1. The difference a few neutrons makes in the fusion of light Nuclei: Structure and Dynamics
Indiana University: T. Steinbach,V. Singh, J. Vadas, B. Wiggins, S. Hudan, RdS
Florida State: I. Wiedenhover, L.T. Baby, S.A. Kuvin, V. Tripathi
Theoretical support: Z. Lin (IU), C.J. Horowitz (IU), S. Umar (Vanderbilt)
Motivation: understand the character of neutron-rich nuclear matter
Understanding neutron-rich matter is important for a broad range of phenomena:
Nucleosynthetic r-process
Neutron-star crusts (X-ray superbursts)
Neutron star mergers
One laboratory to investigate the character of neutron-rich matter is the skin of neutron-rich nuclei
Gain insight into neutron skin by investigating fusion for an isotopic chain of neutron-rich nuclei (interplay of nuclear structure and dynamics)
This work was supported by the U.S. DOE Office of Science under Grant No. DEFG02-88ER-40404

2. Neutron-rich light nuclei allow investigation of fusion near the neutron drip-line
24O + 24O or 28Ne + 28Ne originally proposed as trigger for X-ray superburst.
Most of the extended tail of the neutron density distribution for 24O is achieved with 22O !
Z. Lin and C.J. Horowitz
16O Core
valence neutrons
Neck
Damped density oscillations
Surface waves …
If valence neutrons are loosely coupled to the core, then polarization can result and fusion enhancement will occur.
S. Umar

3. Density constrained TDHF (DC-TDHF)
Once Skyrme interaction is fixed for ground state nuclei, fusion cross-section is parameter free and reproduces measured light nuclei cross-section.
Enhancement of the fusion cross-section at and below the barrier related to neutron transfer for n-rich systems and dynamical effects.
Our starting point: DC-TDHF provides a good description of the fusion excitation function for 16O + 12C and predicts a substantial enhancement for 24O + 12C
R.T. deSouza, et al Phys. Rev. C (2013)
Horowitz et al., Phys. Rev. C 77, (2008)
Umar et al., Phys. Rev. C 85, (2012)

4. Goal Challenges Approach
Develop a technique capable of directly measuring the fusion cross-section with a low intensity (103 – 106 ions/s) radioactive beam at near barrier energies (E/A = 1-3 MeV/A). Measure the dependence of the fusion cross-section on Ecm (fusion excitation function)
Goal
Challenges
Separating the fusion products from beam (1 part in 107 – 108 at the lowest energy)
Low energy of the fusion products
Experimental setup needs to be compact and transportable to make use of different RIB facilities worldwide
Approach
Develop a highly efficient setup to compensate for the low beam intensity.
Demonstrate technique by measuring a well known fusion excitation function : 18O + 12C
Apply technique to the measurement of more neutron-rich systems : 19,20,21O + 12C (22O?)

5. Measuring σfusion using low-intensity beams
Direct detection of evaporation residues (ERs)
Target
Beam
Evap. Residue
Evaporation residues
Evaporated particles
Emission of evaporated particles kicks evaporation residues away from zero degrees
Distinguish fusion residues using ETOF
To measure the fusion count the number of evaporation residues relative to the number of incident O nuclei

6. Predicted Energy and angular distributions of the ERs (PACE4)
nucleon decay channels
 decay channels
Efficient detection of ERs can be accomplished by two annular silicon detectors.
Low energy of ERs requires low threshold detectors.

7. Experimental Details: Florida State Tandem
T.K. Steinbach et al., PRC90, (2014).
Incident Beam: 1-2 MeV/A
Intensity of 18O: 3x105 pps
Target: 100 µg/cm2 carbon foil
T2 and T3: Annular silicon detectors
T2: θLab = °; T3: θLab = °
Time-of-Flight (TOF) between TGT-MCP and Si (T2, T3)
Efficiency for ER detection 75-80%
Design (S5) from Micron Semiconductor low-energy evaporation residues (Entrance window 0.1 – 0.2 m)
Fast timing electronics gives timing resolution of ~ 450 ps (require ~ 1 ns time resolution)

8. Identifying Evaporation Residues
T.K. Steinbach et al., Phys. Rev. C 90, (R) (2014)
Evaporation residues are well separated from elastic and slit scattered beam particles
Slit scattered beam provides a reference line
Alpha particles are also cleanly resolved
NER  # of evaporation residues
NO-18  # of incident 18O nuclei
t  target thickness
ER  efficiency (typically 80%)

9. 18O + 12C Fusion Excitation Function
Measured the cross section for ECM ~ 5.3 – 14 MeV matches existing data (ECM ~ 7 – 14 MeV)
Extends cross-section measurement down to ~800 µb level (~30 times lower than previously measured)
Parameterize with penetration of a parabolic barrier (Wong)
Lowest Eyal data
Rc = 7.34 ± 0.07 fm
V = 7.62 ± 0.04 MeV
h/2 = 2.86 ± 0.09 MeV

10. Compare the 18O + 12C Excitation Function with DC-TDHF
TDHF provides good foundation for describing large amplitude collective motion; 3D Cartesian lattice; Skyrme effective interaction (SLy4); BCS pairing (Lipkin-Nogami extension)
T.K. Steinbach et al.,
PRC 90, (R)
(2014).
Above the barrier, DC-TDHF with pairing predicts a larger cross-section. In this energy regime the quantity expt./DC-TDHF is roughly constant at 0.8
Below the barrier the experimental cross-section falls less steeply with decreasing Ec.m. than the DC-TDHF predictions.
Below the barrier the quantity expt./DC-TDHF increases from 0.8 to approximately 15 at the lowest energy measured.

11. Role of pairing in DC-TDHF
Elimination of pairing acts to increase the fusion cross-section
Underscores the need to accurately treat pairing during the fusion process
Coupled channels calculations (CCFULL) provide essentially the same description as DC-TDHF
CCFULL also over-predicts the cross-section at above barrier energies and decreases more rapidly with decreasing energy as compared to the experimental data.

12. Summary for stable beam experiment: 18O + 12C
Measured excitation function agrees well with existing data (extending it down by a factor of 30!). Measurement made with 105 lower beam intensity!
DC-TDHF under-predicts the fusion cross-section at near and sub-barrier energies. The experimental data exceeds the model calculations by a factor of 15 at the lowest energies measured.
Alpha emission is significantly under-predicted by the statistical decay codes evapOR and PACE4, a common feature for similar systems [J. Vadas et al. Phys. Rev. C 92, (2015)]
With the experimental approach well established by measurement of 18O + 12C we turn to radioactive beams…

13. 19O + 12C at Florida State University
19O produced by: ~68 MeV
Filter with RESOLUT spectrometer
Intensity of 19O: 2-4x103 ions/s
Beam tagging by E-TOF
Target: 100 µg/cm2 carbon foil
T2: θLab = °; T3: θLab = °
Time-of-Flight (TOF) between target-MCP and Si (T2, T3)
18O7+
19O7+
18O6+
Simultaneous measurement of 19O and 18O excitation functions!
Ion chamber

14. Rc is larger by 10% for 19O as compared to 18O
V. Singh et al., Phys. Lett. B 765, 99 (2017).
Fusion excitation functions for 19O + 12C and 18O + 12C were simultaneously measured
The excitation function for 18O matches the results of the high resolution measurement previously performed within the statistical uncertainties.
At all energies 19O + 12C is associated with a significantly large cross-section.
Rc is larger by 10% for 19O as compared to 18O
h is larger by a factor of ~2
(narrower barrier)
16O
18O
19O Rc
7.25 ± 0.25 fm
7.39 ± 0.11 fm
8.1 ± 0.47 fm V
7.93 ± 0.16 MeV
7.66 ± 0.1 MeV
7.73 ± 0.72 MeV
h/2
2.95 ± 0.37 MeV
2.90 ± 0.18 MeV
6.38 ± 1.00 MeV

15. Fusion Enhancement in 19O + 12C
For 18O + 12C
a slightly larger cross-section is observed above the barrier as compared to 16O + 12C
Just below the barrier the cross-section increases slightly to a ratio of ~1.7
For 19O + 12C
Above the barrier, the fusion cross-section for 19O is roughly 20% larger than that for 18O
Just above the barrier at ~9 MeV the fusion cross-section for 19O increases dramatically as compared to 18O.
At the lowest energy measured the cross-section for 19O exceeds that for 18O by approximately a factor of three.

16. Impact of just an extended neutron density distribution?
Z. Lin
C.J. Horowitz (IU)
Drip line!
Sao Paulo
(Barrier penetration model)
While RMF + Sao Paulo provides a reasonable description of the fusion excitation function for 16O + 12C and 18O + 12C, it fails to predict the enhancement observed for 19O + 12C
Frozen density distributions
Dynamics is KEY to understanding the fusion enhancement!

17. Comparison with DC-TDHF
Although DC-TDHF provides a reasonable description of the 19O + 12C
fusion excitation function at the cross-section level shown, it over-predicts the cross-section for 18O + 12C and16O + 12C.
DC-TDHF fails to systematically reproduce the fusion excitation function for the oxygen isotopes for near and sub-barrier energies.
V. Singh et al., Phys. Lett B 765, 99 (2017)

18. If a single neutron leads to a fusion enhancement by a factor of three, what would happen if we have a larger number of neutrons?
… we turn to mid-mass nuclei which have been suggested as a heat source in the neutron star crust.
Compare fusion in 39K + 28Si and 47K + 28Si  a swing of eight neutrons

19. Resolving components in a radioactive beam at ReA3
Rare Ion Purity Detector (RIPD)
Axial field with central anode minimizes charge collection time
Aluminized windows serve as cathodes (0.5 µm mylar)
Integrated fast charge sensitive amplifier
J. Vadas et al.,
NIMA 837 (2016) 28
Risetime ns; Fall time 100 ns
Energy resolution ~8%
At an instantaneous rate of 3 x 105 ions/s the energy resolution is 14%

20. ReA3@MSU: 39,47K + 28Si  67,75As* GANIL: D. Ackermann, A. Chbihi
Western Michigan: M. Famiano
MSU-NSCL: K. Brown
LNL: M. Loriggiola (28Si tgts)
US MCP
Tgt MCP T2
~130 cm
~75 cm
39,47K beam T1
RIPD 1
RIPD 2
Elab = 2.3 – 3 MeV/A
Average intensity ~ 104 p/s
Reaction products distinguished by ETOF
Energy measured in segmented annular silicon detectors (T1, T2) 1° ≤ θlab ≤ 7.3°
Fusion product time-of-flight measured between target MCP and silicon detectors
47K beam contaminated by 36Ar (~5%)
Particle identification performed using ΔE-TOF
ΔE measured in RIPD
TOF measured between two MCP detectors

21. Below the barrier, 47K is enhanced relative to 39K by up to a factor of ~10 at the lowest energy measured

22. Conclusions and Outlook
Developed an efficient method to measure fusion for low-intensity radioactive beams at energies near and below the barrier.
For 18O + 12C:
Measured the fusion cross-section down to the 800 b level (~30x lower than previously measured.)
In the near/sub-barrier regime the enhancement of the fusion cross-section relative to DC-TDHF can be interpreted as a narrower barrier.
For 19O + 12C:
This first measurement indicates a significant fusion enhancement (~ three-fold) due to a single extra neutron as one approaches and goes below the barrier.
DC-TDHF provides a reasonable description for 19O at the cross-section level measured, but it fails to systematically reproduce the fusion excitation function for the oxygen isotopes.
For 39,47K + 28Si: Approximately a 10-fold enhancement is observed just below the barrier.
High quality measurement of the fusion excitation function for an isotopic chain of neutron-rich light nuclei at sub-barrier energies provides a unique opportunity to investigate the neutron-skin and test microscopic models.
Outlook: 20O, 21O + 12C
41,45K + 28Si and 36,44Ar + 28Si

23. Additional slides

24. Present experimental status for neutron-rich light nuclei (near symmetric systems)
10,12,13,14,15C + 12C
P.F.F. Carnelli et al, PRL 112, (2014)
Little data exists for fusion of light neutron-rich nuclei in near symmetric systems
Argonne National Lab. experiment
MUSIC detector with beam intensities of 500 – 5000 ions/sec
Detector limited at higher beam rate intensities
Generally good agreement with coupled channels calculations, BUT all the MUSIC data (closed symbols) are at energies above the barrier!
At near barrier energies:
Only low l-waves (s-wave scattering)
Stronger coupling to collective modes

25. Impact of isovector term in nuclear EOS on fusion
Sensitivity of fusion cross-section to neutron skin thickness
The neutron density distribution of 19O would need to exceed that predicted for 22O for a completely static picture to describe the experimental data
Dynamics is key to understanding the fusion enhancement!