SOTANCP4. Is the Hoyle state condensed? Probing nuclear structure via 3-body decays. University of Birmingham, United Kingdom SOTANCP4.

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1 Is the condensed? Probing nuclear structure via 3-body decays University of Birmingham, United Kingdom 1/29

2 Overview /29

3 Trinity of? 12 C 2/29

4 Cluster description of the 12 C as an equilateral triangle - D 3h symmetry group 5 state measured at 22.4 MeV D.J. Marín-Lámbarri et al. Phys. Rev. Lett. 113, (2014) 3/29

5 Cluster description of the 12 C as an equilateral triangle - D 3h symmetry group measured at 9.8 MeV dilute structure M. Itoh et al. Phys. Rev. C 84, (2011), M. Freer et al. Phys. Rev. C 86, (2012), W. Zimmerman et al. Phys. Rev. Lett. 110, (2013) 3/29

6 Cluster description of the - breathing mode low density 4/29

7 Cluster description of the - breathing mode low density Hoyle rotational band misassigned? 4/29

8 Cluster description of the - breathing mode low density Hoyle rotational band misassigned? Observation of 4 parity doublet member and experimental transition strengths needed 4/29

9 What is an α-condensate (α-gas) state? Bosons/pseudo-bosons - large occupation 0s orbital Fermionic bosonic system N-α particle system 5/29

10 What is an α-condensate (α-gas) state? Bosons/pseudo-bosons - large occupation 0s orbital Fermionic bosonic system N-α particle system N=3: 12 C(0 + 2 ) - A. Tohsaki, H. Horiuchi, P. Schuck, and G. Röpke Phys. Rev. Lett. 87, (2001) Large radius - inelastic electron scattering form factor THSR clustering WF describes data well - no adjustable parameters Y. Funaki et al. Eur. Phys. J. A28 (2006) /29

11 What is an α-condensate (α-gas) state? Bosons/pseudo-bosons - large occupation 0s orbital Fermionic bosonic system N-α particle system N=4: state at 15.1 MeV? [1] al evidence inconclusive [2] 4-α decay limited by Coulomb barrier [3] Channel θw 2 Γ (kev) α α α [1] Y. Funaki, T. Yamada, A. Tohsaki, H. Horiuchi, G. Röpke, and P. Schuck - Phys. Rev. C 82, (2010) [2] K. C. W. Li et al. Phys. Rev. C 95, (2017) [3] Y. Funaki et al., J. Phys. Conf. Ser. 436, (2013) 5/29

12 of condensation If cluster models work so well at describing data, how do we demonstrate the onset of condensation? Potential signatures [1]: [1] Tz. Kokalova et al. Phys. Rev. Lett. 96, (2006) 6/29

13 of condensation If cluster models work so well at describing data, how do we demonstrate the onset of condensation? Potential signatures [1]: Increased radius [1] Tz. Kokalova et al. Phys. Rev. Lett. 96, (2006) 6/29

14 of condensation If cluster models work so well at describing data, how do we demonstrate the onset of condensation? Potential signatures [1]: Increased radius Modification of Coulomb barrier [1] Tz. Kokalova et al. Phys. Rev. Lett. 96, (2006) 6/29

15 of condensation If cluster models work so well at describing data, how do we demonstrate the onset of condensation? Potential signatures [1]: Increased radius Modification of Coulomb barrier 12 C emission from 52 Fe for condensed (solid), cluster (dashed) and g.s. (dotted) [1] Tz. Kokalova et al. Phys. Rev. Lett. 96, (2006) 6/29

16 of condensation If cluster models work so well at describing data, how do we demonstrate the onset of condensation? Potential signatures [1]: Increased radius Modification of Coulomb barrier Decay strengths to other α-gas [1] Tz. Kokalova et al. Phys. Rev. Lett. 96, (2006) 6/29

17 of the direct 3-α BR 3-α BR (%) Year 7/29

18 of the direct 3-α BR 3-α BR (%) Year M. Itoh: < 0.2% direct decay at 95% C.L. 7/29

19 How do we beat this value? 8/29

20 How do we beat this value? Statistics Weeks of beam time and access needed Scales with N counts Factor of 10 improvement 100 times more beam unfeasible by itself 8/29

21 How do we beat this value? Statistics Weeks of beam time and access needed Scales with N counts Factor of 10 improvement 100 times more beam unfeasible by itself Background Preliminary studies: RSDs insufficient - high background Low beam current Several DSSDs giving full event kinematics Misassignment of particles must be avoided 8/29

22 al set-up performed in house at Birmingham MC40 cyclotron Day-time access only - medical isotope producer 9/29

23 al set-up performed in house at Birmingham MC40 cyclotron Day-time access only - medical isotope producer 9/29

24 al set-up performed in house at Birmingham MC40 cyclotron Day-time access only - medical isotope producer 12 C(α, α ) - E b = 40 MeV 4 DSSDs in quad array - measure break-up into 3 α-particles de-e silicon DSSD telescope - measures scattered beam analyzed by R. Smith 9/29

25 Reduction of background al effects that contribute to cleanliness of data: 1 Energy loss of the beam in target thin target µg/cm 2 2 Energy loss of products in target target rotated to minimize travel distance 3 Angular/energy straggling 4 Angular resolution of the detectors more detectors, further away 5 Energy resolution of the detectors calibration every day + MESYTEC pre-amps 6 Pile-up of hits on a single strip DSSDS over RSDs 7 Background due to event mixing 8 Misassignment of hit positions with multiple particles on same detector 10/29

26 Misassignment of hit positions 11/29

27 Event selection de-e telescope can select α-particles 12/29

28 Event selection de-e telescope can select α-particles Multiplicity 3 events in quad array selected (14% efficiency) Separation of data into two sets: 1 All α-particles hit separate detectors (21%) 2 Two α-particles hit one detector, third hits another (73%) 12/29

29 Excitation functions E x from scattered beam and 3 1 well populated at 9.64 MeV 13/29

30 Excitation functions E x from scattered beam 3α E x, Q-value gated and 3 1 well populated at 9.64 MeV Monte Carlo contribution in red with event mixing added to reproduce data (0.03%) 13/29

31 Coup de grâce Final cuts on the x, y and z momenta - quite sensitive type 1 24,000 Hoyle events 14/29

32 Coup de grâce Final cuts on the x, y and z momenta - quite sensitive type 2 69,000 Hoyle events 14/29

33 Dalitz plots Need to separate the two reaction mechanisms 15/29

34 Dalitz plots Need to separate the two reaction mechanisms Understand the phase space 15/29

35 Dalitz plots Need to separate the two reaction mechanisms Understand the phase space Dalitz plot 15/29

36 Dalitz plots Need to separate the two reaction mechanisms Understand the phase space Dalitz plot Relies on looking at the energies of the 3 α-particles in the center of mass ε i = E icm /E tot Taking linear combinations of ε i x = 1 3 (ε 2 ε 1 ) y = 1 3 (2ε 3 ε 2 ε 1 ) 15/29

37 Dalitz plots Sequential decay mode populates red loci 16/29

38 Where do the direct decays lie? Three different models describe the non-sequential contributions: 1 DDΦ 2 DDE 3 DDL 17/29

39 Where do the direct decays lie? Three different models describe the non-sequential contributions: 1 DDΦ Decay into available phase space 2 DDE 3 DDL 17/29

40 Where do the direct decays lie? Three different models describe the non-sequential contributions: 1 DDΦ Decay into available phase space 2 DDE Same energy (smeared by x p) 3 DDL 17/29

41 Where do the direct decays lie? Three different models describe the non-sequential contributions: 1 DDΦ Decay into available phase space 2 DDE Same energy (smeared by x p) 3 DDL Colinear break-up - linear chain structure 17/29

42 MC: DDΦ 2 detectors 3 detectors 18/29

43 MC: DDE 2 detectors 3 detectors 19/29

44 MC: DDL 2 detectors 3 detectors 20/29

45 Penetrabilities 3-body penetrabilities must also be taken into consideration DDΦ distribution - equal energy sharing favored DDP 2 Manifests almost identically as DDE 21/29

46 Dalitz plot - results - hits in 3 different detectors Hoyle decay events - extremely clean 22/29

47 Dalitz plot - results MC sequential decay - hits in 3 different detectors Hoyle decay events - matches well! 22/29

48 Projections Projection of Dalitz plot: α-particles hit 3 detectors 23/29

49 Projections Projection of Dalitz plot: α-particles hit 2 detectors 23/29

50 Branching ratios log-likelihood For each bin i with predicted counts λ i and counts x i : f (x i ; λ i ) = λx e λ x! Log-likelihood therefore: N ln(l(br)) = f (x i ; λ i ) i=1 24/29

51 Branching ratios log-likelihood 24/29

52 Branching ratios Table: Direct decay results BR optimal 95 % C.L % C.L. DDΦ DDE/DDP DDL Taking into account the 3-body penetrability - can set a limit of % Compared to previous experiments (DDΦ) - can set a limit of 0.047% 25/29

53 These results constitute a roughly order of magnitude improvement on previous results Is condensation out of the picture? 26/29

54 These results constitute a roughly order of magnitude improvement on previous results Is condensation out of the picture? From this work: Relative 2-body, 3-body phase space: 0.18% 26/29

55 These results constitute a roughly order of magnitude improvement on previous results Is condensation out of the picture? From this work: Relative 2-body, 3-body phase space: 0.18% Phase space + Coulomb barrier transmission (DDP 2 ): 0.06% 26/29

56 These results constitute a roughly order of magnitude improvement on previous results Is condensation out of the picture? From this work: Relative 2-body, 3-body phase space: 0.18% Phase space + Coulomb barrier transmission (DDP 2 ): 0.06% al DDP 2 limit: < 0.026% 95% C.L. DDP 2 seems incompatible with theory 26/29

57 Theoretical predictions Fadeev 3-body formalism DDE: 0.005%, DDL: 0.03% S. Ishikawa Phys. Rev. C (R) (2014) Semi-classical approach DDE: % H. Zheng et al. Phys. Lett. B (2018) R-matrix model J. Refsgaard et al. - interference of direct and sequential decay Consistent with current results? 27/29

58 Theoretical predictions Fadeev 3-body formalism DDE: 0.005%, DDL: 0.03% S. Ishikawa Phys. Rev. C (R) (2014) Semi-classical approach DDE: % H. Zheng et al. Phys. Lett. B (2018) R-matrix model J. Refsgaard et al. - interference of direct and sequential decay Consistent with current results? DDL easily rejected (<0.0038% 95% C.L.) DDE (<0.026% 95% C.L.) - another order of magnitude needed? DDΦ lower than predicted 0.18% from relative phase space (< 0.047% 95% C.L.) 27/29

59 New experimental results from 93,000 Hoyle decays, order of magnitude improvement on previous limit Consistent with results of D. Dell Aquila et al. Phys. Rev. Lett. 119, (2017) DDP 2 mode incorporating penetrability, prediction above experimental value DDL still conclusively excluded DDE prediction an order of magnitude below current result New experimental technique needed to achieve this? Other observables may offer the smoking-gun signature 28/29

60 29/29