1. Nuclear reactions and solar neutrinos
Trieste Sept. 2002
Episode III
Nuclear reactions and solar neutrinos

2. Nuclear reactions and solar neutrinos
The basis of Nuclear Astrophysics
The spies of nuclear reactions in the Sun
The luminosity constraint
The pp chain
-pp neutrinos
-Be neutrinos
-B neutrinos
What have we learnt about the sun from solar neutrino experiments?

3. Cross sections of astrophysical interest
The Gamow formula:
exp is the penetration probability through barrier, determined by Coulomb interaction
S is the astrophysical factor, determined by nuclear physics, depending on the process involved ( strong, e.m, weak)

4. Stellar burning rates The relevant quantity is:
Gamow
peak
Tunnel
effect
exp[-b/E1/2]
Maxwel
Boltzmann
exp[-E/KT]
where f(E) is the velocity distribution
The main contribution arises from nuclei near the Gamow peak, generally larger than kT:
Eo  ( 1/2 Z1Z2T)2/3
» KeV
Gamow Energy

5. Stellar burning rates vs temperature
The strong energy dependence of the cross section translates into a strong dependence of the rate on the temperature.
This dependence is usually parametrized by a power law:
e.g. : p+p -> d+e++ne a=4
3He(3He,2p)3He a =16
7Be(p,g)8B a =13
This dependence which will be crucial for the determination of neutrino fluxes a
a=dlog<sv>/dlogT

6. Determination of the astrophysical S- factor
Nuclear physics is summarized in S(E), which (in absence of resonances) is a smooth function of E.
S [Kevb]
3He(4He,g)7Be
The measurement near the Gamow peak is generally impossible, one has to extrapolate data taken at higher energies.
Sun

7. The lowest energies frontier
Significant effort has been devoted for lowering the minimal detection energy
Since counting rates become exponentially small, cosmic ray background is a significant limitation.
This has been bypassed by installing acelerators deep underground*.
*Fiorentini, Kavanagh and Rolfs (1991)

8. LUNA result*
LUNA at LNGS has been able to measure 3He+3He at solar Gamow peak.
2 events/month !
S(0)=5.32 (1± 6%)MeVb
*PRL 82(1999) 5205

9. The spies of nuclear reactions in the Sun
The real proof of the occurrence of nuclear reactions is in the dectection of reaction products.
For the Sun, only neutrinos can escape freely from the production region.
By measuring solar neutrinos one can learn about the deep solar interior (and about neutrinos…)

10. The luminosity constraint
The total neutrino flux is immediately derived from the solar constant Ko:
If one assumes that Sun is powered by transforming H into He (Q=26,73MeV):
4p+2e- -> 4He + ?
= if L and L e are conserved
2ne ?
Then one has 2ne for each Q of radiated energy, and the total neutrino produced flux is:

11. Towards neutrino energy spectra
To determine Ftot we did not use anything about nuclear reactions and solar models.
In order to determine the energy distribution of solar neutrinos one has to know the producing reactions rate and their efficiency in the Sun

12. The pp-chain 99,77% p + p  d+ e+ + e 0,23% p + e - + p  d + e
86%
d + p  3He +
~210-5 %
14%
3He + 4He 7Be + 
13,98%
0,02%
7Be + e-  7Li + e
7Be + p  8B + 
3He+3He+2p
7Li + p ->+
8B  8Be*+ e+ +e 2
3He+p+e++e
pp I
pp II
pp III
hep

13. Main components of solar neutrinos
name:
reaction:
spectrum:
[MeV]
abundance:
[cm -2 s-1]
uncertainty:
(1s)
production zone: pp
p+pd+e++e
£0.42 1%
0.1 Ro
7Be
7Be+e-7Li+e
0.861 (90%)
0.383 (10%)
10%
0.06 Ro 8B
8B8Be+e++e
£15
18%
0.05 Ro
from: Bahcall et al ApJ 555(2001) 990

14. A group photo (1)
Neutrino flux [cm-2 s-1 ]
Neutrino Energy [Mev]

15. A group photo (2)
The fraction of neutrino produced inside the sun within dR

16. Remarks:
The production efficiency of the different neutrinos depends on:
1) Nuclear inputs (cross sections)
2)Astrophysical inputs (Lum.,opacity, age,Z/X…) which affect physical conditions of the medium where they are produced: particle density and (most relevant) temperature
Uncertianties on the predicted neutrino fluxes depend thus on nuclear physics and astrophysics (Z/X, opacity age, Lum….). To a good approximation these latter can be reabsorbed in the solar temperature.
Remarks: uncertianties on fluxes are correlated, since they depend on uncertianties on the same physical parameters, i.e. one cannot tune the parameters in order to deplete Be-neutrinos without changing B-neutrinos

17. Dependence on Tc FBe~ Tc 10 FB ~ Tc 20 Fpp~ Tc-0.7
By building different solar models, with varied inputs parameters (within their uncertainties) and by using a power law parametrization, one finds (approximately):
FBe~ Tc 10
FB ~ Tc 20
Fpp~ Tc-0.7
Be neutrinos strong depends on Tc, due to Gamow factor in 3He+4He
B neutrinos has the strongest dependence due both to 3He+4He and (mainly) to 7Be+p
For the conservation of total flux, pp neutrinos decrease with increasing Tc

18. For the sake of precision
All physics cannot be exactly summarized in a single parameter Tc
By using a power law parametrization Fi~Pi b P=Sij, L,Z/X, opa,age
and by varying the SSM inputs around their uncertainties, one has:
Spp S33 S34 S17 L Z/X opa age pp Be B N O T

19. ….anyhow
pp, Be and B neutrinos are mainly determined by the central temperature almost independently of the way we use to vary Tc.
Fi/FiSSM
Tc/TcSSM

20. Recent experimental data on B-n
Superkamiokande (n+e--> n +e- ):
F(B)SK = 2.32 (1± 3.5%) 106 cm-2 s-1 (ne,nm,nt)
SNO - CC (ne+d-> n+n+e+ ):
F(B)SNO=1.75 (1 ± 8.0%) 106 cm-2 s-1 (ne)
Combined*:
F(B)EXP = 5.20 (1 ±18%) 106 cm-2 s-1
flux of total active neutrinos produced in the Sun
agreement with recent SNO - NC (n+d-> n+p+n):
F(B)NC = 6.42 (1 ±25%) 106 cm-2 s-1
SSM: (1 ±18%) 106 cm-2 s-1
* see. Fogli, Lisi,Montanino, Villante PRD 1999; Fogli, Lisi, Montanino, Palazzo PRD 2001

21. What have we learnt on the Sun from solar neutrinos? (1)
The measurement of the (total active) B-neutrino flux, from SK and SNO provides a confirmation to the 1% level of the “central” solar temperature (i.e the temperature at the B-neutrinos production zone, »0.05 Ro)*
Gallium expts (GALLEX and SAGE) have provided the proof the Sun is powered by nuclear reactions (pp-low energy neutrinos have been detected)
* Fiorentini and B.R. PLB 526 (2002) 186

22. What have we learnt on the Sun from solar neutrinos? (2)
These are wonderful confirmations of the SSM, but no quantitative improvement of our knowledge of the solar interior
Future experiment, where individual neutrino fluxes will be measured, and the knowledge of neutrinos survival, will allow the dream of learning on the Sun from neutrinos….

23. Episode IV...
next year?

24. Remarks
So far we neglegcted the energy carried by neutrinos. The general formula for the luminosity constraint is:
Actually the average neutrino energies <E>~ 0.3 MeV can be neglected for an approximate estimate.
i=different species of neutrinos

25. CNO be-cycle
This cycle is responsible for only 1.5% of the solar luminosity
17F
16O
17O
(p,)
(p,)
(e+,e)
13C
13N
15N
12C
15O
14N CN
1,49% NO
0,01%
The overall conversion of 4p
into He is achid with the aid of 12C,
the total energy release is 26.7 MeV
This cycle is governed by the slowest reaction: 14N+p

26. CN-neutrinos F 17F17O+e++e £2 5.63 .106 25% 0.05 Ro name: reaction:
spectrum:
[MeV]
abundance:
[cm -2 s-1]
uncertainty
(1s)
production zone: N
13N13C+e++e
£1.2
19%
0.05 Ro O
15O15N+e++e
£1.7
22%
0.05Ro

27. Status of S17 19+4-2 eVb* (1967) (1983) (2001) (2002)
Junghans et al
PRL 88 (2002)
Junghans
eVb*
(1967)
(1983)
(2001)
(2002)
* racomanded value in Adelberger 1998 compilation, (1s)

28. Sterile neutrinos? We have seen: F(8B)EXP=5.20 (1 ± 18%) 106 cm-2 s-1
F(8B)SSM=5.15 (1 ± 18%) 106 cm-2 s-1
very good agreement between EXP and SSM
similar errors affects both determinations
we can derive an upper bound for sterile neutrinos:
F(8B)sterile< cm-2 s-1 (at 2s)
if sterile neutrinos exist, F(8B)EXP is a lower limit

29. B-neutrinos and “Tc” Power laws: Contribution to uncertainty:
12%
Constrain on Tc from FB, EXP :
11%

30. Helioseismology and Be-neutrinos
Helioseismology can provide information also on the nuclear cross sections of
3He+3He -> a +2p
3He+4He -> 7Be +g
These govern Be-neutrino production, through a scaling law:
F(Be) a S34/S331/2
Can one measure F(Be) by means of Helioseismology?

31. S34 /S34
S34/S34SSM
S33/S33SSM
S34 is costrained at 25% level
S33/S33SSM stay in
Since F(Be) a S34/S331/2
=>F(Be) is determined to within 25%
Also u=P/r satisfies the same scaling relation
u = u (S34/S331/2 ) <-> F(Be)
n(Be) waste more energy than n(pp) . If their production is larger, more H->He is burnt for the same e.m. energy and the molecular weight increases
Since T does not depend on S34 or S33 , sound speed decreases when n(Be) is increased.