Resonance scattering and α- transfer reactions for nuclear astrophysics.

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1 Resonance scattering and α- transfer reactions for nuclear astrophysics. Grigory Rogachev

2 Outline Studying resonances using resonance scattering Studying resonances using transfer reactions

3 Resonances nucleon(s) decay threshold Excited states Electromagnetic decays only GS

4 Tzar bomb. Design yield is 100 MT Practically unlimited yield of thermonuclear explosion is possible due to resonance in 5 He! 3 H + 2 H -> 4 He + n MeV

5 Role of resonances in nuclear astrophysics α α Textbook example: Hoyle state in 12 C at 7.65 MeV 8 Be 12 C α

6 Bulk of energy during the x-ray burst is generated in the hot CNO cycle. Escape from the hot CNO cycle may lead to formation of heavy elements. Possible escape route is 14 O(α,p) 17 F(p,γ) 18 Ne(α,p) 21 Na(p,γ) 22 Mg(α,p) The corresponding nuclear reaction rates are needed to determine the details of the process!

7 It is very difficult to measure the (p,γ) and (α,p) reactions on unstable isotopes directly. Low intensity radioactive beams have to be used and cross sections of the corresponding reactions are very low at energies of interest due to Coulomb barrier. However, resonances often dominate the reaction rate. Detailed study of properties of the most important resonances can greatly improve our knowledge of the corresponding reaction rates and can guide the very difficult direct measurements.

8 The most straightforward way to study resonances is elastic scattering Cross Section p E=3.1 MeV E=3.0 MeV E=2.9 MeV E=2.8 MeV E=2.7 MeV E=2.6 MeV E=2.5 MeV E=2.4 MeV E=2.2 MeV E=2.1 MeV E=2.0 MeV target I~10 12 pps p 12 C detector(s)

9 Is it possible to study resonances in exotic nuclei using the same approach? Cannot make a target out of isotopes with short lifetime. The only solution to this would be the use of radioactive beams. Intensity of radioactive beams is many (6-8) orders of magnitude lower than intensity of stable beams. Numerous measurements at different energy is not an option. p Example: Resonance in 23 Al (four neutrons less than the stable 27 Al isotope). p + 22 Mg 22 Mg 22 Mg (t 1/2 = 3.87 s) 1 H I ~ 10 6 pps

10 Thick Target Inverse Kinematics technique 22 Mg Hydrogen target thick enough to stop 22 Mg due to energy losses. Detectors E=80 MeV 70 MeV 50 MeV 30 MeV 0 MeV K.P. Atremov, et al., Sov. J. Nucl. Phys. (1990)

11 Detectors Beam Beam stops here Target gas (H 2 ; CH 4 ; He)

12 Scattering event Detectors Beam Beam stops here Target gas (H 2 ; CH 4 ; He)

13 Place at which interaction occurs is not known Energy of the beam ion at interaction point is not known Scattering angle is not known However all these can be recovered from: Energy of light recoil in the detector Known location of the detector (angle and distance from the center of the scattering chamber for ex.)

14 E lr E 0 Beam z R E hi E lr θ R θ 0 r Target gas (H 2 ; CH 4 ; He)

15 Collecting it all together: z is the only unknown

16 14 O+p spectrum Lab. frame 14 O+p spectrum CMS counts cross section E lab E cms V.Z. Goldberg, et al, PRC 69, (2004) Texas A&M U data

17 Scattering event Detectors Beam Beam stops here Target gas (H 2 ; CH 4 ; He)

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19 Experimental energy resolution Detectors Beam Target gas (H 2 ; CH 4 ; He)

20 Result of Monte Carlo simulation for typical TTIK experiment

21 Resonance elastic and scattering of protons with RNB s has been used extensively to study structure of protons rich exotic nuclei. ( 8 B, 9 C, 11 N, 12 N, 13 O, 14 O, 14 F, 15 F, 16 F, 18 Ne, 19 Ne, 19 Na, 20 Na, 21 Mg, 22 Mg, 23 Al, 24 Al, 26 Si, 27 P) Z! N! Resonance elastic (α,α) scattering and resonance (α,p) reactions have been measured with radioactive beams 14 O, 18 Ne. Resonance (p,α) reactions on 17,18 F

22 14 F 15 F 11 N 9 C Examples 8 B 7 He 9 He

23 Calibration measurements of the 12 C + α excitation function 12 C + α threshold 180 o 9.58 MeV 1 - state is know to play a decisive role in nucleosynthesis.

24 Inelastic problem Beam Inelastic scattering which happens earlier (at higher energy of beam ion) can produce proton with exact same energy as elastic scattering which happens further downstream. Inelastic scattering Elastic scattering Target gas (H 2 ; CH 4 ; He)

25 Structure of 9 C p 8 B + p 9 C 8 B * p 7 Be G.V. Rogachev, et al., PRC 75 (2007) Experiment cannot distinguish between elastic and inelastic process. Inelastic process produces TWO protons. Proton produced in decay of the first excited state of 8 B shows up as a broad peak at 5 MeV.

26 The first experiment! at SPIRAL, GANIL! 18 Ne + p 19 Na * 18 Ne * p p 17 F F. De Oliveira Santos, et al., Eur. Phys. J. A 24, 237 (2005) B.B. Skorodumov, et al., Phys. Atomic Nuclei 69, 1979 (2006) Ecm (MeV)! 1.0! 2.0! 3.0!

27 Solving inelastic problem Using ToF technique IF then R Beam direction E 0 +!E " E 3 Inelastic scattering E 0 E 3 Elastic scattering Detector!t=R/# h.i. R/# l.i. start stop

28 Collecting it all: 4 He( 16 O,α) 16 O 4 He( 16 O,α) 16 O *

29 ToF method was used to identify 14 O(α,α) and 14 O(α,p) channels in recent TTIK experiment. C.Fu, et al., PRC 77 (2008) Texas A&M data

30 Resonances in Atomic Nuclei FSU Physics Department Colloquium, February 2009 Hybrid (thick/thin) target technique E1 E3 CH 2 p HI HR Target is thick enough for HI to lose significant fraction of it s energy. But thin enough for HI recoils to make it out of the target.

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32 7 Be+p resonance scattering experiment target E lr z θ θ t E hr

33 If then If then

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35 Structure of 8 B

36 Naive model of 8 B 3/2-3/2 - = 0 + ; 1 + ; 2 + ; 3 + 3/2-1/2 - = 1 + ; 2 + 1/2-3/2-3/2-1P1/2 1P3/2 1S1/2 Neutrons Protons

37 Structure of 8 B Ab initio calculations Conventional shell model calculations D. Morris & A. Volya P. Navratil et al., PRC 73, (2006)

38 Structure of 8 B 7 Be+p Dominant configuration for the missing states is 7 Be * (1/2 - )+p. Should be observed in inelastic scattering. D. Halderson, PRC 69, (2004) G.V. Rogachev et al., Phys. Rev. C64 (2001) (R)

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40 7 Be+p resonance scattering experiment

41 7 Be+p resonance scattering experiment (1 + ) J. Mitchell, et al., in preparation

42 Previous measurements of 7 Be(p,p ) H. Yamaguchi, et al., PLB (2009) U. Greife, et al., NIM B 261 (2007) 1089

43 Solving inelastic problem by tracking Position sensitive detector Beam Inelastic scattering Elastic scattering Target gas (H 2 ; CH 4 ; He)

44 18 Ne+α experiment Excitation functions of 18 Ne(α,p) 22 Mg(g.s.) 18 Ne(α,p) 22 Mg(2 st ) 18 Ne(α,p) 22 Mg(3 rd ) reactions was measured in this experiment D. Groombridge, et al. PRC 66, (2002)

45 TACTIC at TRIUMF Slide is courtesy of L. Buchmann!

46 ANASEN: LSU-FSU Array for Nuclear Astrophysics Studies with Exotic Nuclei Three rings of 12 Super X3 silicon-strip detectors backed by 2 cm thick CsI! Annular silicon! strip-array! Position sensitive! proportional counters!

47 Monte Carlo simulation of ANASEN performance O(α,p) 17 F(g.s.) 50 Challenging case of 14 O(α,p) reaction PC hit location (AU) O(α,p) 17 F*(0.5 MeV) Lab proton energy (channel) 0

48 Tracking with active target detector MAYA (Developed at! GANIL, now at TRIUMF)! AT-TPC MSU! ACTAR GANIL! SAMURAI TPC - RIKEN!

49 What is the lowest energy / narrowest resonance, which Can be observed using thick target technique? Γ(2 )=4.0+/-2.5 kev Γ~2 kev 4 He( 14 C,α) 1.8 MeV 1 H( 15 O,p) D.W. Lee, et al., PRC 76 (2007) E.D. Johnson, EPJ A, 42 (2009)

50 For the (α,γ),(α,n) reactions on light and medium mass nuclei Transfer reactions can be used to populate resonances below ~0.5 MeV in c.m. ~ MeV direct measurements ~1.5 MeV (α,α) measurements 0 E c.m.

51 Often low energy resonances that are crucial for the specific reaction rate are known, and most of their properties determined, except for Γ α. Lets consider 14 C(α,γ) reaction as an example.

52 C+! At temperatures below 0.3 T 9 14 C(α,γ) reaction rate may be determined by 1 - and 3 - resonances at 6.20 MeV and 6.40 MeV O " + J =0 T=1

53 α transfer reactions ( 6 Li,d) or ( 7 Li,t) can be used to measure S α spectroscopic factor and deduce the partial Γ widths. However, final result depends on: Optical potentials used for entrance and exit channels. Shape of binding potentials for core-α and α-d(t) formfactors. Number of nodes assumed in the core-α wavefunction. Channel radius parameter.

54 13 C( 6 Li,d) 17 O(1/2 + ; MeV) DWBA calculations at 60 MeV Black curve optical potentials from S. Kubono, et al., PRL 90 (2003) ; Red curve deuteron optical potential from T.K. Li, et al., PRC 13 (1975) 55; Blue curve radius of the 13 C+α formfactor decreased by 25%; Yellow curve +1 node in 13 C+α wavefunction.

55 ALL uncertainties can be drastically reduced if: α transfer reaction is performed at sub-coulomb energy. This eliminates dependence of the calculated cross section on optical potentials. ANCs are extracted from experimental data. This eliminates dependence of the final result on the shape of form-factor binding potentials and number of wavefunction nodes. This approach was used by [C.R. Brune, et al., PRL 83 (1999) 4025] in pioneering 12 C( 6 Li,d) α transfer at sub-coulomb energy experiment, in which the contributions from 16 O sub-threshold resonances to the 12 C(α,γ) reaction rate were determined.

56 7 Li 14 C+ 7 Li -> t+ 18 O 3 H 14 C α 18 O

57 χ 7Li_14C ~f(u,v Coulomb ) 7 Li χ 7Li_14C ~ f(v Coulomb ) + o(f(u)) 7 Li χ 7Li_14C ~ f(v Coulomb ) 7 Li 14 C

58 If reaction is performed at sub-coulomb energy then variation of optical potential parameters produce only small variation in the DWBA cross section. 13 C( 6 Li,d) 2.7 MeV in c.m.s. 15 %

59 7 Li 14 C+ 7 Li -> t+ 18 O 3 H 14 C α 18 O

60 ANC approach ab+a -> aa + b Model ab cluster wavefunction Single-particle ab cluster wavefunction Definition of ANC through single-particle ANC X depends only on entrance and exit channel optical potentials

61 In order to avoid influence of optical potentials the reaction has to be sub-coulomb for both entrance and exit channels. Therefore very low energy (< C Sub-Coulomb Energy d,t Array of Silicon Detectors MeV in c.m.) has to be used. 6,7 Li Target d,t Inverse kinematics can be used to provide additional boost for deuterons and eliminate the 12 C Rotating table!e E 7.5 background.

62 Resonance scattering and 5th European Summer School on Experimental Nuclear Astrophysics, September Triton 2d and 1d spectrum from 14C(7Li,t) reactions Counts 60 Counts " s MeV MeV 1 1! E(MeV) tritons deuterons protons 4 6 E(MeV) MeV Group MeV MeV Group E(MeV) E(MeV) MeV 2+ G.S

63 The sub-coulomb 14 C( 7 Li,t) α-transfer C+! O " + J =0 T=1

64 d!/d" (µb/sr) (a) 1 - at MeV from 6 Li( 14 C,d) (C (1-) /Γ(L+1+η)) 2 = 2.6+/ 0.9 fm -1 d!/d" (µb/sr) Angle (deg) 100 (b) 1 - at MeV from 7 Li( 14 C,t) (C (1-) /Γ(L+1+η)) 2 = 3.0+/ 1.0 fm d!/d" (µb/sr) Angle (deg) (c) 3 - at MeV from 7 Li( 14 C,t) Angle (deg)

65 d!/d" (µb/sr) (a) 1 - at MeV from 6 Li( 14 C,d) Angle (deg) 100 (b) 1 - at MeV from 7 Li( 14 C,t) 80 d!/d" (µb/sr) Angle (deg) (c) 3 - at MeV from 7 Li( 14 C,t) d!/d" (µb/sr) Γ α =(7.8+/-2.7)x10-14 ev Angle (deg)

66 S-factor due to sub-threshold resonance A.M. Mukhamedzhanov and R.E. Tribble, PRC 59, 3418 (1999)

67 14 C(α,γ) Reaction Rate (cm 3 /s mol) DC 1 - at MeV Constructive interference of 1 - and DC 3 - at MeV 4 + at 7.12 MeV temperature (T 9 )

68 14 C(α,γ) Reaction Rate (cm 3 /s mol) at MeV, this work 3 - at MeV, from Hashimoto, et al temperature (T 9 )

69 Contribution of the compound nucleus. States with unnatural parity (0 -,1 +,2 -,etc.) cannot be populated in direct alpha transfer reaction, however they are readily populated through compound nucleus.

70 According to Hauser-Feshbach approach:

71 The sub-coulomb 14 C( 7 Li,t) α-transfer C+! O " + J =0 T=1

72 The low temperature (<0.1 T 9 ) 14 C(α,γ) reactions rate is important in three types of astrophysical environments: N(e -,ν e ) 14 C(α,γ) 18 O (NCO chain) trigger of core helium flashes in low mass stars. 2. NCO trigger of helium flashes in helium accreting white Dwarfs. 3. One of the key reaction in nucleosynthesis of 19 F in AGB stars.

73 Reaction Rate (cm 3 /s mol) DC 1 - at MeV Constructive interference of 1 - and DC 3 - at MeV 4 + at 7.12 MeV temperature (T 9 ) Hashimoto, et al., suggested that at high accretion rates (~10 8 M ) the NCO chain triggers helium flash BEFORE triple-alpha reaction, at temperatures ~0.07 T 9. With the new reaction rate NCO chain is much less effective and triggers at about the same temperature as triple-alpha. E.D. Johnson, Submitted to PRC