Pair Spectroscopy of the Hoyle State - Universitetet i...
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Pair Spectroscopy of the Hoyle State
T. Kibédi
Department of Nuclear Physics Australian National University Canberra, Australia [email protected] Bungle Bungles Star Trails | Mike Salway
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
The triple-a rate in stellar He burning
12C
8Be
a
a
a Hans A. Bethe (1906-2005)
1939: No stable A=5 to 8 elements Triple-a process to bypass the gap; PR 55 (1939) 434
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
The triple-a rate in stellar He burning
Edwin E. Salpeter (1924-2008)
12C
8Be
a
a
a Hans A. Bethe (1906-2005)
1939: No stable A=5 to 8 elements Triple-a process to bypass the gap; PR 55 (1939) 434
1952: Carbon production rate calculated; APJ 115 (1952) 326 4He + 4He + 95 keV → 8Be + g (8Be g.s. resonance) 4He + 8Be → 12C + g
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
The triple-a rate in stellar He burning
Edwin E. Salpeter (1924-2008)
Sir Fred Hoyle (1915-2001)
Hans A. Bethe (1906-2005)
1939: No stable A=5 to 8 elements Triple-a process to bypass the gap; PR 55 (1939) 434
1952: Carbon production rate calculated; APJ 115 (1952) 326 4He + 4He + 95 keV → 8Be + g (8Be g.s. resonance) 4He + 8Be → 12C + g
1953: 4He + 8Be + 310 keV→ 12C + g (resonance at 7.68 MeV) PR 92 (1953) 1095
Carbon production
(0.04%)
0+
2+
0+
4.44 MeV
7.65 MeV
E2
E2
E0
Hoyle state
12C
a
a
a
a-decay
(99.96%)
12C
8Be
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
The triple-a rate in stellar He burning
Edwin E. Salpeter (1924-2008)
Sir Fred Hoyle (1915-2001)
The Crafoord Prize 1997 in Astronomy: “for their pioneering contributions to the study of nuclear processes in stars and stellar evolution”
Carbon production
(0.04%)
0+
2+
0+
4.44 MeV
7.65 MeV
E2
E2
E0
Hoyle state
12C
a
a
a
a-decay
(99.96%)
12C
8Be
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
The triple-a rate in stellar He burning
Edwin E. Salpeter (1924-2008)
Sir Fred Hoyle (1915-2001)
Hans A. Bethe (1906-2005)
1939: No stable A=5 to 8 elements Triple-a process to bypass the gap; PR 55 (1939) 434
1952: Carbon production rate calculated; APJ 115 (1952) 326 4He + 4He + 95 keV → 8Be + g (8Be g.s. resonance) 4He + 8Be → 12C + g
1953: 4He + 8Be + 310 keV→ 12C + g (resonance at 7.68 MeV) PR 92 (1953) 1095
1953: The 7.68 MeV state identified from 14N(d,a)12C PR 92 (1953) 649 Noel Dunbar (1922-2011)
Carbon production
(0.04%)
0+
2+
0+
4.44 MeV
7.65 MeV
E2
E2
E0
Hoyle state
12C
a
a
a
a-decay
(99.96%)
12C
8Be
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New experimental results for the triple-a rate
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
Observation of a 16% alpha-decay branch bypassing the ground state of 8Be (T1/2=10
-16 s; Raduta et al. PRL B705 (2011) 65)
New upper limit: 0.1% (Kiresebom et al. PRL 108 (2012) 202501; Manfredi et al. PRC (2012) 037603)
12C
8Be
a
a
a a
a a
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New experimental results for the triple-a rate
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
2+ excitation of the Hoyle state: E=9.75(10) MeV, G=750(150) keV (Freer et al. PRC86 (2012) 034320)
R(2+)=3.07(13) fm, similar to the Hoyle state (Ogloblin et al. Eur. Phys. J. A49 (2013) 46)
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New theoretical results for the triple-a rate
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
Controversy over calculated reaction rates at low (107 K) temperatures
20 order of magnitude difference to NACRE compilation (Ogata et al. Prog. Theor. Phys. 122 (2009) 1055)
New calculated rates are only few order of magnitude larger (Garido et al. Eur. Phys. J. A47 (2011) 102; Nguyen et al. PRL 109 (2012) 141101, PRC 87 (2013) 054615)
HHR - Hyperspherical Harmonic R-matrix method NACRE - Nuclear Astrophysics Compilation of REaction rates CDCC – Continuum Discretized Coupled Channel BW(3B) - three-body Breit Wigner
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New theoretical results for the triple-a rate
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
New ab initio calculations using lattice simulations
effective field theory reproduce excitation energy (Epelbaum et al. PRL 106 (2011) 192501; PRL 109 (2012) 252501)
3-alpha microscopic cluster model (Vasilevsky et al., PRC 85 (2012) 034318)
E, MeV G, keV
Exp Theor Exp Theor
0+ Bound -7.2746 −11.372
Resonance 0.3796 0.684 0.0085(10) 2.78
2+ Bound -2.8357 −8.931
Resonance 3.89 2.775 430(80) 9.95
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Calculation of the triple-a
rC
rad
EcMMQwhere
kTQkTM
Nr
G
GG
2
123
3
32
2/33
3
)3(
)/exp(2
32
aa
aa
a
aa
The rate per unit volume for the triple-a reaction (Rolfs and Rodney, 1988):
)/exp( 33 kTQr rad aa G
Since Grad << Ga ≈ G, where GGaGrad and T ≈ 108 K:
0+ 7.285 MeV
4.439 MeV
Stable 12C
g GGGG CErad
aG
7.654 MeV
0+
2+ EM decay 0.04% E2 E0 a decay 99.96%
a
Hoyle State
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
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)0()0(
)/exp( 33
EE
kTQr
radrad
rad
aa
G
G
G
G
GG
G
Triple-a rate – how well it is known now
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
“traditional approach”
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)0()0(
)/exp( 33
EE
kTQr
radrad
rad
aa
G
G
G
G
GG
G
Triple-a rate – how well it is known now
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
“traditional approach”
Value Unc. [%]
Q3a 379.35(20) keV 0.05
Grad/G 4.13(11)×10-4 2.7 8
G(E0)
/G
6.75(60)×10-6 8.9 4
G(E0) 57(5)×10-6 eV 8.8 8
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)0()0(
)/exp( 33
EE
kTQr
radrad
rad
aa
G
G
G
G
GG
G
Triple-a rate – how well it is known now
3 4 5 6 7 8 9 10 11
x10 [eV]-5
LWM: 5.7(5) x 10 eV-5
NRM: 6.05(16) x 10 eV-5
RT: 6.16(17) x 10 eV-5
BS: 6.11(30) x 10 eV-5
1956 Fregeau
1964 Crannell & Griffy
1965 Gudden & Strehl
1967 Crannell et al.
1968 Strehl & Schucan
1970 Strehl
2005 Crannell et al.
2010 Chernykh et al.
7+1 measurements Data discrepant
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
“traditional approach”
Value Unc. [%]
Q3a 379.35(20) keV 0.05
Grad/G 4.13(11)×10-4 2.7 8
G(E0)
/G
6.75(60)×10-6 8.9 4
G(E0) 57(5)×10-6 eV 8.8 8
2005 Crannell at al: G(E0)=52.0(14) meV; q=0.27-3.04 fm-1; Extensive data from Darmstadt, Bates-CUA, NIKHEF-K & HEPL
2010 Chernykh et al: G(E0)=62.3(20) meV; q=0.21-0.67 fm-1; Darmstadt S-DALINAC
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)0()0(
)/exp( 33
EE
kTQr
radrad
rad
aa
G
G
G
G
GG
G
Triple-a rate – how well it is known now
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
“traditional approach”
Largest known E0 strength!
in “Wilkinson units” Swi,u. = |Mexp|
2 / |Ms.p.|2 =2.3(2) s.p.u.
Value Unc. [%]
Q3a 379.35(20) keV 0.05
Grad/G 4.13(11)×10-4 2.7 8
G(E0)
/G
6.75(60)×10-6 8.9 4
G(E0) 57(5)×10-6 eV 8.8 8
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Value Unc. [%]
Q3a 379.35(20) keV 0.05
Grad/G 4.13(11)×10-4 2.7 8
G(E0)
/G
6.75(60)×10-6 8.9 4
G(E0) 57(5)×10-6 eV 8.8 8
Grad 3.49(45)×10-3 eV 12.9
)0()0(
)/exp( 33
EE
kTQr
radrad
rad
aa
G
G
G
G
GG
G
Triple-a rate – how well it is known now
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
“traditional approach”
Need 5% accuracy
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New approach to determine Grad
)2()0()2()0()2( EEEEE CECErad GGGGGG g
~98.5% ~1.5% ~0.088% ~9×10-6% ~3×10-5%
Observe both EM transitions in the same experiment to determine relative intensities
)0(1
)2(
11
)0(
)2(E
EE
Erad
aG
G
GG
4.439 MeV
Stable 12C
7.654 MeV
0+
2+ EM decay 0.04% E2 E0 a decay 99.96%
a
Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
Measuring electron-positron pairs
e- - e+ particles share the available kinetic energy:
Ekin=E+ + E-=Eg – 2 mºc2 E+
E-
Need to observe both particles
Pair emission rate: function of Z, Eg, E+, and multipolarity; Born approx.
G(E0) ~ r2(E0) × (E0)
E+ ≈ E-
sep 60
K. Robertson, ANU
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
Measuring electron-positron pairs
e- - e+ particles share the available kinetic energy:
Ekin=E+ + E-=Eg – 2 mºc2 E+
E-
Need to observe both particles
Pair emission rate: function of Z, Eg, E+, and multipolarity; Born approx.
a(E2) = G(E2)/Gg(E2)
E+ ≈ E-
sep 30
K. Robertson, ANU
W(E0) ~ r2(E0) × (E0)
W(E2) = Gg(E2) × a(E2)
ICC
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
(E0) experiment vs. theory
(E0) - not accessible from experiment W(E0) ~ r2(E0) × (E0)
K(E0) / (E0) is known for 5 cases only
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
(E0) experiment vs. theory
Angular correlation data for (E0) is rare
S. Devons and G.R. Lindsey Nature (London) 164 (1949) 539
6.05 MeV E0 in 16O
1.70-1.9 MeV E1 in 206Pb
1.77 MeV M1 in 207Pb
1.76 MeV E0 in 90Zr
A.H. Wuosmaa et al. (APEX ANL) PRC 57 (1998) R2794 SOLID LINE: Ch. Hoffmann et al.
PRC 53 (1996) 2313 DASHED LINE: Born Approximation
Born approximation for low Z
and s<80 is sufficient
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
New pair spectrometer
Absorber system & detector
beam
Si(Li) array @350 mm Six detectors of 236 mm2
FWHM ≈ 2.5 keV Semikon GmBh
Absorbers made from HeavyMet (density 18 gr/cm3)
1 mm thick low Z skin (Torr Seal®)
Acceptance angles: 15.9⁰- 46.9 ⁰ Absolute singles efficiency: 0.5%/4
target
Spectrometer response from simulations
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
Old/New Absorber system
Singles data
~100
12C(p,p’) @ 10.5 MeV 2 mg/cm2 target
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
12C(p,p’) @ 10.5 MeV 2 mg/cm2 target
Pairs hitting the same segment
Old/New Absorber system
Singles data
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
New Absorber system
Electrons & Positrons in coincidence
4.439 MeV E2
E ≈𝐸𝛾 − 1.022 𝑀𝑒𝑉
2
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
New Absorber system
Electrons & Positrons in coincidence
4.439 MeV E2
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
New Absorber system
Electrons & Positrons in coincidence
4.439 MeV E2
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
New Absorber system
Electrons & Positrons in coincidence
4.439 MeV E2
Partial energy deposit from annihilation quanta
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
New Absorber system
Electrons & Positrons in coincidence
4.439 MeV E2
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
New Absorber system
Electrons & Positrons in coincidence
4.439 MeV E2
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
54Fe(p,p’g) @ 6.9 MeV
CSS hpGe
Singles electrons
Sum-coincidence pairs
E0
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
54Fe(p,p’g) @ 6.9 MeV
E.K. Warburton and D.E. Alburger,
Phys. Rev. C 6 (1972) 1224
CSS hpGe
Singles electrons
Sum-coincidence pairs
E0
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
54Fe(p,p’g) @ 6.9 MeV
A. Passoja, Z.Phys. A325 (1981) 299
E.K. Warburton and D.E. Alburger,
Phys. Rev. C 6 (1972) 1224
CSS hpGe
Singles electrons
Sum-coincidence pairs
E0
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
12C(p,p`)12C* pair measurements
(Jun-2012)
4.803 A 9.396 A 6.807 A 12.450 A
55 h beam time with 100 nA on a 2 mg/cm2 target “old” Honey detector (1997), 4.2 mm thick, reduced efficiency,
continuous gain shifts TDC gate of +/- 6 ns wide!
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
12C(p,p`)12C* pair measurements
(Jun-2012)
Courtesy of Mitchel de Vries 800 nA on 3.5 mg/cm2
2 NaI detectors
100 nA on 2.0 mg/cm2
6 Si(Li) detectors
E2 E1
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
Conclusion and outlook
Current status New pair spectrometer based on six Si(Li) detectors combined with a
magnetic lens transporter High energy photon background drastically reduced High coincidence efficiency, optimized for E0 and E2: 1:1 vs. 500:1 (Alburger
1977) Less sensitive for correlation and attenuation effects (E+ ~ E-)
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
Conclusion and outlook
Current status New pair spectrometer based on six Si(Li) detectors combined with a
magnetic lens transporter High energy photon background drastically reduced High coincidence efficiency, optimized for E0 and E2: 1:1 vs. 500:1 (Alburger
1977) Less sensitive for correlation and attenuation effects (E+ ~ E-)
Improvements
9 mm thick Si(Li) array: factor 2 higher efficiency for 7.7 MeV pairs
500 nA proton beam intensity: factor 5 higher yield
Challenges Evaluation of pair conversion efficiency accurately for up to 8 MeV transition
energy MC simulations, radiactive source (207Bi, Fermi-Kurie plot, known E0 transitions (Eg > 4 MeV; 10Be : 6.179 MeV; 14C: 6.588 MeV; 16O : 6.049 MeV; 20Ne : 6.725 MeV, 7.191 MeV; 24Mg: 6.433 MeV; 28Si: 4.979 MeV; 48Ca: 4.284 MeV; 54Fe: 4.291 MeV)
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Tibor Kibèdi , Dep. of Nuclear Physics, ANU, Canberra
Acknowledgement
Collaborators A.E. Stuchbery G.D. Dracoulis
ANU technical staff
A. Cooper A. Graton C. Gudu A. Harding J. Heighway A. Muirhead D. Tsifakis T. Tunningley,
ANU Major Equipment Grant
Students B. Alshahrani P. Copp (Univ. of Wisconsin-La Crosse) A. Devlin V. Margerin M. Ng J. Nute R. Pitt S. Rhen K. Robertson C. Robertson A. Then B. Thorman C. B. Vickers M. de Vries A. Wakhle