various improvements species

Author: johannes-moegerle

src/ryd_numerov/radial/model.py

@@ -162,7 +162,7 @@ def calc_effective_potential_centrifugal(self, x: XType) -> XType:
 
         """
         x2 = x * x
-        return (1 / self.species.reduced_mass_factor) * self.l * (self.l + 1) / (2 * x2)
+        return (1 / self.species.reduced_mass_au) * self.l * (self.l + 1) / (2 * x2)
 
     def calc_effective_potential_sqrt(self, x: XType) -> XType:
         r"""Calculate the effective potential V_sqrt(x) from the sqrt transformation in atomic units.
@@ -183,7 +183,7 @@ def calc_effective_potential_sqrt(self, x: XType) -> XType:
 
         """
         x2 = x * x
-        return (1 / self.species.reduced_mass_factor) * (3 / 32) / x2
+        return (1 / self.species.reduced_mass_au) * (3 / 32) / x2
 
     def calc_total_effective_potential(self, x: XType) -> XType:
         r"""Calculate the total effective potential V_eff(x) in atomic units.

src/ryd_numerov/radial/radial_state.py

@@ -134,7 +134,7 @@ def create_grid(
             if self.l_r <= 10:
                 z_min = 0.0
             else:
-                energy_au = calc_energy_from_nu(self.species.reduced_mass_factor, self.nu)
+                energy_au = calc_energy_from_nu(self.species.reduced_mass_au, self.nu)
                 z_min = self.model.calc_turning_point_z(energy_au)
                 z_min = math.sqrt(0.5) * z_min - 3  # see also compare_z_min_cutoff.ipynb
         else:

src/ryd_numerov/radial/wavefunction.py

@@ -173,9 +173,9 @@ def integrate(self, run_backward: bool = True, w0: float = 1e-10, *, _use_njit:
         grid = self.grid
 
         species = self.radial_state.species
-        energy_au = calc_energy_from_nu(species.reduced_mass_factor, self.radial_state.nu)
+        energy_au = calc_energy_from_nu(species.reduced_mass_au, self.radial_state.nu)
         v_eff = self.model.calc_total_effective_potential(grid.x_list)
-        glist = 8 * species.reduced_mass_factor * grid.z_list * grid.z_list * (energy_au - v_eff)
+        glist = 8 * species.reduced_mass_au * grid.z_list * grid.z_list * (energy_au - v_eff)
 
         if run_backward:
             # During the Numerov integration we define the wavefunction such that it should always stop

src/ryd_numerov/rydberg_state.py

@@ -67,7 +67,7 @@ def get_energy(self, unit: str | None = None) -> PintFloat | float:
         where `\mu = R_M/R_\infty` is the reduced mass and `\nu` the effective principal quantum number.
         """
         nu = self.get_nu()
-        energy_au = calc_energy_from_nu(self.species.reduced_mass_factor, nu)
+        energy_au = calc_energy_from_nu(self.species.reduced_mass_au, nu)
         if unit == "a.u.":
             return energy_au
         energy: PintFloat = energy_au * BaseQuantities["ENERGY"]

src/ryd_numerov/species/species_object.py

@@ -281,7 +281,7 @@ def get_corrected_rydberg_constant(self, unit: str | None = "hartree") -> PintFl
         The corrected Rydberg constant is defined as
 
         .. math::
-            R_M = R_\infty * \frac{m_{Core}}{m_{Core} + m_e}
+            R_M = R_\infty \frac{m_{Core}}{m_{Core} + m_e}
 
         where :math:`R_\infty` is the Rydberg constant for infinite nuclear mass,
         :math:`m_{Core}` is the mass of the core,
@@ -305,18 +305,18 @@ def get_corrected_rydberg_constant(self, unit: str | None = "hartree") -> PintFl
         return corrected_rydberg_constant.to(unit, "spectroscopy").magnitude
 
     @cached_property  # don't remove this caching without benchmarking it!!!
-    def reduced_mass_factor(self) -> float:
-        r"""The reduced mass factor \mu.
+    def reduced_mass_au(self) -> float:
+        r"""The reduced mass mu in atomic units.
 
-        The reduced mass factor
+        The reduced mass in atomic units :math:`\mu / m_e` is given by
 
         .. math::
-            \mu = \frac{m_{Core}}{m_{Core} + m_e}
+            \frac{\mu}{m_e} = \frac{m_{Core}}{m_{Core} + m_e}
 
-        calculated via the corrected Rydberg constant
+        We calculate the reduced mass via the corrected Rydberg constant
 
         .. math::
-            \mu = \frac{R_M}{R_\infty}
+            \frac{\mu}{m_e} = \frac{R_M}{R_\infty}
 
         """
         return self.get_corrected_rydberg_constant("hartree") / rydberg_constant.to("hartree").m
@@ -334,23 +334,17 @@ def calc_nu(
         r"""Calculate the effective principal quantum number nu of a Rydberg state with the given n, l, j_tot and s_tot.
 
         I.e. either look up the energy for low lying states in the nist data (if use_nist_data is True),
-        and calculate nu from the energy.
-        Or calculate nu via the quantum defect theory.
-
-        The effective principal quantum number nu in quantum defect theory
-        is defined as series expansion :math:`\nu = n^* = n - \delta_{lj}(n)`
-        where
+        and calculate nu from the energy via (see also `calc_nu_from_energy`):
 
         .. math::
-            \delta_{lj}(n) = d0_{lj} + d2_{lj} / [n - d0_{lj}(n)]^2 + d4_{lj} / [n - \delta_{lj}(n)]^4 + ...
-
+            \nu = \sqrt{\frac{1}{2} \frac{\mu/m_e}{-E/E_H}}
 
-        is the quantum defect. The energy of the Rydberg state is then given by
+        Or calculate nu via the quantum defect theory,
+        where nu is defined as series expansion :math:`\nu = n^* = n - \delta_{lj}(n)`
+        with the quantum defect
 
         .. math::
-            E_{nlj} / E_H = -\frac{1}{2} \frac{Ry}{Ry_\infty} \frac{1}{n^*}
-
-        where :math:`E_H` is the Hartree energy (the atomic unit of energy).
+            \delta_{lj}(n) = d0_{lj} + d2_{lj} / [n - d0_{lj}(n)]^2 + d4_{lj} / [n - \delta_{lj}(n)]^4 + ...
 
         References:
             - On a New Law of Series Spectra, Ritz; DOI: 10.1086/141591, https://ui.adsabs.harvard.edu/abs/1908ApJ....28..237R/abstract
@@ -365,7 +359,6 @@ def calc_nu(
                 Default is True.
             nist_n_max: Maximum principal quantum number for which to use the NIST energy data.
                 Default is 15.
-            unit: Desired unit for the energy. Default is atomic units "hartree".
 
         """
         if s_tot is None:
@@ -381,7 +374,7 @@ def calc_nu(
             if (n, l, j_tot, s_tot) in self._nist_energy_levels:
                 energy_au = self._nist_energy_levels[(n, l, j_tot, s_tot)]
                 energy_au -= self.get_ionization_energy("hartree")
-                return calc_nu_from_energy(self.reduced_mass_factor, energy_au)
+                return calc_nu_from_energy(self.reduced_mass_au, energy_au)
             logger.debug(
                 "NIST energy levels for (n=%d, l=%d, j_tot=%s, s_tot=%s) not found, using quantum defect theory.",
                 *(n, l, j_tot, s_tot),

src/ryd_numerov/species/utils.py

@@ -2,49 +2,53 @@
 import re
 
 
-def calc_nu_from_energy(reduced_mass_factor: float, energy_au: float) -> float:
+def calc_nu_from_energy(reduced_mass_au: float, energy_au: float) -> float:
     r"""Calculate the effective principal quantum number nu from a given energy.
 
     The effective principal quantum number is given by
 
     .. math::
-        \nu = \sqrt{\frac{1}{2} \frac{\mu}{-E}}
+        \nu
+        = \sqrt{\frac{1}{2} \frac{R_M/R_\infty}{-E/E_H}}
+        = \sqrt{\frac{1}{2} \frac{\mu/m_e}{-E/E_H}}
 
-    where :math:`\mu` is the reduced mass factor and :math:`E` the energy in atomic units.
+    where :math:`\mu/m_e` is the reduced mass in atomic units and :math:`E/E_H` the energy in atomic units.
 
     Args:
-        reduced_mass_factor: The reduced mass factor :math:`\mu = \frac{m_{Core}}{m_{Core} + m_e}`.
-        energy_au: The energy :math:`E` in atomic units (hartree).
+        reduced_mass_au: The reduced mass in atomic units (electron mass).
+        energy_au: The energy in atomic units (hartree).
 
     Returns:
-        The effective principal quantum number :math:`\nu`.
+        The effective principal quantum number nu.
 
     """
-    nu = math.sqrt(0.5 * reduced_mass_factor / -energy_au)
+    nu = math.sqrt(0.5 * reduced_mass_au / -energy_au)
     if abs(nu - round(nu)) < 1e-10:
         nu = round(nu)
     return nu
 
 
-def calc_energy_from_nu(reduced_mass_factor: float, nu: float) -> float:
+def calc_energy_from_nu(reduced_mass_au: float, nu: float) -> float:
     r"""Calculate the energy from a given effective principal quantum number nu.
 
     The energy is given by
 
     .. math::
-        E = -\frac{1}{2} \frac{\mu}{\nu^2}
+        E/E_H
+        = -\frac{1}{2} \frac{R_M/R_\infty}{\nu^2}
+        = -\frac{1}{2} \frac{\mu/m_e}{\nu^2}
 
-    where :math:`\mu` is the reduced mass factor and :math:`\nu` the effective principal quantum number.
+    where :math:`\mu/m_e` is the reduced mass in atomic units and :math:`\nu` the effective principal quantum number.
 
     Args:
-        reduced_mass_factor: The reduced mass factor :math:`\mu = \frac{m_{Core}}{m_{Core} + m_e}`.
+        reduced_mass_au: The reduced mass in atomic units :math:`\mu/m_e = \frac{m_{Core}}{m_{Core} + m_e}`.
         nu: The effective principal quantum number :math:`\nu`.
 
     Returns:
-        The energy :math:`E` in atomic units (hartree).
+        The energy E in atomic units (hartree).
 
     """
-    return -0.5 * reduced_mass_factor / nu**2
+    return -0.5 * reduced_mass_au / nu**2
 
 
 def convert_electron_configuration(config: str) -> list[tuple[int, int, int]]: