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Fusion of 32S + 48Ca near and below the Coulomb barrier

G. M.1, A.M. Stefanini2, C.L.Jiang3, L. Corradi2, S. Courtin4, H.Esbensen3, E. Fioretto2, A. Goasduff4, J.Grebosz5, F. Haas4, A.F.Kifle2, M.Mazzocco1, C.Michelagnoli1, T. Mijatović6, D.Montanari1, K.E.Rehm3, R.Silvestri2, Pushpendra P. Singh2, F. Scarlassara1, S. Szilner6, X.D.Tang7, C.A.Ur1

1 Dipartimento di Fisica e Astronomia, Università di Padova, and INFN, Sez. di Padova, Italy2 INFN, Laboratori Nazionali di Legnaro, Legnaro (Padova), Italy3 Physics Division, Argonne National Laboratory, Argonne, USA4 IPHC, CNRS-IN2P3, Université de Strasbourg, Strasbourg, France5 Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland6 Ruđer Bošković Institute, Zagreb, Croatia7 University of Notre Dame, Notre Dame, USA

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Outline• Fusion excitation function of 32S + 48Ca • Experimental set-up and results• CC calculations • Couplings to transfer channels and barrier

distribution • Logarithmic slope and S factor • Comparison with the similar system 36S + 48Ca• Summary

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Electrostatic separator and E-ΔE-ToF telescope to detect evaporation residues at ≈ Oo

beam

MCP, IC & Si detectorsscattering chamber

+ +

_ _

HV

HV

target

E-ΔE-ToF telescope ER detected here

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Detector set-up, experimental matrix ΔE-ToF and angular distributions

ΔE (cha.)

TOF

(cha

.)

lowest measurable cross section ≈ 0.5-1 μb

degraded beam

fusion on C, F

ER

40Ca + 40Ca

Experimental Angular Distributions

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Vb= 44.57MeV (43.12 MeV)rb = 9.61 fm (9.87 fm)ħω= 3.59 MeV (3.49 MeV)

Barrier parameters

Vo= 75.12MeV (61.81 MeV)a = 0.65 fm (0.65 fm)ro= 1.12 fm (1.17 fm)

Nuclear Potential (Akyüz-Winther)

The lowest 2+ and 3- state in 32S and 48Ca

b3=0.39

b2=0.31

0.180.10

gs32S 48Ca

2+

2+

3-

3-

The fusion excitation function of 32S + 48Ca

1phon = 32S: 2+, 3- 48Ca: 2+, 3- 2phon = 32S: (2+)2, 3- 48Ca: 2+, 3-

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-xp +xn -α +α1 +0.76 -1.30 +0.73 -7.32

2 +5.63 +2.84

3 +0.18 -0.57

4 +0.20 +1.90

32S+48Ca g.s. transfer Q-values (MeV)

Pair transfer Form Factor

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What happens above the barrier …

At high energies the fusion cross sections for 32

S+48

Ca are explained

nicely by the calculation in which the coupling to one pair transfer

channel is schematically taken into account.

Without transfer, the calculation clearly overestimates the experimental

cross sections.

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Comparing with a similar system

A.M. Stefanini et al., PRC 78 (2008) 044607

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32S+48Ca 36S+48Ca

Qfus=+7.66MeV Qfus=+7.55MeV

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The barrier distributions also show interesting features

Double peaked shape of BD for32S+48Ca has been interpreted within a simplified CC calculation including an effective transfer channel coupling.The comparison with the near-by system 36S+48Ca (negative Q-value for transfer channels) that shows a BD with only one main peak supports CC calculation result.

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Fusion cross sections of three systems involving 48Ca

C.L. Jiang et al., PRC 82 (2010) 041601(R)

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Summary• Fusion cross sections of 32S + 48Ca have been measured in a

wide energy range• The fusion barrier distribution has an interesting double-

peaked shape• Below the barrier, the log slope of the exct. function is rather

flat and no maximum of the S factor is observed • The present data are nicely reproduced with CC calculations

using a WS ion-ion potential • The comparison with 36S + 48Ca shows differences that seem

to correlate with coupling effects of Q>0 transfer channels• These transfer couplings possibly push the threshold of

hindrance below the lowest measured energy, but detailed calculations are needed before drawing firm conclusions

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The barrier distributions also show interesting features

A.M.Stefanini et al., PLB 679 (2009) 95

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Our most results on 32S + 48Ca

the logarithmic derivative is rather lowand keeps increasing below the barrier

the barrier distribution isvery wide and and showsan unusual shape

by coupling schematicallya Q>0 transfer channel,the data are well fit

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S(E)

E

Q<0

Q>0?

We recently measured the fusion excitation function of 36S + 48Ca (Q-value=+7.6MeV)

For Q>0 S(E) may not show any maximum no fusion hindrance!

Emin e2 S(E)

Q<0 -Q finite 0Q>0 0 finite ?

-Q0

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C.L.Jiang et al., PRC 73, 014613 (2006)

L(E) = d[ln(Eσ)]/dE

dS/dE = S(E)[L(E) – πη/E]

S has a maximum when dS/dE = 0, i.e. when L(E) = πη/E = LCS

The energy E = ES where this happens has been usuallytaken as the threshold energy for hindrance.

From the empirical systematics of Jiang et al. one obtains

ES ≈ 0.356 [Z1Z2√μ]2/3 MeV

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Scheme of CC calculations

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36S+48Ca

A-WV0= 61.34 MeV r0=1.17 fm a=0.65 fmVb= 42.7 MeV

V0=164.6 MeV r0= 0.90 fm a=0.95 fmVb= 43.3 MeV

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The sensitivity of the experimental set up allows us to measure down to about 600 - 650 nb

ER were detected by two MCP detectors and finally stopped in a 600 mm2 silicon detector placed in the IC

The total length of telescope was ≅ 100 cm with a geometrical solid angle DW ≅ 0.042 msr

The electrostatic deflector transmission was measured for several systems in a wide range of masses, by switching off the filter and by detecting ER at q = 3o and 5o, then comparing the yields with the results of the corresponding measurement with the electrostatic deflector on.

The interpolated value for the present case is: T=0.72±0.03

20

Experimental details

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-xp +xn -α +α1 +1.3 -1.6 +0.6 -8.8

2 +7.1 +2.6

3 +4.9 +0.16

4 +3.9

40Ca+48Ca transfer Q-values (MeV)

-xp +xn -α +α1 +0.76 -1.30 +0.73 -7.32

2 +5.63 +2.84

3 +0.18 -0.57

4 +0.20 +1.90

32S+48Ca g.s. transfer Q-values (MeV)