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

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

3/2- + 3/2- → 0+,1+,2+,3+

There are other predicted levels which have yet to be observed

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+

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)

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

Li metal

12 MeV protons~ 10 mA

7Li(p,n)7Be

7Be beam production

0.2 Ci

0.12 Ci

2*107 7Be/s

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

Silicon Detector Array

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

5762.64keV

5804.77keV

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

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

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

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

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

Inelastic Scattering • Inelastic locus behaves kinematically like protons – Shape

• Inelastic locus is of correct energy (elastic proton energy less 7Be FES energy) - Separation

ΔE

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

5

10

15

20

0

Ecm (MeV)

Inelastic

cm=124

d/d

(

mb/

sr) 50

150

100

Elastic

cm=128

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

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

. . . .

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