7Be neutrino line shifts in the sun. Yongkyu Ko Yonsei University, Korea Particle physics lecture 17 October 2017
Contents Abstract 2. Some terminologies 3. What’s happening in the sun? 4. Electron scattering off Be 5. Some results 6. Borexino measurements 7. Summary and future works
Abstract Nuclear reactions in stars or the sun take place in thermal equilibrium. Nuclear reactions in thermal equilibrium is quite different from that in center of momentum frame, when the masses of incident particles are different. Reaction rates of the burning process could be fine tuned with thermal Lorentz frame and the age of stars is also adjusted. Energy shift of neutrino spectra could give information for the temperature in the core of stars or the sun.
Some Terminologies Nucleus mass and atomic mass Binding Energy
Q value Q >0, the reaction is exothermic, Q <0, the reaction is endothermic.
Several Lorentz frames m1 is a pion(140MeV) with kinetic energy of 100 MeV and m2 is a proton(938MeV) as a target at rest Several Lorentz frames Lab system m1 m2 v=0.81c v=0 K=100MeV v=0.16c c. m system m1 m2 v=0 v=0.74c v=0.16c K=70.6MeV K=13.1MeV Th. Eq. system m1 m2 v=0.15c v=0.67c v=0.32c K=48.8MeV K=48.8MeV
Be electron capture Lab system m1 m2 v=0.0896398c v=0 v=2.109 km/s m1 is an electron(0.510MeV) with kinetic energy of 2.065 keV and m2 is Be nucleus(6534.18 MeV) as a target at rest Be electron capture Lab system m1 m2 v=0.0896398c v=0 K=2.06547 keV v=2.109 km/s c. m system m1 m2 v=0 v=0.0896328c v=2.109 km/s K=2.06515 keV K=0.16 eV Th. Eq. system m1 m2 v=0.000781c v=0.088858c v=0.000788c K=2.02938 keV K=2.02938 keV
Lorentz transformations Energies and momenta in thermal equilibrium system Energies and momentum in center of momentum system Velocity between th-cm
What’s happening in the sun? Structure of the sun Mean escape time of photons : τ=105 yr
We should move to the region of Jupiter or Saturn In the future!
PP chains and CNO cycle in stars Be neutrino come from two-body reactions * Stars with mass > 1.5 solar mass * All stars at the end of main sequence lifetime * Red giant branch 14N(p, )15O reaction is the slowest reaction
Neutrino spectra of our sun
Electron scattering off Be Energy levels of 7Be and 7Li Be: 89.5% decay to the g.s., 10.5% decay to the 1st ex.s.
Electron scattering and electron capture Q value: 891.9 keV Q value: 384.29 keV Energy momentum conservation in Th. Eq. system Useful replacement Energy momentum relation of each particle
Some results Final Neutrino Energy Approximation : where All initial variables can be written in terms of a single variable, namely, the kinetic energy which is depend on the temperature of the sun. K=3/2 kb T
Neutrino energy distributions Final state: ground state Final state: 1st excited state keV keV rad rad Energy width : ΔE=1.101 keV Energy width : ΔE=0.492 keV Energy shift : ΔE=1.377 keV Energy shift : ΔE=1.376 keV John N. Bahcall PRD49 3923(1994) Energy shift : ΔE=1.29 keV Energy shift : ΔE=1.24 keV
Neutrino energy shifts with respect to temperature Final state: ground state Final state: 1st excited state keV keV 106 K 106 K
Borexino Measurement Emax=665 keV for φ=0
Compton like scattering
Summary and future works It is convenient to consider stellar nuclear reactions in thermal equilibrium frame. We calculated neutrino energy shifts 1.377 keV and 1.376 keV of ground state and 1st excited state, respectively at 15.7 million kelvin. The complete neutrino spectrum should include the thermal distribution effect of incident particles. The Borexino detector measures Be neutrinos, the energy shift of Be neutrinos would be hided in the spectrum.
Thank you for your attention.