"Alpha decay 1" "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" "Verify equation (3)" gamma = 2 sqrt(2 m E) / hbar (1/4 pi r2 - sqrt(r1 r2)) r2 = 2 Z alpha hbar c / E C1 = sqrt(2 m) pi alpha c C2 = 4 sqrt(m alpha c / hbar) check(gamma == C1 Z / sqrt(E) - C2 sqrt(Z r1)) "ok" joule = kilogram meter^2 / second^2 kilogram = "kilogram" meter = "meter" second = "second" alpha = 7.2973525643 10^(-3) c = 299792458.0 meter / second h = 6.62607015 10^(-34) joule second hbar = h / float(2 pi) -- mass of alpha particle m = 6.6446573450 * 10^(-27) kilogram C1 = sqrt(2 m) float(pi) alpha c C2 = 4 sqrt(m alpha c / hbar) C1 C2 M1 = 238.0507876 -- U238 M2 = 234.0435998 -- Th234 M3 = 4.002603254 -- helium (electron masses cancel) -- energy of alpha particle in MeV E = (M1 - M2 - M3) 931.49410372 "MeV" E -- energy of alpha particle in joules u = 1.66053906892 10^(-27) kilogram E = (M1 - M2 - M3) u c^2 A = 238.0 Z = 90.0 r1 = A^(1/3) 1.2 10^(-15) meter r2 = 2 Z alpha hbar c / E r1 r2 gamma = C1 Z / sqrt(E) - C2 sqrt(Z r1) gamma T = exp(-2 gamma) T Run