Indirect methods in nuclear astrophysics

Transcription

1 Indirect methods in nuclear astrophysics Livius Trache IFIN HH Bucharest Magurele, Romania 12 th Russbach School on Nuclear Astrophysics Russbach, Austria, 8 14 March 2015

2 Nuclear Physics for Astrophysics Motivation Direct vs indirect measurements: pro & cons Indirect methods Examples Particular: use of RIBs (Radioactive Ion beams) 2

3 Radiative capture reactions * Radiative capture reactions A(p,)B, A(), A(n * Non-resonant or resonant reactions. * At low energy, the probability that the incoming charged particle penetrates the Coulomb barrier: 2 Z 1Z 2e P exp( 2 ), where ( E ) v * The cross section astrophysical S-factor: 1 ( E) exp( 2 ) S( E) E * Reaction rate per particle pair (integrate to determine over E distr): E b SE ( )exp de kt kt E Plane Wave Projectile X Target A γ Coulomb Barrier Stars are cold! E p =10s 100s kev Nuclear Radius R n Final Orbit Nucleus B Projectile Target A Distance r Reactions (that matter) take place in the Gamow energy window. Direct, or non-resonant part * C. Rolfs and W. Rodney, Cauldrons in the Cosmos. 3

4 Warning: we plot and say we determine the astrophysical S factor but we measure cross sections 4

5 Direct measurements problems and solutions low cross sections measure longer?! No, bc background issues! Background from Cosmic rays Environment radioactivity Solution: shielding Passive Active Underground Low cross sections High current accelerators Targets Detect what?! CYCLOTRON INSTITUTE 5

6 -(UNDERGROUND LABORATORY) Use of laboratory with natural shield ( underground physics-for instance LUNA experiment at LNGS-Italy ) 2 H(p,) 3 He GRAN SASSO Stars are cold! GANOW ENERGY 6

7 3MV tandetron in Bucharest suitable for nuclear astrophysics: and light ion beams & ultralow background lab in saltmine 7

8 coinc at 6 MeV kev 1368 kev ~150 ev in 67.5h(2.8 days) for kev 1368 kev 8

9 PRELIMINARY 9

10 M. Smith & E. Rehm + fission barriers?! mass, T 1/2 resonances site, path?! mass, T 1/2 Two big problems: 1. - very small energies and very small cross sections indirect methods 2. - reactions in stars involve(d) radioactive nuclei use RNB 10

11 Nuclear Astrophysics Indirect methods measurements at lab energies cross sections at stellar energies Experiments at 10, 100, 300 MeV/nucleon to assess cross sections at 10, 100, 300 kev Indirect methods in NPA with RNB (w. examples) A. Coulomb dissociation B. Transfer reactions (ANC method) C. Breakup of loosely bound nuclei D. Resonance spectroscopy -decay, resonant elastic scattering, etc E. Trojan Horse Method (non-rnb so far! Just starting ) 11

12 Indirect methods for nuclear astrophysics Measurement at lab energies Comparison with (reaction) calculations Extract (nuclear structure) information Need good additional knowledge (data). Reliable absolute values Calculate astrophysical S-factor or reaction rates 12

13 B. Transfer reactions: the ANC method Depend on OMP * n Factors!!! Transfer reaction B+d A+a peripheral (absorption) Transfer matrix element: M I V I ( ) A d ( ) f Bp ap i d d d d f DWBA d nl j n l j DW 2 d 2 lajald jd Capl j 2 2 bbpl j bapl j A ( C ) ( ) Bpl j A A d d A A d d ANC - independent on binding potential geometry! OMP knowledge crucial for reliable absolute values! Semi-micr proc. JLM interaction (LT ea, PRC, 2000) NA: proton-nucleus also peripheral d SS i nljdepend on geom (r 0,a) of proton-binding potential < 20-40%, ( ) A ( p ) C Bp (Christy and Duck, 1963 Parker and Tombrello, 1964) 2 I nlj (r)=<a-1 A> nlj =S 1/2 nlj (r) r I C W r BpRN 1 ( 2 A A l Bp Bp) A, 2 Bp Bp r Bp 13

14 Cross sections for (p,) from p-transfer reactions with RNB from MARS (Faraday Cup) Er - det. 12 C E - det. (PSSD) 12 N Melamine target 12 MeV/u 99% pure, 4 mm dia Melamine target 12 MeV/u H 2 cryotarget Four telescope system ( the cross ): E PSD 65, 110 m E 500 m 14

15 Example 12 MeV on N 6 C 3 H 6 and C Primary beam: MeV/u 150 pna Secondary beam: 12 MeV/u 2x10 5 pps Elastic cm =8-60 deg. Fit OMP from folding JLM no param adjust! Transfer 14 N( 12 N, 13 O) 13 C fit w. DWBA extract ANC 12 N(p,) 13 O rate evaluated from ANC 15

16 14 N( 12 N, 13 O) proton-transfer react 12 N(p,) 13 O (rap I,II proc) ANC, S-factor 0-2 MeV Reaction rate Transfer & MeV/u TAMU MARS 12 N beam pps A. Banu et al, Phys Rev C 79, (2009) 16

17 # Transfer Reaction: 13 C( 22 Ne, 23 Ne) 12 C # Elastic Scattering: Ne+ 13 C Ne+ 12 C 12 MeV/A Targets 100 μg/cm 2 * OMPs from the entrance/exit channels DWBA. * The Angular distribution for: Transfer Reaction p 1/2 d 5/2 (Q=0.254 MeV) * The reaction is Peripheral 5/2 C Ne fm S C d d 5/2 5/ d 5/2 S ( Al) d ( Ne ) ( Al) *10 fm 3 1 S & C b ( 23 Ne) [fm -1/2 ] p 1/2 d 5/2 T. Al-Abdullah, thesis & PRC

18 Semi-microscopic double folding potentials for nucleus-nucleus collisions Double folding procedure: V ( R) dr1 dr2 ( r1 ) ( r2 ) veff (, E, s), s r1 R r 2 HFB densities (to best match the surfaces) tried various effective interactions (M3Y, DDM3Y, JLM, etc ) Settled for JLM Smearing w. range parameters t V =1.2 fm, t W =1. 75 fm Renormalizations needed N v, N w JLM - uses eff inter of Jeukenne, Lejeune and Mahaux (PRC 16, 1977) n-nucleus Bauge ea (PRC 58, 1998): energy and density dependent independent geometry for real and imaginary potentials normalization independent of partners reproduces ELASTIC and TRANSFER data Checked for loosely bound p-shell nuclei stable beams ~ 10 MeV/u Found N v =0.37(2) N w =1.0(1), t V =1.20 fm, t W =1. 75 fm Extended to RNB: 7 Be, 8 B, 11 C, 12 N, 13 N, 17 F on 12 C, 14 N targets Ur () N Vr (, t ) in W(, r t ) 18 V V W W

19 JLM works for elastic & transfer JLM works for a range of energies E/A=15-50 MeV/u Works for transfer reactions 19

20 Optical Model Potentials for Nucleus-Nucleus collisions for RNBs Works for RNBs TAMU 12 MeV/u G. Tabacaru ea, PRC 73, (2006) 7 Be on melamine Essential to make credible DWBA calc needed in transfer studies Have established semi-microscopic double folding using JLM effective interaction: Established from exps with stable loosely bound p-shell nuclei: 6,7 Li, 10 B, 13 C, MeV/u Independent real and imaginary parts, energy and density depend. Parameters: renormalization coeff. (Nv~ , Nw=1.0) Predicts well elastic scatt for RNBs: 7 Be, 8 B, 11 C, 12 N, 13 N, 17 F, 14 C,... Good results for transfer reactions (tested where possible) L. Trache ea, PRC 61 (2000), F Carstoiu ea PRC 70 (2004) σ/σ R ORNL 10 MeV/u 17 F+ 14 N 170 MeV 14 N( 17 F, 17 F * ) 17 F+ 12 C 170 MeV X C( 17 F, 17 F * ) 14 N+ 13 C 162 MeV X θ c.m. (deg.) J. Blackmon ea, PRC 73, (2005) 12 N on melamine 20 A. Banu ea, PRC 79, 2009.

21 BT Roeder et al, NIM A634 (2011)71 21

22 22

23 Results 14 C(n,) 15 C 14 C+ 13 C elastic 14 C(n,) 15 C exp-theory ANC M. McCleskey et al., Phys Rev C 89, (2014) 23

24 C Nuclear and Coulomb dissociation wfct, probab 1.E+00 1.E-01 1.E-02 Transfer or breakup vs proton capt in 8 B transfer happens here wave fct transfer breakup happens here Whittaker pr capt (p,) happens here 1.E-03 1.E radius (fm) Model-independent shape w. ANC (Whittaker function) 3/12/2015 RIBF PAC15 24

25 Explosive H-burning in novae: 22 Na observation - novae: explosive H-burning of accreting material in binaries star-wd. ~ 30/yr. - rays from the decay of long-lived isotopes like 26 Al have been detected - E=1.275 MeV ray following the decay of 22 Na predicted, but not observed by space gamma-ray telescopes 24 Si 140 ms NeNa cycle 22 Na depletion in novae: how does it happen? - what are the stellar reaction rates for the 22 Mg(p,) 23 Al and 22 Na(p,) 23 Mg? - what about 22 Mg(p,) 23 Al(p,) 24 Si seq. 2p capture? Imp in XRB 25

26 E491 GANIL Gamma-ray detectors: 8 EXOGAM clovers 4% effic. 12 NaI crystals 6% effic. MCP Cocktail beam (mid-target energies): 24 Si 53 MeV/u 23 Al 50 MeV/u 22 Mg 47 MeV/u 21 Na 43 MeV/u 20 Ne 39 MeV/u Trifoil LDC S primary beam 95 MeV/u, ~ 400 W large angular acceptances: 4 (horiz. & vertic. planes) broad momentum acceptance: p/p = 7% A. Banu et al., NIC & PRC 84, (2011) 26

27 GANIL E491 exp 12 C( 22 Mg, 22 Na) 12 N Charge exchange (new & unexpected) 23 Al 22 Mg+p Proton removal (sought) 27

28 Results from 23 Al breakup cs [mb/mev/c] Al breakup (inclusive) exp. data theory (1d5/2) theory (2s1/2) Mg PzCM [MeV/c] 2 + -> 0 + config. mixing of 23 Al ground state ( 23 Al)~200 MeV/c and J =5/2 + If b 2 is s.p. ANC: C 2 =b 2 exp / calc > > =3.90 ± fm 1 28

29 Complementarities: Coulomb and nuclear dissociation Similar results from mirror system: 22 Ne+n-> 23 Ne 13 C( 22 Ne, 23 Ne) 12 C assuming S n =S p [46] T. Gomi, T. Motobayashi et al, JPG 31 (2005) 29

30 Results from 24 Si breakup C 2 ( 24 Si gs ) = fm -1 SF = => first exp determination of the direct comp of 23 Al(p,) 24 Si! 1.E+02 1.E Al(p,g) 24 Si reaction rate 22 Mg(p,) 23 Al(p,) 24 Si seq. 2p capture imp in XRB Note: exp made with 30 pps! A. Banu et al, PRC 86, (2012) react rate [cm3/mol/sec] 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E temp [GK] nonres (shell model) res + nonres (previous work) res-updated (this work) nonres (this work) 30

31 Future: exp NP1412 RIBF 9 C 8 B+p breakup for 8 B(p,) 9 C The reaction is important in the hot pp chains, in explosive H burning, at large temperatures, for creating alternative paths across the A=8 mass gap (see e.g. M. Wiescher et al., Ap. J. 343 (1989)352.) C breakup ANC JLM average Standard Ray Zero-range Franey-Love 1.4 pp IV 8 B(p,) 9 C( 9 B(p) 8 Be() 4 He and rap I 8 B(p,) 9 C(,p) 12 N(p,) 13 O( p,) 14 O. C 2 (fm -1 ) Use breakup of 9 C-> 8 B+p at intermediate energies to obtain 8 B(p,) 9 C at astrophysical energies. Eexisting data from: B. Blank et al., Nucl Phys A624 (1997) MeV/u on C, Al, Sn and Pb targets Trache et al. ANC from breakup, 2002 Beaumel (ANC from (d,n) reaction) T. Motobayashi et al. Coulomb dissociation target Figure. The results of similar calculations for 9 C Average: Ctot Cp Cp 3/2 1/2 =1.22±0.13 fm -1 and S 18 (E)= E+7.34E 2 evb (E in MeV) T Motobayashi 31

32 8 Be(p,) 9 C astrophysical interest H-burning in hot pp chain (pp IV and rap I) at high T, in metal-poor environment T 9 ~ , ~10 5 g/cm 2 super-massive stars in early Universe? 7 Li synthesis in novae?.. ~1 MeV E Gamow ~ kev at T= K capture through continuum dominates

33 Setup 16 O primary beam with two BigRIPS settings for 100 AMeV and 300AMeV common to other HI-p experiments DALI2: not necessary for 9 C 8 B+p, but useful for 9 CBe+2p The standard SAMURAI setting better for k x measurements?

34 9 C nuclear 100MeV/u. Theor estimates by Glauber calc Calculated momentum distributions from 1pbreakup of 9 at 100 MeV/u on a C target. Note: Calculations 9 C with > 7 two Be+2p different large geometries csof the binding potential for the last proton are shown (see text for details). Figure 3. Calculated momentum distributions from 1pbreakup of 9 C at 100 MeV/u on a C target. Calculations with two different geometries of the binding potential for the last proton are shown (see text for details). Interested in the accuracy of absolute values of cross sections. What different models, parameters, codes (and theoreticians) give?! 34

35 AT RIKEN Secondary beam target LI +HI tracking SAMURAI proton and HI hodoscopes X,Y U,V XY UV Si planes after target/before SAMURAI Possible: a) SSD SSD SSD SSD SSD b) DSSD SSD DSSD Problems: i) Delta e problem & ii) p threshold issues

36 Test rigs at WU, TAMU and HIMAC with existing PCB mounting Test with the 2D TTT (300 um) AREA 97.3 x 97.3 mm # strips 128 x per Si, 512 per pair Pitch 756 um Si type available in both n and p (intrinsic). We have one of each Thickness available in both 300 and 500 m, we have 300 m. pf 300 m: 0.35 pf/mm 2 = 26 pf/st; 500 m: 0.21 pf/mm 2 = 15.4 pf/st Si TTT (WU) Si in chamber (TAMU) External view (WU) 36

37 Summary B C Indirect methods w RNB valuable tool for nuclear astrophysics Accuracies of 10 15% can be obtained Q: Good enough?! For better accuracies more work needed, including systematic studies and development of structure and reaction theories (and codes): Work close to proton drip line makes continuum important, antisym, etc Combination of methods is important Q: what are the most imp reactions?! 37

38 D Resonant Reaction Rates * Resonant reaction is a two-step process. * The cross section (Breit-Wigner): * The contribution to the reaction rate: where E r E f 4 H E r 2 E r H 2 2J 12 J J 1 2 f A E 2 2 Er exp es kt kt 2J 1 2J p 12J t 1 = resonance strength r p tot E p r p to determine * C. Rolfs and W. Rodney, Cauldrons in the Cosmos. 38

39 Summary Replaced direct radiative p capture reactions (p,) with: Proton transfer (or n transfer in mirror) Coulomb or nuclear p dissociation Beta delayed p decay a) indirect methods b) RNBs or stable beams Lessons learned: 1. Seek the relevant quantities (ex: SF vs ANC) 2. Model or parameter independent 3. Combination of methods is useful availability important 4. Need more in terms of supportive information for reliable calculations: theories, models (and codes), effective n n interactions, systematics still need good stable beam data OMP, reaction models, 48

40 Collaborators R.E. Tribble, A. Banu *, CA Gagliardi, AM Mukhamedzhanov, M McCleskey, A. Saastamoinen, A. Spiridon, B. Roeder, T. Al Abdullah Texas A&M University F. Carstoiu IFIN HH Bucharest T. Motobayashi, K. Yoneda e.a., RIKEN LG Sobotka e.a. WU, St. Louis E. Pollacco CEA/IRFU Saclay N. Orr (GANIL Caen) W. Catford et al. (Univ of Surrey), M. Chartier et al. (Univ of Liverpool), R. Lemmon, M. Labiche (Daresbury), M. Freer et al. (Univ of Birmingham), F. Negoita (IFIN Bucharest) XD Tang e.a. (Lanzhou) 49