\(\renewcommand\AA{\text{Å}}\)

Neutron scattering potentials

periodictable.nsf

Neutron scattering factors for the elements and isotopes.

For details of neutron scattering factor values, see 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:

>>> 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

neutron_energy()

Return neutron energy given wavelength.

neutron_wavelength()

Return wavelength given neutron energy.

neutron_wavelength_from_velocity()

Return wavelength given neutron velocity.

neutron_scattering()

Computes scattering length density, cross sections and penetration depth for a compound.

neutron_sld()

Computes scattering length density for a compound.

neutron_composite_sld()

Returns a scattering length density for a compound whose composition is variable.

energy_dependent_table()

Lists isotopes with energy dependence.

sld_table()

Lists scattering length densitys for all elements in natural abundance.

absorption_comparison_table()

Compares the imaginary bound coherent scattering length to the absorption cross section.

coherent_comparison_table()

Compares the bound coherent scattering length to the coherent scattering cross section.

total_comparison_table()

Compares the total scattering cross section to the sum of the coherent and incoherent scattering cross sections.

For private tables use init() to set the data.

The neutron scattering information table is reproduced from the Atomic Institute for Austrian Universities[1] (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.

[1]

(1, 2) 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)

[2]	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

[3]	Koester, L., Rauch, H., Seymann. E. (1991) Atomic Data Nuclear Data Tables 49, 65. doi:10.1016/0092-640X(91)90012-S

[4]	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

[5]	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

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

[7]	(1, 2) 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

[8]	Mildner, D.F.R., Lamaze, G.P. (1998) Neutron Transmission of Single-Crystal Sapphire. J Appl Crystallogr 31, 835–840. doi:10.1107/S0021889898005846

[9]	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

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

class periodictable.nsf.Neutron

Bases: object

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 Å. Scale to your beam by dividing by periodictable.nsf.ABSORPTION_WAVELENGTH and multiplying by your wavelength.

• 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 Å·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[1] 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 fm²

has_sld()

Returns True if sld is defined for this element/isotope.

scattering(wavelength=1.798)

Returns neutron scattering information for the element at natural abundance and density.

Parameters:

wavelength : float(s) | Å

Returns:

sld : float(s), float(s), float(s) | 10^-6Å^-2

(real, -imaginary, incoherent) scattering length density

xs : float(s), float(s), float(s) | cm^-1

(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 neutron_scattering() for details.

scattering_by_wavelength(wavelength)

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) | Å

Returns:

b_c : complex(s) | fm

sigma_s : float(s) | barn

sld(wavelength=1.798)

Returns scattering length density for the element at natural abundance and density.

Parameters:

wavelength : float(s) | Å

Returns:

sld : float(s), float(s), float(s) | 10^-6Å^-2

(real, -imaginary, incoherent) scattering length density.

Returns (None, None, None) if sld is not known for this element.

See neutron_scattering() for details.

absorption = None

absorption_units = 'barn'

abundance = 0.0

abundance_units = '%'

b_c = None

b_c_complex = None

b_c_complex_units = 'fm'

b_c_i = None

b_c_i_units = 'fm'

b_c_units = 'fm'

bm = None

bm_i = None

bm_units = 'fm'

bp = None

bp_i = None

bp_units = 'fm'

coherent = None

coherent_units = 'barn'

incoherent = None

incoherent_units = 'barn'

is_energy_dependent = False

nsf_table = None

total = None

total_units = 'barn'

periodictable.nsf.init(table, reload=False)

Loads the Rauch table from the neutron data book.

periodictable.nsf.neutron_energy(wavelength)

Convert neutron wavelength to energy.

Parameters:wavelength : float or vector | Å Returns:energy : float or vector | meV

Wavelength is converted to energy using

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

where:

\(h\) = planck’s constant in J·s

\(m_n\) = neutron mass in kg

periodictable.nsf.neutron_wavelength(energy)

Convert neutron energy to wavelength.

Parameters:energy : float or vector | meV Returns:wavelength : float or vector | Å

Energy is converted to wavelength using

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

where

\(h\) = planck’s constant in J·s

\(m_n\) = neutron mass in kg

periodictable.nsf.neutron_wavelength_from_velocity(velocity)

Convert neutron velocity to wavelength.

Parameters:velocity : float or vector | m/s Returns:wavelength : float or vector | Å

Velocity is converted to wavelength using

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

where

\(h\) = planck’s constant in J·s

\(m_n\) = neutron mass in kg

periodictable.nsf.neutron_scattering(compound, density=None, wavelength=None, energy=None, natural_density=None, table=None)

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) | Å

Neutron wavelength (default=1.798 Å).

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) | 10^-6Å^-2

(real, -imaginary, incoherent) scattering length density.

xs : float(s), float(s), float(s) | cm^-1

(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.

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.[7] 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:

absorption_comparison_table()

coherent_comparison_table()

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.[6]

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:

\[m = \sum{n_k m_k}\ {\rm for\ each\ atom}\ k=1,2,\ldots\]

Cell volume \(V\) (ų/molecule) is molar mass \(m\) over density \(\rho\), with a correction based on Avogadro’s number \(N_A\) (atoms/mol) and the length conversion \(10^8\) Å/cm:

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

Number density \(N\) is the number of scatterers per unit volume:

\[N = \left.\sum{n_k} \right/ V\]

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:

\[\begin{split}\mathrm{Re}(b_c) &= \left.\sum n_k \mathrm{Re}(b_{ck}) \right/ \sum n_k \\ \mathrm{Im}(b_c) &= \left.\sum n_k \mathrm{Im}(b_{ck}) \right/ \sum n_k\end{split}\]

The individual \(\mathrm{Im}(b_{ck})\) values are derived from the absorption cross sections \(\sigma_a\), tabulated at wavelength \(\lambda = 1.798\) Å and scaled to fm (with 1000 fm = 1 barn/Å):

\[\mathrm{Im}(b_{ck}) = -\left. \sigma_{ak} \right/ (1000 \cdot 2 \lambda)\]

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.[4] 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 fm²) and \(\sigma_a\) scaled to barn (with 1000 barn = 1 fm Å):

\[\begin{split}\sigma_c &= \left. 4 \pi |\mathrm{Re}(b_c) + i \mathrm{Im}(b_c)|^2 \right/ 100 \\ \sigma_a &= -\left. 1000 \cdot 4 \pi \left< \mathrm{Im}(b_c) \right> \right/k \ {\rm for} \ k=2\pi / \lambda\end{split}\]

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:

\[\sigma_a' = \sigma_a \lambda' / \lambda_o = \sigma_a \lambda' / 1.798\]

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.[10] Using the total cross section \(\sigma_s\) from the table, the incoherent scattering length is estimated as:

\[\begin{split}\sigma_s &= \left.\sum n_k \sigma_{sk} \right/ \sum n_k \\ \sigma_i &= \sigma_s - \sigma_c \\ b_i &= \sqrt{ 100 \sigma_i / (4 \pi) }\end{split}\]

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 \(\AA^3\)) times their scattering lengths, scaled to \(10^6/\AA^2\) (with \(1/\AA^2\) = \(10^{5} \mathrm{fm}/\AA^3\)). Following the convention of Sears (1992), we define sld as \(\rho = \rho_{\rm re} - i \rho_{\rm im}\).

\[\begin{split}\rho_{\rm re} (10^6 / \AA^2) &= 10 N \mathrm{Re}(b_c) \\ \rho_{\rm im} (10^6 / \AA^2) &= -10 N \mathrm{Im}(b_c) \\ \rho_{\rm inc} (10^6 / \AA^2) &= 10 N b_i\end{split}\]

Similarly, the macroscopic scattering cross section for the sample includes number density:

\[\begin{split}\Sigma_{\rm coh} (1/{\rm cm}) &= N \sigma_c \\ \Sigma_{\rm inc} (1/{\rm cm}) &= N \sigma_i \\ \Sigma_{\rm abs} (1/{\rm cm}) &= N \sigma_a \\ \Sigma_{\rm s} (1/{\rm cm}) &= N \sigma_s\end{split}\]

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 \(e\):

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

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[8] and forward scattering[7], 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 Å). 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:

\[\begin{split}\rho_{\rm re}\,(\mu/\AA^2) &= (N/\AA^3) \, (\mathrm{Re}(b_c)\,{\rm fm}) \, (10^{-5} \AA/{\rm\,fm}) \, (10^6\,\mu) \\ \rho_{\rm im}\,(\mu/\AA^2) &= (N/\AA^3) \, (\sigma_a\,{\rm barn}) \, (10^{-8}\,\AA^2/{\rm barn}) / (2 \lambda\, \AA) \, (10^6\,\mu) \\ &= (N/\AA^3) \, (-\mathrm{Im}(b_c)\,{\rm fm}) \, (10^{-5} \AA/{\rm\,fm}) \, (10^6\,\mu) \\ \rho_{\rm inc}\,(\mu/\AA^2) &= (N/\AA^3) \, \sqrt{(\sigma_i\, {\rm barn})/(4 \pi) \, (100\, {\rm fm}^2/{\rm barn})} \, (10^{-5}\, \AA/{\rm fm}) \, (10^6\, \mu) \\ \Sigma_{\rm coh}\,(1/{\rm cm}) &= (N/\AA^3) \, (\sigma_c\, {\rm barn}) \, (10^{-8}\, \AA^2/{\rm barn}) \, (10^8\, \AA/{\rm cm}) \\ \Sigma_{\rm inc}\,(1/{\rm cm}) &= (N/\AA^3) \,(\sigma_i\, {\rm barn}) \, (10^{-8}\, \AA^2/{\rm barn}) \, (10^8\, \AA/{\rm cm}) \\ \Sigma_{\rm abs}\,(1/{\rm cm}) &= (N/\AA^3) \,(\sigma_a\,{\rm barn}) \, (10^{-8}\, \AA^2/{\rm barn}) \, (10^8\, \AA/{\rm cm}) \\ \Sigma_{\rm s}\,(1/{\rm cm}) &= (N/\AA^3) \,(\sigma_s\,{\rm barn}) \, (10^{-8}\, \AA^2/{\rm barn}) \, (10^8\, \AA/{\rm cm}) \\ t_u\,({\rm cm}) &= 1/(\Sigma_{\rm s}\, 1/{\rm cm} \,+\, \Sigma_{\rm abs}\, 1/{\rm cm})\end{split}\]

periodictable.nsf.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 | Å

Neutron wavelength (default=1.798 Å).

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) | 10^-6Å^-2

(real, -imaginary, incoherent) scattering length density.

Raises:

AssertionError : density is missing.

Returns the scattering length density of the compound. See neutron_scattering() for details.

periodictable.nsf.neutron_composite_sld(materials, wavelength=1.798)

Create a composite SLD calculator.

Parameters:

materials : [Formula]

List of materials

wavelength = 1.798: float OR [float] | Å

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.

periodictable.nsf.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

periodictable.nsf.absorption_comparison_table(table=None, tol=None)

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:

\[\sigma_a = -2 \lambda \mathrm{Im}(b_c) \cdot 1000\]

The wavelength \(\lambda = 1.798 \AA\) is the neutron wavelength at which the absorption is tallied. The factor of 1000 transforms from Å·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     ----
   ...

periodictable.nsf.coherent_comparison_table(table=None, tol=None)

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
         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%
   ...

periodictable.nsf.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. 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%
     70-Zn     0.00    -1.48 -100.0%
     84-Sr     0.00     2.86 -100.0%
   ...

periodictable.nsf.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. 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)
         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%

periodictable.nsf.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

periodictable.nsf.sld_table(wavelength=1, table=None, isotopes=True)

Scattering length density table for wavelength 4.75 Å.

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   0.652 *
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

periodictable.nsf.neutron_sld_from_atoms(*args, **kw)

Deprecated since version 0.91: neutron_sld() accepts dictionaries of {atom: count}.