# -*- 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]_,\ [#Rauch2000]_: ``_ The above site has references to the published values for every entry in the table. We have included these in the documentation directory within the periodictable source package. Some typographical errors have been fixed. In particular, Zn-70 has b_c listed as 6.9 in the table, but 6.0 in the source materials for the table. Note that enteries in the table have been measured independently, so the values for the scattering length of an element or isotope may be inconsistent with the values measured for the corresponding cross section. The comparison table functions highlight these differences. Tables from Sears\ [#Sears1992]_\ [#Sears2006]_, Rauch\ [#Rauch2003]_ and Dawidowski\ [#Dawidowski2013]_ make different choices for the recommended values. These are noted in periodictable issue #59 ``_ with changes from Sears to Rauch `(a) `__ and from Rauch to Dawidowski `(b) `__. The following newer measurements from the literature are included: 1H b_c -3.7423(12) => -3.7395(11) [1] 2H b_c 6.674(6) => 6.6681(27) [1] 4He b_c 3.26(3) => 3.0982(21) [3] (see also [5], which gives 3.075(6)) 4He coherent = total cross sections computed from 4 pi b_c^2/100 natHe computed from isotopic weighting of 3He and 4He natC b_c 6.6484(13) => 6.6472(9) [1] natO b_c 5.805(4) => 5.8037(29) [1] 17O b_c 5.6(5) => 5.867(4) [2] 18O b_c 5.84(7) => 6.009(5) [2] natSn b_c 6.225(2) => 6.2239(13) [1] 154Sm b_c 8.0(1.0) => 8.97(6) [4] 153Eu b_c 8.22(12) => 8.85(3) [4] 191Ir b_c => 12.1(9) [6] 193Ir b_c => 9.71(18) [6] natPb b_c 9.401(2) => 9.4024(13) [1] natBi b_c 8.532(2) => 8.5242(18) [1] He total 1.34(2) => 1.188(5) [5] (ignored; using 4 pi b_c^2/100) Ar total 0.683(4) => 0.683(5) [5] (ignored; existing value is more precise) Kr total 7.68(13) => 7.685(26) [5] Xe total --- => 4.344(17) [5] [1] Snow (2020) 10.1103/PhysRevD.101.062004 [average of values in Table 1] [2] Fischer (2012) 10.1088/0953-8984/24/50/505105 [3] Haun (2020) 10.1103/PhysRevLett.124.012501 [4] Kohlmann (2016) 10.1515/zkri-2016-1984 [5] Haddock (2019) 10.1103/PhysRevC.100.064002 [6] Hannon (2018) 10.1107/S1600576718006064 .. [#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. (https://www.ill.eu/fileadmin/user_upload/ILL/1_About_ILL/Documentation/NeutronDataBooklet.pdf Retrieved March 2008) .. [#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 .. [#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. doi:10.1016/0092-640X(90)90013-A .. [#Sears2006] Sears, V. F. (2006) 4.4.4 Scattering lengths for neutrons. In Prince, E. ed. Intl. Tables for Crystallography C. Kluwer Academic Publishers. pp 444-454. (https://it.iucr.org/Cb/ch4o4v0001/sec4o4o4/) doi:10.1107/97809553602060000103 .. [#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. doi:10.1107/S0021889882011285 .. [#Mildner1998] Mildner, D.F.R., Lamaze, G.P. (1998) Neutron Transmission of Single-Crystal Sapphire. J Appl Crystallogr 31, 835–840. doi:10.1107/S0021889898005846 .. [#Glinka2011] Glinka, C.J. (2011) Incoherent Neutron Scattering from Multi-element Materials. J. Appl. Cryst. 44, 618-624. doi:10.1107/S0021889811008223 .. [#Dawidowski2013] Dawidowski, J., Granada, J. R., Santisteban, J. R., Cantargi, F., & Palomino, L. A. R. (2013). Appendix—Neutron Scattering Lengths and Cross Sections. In F. Fernandez-Alonso & D. L. Price (Eds.), Experimental Methods in the Physical Sciences (Vol. 44, pp. 471–528). Academic Press. doi:10.1016/B978-0-12-398374-9.09989-7 """ #.. [#Koester1991] Koester, L., Rauch, H., Seymann. E. (1991) # Atomic Data Nuclear Data Tables 49, 65. doi:10.1016/0092-640X(91)90012-S #.. [#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 # import numpy as np from numpy import sqrt, pi, asarray, inf from .core import Element, Isotope, default_table from .constants import (avogadro_number, planck_constant, electron_volt, neutron_mass, atomic_mass_constant) from .util import parse_uncertainty __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', ] #: Wavelength [Å] for which neutron scattering cross sections are tabulated. ABSORPTION_WAVELENGTH = 1.798 # [Å] #: Energy [eV] <=> wavelength [Å]: #: E = 1/2 m v² = h² / (2 m λ²) #: E[meV s] = h[J s]²/(2 m_n[u] m_u[kg/u] λ[Å]²/10^20[Å/m]) #: * 1000[meV/eV] / electron_volt[J/eV] ENERGY_FACTOR = ( 1e23 * planck_constant**2/electron_volt / (2 * neutron_mass * atomic_mass_constant)) #: Velocity[m/s] <=> wavelength[Å]: #: h = p λ = m v λ #: λ[Å] = h[J s] / ( m_n[kg] v[m/s] ) 10^10[Å/m] VELOCITY_FACTOR = ( 1e10 * planck_constant / (neutron_mass * atomic_mass_constant)) 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 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 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 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 constant in |Js| $N_b = \sum{ n_i b_i } / V$ $m_n$ = neutron mass in kg """ return (ENERGY_FACTOR/pi) * asarray(sld) _4PI_100 = 4*np.pi/100 class Neutron: 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. This wavelength corresponds to a neutron velocity of 2200 m/s and neutron energy of 25.3 meV. * b_c_complex (fm) Complex coherent scattering length derived from the tabulated values using $b_c - i \sigma_a / (1000 \cdot 2 \lambda)$. Additional columns not used for calculation include: * b_c_i (fm) Imaginary bound coherent scattering length. This is related to absorption cross section by $\sigma_a = 4 \pi \mathrm{Im}(b_c)/k$ 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 $\sigma_c = 4 \pi |\mathrm{Re}(b_c) + i \mathrm{Im}(b_c)|^2/100$. In practice, these values are different, with the following table showing the largest relative difference: ======== ======== ======== ======== ======== Sc 3% Ti 4% V 34% Mn 1% Cd 2% Te 4% Xe 9% Sm 19% Eu 44% Tb 1% Ho 11% W 4% Au 7% Hg 2% Ra 3% ======== ======== ======== ======== ======== * 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_units = "fm" b_c_i = None b_c_i_units = "fm" b_c_complex = None b_c_complex_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 nsf_table = None 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.""" # TODO: use NaN for missing information #return np.isnan(self.b_c * self._number_density) return self.b_c is not None and self._number_density is not None # PAK 2021-04-05: allow energy dependent b_c def scattering_by_wavelength(self, wavelength): r""" Return scattering length and total cross section for each wavelength. For rare earth isotopes this returns the energy-dependent $\mathrm{Re}(b_c)$ and $\mathrm{Im}(b_c)$ interpolated into the scattering length tables. Values are extrapolated with constant values at the ends of the table. Total scattering is returned as $4\pi/100 |b_c|^2$ with no contribution for bound incoherent scattering. :Parameters: *wavelength* \: float(s) | |Ang| :Returns: *b_c* \: complex(s) | fm *sigma_s* \: float(s) | barn """ # TODO: do vector conversion at the end rather than the beginning. if self.nsf_table is None: ones = 1 if np.isscalar(wavelength) else np.ones_like(wavelength) return ones*self.b_c_complex, ones*self.total #energy = neutron_energy(wavelength) #b_c = np.interp(energy, self.nsf_table[0], self.nsf_table[1]) b_c = np.interp(wavelength, self.nsf_table[0], self.nsf_table[1]) # TODO: sigma_s should include an incoherent contribution sigma_s = _4PI_100*abs(b_c)**2 # 1 barn = 1 fm^2 1e-2 barn/fm^2 return b_c, sigma_s def sld(self, *, wavelength=ABSORPTION_WAVELENGTH): r""" Returns scattering length density for the element at natural abundance and density. :Parameters: *wavelength* \: float(s) | |Ang| :Returns: *sld* \: float(s), float(s), float(s) | |1e-6/Ang^2| (*real*, -*imaginary*, *incoherent*) scattering length density. Returns (None, None, None) if sld is not known for this element. See :func:`neutron_scattering` for details. """ # TODO: deprecate in favour of neutron_scattering(el) if not self.has_sld(): return None, None, None return self.scattering(wavelength=wavelength)[0] def scattering(self, *, wavelength=ABSORPTION_WAVELENGTH): r""" Returns neutron scattering information for the element at natural abundance and density. :Parameters: *wavelength* \: float(s) | |Ang| :Returns: *sld* \: float(s), float(s), float(s) | |1e-6/Ang^2| (*real*, -*imaginary*, *incoherent*) scattering length density *xs* \: float(s), float(s), float(s) | |1/cm| (*coherent*, *absorption*, *incoherent*) cross sections. :w *penetration* \: float(s) | cm 1/e penetration length. Returns (None, None, None) if sld is not known for this element. See :func:`neutron_scattering` for details. """ # TODO: deprecate in favour of neutron_scattering(el) # Compute number and absorption density assuming isotope has # same structure as the bulk element if not self.has_sld(): return None, None, None number_density = self._number_density*1e-24 # N/A^3 = N/cm^3 (1e-8 cm/A)^3 b_c, sigma_s = self.scattering_by_wavelength(wavelength) return _calculate_scattering(number_density, wavelength, b_c, sigma_s) def energy_dependent_init(table): from .nsf_tables import ENERGY_DEPENDENT_TABLES for (el_name, iso_num), values in ENERGY_DEPENDENT_TABLES.items(): energy, re_a, im_a, _ = zip(*values) # Ignoring abs(a) wavelength = neutron_wavelength(asarray(energy)*1000) # 1 eV = 1000 meV el = getattr(table, el_name) atom = el if iso_num is None else el[iso_num] xs = asarray(re_a) + 1j*asarray(im_a) #atom.neutron.nsf_table = asarray(energy)*1000, xs atom.neutron.nsf_table = wavelength[::-1], xs[::-1] #print(f"adding {atom}") # Lu nat missing from Lynn and Seeger, so mix Lu[175] and Lu[176] Lu175 = table.Lu[175] Lu176 = table.Lu[176] bc_175 = Lu175.neutron.b_c_complex wavelength, bc_176 = Lu176.neutron.nsf_table bc_nat = (bc_175*Lu175.abundance + bc_176*Lu176.abundance)/100.0 # 1 fm = 1fm * %/100 table.Lu.neutron.nsf_table = wavelength, bc_nat #table.Lu.neutron.total = 0. # zap total cross section 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:]] # 1 fm = (1 barn)(100 fm^2/barn)/(1 A) (1e-5 A/fm) # Note: Sears (1992) uses b = b' - i b'', so negate sigma_a for b''. # Warning: -b_c.imag may be -0, which can mess with your calculations. #if nsf.b_c is None: print(f"b_c unavailable for {columns[0]}") b_c = nsf.b_c if nsf.b_c is not None else np.nan b_c_i = -nsf.absorption/(2000*ABSORPTION_WAVELENGTH) nsf.b_c_complex = b_c + 1j*b_c_i if not np.isnan(b_c): # Ir-191 and Ir-193 don't list scattering cross sections so deduce # them from the bound coherent cross section. Since these are both # odd isotopes there ought to be some incoherent scattering, but # zero is well within the uncertainty measured in bulk Ir. if nsf.coherent is None: nsf.coherent = 4*pi/100*abs(nsf.b_c_complex)**2 if nsf.incoherent is None: nsf.incoherent = 0 if nsf.total is None: nsf.total = nsf.coherent + nsf.incoherent 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 # N/cm^3 = N/cm^3 if isotope_number == 0: # Value for element 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:]] # Add energy-dependent tables energy_dependent_init(table) # TODO: split incoherent into spin and isotope incoherence (eq 17-19 of Sears) # TODO: require parsed compound rather than including formula() keywords in api # Note: docs and function prototype are reproduced in __init__ def neutron_scattering(compound, *, density=None, wavelength=None, energy=None, natural_density=None, table=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(s) | |Ang| Neutron wavelength (default=1.798 |Ang|). *energy* \: float(s) | meV Neutron energy. If energy is specified then wavelength is ignored. *table* \: PeriodicTable Alternate table to use when parsing *compound*. :Returns: *sld* \: float(s), float(s), float(s) | |1e-6/Ang^2| (*real*, -*imaginary*, *incoherent*) scattering length density. *xs* \: float(s), float(s), float(s) | |1/cm| (*coherent*, *absorption*, *incoherent*) cross sections. *penetration* \: float(s) | cm 1/e penetration depth of the beam Returns (None, None, None) if sld is unknown for any component. :Raises: *AssertionError* \: density is missing. .. Note: The returned values will be vectors if *wavelength* is a vector. Neutron scattering cross sections for materials are calculated from tabulated values for the different nuclei. The result is only an approximation. Actual scattering depends on details of sample composition, as well as the incoming neutron energy and sample temperature, especially for light elements. For low energy 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, leading to an estimate of 5.621/cm for H2O as computed compared to ~7.0/cm as measured with 5 meV neutrons at 290K.\ [#May1982]_ The alignment of the neutron spin with the nuclei spin also matters, as demonstrated by $^3\mathrm{He}$ polarizers. The tables themselves are not self-consistent. Because the different quantities are measured indirectly with a variety of techniques, there are discrepencies when converting values from one column to another. These differences can be seen with the following: :func:`absorption_comparison_table` :func:`coherent_comparison_table` :func:`total_comparison_table` For our calculations we use the real part of the bound coherent scattering length $\mathrm{Re}(b_c)$ (labelled b_c in the tables) and the absorption cross section $\sigma_a$ from which we derive the imaginary scattering length, $\mathrm{Im}(b_c)$. See Sears (1992) for details.\ [#Sears1992]_ 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_k m_k}\ {\rm for\ each\ atom}\ k=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_k} \right/ V The coherent scattering length of the molecule is computed from the average scattering length $b_c = \mathrm{Re}(b_c) + i \mathrm{Im}(b_c)$ weighted by frequency: .. math:: \mathrm{Re}(b_c) &= \left.\sum n_k \mathrm{Re}(b_{ck}) \right/ \sum n_k \\ \mathrm{Im}(b_c) &= \left.\sum n_k \mathrm{Im}(b_{ck}) \right/ \sum n_k The individual $\mathrm{Im}(b_{ck})$ values are derived from the absorption cross sections $\sigma_a$, tabulated at wavelength $\lambda = 1.798$ |Ang| and scaled to fm (with 1000 fm = 1 barn/|Ang|): .. math:: \mathrm{Im}(b_{ck}) = -\left. \sigma_{ak} \right/ (1000 \cdot 2 \lambda) Note the sign change relative to $b''$ in Sears (1992), with Eq 2 defining $b = b' - i b''$. Since we are not considering polarized nuclei, the imaginary incoherent contribution is zero and $b'' = -\mathrm{Im}(b_c)$. Some rare earth isotopes are energy-dependent with complex bound coherent scattering length $b_c$ tabulated by energy.\ [#Lynn1990]_ For the given input wavelength $\lambda$, $b_c$ is interpolated from the table values, with the end points used for values outside the tabulated range. The average scattering length is converted to scattering cross sections, with $\sigma_c$ scaled to barn (with 1 barn= 100 |fm^2|) and $\sigma_a$ scaled to barn (with 1000 barn = 1 fm |Ang|): .. math:: \sigma_c &= \left. 4 \pi |\mathrm{Re}(b_c) + i \mathrm{Im}(b_c)|^2 \right/ 100 \\ \sigma_a &= -\left. 1000 \cdot 4 \pi \left< \mathrm{Im}(b_c) \right> \right/k \ {\rm for} \ k=2\pi / \lambda For most elements the scattering length is independent of energy in the thermal neutron energy range so the coherent scattering length $\sigma_c$ is unchanged. The absorption cross section $\sigma_a$ for these elements scales linearly with wavelength and can be adjusted with a simple multiplication: .. math:: \sigma_a' = \sigma_a \lambda' / \lambda_o = \sigma_a \lambda' / 1.798 The incoherent scattering length is more complicated, including contributions from spin incoherence for different possible spin states as well as isotope incoherence from diffuse coherent scattering.\ [#Glinka2011]_ Using the total cross section $\sigma_s$ from the table, the incoherent scattering length is estimated as: .. math:: \sigma_s &= \left.\sum n_k \sigma_{sk} \right/ \sum n_k \\ \sigma_i &= \sigma_s - \sigma_c \\ b_i &= \sqrt{ 100 \sigma_i / (4 \pi) } For the energy dependent rare earth isotopes the total scattering is estimated from $b = \mathrm{Re}(b_c) + i \mathrm{Im}(b_c)$, ignoring any spin incoherence effects. As a result, incoherent scattering for materials with energy-dependent rare earth isotopes with non-zero nuclear spin will be underestimated. The scattering potential can be expressed as a scattering length density (SLD). This is the number density of the scatterers (per |Ang^3|) times their scattering lengths, scaled to |1e-6/Ang^2| (with |1/Ang^2| = $10^{5}$ fm/|Ang^3|). Following the convention of Sears (1992), we define sld as $\rho = \rho_{\rm re} - i \rho_{\rm im}$. .. math:: \rho_{\rm re} (10^6 / Å^2) &= 10 N \mathrm{Re}(b_c) \\ \rho_{\rm im} (10^6 / Å^2) &= -10 N \mathrm{Im}(b_c) \\ \rho_{\rm inc} (10^6 / Å^2) &= 10 N b_i Similarly, the macroscopic scattering cross section for the sample includes number density: .. math:: \Sigma_{\rm coh} (1/{\rm cm}) &= N \sigma_c \\ \Sigma_{\rm inc} (1/{\rm cm}) &= N \sigma_i \\ \Sigma_{\rm abs} (1/{\rm cm}) &= N \sigma_a \\ \Sigma_{\rm s} (1/{\rm cm}) &= 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 (cm) = \left. 1 \right/ (\Sigma_{\rm s} + \Sigma_{\rm abs}) The calculated penetration depth includes the effects of both absorption and incoherent scattering (which spreads the beam over 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 with absorption only. Transmission rate can be computed from $e^{-d/t_u}$ for penetration depth $t_u$ and sample thickness $d$. This does not include many real world effects, such as single phonon scattering\ [#Mildner1998]_ and forward scattering\ [#May1982]_, which result in measured transmission significantly different from the values predicted from nuclear properties alone. There is also a wavelength dependence for single phonon interactions which gives rise to significant inelastic scattering for lighter isotopes (H, D) and/or longer wavelengths (above 5 |Ang|). This factor is both temperature and material dependent and will not be included in the scattering calculations. In particular, penetration length and transmitted flux are going to be significantly overestimated. Including unit conversion with $\mu=10^{-6}$ the full scattering equations are: .. math:: \rho_{\rm re}\,(\mu/Å^2) &= (N/Å^3) \, (\mathrm{Re}(b_c)\,{\rm fm}) \, (10^{-5} Å/{\rm\,fm}) \, (10^6\,\mu) \\ \rho_{\rm im}\,(\mu/Å^2) &= (N/Å^3) \, (\sigma_a\,{\rm barn}) \, (10^{-8}\,Å^2/{\rm barn}) / (2 \lambda\, Å) \, (10^6\,\mu) \\ &= (N/Å^3) \, (-\mathrm{Im}(b_c)\,{\rm fm}) \, (10^{-5} Å/{\rm\,fm}) \, (10^6\,\mu) \\ \rho_{\rm inc}\,(\mu/Å^2) &= (N/Å^3) \, \sqrt{(\sigma_i\, {\rm barn})/(4 \pi) \, (100\, {\rm fm}^2/{\rm barn})} \, (10^{-5}\, Å/{\rm fm}) \, (10^6\, \mu) \\ \Sigma_{\rm coh}\,(1/{\rm cm}) &= (N/Å^3) \, (\sigma_c\, {\rm barn}) \, (10^{-8}\, Å^2/{\rm barn}) \, (10^8\, Å/{\rm cm}) \\ \Sigma_{\rm inc}\,(1/{\rm cm}) &= (N/Å^3) \,(\sigma_i\, {\rm barn}) \, (10^{-8}\, Å^2/{\rm barn}) \, (10^8\, Å/{\rm cm}) \\ \Sigma_{\rm abs}\,(1/{\rm cm}) &= (N/Å^3) \,(\sigma_a\,{\rm barn}) \, (10^{-8}\, Å^2/{\rm barn}) \, (10^8\, Å/{\rm cm}) \\ \Sigma_{\rm s}\,(1/{\rm cm}) &= (N/Å^3) \,(\sigma_s\,{\rm barn}) \, (10^{-8}\, Å^2/{\rm barn}) \, (10^8\, Å/{\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, table=table) assert compound.density is not None, "scattering calculation needs density" #print("sld", compound, compound.density) if energy is not None: wavelength = neutron_wavelength(energy) # PAK: 1.5.3 wavelength now defaults to ABSORPTION_WAVELENGTH elif wavelength is None: wavelength = ABSORPTION_WAVELENGTH # Sum over the quantities molar_mass = num_atoms = 0 b_c = sigma_s = 0 is_energy_dependent = False for element, quantity in compound.atoms.items(): # TODO: use NaN rather than None if not element.neutron.has_sld(): return None, None, None molar_mass += element.mass*quantity num_atoms += quantity # PAK 2021-04-05: allow energy dependent b_c, b'' b_ck, sigma_sk = element.neutron.scattering_by_wavelength(wavelength) #print(f"{element=}; {b_ck=}; {sigma_sk=}") b_c += quantity * b_ck sigma_s += quantity * sigma_sk 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 weighted sums into scattering factors b_c /= num_atoms sigma_s /= num_atoms # Compute number density (N/A^3) # volume A^3/N = ((1 g/mole) / (1 g/cm^3)) / (N/mole) * (10^8 A/cm)^3 cell_volume = (molar_mass/compound.density)/avogadro_number*1e24 number_density = num_atoms / cell_volume # N/A^3 = N/A^3 return _calculate_scattering(number_density, wavelength, b_c, sigma_s) def _calculate_scattering(number_density, wavelength, b_c, sigma_s): r""" :Parameters: *number_density* \: float | N/|Ang^3| Scatterers per unit volume. *wavelength* \: float(s) | |Ang| Neutron wavelength(s). *b_c* \: complex(s) | fm Complex bound coherent scattering length $b_c$. *sigma_c* \: float(s) | barn Total cross section. See neutron_scattering docstring for calculation details. Note: returns -sld_im for historical reasons. """ #print("in scat", number_density, wavelength, b_c, sigma_s) # Compute SLD (1e-6/A^2). Extending Sears (1992) convention, b = b' - i b'', # returning sld = sld_re - i sld_im. sld = 10*number_density * b_c # 1e-6/A^2 = 1/A^3 1 fm 1e-5 A/fm 1e6 1e-6 sld_re, sld_im = sld.real, abs(sld.imag) # PAK 2017-04-21: compute incoherent xs from total xs # PAK 2021-04-20: include imaginary b_c in coherent cross section # Compute coherent and incoherent cross sections (barn) sigma_c = _4PI_100 * abs(b_c)**2 # 1 barn = 1e-2 fm^2 sigma_i = np.maximum(sigma_s - sigma_c, 0.) # 1 barn = 1 barn # Compute incoherent scattering length from incoherent cross section (fm) b_i = sqrt(sigma_i / _4PI_100) # 1 fm = sqrt(1 barn * 1e-2 fm^2/barn) # Compute incoherent scattering length density (1e-6/A^2) sld_inc = number_density * b_i * 10 # 1e-6/A^2 = 1/A^3 1 fm 1e-5 A/fm 1e6 1e-6 # Compute absorption cross section (barn) # Note: Sears (1992) uses b = b' - i b'', so use |Im(b_c)| for sigma_a. sigma_a = 2000 * abs(b_c.imag) * wavelength # 1 barn = 1 fm 1 A 1e5 A/fm 1e-2 barn/fm # print(f"σ_a {sigma_c:.3f} σ_i {sigma_i:.3f} σ_s {sigma_s:.3f} σ_a {sigma_a:.3f}") # Compute macroscopic scattering cross section per unit volume (1/cm) total_xs = number_density * sigma_s # 1/cm = 1/A^3 1 barn 1e-8 A^2/barn 1e8 A/cm coh_xs = number_density * sigma_c abs_xs = number_density * sigma_a inc_xs = number_density * sigma_i # Compute 1/e length (cm) penetration = 1/(abs_xs + total_xs) # 1 cm = 1 / (1/cm) return (sld_re, sld_im, sld_inc), (coh_xs, abs_xs, inc_xs), penetration def neutron_sld(*args, **kw): r""" 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 (default=1.798 |Ang|). *energy* \: float | meV Neutron energy. If energy is specified then wavelength is ignored. *table* \: PeriodicTable Alternate table to use when parsing *compound*. :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` accepts dictionaries of \{atom\: count\}. """ return neutron_scattering(*args, **kw)[0] def D2O_match(compound, **kw): """ Find the D2O contrast match point for the compound. *wavelength* or *energy* select neutron wavelength or energy. Additional keyword arguments (*density*, *natural_density*, *name*, *table*) are passed to :func:`formulas.formula` when parsing the compound. Returns *D2O_fraction* and *SLD* at match point. See :func:`D2O_sld` for details on the calculation. Note that the resulting fraction is only meaningful in [0, 1]. Beyond 100% you will need an additional constrast agent in the 100% D2O solvent to increase the SLD enough to match. """ H2O_sld, D2O_sld, Hsld, Dsld = _D2O_slds(compound, **kw) # SLD(%Dsample + (1-%)Hsample) = SLD(%D2O + (1-%)H2O) # => %SLD(Dsample) + (1-%)SLD(Hsample) = %SLD(D2O) + (1-%)SLD(H2O) # => %(SLD(Dsample) - SLD(Hsample) + SLD(H2O) - SLD(D2O)) # = SLD(H2O) - SLD(Hsample) # => % = 100*(SLD(H2O) - SLD(Hsample)) # / (SLD(Dsample) - SLD(Hsample) + SLD(H2O) - SLD(D2O)) D2O_fraction = ( (H2O_sld[0] - Hsld[0]) / (Dsld[0] - Hsld[0] + H2O_sld[0] - D2O_sld[0])) match_point_sld = mix_values(Dsld, Hsld, D2O_fraction) return D2O_fraction, match_point_sld[0] def D2O_sld(compound, volume_fraction=1., D2O_fraction=0., **kw): """ Compute the neutron SLD for a D2O contrast solution. *compound* is a string or parsed formula object. Labile hydrogen should be marked as H[1] in the formula. These will be substituted according to %D2O in the solvent. The D2O contrast mixture is assumed to be made using pure H2O (with its natural H:D ratios) and pure D2O with no H present, so H[1] will be substituted alternately with H and D when computing mixture SLD. Solvent SLD is calculated using the density at 20 C. Only the coherent scattering crosssection will be matched. Incoherent and absorption crosssections are likely to be different for the compound and the solvent, especially due to the large incoherent crosssection for hydrogen. Note that incoherent scattering does not mix linearly, so the incoherent sld for the mixture will differ slightly from incoherent scattering computed returned from a compound with the same isotope ratios. *volume_fraction* is the portion by volume of solute in the solution. *D2O_fraction* is the portion by volume of D2O in the solvent. *wavelength* or *energy* to select neutron wavelength or energy. Additional keyword arguments (*density*, *natural_density*, *name*, *table*) are passed to :func:`formulas.formula` when parsing the compound. Returns (real, imag, incoh) SLD. """ # TODO: fix incoherent scattering so it is consistent with compound # Need to compute sld from mixture rather than mixing parts H2O_sld, D2O_sld, Hsld, Dsld = _D2O_slds(compound, **kw) solvent_sld = mix_values(D2O_sld, H2O_sld, D2O_fraction) solute_sld = mix_values(Dsld, Hsld, D2O_fraction) solution_sld = mix_values(solute_sld, solvent_sld, volume_fraction) #print(D2O_fraction, volume_fraction) #print(compound, "solvent", solvent_sld) #print(compound, "solute", solute_sld) #print(compound, "solution", solution_sld) return solution_sld def _D2O_slds(compound, **kw): from . import formulas # Water density at 20C; neutron wavelength doesn't matter. sld_args = dict( wavelength=kw.pop("wavelength", None), energy=kw.pop("energy", None), # Note: using get() rather than pop() for table since table can be a # parameter for formula and for neutron_sld (which calls formula) table=kw.get('table', None), ) # TODO: use same table for solvent as solute? H2O_sld = neutron_sld("H2O@0.9982n", **sld_args) D2O_sld = neutron_sld("D2O@0.9982n", **sld_args) mol = formulas.formula(compound, **kw) # Be sure to pull H and H[1] from the table for the compound, otherwise # the elements may not match in the substitution. # TODO: include table in compound so parsed table = default_table(kw.get('table', None)) labile_H, H, D = table.H[1], table.H, table.D Hsld = neutron_sld(mol.replace(labile_H, H), **sld_args) Dsld = neutron_sld(mol.replace(labile_H, D), **sld_args) return H2O_sld, D2O_sld, Hsld, Dsld def mix_values(a, b, fraction): """ Mix two tuples with floating point values according to fraction of a. """ return tuple(aj*fraction + bj*(1-fraction) for aj, bj in zip(a, b)) 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 b_c = sigma_s = 0 for element, quantity in compound.atoms.items(): molar_mass += element.mass*quantity num_atoms += quantity b_ck, sigma_sk = element.neutron.scattering_by_wavelength(wavelength) b_c += quantity * b_ck sigma_s += quantity * sigma_sk return num_atoms, molar_mass, b_c, sigma_s # TODO: compute density from material densities if requested # You ought to be able to use mixby="mass" or "volume" when creating the # calculator, and ignore any density provided. def neutron_composite_sld(materials, wavelength=ABSORPTION_WAVELENGTH): r""" 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. Note that density must be provided for each set of material weights. The density on the individual materials is ignored. The returned slds will be vectors if the input wavelength is a vector and if any of the elements are energy dependent. 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. """ # Input may be a scalar or a sequence. If it is a sequence, turn it into # an array before proceeding. If it is a scalar leave it as a scalar so # that float input returns float output. is_multi = not np.isscalar(wavelength) if is_multi: wavelength = np.asarray(wavelength) # Query all parts of the composition parts = [_sum_piece(wavelength, m) for m in materials] num_atoms_parts, molar_mass_parts, bc_parts, sigma_parts = [ np.array(v) for v in zip(*parts) ] #for name, v in zip("N mass bc b'' total".split(), V): print(name, v) def _compute(weights, density=1): multiweights = weights[:, None] if is_multi else weights # Sum over the quantities molar_mass = np.sum(weights*molar_mass_parts) num_atoms = np.sum(weights*num_atoms_parts) b_c = np.sum(multiweights*bc_parts, axis=0) sigma_s = np.sum(multiweights*sigma_parts, axis=0) # 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 # Compute number density (1/A^3) cell_volume = (molar_mass/density)/avogadro_number*1e24 number_density = num_atoms / cell_volume #print("in compute", b_c, number_density) # Turn sums into scattering factors b_c /= num_atoms sigma_s /= num_atoms # TODO: duplicated from _calculate_scattering # Compute SLD (1e-6/A^2). Extending Sears (1992) convention, b = b' - i b'', # returning sld = sld_re - i sld_im. sld = 10*number_density * b_c # 1e-6/A^2 = 1/A^3 1 fm 1e-5 A/fm 1e6 1e-6 sld_re, sld_im = sld.real, abs(sld.imag) # PAK 2017-04-21: compute incoherent xs from total xs # PAK 2021-04-20: include imaginary b_c in coherent cross section sigma_c = _4PI_100 * abs(b_c)**2 # 1 barn = 1e-2 fm^2 sigma_i = np.maximum(sigma_s - sigma_c, 0.) # 1 barn = 1 barn b_i = sqrt(sigma_i / _4PI_100) # 1 fm = sqrt(1 barn * 1e-2 fm^2/barn) sld_inc = number_density * b_i * 10 # 1e-6/A^2 = 1/A^3 1 fm 1e-5 A/fm 1e6 1e-6 return sld_re, sld_im, sld_inc return _compute def sld_plot(table=None): r""" 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 [PAK: doesn't seem true] # coherent, incoherent, total # The coherent and incoherent scattering cross-sections in barns. # absorption # The thermal absorption cross section in barns at 1.798 A; 25.30 meV; 2200 m/s # # Numbers in parenthesis represents uncertainty. # Numbers followed by '*' are estimated. # Numbers may be given as limit, e.g., <1.0e-6 # # [Paul Kienzle] # * Fix typos such as 70Zn b_c 6.9(1.0) => 6.0(1.0). # * Update bound coherent scattering length for H-1, H-2, He-4, C-12, # O-16, O-17, O-18, Sn-119, Sm-154, Eu-153, Pb-207, Bi-209 # * Update total cross section for He, Kr, Xe # * Usd 63-Eu-151 b_c from 84Mug1. This change is moot since this isotope # has energy dependent isotope coeffs. # * Use calculated values for 4He coh and total, and natHe b_c, coh and total. 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,-3.7395(11),10.817(5),-47.420(14),+/-,1.7583(10),80.27(6),82.03(6),0.3326(7) 1-H-2,0.0149,1,6.6681(27),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,,,3.0985(21),,,,1.2065(16),0,1.2065(16),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-4,99.987,0,3.0982(21),,,,1.2062(16),0,1.2062(16),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,,,6.6472(9),,,,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,,,5.8037(29),,,,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-17,0.039,5/2,5.867(4),5.52(20),5.17(20),,4.20(22),0.004(3),4.20(22),0.236(10) 8-O-18,0.208,0,6.009(5),,,,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-70,0.62,0,6.0(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),7.685(26),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(5) 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,,,6.2239(13),,,,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),0,4.344(17),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(10),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-154,22.8,0,8.97(6),,,,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-151,47.8,5/2,6.92(15),,,E,5.5(2),3.1(4),8.6(4),9100.0(100.0) 63-Eu-153,52.8,5/2,8.85(3),,,,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-191,37.4,3/2,12.1(9),,,,,,,954.0(10.0) 77-Ir-193,62.6,3/2,9.71(18),,,,,,,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,,,9.4024(13),,,,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-209,100,9/2,8.5242(18),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. """ from .util import parse_uncertainty return parse_uncertainty(str.replace('<','').replace('*',''))[0] def sld_table(wavelength=1, table=None, isotopes=True): r""" 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 10.690 1-H 1.008 0.071 -1.582 0.000 10.691 D 2.014 0.141 2.820 0.000 1.709 T 3.016 0.212 2.027 0.000 0.453 He 4.003 0.122 0.569 0.000 0.003 3-He 3.016 0.092 1.054 0.272 0.652 * 4-He 4.003 0.122 0.569 0.000 0.000 ... 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 is not 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): r""" 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 is not None and iso.neutron.is_energy_dependent] if dep: 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, "----")) # Tricky code: Using tolerance of -tol selects for items within tolerance # rather than outside tolerance by using -|a-b| > -tol. elif np.sign(tol)*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: # Don't show isotope details if the isotope defers to the natural # natural abundance for its value. if 'neutron' not in iso.__dict__: #print("dict has", iso.__dict__.keys()) continue 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 \mathrm{Im}(b_c) \cdot 1000 The wavelength $\lambda = 1.798$ |Ang| 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) 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. Use -tol to show elements within tolerance rather than those outside tolerance. :Returns: None Example >>> coherent_comparison_table (tol=0.5) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE Comparison of (4 pi |b_c|^2/100) and coherent Sc 18.40 19.00 -3.2% 45-Sc 18.40 19.00 -3.2% 65-Cu 13.08 14.10 -7.2% 84-Sr 3.14 6.00 -47.6% ... """ print("Comparison of (4 pi |b_c|^2/100) and coherent") sigma_c = lambda el: 4*pi/100*abs(el.neutron.b_c_complex)**2 compare(sigma_c, lambda el: el.neutron.coherent, table=table, tol=tol) def total_comparison_table(table=None, tol=None): r""" 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. Use -tol to show elements within tolerance rather than those outside tolerance. :Returns: None Example >>> total_comparison_table (tol=0.1) Comparison of total cross section to (coherent + incoherent) 84-Kr 6.60 ---- Xe 4.34 3.04 42.9% 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): r""" 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. Use -tol to show elements within tolerance rather than those outside tolerance. :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% 84-Sr 0.00 2.86 -100.0% ... """ print("Comparison of incoherent and (total - 4 pi |b_c|^2/100)") sigma_c = lambda el: 4*pi/100*abs(el.neutron.b_c_complex)**2 compare(lambda el: el.neutron.incoherent, lambda el: el.neutron.total - sigma_c(el), 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(" Σ_c: %g Σ_a: %g Σ_i: %g 1/cm"%xs) print(" μ: %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() #sld_table() #coherent_comparison_table(tol=0.1) #incoherent_comparison_table(tol=0.1) #absorption_comparison_table(tol=0.1) #total_comparison_table(tol=0.1)