Baryosynthesis and Antimatter Generation 149- Use the equation of relativistic kinematics [Equation (3.9)] to calculate the
energy and velocity of the muon from the decay [Equation (6.51)] of a pion at
rest. The neutrino can be considered massless. - Calculate the energy density represented by the mass of all the electrons in the
Universe at the time of photon reheating when the kinetic energy of electrons is
0.2MeV. - When the pions disappear below 140MeV because of annihilation and decay,
some reheating of the remaining particles occurs due to entropy conservation.
Calculate the temperature-increase factor. - Use the equation of relativistic kinematics [Equation (3.9)] and the conserva-
tion of four-momentum to calculate the energy of the photon liberated in Equa-
tion (6.80), assuming that the^4 He nucleus is produced at rest (i.e.,푣p=푣t=
푣He=0). - Free nucleons are favored over deuterons down to a radiation energy of
0.07MeV. What is the ratio of photons with energies exceeding the deuteron
binding energy 2.22MeV to the number of protons at 0.07MeV? - Propose a two-stage fusion process leading to the production of^12 C.
- Gamow’s penetration factor [Equation (6.93)] gives a rough idea about the igni-
tion temperatures in stellar interiors for each fusion reaction. Estimate these
under the simplifying assumption that the burning rates during the different
periods are inversely proportional to the time spans (given at the end of this
chapter). Take the hydrogen burning temperature to be 10^4 K. - Derive a value of weak hypercharge푌=퐵−퐿for the X boson from the reactions
in Equations (6.72) and (6.73).
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