I. I. GONTCHAR, M. V. CHUSHNYAKOV A 3
Figure 3. (a) The excitation functions calculated using the
M3Y double folding dissipative model; (b) The ratio of the
capture cross section calculated using the M3Y double
folding dissipative model to the experimental cross section
versus the relative collision energy.
4. Conclusions
The Woods-Saxon shape for the nucleus-nucleus interac-
tion potential was used extensively in the literature in
order to analyze the precision fusion excitation func-
tions [4,14-16]. Excellent fit was achieved with the dif-
fuseness of this potential ranging from 0.75 up to 1.5 fm.
This is significantly larger than the value of 0.65 fm with
which the elastic scattering cross sections are usually
successfully fitted [7].
This contradiction stimulated us to compose the dissi-
pative trajectory model based on the density-dependent
M3Y NN-forces folded with the nuclear matter distribu-
tion. Resulting poten tial possesses th e normal diffusen ess
about 0.65 fm.
Within the framework of our approach the nucleus-
nucleus collisi on process is modeled as the motion of the
fictitious Brownian particle experiencing the action of
the conservative, dissipative, and stochastic forces. Since
only the collision energies well above the Coulomb barrier
are considered, the quantum effects like tunneling and
channels couplings are not accounted for. Possible re-
tarding character of the dissipation and non-Markovian
nature of the noise are included.
Using this model we reached the agreement with the
data for 16O+208Pb, 28Si+208Pb, 32S+208Pb reactions within
5%. This is done with the universal strength coefficient
of radial friction 2.0x10-2 zs/MeV and with the correla-
tion time of the noise equal to 0.1 zs for 16O+208Pb reac-
tion and 0.15 zs for 28Si+208Pb and 32S+208Pb reactions.
This advance together with successful description of
the capture cross sections for 16O+92Zr and 16O+144Sm
reactions obtained in [6] seems giving a hope to resolve
the long standing problem of apparently large diffuseness
of the nucleus-nucleus potential.
REFERENCES
[1] P. Fröbrich and R. Lipperheide, “Theory of Nuclear Re-
actions,” Oxford Studies in Nuclear Physics, Vol. 18,
Oxford University Press, 1996.
[2] A. C. Berriman, D. J. Hinde, M. Dasgupta, C. R. Morton,
R. D. Butt and J. O. Newton, “Unexpected Inhibition of
Fusion in Nucleus-Nucleus Collision,” Nature, Vol. 413,
2001, pp. 144-147. doi:10.1038/35093069
[3] M. Dasgupta, D. J. Hinde, N. Rowley and A. M. Stefanini,
“Measuring Barriers to Fusion,” Annual Review of Nu-
clear and Particle Science, Vol. 48, 1998, pp. 401-461.
doi:10.1146/annurev.nucl.48.1.401
[4] O. Newton, R. D. Butt, M. Dasgupta, D. J. Hinde, I. I.
Gontchar, C. R. Morton and K. Hagino, “Systematic Fail-
ure of the Woods-Saxon Nuclear Potential to Describe
Both Fusion and Elastic Scattering: Possible Need for a
New Dynamical Approach to Fusion,” Physical Review C,
Vol. 70, 2004, 024605.
[5] K. Hagino, N. Rowley and A. T. Kruppa, “A Program for
Coupled-Channels Calculations with All Order Couplings
for Heavy-Ion Fusion Reactions,” Computer Physics
Communications, Vol. 123, No. 1-3, 1999, pp. 143-152.
doi:10.1016/S0010-4655(99)00243-X
[6] M. V. Chushnyakova and I. I. Gontchar, “Heavy Ion Fu-
sion: Possible Dynamical Solution of the Problem of the
Abnormally Large Diffuseness of the Nucleus-Nucleus
Potential,” Physical Review C, in press.
[7] R. A. Broglia and A. Winther, “Heavy Ion Reaction Lec-
ture Notes, Volume I: Elastic and Inelastic Reactions,”
Benjamin/Cummings Publishing Company, San Fran-
cisco, 1981.
[8] D. H. E. Gross and H. Kalinowski, “Friction Model of
Heavy-Ion Collision,” Physics Reports, Vol. 45, 1978, pp.
175-210. doi:10.1016/0370-1573(78)90031-5
[9] P. Fröbrich, “Fusion and Capture of Heavy Ions above the
Barrier: Analysis of Experimental Data with the Surface
Friction Model,” Physics Reports, Vol. 116, 1984, pp.
337- 400. doi:10.1016/0370-1573(84)90162-5
[10] P. Fröbrich and I. I. Gontchar, “Langevin Description of
Fusion Deep-Inelastic Collisions and Heavy-Ion Induced
Fission,” Physics Reports, Vol. 292, 1998, pp. 131-238.
doi:10.1016/S0370-1573(97)00042-2
[11] I. I. Gontchar and M. V. Chushnyakova, “A C-Code for
the Double-Folding Interaction Potential of Two Spheri-
cal Nuclei,” Computer Physics Communications, Vol.
181, 2010, pp. 168-182.
doi:10.1016/j.cpc.2009.09.007
Copyright © 2013 SciRes. JMP