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 ~ 42 ergs Annual solar output ~ 41 ergs X-ray superbursts thought to be fueled by 12 C + 12 C fusion in the outer crust (3) However, the temperature of the outer crust is too low (~ 3x 6 K) for 12 C fusion (4) (1) Cumming et al., Astrophys. J. Lett. 559, L127 (2001) (2) Strohmayer et al., Astrophys. J. 566, 45 (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 12 C fusion, is the fusion of neutron-rich light nuclei (ex. 24 O + 24 O) (1) If valence neutrons are loosely coupled to the core, then polarization can result and fusion enhancement will occur 16 O Core 16 O Core valence neutrons State of the art TDHF calculations, which follow the collision dynamics, predict a fusion enhancement for neutron-rich system Experimental measurements of the fusion crosssection provide a test of fusion models Umar et al., Phys. Rev. C 85, 055801 (2012) 24 O is currently inaccessible for reaction studies instead study other neutron-rich isotopes of oxygen on 12 C (1) Horowitz et al., Phys. Rev. C 77, 045807 (2008) 2
Evaporation residues Evaporated particles 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 3
Beam Residue Stop time Energy Start time 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%) 18 O beam was provided by the Tandem van de Graaff accelerator at Florida State University 18 O @ E lab = 13.75 36 MeV I Beam ~ 1-4.5x 5 p/s John D. Fox Accelerator Laboratory 4
~ 130 cm ~ 16 cm 18 O BEAM US MCP Detector TGT MCP Detector 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 LCP Det. Array T3 T2 DS MCP Detector 5 Bowman et al., Nucl. Inst. and Meth. 148, 503 (1978) Steinbach et al., Nucl. Inst. and Meth. A 743, 5 (2014)
E (MeV) 35 30 25 20 15 5 18 O + 12 C @ E Lab = 36 MeV E c.m. 18 12 O + C = 14.4 MeV Elastic scattering peak Fusion residues Slit Scattering σ = fusion cross section t = target thickness I = number of incident beam particles N = number of reactions 0 5 15 20 25 30 35 40 TOF (ns) 6 Steinbach et al., PRC 90, 041603(R) (2014)
s (mb) Measured the cross section for E CM ~ 6-14 MeV Measured down to the 2.8 mb level, well below prior measurement of 25 mb 3 Fit data to functional form that describes the penetration of an inverted parabolic barrier: 2 Eyal Low Cross-Section R c = radius of the fusion barrier V = height of the fusion barrier ħω = curvature of the fusion barrier Best fit to experimental data has values: 18 O + 12 C Eyal et al. PRC 13, 1527 (1976) Present Work Fit of Exp Values 6 7 8 9 11 12 13 14 E c.m. (MeV) R c = 7.24 ± 0.16 fm V = 7.62 ± 0.14 MeV ħω = 2.78 ± 0.29 MeV 7 Wong, PRL 31, 766 (1973) Steinbach et al., PRC 90, 041603(R) (2014)
s (mb) 3 / Trend in ratio emphasizes that the experimental and theoretical excitation functions have different shapes s DC-TDHF s Experiment 2 1 1.5 1 0.5 18 O + 12 C Present Work Fit of Exp Values DC-TDHF - No Pairing DC-TDHF - Pairing Coupled Channels 6 7 8 9 11 12 13 14 6 7 8 9 11 12 13 14 E c.m. (MeV) 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 Steinbach et al., PRC 90, 041603(R) (2014) 8
s (mb) 3 2 Measured the fusion cross-section of 18 O + 12 C down to the ~ 650 μb level! 1 Eyal Low Cross-Section 18 O + 12 C 2014 Measurement Fit of 2014 Exp 2015 Measurement DC-TDHF - Pairing New data is consistent with previous measurement Trend of experimental data being above TDHF predictions continues as E cm decreases 5 6 7 8 9 11 12 13 14 E cm (MeV) 9
Extraction of fusion cross-section in sub-barrier domain can be accomplished by direct measurement of evaporation residues using low intensity beams Measured 18 O+ 12 C 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 19 O + 12 C fusion excitation function (May 2015)
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