1. 7Be neutrino line shifts in the sun.
Yongkyu Ko
Yonsei University, Korea
Particle physics lecture 17 October 2017

2. 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

3. 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.

4. Some Terminologies
Nucleus mass and atomic mass
Binding Energy

5. Q value
Q >0, the reaction is exothermic,
Q <0, the reaction is endothermic.

6. 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

7. 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 keV and m2 is Be nucleus( MeV)
as a target at rest
Be electron capture
Lab system m1 m2
v= c
v=0
K= keV
v=2.109 km/s
c. m system m1 m2
v=0
v= c
v=2.109 km/s
K= keV
K=0.16 eV
Th. Eq. system m1 m2
v= c
v= c
v= c
K= keV
K= keV

8. Lorentz transformations
Energies and momenta in thermal equilibrium system
Energies and momentum in center of momentum system
Velocity between th-cm

9. What’s happening in the sun?
Structure of the sun
Mean escape time
of photons : τ=105 yr

10. We should move to the region of Jupiter or Saturn
In the future!

11. 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

12. Neutrino spectra of our sun

13. 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.

14. Electron scattering and electron capture
Q value: keV
Q value: keV
Energy momentum conservation in Th. Eq. system
Useful replacement
Energy momentum relation
of each particle

15. 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

16. 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 PRD (1994)
Energy shift : ΔE=1.29 keV
Energy shift : ΔE=1.24 keV

17. Neutrino energy shifts with respect to temperature
Final state: ground state
Final state: 1st excited state
keV
keV
106 K
106 K

18. Borexino Measurement
Emax=665 keV for φ=0

19. Compton like scattering

20. Summary and future works
It is convenient to consider stellar nuclear reactions in thermal
equilibrium frame.
We calculated neutrino energy shifts keV and 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.

21. Thank you for your attention.