PHY492: Nuclear & Particle Physics. Lecture 8 Fusion Nuclear Radiation: β decay

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1 PHY492: Nuclear & Particle Physics Lecture 8 Fusion Nuclear Radiation: β decay

2 Energy released in nuclear fission and fusion Fission Nucleus A=236 fissions into two nuclei with A~118 B Q 236 A B A A= ( )MeV 210 MeV (~10 7 A=118 chemical reaction) B /A~8.5 MeV B /A~7.6 MeV Only stable elements shown Solar fusion A young star is nearly all ionized hydrogen atoms: p + e Energy released by fusing the protons (p) to form Helium ( 4 He 2 ), B = -28 MeV BUT, Helium is (2p,2n). Who supplied the neutrons? This question separates the majors in physics from pseudo-majors. February 5, 2007 Carl Bromberg - Prof. of Physics 2

3 Solar fusion: First the Weak Interaction Solar energy comes from fusion of Hydrogen nuclei ( 1 H 1, 1 proton) to Helium ( 4 He 2, 2 protons, 2 neutrons) in the sun s core (T = 15x10 6 K). Coulomb barrier is 1.2 MeV = 14x10 9 K Fusion due to tail of the temperature distribution! 1 H + 1 H + e 2 H + e + + e + v e MeV (Weak interaction) 1 H + 2 H 3 He MeV γ 3 He + 3 He 4 He H Net effect: e + + e MeV (2γ ) ( ) ( ) MeV ( ) + 2e 4 He + 2ν e MeV 4 1 H (EM interaction) (Strong followed by EM interaction) (Strong interaction) Other reactions important for neutrino physics 7 Be + e 7 Li + ν e or MeV 8 B 8 Be + e + + ν e + ( 15 MeV) Difficult but convincing experiments have shown that the number of solar electron neutrinos is about 1/2 of that predicted. February 5, 2007 Carl Bromberg - Prof. of Physics 3

4 Fusion reactors Likely research reaction: d + t 4 He + n MeV Q- energy of He nucleus (3.5 MeV) σ- cross section for d+t reaction Three critical parameters: n - nuclei number density τ- time large n can be maintained T- ion temperature Lawson criterion for ignition nτ > L = 12kT σv Q Lasers: Currently nτ =10 21 reached at T = 3x10 6 K, but L~ where σv T 4 L T 3 Need to keep nτ constant while raising temperature a factor of 10! Tokamak: Currently nτ =3x10 19 reached at T = 3x10 8 K, but L min ~3x L constant near this temperature Need to raise nτ a factor of 10 at the same temperature! ITER: International Tokomak to be built in Cadarache, France. must make the Tritium February 5, 2007 Carl Bromberg - Prof. of Physics 4

5 β radiation Free neutron β decay anti electron-neutrino: ν e n p e ν e Half-life N = N 0 e t /τ ; lifetime τ = 886s; half-life: t 1 = ln( 2)τ = 0.693τ = 614s 2 Free protons p n e + ν e energy conservation prevents this decay Energy available Q = ( m n m p m e m ν )c 2 ( ) MeV = = MeV with a negligible mass. nuclear binding energy may allow β + decay Nuclear β decays A X Z A Y Z +1 + e + ν e A X Z A Y Z 1 + e + + ν e Atomic electron capture (EC) A X Z + e A Y Z 1 + ν e These decay reactions are possible if they do not violate energy conservation. The total energy of the final state products must not exceed the total energy of the initial state. February 5, 2007 Carl Bromberg - Prof. of Physics 5

6 β-decay energy considerations In β decay, the initial state nucleus is called the Parent (P) while the final state nucleus is called the Daughter (D). The energy available in the decay, Q, is distributed among the final state products Q = ( M P M D m e m ν )c 2 0 Every particle carries momentum, but M D is = T D + T e + T ν large compared to Q or m e, so that T D ~0. Q T e + T ν ignoring T D β decay changes the Z of the nucleus but A remains constant. A X Z A Y Z +1 + e + ν e A X Z A Y Z 1 + e + + ν e β decay & the semi-empirical mass formula M ( A,Z )c 2 = αa βz + γ Z 2 ± a 5 A 3 4 At fixed A the mass is quadratic in Z. At fixed A, a plot of M(A,Z) vs. Z is parabolic! α = m n c 2 a 1 + a 2 A a 4 β = 4a 4 + ( m n m p m e )c 2 γ = 4a 4 + a 3 A 1 3 February 5, 2007 Carl Bromberg - Prof. of Physics 6

7 Beta stability Even-A results from: even-z & even-n (e-e), or odd-z & odd-n (o-o) At constant A, SEMF is parabolic in Z, with minimum at Z min Pairing term, ±a 5 A -3/4, makes e-e nuclei have a lower minima than o-o Allowed β decays (short lifetimes) Parent and Daughter nuclei have the same parity, and differ in spin by no more than 1 unit (Δj=j D -j P = 0, ±1) β raises Z, β + or EC lowers Z (A=108, e-e are 0 +, o-o are 1 + or 2 + ) Mass Forbidden β decays If allowed decays are absent, larger values of Δj or parity changes will occur but with much longer lifetimes. Largest Δj will have longest lifetime. February 5, 2007 Carl Bromberg - Prof. of Physics 7

8 Parity violation in beta decay The direction of travel reverses in a mirror (parity transformation) Rotating disk moves right, spin points left Rotating disk moves left, spin points left Rotation direction doesn t change in a mirror and therefore spin direction doesn t change in a mirror If the disk is an anti-neutrino emitted in a beta decay, one better not find more anti-neutrinos with spin along, rather than opposite to, the velocity. In a mirror velocity reverses, but spin would not: parity would be violated! Experiment shows that all anti-neutrinos are emitted with their spin in the direction of motion. All the anti-neutrinos are RIGHT HANDED Parity is VIOLATED (maximally) in Weak Interactions February 5, 2007 Carl Bromberg - Prof. of Physics 8

9 Double β decay 100 Mo 42 should be stable (mass 100 Tc 43 > 100 Mo 42 ) Double beta decay, correlated emission of two electrons and two anti-neutrinos, has been observed. Example: Molybdenum Mo Ru e + 2v e + 3 MeV If neutrinos and anti-neutrinos are distinct particles they are Dirac neutrinos. If an anti-neutrino is just a right-handed neutrino, they are called Majorana neutrinos. Then neutrino-less double beta decay becomes possible. Double Beta Decay Neutrino-less Double Beta Decay e - e - v e = v e n W - p p W - n February 5, 2007 Carl Bromberg - Prof. of Physics 9

General Physics (PHY 2140)

General Physics (PHY 2140) Lecture 20 Modern Physics Nuclear Energy and Elementary Particles Fission, Fusion and Reactors Elementary Particles Fundamental Forces Classification of Particles Conservation