Dynamics#

dispersionrelations.dynamics.sR(M_R, G_R)[source]#

Resonance pole location calculated from its mass and width.

Parameters:

M_R (float) – Mass of the particle.
G_R (float) – Width of the particle.

Returns:

sR – The complex pole location.

Return type:

complex

Notes

The pole location is calculated using \(s_R(M_R, \Gamma_R) = (M_R - i \Gamma_R / 2)^2\).

dispersionrelations.dynamics.vertex_VPP__2(s, mP, mP_2=None)[source]#

A vector \(\to\) pseudoscalar–pseudoscalar vertex squared.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mP (float) – Mass of the pseudoscalar with momentum \(p_1\).
mP_2 (float) – Mass of the pseudoscalar with momentum \(p_2\) (if not passed, a case with equal masses will be returned).

Returns:

b – The same shape as input s.

Return type:

array_like

Notes

The vertex \(V(q)\to P(p_1)P(p_2)\) is given by

\[\hat{\beta}_{VPP}^{\mu}(q,p_1,p_2) \propto (p_1 - p_2)^{\mu}.\]

Spin-averaged vertex function

\[\beta_{VPP}^2(q^2, p_1^2, p_2^2) = \frac{\lambda(q^2, p_1^2, p_2^2)}{q^2} .\]

The function returns \(\beta_{VPP}^2(s, m_{P1}^2, m_{P2}^2)/3\), where \(3=(2l+1)\) corresponds to the P-wave \((l=1)\).

dispersionrelations.dynamics.vertex_VPP(s, mP, mP_2=None)[source]#

A vector \(\to\) pseudoscalar–pseudoscalar vertex.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mP (float) – Mass of the pseudoscalar with momentum \(p_1\).
mP_2 (float) – Mass of the pseudoscalar with momentum \(p_2\) (if not passed, a case with equal masses will be returned).

Returns:

b – The same shape as input s.

Return type:

array_like

Notes

This returns the square root of vertex_VPP__2(), i.e. \(\frac{1}{\sqrt{3}}\beta_{VPP}(s, m_{P1}^2, m_{P2}^2)\). For most applications we need the squared version.

dispersionrelations.dynamics.vertex_VVP__2(s, mV, mP)[source]#

A vector \(\to\) vector–pseudoscalar vertex squared.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mV (float) – Mass of the vector with momentum \(k\).
mP (float) – Mass of the pseudoscalar with momentum \(p\).

Returns:

b – The same shape as input s.

Return type:

array_like

Notes

The vertex \(V(q)\to V(k)P(p)\) is given by

\[\hat{\beta}_{VVP}^{(\lambda)\mu}(q, k, p) = \epsilon^{\mu\nu\alpha\beta} n^{(\lambda)}_\nu p_\alpha q_\beta .\]

Spin-averaged vertex function

\[\beta_{VVP}^2(q^2, k^2, p^2) = \frac{\lambda(q^2, k^2, p^2)}{2} .\]

The function returns \(\beta_{VVP}^2(s, m_V^2, m_P^2)/3\), where \(3=(2l+1)\) corresponds to the P-wave \((l=1)\).

dispersionrelations.dynamics.vertex_VVP(s, mV, mP)[source]#

A vector \(\to\) vector–pseudoscalar vertex.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mV (float) – Mass of the vector with momentum \(k\).
mP (float) – Mass of the pseudoscalar with momentum \(p\).

Returns:

b – The same shape as input s.

Return type:

array_like

Notes

This returns the square root of vertex_VVP__2(), i.e. \(\frac{1}{\sqrt{3}}\beta_{VVP}(s, m_V^2, m_P^2)\). For most applications we need the squared version.

dispersionrelations.dynamics.vertex_AVP__2(s, mV, mP)[source]#

An axial vector \(\to\) vector–pseudoscalar vertex squared.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mV (float) – Mass of the vector with momentum \(k\).
mP (float) – Mass of the pseudoscalar with momentum \(p\).

Returns:

b – The same shape as input s.

Return type:

array_like

Notes

The vertex \(A(q)\to V(k)P(p)\) is given by

\[\hat{\beta}_{AVP}^{(\lambda)\mu}(q, k, p) = (q \cdot k) \, n^{(\lambda)\mu} - (n^{(\lambda)} \cdot q) \, k^\mu .\]

Spin-averaged vertex function

\[\beta_{AVP}^2(q^2, k^2, p^2) = 3q^2k^2 + \frac{\lambda(q^2, k^2, p^2)}{2} .\]

The function returns \(\beta_{AVP}^2(s, m_V^2, m_P^2)/3\).

dispersionrelations.dynamics.vertex_AVP(s, mV, mP)[source]#

An axial vector \(\to\) vector–pseudoscalar vertex.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mV (float) – Mass of the vector with momentum \(k\).
mP (float) – Mass of the pseudoscalar with momentum \(p\).

Returns:

b – The same shape as input s.

Return type:

array_like

Notes

This returns the square root of vertex_AVP__2(), i.e. \(\frac{1}{\sqrt{3}}\beta_{AVP}(s, m_V^2, m_P^2)\). For most applications we need the squared version.

dispersionrelations.dynamics.vertex_VAP__2(s, mA, mP)[source]#

A vector \(\to\) axial vector–pseudoscalar vertex squared.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mV (float) – Mass of the axial vector with momentum \(k\).
mP (float) – Mass of the pseudoscalar with momentum \(p\).

Returns:

b – The same shape as input s.

Return type:

array_like

Notes

The vertex \(V(q)\to A(k)P(p)\) is given by

\[\hat{\beta}_{VAP}^{(\lambda)\mu}(q, k, p) = (q \cdot k) \, n^{(\lambda)\mu} - (n^{(\lambda)} \cdot q) \, k^\mu .\]

Spin-averaged vertex function

\[\beta_{VAP}^2(q^2, k^2, p^2) = 3q^2k^2 + \frac{\lambda(q^2, k^2, p^2)}{2} .\]

The function returns \(\beta_{VAP}^2(s, m_A^2, m_P^2)/3\).

dispersionrelations.dynamics.vertex_VAP(s, mA, mP)[source]#

A vector \(\to\) axial vector–pseudoscalar vertex.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mV (float) – Mass of the axial vector with momentum \(k\).
mP (float) – Mass of the pseudoscalar with momentum \(p\).

Returns:

b – The same shape as input s.

Return type:

array_like

Notes

This returns the square root of vertex_VAP__2(), i.e. \(\frac{1}{\sqrt{3}}\beta_{VAP}(s, m_A^2, m_P^2)\). For most applications we need the squared version.

dispersionrelations.dynamics.vertex_VAP_T1__2(s, mA, mP)[source]#

A vector \(\to\) axial vector–pseudoscalar vertex squared.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mV (float) – Mass of the axial vector with momentum \(k\).
mP (float) – Mass of the pseudoscalar with momentum \(p\).

Returns:

b – The same shape as input s.

Return type:

array_like

dispersionrelations.dynamics.vertex_VAP_T2__2(s, mA, mP)[source]#

A vector \(\to\) axial vector–pseudoscalar vertex squared.

Parameters:

s (array_like) – Kinematic variable (can be complex).
mV (float) – Mass of the axial vector with momentum \(k\).
mP (float) – Mass of the pseudoscalar with momentum \(p\).

Returns:

b – The same shape as input s.

Return type:

array_like

dispersionrelations.dynamics.taming_BlattWeisskopf(s, sthr: float, sB: float, l: int = 1, normalize_at_sB: bool = False)[source]#

Blatt–Weisskopf taming factors.

Parameters:

s (array_like) – Kinematic variable (can be complex).
sthr (float) – Threshold of the relevant channel.
sB (float) – Range parameter.
l (int) – Partial wave.
normalize_at_sB (boolean) – If set to True, \(B(s_B) = 1\).

Returns:

B – The same shape as input s.

Return type:

array_like

Raises:

NotImplementedError – The function is only implemented for the partial waves \(l\in\{0,1,2,3,4\}\). Any other input triggers an error.

Notes

The first few Blatt–Weisskopf taming factors are given by [4]

\[\begin{split}\begin{align} B_0(s) &= 1, \\ B_1(s) &= 1 / (x + 1), \\ B_2(s) &= 1 / ((x-3)^2 + 9x), \\ \end{align}\end{split}\]

where \(x=(s-s_{thr}) / (s_B - s_{thr})\).

dispersionrelations.dynamics.taming_spacelike_pole(s, sB: float = 4.0, n: int = 1)[source]#

A simple decaying function, used as a taming factor.

Parameters:

s (array_like) – Kinematic variable (can be complex).
sB (float) – Range parameter.
n (int) – Degree of decay.

Returns:

B – The same shape as input s.

Return type:

array_like

Notes

The function is defined as

\[B_n(s) = \left( \frac{s_B}{s_B + s} \right)^n .\]

This creates a space-like pole (of degree n) at \(s = -s_B\).

dispersionrelations.dynamics.BreitWigner(s, mass: float, width: float)[source]#

Breit–Wigner distribution.

Parameters:

s (array_like) – Four-momentum squared of the propagating particle.
mass (float) – Mass of the propagating particle.
width (float) – Width of the propagating particle.

Returns:

G – The same shape as input s.

Return type:

array_like

Notes

The distribution is defined as [2]

\[G(s, M, \Gamma) = \frac{1}{s - M^2 + i M \Gamma},\]

where \(M\) and \(\Gamma\) are the mass and the width of the propagating particle, correspondingly.

dispersionrelations.dynamics.BreitWignerED(s, mass: float, width_s: callable, width_0: float)[source]#

Breit–Wigner distribution.

Parameters:

s (array_like) – Four-momentum squared of the propagating particle.
mass (float) – Mass of the propagating particle.
width_s (callable) – Energy-dependent width of the propagating particle, must be a function of s, mass, and width_0.
width_0 (float) – A parameter that enters the definition of the energy-dependent width.

Returns:

G – The same shape as input s.

Return type:

array_like

Notes

The distribution is defined as

\[G(s, M, \Gamma_s, \Gamma_0) = \frac{1}{s - M^2 + i M \Gamma_s(s, M, \Gamma_0)},\]

where \(M\) and \(\Gamma_s\) are the mass and the width of the propagating particle, correspondingly. The index \(s\) indicates that the width need not be constant and can depend on energy.

loop_discontinuity(s)[source]#

Discontinuity of the two-body channel self-energy.

Parameters:: s (array_like) – Four-momentum squared of the two-body state.
Returns:: DiscΠ – The same shape as input s.
Return type:: array_like

Notes

We assume the Schwarz reflection principle and therefore,

\[\mathrm{Disc}(\Pi(s)) = 2i \, \mathrm{Im}(\Pi(s)) \, .\]

loop(s, sheet=1)[source]#

Invokes the __call__ method of the parent class, with an added functionality of switching to the second sheet. Computed the self-energy function of the two-body channel.

Parameters:

s (array_like) – Four-momentum squared of the two-body state.
sheet (int, optional) – Riemann sheet number (can only be 1 or 2, other inputs return the first sheet).

Returns:

Π – The same shape as input s.

Return type:

array_like

abstractmethod phase_space_function(s)[source]#

abstractmethod vertex_function_squared(s)[source]#

abstractmethod taming_factor_squared(s)[source]#

vertex_function(s)[source]#

taming_factor(s)[source]#

class dispersionrelations.dynamics.PrecomputedChannel(s_values, integrand_values, threshold, **kwargs)[source]#

Bases: Channel

extrapolated_integrand(s)[source]#

phase_space_function(s)[source]#

vertex_function_squared(s)[source]#

taming_factor_squared(s)[source]#

class dispersionrelations.dynamics.StableTwoBodyChannel(m1, m2, vertex_function_squared=<function vertex_VPP__2>, taming_factor_squared=<function StableTwoBodyChannel.<lambda>>, **kwargs)[source]#

Bases: Channel

Constructs a two-body channel with stable particles with masses m1 and m2.

Parameters:

m1 (float) – Mass of the first particle.
m2 (float) – Mass of the second particle.
vertex_function_squared (callable) – Vertex function squared. Depends on the interaction of the particles.
taming_factor (callable) – Taming factor, to make sure that the integrand does not grow indefinitely.
**kwargs – Other keyword arguments, to be passed to the constructor of the parent class.

Notes

The integrand of the loop is constructed via

\[\mathrm{Disc}(\Pi(s)) = 2i \, \rho(s, m_1^2, m_2^2) \beta^2(s, m_1^2, m_2^2) B^2(s) \, ,\]

where \(\rho\) is the phase space, \(\beta\) is the vertex function, and \(B\) is the taming factor.

phase_space_function(s)[source]#

vertex_function_squared(s)[source]#

taming_factor_squared(s)[source]#

class dispersionrelations.dynamics.UnstableParticle(decay_channel: Channel, pole_location: complex, pole_sheet: int = 2, mass_and_coupling: tuple | None = None, interpolation_points=[1, 2, 5, 10.0, 50.0, 100.0, 1000.0, 100000.0, 100000000.0], interpolation_density=1000)[source]#

Bases: object

Unstable particle.

Parameters:

decay_channel (TwoBodyChannel) – A channel that the particle decays into. The channel does not need to be two-body, as long as it has a threshold and functions integrand and loop.
pole_location (complex) – Location of the resonance pole (see sR()).
pole_sheet (int) – Riemann sheet of the decay channel, on which the resonance lives. For above-threshold resonances, the typical sheet is 2.
mass_and_coupling ((float, float)) – Bare mass and the coupling constant, parameters of the propagator. If passed, pole_location is ignored.
interpolation_points (list) – Intervals to use for interpolating the spectral function.
interpolation_density (int) – Number of points per interpolation interval.

propagator(s, sheet=1)[source]#

Propagator of the unstable particle.

Parameters:

s (array_like) – Four-momentum squared of the propagating particle.
sheet (int, optional) – Riemann sheet number of the decay channel self-energy (can only be 1 or 2, other inputs return the first sheet).

Returns:

G – The same shape as input s.

Return type:

array_like

Notes

The propagator is defined as

\[G(s) = \frac{1}{s - m^2 + g^2 \Pi(s)} \, ,\]

where \(\Pi(s)\) is the self-energy of the decay channel.

spectral_function_CP(s)[source]#

Spectral function of the unstable particle for \(s\in\mathbb{C}\).

Parameters:: s (array_like) – Four-momentum squared of the propagating particle.
Returns:: σ – The same shape as input s.
Return type:: array_like

Notes

The spectral function is defined as

\[\sigma(s) = \frac{1}{\pi} G^{I}(s) G^{II}(s) \, g^2 \mathrm{Im}(\Pi(s)) \, ,\]

which, for real \(s\) reduces to

\[\sigma(s\in\mathbb{R}) = -\frac{1}{\pi} \mathrm{Im}(G(s)) \, .\]

spectral_function_RE(s)[source]#

Spectral function of the unstable particle for \(s\in\mathbb{R}\).

Parameters:: s (array_like) – Four-momentum squared of the propagating particle.
Returns:: σ – The same shape as input s.
Return type:: array_like

Notes

The spectral function is defined as

\[\sigma(s) = -\frac{1}{\pi} \mathrm{Im}(G(s)) \, .\]

An interpolation function is used when possible.

class dispersionrelations.dynamics.SemiStableTwoBodyCut(unstable_particle: UnstableParticle, spectator_mass: float, vertex_function_squared: callable, gl_order: int = 100, split_n: int = 3, integration_split_points: list[float] = [2, 5, 10, 50, 100], interpolation_points: list = [1, 2, 3, 4, 5, 10.0, 30.0, 50.0, 100.0, 1000.0, 10000.0, 100000.0, 1000000.0, 10000000.0, 100000000.0, 1000000000.0], interpolation_density: int = 1000)[source]#

Bases: object

Two-body channel with one unstable particle and one spectator.

Parameters:

unstable_particle (UnstableParticle) – Unstable particle.
spectator_mass (float) – Mass of the spectator particle.
vertex_function (callable) – Vertex function. Depends on the interaction of the particles.
phase_space (callable) – Phase space function.
taming_factor (callable) – Taming factor, to make sure that the integrand does not grow indefinitely.
gl_order (int) – Gauss–Legendre quadrature order.
split_n (int) – Number of intervals per numerical integration.
interpolation_points (list) – Intervals to use for interpolating the spectral function.
interpolation_density (int) – Number of points per interpolation interval.

ImPI_integrand_RE(s, x)[source]#

Integrand for the \(\mathrm{Im}(\Pi(s))\) spectral integral for \(x\in\mathbb{R}\).

Parameters:

s (complex) – Four-momentum squared of the two-body system.
x (array_like) – Four-momentum squared of the unstable particle.

Returns:

f – The same shape as input x.

Return type:

array_like

Notes

The integrand is defined via

\[\mathrm{Im}(\Pi(s)) = \int_{s_\text{thr}}^{(\sqrt{s}-m)^2} \sigma(x) \rho(s, x, m^2) \beta^2(s, x, m^2) B^2(s) \, ,\]

where \(\sigma\) is the spectral function of the unstable particle and \(s_\text{thr}\) is the threshold of the corresponding decay channel.

ImPI_integrand_CP(s, x)[source]#

Integrand for the \(\mathrm{Im}(\Pi(s))\) spectral integral for \(x\in\mathbb{C}\).

Parameters:

s (complex) – Four-momentum squared of the two-body system.
x (array_like) – Four-momentum squared of the unstable particle.

Returns:

f – The same shape as input x.

Return type:

array_like

Notes

The integrand is defined via

\[\mathrm{Im}(\Pi(s)) = \int_{s_\text{thr}}^{(\sqrt{s}-m)^2} \sigma(x) \rho(s, x, m^2) \beta^2(s, x, m^2) B^2(s) \, ,\]

where \(\sigma\) is the spectral function of the unstable particle and \(s_\text{thr}\) is the threshold of the corresponding decay channel.

ImPI_integral(s)[source]#

The \(\mathrm{Im}(\Pi(s))\) spectral integral.

Parameters:: s (complex) – Four-momentum squared of the two-body system.
Returns:: ImΠ – A single complex number.
Return type:: complex

Notes

The integral is defined via

\[\mathrm{Im}(\Pi(s)) = \int_{s_\text{thr}}^{(\sqrt{s}-m)^2} \sigma(x) \rho(s, x, m^2) \beta^2(s, x, m^2) B^2(s) \, ,\]

where \(\sigma\) is the spectral function of the unstable particle and \(s_\text{thr}\) is the threshold of the corresponding decay channel.

For complex values of \(s\), the integral contour is taken to be rectangular (see e.g. [11] for more details).

property ImPI_integral_vectorized#: Vectorized version of dispersionrelations.dynamics.SemiStableTwoBodyCut.ImPI_integral()

ImPI_integral_RE(s)[source]#

The \(\mathrm{Im}(\Pi(s))\) spectral integral for \(s\in\mathbb{R}\).

Parameters:: s (array_like) – Four-momentum squared of the two-body system.
Returns:: ImΠ – The same shape as input s.
Return type:: array_like

Notes

An interpolation function is used when possible.

ImPI_integral_CP(s)[source]#

The \(\mathrm{Im}(\Pi(s))\) spectral integral for \(s\in\mathbb{C}\).

Parameters:: s (array_like) – Four-momentum squared of the two-body system.
Returns:: ImΠ – The same shape as input s.
Return type:: array_like

__call__(s)[source]#

The \(\mathrm{Im}(\Pi(s))\) spectral integral for a generic \(s\).

Parameters:: s (array_like) – Four-momentum squared of the two-body system.
Returns:: ImΠ – The same shape as input s.
Return type:: array_like

Notes

An interpolation function is used when possible for real values of \(s\).

class dispersionrelations.dynamics.SemiStableTwoBodyChannel(twobodycut: SemiStableTwoBodyCut, taming_factor_squared=<function SemiStableTwoBodyChannel.<lambda>>)[source]#

Bases: Channel

phase_space_function(s)[source]#

vertex_function_squared(s)[source]#

taming_factor_squared(s)[source]#

class dispersionrelations.dynamics.TwoPotentialModel(channels: dict[str, Channel], bg_par: dict, res_par: dict, channel_sheets: dict = {}, s_array: ndarray | list = array([1.00000000e-10, 2.27567080e-04, 9.09665005e-04, 2.04629388e-03, 3.63745370e-03, 5.68314446e-03, 8.18336617e-03, 1.11381188e-02, 1.45474024e-02, 1.84112170e-02, 2.27295625e-02, 2.75024389e-02, 3.27298463e-02, 3.84117846e-02, 4.45482539e-02, 5.11392541e-02, 5.81847853e-02, 6.56848474e-02, 7.36394405e-02, 8.20485645e-02, 9.09122195e-02, 1.00230405e-01, 1.10003122e-01, 1.20230370e-01, 1.30912149e-01, 1.42048458e-01, 1.53639299e-01, 1.65684671e-01, 1.78184573e-01, 1.91139007e-01, 2.04547971e-01, 2.18411466e-01, 2.32729493e-01, 2.47502050e-01, 2.62729138e-01, 2.78410757e-01, 2.94546907e-01, 3.11137589e-01, 3.28182800e-01, 3.45682543e-01, 3.63636817e-01, 3.82045622e-01, 4.00908958e-01, 4.20226825e-01, 4.39999222e-01, 4.60226151e-01, 4.80907610e-01, 5.02043601e-01, 5.23634122e-01, 5.45679175e-01, 5.68178758e-01, 5.91132872e-01, 6.14541518e-01, 6.38404694e-01, 6.62722401e-01, 6.87494639e-01, 7.12721408e-01, 7.38402708e-01, 7.64538539e-01, 7.91128901e-01, 8.18173794e-01, 8.45673217e-01, 8.73627172e-01, 9.02035658e-01, 9.30898674e-01, 9.60216222e-01, 9.89988300e-01, 1.02021491e+00, 1.05089605e+00, 1.08203172e+00, 1.11362192e+00, 1.14566666e+00, 1.17816592e+00, 1.21111972e+00, 1.24452804e+00, 1.27839090e+00, 1.31270829e+00, 1.34748021e+00, 1.38270666e+00, 1.41838764e+00, 1.45452315e+00, 1.49111319e+00, 1.52815776e+00, 1.56565687e+00, 1.60361050e+00, 1.64201867e+00, 1.68088137e+00, 1.72019860e+00, 1.75997036e+00, 1.80019665e+00, 1.84087747e+00, 1.88201282e+00, 1.92360270e+00, 1.96564712e+00, 2.00814606e+00, 2.05109954e+00, 2.09450754e+00, 2.13837008e+00, 2.18268715e+00, 2.22745875e+00, 2.27268488e+00, 2.31836554e+00, 2.36450074e+00, 2.41109046e+00, 2.45813471e+00, 2.50563350e+00, 2.55358682e+00, 2.60199466e+00, 2.65085704e+00, 2.70017395e+00, 2.74994539e+00, 2.80017136e+00, 2.85085186e+00, 2.90198690e+00, 2.95357646e+00, 3.00562056e+00, 3.05811918e+00, 3.11107234e+00, 3.16448003e+00, 3.21834224e+00, 3.27265899e+00, 3.32743027e+00, 3.38265609e+00, 3.43833643e+00, 3.49447130e+00, 3.55106071e+00, 3.60810464e+00, 3.66560311e+00, 3.72355610e+00, 3.78196363e+00, 3.84082569e+00, 3.90014228e+00, 3.95991340e+00, 4.02013905e+00, 4.08081924e+00, 4.14195395e+00, 4.20354320e+00, 4.26558697e+00, 4.32808528e+00, 4.39103812e+00, 4.45444548e+00, 4.51830738e+00, 4.58262381e+00, 4.64739477e+00, 4.71262027e+00, 4.77830029e+00, 4.84443484e+00, 4.91102393e+00, 4.97806755e+00, 5.04556569e+00, 5.11351837e+00, 5.18192558e+00, 5.25078732e+00, 5.32010359e+00, 5.38987439e+00, 5.46009972e+00, 5.53077959e+00, 5.60191398e+00, 5.67350291e+00, 5.74554636e+00, 5.81804435e+00, 5.89099687e+00, 5.96440392e+00, 6.03826550e+00, 6.11258161e+00, 6.18735225e+00, 6.26257743e+00, 6.33825713e+00, 6.41439137e+00, 6.49098013e+00, 6.56802343e+00, 6.64552126e+00, 6.72347362e+00, 6.80188051e+00, 6.88074193e+00, 6.96005788e+00, 7.03982836e+00, 7.12005337e+00, 7.20073292e+00, 7.28186699e+00, 7.36345560e+00, 7.44549874e+00, 7.52799641e+00, 7.61094860e+00, 7.69435533e+00, 7.77821660e+00, 7.86253239e+00, 7.94730271e+00, 8.03252756e+00, 8.11820695e+00, 8.20434087e+00, 8.29092931e+00, 8.37797229e+00, 8.46546980e+00, 8.55342184e+00, 8.64182841e+00, 8.73068951e+00, 8.82000514e+00, 8.90977531e+00, 9.00000000e+00]))[source]#

Bases: object

store_parameters(new_bg_par=None, new_res_par=None)[source]#

precompute()[source]#

compute_bg(new_bg_par=None)[source]#

compute_res(new_res_par=None)[source]#

compute_everything(bg_par=None, res_par=None)[source]#

new_s_array(s_array)[source]#

T_matrix_bg()[source]#

T_matrix_res()[source]#

T_matrix()[source]#

S_matrix()[source]#

form_factor()[source]#