Neutron stars, remnant cores following supernova explosions, are highly interesting astrophysical environments

In particular, accreting neutron stars presents a unique environment for nuclear reactions

Identified as the origin of energetic X-ray superbursts (1,2)

X-ray superburst ~1042 ergs

Annual solar output ~1041 ergs

X-ray superbursts thought to be fueled by 12C + 12C fusion in the outer crust (3)

However, the temperature of the outer crust is too low (~ 3x106 K) for 12C fusion (4)

(1) Cumming et al., Astrophys. J. Lett. 559, L127 (2001) (2) Strohmayer et al., Astrophys. J. 566, 1045 (2002)

(3) Horowitz et al., Phys. Rev. C 77, 045807 (2008) (4) Haensel et al., Neutron Stars 1, 2007

One potential heat source, proposed to heat the crust of neutron stars and allow 12C fusion, is the fusion of neutron-rich light nuclei (ex. 24O + 24O) (1)

If valence neutrons are loosely coupled to the core, then polarization can result and fusion enhancement will occur

16O

Core

16O

Core

valence

neutrons

(1) Horowitz et al., Phys. Rev. C 77, 045807 (2008)

2

State of the art TDHF calculations, which follow the collision dynamics, predict a fusion enhancement for neutron-rich system

Experimental measurements of the fusion cross-section provide a test of fusion models

24O is currently inaccessible for reaction studies – instead study other neutron-rich isotopes of oxygen on 12C

Umar et al., Phys. Rev. C 85, 055801 (2012)

Exited compound nuclei decay by emission of p, n, and α particles – the resulting heavy nuclei are called evaporation residues.

Emission of these evaporated particles kick evaporation residues off of zero degrees, thus allowing direct measurement of evaporation residues

The fusion cross-section can be measured by measuring the number of evaporation residues relative to incident oxygen nuclei

Evaporation residues Evaporated particles

3

Stop time

Energy

Start time

Beam Residue

To distinguish fusion residues from beam particles, one needs to measure:

Energy of the particle (ΔE/E ~ 2%)

Time-of-flight of the particle (Δt/t ~ 7%)

18O beam was provided by the Tandem van de Graaff accelerator at Florida State University

18O @ Elab = 13.75 – 36 MeV IBeam ~ 1 - 4.5x105 p/s

John D. Fox Accelerator Laboratory

4

Time-of-flight of beam measured between US and TGT MCP detector

Elastically scattered beam particles and evaporation residues:

Time-of-flight measured between TGT MCP and Si detectors

Energy measured in annular Si detectors (T2, T3)

DS MCP detector allows random rejection

18O BEAM

US MCP

Detector

TGT MCP

Detector T2

~ 130 cm ~ 16 cm

DS MCP

Detector

T3 LCP Det.

Array

Bowman et al., Nucl. Inst. and Meth. 148, 503 (1978)

Steinbach et al., Nucl. Inst. and Meth. A 743, 5 (2014)

5

TOF (ns)5 10 15 20 25 30 35 40

E (

Me

V)

0

5

10

15

20

25

30

35C

12O +

18

= 14.4 MeVc.m.E

Elastic scattering peak

Slit Scattering

Fusion residues

18O + 12C @ ELab = 36 MeV

σ = fusion cross section

t = target thickness

I = number of incident beam particles

N = number of reactions

Steinbach et al., PRC 90, 041603(R) (2014)

6

(MeV)c.m.E6 7 8 9 10 11 12 13 14

(m

b)

s

10

210

310

Eyal Low Cross-Section

C12O + 18

, 1527 (1976) 13 PRCet al.Eyal

Present Work

Fit of Exp Values

Wong, PRL 31, 766 (1973)

Steinbach et al., PRC 90, 041603(R) (2014)

Measured the cross section for ECM ~ 6-14 MeV

Measured down to the 2.8 mb level, well below prior measurement of 25 mb

Fit data to functional form that describes the penetration of an inverted parabolic barrier:

Best fit to experimental data has values:

Rc = radius of the fusion barrier

V = height of the fusion barrier

ħω = curvature of the fusion barrier

Rc = 7.24 ± 0.16 fm V = 7.62 ± 0.14 MeV ħω = 2.78 ± 0.29 MeV

7

Steinbach et al., PRC 90, 041603(R) (2014)

(MeV)cmE6 7 8 9 10 11 12 13 14

(m

b)

s

1

10

210

310

C12

O + 18

Present Work

Fit of Exp Values

DC-TDHF - No Pairing

DC-TDHF - Pairing

Coupled Channels

(MeV)c.m.E6 7 8 9 10 11 12 13 14

DC

-TD

HF

s /

E

xp

eri

me

nt

s 0.5

1

1.5

Trend in ratio emphasizes that the experimental and theoretical excitation functions have different shapes

Increase in the ratio can be interpreted as a larger tunneling probability

This enhanced tunneling probability can be associated with a narrower barrier

Dramatic increase in experimental cross-section relative to DC-TDHF occurs at energies below 7 MeV

Demonstrates the importance of measuring the sub-barrier fusion cross-section

8

Measured the fusion cross-section of 18O + 12C down to the ~ 650 μb level!

New data is consistent with previous measurement

Trend of experimental data being above TDHF predictions continues as Ecm decreases

(MeV)cmE5 6 7 8 9 10 11 12 13 14

(m

b)

s

1

10

210

310

Eyal Low Cross-Section

C12

O + 18

2014 Measurement

Fit of 2014 Exp

2015 Measurement

DC-TDHF - Pairing

9

Extraction of fusion cross-section in sub-barrier domain can be accomplished by direct measurement of evaporation residues using low intensity beams

Measured 18O+12C fusion cross-section 40 times lower than previous measurements (~ 650 μb level)

Comparison of experimental cross-section with DC-TDHF prediction reveals a difference in the shape of the fusion excitation function (i.e. different barrier)

Rapid increase in the ratio of the experimental to theoretical cross-section demonstrates the importance of measuring the fusion cross-section below the barrier

Ready to measure 19O + 12C fusion excitation function (May 2015)

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Indiana University Nuclear Chemistry: R.T. deSouza, S. Hudan, V. Singh, J. Vadas,

B.B. Wiggins, J. Schmidt

Florida State University: I. Wiedenhover, L. Baby, S. Kuvin

Vanderbilt University:

A.S. Umar, V.E. Oberacker

DOE under Grant No. DEFG02-88ER-40404