Nuclear Reaction Rates
9 – Nuclear reaction rates introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1 9.1 – Nuclear decays: Neutron decay By increasing the neutron number, the gain in binding energy of a nucleus due to the volume term is exceeded by the loss due to the growing asymmetry term. After that, no more neutrons can be bound, the neutron drip line is reached beyond which, neutron decay occurs: (Z, N) à (Z, N - 1) + n (9.1) Q-value: Qn = m(Z, N) - m(Z, N-1) - mn (9.2) Neutron Separation Energy Sn Sn(Z, N) = m(Z, N-1) + mn - m(Z, N) = -Qn for n-decay (9.3) Neutron drip line: Sn = 0 Beyond the drip line Sn < 0 neutron unbound Gamma-decay • When a reaction places a nucleus in an excited state, it drops to the lowest energy through gamma emission • Excited states and decays in nuclei are similar to atoms: (a) they conserve angular momentum and parity, (b) the photon has spin = 1 and parity = -1 • For orbital with angular momentum L, parity is given by P= (-1)L • To first order, the photon carries away the energy from an electric dipole transition in nuclei. But in nuclei it is easier to have higher order terms in than in atoms. introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 2 Proton decay Proton Separation Energy Sp: Sp(Z,N) = m(Z-1,N) + mp - m(Z,N) (9.4) Proton drip line: Sp = 0 beyond the drip line: Sp < 0 the nuclei are proton unbound α-decay α-decay is the emission of an a particle ( = 4He nucleus) The Q-value for a decay is given by Q "m(Z,A) m(Z 2,A 4) m $c2 α = # − − − − α % (9.5) Decay lifetimes Nuclear lifetimes for decay through all the modes described so far depend not only on the Q-values, but also on the conservation of other physical quantities, such as angular momentum.
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