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Structure of 8 B through 7 Be+p scattering.

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### Structure of 8B through 7Be+p scattering

1Jake Livesay, 2DW Bardayan, 2JC Blackmon, 3KY Chae, 4AE Champagne, 5C Deibel, 4RP Fitzgerald, 1U Greife, 6KL Jones, 6MS Johnson, 7RL Kozub, 3Z Ma, 7CD Nesaraja, 6SD Pain, 1F Sarazin, 7JF Shriner Jr., 4DW Stracener, 2MS Smith, 6JS Thomas, 4DW Visser, 5C Wrede

1Colorado School of Mines

2Oak Ridge National Laboratory

3University of Tennessee at Knoxville

4University of North Carolina

5Yale University

6Rutgers University

7Tennessee Tech University

3/10/2014

ORNL Workshop

Outline of Talk

- Motivation
- Previous Measurements
- Making 7Be (TUNL)
- Experimental Setup (HRIBF)
- Normalization
- Preliminary Results
- Future Work

Predicted Positive Parity States

Positive Parity States come from coupling of proton and neutron in p shells

There are other predicted levels which have yet to be observed

3/2- + 3/2- → 0+,1+,2+,3+

Basic shell Model Prediction

7Be ground state is 3/2- due to the unpaired 3/2- neutron – a very proton rich nucleus

p 1/2

7Be+ (l=0) p 3/2 proton is an elastic scattering reaction with expected positive parity states: 0+ ,1+ ,2+ ,3+

p 3/2

7Be+ (l=1) p 1/2 proton is an inelastic scattering reaction with expected positive parity states: 0+ ,1+ ,2+

s 1/2

proton

neutron

7Be(p,p)7Be CRC-Louvain-le-Neuve

C. Angulo et al., NPA 716 (2003)

7Be(p,)8B extrapolationJunghans et al. (2003)

P. Descouvemont, PRC 70 (2004)

7Be+p: a01= 25 9 fm, a02 = -7 3 fm

7Li+n: a01= 0.87 0.07 fm, a02 = -3.63 0.05 fm

- Uncertainty in shape of d/d and 7Be(p,) extrapolation to solar energies dominated by s-wave scattering lengths

~ 5% uncertainty in S17(0)

Previous Measurements of 7Be(p,p)

3+ at 2.32 MeV

- Agrees with literature value for 3+
- Doesn’t locate other positive parity states in region
- Two measurements nearly overlap in energy

2- at 3.5 MeV

1+ at 1.3 MeV – ruled out

Rogachev et al, PRC 2002

7Be(p,p)7Be Setup

7Be and protons

7Be

Thin Target

- 17 bombarding energies
- 100 g/cm2 CH2 target
- Ecm = 0.4 to 3.3 MeV
- θ 1cm=80-128, θ2cm=118-152, θtotal=80 - 152
- Normalization to 7Be+Au scattering and to 7Be+12C

Thick Target

- 14 MeV beam of 7Be
- 4.3 mg/cm2 CH2

Silicon Detector Array

- 16 Strips per detector
- 40 keV energy resolution
- 128 channels of electronics

5804.77keV

5762.64keV

12C(7Be,7Be)12C

Ecm = 2.5 MeV

10

Livesay et al.

SIDAR strip

d/d (mb/sr)

Rutherford

5

1

cm (degrees)

E (MeV)

0

4

8

12

16

20

7Be+Au & 7Be+12C Scattering7Be+p beam current determined by fitting 7Be +12C cross section

12C(7Be,7Be)12C

Ecm = 9.5 MeV

Livesay et al.

(d/dRutherford

DWUCK5

lab (degrees)

50.08

48.94

47.76

46.52

45.22

43.85

42.42

40.92

39.35

37.71

35.99

34.19

32.31

30.35

28.31

26.19

7Be+12C

Protons elastically scattered from 7Be

7Be+p

2.903 6.154

Spectra without Inelastic Peak (7 MeV)Spectra with Inelastic Scattering

Elastic 7Be+p

Elastic 7Be+12C

Inelastic 7Be+p

α

Some background is due to knocked-out C from the target

Thick Target Method

p

7Be

- Energy loss in thin target is much less than excited state energy

Ep = Ebeam –ΔEbeam-ΔEp

p’

7Be

Ep’ = Ebeam –ΔEbeam’-ΔEp’-Eexcited state

Many positions in target can produce equal elastic and inelastic energies

ΔEbeam’- ΔE p’ - Eexc = ΔEbeam - ΔEp

Thick-target excitation function

Thick target good for comparison to previous measurement – but difficult to analyze and not as informative as thin target

1+

Background

7Be+12C

Front of target protons above this energy forbidden by beam energy

Counts/channel

Counts/channel

Ecm (keV)

Inelastic Scattering

- Inelastic locus behaves kinematically like protons – Shape
- Inelastic locus is of correct energy (elastic proton energy less 7Be FES energy) - Separation

Inelastic Prediction

General behavior of inelastic prediction consistent with data

Simultaneous Fit of Elastic and Inelastic

- Fitting must be done simultaneously for many dimensions
- This requires a single set of resonance parameters for whole data set
- Consequence is that total χ2 must be considered

Thin-target data

- Example of p and p` at one angle
- Possible positive parity resonance observed in inelastic channel
- Not the known 3+
- 3+ f-wave in inelastic
- Ecm~ 2.3 MeV
- Possible: J=0+, 1+, 2+
- Accurate absolute normalization should allow accurate determination of scattering lengths
- Resonance is too high in energy to significantly affect S(0), but may explain some of the higher energy behavior

150

Elastic

cm=128

100

50

d/d (mb/sr)

20

Inelastic

cm=124

15

10

5

0

Ecm (MeV)

Minimization versus Grid Search

Minimization versus Grid Searchχ2

χ2

parameteri

parameteri

- Grid Search
- +Allows for arbitrarily precise parameter search
- -Eats up computer time
- Minimization
- -Favors nearest minima (would be plus for well-known landscape)
- +Converges quickly based on local curvature

parameterj

parameterj

Minimization tends toward broad minima – not necessarily the deepest. This is a well known weakness of purely minimizing routines.

Combined Grid-Powell Technique may lift this weakness – but add considerable CPU time

Current Analysis

Grid search gets quickly out of hand

x11 x12 x13 . . x1n

- Multi Calculations being performed with large parameter space – grid search
- Search requires iteration over assignments of Jπ, energies and widths

#calculations = #steps(#parameters)

5steps(12 parameters) ≈ 2.4 106 Calculations

x11 x12 . . . x2n

x11 . . . .

. .

. .

xn1 xn2 xn3 . . . xnn

Future Work

- Determine Resonance Parameters of states in the region of 1 to 4 MeV and sensitivity to each parameter
- Another 7Be(p,p) experiment would help to flesh out the cross section above 3.5 MeV
- Determine scattering lengths from low energy data.

SIDAR Lampshade Configuration

- Increased solid-angle coverage
- Can be configured for ΔE-E telescopes
- Extends angular coverage to more ‘backward’ angles

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