1. Extracting β4 from sub-barrier backward quasielastic scattering
Huanqiao Zhang and Huiming Jia
Nuclear Reaction Group, China Institute of Atomic Energy

2. Outline ♠ Introduction ♠ Traditional methods
♠ A method based on the coupling effect
♠ Summary

3. Introduction: Nuclear shape:
Nucleus: a quantum many-body system –> wave function;
Phenomenally: liquid drop –> shape;

4. Current situation for β4 :
Introduction:
Current situation for β4 :
Experiment:
Stable nucleus:
…difficult to extract, especially its sign;
…model dependent with big error;
…less information.
Radioactive nucleus:
…only some information for β2 (B(E2)) very recently.
c.f.: Phys. Rev. C 89, (122,124,126Cd); (29,30Na); (2014)….
Theory:
macro-microscopic model, c.f. P. Möller et al., Atomic Data and Nuclear Data Tables, 59, 185 (1995). …
…MICROSCOPIC structure of nuclei - a computational challenge… Silvia Leoni’s talk

5. Traditional methods
◆sub- or above-barrier (& high energy) α scattering, c.f. I.Y. Lee et al., Phys. Rev. C 12, 1483 (1975).
---the scattering excitation function.
◆ Near-barrier heavy-ion scattering (β4N), c.f. J.S. Vaagen et al., Phys. Lett. B 91,361(1980).
---the scattering angular distribution.
◆high energy ( MeV) electron scattering (charge dist.), c.f. T. Cooper et al., Phys. Rev. C 13, (1976).
---the form factors with the momentum transfer.
◆muonic (super-heavy quasi-electron) atomic x-ray, c.f. R.J. Powers et al., Phys. Rev. Lett. 34, 492 (1975).
---the atomic energy level.
◆ …
Nucleus
Method β2 β4
Ref.
184W
HI scattering
0.231
-0.11
PLB 91, 361 (1980)
α scattering
0.254
-0.089
PRL 33, 383 (1974)

6. R.C. Lemmon et al., Phys. Lett. B 316, 32 (1993).
A method based on the coupling effect
Strong dependence of sub-barrier fusion on the (plus/minus) nuclear hexadecapole deformation
+0.05
0.0
-0.05
β4:
R.C. Lemmon et al., Phys. Lett. B 316, 32 (1993).

7. To study nuclear structure by using nuclear reaction.
A method based on the coupling effect
Barrier distribution from fusion (Transmission):
Above barrier: big error (due to the big fusion cross section);
Below barrier: small cross section (longer beam time) and increasing background;
R (Reflection)
T (Transmission)
beam
Complementary assumption:
T = 1 - R
Quasielastic excitation function at backward angle (Reflection) :
Below barrier: big cross section & sensitive to the coupling effect, i.e. deformation parameter.
To study nuclear structure by using nuclear reaction.

8. A method based on the coupling effect
F.C.
Beam
For Rutherford
For QEL
Target
Experimental setup:
1. Backward quasi-elastic scat. (QEL = R) at 175°
QEL: the direct reaction processes -- elastic, inelastic, transfer… (cannot be separated here).
2. Rutherford scat. at 41°(for normalization).
The schematic of the setup.

9. A method based on the coupling effect
♠ System property (16O + 152Sm, 170Er, 174Yb):
Projectile: 16O spherical;
Targets: 152Sm, 170Er, 174Yb (typical rare-earth) – similar (big) β2, but different β > To highlight β4 effect!
♠ Data analysis:
CCFULL: scattering edition.
(energy independent bare) Woods-Saxon potential: V0, r0v = 1.20 fm, av = 0.65 fm;
VB: R = 0.5.
♠ Why deep sub-barrier:
simple experiment, simple mechanism, dominant deformation effect, less nuclear distortion of the Coulomb orbit, less influence of the inner potential...

10. A method based on the coupling effect
Quasi-elastic scattering excitation function for 16O + 152Sm, 170Er, 174Yb systems.

11. H.M. Jia et al., Phys. Rev. C 90, 031601(R) (2014)
A method based on the coupling effect
CCFULL
K. Hagino et al., Comput. Phys. Commun. 123, 143 (1999).
Data normalization:
…to reproduce the best apparent fit.
H.M. Jia et al., Phys. Rev. C 90, (R) (2014)

12. H.M. Jia et al., Phys. Rev. C 90, 031601(R) (2014)
A method based on the coupling effect
H.M. Jia et al., Phys. Rev. C 90, (R) (2014)

13. H.M. Jia et al., Phys. Rev. C 90, 031601(R) (2014)
A method based on the coupling effect
a least-squares
analysis
★ Referee:
Given the sensitivity of fusion to hexadecapole deformation, one may have expected the quasi-elastic data to reflect this sensitivity too. This work is the first one to show this experimentally.
★ Editor:
This paper presents a highly sensitive new technique to explore unusual nuclear shapes in exotic short-lived nuclei far from stability. Exploiting heavy-ion collisions at energies below the Coulomb barrier, such that the nuclei do not fuse, the work uncovers evidence for hexadecapole shapes in which the nucleus looks like an indented ellipsoid.
H.M. Jia et al., Phys. Rev. C 90, (R) (2014)

14. Summary
♠Hexadecapole deformation β4 is usually difficult to extract experimentally and the traditional methods give inconsistent results with bigger errors.
♠ A new sensitive method was proposed to extract the hexadecapole deformation parameter based on the coupling effect in the sub-barrier heavy-ion nuclear reaction.
♠ The extracted β4 values based on the fixed β2 are consistent well with the available results obtained from the traditional methods.
♠ This method is very meaningful for the radioactive nucleus, but the feasibility may need further theoretical consideration.

15. Thanks for your attention