Towards a unified description of evaporation-residue fusion cross-sections above the barrier

Abstract

PACS 25.70.Jj -Fusion and fusion-fission reactions PACS 25.70. -z -Low and intermediate energy heavy-ion reactionsAbstract -A meticulous study of nearly 300 fusion-evaporation cross section data reveals that, when properly scaled, fusion excitation function complies with a universal homographic law which is, within experimental errors, reaction system independent. From a such complete and summed complete and incomplete fusion excitation functions extracted are the limiting energy for the complete fusion and the main characteristics (onset, maximum and vanishing) of the incomplete fusion. The DYWAN microscopic transport model correctly predicts the incomplete fusion cross section for incident energies 15A MeV and suggests that the nuclear transparency is at the origin of fusion disappearance.

A unified homographic law for fusion excitation functions above the barrier

“…The inset in the main inset displays the ratio of CF and CF+IF best-fit excitation functions as a function of E avail . [5,6]. These 57 CF σ red data points belonging to the 14 reaction systems and obtained with the heuristic σ reac discussed above are displayed in the main inset of figure 5 as a function of E avail .…”

“…In order to compare so many different systems it is not enough to scale only the cross sections. We have shown [5,6] that energy has to be scaled too. In order to express on the same footing the mass asymmetric systems with those which are mass symmetric the system energy should be expressed in units of the so-called system available energy that is nothing but the center-of-mass energy per nucleon…”

“…In two recent papers [5,6] we have published a systematic study of both CF and IF fusion cross sections σ fus for incident energies E lab /nucleon = E in higher than about 3A -4A MeV. From the works published during the past 40 years we have collected 382 CF and CF+IF σ fus data points belonging to 81 reaction systems with a vast variety of projectile-target pairs.…”

“…By properly reducing σ fus values with the (total) reaction cross section σ reac and by applying an original energy scaling we have demonstrated that, irrespectively of the details of a given reaction system, the fusion excitation function follows a simple universal functional law. On that way we have been able to identify those data points for which, the most likely, the reported σ fus values suffer from a non-fusion contribution [5,6] and those for which other reaction mechanism has been erroneously identified as fusion [7]. Discarding these data one ends with 76 systems and 316 CF+IF σ fus data points plus 57 CF data points.…”

“…where a, b, and c are free parameters and E is taken as E avail [5,6]. 24Mg+12C 12C+27Al 16O+24Mg 20Ne+20Ne 28Si+12C 16O+26Mg 18O+24Mg 16O+27Al 32S+12C 20Ne+26Mg 20Ne+27Al 20Ne+27Al 35Cl+12C 16O+32S 16O+40Ca 28Si+28Si 28Si+28Si 32S+24Mg 19F+40Ca 32S+27Al 35Cl+24Mg 12C+48Ti 23Na+40Ca 16O+48Ti 40Ar+27Al 28Si+40Ca 12C+58Ni 36Ar+KCl 12C+63Cu 40Ar+40Ca 40Ca+40Ca 58Ni+27Al 24Mg+63Cu 48Ti+45Sc 36Ar+58Ni 16O+92Mo 32S+76Ge 40Ar+68Zn 52Cr+56Fe 19F+93Nb 64Zn+48Ti 58Ni+58Ni 18O+100Mo 78Kr+40Ca 82Kr+40Ca 12C+124Sn 14N+124Sn 20Ne+124Sn 40Ar+109Ag 84Kr+65Cu 40Ar+116Sn 40Ar+121Sb 16O+146Nd 132Xe+30Si 40Ar+124Sn 14N+154Sm 14N+159Tb 16O+159Tb 20Ne+159Tb 58Ni+124Sn 20Ne+169Tm 12C+182W 19F+175Lu 40Ar+154Sm 14N+181Ta 16O+181Ta 40Ar+164Dy 24Mg+181Ta 40Ar+165Ho 12C+197Au 14N+197Au 16O+197Au 16O+197Au 20Ne+197Au 40Ar+197Au 14N+232Th 40Ar+238U Figure 3.…”