Applications of nuclear physics in neutrino physics Emanuel Ydrefors E. Ydrefors (KTH) Neutrino physics 1 / 16
Outline of lecture Brief introduction to neutrinos Nuclear beta decay Neutrino-nucleus scattering E. Ydrefors (KTH) Neutrino physics 2 / 16
Standard Model: Quarks and leptons E. Ydrefors (KTH) Neutrino physics 3 / 16
The neutrino One of the particles in the Standard Model Three known flavors (+ their antiparticles): ν e, ν µ, ν τ. Produced in weak interactions such as nuclear beta decay. They have small but non-zero masses: m ν 0.31 ev. This shows that the Standard Model is incomplete! Properties of the neutrino are studied by using "nuclear laboratories". E. Ydrefors (KTH) Neutrino physics 4 / 16
The neutrino: Important information carriers Neutrinos interact very weakly with matter. Therefore, neutrinos produced in e.g. supernovae can be studied with detectors placed on Earth. Such studies are important for astrophysical applications like supernova modelling. E. Ydrefors (KTH) Neutrino physics 5 / 16
Nuclear beta decay Neutron decay: n p + e + ν e, τ 15 min (1) Nuclear beta decay: β decay: (A, Z) (A, Z + 1) + e + ν e (2) β + decay: Electron capture: (A, Z) (A, Z 1) + e + + ν e (3) (A, Z) + e (A, Z 1) + ν e (4) E. Ydrefors (KTH) Neutrino physics 6 / 16
Calculation of rates for allowed beta decay J = 0, 1 and π i π f = 1 The half-life can be written in the form f 0 t 1/2 = κ (B F + B GT ), (5) where κ = 6147s, and B F = g2 V 2J i + 1 M F 2, B GT = g2 A 2J i + 1 M GT 2 (6) Plain values: g V = 1.0 and g A = 1.26. But, often g eff A = 1.0 is used in applications. E. Ydrefors (KTH) Neutrino physics 7 / 16
Nuclear matrix elements for allowed beta decay Fermi matrix element M F = (J f 1 J i ) = (a 1 b)(j f [c a c b] 0 J i ) (7) ab Gamow-Teller matrix element M GT = (J f σ J i ) = 1 3 (a σ b)(j f [c a c b] 1 J i ) (8) Conventions: a = (n a, l a, j a ), α = (a, m α ), and c a = ( 1) j a+m α c α. ab The reduced transition densities (J f [c a c b] L J i ) contain the nuclear structure dependence and are computed from the adopted nuclear model (e.g. Shell Model, TDA, RPA,...) The single-particle matrix elements depend only on the single-particle states (i.e. the mean field) E. Ydrefors (KTH) Neutrino physics 8 / 16
Neutrino-nucleus scattering Neutrinos and their properties are studied by using neutrino scatterings off nuclei. Charged-current (anti-)neutrino-nucleus scattering (A, Z) + ν e (A, Z + 1) + e (9) (A, Z) + ν e (A, Z 1) + e + (10) Neutral-current scattering (A, Z) + ν (A, Z) + ν (11) (A, Z) + ν (A, Z) + ν (12) The neutrinos can be from artificial sources or from astrophysical ones (the Sun, Supernovae) In this lecture: Neutrino energies in the range E 0 80 MeV E. Ydrefors (KTH) Neutrino physics 9 / 16
Neutrino detection Neutrino interactions are rare so large detectors are needed! The figure shows the Super-Kamiokande detector (Japan) which consists of 50 000 tons of water. E. Ydrefors (KTH) Neutrino physics 10 / 16
Transitions involved in neutrino scattering CC ( ν) (A, Z 1) NC (A, Z) CC (ν) (A, Z + 1) E. Ydrefors (KTH) Neutrino physics 11 / 16
Basic formalism for the ν-nucleus scattering lepton current jµ lept e p µ k µ q µ k µ (A, Z) ν e p µ (A, Z + 1) W + hadron current Jµ Q 2 = q µ q µ M 2 W = f H eff i = G d 3 xl 2 µ e iq x f J µ i Here a µ = (a 0, a) and a µ b µ = a 0 b 0 a b. Nuclear-structure dependence contained in f J µ i E. Ydrefors (KTH) Neutrino physics 12 / 16
Spherical tensors Define the spherical components of the unit vectors as e ±1 = 1 2 (e q1 ± e q2 ), e 0 = e q3 (13) E. Ydrefors (KTH) Neutrino physics 13 / 16
Neutrino cross section Multipole expansion of f H eff i by using e iq x = i 4π(2l l + 1)j l ( q x )Y l0 (θ, φ) (14) l After a rather long derivation... d 2 σ dωdω = ( G2 k f ɛ f ) π (2J i + 1) F(Z, ɛ f ) σ J CL + σ J T, J=0 J=1 Total cross section σ(e i ) obtained by integrating over the angles and summing up the contributions from all final nuclear states. Number of detected neutrinos n σ For supernova neutrinos σ ν = 1 T 3 νf 2 (α ν ) de ν E 2 νσ(e ν ) 1+exp(E ν /T ν α ν ) E. Ydrefors (KTH) Neutrino physics 14 / 16
Nuclear matrix elements The nuclear-structure dependence contained in nuclear matrix elements of one-body operators 1 (J f T J J i ) = 2J + 1 (a T J b)(j f [c a c b] J J i ) (15) ab Most important operators are of the forms F V (q)j 0 (qx), F A (q)j 0 (qx)σ, F A (q)[j 1 (qx)y 1 σ] 0,1,2 In the limit q 0, j 0 (qx) 1 and j 1 (qx) 0. E. Ydrefors (KTH) Neutrino physics 15 / 16
Summary Nuclear-structure calculations are important for many applications in neutrino physics and nuclear astrophysics Neutrino-nucleus scattering can be used to probe properties of the neutrino. However, accurate knowledge about the nuclear structure of the relevant target are needed. E. Ydrefors (KTH) Neutrino physics 16 / 16