,0.454(10),0.92(3),1.37(3),70.5(3)
3-Li-6,7.5,1,2.0(1),0.67(14),4.67(17),+/-,0.51(5),0.46(5),0.97(7),940.0(4.0)
3-Li-7,92.5,3/2,-2.22(2),-4.15(6),1.00(8),+/-,0.619(11),0.78(3),1.40(3),0.0454(3)
4-Be-9,100,3/2,7.79(1),,,,7.63(2),0.0018(9),7.63(2),0.0076(8)
5-B,,,5.30(4),,,,3.54(5),1.70(12),5.24(11),767.0(8.0)
5-B-10,19.4,3,-0.2(4),-4.2(4),5.2(4),,0.144(6),3.0(4),3.1(4),3835.0(9.0)
5-B-11,80.2,3/2,6.65(4),5.6(3),8.3(3),,5.56(7),0.21(7),5.77(10),0.0055(33)
6-C,,,6.6484(13),,,,5.551(2),0.001(4),5.551(3),0.00350(7)
6-C-12,98.89,0,6.6535(14),,,,5.559(3),0,5.559(3),0.00353(7)
6-C-13,1.11,1/2,6.19(9),5.6(5),6.2(5),+/-,4.81(14),0.034(11),4.84(14),0.00137(4)
7-N,,,9.36(2),,,,11.01(5),0.50(12),11.51(11),1.90(3)
7-N-14,99.635,1,9.37(2),10.7(2),6.2(3),,11.03(5),0.50(12),11.53(11),1.91(3)
7-N-15,0.365,1/2,6.44(3),6.77(10),6.21(10),,5.21(5),0.00005(10),5.21(5),0.000024(8)
8-O,,,5.805(4),,,,4.232(6),0.000(8),4.232(6),0.00019(2)
8-O-16,99.75,0,5.805(5),,,,4.232(6),0,4.232(6),0.00010(2)
8-O-17,0.039,5/2,5.6(5),5.52(20),5.17(20),,4.20(22),0.004(3),4.20(22),0.236(10)
8-O-18,0.208,0,5.84(7),,,,4.29(10),0,4.29(10),0.00016(1)
9-F-19,100,1/2,5.654(12),5.632(10),5.767(10),+/-,4.017(14),0.0008(2),4.018(14),0.0096(5)
10-Ne,,,4.566(6),,,,2.620(7),0.008(9),2.628(6),0.039(4)
10-Ne-20,90.5,0,4.631(6),,,,2.695(7),0,2.695(7),0.036(4)
10-Ne-21,0.27,3/2,6.66(19),,,,5.6(3),0.05(2),5.7(3),0.67(11)
10-Ne-22,9.2,0,3.87(1),,,,1.88(1),0,1.88(1),0.046(6)
11-Na-23,100,3/2,3.63(2),6.42(4),-1.00(6),+/-,1.66(2),1.62(3),3.28(4),0.530(5)
12-Mg,,,5.375(4),,,,3.631(5),0.08(6),3.71(4),0.063(3)
12-Mg-24,78.99,0,5.49(18),,,,4.03(4),0,4.03(4),0.050(5)
12-Mg-25,10,5/2,3.62(14),4.73(30),1.76(20),+/-,1.65(13),0.28(4),1.93(14),0.19(3)
12-Mg-26,11,0,4.89(15),,,,3.00(18),0,3.00(18),0.0382(8)
13-Al-27,100,5/2,3.449(5),3.67(2),3.15(2),,1.495(4),0.0082(6),1.503(4),0.231(3)
14-Si,,,4.15071(22),,,,2.1633(10),0.004(8),2.167(8),0.171(3)
14-Si-28,92.2,0,4.106(6),,,,2.120(6),0,2.120(6),0.177(3)
14-Si-29,4.7,1/2,4.7(1),4.50(15),4.7(4),+/-,2.78(12),0.001(2),2.78(12),0.101(14)
14-Si-30,3.1,0,4.58(8),,,,2.64(9),0,2.64(9),0.107(2)
15-P-31,100,1/2,5.13(1),,,+/-,3.307(13),0.005(10),3.312(16),0.172(6)
16-S,,,2.847(1),,,,1.0186(7),0.007(5),1.026(5),0.53(1)
16-S-32,95,0,2.804(2),,,,0.9880(14),0,0.9880(14),0.54(4)
16-S-33,0.74,3/2,4.74(19),,,+/-,2.8(2),0.3(6),3.1(6),0.54(4)
16-S-34,4.2,0,3.48(3),,,,1.52(3),0,1.52(3),0.227(5)
16-S-36,0.02,0,3.0(1.0)*,,,,1.1(8),0,1.1(8),0.15(3)
17-Cl,,,9.5792(8),,,,11.528(2),5.3(5),16.8(5),33.5(3)
17-Cl-35,75.77,3/2,11.70(9),16.3(2),4.0(3),+/-,17.06(6),4.7(6),21.8(6),44.1(4)
17-Cl-37,24.23,3/2,3.08(6),3.10(7),3.05(7),+/-,1.19(5),0.001(3),1.19(5),0.433(6)
18-Ar,,,1.909(6),,,,0.458(3),0.225(5),0.683(4),0.675(9)
18-Ar-36,0.34,0,24.9(7),,,,77.9(4),0,77.9(4),5.2(5)
18-Ar-38,0.07,0,3.5(3.5),,,,1.5(3.1),0,1.5(3.1),0.8(5)
18-Ar-40,99.59,0,1.7,,,,0.421(3),0,0.421(3),0.660(9)
19-K,,,3.67(2),,,,1.69(2),0.27(11),1.96(11),2.1(1)
19-K-39,93.3,3/2,3.79(2),5.15,1.51,+/-,1.76(2),0.25(11),2.01(11),2.1(1)
19-K-40,0.012,4,3.1(1.0)*,,,,1.1(6),0.5(5)*,1.6(9),35.0(8.0)
19-K-41,6.7,3/2,2.69(8),,,,0.91(5),0.3(6),1.2(6),1.46(3)
20-Ca,,,4.70(2),,,,2.78(2),0.05(3),2.83(2),0.43(2)
20-Ca-40,96.94,0,4.78(5),,,,2.90(2),0,2.90(2),0.41(2)
20-Ca-42,0.64,0,3.36(10),,,,1.42(8),0,1.42(8),0.68(7)
20-Ca-43,0.13,7/2,-1.56(9),,,,0.31(4),0.5(5),0.8(5),6.2(6)
20-Ca-44,2.13,0,1.42(6),,,,0.25(2),0,0.25(2),0.88(5)
20-Ca-46,0.003,0,3.55(21),,,,1.6(2),0,1.6(2),0.74(7)
20-Ca-48,0.18,0,0.39(9),,,,0.019(9),0,0.019(9),1.09(14)
21-Sc-45,100,7/2,12.1(1),6.91(22),18.99(28),+/-,19.0(3),4.5(3),23.5(6),27.5(2)
22-Ti,,,-3.370(13),,,,1.485(2),2.87(3),4.35(3),6.09(13)
22-Ti-46,8,0,4.72(5),,,,3.05(7),0,3.05(7),0.59(18)
22-Ti-47,7.5,5/2,3.53(7),0.46(23),7.64(13),,1.66(11),1.5(2),3.2(2),1.7(2)
22-Ti-48,73.7,0,-5.86(2),,,,4.65(3),0,4.65(3),7.84(25)
22-Ti-49,5.5,7/2,0.98(5),2.6(3),-1.2(4),,0.14(1),3.3(3),3.4(3),2.2(3)
22-Ti-50,5.3,0,5.88(10),,,,4.80(12),0,4.80(12),0.179(3)
23-V,,,-0.443(14),,,,0.01838(12),5.08(6),5.10(6),5.08(4)
23-V-50,0.25,6,7.6(6)*,,,,7.3(1.1),0.5(5)*,7.8(1.0),60.0(40.0)
23-V-51,99.75,7/2,-0.402(2),4.93(25),-7.58(28),+/-,0.0203(2),5.07(6),5.09(6),4.9(1)
24-Cr,,,3.635(7),,,,1.660(6),1.83(2),3.49(2),3.05(6)
24-Cr-50,4.35,0,-4.50(5),,,,2.54(6),0,2.54(6),15.8(2)
24-Cr-52,83.8,0,4.914(15),,,,3.042(12),0,3.042(12),0.76(6)
24-Cr-53,9.59,3/2,-4.20(3),1.16(10),-13.0(2),,2.22(3),5.93(17),8.15(17),18.1(1.5)
24-Cr-54,2.36,0,4.55(10),,,,2.60(11),0,2.60(11),0.36(4)
25-Mn-55,100,5/2,-3.750(18),-4.93(46),-1.46(33),,1.75(2),0.40(2),2.15(3),13.3(2)
26-Fe,,,9.45(2),,,,11.22(5),0.40(11),11.62(10),2.56(3)
26-Fe-54,5.8,0,4.2(1),,,,2.2(1),0,2.2(1),2.25(18)
26-Fe-56,91.7,0,10.1(2),,,,12.42(7),0,12.42(7),2.59(14)
26-Fe-57,2.19,1/2,2.3(1),,,,0.66(6),0.3(3)*,1.0(3),2.48(30)
26-Fe-58,0.28,0,15(7),,,,28.0(26.0),0,28.0(26.0),1.28(5)
27-Co-59,100,7/2,2.49(2),-9.21(10),3.58(10),+/-,0.779(13),4.8(3),5.6(3),37.18(6)
28-Ni,,,10.3(1),,,,13.3(3),5.2(4),18.5(3),4.49(16)
28-Ni-58,67.88,0,14.4(1),,,,26.1(4),0,26.1(4),4.6(3)
28-Ni-60,26.23,0,2.8(1),,,,0.99(7),0,0.99(7),2.9(2)
28-Ni-61,1.19,3/2,7.60(6),,,,7.26(11),1.9(3),9.2(3),2.5(8)
28-Ni-62,3.66,0,-8.7(2),,,,9.5(4),0,9.5(4),14.5(3)
28-Ni-64,1.08,0,-0.37(7),,,,0.017(7),0,0.017(7),1.52(3)
29-Cu,,,7.718(4),,,,7.485(8),0.55(3),8.03(3),3.78(2)
29-Cu-63,69.1,3/2,6.477(13),,,+/-,5.2(2),0.006(1),5.2(2),4.50(2)
29-Cu-65,30.9,3/2,10.204(20),,,+/-,14.1(5),0.40(4),14.5(5),2.17(3)
30-Zn,,,5.680(5),,,,4.054(7),0.077(7),4.131(10),1.11(2)
30-Zn-64,48.9,0,5.23(4),,,,3.42(5),0,3.42(5),0.93(9)
30-Zn-66,27.8,0,5.98(5),,,,4.48(8),0,4.48(8),0.62(6)
30-Zn-67,4.1,5/2,7.58(8),5.8(5),10.1(7),+/-,7.18(15),0.28(3),7.46(15),6.8(8)
30-Zn-68,18.6,0,6.04(3),,,,4.57(5),0,4.57(5),1.1(1)
30-Zn-70,0.62,0,6.9(1.0)*,,,,4.5(1.5),0,4.5(1.5),0.092(5)
31-Ga,,,7.288(2),,,,6.675(4),0.16(3),6.83(3),2.75(3)
31-Ga-69,60,3/2,8.043(16),6.3(2),10.5(4),+/-,7.80(4),0.091(11),7.89(4),2.18(5)
31-Ga-71,40,3/2,6.170(11),5.5(6),7.8(1),+/-,5.15(5),0.084(8),5.23(5),3.61(10)
32-Ge,,,8.185(20),,,,8.42(4),0.18(7),8.60(6),2.20(4)
32-Ge-70,20.7,0,10.0(1),,,,12.6(3),0,12.6(3),3.0(2)
32-Ge-72,27.5,0,8.51(10),,,,9.1(2),0,9.1(2),0.8(2)
32-Ge-73,7.7,9/2,5.02(4),8.1(4),1.2(4),,3.17(5),1.5(3),4.7(3),15.1(4)
32-Ge-74,36.4,0,7.58(10),,,,7.2(2),0,7.2(2),0.4(2)
32-Ge-76,7.7,0,8.2(1.5),,,,8.0(3.0),0,8.0(3.0),0.16(2)
33-As-75,100,3/2,6.58(1),6.04(5),7.47(8),+/-,5.44(2),0.060(10),5.50(2),4.5(1)
34-Se,,,7.970(9),,,,7.98(2),0.32(6),8.30(6),11.7(2)
34-Se-74,0.9,0,0.8(3.0),,,,0.1(6),0,0.1(6),51.8(1.2)
34-Se-76,9,0,12.2(1),,,,18.7(3),0,18.7(3),85.0(7.0)
34-Se-77,7.5,0,8.25(8),,,,8.6(2),0.05(25),8.65(16),42.0(4.0)
34-Se-78,23.5,0,8.24(9),,,,8.5(2),0,8.5(2),0.43(2)
34-Se-80,50,0,7.48(3),,,,7.03(6),0,7.03(6),0.61(5)
34-Se-82,8.84,0,6.34(8),,,,5.05(13),0,5.05(13),0.044(3)
35-Br,,,6.79(2),,,,5.80(3),0.10(9),5.90(9),6.9(2)
35-Br-79,50.49,3/2,6.79(7),,,+/-,5.81(2),0.15(6),5.96(13),11.0(7)
35-Br-81,49.31,3/2,6.78(7),,,+/-,5.79(12),0.05(2),5.84(12),2.7(2)
36-Kr,,,7.81(2),,,,7.67(4),0.01(14),7.68(13),25.0(1.0)
36-Kr-78,0.35,0,,,,,,0,,6.4(9)
36-Kr-80,2.5,0,,,,,,0,,11.8(5)
36-Kr-82,11.6,0,,,,,,0,,29.0(20.0)
36-Kr-83,11.5,9/2,,,,,,,,185.0(30.0)
36-Kr-84,57,0,,,,,,0,6.6,0.113(15)
36-Kr-86,17.3,0,8.07(26),,,,8.2(4),0,8.2(4),0.003(2)
37-Rb,,,7.08(2),,,,6.32(4),0.5(4),6.8(4),0.38(1)
37-Rb-85,72.17,5/2,7.07(10),,,,6.2(2),0.5(5)*,6.7(5),0.48(1)
37-Rb-87,27.83,3/2,7.27(12),,,,6.6(2),0.5(5)*,7.1(5),0.12(3)
38-Sr,,,7.02(2),,,,6.19(4),0.06(11),6.25(10),1.28(6)
38-Sr-84,0.56,0,5.0(2.0),,,,6.0(2.0),0,6.0(2.0),0.87(7)
38-Sr-86,9.9,0,5.68(5),,,,4.04(7),0,4.04(7),1.04(7)
38-Sr-87,7,9/2,7.41(7),,,,6.88(13),0.5(5)*,7.4(5),16.0(3.0)
38-Sr-88,82.6,0,7.16(6),,,,6.42(11),0,6.42(11),0.058(4)
39-Y-89,100,1/2,7.75(2),8.4(2),5.8(5),+/-,7.55(4),0.15(8),7.70(9),1.28(2)
40-Zr,,,7.16(3),,,,6.44(5),0.02(15),6.46(14),0.185(3)
40-Zr-90,51.48,0,6.5(1),,,,5.1(2),0,5.1(2),0.011(59
40-Zr-91,11.23,5/2,8.8(1),7.9(2),10.1(2),+/-,9.5(2),0.15(4),9.7(2),1.17(10)
40-Zr-92,17.11,0,7.5(2),,,,6.9(4),0,6.9(4),0.22(6)
40-Zr-94,17.4,0,8.3(2),,,,8.4(4),0,8.4(4),0.0499(24)
40-Zr-96,2.8,0,5.5(1),,,,3.8(1),0,3.8(1),0.0229(10)
41-Nb-93,100,9/2,7.054(3),7.06(4),7.35(4),+/-,6.253(5),0.0024(3),6.255(5),1.15(6)
42-Mo,,,6.715(20),,,,5.67(3),0.04(5),5.71(4),2.48(4)
42-Mo-92,15.48,0,6.93(8),,,,6.00(14),0,6.00(14),0.019(2)
42-Mo-94,9.1,0,6.82(7),,,,5.81(12),0,5.81(12),0.015(2)
42-Mo-95,15.72,5/2,6.93(7),,,,6.00(10),0.5(5)*,6.5(5),13.1(3)
42-Mo-96,16.53,0,6.22(6),,,,4.83(9),0,4.83(9),0.5(2)
42-Mo-97,9.5,5/2,7.26(8),,,,6.59(15),0.5(5)*,7.1(5),2.5(2)
42-Mo-98,23.78,0,6.60(7),,,,5.44(12),0,5.44(12),0.127(6)
42-Mo-100,9.6,0,6.75(7),,,,5.69(12),0,5.69(12),0.4(2)
43-Tc-99,210000 Y,9/2,6.8(3),,,,5.8(5),0.5(5)*,6.3(7),20.0(1.0)
44-Ru,,,7.02(2),,,,6.21(5),0.4(1),6.6(1),2.56(13)
44-Ru-96,5.8,0,,,,,,0,,0.28(2)
44-Ru-98,1.9,0,,,,,,0,,<8.0
44-Ru-99,12.7,5/2,,,,,,,,6.9(1.0)
44-Ru-100,12.6,0,,,,,,0,,4.8(6)
44-Ru-101,17.07,5/2,,,,,,,,3.3(9)
44-Ru-102,31.61,0,,,,,,0,,1.17(7)
44-Ru-104,18.58,0,,,,,,0,,0.31(2)
45-Rh-103,100,1/2,5.90(4),8.15(6),6.74(6),,4.34(6),0.3(3)*,4.6(3),144.8(7)
46-Pd,,,5.91(6),,,,4.39(9),0.093(9),4.48(9),6.9(4)
46-Pd-102,1,0,7.7(7)*,,,,7.5(1.4),0,7.5(1.4),3.4(3)
46-Pd-104,11,0,7.7(7)*,,,,7.5(1.4),0,7.5(1.4),0.6(3)
46-Pd-105,22.33,5/2,5.5(3),,,+/-,3.8(4),0.8(1.0),4.6(1.1),20.0(3.0)
46-Pd-106,27.33,0,6.4(4),,,,5.1(6),0,5.1(6),0.304(29)
46-Pd-108,26.71,0,4.1(3),,,,2.1(3),0,2.1(3),8.5(5)
46-Pd-110,11.8,0,7.7(7)*,,,,7.5(1.4),0,7.5(1.4),0.226(31)
47-Ag,,,5.922(7),,,,4.407(10),0.58(3),4.99(3),63.3(4)
47-Ag-107,51.8,1/2,7.555(11),8.14(9),5.8(3),+/-,7.17(2),0.13(3),7.30(4),37.6(1.2)
47-Ag-109,48.2,1/2,4.165(11),3.24(8),6.9(2),+/-,2.18(1),0.32(5),2.50(5),91.0(1.0)
48-Cd,,,4.83(5),,,E,3.04(6),3.46(13),6.50(12),2520.0(50.0)
48-Cd-106,1.2,0,5.0(2.0)*,,,,3.1(2.5),0,3.1(2.5),1.0(2.0)
48-Cd-108,0.9,0,5.31(24),,,,3.7(1),0,3.7(1),1.1(3)
48-Cd-110,12.39,0,5.78(8),,,,4.4(1),0,4.4(1),11.0(1.0)
48-Cd-111,12.75,1/2,6.47(8),,,,5.3(2),0.3(3)*,5.6(4),24.0(5.0)
48-Cd-112,24.07,0,6.34(6),,,,5.1(2),0,5.1(2),2.2(5)
48-Cd-113,12.36,1/2,-8.0(1),,,E,12.1(4),0.3(3)*,12.4(5),20600.0(400.0)
48-Cd-114,28.86,0,7.48(5),,,,7.1(2),0,7.1(2),0.34(2)
48-Cd-116,7.58,0,6.26(9),,,,5.0(2),0,5.0(2),0.075(13)
49-In,,,4.065(20),,,,2.08(2),0.54(11),2.62(11),193.8(1.5)
49-In-113,4.28,9/2,5.39(6),,,,3.65(8),0.000037(5),3.65(8),12.0(1.1)
49-In-115,95.72,9/2,4.00(3),2.1(1),6.4(4),,2.02(2),0.55(11),2.57(11),202.0(2.0)
50-Sn,,,6.225(2),,,,4.871(3),0.022(5),4.892(6),0.626(9)
50-Sn-112,1,0,6.0(1.0)*,,,,4.5(1.5),0,4.5(1.5),1.00(11)
50-Sn-114,0.66,0,6.0(3),,,,4.8(5),0,4.8(5),0.114(30)
50-Sn-115,0.35,1/2,6.0(1.0)*,,,,4.5(1.5),0.3(3)*,4.8(1.5),30.0(7.0)
50-Sn-116,14.3,0,6.10(1),,,,4.42(7),0,4.42(7),0.14(3)
50-Sn-117,7.61,1/2,6.59(8),0.22(10),-0.23(10),,5.28(8),0.3(3)*,5.6(3),2.3(5)
50-Sn-118,24.03,0,6.23(4),,,,4.63(8),0,4.63(8),0.22(5)
50-Sn-119,8.58,1/2,6.28(3),0.14(10),0.0(1),,4.71(8),0.3(3)*,5.0(3),2.2(5)
50-Sn-120,32.86,0,6.67(4),,,,5.29(8),0,5.29(8),0.14(3)
50-Sn-122,4.72,0,5.93(3),,,,4.14(7),0,4.14(7),0.18(2)
50-Sn-124,5.94,0,6.15(3),,,,4.48(8),0,4.48(8),0.133(5)
51-Sb,,,5.57(3),,,,3.90(4),0.00(7),3.90(6),4.91(5)
51-Sb-121,57.25,5/2,5.71(6),5.7(2),5.8(2),,4.10(9),0.0003(19),4.10(19),5.75(12)
51-Sb-123,42.75,7/2,5.38(7),5.2(2),5.4(2),,3.64(9),0.001(4),3.64(9),3.8(2)
52-Te,,,5.68(2),,,,4.23(4),0.09(6),4.32(5),4.7(1)
52-Te-120,0.09,0,5.3(5),,,,3.5(7),0,3.5(7),2.3(3)
52-Te-122,2.4,0,3.8(2),,,,1.8(2),0,1.8(2),3.4(5)
52-Te-123,0.87,1/2,-0.05(25),-1.2(2),3.5(2),,0.002(3),0.52(5),0.52(5),418.0(30.0)
52-Te-124,4.61,0,7.95(10),,,,8.0(2),0,8.0(2,6.8(1.3)
52-Te-125,6.99,1/2,5.01(8),4.9(2),5.5(2),,3.17(10),0.008(8),3.18(10),1.55(16)
52-Te-126,18.71,0,5.55(7),,,,3.88(10),0,3.88(10),1.04(15)
52-Te-128,31.79,0,5.88(8),,,,4.36(10),0,4.36(10),0.215(8)
52-Te-130,34.48,0,6.01(7),,,,4.55(11),0,4.55(11),0.29(6)
53-I-127,100,5/2,5.28(2),6.6(2),3.4(2),,3.50(3),0.31(6),3.81(7),6.15(6)
54-Xe,,,4.69(4),,,,3.04(4),0,,23.9(1.2)
54-Xe-124,0.1,0,,,,,,0,,165.0(20.0)
54-Xe-126,0.09,0,,,,,,0,,3.5(8)
54-Xe-128,1.9,0,,,,,,0,,<8.0
54-Xe-129,26.14,1/2,,,,,,,,21.0(5.0)
54-Xe-130,3.3,0,,,,,,0,,<26.0
54-Xe-131,21.18,3/2,,,,,,,,85.0(10.0)
54-Xe-132,26.89,0,,,,,,0,,0.45(6)
54-Xe-134,10.4,0,,,,,,0,,0.265(20)
54-Xe-136,8.9,0,,,,,,0,,0.26(2)
55-Cs-133,100,7/2,5.42(2),,,+/-,3.69(15),0.21(5),3.90(6),29.0(1.5)
56-Ba,,,5.07(3),,,,3.23(4),0.15(11),3.38(10),1.1(1)
56-Ba-130,0.1,0,-3.6(6),,,,1.6(5),0,1.6(5),30.0(5.0)
56-Ba-132,0.09,0,7.8(3),,,,7.6(6),0,7.6(6),7.0(8)
56-Ba-134,2.4,0,5.7(1),,,,4.08(14),0,4.08(14),2.0(1.6)
56-Ba-135,6.59,3/2,4.66(10),,,,2.74(12),0.5(5)*,3.2(5),5.8(9)
56-Ba-136,7.81,0,4.90(8),,,,3.03(10),0,3.03(10),0.68(17)
56-Ba-137,11.32,3/2,6.82(10),,,,5.86(17),0.5(5)*,6.4(5),3.6(2)
56-Ba-138,71.66,0,4.83(8),,,,2.94(10),0,2.94(19),0.27(14)
57-La,,,8.24(4),,,,8.53(8),1.13(19),9.66(17),8.97(2)
57-La-138,0.09,5,8.0(2.0)*,,,,8.0(4.0),0.5(5)*,8.5(4.0),57.0(6.0)
57-La-139,99.91,7/2,8.24(4),11.4(3),4.5(4),+/-,8.53(8),1.13(15),9.66(17),8.93(4)
58-Ce,,,4.84(2),,,,2.94(2),0.00(10),2.94(10),0.63(4)
58-Ce-136,0.19,0,5.76(9),,,,4.23(13),0,4.23(13),7.3(1.5)
58-Ce-138,0.26,0,6.65(9),,,,5.64(15),0,5.64(15),1.1(3)
58-Ce-140,88.48,0,4.81(9),,,,2.94(11),0,2.94(11),0.57(4)
58-Ce-142,11.07,0,4.72(9),,,,2.84(11),0,2.84(11),0.95(5)
59-Pr-141,100,5/2,4.58(5),,,+/-,2.64(6),0.015(3),2.66(6),11.5(3)
60-Nd,,,7.69(5),,,,7.43(19),9.2(8),16.6(8),50.5(1.2)
60-Nd-142,27.11,0,7.7(3),,,,7.5(6),0,7.5(6),18.7(7)
60-Nd-143,12.17,7/2,14.0(2.0)*,,,,25.0(7.0),55.0(7.0),80.0(2.0),337.0(10.0)
60-Nd-144,23.85,0,2.8(3),,,,1.0(2),0,1.0(2),3.6(3)
60-Nd-145,8.5,7/2,14.0(2.0)*,,,,25.0(7.0),5.0(5.0)*,30.0(9.0),42.0(2.0)
60-Nd-146,17.22,0,8.7(2),,,,9.5(4),0,9.5(4),1.4(1)
60-Nd-148,5.7,0,5.7(3),,,,4.1(4),0,4.1(4),2.5(2)
60-Nd-150,5.6,0,5.28(20),,,,3.5(3),0,3.5(3),1.2(2)
61-Pm-147,2.62 Y,7/2,12.6(4),,,,20.0(1.3),1.3(2.0),21.3(1.5),168.4(3.5)
62-Sm,,,0.00(5),,,E,0.422(9),39.0(3.0),39.4(3.0),5922.0(56.0)
62-Sm-144,3.1,0,-3.0(4.0)*,,,,1.0(3.0),0,1.0(3.0),0.7(3)
62-Sm-147,15,7/2,14.0(3.0),,,,25.0(11.0),14.0(19.0.),39.0(16.0),57.0(3.0)
62-Sm-148,11.2,0,-3.0(4.0)*,,,,1.0(3.0),0,1.0(3.0),2.4(6)
62-Sm-149,13.8,7/2,18.7(28),,,E,63.5(6),137.0(5.0),200.0(5.0),42080.0(400.0)
62-Sm-150,7.4,0,14.0(3.0),,,,25.0(11.0),0,25.0(11.0),104.0(4.0)
62-Sm-152,26.7,0,-5.0(6),,,,3.1(8),0,3.1(8),206.0(6.0)
62-Sm-154,22.8,0,8.0(1.0),,,,11.0(2.0),0,11.0(2.0),8.4(5)
63-Eu,,,5.3(3),,,E,6.57(4),2.5(4),9.2(4),4530.0(40.0)
63-Eu-151,47.8,5/2,,,,E,5.5(2),3.1(4),8.6(4),9100.0(100.0)
63-Eu-153,52.8,5/2,8.22(12),,,,8.5(2),1.3(7),9.8(7),312.0(7.0)
64-Gd,,,9.5(2),,,E,29.3(8),151.0(2.0),180.0(2.0),49700.0(125.0)
64-Gd-152,0.2,0,10.0(3.0)*,,,,13.0(8.0),0,13.0(8.0),735.0(20.0)
64-Gd-154,2.2,0,10.0(3.0)*,,,,13.0(8.0),0,13.0(8.0),85.0(12.0)
64-Gd-155,14.9,3/2,13.8(3),,,E,40.8(4),25.0(6.0),66.0(6.0),61100.0(400.0)
64-Gd-156,20.6,0,6.3(4),,,,5.0(6),0,5.0(6),1.5(1.2)
64-Gd-157,15.7,3/2,4.0(2.0),,,E,650.0(4.0),394.0(7.0),1044.0(8.0),259000.0(700.0)
64-Gd-158,24.7,0,9.0(2.0),,,,10.0(5.0),0,10.0(5.0),2.2(2)
64-Gd-160,21.7,0,9.15(5),,,,10.52(11),0,10.52(11),0.77(2)
65-Tb-159,100,3/2,7.34(2),6.8(2),8.1(2),+/-,6.84(6),0.004(3),6.84(6),23.4(4)
66-Dy,,,16.9(3),,,,35.9(8),54.4(1.2),90.3(9),994.0(13.0)
66-Dy-156,0.06,0,6.1(5),,,,4.7(8),0,4.7(8),33.0(3.0)
66-Dy-158,0.1,0,6.0(4.0)*,,,,5.0(6.0),0,5.(6.),43.0(6.0)
66-Dy-160,2.3,0,6.7(4),,,,5.6(7),0,5.6(7),56.0(5.0)
66-Dy-161,18.9,5/2,10.3(4),,,,13.3(1.0),3.0(1.0),16.0(1.0),600.0(25.0)
66-Dy-162,25.5,0,-1.4(5),,,,0.25(18),0,0.25(18),194.0(10.0)
66-Dy-163,24.9,5/2,5.0(4),6.1(5),3.5(5),,3.1(5),0.21(19),3.3(5),124.0(7.0)
66-Dy-164,28.2,0,49.4(5),,,,307.0(3.0),0,307.0(3.0),2840.0(40.0)
67-Ho-165,100,7/2,8.44(3),6.9(2),10.3(2),+/-,8.06(8),0.36(3),8.42(16),64.7(1.2)
68-Er,,,7.79(2),,,,7.63(4),1.1(3),8.7(3),159.0(4.0)
68-Er-162,0.14,0,9.01(11),,,,9.7(4),0,9.7(4),19.0(2.0)
68-Er-164,1.6,0,7.95(14),,,,8.4(4),0,8.4(4),13.0(2.0)
68-Er-166,33.4,0,10.51(19),,,,14.1(5),0,14.1(5),19.6(1.5)
68-Er-167,22.9,7/2,3.06(5),5.3(3),0.0(3),,1.1(2),0.13(6),1.2(2),659.0(16.0)
68-Er-168,27,0,7.43(8),,,,6.9(7),0,6.9(7),2.74(8)
68-Er-170,15,0,9.61(6),,,,11.6(1.2),0,11.6(1.2),5.8(3)
69-Tm-169,100,1/2,7.07(3),,,+/-,6.28(5),0.10(7),6.38(9),100.0(2.0)
70-Yb,,,12.41(3),,,,19.42(9),4.0(2),23.4(2),34.8(8)
70-Yb-168,0.14,0,-4.07(2),,,E,2.13(2),0,2.13(2),2230.0(40.0)
70-Yb-170,3,0,6.8(1),,,,5.8(2),0,5.8(2),11.4(1.0)
70-Yb-171,14.3,1/2,9.7(1),6.5(2),19.4(4),,11.7(2),3.9(2),15.6(3),48.6(2.5)
70-Yb-172,21.9,0,9.5(1),,,,11.2(2),0,11.2(2),0.8(4)
70-Yb-173,16.3,5/2,9.56(10),2.5(2),13.3(3),,11.5(2),3.5,15,17.1(1.3)
70-Yb-174,31.8,0,19.2(1),,,,46.8(5),0,46.8(5),69.4(5.0)
70-Yb-176,12.7,0,8.7(1),,,,9.6(2),0,9.6(2),2.85(5)
71-Lu,,,7.21(3),,,,6.53(5),0.7(4),7.2(4),74.0(2.0)
71-Lu-175,97.4,7/2,7.28(9),,,,6.59(5),0.6(4),7.2(4),21.0(3.0)
71-Lu-176,2.6,7,6.1(2),,,,4.7(2),1.2(3),5.9,2065.(35.)
72-Hf,,,7.77(14),,,,7.6(3),2.6(5),10.2(4),104.1(5)
72-Hf-174,0.184,0,10.9(1.1),,,,15.0(3.0),0,15.0(3.0),561.0(35.0)
72-Hf-176,5.2,0,6.61(18),,,,5.5(3),0,5.5(3),23.5(3.1)
72-Hf-177,18.5,0,0.8(1.0)*,,,,0.1(2),0.1(3),0.2(2),373.0(10.0)
72-Hf-178,27.2,0,5.9(2),,,,4.4(3),0,4.4(3),84.0(4.0)
72-Hf-179,13.8,9/2,7.46(16),,,,7.0(3),0.14(2),7.1(3),41.0(3.0)
72-Hf-180,35.1,0,13.2(3),,,,21.9(1.0),0,21.9(1.0),13.04(7)
73-Ta,,,6.91(7),,,,6.00(12),0.01(17),6.01(12),20.6(5)
73-Ta-180,0.012,9,7.0(2.0)*,,,,6.2(3.5),0.5(5)*,7.0(4.0),563.0(60.0)
73-Ta-181,99.98,7/2,6.91(7),,,+/-,6.00(12),0.011(2),6.01(12),20.5(5)
74-W,,,4.755(18),,,,2.97(2),1.63(6),4.60(6),18.3(2)
74-W-180,0.13,0,5.0(3.0)*,,,,3.0(4.0),0,3.0(4.0),30.0(20.0)
74-W-182,26.3,1/2,7.04(4),,,,6.10(7),0,6.10(7),20.7(5)
74-W-183,14.3,1/2,6.59(4),6.3(4),7.0(4),,5.36(7),0.3(3)*,5.7(3),10.1(3)
74-W-184,30.7,0,7.55(6),,,,7.03(11),0,7.03(11),1.7(1)
74-W-186,28.6,0,-0.73(4),,,,0.065(7),0,0.065(7),37.9(6)
75-Re,,,9.2(2),,,,10.6(5),0.9(6),11.5(3),89.7(1.0)
75-Re-185,37.5,5/2,9.0(3),,,,10.2(7),0.5(9),10.7(6),112.0(2.0)
75-Re-187,62.5,5/2,9.3(3),,,,10.9(7),1.0(6),11.9(4),76.4(1.0)
76-Os,,,10.7(2),,,,14.4(5),0.3(8),14.7(6),16.0(4.0)
76-Os-184,0.02,0,10.0(2.0)*,,,,13.0(5.0),0,13.0(5.0),3000.0(150.0)
76-Os-186,1.6,0,12.0(1.7),,,,17.0(5.0),0,17.0(5.0),80.0(13.0)
76-Os-187,1.6,1/2,10.0(2.0)*,,,,13.0(5.0),0.3(3)*,13.0(5.0),320.0(10.0)
76-Os-188,13.3,0,7.8(3),,,,7.3(6),0,7.3(6),4.7(5)
76-Os-189,16.1,3/2,11.0(3),,,,14.4(8),0.5(5)*,14.9(9),25.0(4.0)
76-Os-190,26.4,0,11.4(3),,,,15.2(8),0,15.2(8),13.1(3)
76-Os-192,41,0,11.9(4),,,,16.6(1.2),0,16.6(1.2),2.0(1)
77-Ir,,,10.6(3),,,,14.1(8),0.0(3.0),14.0(3.0),425.0(2.0)
77-Ir-191,37.4,3/2,,,,,,,,954.0(10.0)
77-Ir-193,62.6,3/2,,,,,,,,111.0(5.0)
78-Pt,,,9.60(1),,,,11.58(2),0.13(11),11.71(11),10.3(3)
78-Pt-190,0.01,0,9.0(1.0),,,,10.0(2.0),0,10.0(2.0),152.0(4.0)
78-Pt-192,1.78,0,9.9(5),,,,12.3(1.2),0,12.3(1.2),10.0(2.5)
78-Pt-194,32.9,0,10.55(8),,,,14.0(2),0,14.0(2),1.44(19)
78-Pt-195,33.8,1/2,8.91(9),9.5(3),7.2(3),+/-,9.8(2),0.13(4),9.9(2),27.5(1.2)
78-Pt-196,25.3,0,9.89(8),,,,12.3(2),0,12.3(2),0.72(4)
78-Pt-198,7.2,0,7.8(1),,,,7.6(2),0,7.6(2),3.66(19)
79-Au-197,100,3/2,7.90(7),6.26(10),9.90(14),+/-,7.32(12),0.43(5),7.75(13),98.65(9)
80-Hg,,,12.595(45),,,,20.24(5),6.6(1),26.8(1),372.3(4.0)
80-Hg-196,0.15,0,30.3(1.0),,,E,115.0(8.0),0,115.0(8.0),3080.0(180.0)
80-Hg-198,10.1,0,,,,,,0,,2.0(3)
80-Hg-199,16.9,0,16.9(4),,,E,36.0(2.0),30.0(3.0),66.0(2.0),2150.0(48.0)
80-Hg-200,23.1,0,,,,,,0,,<60.0
80-Hg-201,13.2,3/2,,,,,,,,7.8(2.0)
80-Hg-202,29.7,0,11.002(43),,,,15.2108(2),0,15.2108(2),4.89(5)
80-Hg-204,6.8,0,,,,,,0,,0.43(10)
81-Tl,,,8.776(5),,,,9.678(11),0.21(15),9.89(15),3.43(6)
81-Tl-203,29.5,1/2,8.51(8),9.08(10),6.62(10),,6.14(28),0.14(4),6.28(28),11.4(2)
81-Tl-205,70.5,1/2,8.87(7),5.15(10),9.43(10),+/-,11.39(17),0.007(1),11.40(17),0.104(17)
82-Pb,,,9.401(2),,,,11.115(7),0.0030(7),11.118(7),0.171(2)
82-Pb-204,1.4,0,10.893(78),,,,12.3(2),0,12.3(2),0.65(7)
82-Pb-206,24.1,0,9.221(78),,,,10.68(12),0,10.68(12),0.0300(8)
82-Pb-207,22.1,1/2,9.286(16),,,+/-,10.82(9),0.002(2),10.82(9),0.699(10)
82-Pb-208,52.4,0,9.494(30),,,,11.34(5),0,11.34(5),0.00048(3)
83-Bi-209,100,9/2,8.532(2),8.26(1),8.74(1),,9.148(4),0.0084(19),9.156(4),0.0338(7)
88-Ra-226,1620 Y,0,10.0(1.0),,,,13.0(3.0),0,13.0(3.0),12.8(1.5)
90-Th-232,100,0,10.31(3),,,,13.36(8),0,13.36(8),7.37(6)
91-Pa-231,32500 Y,3/2,9.1(3),,,,10.4(7),0.1(3.3),10.5(3.2),200.6(2.3)
92-U,,,8.417(5),,,,8.903(11),0.005(16),8.908(11),7.57(2)
92-U-233,159000 Y,5/2,10.1(2),,,,12.8(5),0.1(6),12.9(3),574.7(1.0)
92-U-234,0.005,0,12.4(3),,,,19.3(9),0,19.3(9),100.1(1.3)
92-U-235,0.72,7/2,10.50(3),,,,13.78(11),0.2(2),14.0(2),680.9(1.1)
92-U-238,99.27,0,8.407(7),,,,8.871(11),0,8.871(11),2.68(2)
93-Np-237,2140000 Y,5/2,10.55(10),,,,14.0(3),0.5(5)*,14.5(6),175.9(2.9)
94-Pu-239,24400 Y,1/2,7.7(1),,,,7.5(2),0.2(6),7.7(6),1017.3(2.1)
94-Pu-240,6540 Y,0,3.5(1),,,,1.54(9),0,1.54(9),289.6(1.4)
94-Pu-242,376000 Y,0,8.1(1),,,,8.2(2),0,8.2(2),18.5(5)
95-Am-243,7370 Y,5/2,8.3(2),,,,8.7(4),0.3(2.6),9.0(2.6),75.3(1.8)
96-Cm-244,17.9 Y,0,9.5(3),,,,11.3(7),0,11.3(7),16.2(1.2)
96-Cm-246,4700 Y,0,9.3(2),,,,10.9(5),0,10.9(5),1.36(17)
96-Cm-248,340000 Y,0,7.7(2),,,,7.5(4),0,7.5(4),3.00(26)\
"""

# Imaginary values for select isotopes
# isotope, b_c_i, bp_i, bm_i
nsftableI = """\
2-He-3,-1.48,,-5.925
3-Li-6,-0.26,-0.08(1),-0.62(2)
5-B,-0.21,,
47-Ag-107,-0.01,,
47-Ag-109,-0.025,,
48-Cd,-1.2,,
48-Cd-113,-12,,
49-In,-0.054,,
49-In-115,-0.056,,
52-Te-123,-0.1,,
62-Sm,-1.5,,
62-Sm-149,-11,,
64-Gd,-13.6,,
64-Gd-155,-10.3,,
71-Lu-176,-0.57(2),,
80-Hg-196,-0.8,,\
"""
# Excluding the following because the measurements for the real parts
# were not used in nsftable table.
# 63-Eu-151,-2.46,,
# 64-Gd-157,-47,-75,



def fix_number(str):
    """
    Converts strings of the form e.g., 35.24(2)* into numbers without
    uncertainty. Also accepts a limited range, e.g., <1e-6, which is
    converted as 1e-6.  Missing values are set to 0.
    """
    if str == '':
        return None
    idx = str.find('(')
    if idx >= 0:
        str = str[0:idx]
    if str[0] == '<':
        str = str[1:]
    return float(str)

def sld_table(wavelength=1, table=None, isotopes=True):
    """
    Scattering length density table for wavelength 4.75 |Ang|.

    :Parameters:

        *table* : PeriodicTable
            If *table* is not specified, use the common periodic table.

        *isotopes* = True : boolean
            Whether to consider isotopes or not.

    :Returns: None

    Example

        >>> sld_table(wavelength=4.75)  # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
         Neutron scattering length density table
        atom       mass density     sld    imag   incoh
        H         1.008   0.071  -1.582   0.000  10.691
        1-H       1.008   0.071  -1.583   0.000  10.691
        D         2.014   0.141   2.823   0.000   1.705
        T         3.016   0.212   2.027   0.000   0.453
        He        4.003   0.122   0.598   0.000   0.035
        3-He      3.016   0.092   1.054   0.272   0.706 *
        4-He      4.003   0.122   0.598   0.000   0.035
           ...
        248-Cm  248.072  13.569   2.536   0.000   0.207
        * Energy dependent cross sections
    """
    table = default_table(table)
    # Table for comparison with scattering length density calculators
    # b_c for Sc, Te, Xe, Sm, Eu, Gd, W, Au, Hg are different from Neutron News
    # The Rauch data have cited references to back up the numbers
    # (see doc directory), though it is not clear what criteria are
    # used to select amongst the available measurements.
    print(" Neutron scattering length density table")
    print("%-7s %7s %7s %7s %7s %7s"
          %('atom', 'mass', 'density', 'sld', 'imag', 'incoh'))
    for el in table:
        if el.neutron.has_sld():
            coh, jcoh, inc = el.neutron.sld(wavelength=wavelength)
            print("%-7s %7.3f %7.3f %7.3f %7.3f %7.3f%s"
                  %(el, el.mass, el.density, coh, jcoh, inc,
                    ' *' if el.neutron.is_energy_dependent else ''))
            if isotopes:
                isos = [iso for iso in el if iso.neutron != None and iso.neutron.has_sld()]
            else:
                isos = []
            for iso in isos:
                coh, jcoh, inc = iso.neutron.sld(wavelength=wavelength)
                print("%-7s %7.3f %7.3f %7.3f %7.3f %7.3f%s"
                      %(iso, iso.mass, iso.density, coh, jcoh, inc,
                        ' *' if iso.neutron.is_energy_dependent else ''))
    print("* Energy dependent cross sections")

def energy_dependent_table(table=None):
    """
    Prints a table of energy dependent isotopes.

    :Parameters:
        *table* : PeriodicTable
            If *table* is not specified, use the common periodic table.

    :Returns: None

    Example

        >>> energy_dependent_table()
        Elements and isotopes with energy dependent absorption:
            He-3
            Cd Cd-113
            Sm Sm-149
            Eu Eu-151
            Gd Gd-155 Gd-157
            Yb-168
            Hg-196 Hg-199
    """
    table = default_table(table)
    # List of energy dependent elements and isotopes
    print("Elements and isotopes with energy dependent absorption:")
    for el in table:
        if not hasattr(el, 'neutron'):
            continue
        dep = []
        if el.neutron.is_energy_dependent:
            dep += [str(el)]
        dep += [str(el)+'-'+str(iso.isotope)
                for iso in el
                if iso.neutron != None and iso.neutron.is_energy_dependent]
        if len(dep) > 0:
            print("    " + " ".join(dep))

def _diff(iso, a, b, tol=0.01):
    if None in (a, b):
        if a is not None or b is not None:
            if a is None and b > tol:
                print("%10s %8s %8.2f"%(iso, "----", b))
            elif b is None and a > tol:
                print("%10s %8.2f %8s"%(iso, a, "----"))
    elif abs(a - b) > tol:
        print("%10s %8.2f %8.2f %5.1f%%"
              % (iso, a, b, (100*(a-b)/b if b != 0 else inf)))

def compare(fn1, fn2, table=None, tol=0.01):
    table = default_table(table)
    for el in table:
        try:
            res1 = fn1(el)
        except Exception:
            res1 = None
        try:
            res2 = fn2(el)
        except Exception:
            res2 = None
        _diff(el, res1, res2, tol=tol)
        for iso in el:
            try:
                res1 = fn1(iso)
            except Exception:
                res1 = None
            try:
                res2 = fn2(iso)
            except Exception:
                res2 = None
            _diff(iso, res1, res2, tol=tol)

def absorption_comparison_table(table=None, tol=None):
    r"""
    Prints a table comparing absorption to the imaginary bound coherent
    scattering length b_c_i.  This is used to checking the integrity
    of the data and formula.

    The relationship between absorption and b_c_i is:

    .. math::

        \sigma_a = -2 \lambda b_i \cdot 1000

    The wavelength $\lambda = 1.798 \AA$ is the neutron wavelength at which
    the absorption is tallied. The factor of 1000 transforms from
    |Ang|\ |cdot|\ fm to barn.

    :Parameters:
        *table* : PeriodicTable
            The default periodictable unless a specific table has been requested.
        *tol* = 0.01 : float | barn
            Show differences greater than this amount.

    :Returns: None

    Example

        >>> absorption_comparison_table (tol=0.5) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
        Comparison of absorption and (-2000 lambda b_c_i)
              3-He  5333.00  5322.08   0.2%
                Li    70.50     ----
              6-Li   940.00   934.96   0.5%
                 B   767.00   755.16   1.6%
              10-B  3835.00     ----
                 N     1.90     ----
           ...

    """

    print("Comparison of absorption and (-2000 lambda b_c_i)")
    compare(lambda el: el.neutron.absorption,
            lambda el: -2000*el.neutron.b_c_i*ABSORPTION_WAVELENGTH,
            table=table, tol=tol)
    return

def coherent_comparison_table(table=None, tol=None):
    r"""
    Prints a table of $4 \pi b_c^2/100$ and coherent for each isotope.
    This is useful for checking the integrity of the data and formula.

    The table only prints where b_c exists.

    :Parameters:
        *table* : PeriodicTable
            The default periodictable unless a specific table has been requested.
        *tol* = 0.01 : float | barn
            Amount of difference to show

    :Returns: None

    Example

        >>> coherent_comparison_table (tol=0.5) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
        Comparison of (4 pi b_c^2/100) and coherent
                 n   172.03    43.01 300.0%
               1-n   172.03    43.01 300.0%
                Sc    18.40    19.00  -3.2%
             45-Sc    18.40    19.00  -3.2%
             65-Cu    13.08    14.10  -7.2%
             70-Zn     5.98     4.50  33.0%
             84-Sr     3.14     6.00 -47.6%
           ...

    """
    print("Comparison of (4 pi b_c^2/100) and coherent")
    compare(lambda el: 4*pi/100*el.neutron.b_c**2,
            lambda el: el.neutron.coherent,
            table=table, tol=tol)

def total_comparison_table(table=None, tol=None):
    """
    Prints a table of neutron.total and sum coh,inc for each
    isotope where these exist.  This is used to checking the integrity
    of the data and formula.

    :Parameters:
        *table* : PeriodicTable
            The default periodictable unless a specific table has been requested.
        *tol* = 0.01 : float | barn
            Amount of difference to show

    :Returns: None

    Example

        >>> total_comparison_table (tol=0.1)
        Comparison of total cross section to (coherent + incoherent)
                 n    43.01     ----
               1-n    43.01     ----
             84-Kr     6.60     ----
            149-Sm   200.00   200.50  -0.2%
                Eu     9.20     9.07   1.4%
                Gd   180.00   180.30  -0.2%
            155-Gd    66.00    65.80   0.3%
            161-Dy    16.00    16.30  -1.8%
            180-Ta     7.00     6.70   4.5%
            187-Os    13.00    13.30  -2.3%

    """

    print("Comparison of total cross section to (coherent + incoherent)")
    compare(lambda el: el.neutron.total,
            lambda el: el.neutron.coherent+el.neutron.incoherent,
            table=table, tol=tol)


def incoherent_comparison_table(table=None, tol=None):
    """
    Prints a table of incoherent computed from total and b_c with incoherent.

    :Parameters:
        *table* : PeriodicTable
            The default periodictable unless a specific table has been requested.
        *tol* = 0.01 : float | barn
            Amount of difference to show

    :Returns: None

    Example

        >>> incoherent_comparison_table (tol=0.5) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
        Comparison of incoherent and (total - 4 pi b_c^2/100)
                Sc     4.50     5.10 -11.8%
             45-Sc     4.50     5.10 -11.8%
             65-Cu     0.40     1.42 -71.7%
             70-Zn     0.00    -1.48 -100.0%
             84-Sr     0.00     2.86 -100.0%
            113-Cd     0.30     4.36 -93.1%
           ...

    """

    print("Comparison of incoherent and (total - 4 pi b_c^2/100)")
    compare(lambda el: el.neutron.incoherent,
            lambda el: el.neutron.total - 4*pi/100*el.neutron.b_c**2,
            table=table, tol=tol)

def print_scattering(compound, wavelength=ABSORPTION_WAVELENGTH):
    """
    Print the scattering for a single compound.
    """
    from . import formulas
    compound = formulas.formula(compound)
    density = compound.density if compound.density is not None else 1.0
    sld, xs, penetration = neutron_scattering(compound, wavelength=wavelength,
                                              density=density)
    print("%s at %g Ang  (density=%g g/cm^3)"
          % (str(compound), wavelength, density))
    print("  sld: %g + %g j  (%g incoherent)  1e-6/Ang^2"%sld)
    print("  sigma_c: %g  sigma_i: %g  sigma_a: %g  1/cm"%sld)
    print("  mu: %g 1/cm  1/e penetration: %g cm"%(1/penetration, penetration))

def main():
    """
    Simple command line interface, showing the predicted neutron scattering.

    Usage::

        python -m periodictable.nsf [-Lwavelength] compound@density compound@density ...

    For example::

        $ python -m periodictable.nsf XeF6@3.56
        scattering for XeF6 at 1.798 Ang  (density=3.56 g/cm^3)
          sld: 3.37503 + 0.000582313 j  (0.402605 incoherent)  1e-6/Ang^2
          sigma_c: 3.37503  sigma_i: 0.000582313  sigma_a: 0.402605  1/cm
          1/e penetration: 2.23871 cm
    """

    import sys
    compounds = sys.argv[1:]
    if compounds[0].startswith('-L'):
        wavelength = float(compounds[0][2:])
        compounds = compounds[1:]
    else:
        wavelength = ABSORPTION_WAVELENGTH
    for c in compounds:
        print_scattering(c, wavelength)

if __name__ == "__main__":
    main()