Spin-isospin Modes Implications for Astrophysics. Muhsin N. Harakeh GSI, Darmstadt & KVI, Groningen

Transcription

1 Spin-isospin Modes Implications for Astrophysics & Double-β Decay Muhsin N. Harakeh GSI, Darmstadt & KVI, Groningen International School of Physics Enrico Fermi From the Big Bang to the Nucleosynthesis Varenna (Lake Como), July

2 1. Introduction: Giant resonances 2. Importance of studying GT + in fp-shell nuclei 3. Experimental method 4. Case Study: 58 Ni 5. Measurements on several fp-shell nuclei 6. Measurements on 2β-decaying nuclei 7. Conclusions and outlook 2

3 ISGDR?? 3

4 Microscopic structure of ISGDR Transition operator L= 1 ry 1 r 3 Y 1.. i 0 i 0 i i Ο = + + spurious center of mass motion overtone 3 ħω excitation (overtone of c.o.m. motion) 4

5 Nucleus Many-body system with a finite size Vibrations S=0, T=0 Multipole expansion with r, Y lm, τ, σ S=0, T=1 S=0, T=1 S=1, T=1 S=1, T=1 L=0: Monopole ISGMR IAS IVGMR GTR IVSGMR L=1: Dipole r 2 Y 0 τy 0 τ r 2 Y 0 τ σ Y 0 τ σ r 2 Y 0 ISGDR IVGDR IVSGDR r 3 Y 1 τ ry 1 τσ ry 1 L=2: Quadrupole L=3: Octupole ISGQR r 2 Y 2 LEOR, HEOR r 3 Y 3 IVGQR τ r 2 Y 2 5 IVSGQR τσ r 2 Y 2

6 L=0 L=1 ISGMR ISGDR L=2 L=3 ISGQR ISGOR 6 M. Itoh

7 In fluid mechanics, compressibility is a measure of the relative volume change of a fluid as a response to a pressure change. 1 V β = V P where P is pressure, V is volume. Incompressibility or bulk modulus (K) is a measure of a substance's resistance to uniform compression and can be formally defined: P K = V V 7

8 For the equation of state of symmetric nuclear matter at saturation nuclear density: d( E/ A) = dρ ρ = ρ 0 0 and one can derive the incompressibility of nuclear matter: K nm = 9 ρ ( 2 dρ ρ = ρ 2 2 d ( E / A ) 0 J.P. Blaizot, Phys. Rep. 64 (1980) 171 E/A: binding energy per nucleon ρ : nuclear density : nuclear density at saturation ρ 0 8

9 Equation of state (EOS) of nuclear matter: More complex than for infinite neutral liquids: Neutrons and protons with different interactions Coulomb interaction of protons 1. Governs the collapse and explosion of giant stars (supernovae) 2. Governs formation of neutron stars (mass, radius, crust) 3. Governs collisions of heavy ions. 4. Important ingredient in the study of nuclear properties. 9

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12 Isoscalar Excitation Modes of Nuclei Hydrodynamic models/giant Resonances Coherent vibrations of nucleonic fluids in a nucleus. Compression modes : ISGMR, ISGDR In Constrained and Scaling Models: E ISGMR =ћ K m r A 2 E ISGDR =ћ 27 K + ε 7 A F m r ε F is the Fermi energy and the nucleus incompressibility: K A =[r 2 (d 2 (E/A)/dr 2 )] r =R0 J.P. Blaizot, Phys. Rep. 64 (1980)

13 Giant resonances Macroscopic properties: E x, Γ, %EWSR Isoscalar giant resonances; compression modes ISGMR, ISGDR Incompressibility, symmetry energy K A = K vol + K surf A 1/3 + K sym ((N Z)/A) 2 +K Coul Z 2 A 4/3 13

14 α particle α particle Nucleus, e.g. 208 Pb Inelastic α scattering 14

15 dσ/d dω (mb/sr) Pb(α,α ) E α = 386 MeV E x = 14.5 MeV L=0, T=0 L=1, T=0 L=2, T=0 L=3, T=0 ISGMR, ISGDR ISGQR, HEOR 100 % EWSR At E x = 14.5 MeV θ cm. (degree)

16 Uchida et al., RCNP (α,α α,α ) spectra at 386 MeV 116 Sn ISGDR ISGDR ISGMR ISGMR MDA results for L=0 and L=1 ISGDR ISGDR ISGMR ISGMR

17 From GMR data on 208 Pb and 90 Zr, K = 240 ± 10 MeV [See, e.g., G. Colò et al., Phys. Rev. C 70 (2004) ] This number is consistent with both ISGMR and ISGDR Data and with non-relativistic and relativistic calculations

18 Isoscalar GMR strength distribution in Sn-isotopes obtained by Multipole Decomposition Analysis of singles spectra obtained in A Sn(α,α α ) measurements at incident energy 400 MeV and angles from 0º to 9º

19 K τ = ± 100 MeV

20 Spin-isospin excitations Neutral (ν,ν ν ) and charged (ν e,e ), (ν e,e + ) currents NC Inelastic electron and proton scattering M0, M1, M2 CC Charge-exchange reactions Isovector charge-exchange modes GTR, IVSGMR, IVSGDR, etc. Importance for nuclear astrophysics, ν-physics, 2β-decay, n-skin thickness, etc. (p,n), ( 3 He,t) {GT }; (n,p), (d, 2 He) & (t, 3 He) {GT + } 20

21 Charge-exchange probes (p,n)-type ( T z = -1) (n,p)-type ( T z = +1) β -decay (p,n) ( 3 He,t) heavy ion β + -decay (n,p) (d, 2 He) (t, 3 He) heavy ion; ( 7 Li, 7 Be) Energy per nucleon (>100 MeV/u) Spin-flip versus non-spin-flip Complexity of reaction mechanism Experimental considerations 21

22 Spin-isospin excitations n p L=0 S=1 T=1 GTR Gamow-Teller transitions; Isospin ( T=1) Spin ( S=1) Advantages Cross section peaks at θ ( L=0) Strong excitation of GT states at E/A= MeV/u 22

23 Spin-flip & GT transitions GT T 0 +1 GT T 0 GT T 0-1 GT ( 3 He,t), (p,n) S=1 M1 M1 T 0 +1 T 0 (e,e ), (p,p ) difficult! GT T GT + (n,p), (d, 2 He), (t, 3 He) GS T 0-1 (N-1, Z+1) 0 + GS T 0 (N, Z) 23 GS T 0 +1 (N+1, Z-1)

24 ( 3 He,t) Reaction above 150 MeV/u Energy dependence of effective interactions. 150 MeV/u V 0 part: Minimum. V σt part: Relatively large. V t part: Minimum. ev fm 3 ) V (Me V c τ V c 0 V c στ V c σ E (MeV) 24

25 Why are Gamow-Teller transitions in fp-shell nuclei important? Role of fp-shell nuclei in supernova explosions: Core of supernova star is composed of fp-shell nuclei. electron capture Neutrino absorption cross sections by fp-shell nuclei are essential in understanding of nuclear synthesis in Supernova explosions in cosmos. Difficulties in shell-model calculations for fp-shell nuclei. Importance to measure spin-isospin responses of fp-shell nuclei to gauge theoretical calculations. 25

26 The ( 3 He,t) reaction at 0 degree Cross sections at E( 3 He)=450 MeV, q=0 for ( 3 He,t) reactions dσ µ µ k = + στ dω ( π ) k i f f D 2 D 2 ( ( ) ( )) 2 2 Nτ Jτ B F N Jστ B GT h i T. N. Taddeucci et al., Nucl. Phys. A469, 125 (1987) I. Bergqvist et al., Nucl. Phys. A469, 648 (1987) Neutrino absorption cross sections Importance of charge-exchange reactions at intermediate energies 26 26

27 Measuring GT strengths dσ dω ( q = 0) = KN D J στ 2 B( GT ) kinematic factor distortion factor Gamow-Teller strength nucleon-nucleus interaction Calibration of B(GT) to cross section for known transitions (e.g. from β-decay) 27 27

28 M. Fujiwara et al. PRL 85 (2000) E x (MeV) (p,n) ( 3 He,t) B(GT) 0.32± ± ±

29 Beam line WS-course Grand-Raiden Spectrometer T. Wakasa et al., NIM A482 ( 02) 79. High-dispersive WS-course 29 RCNP Ring Cyclotron 29

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31 Decomposition of the isospin component of the excited state in 58 Cu Isospin of 58 Ni g.s. : T 0 =1 In principle, comparison among (n,p), (p,p), (p,n) spectra Separates isospin components But, very difficult in practice because of high level density for T=1 and T=2 states. CG σ T=0 :σ T=1 :σ T=2 = 2:3:1 (T 0 =1) 31 31

32 Comparison of ( 3 He,t) and (e,e ) spectra Comparison of ( 3 He,t) with (e,e ) spectra Try to separate isospin σ(t=1):σ(t=2) components At E x = 6-10 MeV (T=1 region) = 1 : 1 Rather good correspondence At E x =10-15 MeV (T=2 region) No good correspondence σ(t=1):σ(t=2) = 3 : 1 Fujita et al., Phys. Lett. B 365, 29 (1996). Fujita et al., Eur. Phys. J A13, 411 (2002)

33 (p, n) spectra for Fe and Ni Isotopes 33 Rapaport & Sugarbaker Rev. Mod. Phys. ( 94) 33

34 26 Mg(p,n) 26 Al & 26 Mg( 3 He,t) 26 Al spectra R. Madey et al., PRC 35 ( 87) 2001 IAS, 0 + Y. Fujita et al., PRC 67 ( 03) Prominent states are GT states and the IAS! 34 34

35 54 Fe(p,n) & 54 Fe( 3 He,t) B(GT) 0.74(5) 54 Fe(p, n) 54 Co B.D. Anderson et al., PRC B(GT) 0.50(6) 35 35

36 Determination of GT + Strength and its Astrophysical Implications 36 36

37 Nuclear processes and energy household of supernovae 37

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41 Determination of GT Strength is imperative Courtesy of D. Frekers 41

42 Electron capture in fp-shell In supernova explosions, electron capture (EC) on fp-shell nuclei plays a dominant role during the last few days of a heavy star [presupernova stage; deleptonization core collapse subsequent type IIa Supernova (SN) explosion] Bethe et al. (1979) The rate for EC is governed by the GT + strength distribution at low excitation energy; not accessible to β-decay. Fuller, Fowler and Newman (FFN) ( ); estimates of stellar rates in stellar environments using s.p. model. Caurier et al., Martínez-Pinedo & Langanke (1999), Otsuka et al. Large shell-model calculations marked deviations from FFN EC rate; generally smaller EC rates. Experiments and theory relied on (n,p) data (TRIUMF) which have a rather poor energy resolution. 42

43 fp-shell nuclei: large scale shell model calculations E. Caurier et al. NPA 653 (1999) 439 Stellar weak reaction rates with improved reliability Large scale shell model (SM) calculations Tuned to reproduce GT + strength measured in (n,p) (n,p) data from TRIUMF GT + strength from SM Folded with energy resolution Case study: 58 Ni 43

44 Exclusive excitations S= T=1: (d, 2 He) 2 He p p A, Z d A, Z-1 3 S 1 deuteron 1 S 0 di-proton ( 2 He) 1 S 0 dominates if (relative) 2-proton kinetic energy ε < 1 MeV (n,p)-type probe with exclusive S=1 character (GT + transitions) But near 0 : tremendous background from d-breakup 44

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46 KVI Big-Bite Spectrometer (BBS) in coincidence with EDEN (neutrons) SiLi ball (protons) 46

47 M. Hagemann et al., NIM A437 (1999) 459 V.M. Hannen et al., NIM A500 (2003) 68 Setup: ESN detector Focal-Plane Detector: (FPDS): 2 VDCs Focal-Plane Polarimeter: (FPP): 4 MWPCs & graphite analyzer features a.o.: fast readout VDC readout pipeline TDC s VDC decoding using imaging techniques DSP based online analysis Bari, Darmstadt, Gent, Iserlohn, KVI, Milano, Münster, TRIUMF 47

48 Good double tracking Use VDC information Good phase-space coverage for small relative proton energies S. Rakers et al., NIM A481 (2002) 253 phase space limited by dω and p/p measured 48

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50 Exclusive measurement of S= T =1 strength: 12 C(d, 2 He) 12 B E d = 171 MeV, θ = 0 1/10 Shell-model calculations 4 ħω & 6 ħω (G. Martínez-Pinedo) B (GT + ) (S. Rakers) 50

51 (p,n) vs (d, 2 He): Calibration Self-conjugate 24 Mg S. Rakers et al. PRC 65 (2002)

52 Experimental cross section and GT strength Bexp(GT+) = 1 dσ (q = 0) dω dσ (GT ) dω unit cross section extrapolated (DWBA) 52

53 GT Strength in 12 B and 24 Na from (d, 2 He) reaction Target Reference data Present data E x B(GT - ) E x dσ/dω(q=0) σ(l=0)/σ(τοτ) σ(τοτ) B(GT + ) [MeV] [MeV] [mb/sr] (q=0) (C=0.267) 12 B ± ± ± ± Na ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

54 (d, 2 He) as GT + probe in fp-shell nuclei 58 Ni(d, 2 He) 58 Co E=85A MeV 58 Ni(n,p) 58 Co E=198 MeV M. Hagemann et al. PLB 579 (2004)

55 GT Strength in 58 Co from (d, 2 He) reaction E x dσ/dσ(0.5 ) σ(l=0)/σ(τοτ) B(GT+) [MeV] [mb/sr] ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

56 GT + strength: comparison (n,p), (d, 2 He) & theory Up to 4 MeV excitation: 13 GT transitions measured (d, 2 He) Strength rebinned in 1 MeV bins Significant differences Pinedo/Langanke Caurier et al.. Updated shell model calculations by Martínez-Pinedo/Langanke

57 Electron capture rate 2 ( Q ω ) F ( Z, ) λ B ( GT ) ω p ω S ( ω, T ) dω ec i + i i ω l With B i (GT) Gamow-Teller strength distribution ω and p energy and momentum of electrons S e (ω,t) Fermi-Dirac distribution electron gas at temperature T 57 e

58 e - -capture rates using experimental strengths (Martínez-Pinedo, Langanke) T 9 = 2.26 ρ = g/cm 3 Y e = 0.48 Evolution of core of 25 M ס star. Conditions following silicon depletion. T 9 = 4.05 ρ = g/cm 3 Y e = 0.48 [Heger et al., Astrophys. J. 560 (2001) 307] T 9 Calculate EC rates as function of T 9 for GT transitions from 58 Ni g.s. Strength deviations at low excitation rates deviation at low T 58

59 58 Ni: comparison of e-capture rates theory/experiment λ d, 2 ec / λ ec (d He) T 9 (n,p) 198 MeV Pinedo, Langanke Caurier et al. FFN Influence of GT strength distribution on calculated capture rate is dramatic, especially at low temperatures rates vary up to a factor 5-6 FFN not too far off large scale shell-model calculations fail at low T calculations with improved residual interaction in reasonable agreement 59

60 51 V(d, 2 He) 51 Ti: B(GT + ) for proton-odd fp-shell nucleus 51 V g.s. (J π =7/2, T=5/2) 51 Ti (J π =5/2, 7/2, 9/2, T=7/2) Independent single-particle model (FFN): E x (GTR)=3.83 MeV C. Bäumer et al., PRC 68, (R) (2003) 60

61 C. Bäumer et al., PRC 68, (R) (2003) 61 i i

62 51 V(d, 2 He): Angular distributions of dσ/dω 62

63 51 V(d, 2 He): Comparison with shell-model calculations Experimental result Full fp-shell model calculations quenching factor (0.74) 2 G. Martínez-Pinedo, K. Langanke 63

64 50 V(d, 2 He): GT + transitions from odd-odd nucleus 50 V GT + 50 Ti J π =6 + J π =5 +, 6 +, 7 + T=2 T=3 GT-centroid located at ~ 9 MeV 64

65 56 Fe(d, 2 He): Comparison with shell-model calculations Experiment 65 Full fp-shell model calculations (KB3G) (G. Martínez-Pinedo)

66 61 Ni(d, 2 He) 61 Co: GT + distribution 57 Fe(d, 2 He) 57 Mn: GT + distribution 66 66

67 67 Zn(d, 2 He) 67 Cu: GT + distribution No shell-model calculations yet 67 67

68 GT + centroid comparison

69 WW = Woosley-Weaver Model calculations (FFN rates) LMP = Langanke-Martínez-Pinedo Large shell-model calculations {G. Martínez-Pinedo et al., NPA 777 (2006) 395} 69

70 Y e = Central electron-to-baryon ratio 70

71 Conclusions Presupernova models depend sensitively on EC rates. GT + transitions in fp-shell nuclei play a decisive role in determining EC rates and thus provide input into modeling of explosion dynamics of massive stars. Large shell-model calculations are needed especially as function of T. (Caurier et al.; Martínez-Pinedo & Langanke [KB3G]; Otsuka et al. [GXPF]) smaller EC rates for A=45-60 than FFN Larger Y e (electron to baryon ratio) and smaller iron core mass (Heger et al.) New high resolution (d, 2 He) experiments provide essential tests for shell model calculations at 0 T. 71

72 ββ decay 2νββ decay Allowed in SM and observed in many cases Accessible through chargeexchange reactions in (n,p) and (p,n) direction [e.g. (d, 2 He) or ( 3 He,t)]

73 Forbidden in MSM Lepton number violated Neutrino enters as virtual particle, q~0.5fm Mass of Majorana neutrino!!

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79 96Mo

80 In (p,n) direction: 1 - exceptionally small B(GT ) below 6 MeV 2 - concentrated in one low-lying level only

81 (d, 2 He) ( 3 He,t) E x (MeV) B(GT + ) = 0.3 B(GT ) = 0.15 T With this 1 level only (2 νββ ) = (2.4 ± 0.3) 10 years calc. 19 1/2 T (2 νββ = (2.2 ± 0.4) 10 years (NEMO3-result) exp. 19 1/2

82 Conclusions Charge-exchange reactions provide important input for 2νββ decay ME; i.e. (d, 2 He) (t, 3 He) for GT + leg and ( 3 He,t) for the GT leg 96 Zr and 100 Mo exhibit Single-State-Dominance (at 0.69 MeV ( 96 Zr) and g.s. ( 100 Mo)) 82

83 Outlook Radioactive ion beams will be available at energies where it will be possible to study GT transitions (RIKEN, NSCL, FAIR, EURISOL) Determine GT ± strength in unstable sd & fp shell nuclei Electron capture rates (presupernova) and neutrino capture rates and inelastic scattering cross sections Use IV(S)GDR as tool to determine n-skin Charge-exchange cross section proportional to n-skin Exotic excitations such as Double GT 83

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85 Nuclear structure studies with CE (d, 2 He) reactions in inverse kinematics - Possible at FAIR and RIKEN (intermediate beam energies are needed!) p Approach (at FAIR): measure the recoiling protons heavy projectile Courtesy Lucia-Ana Popescu d-target p recoiling protons heavy ejectile Inconvenience: difficulty to detect the lowenergy protons 85

86 How low? kinematic calculations E( 2 He) [M MeV] Example: 2 H( 64 Ni, 64 Co) 2 He E( 64 Ni) = 350MeV/u θ c.m. [deg] 86

87 How low? kinematic calculations E( 2 He) [M MeV] Example: 2 H( 64 Ni, 64 Co) 2 He E( 64 Ni) = 350MeV/u region of interest low-energy protons! θ c.m. [deg] 87

88 Detection FAIR Use of EXL recoil detector is under evaluation Design & implementation of a dipole magnet for the momentum analysis of the protons 88

89 EuroSuperNova Collaboration C. Bäumer 1, R. Bassini 2, A.M. van den Berg 3, N. Blasi 2, B. Davids 3, D. De Frenne 4, R. De Leo 5, D. Frekers 1, E.-W. Grewe 1, P. Haefner 1, M. Hagemann 4, V.M. Hannen 3, M.N. Harakeh 3, J. Heyse 4, F. Hofmann 6, M. Hunyadi 3, M. de Huu 3, E. Jacobs 4, B.C. Junk 1, A. Korff 1, K. Langanke 7, A. Negret 4, P. von Neuman-Cosel 6, L. Popescu 4, S. Rakers 1, A. Richter 6, H. Sohlbach 8, H.J. Wörtche 3 1 Westfälische Wilhelms-Universität, Münster 2 INFN, Milan 3 Kernfysisch Versneller Instituut Groningen 4 University Gent 5 University Bari 6 Technische Universität Darmstadt 7 University Aarhus 8 Märkische Fachhochschule Iserlohn 89

90 Zero-degree spectrum only one 1 + state visible Finite-degree spectrum ( ) Θ ~ 2 cm 90 2 states quickly become visible