1. Experimental Nuclear Astrophysics: Key aspects & Open problems Marialuisa Aliotta School of Physics University of Edinburgh Nuclear Physics Autumn Retreat September, 5-6 2002 stellar evolution and nuclear physics nuclear reactions in stars laboratory measurements electron screening effect stopping power measurements

2. Stellar evolution and nuclear physics energy production stability against collapse synthesis of “metals” thermonuclear reactions BIRTH gravitational contraction explosion ejection DEATH mixing of interstellar gas abundance distribution of the elements Interstellar gasStars

3. Reactions between charged particles E kin ~ kT (keV) << E coul ~ Z 1 Z 2 (MeV) Gamow peakE 0 = f(Z 1, Z 2, T) Gamow peak tunnelling through Coulomb barrier  exp(- ) Maxwell-Boltzmann distribution  exp(-E/kT) relative probability energy kTE0E0 kT << E 0 << E coul 10 -12 barn <  < 10 -9 barn EXPERIMENTAL DIFFICULTIES ! tunnelling through barrier  exp(-2  ) = Z 1 Z 2 e 2  v v Sommerfeld parameter Coulomb barrier RnRn RtRt EcEc 0 E most effective energy region for thermonuclear reactions ( )

4. LOGARITMIC SCALE  direct measurements E0E0 E coul Coulomb barrier  (E) non-resonant resonance non resonant process interaction energy E extrapolation direct measurement 0 S(E) extrapolation needed ! Transform:  (E) = S(E) exp(-2  ) astrophysical S(E)-factor non-nuclear (for s-waves only!) LINEAR SCALE Reaction cross section

5. DANGER OF EXTRAPOLATION ! -E r ErEr low-energy tail of broad resonance sub-threshold resonance

6. Resonant reaction  (E)   a  b (E-E r ) 2 + (  /2) 2 Breit-Wigner formula V rr0r0 E incident nucleusErEr 0 E r+1 E1E1 E2E2   v  tot =  v  r +  v  n-r interference effects negligible low-energy tail of broad resonance non resonant process -E r ErEr interaction energy E extrapolation direct measurement sub-threschold resonance 0 S(E) Extrapolation

7. The LUNA Project Laboratory Underground for Nuclear Astrophysics Pioneering project LUNA phase I 50 kV accelerator Gran Sasso – Italy 1400 m rock shielding factor ~ 10 6 3 He( 3 He,2p) 4 He FIRST measurement within Gamow Peak no extrapolation here! lowest energy:  = 20 femto-barn (1 event per month) electron screening: U e = 340  50 eV U ad = 240 eV ?

8. LUNA Phase II installed tested calibrated Astrophysical region: 20-80 keV Angulo et al. 01 400 kV accelerator C N O 13 15 12 131415 678 CNO cycle Investigate: 14 N(p,  ) 15 O energy generation rate in massive main sequence stars (slowest reaction in CNO cycle)

9. Electron screening effect  (E) = S(E) exp(-2  ) enhanced cross-section by a factor: interaction ions atoms/molecules (projectile) (target) penetration through Coulomb barrier between bare nuclei RnRn RtRt Coulomb potential EcEc 0 E bare E 0 bare S(E) S(E) extrapolation from fit to high-energy data screened S(E) fit to measured low-energy data  Ue Ue E  s (E)  b (E) f(E) = S s (E) = S b (E) = E + U e exp(  U e /E) in the laboratory: in stellar plasmas: ions in sea of free electrons Debye-Hückel radius R D (T,  ) PROBLEM: experimental Ue >> theoretical Ue

10. screened E + U e RaRa U e  Z 1 Z 2 e 2 /R a typically: U e << E

11. A laboratory measurement LUNA collaboration: investigation on electron screening 3 He(d,p) 4 He measurement of stopping powers (log. scale) Energy 0  (E) astrophysical domain EE  e.g. at E ~ 10 keV  E/E  0.2%   /   6% 3 He(d,p) 4 He precise knowledge of interaction energy is required! extrapolated values (SRIM 2000) measured values (SRIM 2000) stopping power of He gas for D higher cross-sections lower S(E)-factors lower U e values! energy loss of beam in target lower stopping powers Why are stopping powers important? main uncertainty

12. 3 He gas (D 2 ) D 1,2,3 ( 3 He + ) + Experimental setup yield measurement as function of gas pressure  (E-  E det )  (E)  Y(E, p) Y(E,p  0) proportional to stopping power  !

13. Stopping powers main contribution to beam energy loss: interaction with electrons in target medium energy transfer  electron ionization  electron excitation (m d +m e ) 2 4 m d m e E d =EeEe max. energy transfer: (in a single encounter) in He atoms: E e (1s   ) = 24.6 eV  E d = 22.6 keV E e (1s  2s) = 19.8 eV  E d = 18.2 keV threshold effect ?! for E d < 18.2 keV  “electronic stopping power“ vanishes

14. Astrophysical S(E) - factors S(E) bare from Geist et al. (1999) (normalized to exp. data) S(E) screen. absolute values - E cm = 5-60 keV [ 3 He(d,p) 4 He] 3 He(d,p) 4 He U e =219  7 eV U e = 120 eV theo

15.  electron screening: still an open problem  U e is function of energy however: U e = const. in the fit  correct models for U e ?  reliable extrapolation for S(E) bare ?  correct stopping powers? Considerations & open questions

16. Germany - Bochum Italy – Napoli - Genova - Milano - Padova - Catania - Torino Hungary - Debrecen Portugal- Lisboa Denmark- Aarhus UK- Edinburgh The Collaboration

18. 2. charged particlesCoulomb barrier Two types of reactions: E kin ~ kT (keV) << E coul ~ Z 1 Z 2 (MeV) tunnelling through barrier  exp(-2  ) = Z 1 Z 2 e 2  v v Sommerfeld parameter Coulomb barrier RnRn RtRt EcEc 0 E ( ) Typically: Gamow peak tunnelling through Coulomb barrier  exp(- ) Maxwell-Boltzmann distribution  exp(-E/kT) relative probability energy kTE0E0 Gamow peak effective energy for thermonuclear fusion reactions E 0 = f(Z 1, Z 2, T) kT << E 0 << E coul 10 -12 barn <  < 10 -9 barn reaction cross section  1/v ~ constant 1. neutron captureno Coulomb barrier

19. As star evolves: T changes need analytic function  (E) depends on reaction mechanism Nuclear reactions in Stars STAR = highly ionised plasma at temperature T non-relativistic non-degenerate gas in thermodynamic equilibrium Maxwell-Boltzmann distribution of relative velocity (i.e. energy) between particles reaction 1 + 2  3 + 4 Q 12 > 0 total reaction rate reaction rate (per particle pair) energy production rate = KEY quantity

20. Experimental Nuclear Astrophysics Laboratory investigation of nuclear reactions at energies of astrophysical relevance Quiescent burning modes stable nuclei timescales ~ 10 9 y E 0 ~ few keV 10 -12 barn <  < 10 -9 barn extrapolations background long measurements pure targets high beam currents underground laboratories Explosive burning modes unstable nuclei timescales ~ 10 -3 – 10 2 s E 0 ~ MeV Features Problems unknown nuclear properties low beam intensities beam-induced background Requirements radioactive ion beams large area detectors high detection efficiency Stellar evolution

21. Experimental techniques Charged-particle induced reactions ‘stable beams’‘unstable beams’ ad hoc techniques problems: low intensities beam-induced background specifically designed detectors Beam requirements: high currents (   A) high energy resolution (  keV) high quality and time stability Target requirements: high stability against heavy beam loads as ‘clean’ as possible