The evaluation of a new method to extract spectroscopic factors using asymptotic normalization coefficients and the astrophysical 14C(n,γ)15C reaction

rate

Matthew McCleskey

Neutron capture on unstable nuclei• Neutron direct capture reaction cross sections on unstable nuclei are

needed for nuclear astrophysics (BBN, s- and r-processes), stockpile stewardship and for new reactor designs.

• Because no neutron target exists, and many of the nuclei of interest are short-lived indirect methods using inverse kinematics at laboratory energies need to be developed.

• Unlike proton direct capture, which is peripheral and where the cross section can be determined using the ANC, neutron capture is not as simple, may have a significant contribution from the interior – most n-capture is s-wave → Must use SF– some cases may be dominated by p-wave capture → Use ANC

New method

• Need peripheral reaction to determine ANC

• Need non-peripheral reaction to get SF

A new method to extract SFs has been proposed* that utilizes the ANC to fix experimentally the SPANC and thus determine the SF.

*AM Mukhamedzhanov and FM Nunes Phys Rev C 017602 (2005)

15C↔14C+n system is being used as a test case for this method. Will also use the ANC found to calculate the 14C(n,γ)15C reaction rate

New method

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The matrix element can be split into external and internal parts:

One can then define a function

the experimental counterpart of which is

Comparing these two functions experimentally fixes the SPANC therefore giving the correct SF:

13C(14C,15C)12C (peripheral- ANC)

Neutron transfer reaction with 12 MeV/nucleon 14C accelerated by the K500 cyclotron at TAMU Sept. 2007 and May 2009. Reaction products detected using the MDM spectrometer/Oxford detector.

15C→14C + n (peripheral- ANC) Breakup reaction measured at 60 MeV/u at GANIL and MSU C2 = 1.48 ± 0.18 fm-1 (Trache 2002), C2=1.64±.04 fm-1 (Summers 2008)

d(14C,p)15C (peripheral-ANC) (d,p) in inverse kinematics measured at 11.7 MeV/nucleon with TECSA

14C(d,p)15C (peripheral at low E- ANC, at higher E becomes non-peripheral-ANC and Spectroscopic factor)

Experiment performed at TAMU Feb. 2008 and Aug. 2010 with Ed=60MeV from K500, reaction products detected with MDM spectrometer/Oxford detector

Experimental Overview

13C(14C,15C)12C

MDM spectrometer

(D.M. Pringle et al. NIM A245 (1986) pg. 230-247)

Oxford detector

•ionization chamber filled with ~50 torr isobutane•anode plates to measure energy loss•plastic scintillator to measure residual energy•4 resistive wires (avalanche counters) to give position

Particle ID: 14C+13C

15C 14C48Ti/56Fe (imp.)27Al/28Si (imp.)16O (imp.)Elastic g.s.½+ 13C5/2+ / 3/2- 13C2+ 12C (imp.)

Reconstructed target angle

Foc

al p

lane

pos

itio

n∆E

Eres

Foc

al p

lane

pos

itio

n

Reconstructed target angle

½ + 15C (ground state)5/2+ 15C 0.74 MeV2+ 12C and 5/2+ 15C 5.17 MeV

Finding an OMP

V (MeV)

W (MeV)

rv (fm) rw (fm) av (fm) aw (fm) χ2 Jv (MeV fm3)

Rv (fm) Jw (MeV fm3)

Rw (fm)

WS1 77.1 13.32 0.987 1.209 0.703 0.723 3.09 225 4.480 68 5.206

WS2 118.7 14.15 0.927 1.191 0.690 0.739 3.4 292 4.275 69 5.182

WS3 162.4 15.03 0.891 1.169 0.674 0.767 3.59 357 4.132 71 5.169

WS4 203.1 16.04 0.894 1.133 0.627 0.825 3.6 438 4.038 71 5.183

WS5 248.8 16.66 0.885 1.115 0.606 0.848 3.65 516 3.965 72 5.180

• Grid search in V– Use OMP of WS form:

– Fit other 5 parameters for each V, pick several values of V for further fitting

OMP CU V iW V

• Double folding calculation–Semi-microscopic approach–Double folding calculation using JLM effective interaction–Only 2 parameters (normalizations) to fit

Finding an OMP

• Grid search in V– Use OMP of WS form:

– Fit other 5 parameters for each V, pick several values of V for further fitting

OMP CU V iW V

Transfer: 13C(14C,15C)12C

←using OMPs from grid search

←using OMP from double folding

DWBA calculations performed using PTOLEMY, using different potentials

ANC results from HI

SF2s1/2 1/2

22sC (fm-1) SF1d5/2

5/2

21dC x10-3 (fm-1)

WS1-WS1 1.22 2.30 1.13 4.45

WS2-WS2 1.16 2.18 1.02 4.03

WS3-WS3 1.04 1.95 1.13 4.46

WS4-WS4 0.98 1.83 1.20 4.74

WS5-WS5 1.14 2.14 1.25 4.94

DF 1.15 2.16 1.09 4.28

Average 1.12 2.09 1.14 4.48

Uncertainties: 4% target thickness, 3% normalization to the number of incident particles, 5% data extraction and disentanglement from the 1st excited state of 15C, 6% statistical uncertainty and 10%

systematic uncertainty in the calculations. This gives overall uncertainty of 14% for the ANC2

1st excited state had lower statistical uncertainty (~1%) giving an overall uncertainty for that ANC2 of 13%

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d(14C,p)15C

TECSA(Texas A&M-Edinburgh-Catania Silicon Array)

TECSA : d(14C,p)15C

MARS

Radioactive beam from MARS

TECSA target TECSA silicon ring array

Distance to target determines angular range

For 14C beam, no primary (production) target in MARS is used.

TECSA target is CD2 ~250μg/cm2 thick

TECSA: d(14C,p)15C

ADWA calculation using FRESCO with CH89 nucleon potentials(Adiabatic Distorted Wave Approximation)

Results from d(14C,p)15C

22 1/2C =2.01 0.24s

2 31 5/2 (4.06 0.49) 10dC

ANC for ground state: fm-1

Uncertainties: 2% due to target thickness, 2% incident beam normalization, 4% for the analysis and < 2% for statistics. This combined with a 10% systematic uncertainty gives an overall error in C2 of 12%.

ANC for 1st excited state: fm-1

14C(d,p)15C

14C(d,p)15C

• 60 MeV deuteron beam impinges on thin, enriched 14C target

• Higher energy and light projectile means that this reaction is expected to be not peripheral, so we can extract the spectroscopic factor using the previously determined ANC

• Used MDM spectrometer and Oxford detector- Same setup as for HI, but with more gas pressure and a much thicker scintillator to stop protons

• Particle ID in scintillator:Protons

Deuterons

14C(d,p)15C

Position in focal plane (mm)

coun

ts

14C(d,p)15C

Angular distributions and ADWA calculations performed using FRESCO

Rexp vs RDW

Weak dependence indicates a peripheral reaction, so even at 60 MeV deuteron energy we can get the ANC… but no information about the SF

This figure shows an upper limit of r0 of ~1.15

fm, which corresponds to b2 = 4.01∙10-3 fm-1.

From the relation

one obtains a lower limit of SF=1.05

2

2

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Recall:

1st exc. Rexp vs. RthGS Rexp vs. Rth

Summary of the ANC for 15C↔14C+n

22 1/2sC 2

1 5/2dCexperiment

HI transfer 2.09 ± 0.29 (4.48 ± 0.58)∙10-3

TECSA d(14C,p)15C

2.01 ± .24 (4.06±.49) ∙10-3

60 MeV (d,p) 1.76±0.29

Average 1.96±0.16 (4.23±0.38)∙10-3

Summary of the ANC for 15C↔14C+n

(fm-1) (fm-1)

Trache 2002 1.48±0.18

Timofeyuk 2006 1.89±0.11

Pang 2007 2.14

Summers 2008 1.64±0.03

Akram 2011 1.64±0.26 3.55±0.43

This work 1.96±0.16 4.23±0.38

5/2

21dC

1/2

22sC

Astrophysical 14C(n,γ)15C rate

• Important for:– Inhomogeneous BBN– Depletion of CNO isotopes in AGB stars– Effect on seed nuclei for r-process in core-collapse SN

• Dominated by p-wave capture → peripheral reaction, can use ANC• Calculate rate using the code RADCAP

– Include capture to GS and 1st exc state

Black squares are the direct measurement (Reifarth et al. PRC 77 015804 (2009)), blue is calculation using the ANC, red lines show uncertainty in the calculation due to the uncertainty in the ANC

AcknowledgementsCollaborators:

R. Tribble, L. Trache, A. Mukhamedzhanov, F. Carstoiu, A. Alharby, A. Banu, V. Goldberg, Y.-W. Lui, B. Roeder, E. Simmons, A. Spiridon

Special thanks:

N. Nguyen

Work funded by:

NNSA-SSAA, DOE