Detailed R-matrix analysis of 7 Li ( p , ) at 441keV Michael Munch, - PowerPoint PPT Presentation

Detailed R-matrix analysis of 7 Li ( p , γ ) at 441keV Michael Munch, Oliver Sølund Kirsebom, Jacobus Andreas Swartz, Karsten Riisager and Hans Otto Uldall Fynbo Department for Physics and Astronomy, Aarhus University May 24 th 2018, NMNP

8 Be 1 + 18.2 1 + 17.6 2 + 16.9 2 + T = 0 + 1 16.6 4 + 11.35 2 + αα cluster 3.03 g.s. 0 + -0.09 8 Be α + α 1

8 Be intruders? 1 + 18.2 1 + 17.6 2 + 16.9 2 + T = 0 + 1 16.6 2 + ∼ 15 Hyldegaard et al. 2010 0 + ∼ 12 4 + 11.35 Caurier et al. 2001 0 + ∼ 6 Barker 1969 2 + αα cluster 3.03 g.s. 0 + -0.09 8 Be α + α S. Hyldegaard. “Beta-decay studies of 8Be and 12C”. PhD thesis. Aarhus University, 2010 E. Caurier et al. Physical Review C 64 (2001), p. 051301 F. C. Barker et al. Australian Journal of Physics 21 (1968), p. 239 2

ab initio -28 + ;2 1 S[422] 0 -32 8 Be Quantum Monte Carlo -36 3 D[431] + ;0+1 3 + ;0+1 calculations by Pastore et al. 1 3 P[431] -40 + ;0+1 2 Energy (MeV) 7 Li+p -44 Includes most transistions. + ;0 1 G[44] 4 -48 Isospin mixing “by hand” -52 + ;0 1 D[44] 2 + ;0 -56 1 S[44] 0 α+α -60 S. Pastore et al. Physical Review C 90 (2014), p. 024321 3

7 Li ( p , γ ) 1 + 17.6 Resonant 17.25 2 + 7 Li + p 16.9 Direct αα 2 + 16.6 γ 2 + 3.03 αα g.s. 0 + -0.092 8 Be α + α 4

Previous measurement of 7 Li ( p , γ ) 8 Be NaI Ge Magnetic spectronometer D. Zahnow et al. Zeitschrift f¨ ur Physik A 351 (1995), pp. 229–236 W. E. Sweeney et al. Physical Review 182 (1969), pp. 1007–1021 5

Problems: ◮ Non-trivial response function ◮ Poor resolution ◮ Limited range ◮ Background ◮ No interference Solution: ◮ Indirect γ -ray spectoscopy 6

Experiment 3 H + beam by 5MV Van de Graaff accelerator ∼ 1nA Two 5x5cm 16x16 Double Sided Silicon Strip Detectors Detection: position, energy and time Coincidences 7

Coincidences 8 1 6 CM Energy difference [MeV] 19 F ( p , α ) 16 O 0 4 Protons − 1 2 16 17 18 6 Li ( p , 3 He ) α 0 7 Li ( p , α ) α 7 Li ( p , γ ) αα − 2 − 4 19 F ( p , α ) 16 O − 6 − 8 0 2 4 6 8 10 12 14 16 18 20 8 Be Excitation energy [MeV] 8

Spectrum Determine widths by integration. 10 3 10 1 10 2 Counts per 100keV 10 0 0 15.9 16.2 16.5 16.8 17.1 10 1 10 0 0 0 2 4 6 8 10 12 14 16 18 Excitation energy [MeV] 9

R-matrix β -decay studies: “interfernce is important for 8 Be”. Sequential decay R-matrix expression. (Expression in appendix) λ α λ ′ 1 λ ′ 2 Initial α ′ λ ′ 3 r ′ λ ′ 4 Compound r ′ Threshold 10

Model 3 Model 1 + 2 + background pole + 0 + intruder 10 3 Model 3 10 2 Counts per 100keV 10 1 10 0 10 − 1 10 − 2 10 − 3 0 3 6 9 12 15 18 Excitation energy [MeV] 0 + 2 + 2 + Total 1 1 3 0 + 2 + 2 + 2 2 4 11

Conclusions Parameter Present Lit. GFMC R-Mat. Γ 0 1 (eV) - 15.0(18) 12.0(3) 13.8(4) Γ 2 1 (eV) 6.0(3) 6.7(13) 3.8(2) 5.01(11) Γ 2 2 (meV) 35(3) 32(3) 29.7(3) 38(2) Γ 2 3 (meV) 2.1(6) 1.3(3) 2.20(5) 1.6(5) Evidence for 0 + at 12 . 0(3) MeV with Γ α = 2 . 4(5) MeV and Γ M 1 = 12(3) eV. Insufficient comparison for “intermediary” region. Needs theoretical spectrum. GFMC discrepancy depends on 1 + isospin mixing. arXiv: 1802.10404 12

Shadowed readout I no no Readout Empty Idle requested? modules Multi event Shadow yes Check event count Empty modules Parse data Release DT Copy data Every n bytes Shadow 13

Shadowed readout II Collaboration with Haakan Johanson (Chalmers) 100 RIO 4 80 Livetime [%] 60 40 20 Shadow (8k) SiCy (170) BLT ( ∞ ) Shadow (8k) SiCy ( ∞ ) MBLT ( ∞ ) Shadow MBLT (8k) 0 0 50 100 150 200 250 300 Trigger request frequency [kHz] 14

Appendix 0: 8 B ( βα ) Counts / 10 keV 4 10 3 10 2 10 10 data Entries 300 1 Mean 1.476e+04 Std Dev 642 − 1 10 14000 14500 15000 15500 16000 16500 17000 E [keV] x 3 2 1 0 − 1 − 2 − 3 14000 14500 15000 15500 16000 16500 17000 Courtesy of Andreas Gad 15

Appendix I: R-matrix expression Proceeding via narrow resonance Γ 0 λ c δ Γ 0 λ ′ c ′ ( E ′ 2 r ′ ) d σ αα ′ ( E ′ 2 r ′ ) = π � c p / 2) 2 , g J λ − E ) 2 + ( � ( E 0 k 2 c p Γ 0 dE ′ 2 a s ℓ s ′ ℓ ′ Density of states: 2 r ′ ) = 2 P c ′ 2 P r ′ 2 � � δ Γ 0 � γ µ r ′ ˜ γ λ c ′ ( ν ) ˜ ˜ A νµ � � λ c ′ ( E ′ 2 π � � νµ γ -ray “penetrability”: P c ′ = E 2 L +1 Observed widths: γ 2 2 P c ′ ˜ � λ c ′ ( λ ′ ) Γ 0 λ ′ δ Γ 0 2 r ′ ) dE ′ λ c ′ ( λ ′ ) = . 2 ≈ λ c ′ ( E ′ dS c γ 2 � 1 + Σ c ˜ � ˜ λ ′ c dE E λ ′ 16

Appendix II: Models 10 3 Model 1 10 2 Counts per 100keV 10 1 10 0 10 3 Model 3 10 − 1 10 2 Counts per 100keV 10 − 2 10 1 10 − 3 10 0 0 3 6 9 12 15 18 Excitation energy [MeV] 10 − 1 10 3 Model 2 10 − 2 10 2 10 − 3 Counts per 100keV 0 3 6 9 12 15 18 10 1 Excitation energy [MeV] 10 0 0 + 2 + 2 + Total 1 1 3 0 + 2 + 2 + 2 2 4 10 − 1 10 − 2 10 − 3 0 3 6 9 12 15 18 Excitation energy [MeV] 17

Appendix III: Numbers Parameter Model 1 Model 2 Model 3 3008 +55 E 2 1 , (keV) 2960(22) 2969(11) − 9 γ 2 1 , M 1 (10 − 11 × eV − 1 ) 3 . 31(3) 3 . 22(6) 3 . 13(3) Γ 0 2 1 , M 1 (eV) 5 . 57(11) 5 . 3(2) 5 . 01(11) γ 2 1 , E 2 (10 − 22 × eV − 3 ) − 4 . 2(12) − 4(500) 0 . 9(592) Γ 0 2 1 , E 2 (meV) 1 . 9(12) < 10 meV < 1 meV √ − 29 . 9 +0 . 3 γ 2 1 ,α 2 ( keV) − 29 . 3(5) 28 . 6(3) − 1 . 5 Γ 0 2 1 ,α 2 (MeV) 1701(27) 1601(45) 1546(25) Parameter Model 1 Model 2 Model 3 E 2 2 (keV) 16 629(11) 16 588(5) 16 590(5) E 0 1 (keV) [0] [0] [0] γ 2 2 , M 1 (10 − 11 × eV − 1 ) 11 . 6(7) 12 . 7(4) 12 . 9(4) γ 0 1 M 1 (10 − 11 × eV − 1 ) 4 . 35(5) 4 . 36(6) [4 . 36] Γ 0 2 2 , M 1 (meV) 27 . 9(17) 38(2) 38(2) Γ 0 0 1 M 1 (eV) 13 . 7(3) 13 . 8(4) [13.8] √ √ γ 2 2 ,α 2 ( keV) [3.1] [3.1] [3.1] γ 0 1 α 0 ( keV) [22.1] [22.1] [22.1] Γ 0 2 2 ,α 2 (keV) [108] [108] [108] Γ 0 0 1 α 0 (eV) [5.57] [5.57] [5.57] E 2 3 (keV) [16922] 16 912(25) 16 910(23) E 0 2 (MeV) - - 12 . 0(3) γ 2 3 , M 1 (10 − 11 × eV − 1 ) 3 . 2 +1 . 7 4 . 3(8) 4 . 5(7) γ 0 2 M 1 (10 − 11 × eV − 1 ) - - 0 . 58(8) − 0 . 9 Γ 0 Γ 0 2 3 , M 1 (meV) 0 . 8(8) 1 . 4(5) 1 . 6(5) 0 2 M 1 (eV) - - 12(3) √ √ γ 2 3 ,α 2 ( keV) [2.2] [2.2] [2.2] γ 0 2 α 0 ( keV) - - − 15 . 2(15) Γ 0 2 3 ,α 2 (keV) [74] [74] [74] Γ 0 0 2 α 0 (MeV) - - 2 . 4(5) E 2 4 (MeV) - 24(3) [24] γ 2 4 , M 1 (10 − 11 × eV − 1 ) - − 1 . 1(2) − 1 . 8(2) Γ 0 2 4 , M 1 (meV) - 57(20) 160(40) √ γ 2 4 ,α 2 ( keV) - 38(7) 35 . 9(18) Γ 0 2 4 ,α 2 (MeV) - 20(8) 18 . 0(18) χ 2 / ndf 878 / 735 838 / 731 808 / 730 P (%) 0.02 0.36 2.3 18

Appendix IV: Resonance scan Yield of 2 α between 2 and 3MeV. 400 300 Yield [1/uC] 200 100 0 430 440 450 460 470 480 Proton energy [keV] 19