1. Fusion of 16,18O + 58Ni at energies near the Coulomb barrier
Huiming Jia
Nuclear Reaction Group, China Institute of Atomic Energy

2. Outline ♠ Introduction ♠ Some available result for O + Ni
♠ Experiment and result
♠ Systematic analysis
♠ Conclusion

3. Introduction Basic aspect:
Fusion reaction between heavy-ions involves complex mass rearrangement and therefore complex reaction dynamics.
…offer an opportunity for examining and improving the theories for the reaction dynamics.
Some relevance:
…the production mechanism of the solar energy.
…the production of nuclei in massive pre-supernova stars via tunneling processes.
…the current successful way for synthesizing the new elements and especially the superheavy elements (SHE).

4. Introduction: theoretical description…
A single barrier penetration…
Barrier Distribution
Quantum
Classical
Coupled-channels (CC) effects -> Multi-dimensional barrier penetration.
Neck-formation model: NPA 472, 571 (1987); 500, 195 (1989); PLB 201, 22 (1988).
CCFULL: K. Hagino et al., Comput. Phys. Commun.123, 143 (1999).
Semiclassical approach - Pollarolo: Phys. Rev. C 62, (2000).
Semiclassical approach - Zagrebaev: Phys. Rev. C 67, (R) (2003).
Microscopic DC-TDHF: R. Keser et al., Phys. Rev. C 85, (2012). ……

5. Introduction
The CC effect due to inelastic excitation states has been described well, but the positive Q-value neutron transfer (PQNT) effect is still not clear.
…first experimental discovery: Beckerman et al., Phys. Rev. Lett. 45, 1472 (1980).
…first theoretical explanation: Broglia et al, Phys. Rev. C 27, R2433 (1983); Phys. Lett. B 133, 34 (1983).
♠…the rudiment of the multi- dimensional barrier penetration model.
♠…the origin of the idea that the increased kinetic energy, in the intermediate-channel after n-transfer, enhances the fusion cross section.

6. Introduction Experimental inconsistence: …positive Q-value n-pickup…
A.M. Stefanini et al., Phys. Rev. C 52, R1727 (1995).
Experimental inconsistence:
…positive Q-value n-pickup…
But, most systems for the corresponding n- stripping show no such an effect: 17O + 117Sn (Q-1n = MeV), 18O + 74Ge,112Sn, 36S + 58Ni…
…only one system shows enhancement due to the positive Q-value n-stripping system: 18O + 58Ni, Q-2n = MeV.
Some experimental study of the correlation of the fusion enhancement with the transfer reactions.
P. Jacobs et al., Phys. Lett. B 175, 271 (1986)
Theoretical difficulty:
♠ The complexity of the transfer reaction: orbital populations, optimal Q-window…
♠ Coupling: form factor, coupling strength…

7. Some available result for O + Ni
D. Pereira et al., PRC 73, (2006)
A.M. Borges et al., Phys. Rev. C 46, 2360 (1992).
Q-2n = MeV
…bigger error.
…not extend to lower energy region.
Explanation:
2n stripping leads to the population of the 2n-pairing vibrational state of 60Ni.

8. Some available result for O + Ni
R.F. Simões et al., Phys. Lett. B527, 187 (2002).
‘qe’: quasi-elastic scat., including the direct processes of elastic, inelastic and transfer…
@ θlab. = 161°
…a sign of a larger quasi- elastic flux deviated to fusion.
…a complex barrier distribution.

9. Some available result for O + Ni
PACE4: 31.21, 31.59MeV
V.I. Zagrebaev, Phys. Rev. C 67, (R) (2003).
Experimental data from A.M. Borges et al., Phys. Rev. C 46, 2360 (1992).

10. H.Q. Zhang et al., Chin. Phys. C 34, 1628 (2010).
Experiment and result
♠ Electrostatic deflector
♠ HI-13 tandem accelerator at CIAE
♠ Separation:
electrical rigidity η = E/q;
Optimal high voltage;
♠ Identification:
TOF-E (MCP + QSD);
♠ Angular distribution;
♠ Transmission efficiency.
H.Q. Zhang et al., Chin. Phys. C 34, 1628 (2010).

11. Experiment and result
♠ Beam: 16,18O, 2-20 pnA, 31.8 – 60 MeV, energy step 2.4/1.2/0.6 MeV.
♠ Target: 58Ni, 99.80% isotope enrichment.
♠ Beam monitors: 4 Si detectors at θlab. = 17°.

12. Experiment and result
CCFULL: K. Hagino et al., Comput. Phys. Commun.123, 143 (1999).
Akyüz -Winther Potential (energy-independent bare)

13. Experiment and result …modest fusion enhancement effect!
…the possible difference between DFus and DQEL?

14. Systematic analysis
The Q-value for multi-neutron pickup from g.s. to g.s.
CCFULL
…bare Akyüz-Winther energy-independent potential
+ inelastic coupled-channels effect.

15. Systematic analysis
Residual enhancement (RE) (except inelastic coupling effect)
Benchmark: RE ~ 1 for the reference systems without expected PQNT effect.
C.L. Jiang et al.,
Phys. Rev. C 82, (R) (2010).

16. Systematic analysis
…a positive-going correlation of RE with the Q-values.

17. Systematic analysis
…a negative-going correlation of RE with the Q-values.
？the inelastic effect of 94Zr.
？the effect of the pairing-vibration state 02+ after 2n transfer

18. Conclusion
The fusion excitation function of 16,18O + 58Ni at near-barrier energy region was re-measured with high precision.
Only modest fusion enhancement effect for 18O + 58Ni compared with the available data and coupled-channels calculations, although of the high Q-2n value.
Systematic analysis based on CCFULL code may provide a further reliable proof for the occurrence of the PQNT effect.
The systematic analysis gives a visualized sub-barrier fusion enhancement excluding the inelastic coupling effect. This shows a complex correlation of the enhancement effect with the neutron- transfer channels.

19. Thanks for your attention!