From fusion hindrance to oscillations in the Si + Si · PDF fileFrom fusion hindrance to oscillations in the 28Si + 28Si system . Layout ... Logarithmic$slope$and$S(factor$for$28Si+30Si$

G. Montagnoli Università degli studi di Padova - INFN

G.Montagnoli ECT* - Trento, May 2014

From fusion hindrance to oscillations in the 28Si + 28Si system

Layout

•  The sub-‐barrier trend of the fusion excita3on func3on of 28Si+28Si compared with theore3cal CC analysis •  The observed oscilla3ons above the barrier: their meaning

and the interpreta3on within the same model •  A comparison with the near-‐by system 28Si+30Si for which we

extended the previous measurements by an order of magnitude down to ≈ 4 μb

•  Summary


28Si+28Si


We found very aHrac3ve to inves3gate the behavior of 28Si+28Si fusion at deep sub-‐barrier energies, because this system has a posi3ve Q value for fusion Q = +10.9 MeV, similar to the lighter heavy-‐ion cases. The oblate deforma3on of 28Si may have also an important role at deep sub-‐barrier energies. This medium-‐mass system is a good candidate to look for above-‐barrier oscilla3ons that can provide valuable informa3on about the ion-‐ion poten3al and put constraints on CC calcula3ons. The aim is to describe the trend of sub-‐barrier excita3on func3on and the observed high energy oscilla3ons within the same CC model .

Experimental results obtained detec3ng the Fusion-‐Evapora3on Residues


Fusion excita3on func3on

10

100

1000

104

105

106

107

-15 -10 -5 0 5 10 15 20d σ

/dΩ

(a.u

.)θ

lab (deg)

28Si+28Si

108

83.5

Elab (MeV)

74

67

58 0.0001

0.001

0.01

0.1

1

10

100

1000

44 48 52 56 60 64 68 72 76

Gary

σfu

s (m

b)

Elab (MeV)

28Si + 28Si

ER angular distribu3ons

S. Gary and C. Volant, PRC 25, 1877 (1982)


The case of 28Si +28Si: measurement of sub-‐barrier fusion

•  Woods-Saxon and M3Y+rep. Potential •  CC with 2+ and 3- states including nuclear deformation •  Short range imaginary potential

S-‐factor and logarithmic slope of 28Si+28Si


The resul3ng barrier distribu3on


Ion-‐ion poten3als for 28Si+28Si


Fusion cross sec3ons in different energy ranges


High energy structures of fusion excita3on func3ons


The fusion excitation function of 28Si+28Si

(the blue points were measured with ΔElab = 0.5 MeV, and 1% statistical error)


0

80

160

240

320

400

480

560

640

44 48 52 56 60 64 68 72 76

Gary σ

fus (

mb)

Elab (MeV)

28Si + 28Si

0.0001

0.001

0.01

0.1

1

10

100

1000

44 48 52 56 60 64 68 72 76

Gary

σfu

s (m

b)

Elab (MeV)

28Si + 28Si

Structures in fusion excitation function of light systems

•  Oscillatory structures were recently interpreted due to the penetration of successive centrifugal barriers

•  A shallow ion-ion potential is needed to

fit the data above (and below) the barrier.

•  èè Look for above-barrier oscillations

in heavier systems, where sub-barrier hindrance is stronger and better established.

•  Clearly observing such oscillations would

put strong constraints on the ion-ion potential in a wide energy range.

H.Esbensen, PRC77, 054608 (2008); PRC85, 064611 (2012) C.Y.Wong, PRC86, 064603 (2012)


Using the first derivative of the excitation function d(Eσ)/dE makes it easier to observe oscillations

The case of 16O + 16O

E

D.L.Hill and J.A.Wheeler, PR 89, 1102 (1953) C.Y.Wong, PRL 31, 766 (1973) I.Tserruya et al., PRC 18, 1688 (1978)


The existing situation for 28Si+28Si

S. Gary and C. Volant, PRC 25, 1877 (1982) Y. Nagashima et al., PRC 33, 176 (1986)

Esbensen



Energy-weighted derivative of the excitation function for 28Si+28Si above the barrier

500

1000

1500

2000

2500

3000

62 64 66 68 70 72 74 76

d(E σ

)/dE

(mb)

Elab

(MeV)

28Si+28Si


500

1000

1500

2000

2500

3000

62 64 66 68 70 72 74 76

June 2013Dec. 2012

d(Eσ

)/dE

(mb)

Elab (MeV)

28Si + 28Si

Comparison with the result of the preliminary run of Dec. 2012


The energy difference between successive barriers: (twice as that for a symmetric system like 28Si + 28Si, i.e. ≈1.52 MeV)

0

500

1000

1500

2000

2500

3000

3500

62 64 66 68 70 72 74 76

Dec. 2012June 2013

H. Esbensen PRC 85, 064611 (2012)

d(Eσ

)/dE

(mb)

Elab

(MeV)

28Si+28Si

L=20

Comparison with the result of the preliminary run of Dec. 2012 and with a recent CC calculation


CC results are very sensi3ve to the parameters of M3Y+rep poten3als and of the small imaginary term

First deriva3ve of the energy–weighted cross sec3on

28Si + 30Si: new measurement and comparison


Fusion excita3on func3on of 28Si+30Si


10-3

10-2

10-1

100

101

102

103

20 25 30 35 40 45

mf (

mb)

Ecm (MeV)

28Si + 30Si

GaryANL-revLegnaro

Cn-13 sol-2Cn-10 sol-2Ch-1 sol-2

S.Gary and C.Volant, PRC 25, 1877 (1982) C.L.Jiang et al., PRC 78, 017601 (2008)


C.L.Jiang at al. PRC 78, 017601 (2008) G.Montagnoli et al., this work

Logarithmic slope and S-‐factor for 28Si+30Si

The fusion hindrance is a general heavy-‐ion phenomenon and there is some evidence that this is independent of the sign of fusion Q-‐value.

Excita3on func3ons of 28Si+28,30Si


0.0001

0.001

0.01

0.1

1

10

100

1000

22 24 26 28 30 32 34 36

28Si + 28Si28Si + 30Si LNL28Si + 30Si Jiang

σfu

s (mb)

Ec.m. (MeV)

CC analysis of Si+Si systems


10-3

10-2

10-1

100

101

102

103

22.5 25 30 35

mf (

mb)

Ecm (MeV)

28Si + 30SiM3Y+rep

28+28 Legnaro28+30 Argonne28+30 Legnaro

30+30 Bozek


Summary

•  Fusion cross section of 28Si+28Si have been measured in a wide energy range down to the µb region.

•  The observation of high energies oscillations puts strong

constraints on the ion-ion potential in a wide energy range. •  Comparing 28Si+28Si with extended measurements for 28Si

+30Si shows very different behaviors below the barrier, possibly due to the oblate deformation of 28Si.

•  The low energy excitation function and the oscillations observed above the barrier for 28Si+28Si can be described in the same theoretical frame. Work is in progress.

Our collaboration

G.Montagnoli, D.Montanari, F.Scarlassara, M.Mazzocco, C.Michelagnoli C.Parascandolo, E.Strano, D.Torresi Dept. of Physics and Astronomy, Univ. of Padova and INFN-Padova, Italy A.M.Stefanini, L.Corradi, E.Fioretto, H.M.Jia INFN, Laboratori Nazionali di Legnaro, Legnaro (Padova), Italy S.Szilner, T.Mijatovic Ruder Boskovic Institute, Zagreb, Croatia H.Esbensen, C.L.Jiang Physics Division, Argonne National Laboratory, Argonne, Illinois, USA S.Courtin, F.Haas, A.Goasduff, D.Bourgin IPHC, CNRS-IN2P3, Univ. Louis Pasteur, Strasbourg Cedex 2, France J.Grebosz Institute of Nuclear Physics, Cracow, Poland


Theore3cal analysis

New Analysis: •  Poten3al M3Y + repulsion with based on 28Si density with radius R=3.14 fm Diffuseness a=0.48 fm Op3mum diffuseness for the repulsion term ar=0.398 fm Immaginary poten3al to increase the absorp3on and improve the fit at low energy w0=5MeV with diff. aw=0.3 fm.


Coupled channels elas3c and 2+, 3-‐ 2+×2+ of target and projec3le with mutual excita3on of 2+, 3-‐ and of 2+×2+

Documents

From fusion hindrance to oscillations in the Si + Si · PDF fileFrom fusion hindrance to oscillations in the 28Si + 28Si system . Layout ... Logarithmic$slope$and$S(factor$for$28Si+30Si$