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

Detailed R-matrix analysis of 7Li(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 24th 2018, NMNP

8Be

• 0.09

α + α g.s. 0+

8Be

3.03 2+ 11.35 4+ 16.6 2+ 16.9 2+ T = 0 + 1 17.6 1+ 18.2 1+ αα cluster

1

8Be intruders?

• 0.09

α + α ∼ 6 0+ Barker 1969 ∼ 15 2+ Hyldegaard et al. 2010 ∼ 12 0+ Caurier et al. 2001 g.s. 0+

8Be

3.03 2+ 11.35 4+ 16.6 2+ 16.9 2+ T = 0 + 1 17.6 1+ 18.2 1+ αα cluster

• 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

Quantum Monte Carlo calculations by Pastore et al. Includes most transistions. Isospin mixing “by hand”

• 60
• 56
• 52
• 48
• 44
• 40
• 36
• 32
• 28

Energy (MeV)

1S[422] 3P[431] 3D[431] 1G[44] 1D[44] 1S[44]

2

+;0 +;0

4

+;0

2

+;0+1

1

+;0+1

3

+;0+1 +;2

α+α

7Li+p

8Be

• S. Pastore et al. Physical Review C 90 (2014), p. 024321

3

7Li(p, γ)

g.s. 0+

8Be

3.03 2+ 16.6 2+ 16.9 2+ 17.6 1+ 17.25

7Li + p

Resonant Direct αα γ αα

• 0.092

α + α

4

Previous measurement of 7Li(p, γ)8Be

NaI Magnetic spectronometer Ge

• 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

3H+ beam by 5MV Van de Graaff accelerator ∼1nA

Two 5x5cm 16x16 Double Sided Silicon Strip Detectors Detection: position, energy and time Coincidences

7

Coincidences

2 4 6 8 10 12 14 16 18 20 8Be Excitation energy [MeV] −8 −6 −4 −2 2 4 6 8

CM Energy difference [MeV]

6Li(p, 3He)α 7Li(p, α)α 19F(p, α)16O 19F(p, α)16O

Protons

7Li(p, γ)αα

16 17 18 −1 1

8

Spectrum

Determine widths by integration.

2 4 6 8 10 12 14 16 18

Excitation energy [MeV]

100 101 102 103

Counts per 100keV

15.9 16.2 16.5 16.8 17.1 100 101

9

R-matrix

β-decay studies: “interfernce is important for 8Be”. Sequential decay R-matrix expression. (Expression in appendix)

λ′

4

Compound λ′

3

λ′

2

λ′

1

λ Initial α α′ r

′

r′ Threshold

10

Model 3

Model 1 + 2+ background pole + 0+ intruder

3 6 9 12 15 18

Excitation energy [MeV]

10−3 10−2 10−1 100 101 102 103

Counts per 100keV Model 3

0+

1

0+

2

2+

1

2+

2

2+

3

2+

4

Total

11

Conclusions

Parameter Present Lit. GFMC R-Mat. Γ01 (eV)

• 15.0(18)

12.0(3) 13.8(4) Γ21 (eV) 6.0(3) 6.7(13) 3.8(2) 5.01(11) Γ22 (meV) 35(3) 32(3) 29.7(3) 38(2) Γ23 (meV) 2.1(6) 1.3(3) 2.20(5) 1.6(5) Evidence for 0+ at 12.0(3) MeV with Γα = 2.4(5) MeV and ΓM1 = 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

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

13

Shadowed readout II

Collaboration with Haakan Johanson (Chalmers)

50 100 150 200 250 300

Trigger request frequency [kHz]

20 40 60 80 100

Livetime [%]

RIO 4

Shadow (8k) Shadow (8k) Shadow MBLT (8k) SiCy (170) SiCy (∞) BLT (∞) MBLT (∞)

14

Appendix 0: 8B(βα)

[keV]

x

E 14000 14500 15000 15500 16000 16500 17000 Counts / 10 keV

1 −

10 1 10

2

10

3

10

4

10

data Entries 300 Mean 1.476e+04 Std Dev 642

14000 14500 15000 15500 16000 16500 17000 3 − 2 − 1 − 1 2 3 Courtesy of Andreas Gad

15

Appendix I: R-matrix expression

Proceeding via narrow resonance dσαα′(E ′

2r′)

dE ′

2

= π k2

a

• sℓs′ℓ′

gJ Γ0

λc δΓ0 λ′c′(E ′ 2r′)

(E 0

λ − E)2 + ( cp Γ0 cp/2)2 ,

Density of states: δΓ0

λc′(E ′

2r′) = 2Pc′2Pr′

2π

• νµ

˜ γλc′(ν)˜ γµr′ ˜ Aνµ

• 2

γ-ray “penetrability”: Pc′ = E 2L+1 Observed widths: Γ0

λc′(λ′) =

• λ′ δΓ0

λc′(E ′

2r′) dE ′

2 ≈

2Pc′˜ γ2

λc′(λ′)

1 + Σc˜ γ2

λ′c dSc dE

• ˜

Eλ′

.

16

Appendix II: Models

3 6 9 12 15 18

Excitation energy [MeV]

10−3 10−2 10−1 100 101 102 103

Counts per 100keV Model 1

3 6 9 12 15 18

Excitation energy [MeV]

10−3 10−2 10−1 100 101 102 103

Counts per 100keV Model 2

3 6 9 12 15 18

Excitation energy [MeV]

10−3 10−2 10−1 100 101 102 103

Counts per 100keV Model 3

0+

1

0+

2

2+

1

2+

2

2+

3

2+

4

Total

17

Appendix III: Numbers

Parameter Model 1 Model 2 Model 3 E01 (keV) [0] [0] [0] γ01M1 (10−11 × eV−1) 4.35(5) 4.36(6) [4.36] Γ0

01M1 (eV)

13.7(3) 13.8(4) [13.8] γ01α0 ( √ keV) [22.1] [22.1] [22.1] Γ0

01α0 (eV)

[5.57] [5.57] [5.57] E02 (MeV)

• 12.0(3)

γ02M1 (10−11 × eV−1)

• 0.58(8)

Γ0

02M1 (eV)

• 12(3)

γ02α0 ( √ keV)

• −15.2(15)

Γ0

02α0 (MeV)

• 2.4(5)

Parameter Model 1 Model 2 Model 3 E21, (keV) 3008+55

−9

2960(22) 2969(11) γ21,M1 (10−11 × eV−1) 3.31(3) 3.22(6) 3.13(3) Γ0

21,M1 (eV)

5.57(11) 5.3(2) 5.01(11) γ21,E2 (10−22 × eV−3) −4.2(12) −4(500) 0.9(592) Γ0

21,E2 (meV)

1.9(12) < 10 meV < 1 meV γ21,α2 ( √ keV) −29.9+0.3

−1.5

−29.3(5) 28.6(3) Γ0

21,α2 (MeV)

1701(27) 1601(45) 1546(25) E22 (keV) 16 629(11) 16 588(5) 16 590(5) γ22,M1 (10−11 × eV−1) 11.6(7) 12.7(4) 12.9(4) Γ0

22,M1 (meV)

27.9(17) 38(2) 38(2) γ22,α2 ( √ keV) [3.1] [3.1] [3.1] Γ0

22,α2 (keV)

[108] [108] [108] E23 (keV) [16922] 16 912(25) 16 910(23) γ23,M1 (10−11 × eV−1) 3.2+1.7

−0.9

4.3(8) 4.5(7) Γ0

23,M1 (meV)

0.8(8) 1.4(5) 1.6(5) γ23,α2 ( √ keV) [2.2] [2.2] [2.2] Γ0

23,α2 (keV)

[74] [74] [74] E24 (MeV)

• 24(3)

[24] γ24,M1 (10−11 × eV−1)

• −1.1(2)

−1.8(2) Γ0

24,M1 (meV)

• 57(20)

160(40) γ24,α2 ( √ keV)

• 38(7)

35.9(18) Γ0

24,α2 (MeV)

• 20(8)

18.0(18) χ2/ndf 878/735 838/731 808/730 P (%) 0.02 0.36 2.3

18

Appendix IV: Resonance scan

Yield of 2α between 2 and 3MeV.

430 440 450 460 470 480

Proton energy [keV]

100 200 300 400

Yield [1/uC] 19