A barrier-penetration model for heavy-ion fusion, valid at all energies

Abstract

We present a barrier-penetration model for heavy-ion fusion valid from the lowest energies available up to the largest energies for which the critical-radius picture is realistic. The parameters of the model are a critical radius and the parameters of a nucleus-nucleus interaction, whose form factor can be chosen freely. Fusion cross sections for a large number of systems, for which low-energy data exist, are fitted with a Woods-Saxon potential. Realistic parameters are obtained for the Coulomb barrier. Different applications and some limitations of the model are discussed.

Smooth double barriers in quantum mechanics

“…5 High energy physics. A barrier penetration model has been developed for heavy ion fusion, 6 taking into account the realistic features of the Coulomb potential for the case of nuclei. The typical barrier shapes encountered for nuclei conform to double barriers.…”

Fusion Reactions Between Heavy Nuclei

“…Other measurements have shown similar effects (129,130,(232)(233)(234) that seem to be related to valence nucleon effects and to deformation effects (156,158,159,235). Theoretical considerations of sub-barrier fusion have included barrier penetration models (236)(237)(238)(239)(240)(241)(242), the incoming wave boundary condition model (40,52,243), the optical model ( 244), the WKB model (245), and a deformed nucleus, coupled channel model (246). For some systems barrier penetration models have been fitted to the data (55,125,128,(247)(248)(249)(250) and the de-excitation of fusion residues in the sub-barrier region has been considered using the statistical model (5 1, 94).…”

“…12-20, 61, 62, 71, 86, 87, 98, 104, 105, 130--132, 143, 145, 158, 173, 197, 198, 217, 223, 225, 229, 258, 274, 282,283, 307,308, 312, 316,325-327, 330, 333, 336-338, 357-359, 378 13C : 21, 22, 63-65 14C : 66 14N : 3-5, 23-38, 67, 68, 72, 73, 106, 163, 17 4, 175, 184, 216, 221, 226, 230, 292, 293, 339, 379 15N : 29, 30, 107 160: 1,6, 31-39, 74-8 2, 88, 89,99, 100, 108-1 14, 133-136, 144, 146, 148, 149, 157, 172, 176, 177, 185, 199-201, 204, 220, 228, 255, 259, 263, 265, 271, 273, 275-278, 287, 294, 295, 304, 309, 310, 313, 314, 320, 321, 328, 331, 334, 340, 341-343, 352, 353, 360--362, 380 170: 7, 8, 40--42, 69,83, 115 180: 2, 43-47, 70, 90, 116, 1 17, 137, 264 '9F : 48-51, 85, 91, 288, 3l7, 322 2°Ne : 52-55, 92, 118-122, 150,.151, 202, 231, 256, 266, 267, 296, 297, 323, 332, 344-346, 363, 364, 371, 381 22Ne : 289 24 Mg : 93, 138, 203 26 Mg : 9 4 126,159,160,166,168,179,180,186,188,189,190,193, 218,236,242,243,247,248,[260][261][262]209,222,227,232,241,245,249,269,270,272,280,281, 291,[298][299][300]318,319,324,[347][348][349]…”

Effective fusion barrier transmission model for heavy-ion fusion

“…Thus, the model is consistent with the heavy-ion elastic scattering which provides reliable information regarding OMP only in the surface region. Other attempts [14,15] to obtain improved versions of BTM are successful in a limited sense, but their relations with OMP and the DRM are not clear. If one accepts the assumption of the DRM [12] that the fusion process gets initiated through the elastic channel and is related to the loss of flux, such that 0 , is governed by W(r) in the region r S RF, one visualises that the fusion takes place between the interacting nuclei approaching each other when they penetrate into the sphere r = RF.…”