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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
ORNL Workshop
1Colorado School of Mines2Oak Ridge National Laboratory3University of Tennessee at Knoxville4University of North Carolina5Yale University6Rutgers University7Tennessee Tech University
04/19/23
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Outline of Talk
• Motivation• Previous Measurements• Making 7Be (TUNL)• Experimental Setup
(HRIBF)• Normalization• Preliminary Results• Future Work
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Predicted Positive Parity States
Positive Parity States come from coupling of proton and neutron in p shells
3/2- + 3/2- → 0+,1+,2+,3+
There are other predicted levels which have yet to be observed
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Basic shell Model Prediction
7Be ground state is 3/2- due to the unpaired 3/2-
neutron – a very proton rich nucleus
proton neutron
s 1/2
p 3/2
p 1/2
7Be+ (l=0) p 3/2 proton is an elastic scattering reaction with expected positive parity states: 0+ ,1+ ,2+ ,3+ 7Be+ (l=1) p 1/2 proton is an inelastic scattering reaction with expected positive parity states: 0+ ,1+ ,2+
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7Be(p,)8B extrapolation
• Uncertainty in shape of d/d and 7Be(p,) extrapolation to solar energies dominated by s-wave scattering lengths
P. Descouvemont, PRC 70 (2004)
7Be+p: a01= 25 9 fm, a02 = -7 3 fm7Li+n: a01= 0.87 0.07 fm, a02 = -3.63
0.05 fm
Junghans et al. (2003)
C. Angulo et al., NPA 716 (2003)
7Be(p,p)7Be CRC-Louvain-le-Neuve
~ 5% uncertainty in S17(0)
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Previous Measurements of 7Be(p,p)
2- at 3.5 MeV
Rogachev et al, PRC 2002
•Agrees with literature value for 3+
•Doesn’t locate other positive parity states in region
•Two measurements nearly overlap in energy
3+ at 2.32 MeV
1+ at 1.3 MeV – ruled out
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Li metal
12 MeV protons~ 10 mA
7Li(p,n)7Be
7Be beam production
0.2 Ci
0.12 Ci
2*107 7Be/s
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Thick Target
• 14 MeV beam of 7Be
• 4.3 mg/cm2 CH2
7Be(p,p)7Be Setup
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
7Be and protons
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Silicon Detector Array
•16 Strips per detector•40 keV energy resolution•128 channels of electronics
5762.64keV
5804.77keV
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cm (degrees)
d/
d
(m
b/s
r)
12C(7Be,7Be)12C
Ecm = 2.5 MeV
Rutherford
Livesay et al.
DWUCK5
Livesay et al.
0 4 12 20168
10
1
15
5
E (MeV)
SID
AR
str
ip7Be+Au & 7Be+12C Scattering
(d/
d
Ru
therf
ord
lab (degrees)
12C(7Be,7Be)12C
Ecm = 9.5 MeV
7Be+p beam current
determined by fitting 7Be +12C
cross section
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Spectra without Inelastic Peak (7 MeV)
Protons elastically scattered from 7Be
7Be scattered from 12C
7Be+12C
7Be+p
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
2.903 6.154
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Spectra with Inelastic Scattering
Elastic 7Be+p
Inelastic 7Be+p
α
Elastic 7Be+12C
Some background is due to knocked-out C from the target
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Thick Target Method
7Be
p
Ep = Ebeam –ΔEbeam-ΔEp
7Be
p’
Ep’ = Ebeam –ΔEbeam’-ΔEp’-Eexcited state
ΔEbeam’- ΔE p’ - Eexc = ΔEbeam - ΔEp
Many positions in target can produce equal elastic and inelastic energies
•Energy loss in thin target is much less than excited state energy
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Ecm (keV)
Thick-target excitation Thick-target excitation functionfunction
Cou
nts/
chan
nel
1+
Front of target protons above
this energy forbidden by beam energy
Background
7Be+12C
Thick target good for comparison to previous measurement – but difficult to analyze and not as informative as thin target
Cou
nts
/ch
an
nel
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Inelastic Scattering • Inelastic locus behaves kinematically like protons – Shape
• Inelastic locus is of correct energy (elastic proton energy less 7Be FES energy) - Separation
ΔE
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Inelastic Prediction
General behavior of inelastic prediction consistent with data
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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
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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
5
10
15
20
0
Ecm (MeV)
Inelastic
cm=124
d/d
(
mb/
sr) 50
150
100
Elastic
cm=128
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Minimization versus Grid Search
• Grid Search
1. +Allows for arbitrarily precise parameter search
2. -Eats up computer time
• Minimization
1. -Favors nearest minima (would be plus for well-known landscape)
2. +Converges quickly based on local curvature
χ2
parameteri
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
Minimization versus Grid Search
χ2
parameteri
parameterj
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Current Analysis
• Multi Calculations being performed with large parameter space – grid search
• Search requires iteration over assignments of Jπ, energies and widths
Grid search gets quickly out of hand
76
76.5
77
77.5
78
78.5
79
79.5
80
5500 6000 6500 7000 7500 8000 8500
#calculations = #steps(#parameters)
5steps(12 parameters) ≈ 2.4 106 Calculations
x11 x12 x13 . . x1nx11 x12 . . . x2nx11 . . . .
xn1 xn2 xn3 . . . xnn
. . . .
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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.
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SIDAR Lampshade Configuration
•Increased solid-angle coverage
•Can be configured for ΔE-E telescopes
•Extends angular coverage to more ‘backward’ angles