1. Nuclear Astrophysics at LNS Claudio Spitaleri Claudio Spitaleri Catania University-Italy Laboratori Nazionali del Sud- Catania-Italy Meeting LEA COLLIGA – LNS, Cataia, 13-16 oct. 2008

2. NUCLEAR ASTROPHYSIC AT LNS : A- Reactions studied via Trojan Horse Method (three-body reactions) B- Reactions with (two-body reactions)

3. (primordial nucleosynthesis,stellar evolution, novae, supernovae,….) For various processes (pp chain, CNO cycles, s,r,p,rp…) Nuclear reaction rates are basic input in many astrophysical models To obtain the reaction-rates the measurements of nuclear cross sections  (E) are NECESSARY Direct measurement of cross sections at relevant energies is the best way to obtain the cross sections BUT….. in the measurements between charge perticles two limits are present: -Coulomb barrier -Electron screening Ideally

4. The main limit in the charged particle cross section measurements at astrophysical energies is the presence of the Coulomb barrier between the interacting nuclei E cm Mev)  (E) n b Due to its presence : -extremely small cross sections s(E) with strong energy dependence -the astrophysical relevant energies E G (Gamov peak) usually are not accessible in general, direct evaluation of the cross sections is: -severely hindered -and in some cases even beyond present technical possibilities -and in some cases even beyond present technical possibilities. Gamow energy

5. E cm Mev) S(E) keV B  (E) n b Gamow energy A possible solution to evaluate these cross sections consist in using the Extrapolation through the Astrophysical S(E)- factor defined via the standard equation bare nucleus Cross- section bare nucleus Astrophysical factor b  b (E)= (1/E)exp(-2  ) S b (E) (uncertainties in the extrapolation !!!!)

6. To avoid the problem of uncertainties in the extrapolation procedure Experimental technique were improved and some experiments were performed at Gamow energy. BUT NEW EFFECT WERE DISCOVERED: ELECTRON SCREENING The relevant source of uncertainty in extrapolating the S(E)-factor at astrophysical energies (down to zero energy) is the enhancement due to the electron screening effect !!!! S(E) (MeV b) S(E) (MeV b) 3 He( 3 He,2p) 4 He S s (E) E cm (keV) S(E) (MeV b) S(E) (MeV b) E cm (keV) 3 He( 2 H,p) 4 He S b (E) S s (E) Critical point: due to electron screening, EXTRAPOLATION it is necessary as a “standard solution” in order to extract cross sections at Gamow energy GRAN SASSO

7. THE DANGER OF EXTRAPOLATION was strikingly demonstrated in the case of radiative capture reaction 2 H(d,  ) 4 He new experimental approaches are needed to reduce the uncertainties EXTRAPOLATION new low-energy data 2 H(d,  ) 4 He NUCLEAR REACTIONS BETWEEN CHARGED PARTICLES: DANGER OF EXTRAPOLATION

8. 6 Li(d,  4 He E( KeV) Bare nucleus Shielded nucleus S(E) (MeV b E cm (keV) 11 B(p,  ) 8 Be 9 Be(p,  ) 6 Li S(E) (MeV b) E cm (keV) S(E) (MeV b) E (KeV) 3 He( 2 H,p) 4 He S(E) (MeV b) E cm (keV)

9. In fact to avoid extrapolations, experimental techniques were improved; After improving measurements (at very low energies), electron screening effects were discovered; To extract from direct (shielded) measurements the bare astrophysical S b (E) -factor, necessary for astrophysics extrapolation were performed at higher energy WHY INDIRECT METHODS ARE NEEDED? In any case… Extrapolation is necessary

10. NEW METHODS ARE NECESSARY -to measure cross sections at never reached energies -to retrieve information on electron screening effect when ultra-low energy measurements are available. INDIRECT METHODS ARE NEEDED

11. a) - Coulomb dissociation (CD) b) - Asymptotic Normalization Coefficients (ANC) c)- Transfer reactions d) -  -delayed particle emission e) - The Trojan Horse Method (THM) MAIN INDIRECT METHODS

12. - Trojan Horse Method Main application: Charged particle bare nucleus cross section measurements at astrophysical energies BASIC IDEA It is possible to extract astrophysically relevant two-body cross section  (E) B + x  C + D quasi- free from quasi- free contribution of an appropriate three-body reaction A + B  C + D + S G.Baur: Phys. Lett.B178,(1986),135

13. Can be described by a Feynmam diagram Three body reactions A + B  C + D + S -The A nucleus present a strong cluster structure: A = x  S clusters QUASI-FREE QUASI-FREE REACTION MECHANISM: Generality x B D C A S -The upper vertex describes the virtual break up of the target nucleus A into the cluster x (participant) and S -The S cluster acts as a spectator to x+ B  C + D virtual reaction which takes place in the lower vertex (pole)

14. QUASI-FREE QUASI-FREE REACTION MECHANISM: Generality The cross section of the three body reaction can be factorized into two terms corresponding to the two vertices  (q) xs 2 dΩ dσ Half- Off energy shell KF dE C d  C d  D d3σd3σ  With this approximation the simplest suitable theoretical approach is the PWIA A x B D C A S ( d  /d  ) is the half-off-energy-shell differential cross-section |  (q xS )| 2 describes the intercluster (x-S) momentum distribution KF is a kinematical factor

15. INDIRECT TWO-BODY CROSS SECTION : QUASI-FREE REACTIONS = dΩ dσ x + B  C + D Indirect 2-body cross section KF |  (q xs )| 2 d3σd3σ Measured  (q) xs 2 dΩ dσ half- Off energy shell KF d3σd3σ  Calculated dE c d  c d  D half-off energy shell Above barrier E cm >E Coulomb Barrier x-B QUASI-FREE REACTIONS E c.m. is given in postcollision prescription by prescription by E cm = E C-D - Q 2B E cm = E C-D - Q 2B Q 2b is the two-body Q-value of Q 2b is the two-body Q-value of the x + B  C + D reaction the x + B  C + D reaction E C-D is the relative energy between the outgoing between the outgoing particles c and D particles c and D

16.  dΩ dσ x + B  C + D Indirect 2-body cross section half-off energy shell Above barrier E cm > Coulomb Barrier x-B = dΩ dσ x + B  C + D Direct 2-body cross section on energy shell Zadro et al. PRC.40,(1989)181 Direct excitation function Indirect excitation function LNS-Catania E li =28-48 MeV (1979) 7 Li(d,  )n INDIRECT TWO-BODY CROSS SECTION : QUASI-FREE REACTIONS

17.  dΩ dσ x + B  C + D Indirect 2-body cross section half-off energy shell Above barrier E cm > E Coulomb Barrier x-B = dΩ dσ x + B  C + D Direct 2-body cross section on energy shell Direct excitation function Indirect excitation function LNS-Catania E li =22-37 MeV (1980) PWIA G. Calvi et al.: Phys.Rev.C 41,(1990),1848 6 Li(p,  ) 3 He

18.  dΩ dσ x + B  C + D Indirect 2-body cross section half-off energy shell Above barrier E cm > Coulomb Barrier x-B = dΩ dσ x + B  C + D Direct 2-body cross section on energy shell Direct excitation function Indirect excitation function LNS-Catania E 12C =16-20 MeV (1999) 12 C +   + 12 C MPWBA C.Spitaleri et al: E.P.J A 7,(2000),181 M.G. Pellegriti et al. NPA688,543 (2001) INDIRECT TWO-BODY CROSS SECTION : QUASI-FREE REACTIONS

19. TROJAN HORSE: The incoming “Trojan horse “ particle A is accelerated at energies E A above the Coulomb barrier energy (E AB ) Coul. Bar 1- E A > (E AB ) Coulomb Barrier A + B  C + D + S 2- E cm < E Coulomb Barrier x-B E c.m. is given in postcollision prescription by prescription by E cm = E C-D - Q 2B E cm = E C-D - Q 2B Q 2b is the two-body Q-value of Q 2b is the two-body Q-value of the x + B  C + D reaction the x + B  C + D reaction E C-D is the relative energy between the outgoing between the outgoing particles c and D particles c and D x B D C A S ENERGY PRESCRIPTIONS (under (under proper kinematical conditions) E cm = 0

20. INDIRECT TWO-BODY CROSS SECTION = dΩ dσ x + B  C + D Indirect 2-body cross section KF |  (q xs )| 2 d3σd3σ [Gl][Gl] Penetrability factor R)(kFR)(kG 1 )(q G ax 2 l 2 l l   Measured  (q) xs 2 dΩ dσ half- Off energy shell KF d3σd3σ  Calculated dE c d  c d  D half-off shell Exp. Below barrier correction for the Penetration factor is necessary E cm < E Coulomb Barrier x-B

21. INDIRECT TWO-BODY CROSS SECTION  dΩ dσ x + B  C + D Indirect 2-body cross section half-off shell dΩ dσ x + B  C + D -No absolute cross section is measurable BUT -If the excitation functions at energies below Coulomb barrier is known from direct measurements -The absolute value of S(E) must be found by normalization to direct measurements at higher energies. Direct 2-body cross section

22. INDIRECT TWO-BODY CROSS SECTION  dΩ dσ x + B  C + D Indirect 2-body cross section half-off shell dΩ dσ x + B  C + D 7 Li(p,  ) 4 He 6 Li(d,  ) 4 He Energy dependence of the half- off-shell (red dashed line) and on- shell (black solid line) astrophysical factors for (a) the 7 Li(p,  ) 4 He reaction (b) 6 Li(d,  ) 4 He reaction are the same ! La Cognata et al: PRC (2008) Direct 2-body cross section on-shell

24. Depletion lights nuclei: Li, B, Be ELECTRON SCREENING DIRECT REACTIONS 1- 7 Li +p   +  2- 3- 6 Li +d   4- 5- 6 Li + p   + 3 He 6- INDIRECT REACTIONS 7 Li + d   + n spett. 7 Li + 3 He   + d spett 6 Li + 6 Li  + a spett. 6 Li + 3 He   + d spett 6 Li + d   + 3 He + n spett. 6 Li + 3 He   + 3 He + d spett

25. Depletion lights nuclei: Li, B, Be ELECTRON SCREENING DIRECT REACTIONS INDIRECT REACTIONS 7- 11 B + p  8 Be  +   8- 11 B + p  8 Be  +   9- 10 B + p  7 Be   11 B + d  8 Be  +  + n spett. 10 B + p  7 Be  + n spett. 10- 9 B + p  6 Li  9 B + d  6 Li  + n spett. 11- 3 He + d   + p 12- d + d  p + t 13- d + d  p + t 14 - d + d  3 He + n Primordial nucleosyntesis :  3 He + 6 Li   + p +  spett d + 6 Li  p + t +  spett 3 He + d  t + p + p spett 3 He + d  3 He + n + p spett

27. The Fluorine problem in the AGB : DIRECT REACTIONS INDIRECT REACTIONS 15- 15 N + p   + 12 C 16 - 18 O + p   + 15 N 17- 19 F +   p + 22 Ne 15 N + d   + 12 C + n spett. 18 O + d   + 15 N + n spett. 19 F + 6 Li  p + 22 Ne + d spett. Novae: 18 - 17 O + p   + 14 N 19- 18 F + p   + 15 O 17 O + d   + 14 N + n spett. 18 F + p   + 15 O + n spett.

28. RESULTS

29. 7 Li + p   +   S 0 =55  3 keV b Depletion lights nuclei: Li, B, Be ELECTRON SCREENING 1- S(E)-factor 7 Li( p,   Spitaleri et al. PRC 60,055802, (1999) M.Lattuada et al. ApJ 562,1076(2001) U e (ad) U e (THM) 7 Li+pU e (Dir) 7 Li+p 186 eV330 ± 40 eV300 ± 160 eV

30. 6 Li + d   +  S 0 = 16.9 MeV b Depletion lights nuclei: Li, B, Be ELECTRON SCREENING 2- S(E)-factor 6 Li( d,   Cherubini et al. ApJ 457, 655, (1996) Spitaleri et al. PRC 63,055801, (2001) U e (ad) U e (THM) 6 Li+dU e (Dir) 6 Li+d 186 eV340 ± 50 eV330 ± 120 eV

31. 6 Li+p  + 3 He So = 3  0.9 MeVb Depletion lights nuclei: Li, B, Be ELECTRON SCREENING 3- S(E)-factor 6 Li(p,  3 He Tumino et al. PRC 67,085803 (2003) U e (ad) U e (THM) 6 Li+pU e (Dir) 6 Li+p 186 eV435 ± 40 eV440 ± 80 eV

32. Li reactions U e (ad) U e (THM) 6 Li+dU e (Dir) 6 Li+d 186 eV340 ± 50 eV330 ± 120 eV U e (ad) U e (THM) 6 Li+pU e (Dir) 6 Li+p 186 eV435 ± 40 eV440 ± 80 eV U e (ad) U e (THM) 7 Li+pU e (Dir) 7 Li+p 186 eV330 ± 40 eV300 ± 160 eV 7 Li + p   +  S 0 =55  3 keV b 6 Li + d   +  S 0 = 16.9 MeV b 6 Li+p  + 3 He So = 3  0.9 MeVb 6 Li+d   +  7 Li+p   +  6 Li+p   + 3 He R-matrix calculation direct data

33. 4- S(E)-factor 11 B(p,α 0 ) 8 Be θ CM (deg) THM Data θ CM (deg) THM Data Becker et al.,  Becker et al. 1987….. S(0) extr =2.10  0.13 (MeV b) S(0) THM =2.23  0.24 (MeV b) 2H2H p 11 B n 8 Be α I II

34. 4- S(E)-factor 11 B(p,α 0 ) 8 Be THM Data 2H2H p 11 B n 8 Be α S(0) extr =2.10  0.13 (MeV b) S(0) THM =2.23  0.24 (MeV b)  Becker et al. 1987….. E 11B = 27 MeV LNS- Catania

35. 5- S(E)-factor 10 B(p,α 0 ) 7 Be THM Data 2H2H p 10 B n 7 Be α S(0) extr =1800  500 (MeV b)  Angulo et al. 1998….. E 10B = 24.4 MeV LNS- Catania a.un. Gamow energy EXTRAPOLATION 10 B(p,α 0 ) 7 Be

36. 6- S(E)-factor 9 Be(p,α 0 ) 6 Li THM Data 2H2H p 9 Be n 6 Li α Qun Gang Weng et al. PRC 78,035805, (2008) E 9Be = 23 MeV CIAE- Beijing 9 Be(p,α 0 ) 6 Li

38. S(0) ±  S(0) MeVb Present work Zyskind 79 Redder 82 THM R- matrix Direct data 62 ± 10 64 ± 6 78 ± 6 65 ± 4 7- S(E)-factor 15 N (p,α 0 ) 12 C CYCLOTRON- TAMU E 15N = 60 MeV La Cognata et al. PRC76, 65804, (2007)

41. 8- 18 O(p,α 0 ) 15 N THM Data 2H2H p 18 O n 15 N α E 18O = 54 MeV LNS- Catania M.La Cognata et al. PRL, 101,152501,(2008)

43. 9- 17 O(p,α 0 ) 14 N THM Data 2H2H p 17 O n 14 N α E 17O = 41 MeV LNS- Catania σ(E) THM (arb. un.) E c.m. (MeV) M.L.Sergi et al. To be submitted

45. CARBON BURNING: 12 C + 12 C INDIRECT REACTIONS a - 12 C + 12 C   + 20 Ne b- 12 C + 12 C  p+ 23 Na LNS - 2009 INDIRECT REACTIONS 16 O + 12 C   + 20 Ne +  spett. 16 O + 12 C  p+ 23 Na +  spett. 1- PERSPECTIVE THM Data 16 O 12 C α 20 Ne α THM Data 16 O 12 C α 23 Na p

46. 19 F + p  16 O + a 0 19 F + d  16 O + a 0 + n spett. submitted PAC 2009 LNS AGB: INDIRECT REACTIONS PERSPECTIVE THM Data 2H2H p 19 F n 16 O a0a0

47. Depletion lights nuclei: Li, B, Be ELECTRON SCREENING PERSPECTIVE THM Data 2H2H n 9 Be n 8 Be d DIRECT REACTIONS INDIRECT REACTIONS 9 Be + p  8 Be + d 9 Be + d  8 Be + d + n spett. submitted PAC 2009 LNS

49. Nucleus Trojan Horse cluster s Inter cluster momentum l-relative Bindind energy (MeV) 1dp-n02.225 2td-n06.257 3 3 Hed-p05.494 4 6 Li d-  01.475 5 7 Li t-  12.468 6 7 Be 3 He-  11.587 7 9 Be 5 He-  02.467 IN PRINCIPLE: It is possible to study nuclear reactions induced by light nuclear particles (both stable and unstable).

50. Indirect Beam “Trojan Horse nucleus” 1 n d, 3 H 2 p d, 3 He 3 d 3 He, 3 H, 6 Li 4 t 7 Li 5 3 He 7 Be 6  6 Li, 7 Li, 7 Be, 9 Be 7 5 He 9 Be IN PRINCIPLE: It is possible to study nuclear reactions induced by light nuclear particles (both stable and unstable).

51. Reactions with neutron Test : 6 Li+ d   + t + p 2H2H n 6 Li p t α Tandem –LNS, Catania (2004) Tandem- LNS, Catania (2006) E 6Li =14 MeV

52. Reactions with neutron INDIRECT REACTIONS 17 O + n   + 14 C TANDEM a- LNS 2007 b-Notre Dame 2008 INDIRECT REACTIONS 17 O + d   + 14 C+ p spett. PERSPECTIVE THM Data 2H2H n 17 O p 14 C a0a0

53. Reactions with RIB 8 Li +   11 B + n Reactions studied in direct via

54. 8 Li( ,n) 11 B reaction First measurement: (indirect) 11 B(n,  ) 8 Li  8 Li( ,n) 11 B T. Paradellis, et al., Z. Phys. A 337 (1990) 211 11 B inclusive R.N. Boyd et al., Phys. Rev. Lett. 68 (1992) 1283 X. Gu et al., Phys. Lett. B 343 (1995) 31 n inclusive S. Cherubini et al., Eur. Phys. J. A 20 (2004) 355 A. Del Zoppo et al., Nucl. Instr. Meth. A 58 (2007) 783 M. La Cognata et al., Phys. Lett. B. 664 (2008) 157 11 B-n exclusive Y. Mizoi et al., Phys. Rev. C 62, 065081 (2000) H. Ishiyama et al., Phys. Lett. B 640, 82 (2006)

56. From 11 B(n,  ) 8 Li  only ground state contribution Lower limit for cross section

57. 11 B Inclusive

58. 11 B-n Esclusive

59. n Inclusive  LNS

60. EXCYT

62. DIRECT REACTION 8 Li + p  d + 7 Li 8 Li + d  t + 7 Li PERSPECTIVE

63. SUMMARY -The main advantages of the THM are that the extracted cross section of the binary subprocess does not contain the Coulomb barrier factor. No Coulomb barrier effects -TH cross section can be used to determine the energy dependence of the astrophysical factor, S(E), of the binary process x+ B  c + C,down to zero relative kinetic energy of the particles x and B without distortion due to electron screening. No extrapolation No electron screening effects -It is possible to measure excitation function in a “ relatively” short time because typical order of magnitude for a three- body cross- section is of oder 10-100 mb - -Possibility of application to the radioactive beam measurements; - No complex experimental apparatus. -At low energies where electron screening becomes important, comparison of the astrophysical factor determinated from the TM Method to the direct result provides a determination of the screening potential.

64. C.S., S. CHERUBINI, V. CRUCILLÀ, M.GULINO, M.LA COGNATA, M.LAMIA, C. LI,R.G.PIZZONE, S.PUGLIA, G.RAPISARDA, S.ROMANO, L.SERGI, S.TUDISCO, A.TUMINO Laboratori Nazionali del Sud, Catania, Italy and Università di Catania, Italy C.ROLFS Experimentalphysik III Physik mit Ionenstrahlen, Bochum University, Germany A.COC, CSNSM, Orsay,France F.HAMMACHE, N. DE SERVEILLE IPN, Orsay, France S. KUBONO, S. HAYAKAWA, Y. WAKABAYASHI,H. YAMAGUCHI N. IWASA, S. KATO, S. NISHIMURA, T. TERANISHI RIKEN Wako, Japan Center for Nuclear Study, Tokyo University, Japan A.MUKHAMEDZHANOV, R.TRIBBLE, L.TRACHE,V.GOLDBERG Ciclotron Institute, Texas A&M University, Usa S. ZHOU, Q. WEN China International Atomic Energy, Beijing, China

65. V.BURJAN, V.KROHA, J. MRAZEK Nuclear Physics Institute, Academic of Science,Rez, Czech Rep Z.ELEKES, Z.FULOP, G.GYURKY, G.KISS, E.SOMORJAI Inst. of Nuclear Research ofAcademic of Science Debrecen,Ungaria G.ROGACHEV Florida State University, Tallahassee,Florida, USA N.CARLIN, M.GAMEIRO MUNHOZ, M.GIMENEZ DEL SANTO, R.LIGUORI NETO, M.DE MOURA, F.SOUZA, A.SUAIDE, E.SZANTO, A.SZANTO DE TOLEDO Dipartimento de Fisica Nucleare, Universidade de Sao Paulo,Brasil

66. THANK YOU

67. Giovanni Domenico TIEPOLO Italian painter, Venetian school (b. 1727, Venezia, d. 1804, Venezia)