Hans Bethe

Kopylov A.V. Erice School/Workshop 2009 on Neutrinos in Cosmology, in Astro, in Particle and in Nuclear Physics in Erice/Trapani/Sicily/Italy

on September 16 – 24 in Centro Ettore Majorana in Erice

Prospects to observe a CNO cycle by solar

neutrinos.

Institute for Nuclear Research of Russian Academy of Sciences Moscow, Russia

(Work done in collaboration with V. Petukhov)A.Kopylov and V.Petukhov JCAP10(2008)007; JCAP08(2009)006

Supported by Russian Fund of Basic Research

Scientific motivation to detect neutrinos from CNO cycle

Neutrino fluxes in case of mixing.The prospects for future CNO experiments.

Hans Bethe

“Energy production in stars”Phys.Rev. 55 (1939) 434

“Űber Elementumwandlungen in Innern der Sterne”Physikalische Zeitschrift 39 (1938) 633

Carl von Weizsäcker



Carbon-Nitrogen cycle:~1% of energy generationIn the Sun

Main source of energy at higher masses

Flux F 13 Flux F 15

CNO cycle is closed at stellar temperatures: Couture A.”19F(p,)20Ne and theStellar CNO burning cycle”2005 PhD Dissertation Notre Dame, Indiana

Kopylov A.V. Erice School/Workshop 2009 on Neutrinos in Cosmology, in Astro, in Particle and in Nuclear Physics in Erice/Trapani/Sicily/Italy on September 16 – 24 in Centro Ettore Majorana in Erice

0,0 0,1 0,2 0,3 0,4 0,5

10-5

10-4

10-3

10-2

10-1

R/RO

4He

3He

12C

14N

16O

J.N.Bahcall, A.M.Serenelli and S.Basu(2005) Astrophys. J. 621, L85

Neutrinos from CNO

Cycle


Bahcall-Pinsonneault and…


-10%

-20% -40%

Bahcall J.N., Serenelli A.M. and Basu S, (2005) Astrophys.J. 621, L85


E n e r g y b a l a n c e0.918fpp+ 0.002fpep+ 0.07f7+ 0.01fCNO = 1

0.918fpp+ 0.002fpep= 1 - 0.07f7 - 0.01fCNO

CNO neutrinos are the last missing chain in the energy balance of the Sun

The observed luminosity – what was generated 40000 years ago,

the neutrino fluxes – what is generated now, i.e. to compare present with the past.

Z.Fazel, J.P.Rozelot, S.Lefebre, A.Ajabshirizadeh and S.Pireaux, arXiv: 0909.0194 v1 [astro-ph.SR]



0.918fpp+ 0.002fpep= 1 - 0.07f7 - 0.01fCNO


Uncertainty in Borexino: 10% - now, 5% - in futureTo have the same contribution to the uncertainty in the evaluation of the total flux of pp-neutrinos one should measure the CNO flux with the uncertainty of about 35% the uncertainty of a lithium experiment about 10% 4 runs 90 days each with 10 tons of lithium and 30% efficiency of counting of 7Be

Borexino hep-ph 0905.2526

fpp

fCNO

fpp= 1.004 +0.008-0.02

The statement fpp= 1.00 ± 0.01is not true, although one can find it in a number of reports!



0.918fpp+ 0.002fpep= 1 - 0.07f7 - 0.01fCNO


Uncertainty in Borexino: 10% - now, 5% - in futurePrecise measurements of the fluxes of F7 and F13+F15 enable to find the total flux of neutrinos, generated in the Sun – analogous to a neutral current measurements in SNO experiment (if there’s no transition to sterile neutrinos).To discover sterile neutrinos one should measure precisely the flux of electron pp-neutrinos as well.

Borexino hep-ph 0905.2526

fpp

fCNO

fpp= 1.004 +0.008-0.02

The statement fpp= 1.00 ± 0.01is not true, although one can find it in a number of reports!

What are the fluxes F13 and F15 if the core of the Sun gets mixed with peripheral layers? To be compatible with the results of helioseismology to stay within the fixed surface abundances:(a) 4He: = 1.8% (b) 1H: = 0.6% (c) 12C: = 12% (d) 12N: = 15%

and with mean molecular weight = 4/(6X+Y+2) = 0.5% in the solar core r < 0.2RSun

0,0 0,2 0,4 0,6 0,8 1,010-5

10-4

10-3

10-2

R/ RO

12C diff.

14N diff.

16O diff.

12C

14N

16O



1212 12 15 15 12 12

0

1313 13 12 12 13

1414 14 13 13 14 14

0

1515 15

( ) 12( ) ( ) ( ) ( ) ( ( ) ( ))

15

( ) 13( ) ( ) ( ) ( ) ( )

12

( ) 14( ) ( ) ( ) ( ) ( ( ) ( ))

13

( )( ) ( )

dX CC X C N X N k X C X C

dt

dX CC X C C X C k X C

dt

dX NN X N C X C k X N X N

dt

dX NN X N

dt

14 14 1515( ) ( ) ( )

14N X N k X N

ApNHXA ZA

Z )()( 1 [s-1]

ApZ=σ(ZA+p)∙v , where v [cm s-1] – relative velocity

)2exp()(

)( E

ESpAZ

σ(ZA+p) reaction cross-section, η = 2πq2/hv Sommerfeld parameter,

S(E) correction for 14N(p,γ )15O from LUNA coll. arXive:nucl/ex-0602012

ApN Z

A [cm3mole-1s-1] – reaction rate,

(G.R.Caughlan, W.A.Fowler, Atomic Data and Nuclear Data Tables, V.40, #2, 283-334, 1988)

(15

12 etc. is the ratio of atomic weights 12C and 15N)

X0 – isotope’s abundance in radiative zone, k [t-1] – mixing coefficient

The set of equations for a CNO cycle:

Only temporal evolution,

coordinates are omitted !



12 1 ' 2 3 3 4 1 1

11 11 33 34 0

32 3 3 4 2 1 ' 3 3

33 34 11 11 0

42 3 3 4

33 34 0

( ) 3 1 1( ) ( ) ( ) ( ) ( ) ( ( ) ( ))

2 9 12

( ) 1 1 3( ) ( ) ( ) ( ) ( ) ( ( ) ( ))

3 4 2

( ) 2 1( ) ( ) ( ) ( (

9 3

dX HX H X He X He X He k X H X H

dt

dX HeX He X He X He X H k X He X He

dt

dX HeX He X He X He k X

dt

4 4) ( ))He X He

and the one for pp chain:

ij =NA<AiAj>

Two sets are solved independently, very smalllink between these two sets…


D u

r a

t I

o n

o

f

m I

x I

n g

versus the abundance of 4He on the surface

Mean molecular weight is more limiting than Ysurf


versus the abundance of 14N on the surface

D u

r a

t I

o n

o

f

m I

x I

n g

and more limiting than the abundance of 14N on the surface


D u

r a

t I

o n

o

f

m I

x I

n g

versus the neutrino flux F13

Big changes of F13


D u

r a

t I

o n

o

f

m I

x I

n g


and no noticeable change of F15


D u

r a

t I

o n

o

f

m I

x I

n g


The change of F7 is well below the accuracy of Borexino

e- - scattering

0,4 0,6 0,8 1,0 1,2 1,410-3

10-2

10-1

100

Reco

il Sp

ectr

a, a

.u.

Electron kinetic energy, MeV

F(13N)

SSM

F(13N)

SSMx3

F(13N)

SSMx5

0,3 0,6 0,9 1,2

0,2

0,4

0,6

0,8

1,0

1,2

Electron kinetic energy, MeV

Reco

il Sp

ectr

a, a

.u.

F(13N)

SSM

F(13N)

SSMx3

F(13N)

SSMx5

F(13N)

SSMx10


To have the data from independent experiments - the key issue.




7Li + e > 7Be + e-

Both initial and final states are mirror nuclei. The transition is super-allowed. The cross-section is high and can be calculated with very good accuracy, better than 1%.

The abundance of 7Li in natural lithium is high (93%), the mass of the target is small (~10 tons).

The threshold is 0.86 MeV, I.e. very high sensitivity to neutrinos of medium energy

(7Be, pep, CNO)

V.A.Kuzmin and G.Zatsepin

On the neutrino spectroscopy of the Sun, in Proceedings of 9th International Cosmic Ray Conference, London, 1965, p.1024

J.N.Bahcall Phys.Lett. 13 (1964) 332

J.N.Bahcall Phys.Rev.Lett. 23 (1969) 251

Fig.1 from : A. Kopylov and V. Petukhov, Physics Letters, B 544(2002)11-15


I –Low Z and no mixing, II – Low Z, III – Low Z with mixing, IV – High Z,V – High Z with mixing. I and V are in a strong (3) contradiction, i.e. the most informative regions, (III&IV) – marginal.

20 SNU – 1.5 cpdIn 10 tons of Li.If the efficiency of Counting ~30%, then~10% stat. acc.For 1 year of expos. ~4% for 10 years

The uncertainties for 10 tons of lithium 10 years of experiment

f13 Z

Integral measurements



CONCLUSIONS

Neutrinos from CNO cycle are the last missing chain in the energy balance of the Sun. This is the main motivation to study the CNO neutrinos in future experiments.

The measurement of the fluxes of CNO neutrinos is vital for the resolution of HIGH Z – LOW Z problem.

The internal core mixing has a signature which can be identified in future measurements as the increased flux F13 .

Newly developed electronic detectors measuring the differential spectrum are approaching the sensitivity adequate to “see” the CNO neutrinos.

A radiochemical lithium detector as an integral detector of solar neutrinos has good prospects for independent measurements. At present the R&D efforts are concentrated to reach the level of about 30% for the efficiency of counting of 7Be.



ACKNOWLEDGEMENTS

The work on a lithium project was partially supported by Russian Fund of Basic Research (RFBR) :

grants 04-02-16678, 07-02-00136A Deep appreciation to RFBR for the support of my attendance to Erice School/Workshop

Many thanks to organizing committee for invitation to come to Erice and for all efforts

Thank you

Documents

Hans Bethe