Three-body decay: the case of 12 C 3α O. S. Kirsebom Bordeaux, June 2011 Department of Physics and Astronomy, Aarhus University, Denmark & TRIUMF, Vancouver, BC, Canada 1 / 37
Disclaimer: proton-free talk 3α breakup of 12 C resonances 2p radioactivity, e.g. 6 Be 2 / 37
General remarks Rich in physics emergence of clusters (α particle) α-α interaction (nuclear as well as electromagnetic) quantum tunnelling (three-body centrifugal and Coulomb barrier) Bose symmetry Experimental method measure distribution of α-particle momenta (complete kinematics advantageous) Challenges sophisticated detector setup complicated data analysis interpretation of data rests on theoretical models 3 / 37
Historical introduction (α clustering and α decay) 4 / 37
Very early days of nuclear physics At that time one was tempted to consider alpha particles as basic building blocks of nuclei. However, from those days a warning from Schrödinger still persists in my mind. During the late twenties he chided the participants in a Berlin seminar for their lack of imagination. In his impulsive manner he said: Just because you see alpha particles coming out of the nucleus, you should not necessarily conclude that inside they exist as such. (J. Hans D. Jensen, Nobel lecture 1963) J. Hans D. Jensen Late 1920s E. Schrödinger 5 / 37
Birth of the α-cluster model Bethe and Bacher (1936), Wefelmeier (1937), Wheeler (1937), and von Weizsäcker (1938) 6 / 37
New understanding The alpha particle loses its identity in the compact nucleus Ikeda, Takigawa, Horiuchi (1968) 7 / 37
α clustering in 12 C 15.96 16.11, 2 + T = 1 15.11, 1 + T = 1 p + 11 B 14.08, 4 + 13.35, 4 12.71, 1 + 1953: Hoyle state (7.65 MeV, 0 + ) predicted and discovered F. Hoyle 11.83, 2 10.84, 1 10.3, 0 + 9.64, 3 1956: Morinaga interpretes Hoyle state as a rotationless linear chain of three α particles and predicts 2 + rotational excitation of the Hoyle state at 9.7 MeV 7.27 7.65, 0 + α + α + α H. Morinaga 4.44, 2 + α! α! α! 0.0, 0 + 12 C 8 / 37
Claims of observation Table: Claims of observation of the 2 + rotational excitation of the Hoyle state Ref. Exp. method E (MeV) Γ (MeV) John et al. (2003) Itoh et al. (2004) Freer et al. (2007) Freer et al. (2009) Hyldegaard et al. (2010) Freer et al. (2011) 12 C(α, α ) 12 C 11.46 0.43 12 C(α, α ) 12 C 9.9 1.0 12 C( 12 C, 3α) 12 C 11.16 12 C(p, p ) 12 C 9.6 0.6 12 B(β ) 12 C and 12 N(β + ) 12 C 11 12 C(α, 3α)α and 9 Be(α, 3α)n 9.4 Inferred from the observation of a possible 4 + state at 13.3 MeV. 9 / 37
α decay and nuclear structure It is remarkable that very little information about nuclear structure could be gained from the study of alpha decay. Max von Laue has pointed this out very clearly in a letter to Gamow in 1926; he congratulated Gamow on his explanation of the Geiger-Nuttal law in terms of the tunneling effect and then went on: however, if the alpha decay is dominated by quantum phenomena in the region outside the nucleus, we obviously cannot learn much about nuclear structure from it. (J. Hans D. Jensen, Nobel lecture 1963) J. Hans D. Jensen G. Gamow M. von Laue 10 / 37
Theoretical models of 12 C 3α 11 / 37
Theoretical models of 12 C 3α sequential democratic/direct three-body (α-cluster model) 12 / 37
Sequential 12.71, 1 + 3.0, 2 + 7.27 0.0, 0 + 12 C 8 Be α + α + α 13 / 37
Sequential Physical ingredients R-matrix parametrization of α-α resonance ( 8 Be 2 +) angular correlations due to spin-parity conservation symmetrization of decay amplitude f = (l m a m b j b m b j am a)y ma m b l (Θ 1, Φ 1)Y m b l (θ 2, φ 2) m b Γ 1Γ 2/ E 1E 23e i(ω l φ l ) e i(ω l φ l ) E 0 γ2 2[S l (E23) S l (E0)] E23 i 1 2 Γ2 D. P. Balamuth et al., Phys. Rev. C 10 (1974) 975 H. O. U. Fynbo et al., Phys. Rev. Lett. 91 (2003) 082502 14 / 37
Democratic/direct five variables {E 1, Ω x, Ω y } expand decay amplitude in hyperspherical harmonics f JM = n B n Φ JM n (E 1, Ω x, Ω y ) hypermomentum K = l x + l y + 2n three-body centrifugal barrier V c.b. (K + 3 2 )(K + 5 2 )/ρ2 ρ = x 2 + y 2 only retain lowest-order term allowed by symmetries expected to work best for low excitation energies A. A. Korsheninnikov, Sov. J. Nucl. Phys. 52 (1990) 827 15 / 37
Three-body (α-cluster model) hyperspherical variables {ρ, α, Ω x, Ω y } expand wave function in hyperspherical harmonics Ω = {α, Ω x, Ω y } Ψ JM = ρ 5/2 n f n (ρ) Φ JM n (ρ, Ω) solve Faddeev equations in coordinate space phenomenological Ali-Bodmer α-α potential three-body short-range potential V 3b (ρ) complex scaling method used to compute resonances x = ρ sin α y = ρ cos α R. Álvarez-Rodríguez et al., Eur. Phys. J. A 31 (2007) 303 and references therein 16 / 37
Experiment 17 / 37
Experimental method and setup 3 He + 10 B p + 3α at 4.9 MeV 3 He + 11 B d + 3α at 8.5 MeV M. Alcorta et al., Nucl. Instr. Meth. A 605 (2009) 318 18 / 37
Excitation spectrum 19 / 37
Dalitz-plot analysis technique 20 / 37
Dalitz plot ε 1 ρ ϕ ε 3 ε 2 21 / 37
Experimental Dalitz plots Experimental Dalitz plots for three selected states 11.83 MeV, 2 12.71 MeV, 1 + 13.35 MeV, 4 max 0 What is the origin of the observed structures? 22 / 37
Symmetries Forbidden regions owing to spin-parity conservation and Bose symmetry C. Zemach, Phys. Rev. 133 (1964) B1201 23 / 37
Sequential bands Bands of increased intensity owing to the 8 Be 2 + resonance 11.83 MeV 12.71 MeV 13.35 MeV 24 / 37
Qualitative analysis 11.83 MeV, 2 12.71 MeV, 1 + 13.35 MeV, 4 25 / 37
Comparison to theory 26 / 37
Quantitave analysis 12.71 MeV, 1 + 12.71 MeV, 1 + Democratic Sequential I 12.71 MeV, 1 + 13.35 MeV, 4 max Three-body Sequential II 0 27 / 37
Quantitave analysis 12.71 MeV, 1 + Democratic Three-body Experiment Sequential I Sequential II Background 3.0 2.0 2.0 dn dρ 1 ρ 1.0 dn dϕ 1.0 0 0 0.2 0.4 0.6 0.8 1.0 ρ 0 0 20 40 60 ϕ (degree) 28 / 37
Quantitave analysis 11.83 MeV, 2 11.83 MeV, 2 Democratic Sequential I 11.83 MeV, 2 12.71 MeV, 1 + 13.35 MeV, 4 max Three-body Sequential II 0 29 / 37
Quantitave analysis 11.83 MeV, 2 Democratic Three-body Experiment Sequential I Sequential II Background 2.0 2.0 dn dρ 1 ρ 1.0 dn dϕ 1.0 0 0 0.2 0.4 0.6 0.8 1.0 ρ 0 0 20 40 60 ϕ (degree) 30 / 37
Broad states 31 / 37
12.25 12.50 MeV 32 / 37
Complications Possible background from 3 He + 11 B 6 Li + 8 Be d + α + α + α owing to broad resonances in 6 Li 33 / 37
Complications Four-body problem? distance separating d and 12 C at time of 3α breakup: x = vτ = v /Γ d 12 C Coulomb energy: x E C = 1.4 Z 1Z 2 x fm MeV if Γ > 0.6 1 MeV, E C /Q > 10% where Q is the 3α breakup energy if Γ = 1 2 MeV, the de Broglie wave length λ = h/p is comparable to x 34 / 37
Conclusion 35 / 37
Summary and conclusion 3α breakup and 2p radioactivity: two examples of three-body decay α momentum distribution sensitive to short-range structure? Complete kinematics measurement and Dalitz-plot analysis Symmetries and final-state interactions ( 8 Be 2 + resonance) Full three-body calculation reproduces the gross structures of the Dalitz distribution, but fails to reproduce the detailed shape (effect of short-range structure?) Outlook: apply similar analysis to very broad states O. S. Kirsebom et al., Phys. Rev. C 81 (2010) 064313 36 / 37
The end Collaboration O. S. Kirsebom 1, M. Alcorta 2, M. J. G. Borge 2, M. Cubero 2, C. Aa. Diget 3, R. Dominguez-Reyes 2, L. M. Fraile 4, B. R. Fulton 3, H. O. U. Fynbo 1, D. Galaviz 2, S. Hyldegaard 1, B. Jonson 5, M. Madurga 2, A. Muñoz Martin 6, T. Nilsson 5, G. Nyman 5, A. Perea 2, K. Riisager 1, O. Tengblad 2 and M. Turrion 2 1 Department of Physics and Astronomy, Aarhus University, Denmark 2 Instituto de Estructura de la Materia, CSIC, Madrid, Spain 3 Department of Physics, University of York, UK 4 PH Department, CERN, Geneva, Switzerland 5 Fundamental Physics, Chalmers University of Technology, Goteborg, Sweden 6 CMAM, Universidad Autonoma de Madrid, Spain 37 / 37