`Hyperfine`

class nexus.Hyperfine(id='', weight=1.0, isomer=0.0, magnetic_field=0.0, magnetic_theta=0.0, magnetic_phi=0.0, quadrupole=0.0, quadrupole_alpha=0.0, quadrupole_beta=0.0, quadrupole_gamma=0.0, quadrupole_asymmetry=0.0, texture=1.0, lamb_moessbauer=0.0, broadening=1.0, isomer_dist=None, magnetic_field_dist=None, magnetic_theta_dist=None, magnetic_phi_dist=None, quadrupole_dist=None, quadrupole_alpha_dist=None, quadrupole_beta_dist=None, quadrupole_gamma_dist=None, quadrupole_asymmetry_dist=None, isotropic=False)

Defines a set of hyperfine parameters acting on a Moessbauer isotope. Parameters can have distributions of type Distribution. Special random 2D and 3D distributions are available.

Parameters:

id (string) – User identifier.
weight (float or Var) – Relative weight of the site, > 0.
isomer (float or Var) – Isomer shift (mm/s).
magnetic_field (float or Var) – Magnetic hyperfine field amplitude (Tesla).
magnetic_theta (float or Var) – Polar angle of the magnetic field with respect to the beam propagation direction - photon \(k\) vector (degree).
magnetic_phi (float or Var) – Azimuthal angle of the magnetic field with respect to the \(sigma\) direction of the beam (degree).
quadrupole (float or Var) – Quadrupole splitting (\(QS\)) value (mm/s). It is :math: QS = frac{c}{E_{trans}} frac{eQ_iV_{zz}}{2}`, with \(Q_i\) being the quadrupole moment of ground or excited state. For isotopes with only one quadrupole split state, the given value represents the value of the split state. For isotopes with split ground and excited state, it represents the quadrupole splitting of the excited state. The ground state quadrupole energy is then scaled by the ratio of the quadrupole moments \(Q_g/Q_e\).
quadrupole_alpha (float or Var) – Euler angle of the electric field gradient \(\alpha\) in extrinsic ZYZ convention (degree).
quadrupole_beta (float or Var) – Euler angle of the electric field gradient \(\beta\) in extrinsic ZYZ convention (degree).
quadrupole_gamma (float or Var) – Euler angle of the electric field gradient \(\gamma\) in extrinsic ZYZ convention (degree).
quadrupole_asymmetry (float or Var) – Asymmetry parameter of the electric field gradient, 0 to 1.
texture (float or Var) –
Texture coefficient between 0 and 1. It assumes the directional parameters of the site with a ratio of texture and a 3D isotropic distribution of the parameters with the ration 1 - texture. If isotropic is True it is not taken into account. Setting texture to 0 is the same as to set isotropic to True.

Added in version 1.2.0.
lamb_moessbauer (float or Var) –
Lamb-Moessbauer factor of the hyperfine site. Only used when the lamb_moessbauer of the material is None.

Added in version 1.2.0.
broadening (float or Var) –
Optional inhomogeneous broadening parameter. It multiplies with the natural linewidth.

Added in version 1.2.0.
isomer_dist (Distribution) – Distribution to the isomer shift (mm/s).
magnetic_field_dist (Distribution) – Distribution to the magnetic hyperfine field amplitude (Tesla).
magnetic_theta_dist (Distribution) – Distribution to the polar angle of the magnetic field with respect to the beam propagation direction - photon \(k\) vector (degree).
magnetic_phi_dist (Distribution) – Distribution to the azimuthal angle of the magnetic field with respect to the \(sigma\) direction of the beam (degree).
quadrupole_dist (Distribution) – Distribution to the quadrupole splitting amplitude (mm/s).
quadrupole_alpha_dist (Distribution) – Distribution to the Euler angle of the electric field gradient \(\alpha\) in extrinsic ZYZ convention (degree).
quadrupole_beta_dist (Distribution) – Distribution to the Euler angle of the electric field gradient \(\beta\) in extrinsic ZYZ convention (degree).
quadrupole_gamma_dist (Distribution) – Distribution to the Euler angle of the electric field gradient \(\gamma\) in extrinsic ZYZ convention (degree).
quadrupole_asymmetry_dist (Distribution) – Distribution to the asymmetry parameter of the electric field gradient, 0 to 1.
isotropic (bool) –
If True the hyperfine site is set to 3D angular distribution. The site parameters (the angels between the magnetic field and the quadrupole) are fixed.

Changed in version 1.2.0: Prior to version 1.2.0, it overrides all other distributions on angular values applied to the Hyperfine object. Since version 1.2.0 the random distributions are kept.

id

User identifier.

Type:: string

weight

Relative weight of the site, > 0.

Type:: Var

isomer

Isomer shift (mm/s).

Type:: Var

magnetic_field

Magnetic hyperfine field amplitude (Tesla).

Type:: Var

magnetic_theta

Polar angle of the magnetic field with respect to the beam propagation direction - photon \(k\) vector (degree).

Type:: Var

magnetic_phi

Azimuthal angle of the magnetic field with respect to the \(sigma\) direction of the beam (degree).

Type:: Var

quadrupole

Quadrupole splitting (\(QS\)) value (mm/s). It is :math: QS = frac{c}{E_{trans}} frac{eQ_iV_{zz}}{2}`, with \(Q_i\) being the quadrupole moment of ground or excited state. For isotopes with only one quadrupole split state, the given value represents the value of the split state. For isotopes with split ground and excited state, it represents the quadrupole splitting of the excited state. The ground state quadrupole energy is then scaled by the ratio of the quadrupole moments \(Q_g/Q_e\).

Type:: float or Var

quadrupole_alpha

Euler angle of the electric field gradient \(\alpha\) in extrinsic ZYZ convention (degree).

Type:: Var

quadrupole_beta

Euler angle of the electric field gradient \(\beta\) in extrinsic ZYZ convention (degree).

Type:: Var

quadrupole_gamma

Euler angle of the electric field gradient \(\gamma\) in extrinsic ZYZ convention (degree).

Type:: Var

quadrupole_asymmetry

Asymmetry parameter of the electric field gradient, 0 to 1.

Type:: Var

texture

Texture coefficient between 0 and 1. It assumes the directional parameters of the site with a ratio of texture and a 3D isotropic distribution of the parameters with the ration 1 - texture. If isotropic is True it is not taken into account. Setting texture to 0 is the same as to set isotropic to True.

Added in version 1.2.0.

Type:: Var

lamb_moessbauer

Lamb-Moessbauer factor of the hyperfine site. Only used when the lamb_moessbauer of the material is None.

Added in version 1.2.0.

Type:: Var

broadening

Optional inhomogeneous broadening parameter. It multiplies with the natural linewidth.

Added in version 1.2.0.

Type:: float or Var

isomer_dist

Distribution to the isomer shift (mm/s).

Type:: Distribution

magnetic_field_dist

Distribution to the magnetic hyperfine field amplitude (Tesla).

Type:: Distribution

magnetic_theta_dist

Distribution to the polar angle of the magnetic field with respect to the beam propagation direction - photon \(k\) vector (degree).

Type:: Distribution

magnetic_phi_dist

Distribution to the azimuthal angle of the magnetic field with respect to the \(sigma\) direction of the beam (degree).

Type:: Distribution

quadrupole_dist

Distribution to the quadrupole splitting amplitude (mm/s).

Type:: Distribution

quadrupole_alpha_dist

Distribution to the Euler angle of the electric field gradient \(\alpha\) in extrinsic ZYZ convention (degree).

Type:: Distribution

quadrupole_beta_dist

Distribution to the Euler angle of the electric field gradient \(\beta\) in extrinsic ZYZ convention (degree).

Type:: Distribution

quadrupole_gamma_dist

Distribution to the Euler angle of the electric field gradient \(\gamma\) in extrinsic ZYZ convention (degree).

Type:: Distribution

quadrupole_asymmetry_dist

Distribution to the asymmetry parameter of the electric field gradient, 0 to 1.

Type:: Distribution

isotropic

If True the hyperfine site is set to 3D angular distribution. The site parameters (the angels between the magnetic field and the quadrupole) are fixed.

Changed in version 1.2.0: Prior to version 1.2.0, it overrides all other distributions on angular values applied to the Hyperfine object. Since version 1.2.0 the random distributions are kept.

Type:: bool

BareHyperfines

Holds all hyperfine parameters combinations assigned to the site. So each explicit parameter combination due to distributions.

Type:: List of BareHyperfine

ClearRandomDistribution(target)

Clears the selected random or spherical distribution.

Added in version 1.2.0.

Parameters:: target (string) – mag for magnetic distributions. efg for quadrupole distributions. all for mag and efg.

Copy(ref_dist=True)

Copy the Hyperfine object.

Parameters:: ref_dist (bool) – Determines whether the distribution references should be copied as well (True) or not (False). The distributions itself are not copied, just the reference is passed to the new object. Changing values in the distributions will affect both the original and the copied Hyperfine object. Hyperfine site nx.Distributions are not copied but use same reference.

GetIsomerDistribution()

Get the isomer distribution.

Returns:: isomer values, relative weight
Return type:: ndarray, ndarray

GetMagneticFieldDistribution()

Get the magnetic field distribution.

Returns:: magnetic field values, relative weight
Return type:: ndarray, ndarray

GetMagneticPhiDistribution()

Get the magnetic phi angle distribution.

Returns:: magnetic phi values, relative weight
Return type:: ndarray, ndarray

GetMagneticThetaDistribution()

Get the magnetic theta angle distribution.

Returns:: magnetic theta values, relative weight
Return type:: ndarray, ndarray

GetQuadrupoleAlphaDistribution()

Get the quadrupole alpha angle distribution.

Returns:: quadrupole alpha angle values, relative weight
Return type:: ndarray, ndarray

GetQuadrupoleAsymmetryDistribution()

Get the quadrupole asymmetry distribution.

Returns:: quadrupole asymmetry values, relative weight
Return type:: ndarray, ndarray

GetQuadrupoleBetaDistribution()

Get the quadrupole beta angle distribution.

Returns:: quadrupole beta angle values, relative weight
Return type:: ndarray, ndarray

GetQuadrupoleDistribution()

Get the quadrupole distribution.

Returns:: quadrupole values, relative weight
Return type:: ndarray, ndarray

GetQuadrupoleGammaDistribution()

Get the quadrupole gamma angle distribution.

Returns:: quadrupole gamma angle values, relative weight
Return type:: ndarray, ndarray

SetIsomerDistribution(dist)

Set an isomer shift distribution.

Parameters:: dist (Distribution) – Distribution applied to the isomer shift.

SetMagneticFieldDistribution(dist)

Set a magnetic field distribution.

Parameters:: dist (Distribution) – Distribution applied to the magnetic field.

SetMagneticPhiDistribution(dist)

Set a magnetic field azimuthal angle distribution.

Parameters:: dist (Distribution) – Distribution applied to the magnetic field azimuthal angle.

SetMagneticThetaDistribution(dist)

Set a magnetic field polar angle distribution.

Parameters:: dist (Distribution) – Distribution applied to the magnetic field polar angle.

SetQuadrupoleAlphaDistribution(dist)

Set a quadrupole distribution in the \(\alpha\) angle.

Parameters:: dist (Distribution) – Distribution applied to \(\alpha\).

SetQuadrupoleAsymmetryDistribution(dist)

Set a quadrupole distribution in the quadrupole asymmetry.

Parameters:: dist (Distribution) – Distribution applied to the quadrupole asymmetry.

SetQuadrupoleBetaDistribution(dist)

Set a quadrupole distribution in the \(\beta\) angle.

Parameters:: dist (Distribution) – Distribution applied to \(\beta\).

SetQuadrupoleDistribution(dist)

Set a quadrupole distribution.

Parameters:: dist (Distribution) – Distribution applied to the quadrupole amplitude.

SetQuadrupoleGammaDistribution(dist)

Set a quadrupole distribution in the \(\gamma\) angle.

Parameters:: dist (Distribution) – Distribution applied to \(\gamma\).

SetRandomDistribution(target, type, points=401, method='model', order=1)

Set a random distribution in the magnetic hyperfine field or the electric field gradient. For a hyperfine site random magnetic and random quadrupole magnitude distributions can be set in parallel.

Changed in version 1.2.0: In versions < 1.2.0 this function provided a real random distribution of vectors. However, this requires a large number of points and random sampling does not guarantee the correct spectrum. Since 1.2.0, complete random distributions are removed. Now two optimized versions are implemented. A new averaging method uses a group theoretical approach for optimized sampling of vectors. This method “model” should be used for most cases as it reduces the number of points needed considerably. The random distribution method “random” is still available but now use an optimized random sampling of points based on permutations and mirroring of random vectors, which leads to much better results. This algorithm requires multiple of 48 points for 3D and multiple of 8 points for 2D distributions and will choose a possible number of points closest to your point number input.

Note

For a quadrupole distribution a random orientation of the asymmetry parameter is not included. Only Vzz is randomly chosen and \(\alpha\) is always zero.

Parameters:

target (string) – mag for magnetic distributions. efg for quadrupole distributions. none to reset all angular distributions.
type (string) – 3D for 3-dimensional distribution or for 2-dimensional distributions one of the following options: 2Dks, 2Dkp, 2Dsp, 2Dsk, 2Dpk, 2Dps. Convention for 2Dxy is that xy give the plane of the distribution. x and y can be k (k-vector direction), s (\(sigma\) polarization direction) or p (\(pi\) polarization direction).
points (int) –
Number of points for the distribution. Only used for method random. Default is 401 points.

Changed in version 1.2.0.
method (string) –
random for random selection of points, which are permuted and mirrored. model for selected points to average over the parameter after [Hasselbach].

Added in version 1.2.0.
order (int) –
The order parameter determines the number of basis sets used in the spherical 3D approximation of the average method, not for the 2D one. For order=1 48 vectors are used, up to 1008 vectors for order=6. Default is 1.

Added in version 1.2.0.

Note

A hyperfine site should not have too many distributions. Each distribution point number multiplies with the previously set distribution points. For example, having three distributions with each 30 points will result in 27000 distribution points in total for the site. In this case the calculations of the transitions takes quite long. As a rule of thumb try to stay below 1000 distribution points per Hyperfine object. For 3D random distributions in the magnetic field and the quadrupole splitting set Hyperfine.isotropic to True. This will results in considerable faster calculations than setting two 3D distributions.

Examples

Various ways to define a Hyperfine object without distributions.

site = nx.Hyperfine(
  id = "user hyperfine site",
  weight = 1,
  isomer = -0.11,
  magnetic_field = 0,
  magnetic_theta = 0,
  magnetic_phi = 45,
  quadrupole = 0.8,
  quadrupole_alpha = 90,
  quadrupole_beta = 45,
  quadrupole_gamma = 0,
  quadrupole_asymmetry = 0.05,
  isotropic = False)

site.quadrupole.value = 0

site.magnetic_field = 33

site.isotropic = True

print(site)

different ways to define distributions on hyperfine parameters

gauss_dist_mag = nx.lib.distribution.Gaussian(points = 11, fwhm = 3)

# initializer definition of magnetic field distribution
site = nx.Hyperfine(isomer = -0.11,
                    magnetic_field = 33,
                    magnetic_field_dist = gauss_dist_mag)

site = nx.Hyperfine(isomer = -0.11,
                    magnetic_field = 33)

# isomer distribution via set method
gauss_dist_isomer = nx.lib.distribution.Gaussian(points = 11, fwhm = 0.2)

site.SetIsomerDistribution(gauss_dist_isomer)

Random distributions have to be applied by set methods

site.SetRandomDistribution("efg", "3D", 201)

site.SetRandomDistribution("mag", "2Dsk", 201)

Hyperfine

`Hyperfine`