"Alpha decay" "Verify equation (1)" check(integral(cos(u)^2,u) == 1/2 u + 1/4 sin(2 u)) "ok" "Verify equation (2)" u1 = arcsin(sqrt(r1/r2)) u2 = 1/2 pi check(defint(cos(u)^2,u,u1,u2) == 1/4 pi - 1/2 arcsin(sqrt(r1/r2)) - 1/4 sin(2 arcsin(sqrt(r1/r2)))) "ok" -- CODATA Internationally recommended 2022 values -- https://physics.nist.gov/cuu/Constants/ -- c, e, h, and k are exact values a0 = 5.29177210544 10^(-11) meter alpha = 7.2973525643 10^(-3) c = 299792458.0 meter / second e = 1.602176634 10^(-19) coulomb epsilon0 = 8.8541878188 10^(-12) farad / meter h = 6.62607015 10^(-34) joule second hbar = h / float(2 pi) k = 1.380649 10^(-23) joule / kelvin me = 9.1093837139 10^(-31) kilogram mp = 1.67262192595 10^(-27) kilogram mu0 = 1.25663706127 10^(-6) newton / ampere^2 -- derived units coulomb = ampere second farad = coulomb / volt joule = kilogram meter^2 / second^2 newton = kilogram meter / second^2 tesla = kilogram / second^2 / ampere volt = joule / coulomb -- base units (for printing) ampere = "ampere" kelvin = "kelvin" kilogram = "kilogram" meter = "meter" second = "second" u = 1.66053906892 10^(-27) kilogram M238 = 238.0507884 u M234 = 234.0435998 u M4 = 4.00260325413 u -- electron masses cancel E = (M238 - M234 - M4) 931.49410372 "MeV" / u E E = (M238 - M234 - M4) c^2 A = 238.0 Z = 92.0 r1 = A^(1/3) 1.2 10^(-15) meter r2 = 2 (Z - 2) alpha hbar c / E r1 r2 pi = float(pi) m = 4.001506179129 u gamma = sqrt(2 m E) / hbar r2 * (pi/2 - arcsin(sqrt(r1/r2)) - sqrt(r1/r2) sqrt(1 - r1/r2)) gamma T = exp(-2 gamma) T Run