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Role of the nuclear shell structure and orientation angles of deformed reactants
in complete fusion
Joint Institute for Nuclear ResearchFlerov Laboratory of Nuclear Reactions
Nasirov A.K.
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A.K. Nasirov1,2, G. Giardina3, A. Fukushima4, Y. Aritomo1,4, G. Mandaglio3, A.I. Muminov2,
M. Ohta4, T. Wada4, R.K. Utamuratov2
1. Flerov Laboratory of Nuclear Reactions JINR, Dubna, Russia2. Heavy Ion Physics Department, INP, Tashkent, Uzbekistan3. INFN, Sezione di Catania, and Dipartimento di Fisica dell‘ Universitá di Messina, Italy4. Department of Physics, Konan University, Kobe, Japan
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Content
Introduction
Main mechanisms of heavy ion collisions at low energies
Dependence of capture and fusion dynamics on the mass, mass asymmetry, shape nuclei and orientation angles of their symmetry axis
Role of the peculiarities of shell structure in complete fusion
Conclusion
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Difference between paths of the capture and deep inelastic collisions
i
ТКЕ-total kinetic energy
V( R ) – nucleus-nucleus
potential
E*DNS – excitation energy of double nuclear system
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Comparison of the friction coefficients, calculated by different methods
D. H. E. Gross and H. Kalinowski, Phys. Rep. 45, (1978) 175.
Solid line – G.G. Adamian, et al. PRC
56 (1997) 373
Long dashed --
Short dashed- -
Dotted -
Temperatura= 2 MeV
Temperatura= 1 MeV
Temperatura= 0.5 MeV
By Yamaji et al(microscopic):
S. Yamaji and A. Iwamoto,
Z. Phys. A 313, (1983) 161.
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Reaction mechanisms following after capture:fast-fission, quasi-fission and fusion-fission.
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Fast-fission of the mononucleus
A.J. Sierk, Phys.Rev. C, 33 (1986) 2039
Lfus > L > Lfis.bar
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Potential energy surface for fusion of compound nucleus 284114
Udr (A, Z, , ß1 , α1 ; ß2 , α2 ) = B1 + B2 + V (A, Z, ß1 , α1 ; ß2 , α2 ; R)- (BC N + VC N (L ))
a- entrance channel;b-fusion channel;c and d are quasifission channels
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Potential energy surface for fusion of compound nucleus 214Th
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Nucleus-nucleus potential as a function of the distance between nuclei and orientation their axial symmetry axis
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Nucleus-nucleus interaction potential
2
1
2
1
2
2)(
2202
)(2
20
2/12
321
22121
)(cos7
3)(cos
20
9
),,(
i ii
iii
ii
C
PRPReR
ZZ
eR
ZZRV
rdrfRrRV effnucl
3)0(2
)0(2
)0(1
)0(121 )()(),,(
.)(1()(
exp1),,,,(
1
20)(
2)(2
)0(
a
YRtRrRr
iii
oiiiiiii
221
2
]([2
)1(
R
llVrot
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Dependence of the capture and fusion cross sections on the orientation angle of the axial symmetry axis of reactants
}),,,{,,(
}),,,{,,(}),,,{;,(}),,,{;,(
iiiirot
iiiinucliiiiCouliiiinucnuc
AZLRV
AZLRVAZLRVAZLRV
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Dynamics of capture of projectile by target-nucleus
dyn
dynlab LLorLLif
LLLifLET
min
min21 ,0
,1),;,(
cap (Elab,L; 1 ,2)= (2L +1) T(Elab, L; 1 ,2)
R
RR
R
RVtRR
dt
RRdR
)()(
)()()( 2
effeff RRtRtRRdt
dL2211)()()(
,22110 JJJL R
222
222
211
2 JJJE Rrot
Ldyn and Lmin are determined by dynamics of collision and calculated by solution of equations of motion for the collision trajectory:
fus (Elab ,L) =cap(Elab ,L; 1 ,2) PCN(Elab ,L; 1 ,2) {}
2
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Partial fusion cross section as a function of the orientation of axial symmetry axis of reactants
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Comparison of the capture and fusion excitation functions with the experimental data and Langevin calculations
S. Mitsuoka, et al.
PRC 62 (2000) 054603.
Y. Aritomo, M. Ohta, Nucl.Phys. A744
(2004) 3
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Quasifission cross sections as a function of the orientation angles of colliding nuclei
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Dependence of the fusion and quasifission cross sections on the orientations of colliding nuclei
Nasirov A.K. et al
Nucl. Phys.A759 (2005) 342
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Comparison capture and fusion cross sections for the 16O+238U reaction
There is quasifission
Hinde et al., Phys. Rev. Lett.
74 (1995) 1295
There is not quasifission
K. Nishio et al., Phys.Rev.Lett.
93 (2004) 162701
Nasirov A.K. et al
Nucl. Phys.A759 (2005) 342
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Dependence of the driving potential (а) and quasifission barrier (b) on the mutual orientations of the axial symmetry axes of nuclei
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The role of the entrance channel and shell structure of reactants at formation of the evaporation residues in reactions leading to the same compound nucleus 216Th:a) Capture b) Complete fusionc) Evaporation residuescross sections.
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Driving potential Udriving ( c ) for reactions 40Ar+172Hf, 86Kr+130Xe, 124Sn+92Zr leading to formation of compound nucleus 216Th :
Udriving=B1+B2-B(1+2)+V( R )
Due to peculiarities of shell structure Bfus (Kr) > Bfus (Kr) and, consequently,
fus (Kr+Xe) < fus(Zr+Sn)
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Angular momentum distribution for the complete fusion σfus
(L) (Elab) as
a function of momentum and and beam energy for reactions leading
to formation of 216Th.
G. Fazio, et al., Journal of the Physical Society of Japan 388, 2509 (2003).
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Effect of the entrance channel on the fission branching ratio of the excited compound nucleus 220Th
Comparison of the fusion and evaporation residue (total neutron emissions) cross sectionsfor the 16O+204Pb (I) and 124Sn+96Zr (II) reactions.
Comparison of the fission branching ratio Γf / Γtot for the 16O+204Pb (red) and 124Sn+96Zr (blue) reactions
G. Fazio, .., Nasirov A.K., et al. Eur. Phys. Jour. A, 2005
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Fusion angular momentum distribution for the reaction 16O+204Pb и 96Zr+124Sn
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Conclusions
1. An advantage of the orientation angles 60o < α <90o for observation maximum values of fusion cross section is demonstrated by the analysis of dependence of the capture dynamics and fusion and quasifission barriers on the orientation of the axial symmetry axis of reactants.
2. The results of calculation showed that increase of beam energy leads only to involving of the larger orientation angles. If the colliding nuclei undergo the ``tip-tip" collisions only an increase of the beam energy does not lead to increase fusion cross section.
3. The angular momentum of the compound nucleus depends strongly on the dynamics of capture and peculiarities of shell structure at transformation of the dinuclear system into compound nucleus.
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THANK YOU
I am grateful to the Poland – Russian Bogoliubov - Infeld Program for the support my participation in this Workshop.
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Evaporation residue for 48Ca+249Cf reaction
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