Introduction Experimental Setup Analysis Results

Direct Observation of a New 2+ State in 12Cthrough the 12C + γ → 3α Reaction

William Zimmerman

Triangle Universities Nuclear Laboratory

University of Connecticut

Chiral Dynamics 2012

Introduction Experimental Setup Analysis Results

Astrophysics

Triple-α Process:

M. Hjorth-Jensen, Physics 4, 38 (2011)

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Hoyle State

12C0+

0+Hoyle State

7.65

2+4.44

8Be + α7.37

? 2+ ?

Fynbo & Freer, Physics 4, 94 (2011)

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Hoyle State

12C0+

0+Hoyle State

7.65

2+4.44

8Be + α7.37

? 2+ ?

Fynbo & Freer, Physics 4, 94 (2011)

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Hoyle State

12C0+

0+Hoyle State

7.65

2+4.44

8Be + α7.37

? 2+ ?

Fynbo & Freer, Physics 4, 94 (2011)

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Triple-α Reaction Rates

Temperature (109 K)

N2〈σ

v〉(c

m6m

ol-2s-

1)

2 4 6 810-11

10-10

10-9

NACRE

JINA

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

12C(γ,α)8Be

12C0+

3−9.64 MeV

0+10.3 MeV

2+

8Be + α

γ-ray beam will not excite0+ state and will excite 3−

state with very smallprobability.

Measuring α-particleangular distribution givesJπ of state.

Measuring cross sectionover several γ-ray beamenergies gives Γα, Γγ , andEres

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

12C(γ,α)8Be

12C0+

3−9.64 MeV

0+10.3 MeV

2+

8Be + α

γ-ray beam will not excite0+ state and will excite 3−

state with very smallprobability.

Measuring α-particleangular distribution givesJπ of state.

Measuring cross sectionover several γ-ray beamenergies gives Γα, Γγ , andEres

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

12C(γ,α)8Be

12C0+

3−9.64 MeV

0+10.3 MeV

2+

8Be + α

γ-ray beam will not excite0+ state and will excite 3−

state with very smallprobability.

Measuring α-particleangular distribution givesJπ of state.

Measuring cross sectionover several γ-ray beamenergies gives Γα, Γγ , andEres

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

12C(γ,α)8Be

12C0+

3−9.64 MeV

0+10.3 MeV

2+

8Be + α

γ-ray beam will not excite0+ state and will excite 3−

state with very smallprobability.

Measuring α-particleangular distribution givesJπ of state.

Measuring cross sectionover several γ-ray beamenergies gives Γα, Γγ , andEres

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

12C(γ,α)8Be

Measuring 12C(γ, α)8Be requires:

Intense, monoenergetic γ-ray beam

Detector capable of measuring angular distributions ofrecoiling α-particles with little or no background

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

12C(γ,α)8Be

Measuring 12C(γ, α)8Be requires:

Intense, monoenergetic γ-ray beam

Detector capable of measuring angular distributions ofrecoiling α-particles with little or no background

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

12C(γ,α)8Be

Measuring 12C(γ, α)8Be requires:

Intense, monoenergetic γ-ray beam

Detector capable of measuring angular distributions ofrecoiling α-particles with little or no background

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

HIγS Facility

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

HIγS O-TPC

drift chamber

photomultiplier tubes

mirror optics chain

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

HIγS O-TPC

Drift Chamber

cathode grid

anode grid

first avalanche grid

second avalanche grid

quartz window

γ-ray beam

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

HIγS O-TPC

Optics Chain

CCD camera

micro-channel plate

auxiliary lens assembly

electrostatic demagnifier

main lens assembly

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

HIγS O-TPC

drift chamber

photomultiplier tubes

mirror optics chain

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Background Rejection

Spark Cosmic

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Event Identification

12C(γ,α)8Be 16O(γ,α)12C

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Event Identification

12C(γ,α)8Be 16O(γ,α)12C

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Time Projection

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Time Projection

12C(γ,α)8Be

-20 -10 0 100.00

0.05

0.10

0.15

@mmD

16O(γ,α)12C

-50 -40 -30 -20 -10 0 100.00

0.02

0.04

0.06

0.08

0.10

@mmD

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Time Projection

12C(γ,α)8Be

fADC channel [10nsec/channel]900 950 1000 1050 1100 1150 1200 1250

A.U

.

0

50

100

150

200

250

300

16O(γ,α)12C

fADC channel [10nsec/channel]800 900 1000 1100 1200 1300 1400

A.U

.-20

0

20

40

60

80

100

120

140

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Time Projection

fADC channel [10nsec/channel]800 900 1000 1100 1200 1300 1400

A.U

.

-20

0

20

40

60

80

100

120

140fADC channel [10nsec/channel]

900 950 1000 1050 1100 1150 1200 1250

A.U

.

0

50

100

150

200

250

300

16O(γ,α)12C event,fit assuming 16O(γ,α)12C

12C(γ,α)8Be event,fit assuming 12C(γ,α)8Be

fADC channel [10nsec/channel]800 900 1000 1100 1200 1300 1400

A.U

.

-20

0

20

40

60

80

100

120

140fADC channel [10nsec/channel]

900 950 1000 1050 1100 1150 1200 1250

A.U

.

0

50

100

150

200

250

300

16O(γ,α)12C event,fit assuming 12C(γ,α)8Be

12C(γ,α)8Be event,fit assuming 16O(γ,α)12C

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Angular Distributions

θ was calculated for each event from the track image andfrom the time projection.

Angular distributions were fit in terms of |E1|, |E2|, φ12:

W (θ) =3

2sin2 θ

×(

3|E1|2 + 25|E2|2 cos2 θ + 10√

3|E1||E2| cosφ12 cos θ)

Since angular information is available for each event,Unbinned Maximum Likelihood fits were used.

L(|E1|, |E2|, φ12) =n∏i=1

W (θi)

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Angular Distributions

θ was calculated for each event from the track image andfrom the time projection.

Angular distributions were fit in terms of |E1|, |E2|, φ12:

W (θ) =3

2sin2 θ

×(

3|E1|2 + 25|E2|2 cos2 θ + 10√

3|E1||E2| cosφ12 cos θ)

Since angular information is available for each event,Unbinned Maximum Likelihood fits were used.

L(|E1|, |E2|, φ12) =n∏i=1

W (θi)

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Angular Distributions

θ was calculated for each event from the track image andfrom the time projection.

Angular distributions were fit in terms of |E1|, |E2|, φ12:

W (θ) =3

2sin2 θ

×(

3|E1|2 + 25|E2|2 cos2 θ + 10√

3|E1||E2| cosφ12 cos θ)

Since angular information is available for each event,Unbinned Maximum Likelihood fits were used.

L(|E1|, |E2|, φ12) =

n∏i=1

W (θi)

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Angular Distributions

θcm (deg)

Events

/(6

deg)

0 20 40 60 80 100 120 140 160 180

20

40

60

80

100 Eγ = 9.8 MeV

σE2/σ = 96.8 %

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Cross Section

Eγ (MeV)

σ(µ

b)

8 9 10 11 12 13 140

2

4

6

8

E2 cross section

E1 cross section

Fit 2+ resonance

Known 1− resonance

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Cross Section

Eγ (MeV)

σ(µ

b)

8 9 10 11 12 13 140

2

4

6

8

E2 cross section

E1 cross section

Fit 2+ resonance

Known 1− resonance

Eres Γα(res) Γγ0(res) B(E2 : 2+2 → 0+

1 )(MeV) (keV) (meV) (e2fm4)

10.03(11) 800(130) 60(10) 0.73(13)

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Phase

E1-E2 phase difference:

φ12 = δ2 − δ1 + arctan (η/2)

Nuclear phase shifts:

δ` = arctan

(Γ`

2 (Er` −∆` − Ecm)

)− φ`

Hard sphere scattering phase shift:

φ` = arctan

[F`G`

]r=a

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Phase

E1-E2 phase difference:

φ12 = δ2 − δ1 + arctan (η/2)

Nuclear phase shifts:

δ` = arctan

(Γ`

2 (Er` −∆` − Ecm)

)− φ`

Hard sphere scattering phase shift:

φ` = arctan

[F`G`

]r=a

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Phase

Eγ (MeV)

φ12(d

eg)

8 9 10 11 12 13 14

0

40

80

120

φ12 (calculated)

φ12 (measured)

δ1

δ2

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Triple-α Reaction Rates

Temperature (109 K)

N2〈σ

v〉(c

m6m

ol-2s-

1)

2 4 6 810-11

10-10

10-9

NACRE

JINA

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Triple-α Reaction Rates

Temperature (109 K)

N2〈σ

v〉(c

m6m

ol-2s-

1)

2 4 6 810-11

10-10

10-9

NACRE

HIγS

JINA

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Summary

2+2

Eres Γα(res) Γγ0(res) B(E2 : 2+2 → 0+

1 )(MeV) (keV) (meV) (e2fm4)

10.03(11) 800(130) 60(10) 0.73(13)

2+2 in 12C has been directly observed through the

12C + γ → 3α reaction.

Recent ab initio EFT lattice calculations performed byEpelbaum, Krebs, Lahde, Lee, and Meißner predict the 2+

2

2 MeV above the Hoyle State.

Revised triple-α reaction rates can affect nucleosynthesis ofheavy elements during explosive astrophysics scenarios.

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Summary

2+2

Eres Γα(res) Γγ0(res) B(E2 : 2+2 → 0+

1 )(MeV) (keV) (meV) (e2fm4)

HIγS 10.03(11) 800(130) 60(10) 0.73(13)EFT 9.65 2(1)

2+2 in 12C has been directly observed through the

12C + γ → 3α reaction.

Recent ab initio EFT lattice calculations performed byEpelbaum, Krebs, Lahde, Lee, and Meißner predict the 2+

2

2 MeV above the Hoyle State.

Revised triple-α reaction rates can affect nucleosynthesis ofheavy elements during explosive astrophysics scenarios.

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Summary

2+2

Eres Γα(res) Γγ0(res) B(E2 : 2+2 → 0+

1 )(MeV) (keV) (meV) (e2fm4)

HIγS 10.03(11) 800(130) 60(10) 0.73(13)EFT 9.65 2(1)

2+2 in 12C has been directly observed through the

12C + γ → 3α reaction.

Recent ab initio EFT lattice calculations performed byEpelbaum, Krebs, Lahde, Lee, and Meißner predict the 2+

2

2 MeV above the Hoyle State.

Revised triple-α reaction rates can affect nucleosynthesis ofheavy elements during explosive astrophysics scenarios.

William Zimmerman Direct Observation of a New 2+ State in 12C

Introduction Experimental Setup Analysis Results

Acknowledgments

Mohammad Ahmed, Seth Henshaw, Jonathan Mueller,Sean Stave, and Henry Weller

Triangle Universities Nuclear Laboratory

Moshe GaiLaboratory for Nuclear Science at Avery Point

William Zimmerman Direct Observation of a New 2+ State in 12C

Event Identification

(χ2c − χ2

o)/(χ2c + χ2

o)

Events

-1 -0.5 0 0.5 1

10

20

30

40

50

12C(γ,α)8Be 16O(γ,α)12C

William Zimmerman Direct Observation of a New 2+ State in 12C

16O(γ,α)12C

Ecm [MeV]

φ12[deg]

2.2 2.4 2.6 2.8 3.0 3.2

20

30

40

50

60

70

80

90

HIγS

Elastic scattering

William Zimmerman Direct Observation of a New 2+ State in 12C