The M3Y Double Folding Dissipative Model in Agreement with Precise Fusion Cross Sections

I. I. Gontchar, M. V. Chushnyakova

Physics and Chemistry Department, Omsk State Transport University, Omsk, Russia.

DOI: 10.4236/jmp.2013.45B001                

Abstract

Large numbers of precision fusion excitation functions were fitted in the literature using the nucleus-nucleus interaction potential having the Woods-Saxon shape. The diffuseness of this potential fusion ranges from 0.75 to 1.5 fm. This is much larger than the value of 0.65 fm required by the elastic scattering data. Trying to resolve this contradiction we develop the dissipative trajectory model based on the density-dependent M3Y NN-forces folded with the nuclear matter distribution. Resulting potential possesses the normal diffuseness about 0.65 fm. With this potential we reach the agreement with the data for ¹⁶O+²⁰8Pb, ²⁸Si+²⁰⁸Pb, ³²S+²⁰⁸Pb reactions within 5%.

Keywords

Heavy Ion Fusion; M3Y NN-Forces; Double Folding Potential; Fusion Excitation Function

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. Fröbrich and R. Lipperheide, “Theory of Nuclear Reactions,” 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 Nuclear 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 Failure of the Woods-Saxon Nuclear Po-tential to Describe Both Fusion and Elastic Scattering: Possible Need for a New Dynamical Approach to Fusion,” Physical Re-view C, Vol. 70, 2004, 024605.
[5]	K. Hagino, N. Rowley and A. T. Kruppa, “A Program for Coupled-Channels Calcula-tions with All Order Couplings for Heavy-Ion Fusion Reac-tions,” Computer Physics Communications, Vol. 123, No. 1-3, 1999, pp. 143-152. doi:10.1016/S0010-4655(99)00243-X
[6]	M. V. Chushnya-kova and I. I. Gontchar, “Heavy Ion Fusion: 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 Lecture Notes, Volume I: Elastic and Inelastic Reactions,” Benjamin/Cummings Publishing Company, San Francisco, 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 Inte-raction Potential of Two Spherical Nuclei,” Computer Physics Communications, Vol. 181, 2010, pp. 168-182. doi:10.1016/j.cpc.2009.09.007
[12]	Dao T. Khoa, G. R. Sat-chler and W. von Oertzen, “Nuclear Incompressibility and Desnity Dependent NN Interactions in the Folding Model for Nucleus-Nucleus Potentials,” Physical Review C, Vol. 56, 1997, pp. 954-969. doi:10.1103/PhysRevC.56.954
[13]	I. Angeli, “A Consistent Set of Nuclear rms Charge Radii: Properties of the Radius Surface R(N,Z) ,” Atomic Data and Nuclear Data Tables, Vol. 87, 2004, pp. 185-206. doi:10.1016/j.adt.2004.04.002
[14]	C. R. Morton, A. C. Berriman, M. Dasgupta, D. J. Hinde, J. O. Newton, K. Hagino and I. J. Thompson, “Coupled-Channels Analysis of the 16O+208Pb Fusion Barrier Distribution,” Physical Review C, Vol. 60, No. 044608, 1999.
[15]	D. J. Hinde, C. R. Morton, M. Dasgupta, J. R. Leigh, J. C. Mein and H. Timmers, “Competition Between Fusion-Fis- sion and Quasi-Fission in the Reaction 28Si+208Pb,” Nuclear Physics, Vol. A592, 1995, pp. 271-289
[16]	D. J. Hinde, M. Dasgupta, N. Herrald, R. G. Nielson, J. O. Newton and M.A. Lane, “Isotopic Dependence of Fusion Barrier Energies in Reactions Forming Heavy Elements,” Physical Review C, Vol. 75, No. 054603, 2007.