Rewrite default units and constants

Adopt new SI definition and CODATA 2018 values, create Gaussian context
hgrecco · May 23, 2019 · 3ad5c2b · 3ad5c2b
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diff --git a/AUTHORS b/AUTHORS
@@ -19,6 +19,7 @@ Other contributors, listed alphabetically, are:
 * Felix Hummel <felix@felixhummel.de>
 * Francisco Couzo <franciscouzo@gmail.com>
 * Giel van Schijndel <me@mortis.eu>
+* Ignacio Fdez. Galván <jellby@yahoo.com>
 * James Rowe <jnrowe@gmail.com>
 * Jim Turner <jturner314@gmail.com>
 * Joel B. Mohler <joel@kiwistrawberry.us>

diff --git a/pint/constants_en.txt b/pint/constants_en.txt
@@ -1,53 +1,73 @@
 # Default Pint constants definition file
 # Based on the International System of Units
 # Language: english
-# Source: http://physics.nist.gov/cuu/Constants/Table/allascii.txt
-# :copyright: 2013 by Pint Authors, see AUTHORS for more details.
+# Source: https://physics.nist.gov/cuu/Constants/
+#         https://physics.nist.gov/PhysRefData/XrayTrans/Html/search.html
+# :copyright: 2013,2019 by Pint Authors, see AUTHORS for more details.
 
-ln10 = 2.302585092994046
+#### MATHEMATICAL CONSTANTS ####
+# As computed by Maxima with fpprec:50
 
-speed_of_light = 299792458 * meter / second = c
-standard_gravity = 9.806650 * meter / second ** 2 = g_0 = g_n = gravity
-vacuum_permeability = 4 * pi * 1e-7 * newton / ampere ** 2 = mu_0 = magnetic_constant
-vacuum_permittivity = 1 / (mu_0 * c **2 ) = epsilon_0 = electric_constant
-Z_0 = mu_0 * c = impedance_of_free_space = characteristic_impedance_of_vacuum
+#pi    = 3.1415926535897932384626433832795028841971693993751 = π  # pi
+tansec = 4.8481368111333441675396429478852851658848753880815e-6   # tangent of 1 arc-second ~ arc_second/radian
+ln10   = 2.3025850929940456840179914546843642076011014886288      # natural logarithm of 10
+wien_x = 4.9651142317442763036987591313228939440555849867973      # solution to (x-5)*exp(x)+5 = 0 => x = W(5/exp(5))+5
+wien_u = 2.8214393721220788934031913302944851953458817440731      # solution to (u-3)*exp(u)+3 = 0 => u = W(3/exp(3))+3
 
-# 0.000 000 29 e-34
-planck_constant = 6.62606957e-34 J s = h
-hbar = planck_constant / (2 * pi) = ħ
+#### DEFINED EXACT CONSTANTS ####
 
-# 0.000 80 e-11
-newtonian_constant_of_gravitation = 6.67384e-11 m^3 kg^-1 s^-2
+speed_of_light = 299792458 m/s = c = c_0                      # since 1983
+planck_constant = 6.62607015e-34 J s = h                      # since May 2019
+elementary_charge = 1.602176634e-19 C = e                     # since May 2019
+avogadro_number = 6.02214076e23                               # since May 2019
+boltzmann_constant = 1.380649e-23 J K^-1 = k = k_B            # since May 2019
+standard_gravity = 9.80665 m/s^2 = g_0 = g0 = g_n = gravity   # since 1901
+standard_atmosphere = 1.01325e5 Pa = atm = atmosphere         # since 1954
+conventional_josephson_constant = 4.835979e14 Hz / V = K_J90  # since Jan 1990
+conventional_von_klitzing_constant = 2.5812807e4 ohm = R_K90  # since Jan 1990
 
-# 0.000 000 035 e-19
-# elementary_charge = 1.602176565e-19 C = e
+#### DERIVED EXACT CONSTANTS ####
+# Floating-point conversion may introduce inaccuracies
 
-# 0.000 0075
-molar_gas_constant = 8.3144621 J mol^-1 K^-1 = R
+zeta = c / (cm/s) = ζ
+dirac_constant = h / (2 * π) = ħ = hbar = atomic_unit_of_action = a_u_action
+avogadro_constant = avogadro_number * mol^-1 = N_A
+molar_gas_constant = k * N_A = R
+faraday_constant = e * N_A
+conductance_quantum = 2 * e ** 2 / h = G_0
+magnetic_flux_quantum = h / (2 * e) = Φ_0 = Phi_0
+josephson_constant = 2 * e / h = K_J
+von_klitzing_constant = h / e ** 2 = R_K
+stefan_boltzmann_constant = 2 / 15 * π ** 5 * k ** 4 / (h ** 3 * c ** 2) = σ = sigma
+first_radiation_constant = 2 * π * h * c ** 2 = c_1
+second_radiation_constant = h * c / k = c_2
+wien_wavelength_displacement_law_constant = h * c / (k * wien_x)
+wien_frequency_displacement_law_constant = wien_u * k / h
 
-# 0.000 000 0024 e-3
-fine_structure_constant = 7.2973525698e-3
+#### MEASURED CONSTANTS ####
+# Recommended CODATA-2018 values
+# To some extent, what is measured and what is derived is a bit arbitrary.
+# The choice of measured constants is based on convenience and on available uncertainty.
+# The uncertainty in the last significant digits is given in parentheses as a comment.
 
-# 0.000 000 27 e23
-avogadro_number = 6.02214129e23 mol^-1 =N_A
+newtonian_constant_of_gravitation = 6.67408e-11 m^3/(kg s^2) = = gravitational_constant    # (15)
+rydberg_constant = 1.0973731568160e7 * m^-1 = R_∞ = R_inf                                  # (21)
+electron_g_factor = -2.00231930436256 = g_e                                                # (35)
+atomic_mass_constant = 1.66053906660e-27 kg = m_u                                          # (50)
+electron_mass = 9.1093837015e-31 kg = m_e = atomic_unit_of_mass = a_u_mass                 # (28)
+proton_mass = 1.67262192369e-27 kg = m_p                                                   # (51)
+neutron_mass = 1.67492749804e-27 kg = m_n                                                  # (95)
+lattice_spacing_of_Si = 1.920155716 m = d_220                                              # (32)
+K_alpha_Cu_d_220 = 0.80232719                                                              # (22)
+K_alpha_Mo_d_220 = 0.36940604                                                              # (19)
+K_alpha_W_d_220 = 0.108852175                                                              # (98)
 
-# 0.000 0013 e-23
-boltzmann_constant = 1.3806488e-23 J K^-1 = k
+#### DERIVED CONSTANTS ####
 
-# 0.000 021 e-8
-stefan_boltzmann_constant = 5.670373e-8 W m^-2 K^-4 = σ
-
-# 0.000 0053 e10
-wien_frequency_displacement_law_constant = 5.8789254e10 Hz K^-1
-
-# 0.000 055
-rydberg_constant = 10973731.568539 m^-1
-
-# 0.000 000 40 e-31
-electron_mass = 9.10938291e-31 kg = m_e
-
-# 0.000 000 074 e-27
-neutron_mass = 1.674927351e-27 kg = m_n
-
-# 0.000 000 074 e-27
-proton_mass = 1.672621777e-27 kg = m_p
+fine_structure_constant = (2 * h * R_inf / (m_e * c)) ** 0.5 = α = alpha
+vacuum_permeability = 2 * α * h / (e ** 2 * c) = µ_0 = mu_0 = mu0 = magnetic_constant
+vacuum_permittivity = e ** 2 / (2 * α * h * c) = ε_0 = epsilon_0 = eps_0 = eps0 = electric_constant
+impedance_of_free_space = 2 * α * h / e ** 2 = Z_0 = characteristic_impedance_of_vacuum
+coulomb_constant = α * hbar * c / e ** 2 = k_C
+classical_electron_radius = α * hbar / (m_e * c) = r_e
+thomson_cross_section = 8 / 3 * π * r_e ** 2 = σ_e = sigma_e