from fusion hindrance to oscillations in the si + si · pdf filefrom fusion hindrance to...
Post on 09-Mar-2018
229 Views
Preview:
TRANSCRIPT
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
G.Montagnoli ECT* - Trento, May 2014
28Si+28Si
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
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)
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
The resul3ng barrier distribu3on
G.Montagnoli ECT* - Trento, May 2014
Ion-‐ion poten3als for 28Si+28Si
G.Montagnoli ECT* - Trento, May 2014
Fusion cross sec3ons in different energy ranges
G.Montagnoli ECT* - Trento, May 2014
High energy structures of fusion excita3on func3ons
G.Montagnoli ECT* - Trento, May 2014
The fusion excitation function of 28Si+28Si
(the blue points were measured with ΔElab = 0.5 MeV, and 1% statistical error)
G.Montagnoli ECT* - Trento, May 2014
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)
G.Montagnoli ECT* - Trento, May 2014
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)
G.Montagnoli ECT* - Trento, May 2014
The existing situation for 28Si+28Si
S. Gary and C. Volant, PRC 25, 1877 (1982) Y. Nagashima et al., PRC 33, 176 (1986)
Esbensen
G.Montagnoli ECT* - Trento, May 2014
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
Fusion excita3on func3on of 28Si+30Si
G.Montagnoli ECT* - Trento, May 2014
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)
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
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
G.Montagnoli ECT* - Trento, May 2014
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.
G.Montagnoli ECT* - Trento, May 2014
Coupled channels elas3c and 2+, 3-‐ 2+×2+ of target and projec3le with mutual excita3on of 2+, 3-‐ and of 2+×2+
top related