Optical potentials

This page collects the built-in optical-potential interfaces, parameterizations, and helper utilities.

Optical-potential models and helper potential forms.

class jitr.optical_potentials.LocalOpticalPotential(scale_radii_by_At_and_Ap=False)

Bases: SingleChannelOpticalModel

Simple local optical potential with optional nucleus-nucleus radius scaling.

Parameters:

scale_radii_by_At_and_Ap (bool)

radius_factor(reaction_model)

Return the radius scaling factor for the current reaction.

Return type:

float

Parameters:

reaction_model (Reaction)

evaluate(rgrid, reaction_model, kinematics_model, Vv, rv, av, Wv, rw, aw, Wd, Vd, rd, ad, Vso, Wso, rso, aso, rC)

Evaluate the local optical-potential terms on rgrid.

Return type:

tuple[complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]] | float | ndarray[tuple[Any, ...], dtype[double]]]

Parameters:

• rgrid (float | ndarray[tuple[Any, ...], dtype[float64]])

• reaction_model (Reaction)

• kinematics_model (ChannelKinematics)

• Vv (float)

• rv (float)

• av (float)

• Wv (float)

• rw (float)

• aw (float)

• Wd (float)

• Vd (float)

• rd (float)

• ad (float)

• Vso (float)

• Wso (float)

• rso (float)

• aso (float)

• rC (float)

class jitr.optical_potentials.SingleChannelOpticalModel(params)

Bases: object

Base class for local single-channel optical potentials.

Parameters:

params (list[str])

evaluate(rgrid, reaction, kinematics, *params)

Evaluate central, spin-orbit, and Coulomb terms on rgrid.

Return type:

tuple[complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]] | float | ndarray[tuple[Any, ...], dtype[double]]]

Parameters:

• rgrid (float | ndarray[tuple[Any, ...], dtype[float64]])

• reaction (Reaction)

• kinematics (ChannelKinematics)

• params (float)

jitr.optical_potentials.coulomb_charged_sphere(r, zz, r_c)

Return the Coulomb potential of a uniformly charged sphere.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• zz (float)

• r_c (float)

jitr.optical_potentials.perey_buck_nonlocal(r, rp, *params)

Return the Perey-Buck nonlocal kernel factor.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float)

• rp (float)

• params (float)

jitr.optical_potentials.regular_inverse_r(r, r_c)

Return 1/r regularized inside a sphere of radius r_c.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• r_c (float)

jitr.optical_potentials.surface_peaked_gaussian_potential(r, *params)

Return a simple surface-peaked Gaussian potential.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• params (float)

jitr.optical_potentials.thomas_mean_square_radius(R, a)

Return the mean-square radius for the Thomas spin-orbit shape.

Return type:

float

Parameters:

• R (float)

• a (float)

jitr.optical_potentials.thomas_safe(r, R, a)

Evaluate the Thomas spin-orbit shape without overflow issues.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• R (float)

• a (float)

jitr.optical_potentials.thomas_volume_integral(V, R, a)

Return the volume integral for the Thomas spin-orbit shape.

Return type:

float

Parameters:

• V (float)

• R (float)

• a (float)

jitr.optical_potentials.woods_saxon_mean_square_radius(R, a)

Return the mean-square radius for a Woods-Saxon term.

Return type:

float

Parameters:

• R (float)

• a (float)

jitr.optical_potentials.woods_saxon_potential(r, *params)

Return a Woods-Saxon potential with complex depth V + iW.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• params (float)

jitr.optical_potentials.woods_saxon_prime(r, *params)

Return the radial derivative of a Woods-Saxon potential.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• params (float)

jitr.optical_potentials.woods_saxon_prime_mean_square_radius(R, a)

Return the mean-square radius for a derivative Woods-Saxon term.

Return type:

float

Parameters:

• R (float)

• a (float)

jitr.optical_potentials.woods_saxon_prime_safe(r, R, a)

Evaluate the radial derivative of the Woods-Saxon shape safely.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• R (float)

• a (float)

jitr.optical_potentials.woods_saxon_prime_volume_integral(V, R, a)

Return the volume integral for a derivative Woods-Saxon term.

Return type:

float

Parameters:

• V (float)

• R (float)

• a (float)

jitr.optical_potentials.woods_saxon_safe(r, R, a)

Evaluate a Woods-Saxon shape while avoiding overflow in exp.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• R (float)

• a (float)

jitr.optical_potentials.woods_saxon_volume_integral(V, R, a)

Return the volume integral for a Woods-Saxon term.

Return type:

float

Parameters:

• V (float)

• R (float)

• a (float)

jitr.optical_potentials.yamaguchi_potential(r, rp, *params)

Return the Yamaguchi separable nonlocal potential.

Return type:

float

Parameters:

• r (float)

• rp (float)

• params (float)

jitr.optical_potentials.yamaguchi_swave_delta(k, *params)

Return the analytic s-wave phase shift for the Yamaguchi potential.

Return type:

double

Parameters:

• k (float)

• params (float)

Base classes and helpers for single-channel optical potentials.

class jitr.optical_potentials.omp.SingleChannelOpticalModel(params)

Bases: object

Base class for local single-channel optical potentials.

Parameters:

params (list[str])

evaluate(rgrid, reaction, kinematics, *params)

Evaluate central, spin-orbit, and Coulomb terms on rgrid.

Return type:

tuple[complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]] | float | ndarray[tuple[Any, ...], dtype[double]]]

Parameters:

• rgrid (float | ndarray[tuple[Any, ...], dtype[float64]])

• reaction (Reaction)

• kinematics (ChannelKinematics)

• params (float)

jitr.optical_potentials.omp.central(r, Vv, Rv, av, Wv, Rw, aw, Wd, Vd, Rd, ad)

Evaluate the default Woods-Saxon central potential.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• Vv (float)

• Rv (float)

• av (float)

• Wv (float)

• Rw (float)

• aw (float)

• Wd (float)

• Vd (float)

• Rd (float)

• ad (float)

jitr.optical_potentials.omp.spin_orbit(r, Vso, Wso, Rso, aso)

Evaluate the default Thomas-form spin-orbit potential.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• Vso (float)

• Wso (float)

• Rso (float)

• aso (float)

class jitr.optical_potentials.omp.LocalOpticalPotential(scale_radii_by_At_and_Ap=False)

Bases: SingleChannelOpticalModel

Simple local optical potential with optional nucleus-nucleus radius scaling.

Parameters:

scale_radii_by_At_and_Ap (bool)

radius_factor(reaction_model)

Return the radius scaling factor for the current reaction.

Return type:

float

Parameters:

reaction_model (Reaction)

evaluate(rgrid, reaction_model, kinematics_model, Vv, rv, av, Wv, rw, aw, Wd, Vd, rd, ad, Vso, Wso, rso, aso, rC)

Evaluate the local optical-potential terms on rgrid.

Return type:

tuple[complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]] | float | ndarray[tuple[Any, ...], dtype[double]]]

Parameters:

• rgrid (float | ndarray[tuple[Any, ...], dtype[float64]])

• reaction_model (Reaction)

• kinematics_model (ChannelKinematics)

• Vv (float)

• rv (float)

• av (float)

• Wv (float)

• rw (float)

• aw (float)

• Wd (float)

• Vd (float)

• rd (float)

• ad (float)

• Vso (float)

• Wso (float)

• rso (float)

• aso (float)

• rC (float)

The Koning-Delaroche potential is a common optical potential for nuclear scattering. It is provided here in simplified form specifically to address this need.

See the [Koning-Delaroche paper](https://www.sciencedirect.com/science/article/pii/S0375947402013210) for details. Equation references are with respect to (w.r.t.) this paper.

jitr.optical_potentials.kduq.get_param_names(projectile)

Get the names of the parameters for the given projectile, in the order they are returned by the get_samples function.

Return type:

list[str]

Parameters:

projectile (tuple[int, int])

jitr.optical_potentials.kduq.get_samples(projectile, posterior='federal')

Get the posterior samples for the given projectile (neutron or proton) from the KDUQ Federal or Democratic posteriors.

See [Pruitt, et al., 2023] (https://journals.aps.org/prc/pdf/10.1103/PhysRevC.107.014602) for details on the KDUQ posteriors.

Parameters:

• projectile (tuple[int, int]) – tuple (Ap, Zp) of the projectile. Must be (1, 0) for neutron or (1, 1) for proton.

• posterior (str) – Which KDUQ posterior to return samples from. Must be either "federal" or "democratic". Defaults to "federal".

Return type:

ndarray

Returns:

An array of shape (NUM_POSTERIOR_SAMPLES, num_params) containing the posterior samples for the given projectile.

jitr.optical_potentials.kduq.Vv(E, v1, v2, v3, v4, Ef)

energy-dependent, volume-central strength - real term, Eq. (7)

Return type:

float

Parameters:

• E (float)

• v1 (float)

• v2 (float)

• v3 (float)

• v4 (float)

• Ef (float)

jitr.optical_potentials.kduq.Wv(E, w1, w2, Ef)

energy-dependent, volume-central strength - imaginary term, Eq. (7)

Return type:

float

Parameters:

• E (float)

• w1 (float)

• w2 (float)

• Ef (float)

jitr.optical_potentials.kduq.Wd(E, d1, d2, d3, Ef)

energy-dependent, surface-central strength - imaginary term (no real term), Eq. (7)

Return type:

float

Parameters:

• E (float)

• d1 (float)

• d2 (float)

• d3 (float)

• Ef (float)

jitr.optical_potentials.kduq.Vso(E, vso1, vso2, Ef)

energy-dependent, spin-orbit strength — real term, Eq. (7)

Return type:

float

Parameters:

• E (float)

• vso1 (float)

• vso2 (float)

• Ef (float)

jitr.optical_potentials.kduq.Wso(E, wso1, wso2, Ef)

energy-dependent, spin-orbit strength — imaginary term, Eq. (7)

Return type:

float

Parameters:

• E (float)

• wso1 (float)

• wso2 (float)

• Ef (float)

jitr.optical_potentials.kduq.delta_VC(E, Vcbar, v1, v2, v3, v4, Ef)

energy dependent Coulomb correction term, Eq. 23

Return type:

float

Parameters:

• E (float)

• Vcbar (float)

• v1 (float)

• v2 (float)

• v3 (float)

• v4 (float)

• Ef (float)

jitr.optical_potentials.kduq.central(r, Vv, Rv, av, Wv, Rwv, awv, Wd, Rd, ad)

Koning-Delaroche central terms at a given energy.

This matches Eq. (7) in Koning and Delaroche (2003).

Parameters:

• r (float | ndarray) – The radius at which to evaluate the potential.

• Vv (float) – The real central depth.

• Rv (float) – The real central radius parameter.

• av (float) – The real central diffuseness parameter.

• Wv (float) – The imaginary volume depth.

• Rwv (float) – The imaginary volume radius parameter.

• awv (float) – The imaginary volume diffuseness parameter.

• Wd (float) – The imaginary surface depth.

• Rd (float) – The imaginary surface radius parameter.

• ad (float) – The imaginary surface diffuseness parameter.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

jitr.optical_potentials.kduq.spin_orbit(r, Vso, Rso, aso, Wso, Rwso, awso)

Koning-Delaroche spin-orbit terms at a given energy.

This matches Eq. (7) in Koning and Delaroche (2003).

Parameters:

• r (float | ndarray) – The radius at which to evaluate the potential.

• Vso (float) – The real spin-orbit depth.

• Rso (float) – The real spin-orbit radius parameter.

• aso (float) – The real spin-orbit diffuseness parameter.

• Wso (float) – The imaginary spin-orbit depth.

• Rwso (float) – The imaginary spin-orbit radius parameter.

• awso (float) – The imaginary spin-orbit diffuseness parameter.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

class jitr.optical_potentials.kduq.Global(projectile, param_fpath=None)

Bases: object

Global Koning-Delaroche parameters

Parameters:

• projectile (tuple)

• param_fpath (Path | None)

get_params(A, Z, Elab)

Return Koning-Delaroche central, spin-orbit, and Coulomb parameters.

Return type:

tuple[tuple[float, ...], tuple[float, ...], tuple[float, ...]]

Parameters:

• A (int)

• Z (int)

• Elab (float)

jitr.optical_potentials.kduq.calculate_params(projectile, target, Elab, Ef_0, Ef_A, v1_0, v1_asymm, v1_A, v2_0, v2_A, v3_0, v3_A, v4_0, rv_0, rv_A, av_0, av_A, w1_0, w1_A, w2_0, w2_A, d1_0, d1_asymm, d2_0, d2_A, d2_A2, d2_A3, d3_0, rd_0, rd_A, ad_0, ad_A, Vso1_0, Vso1_A, Vso2_0, Wso1_0, Wso2_0, rso_0, rso_A, aso_0, rc_0=0.0, rc_A=0.0, rc_A2=0.0)

Calculate the arguments for the central, spin_orbit, and coulomb_charged_sphere functions corresponding to the KDUQ potential for a given projectile, target, lab energy, and the KDUQ parameters.

Parameters:

• projectile (tuple) – tuple (Ap, Zp) of the projectile.

• target (tuple) – tuple (A, Z) of the target.

• Elab (float) – Laboratory energy of the projectile in MeV.

• Ef_0 (float) – Base Fermi energy.

• Ef_A (float) – Atomic mass number modifier for Fermi energy.

• v1_0 (float) – Parameters for the Koning-Delaroche potential. See Table V and the Appendix of Pruitt et al., 2023 for details.

• v1_asymm (float) –

  Parameters for the Koning-Delaroche potential. See Table V and the Appendix of Pruitt et al., 2023 for details.

• ... –

  Parameters for the Koning-Delaroche potential. See Table V and the Appendix of Pruitt et al., 2023 for details.

• rc_A2 (float) –

  Parameters for the Koning-Delaroche potential. See Table V and the Appendix of Pruitt et al., 2023 for details.

• v1_A (float)

• v2_0 (float)

• v2_A (float)

• v3_0 (float)

• v3_A (float)

• v4_0 (float)

• rv_0 (float)

• rv_A (float)

• av_0 (float)

• av_A (float)

• w1_0 (float)

• w1_A (float)

• w2_0 (float)

• w2_A (float)

• d1_0 (float)

• d1_asymm (float)

• d2_0 (float)

• d2_A (float)

• d2_A2 (float)

• d2_A3 (float)

• d3_0 (float)

• rd_0 (float)

• rd_A (float)

• ad_0 (float)

• ad_A (float)

• Vso1_0 (float)

• Vso1_A (float)

• Vso2_0 (float)

• Wso1_0 (float)

• Wso2_0 (float)

• rso_0 (float)

• rso_A (float)

• aso_0 (float)

• rc_0 (float)

• rc_A (float)

Return type:

tuple[tuple[float, ...], tuple[float, ...], tuple[float, ...]]

Returns:

(central_params, spin_orbit_params, coulomb_params) where central_params is (vv, Rv, av, wv, Rwv, awv, wd, Rd, ad), spin_orbit_params is (vso, Rso, aso, wso, Rwso, awso), and coulomb_params is (Z*Zp, RC).

class jitr.optical_potentials.kduq.KDUQ(projectile)

Bases: SingleChannelOpticalModel

Koning-Delaroche Uncertainty Quantification (KDUQ) optical potential model.

Parameters:

projectile (tuple)

evaluate(rgrid, reaction, kinematics, *params)

Evaluate the KDUQ central, spin-orbit, and Coulomb terms.

Return type:

tuple[complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]], float | ndarray[tuple[Any, ...], dtype[double]]]

Parameters:

• rgrid (float | ndarray)

• reaction (Reaction)

• kinematics (ChannelKinematics)

• params (float)

The CHUQ potential is a global phenomenological nucleon-nucleus optical potential

See [Pruitt, et al., 2023] (https://journals.aps.org/prc/pdf/10.1103/PhysRevC.107.014602), or the original CH89 paper [Varner, et al., 1991] (https://www.sciencedirect.com/science/article/pii/037015739190039O?via%3Dihub) for details. Equation references are with respect to the former paper.

jitr.optical_potentials.chuq.get_param_names()

Get the names of the parameters for the given projectile, in the order they are returned by the get_samples function.

Return type:

list[str]

jitr.optical_potentials.chuq.get_samples(posterior='federal')

Get the posterior samples for the given projectile (neutron or proton) from the CHUQ Federal or Democratic posteriors.

See [Pruitt, et al., 2023] (https://journals.aps.org/prc/pdf/10.1103/PhysRevC.107.014602) for details on the CHUQ posteriors.

Parameters:

posterior (str) – Which CHUQ posterior to return samples from. Must be either "federal" or "democratic". Defaults to "federal".

Return type:

ndarray

Returns:

An array of shape (NUM_POSTERIOR_SAMPLES, num_params) containing the posterior samples, ordered according to get_param_names().

jitr.optical_potentials.chuq.central(r, V, W, Wd, Rv, av, Rd, ad)

Form of the central term of the CHUQ potential, given by Eqs. A7-8 of [Pruitt, et al., 2023]

Parameters:

• r (float | ndarray) – The radius at which to evaluate the potential.

• V (float) – The depth of the real central potential.

• W (float) – The depth of the imaginary volume potential.

• Wd (float) – The depth of the imaginary surface potential.

• Rv (float) – The radius of the real central potential.

• av (float) – The diffuseness of the real central potential.

• Rd (float) – The radius of the imaginary potential.

• ad (float) – The diffuseness of the imaginary potential.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

jitr.optical_potentials.chuq.spin_orbit(r, Vso, Rso, aso)

Form of the spin-orbit term of the CHUQ potential, given by Eqs. A7-8 of [Pruitt, et al., 2023]

Parameters:

• r (float | ndarray) – The radius at which to evaluate the potential.

• Vso (float) – The depth of the spin-orbit potential.

• Rso (float) – The radius of the spin-orbit potential.

• aso (float) – The diffuseness of the spin-orbit potential.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

jitr.optical_potentials.chuq.calculate_params(projectile, target, Elab, V0=52.9, Ve=-0.299, Vt=13.1, r0=1.25, r0_0=-0.225, a0=0.69, Wv0=7.8, Wve0=35.0, Wvew=16.0, rw=1.33, rw_0=-0.42, aw=0.69, Ws0=10.0, Wst=18.0, Wse0=36.0, Wsew=37, Vso=5.9, rso=1.34, rso_0=-1.2, aso=0.63, rc=1.24, rc_0=0.12)

Calculate the arguments for the central, spin_orbit, and coulomb_charged_sphere functions corresponding to the CHUQ potential for a given projectile, target, lab energy, and the CHUQ parameters.

Parameters:

• projectile (tuple) – tuple (Ap, Zp) of the projectile.

• target (tuple) – tuple (A, Z) of the target.

• Elab (float) – Laboratory energy of the projectile in MeV.

• V0 (float) – Parameters for the Chapel-Hill optical model potential. See Table V and the Appendix of Pruitt et al., 2023 and Table 3 of Varner et al., 1991 for details.

• Ve (float) –

  Parameters for the Chapel-Hill optical model potential. See Table V and the Appendix of Pruitt et al., 2023 and Table 3 of Varner et al., 1991 for details.

• ... –

  Parameters for the Chapel-Hill optical model potential. See Table V and the Appendix of Pruitt et al., 2023 and Table 3 of Varner et al., 1991 for details.

• rc_0 (float) –

  Parameters for the Chapel-Hill optical model potential. See Table V and the Appendix of Pruitt et al., 2023 and Table 3 of Varner et al., 1991 for details.

• Vt (float)

• r0 (float)

• r0_0 (float)

• a0 (float)

• Wv0 (float)

• Wve0 (float)

• Wvew (float)

• rw (float)

• rw_0 (float)

• aw (float)

• Ws0 (float)

• Wst (float)

• Wse0 (float)

• Wsew (float)

• Vso (float)

• rso (float)

• rso_0 (float)

• aso (float)

• rc (float)

Return type:

tuple[tuple[float, ...], tuple[float, ...], tuple[float, ...]]

Returns:

(central_params, spin_orbit_params, coulomb_params) where central_params is (V0, Wv, Ws, R0, a0, Rw, aw), spin_orbit_params is (Vso, Rso, aso), and coulomb_params is (Z*Zp, RC).

jitr.optical_potentials.chuq.coulomb_correction(A, Z, RC)

Coulomb correction for proton energy

Return type:

float

Parameters:

• A (int)

• Z (int)

• RC (float)

class jitr.optical_potentials.chuq.Global(param_fpath=None)

Bases: object

Global optical potential in CHUQ form.

Parameters:

param_fpath (Path | None)

get_params(projectile, target, Elab)

Return CHUQ central, spin-orbit, and Coulomb parameters.

Return type:

tuple[tuple[float, ...], tuple[float, ...], tuple[float, ...]]

Parameters:

• projectile (tuple[int, int])

• target (tuple[int, int])

• Elab (float)

class jitr.optical_potentials.chuq.CHUQ

Bases: SingleChannelOpticalModel

Chapel-Hill Uncertainty Quantification (CHUQ) optical potential model.

Note that CH89 is Lane consistent, so the same parameters can be used for both neutron and proton projectiles.

evaluate(rgrid, reaction, kinematics, *params)

Evaluate the CHUQ central, spin-orbit, and Coulomb terms.

Return type:

tuple[complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]], float | ndarray[tuple[Any, ...], dtype[double]]]

Parameters:

• rgrid (float | ndarray)

• reaction (Reaction)

• kinematics (ChannelKinematics)

• params (float)

The Whitehead-Lim-Holt potential is a global mcroscopic nucleon-nucleus optical potential

See the [Whitehead et al., 2021] (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.182502) for details. Equation references are with respect to (w.r.t.) this paper.

jitr.optical_potentials.wlh.get_param_names(projectile)

Get the names of the parameters for the given projectile, in the order they are returned by the get_samples function.

Return type:

list[str]

Parameters:

projectile (tuple[int, int])

jitr.optical_potentials.wlh.get_samples(projectile)

Get the parameter samples for the WLH potential for the given projectile.

Parameters:

projectile (tuple[int, int]) – tuple (A, Z) of the projectile. Should be (1, 0) for neutron and (1, 1) for proton.

Return type:

ndarray

jitr.optical_potentials.wlh.spin_orbit(r, Uso, Rso, aso)

Form of the spin-orbit term in the WLH potential. See Eq. (2) of Whitehead et al., 2021.

Parameters:

• r (float | ndarray) – Radial coordinate(s) at which to evaluate the potential.

• Uso (float) – Spin-orbit strength parameter.

• Rso (float) – Spin-orbit radius parameter.

• aso (float) – Spin-orbit diffuseness parameter.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

jitr.optical_potentials.wlh.central(r, Uv, Rv, av, Uw, Rw, aw, Ud, Rd, ad)

Form of the central term in the WLH potential. See Eq. (2) of Whitehead et al., 2021.

Parameters:

• r (float | ndarray) – Radial coordinate(s) at which to evaluate the potential.

• Uv (float) – Real volume potential strength parameter.

• Rv (float) – Real volume potential radius parameter.

• av (float) – Real volume potential diffuseness parameter.

• Uw (float) – Imaginary volume potential strength parameter.

• Rw (float) – Imaginary volume potential radius parameter.

• aw (float) – Imaginary volume potential diffuseness parameter.

• Ud (float) – Imaginary surface potential strength parameter.

• Rd (float) – Imaginary surface potential radius parameter.

• ad (float) – Imaginary surface potential diffuseness parameter.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

class jitr.optical_potentials.wlh.Global(projectile, param_fpath=None)

Bases: object

Global optical potential in WLH form.

Parameters:

• projectile (tuple)

• param_fpath (Path | None)

get_params(A, Z, Elab)

Return WLH central, spin-orbit, and Coulomb parameters.

Return type:

tuple[tuple[float, ...], tuple[float, ...], tuple[float, ...]]

Parameters:

• A (int)

• Z (int)

• Elab (float)

jitr.optical_potentials.wlh.calculate_params(projectile, target, Elab, uv0, uv1, uv2, uv3, uv4, uv5, uv6, rv0, rv1, rv2, rv3, av0, av1, av2, av3, av4, uw0, uw1, uw2, uw3, uw4, rw0, rw1, rw2, rw3, rw4, rw5, aw0, aw1, aw2, aw3, aw4, ud0, ud1, ud3, ud4, rd0, rd1, rd2, ad0, uso0, uso1, rso0, rso1, aso0, aso1)

Calculate the arguments for the central, spin_orbit, and coulomb_charged_sphere functions corresponding to the WLH potential for a given projectile, target, lab energy, and the WLH parameters.

Parameters:

• projectile (tuple) – tuple (A, Z) of the projectile.

• target (tuple) – tuple (A, Z) of the target.

• Elab (float) – Laboratory energy in MeV.

• uv0 (float) – Parameters of the WLH potential. See Whitehead et al., 2021 for details.

• uv1 (float) –

  Parameters of the WLH potential. See Whitehead et al., 2021 for details.

• ... –

  Parameters of the WLH potential. See Whitehead et al., 2021 for details.

• aso1 (float) –

  Parameters of the WLH potential. See Whitehead et al., 2021 for details.

• uv2 (float)

• uv3 (float)

• uv4 (float)

• uv5 (float)

• uv6 (float)

• rv0 (float)

• rv1 (float)

• rv2 (float)

• rv3 (float)

• av0 (float)

• av1 (float)

• av2 (float)

• av3 (float)

• av4 (float)

• uw0 (float)

• uw1 (float)

• uw2 (float)

• uw3 (float)

• uw4 (float)

• rw0 (float)

• rw1 (float)

• rw2 (float)

• rw3 (float)

• rw4 (float)

• rw5 (float)

• aw0 (float)

• aw1 (float)

• aw2 (float)

• aw3 (float)

• aw4 (float)

• ud0 (float)

• ud1 (float)

• ud3 (float)

• ud4 (float)

• rd0 (float)

• rd1 (float)

• rd2 (float)

• ad0 (float)

• uso0 (float)

• uso1 (float)

• rso0 (float)

• rso1 (float)

• aso0 (float)

Return type:

tuple[tuple[float, ...], tuple[float, ...], tuple[float, ...]]

Returns:

(central_params, spin_orbit_params, coulomb_params) where central_params is (uv, Rv, av, uw, Rw, aw, ud, Rd, ad), spin_orbit_params is (uso, Rso, aso), and coulomb_params is (Z*Zp, RC).

class jitr.optical_potentials.wlh.WLH(projectile)

Bases: SingleChannelOpticalModel

The Whitehead-Lim-Holt global optical potential for nucleon-nucleus scattering.

Parameters:

projectile (tuple)

evaluate(rgrid, reaction, kinematics, *params)

Evaluate the central, spin-orbit, and Coulomb terms of the WLH potential on the given radial grid for the specified reaction and kinematics, using the provided potential parameters.

Parameters:

• rgrid (float | ndarray[tuple[Any, ...], dtype[double]]) – Radial coordinate or grid in fm.

• reaction (Reaction) – Reaction for which to calculate the parameters.

• kinematics (ChannelKinematics) – Kinematics of the reaction channel.

• *params (float) –

  Parameters of the WLH potential. See Whitehead et al., 2021 for details.

Return type:

tuple[complex | ndarray[tuple[Any, ...], dtype[cdouble]], complex | ndarray[tuple[Any, ...], dtype[cdouble]], float | ndarray[tuple[Any, ...], dtype[double]]]

Returns:

(U_central, U_spin_orbit, U_coulomb) evaluated on the radial grid.

Analytic local and nonlocal optical-potential building blocks.

jitr.optical_potentials.potential_forms.perey_buck_nonlocal(r, rp, *params)

Return the Perey-Buck nonlocal kernel factor.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float)

• rp (float)

• params (float)

jitr.optical_potentials.potential_forms.woods_saxon_potential(r, *params)

Return a Woods-Saxon potential with complex depth V + iW.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• params (float)

jitr.optical_potentials.potential_forms.woods_saxon_prime(r, *params)

Return the radial derivative of a Woods-Saxon potential.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• params (float)

jitr.optical_potentials.potential_forms.woods_saxon_safe(r, R, a)

Evaluate a Woods-Saxon shape while avoiding overflow in exp.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.woods_saxon_prime_safe(r, R, a)

Evaluate the radial derivative of the Woods-Saxon shape safely.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.thomas_safe(r, R, a)

Evaluate the Thomas spin-orbit shape without overflow issues.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.surface_peaked_gaussian_potential(r, *params)

Return a simple surface-peaked Gaussian potential.

Return type:

complex | ndarray[tuple[Any, ...], dtype[cdouble]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• params (float)

jitr.optical_potentials.potential_forms.woods_saxon_volume_integral(V, R, a)

Return the volume integral for a Woods-Saxon term.

Return type:

float

Parameters:

• V (float)

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.woods_saxon_mean_square_radius(R, a)

Return the mean-square radius for a Woods-Saxon term.

Return type:

float

Parameters:

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.woods_saxon_prime_volume_integral(V, R, a)

Return the volume integral for a derivative Woods-Saxon term.

Return type:

float

Parameters:

• V (float)

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.woods_saxon_prime_mean_square_radius(R, a)

Return the mean-square radius for a derivative Woods-Saxon term.

Return type:

float

Parameters:

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.thomas_volume_integral(V, R, a)

Return the volume integral for the Thomas spin-orbit shape.

Return type:

float

Parameters:

• V (float)

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.thomas_mean_square_radius(R, a)

Return the mean-square radius for the Thomas spin-orbit shape.

Return type:

float

Parameters:

• R (float)

• a (float)

jitr.optical_potentials.potential_forms.coulomb_charged_sphere(r, zz, r_c)

Return the Coulomb potential of a uniformly charged sphere.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• zz (float)

• r_c (float)

jitr.optical_potentials.potential_forms.regular_inverse_r(r, r_c)

Return 1/r regularized inside a sphere of radius r_c.

Return type:

float | ndarray[tuple[Any, ...], dtype[double]]

Parameters:

• r (float | ndarray[tuple[Any, ...], dtype[float64]])

• r_c (float)

jitr.optical_potentials.potential_forms.yamaguchi_potential(r, rp, *params)

Return the Yamaguchi separable nonlocal potential.

Return type:

float

Parameters:

• r (float)

• rp (float)

• params (float)

jitr.optical_potentials.potential_forms.yamaguchi_swave_delta(k, *params)

Return the analytic s-wave phase shift for the Yamaguchi potential.

Return type:

double

Parameters:

• k (float)

• params (float)