A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions

Abstract

A FORTRAN77 program is presented that calculates fusion cross sections and mean angular momenta of the compound nucleus under the influence of couplings between the relative motion and several nuclear collective motions. The no-Coriolis approximation is employed to reduce the dimension of coupled-channels equations. The program takes into account the effects of non-linear couplings to all orders, which have been shown to play an important role in heavy-ion fusion reactions at subbarrier energies. Distribution format: ASCIIComputer for which the program is designed and others on which it has been tested: any UNIX work-station or PC. The program has been tested on DEC and DEC-Alpha. Operating system or monitor under which the program has been tested: UNIX Programming language used: FORTRAN 77Keywords: Heavy-ion subbarrier fusion reactions, coupled-channel equations, higher order coupling, no-Coriolis approximation, incoming wave boundary condition, fusion cross section, mean angular momentum, spin distribution, fusion barrier distribution, multidimensional quantum tunneling Nature of physical problem It has by now been well established that fusion reactions at energies near and below the Coulomb barrier are strongly influenced by couplings of the relative motion of the colliding nuclei to several nuclear intrinsic motions. Recently, precisely measured fusion cross sections have become available for several systems, and a distribution of the Coulomb barrier, which is originated from the channel couplings, have been extracted. It has been pointed out that the linear coupling approximation, which has often been used in coupledchannels calculations, is inadequate in order to analyze such high presicion experimental data. The program CCFULL solves the coupled-channels equations to compute fusion cross sections and mean angular momenta of compound nucleus, taking into account the couplings to all orders. Method of solutionCCFULL directly integrates coupled second order differential equations using the modified Numerov method. The incoming wave boundary condition is employed and a barrier penetrability is calculated for each partial wave. Nuclear coupling matrix elements are evaluated by using the matrix diagonalisation method once the physical space has been defined. Restrictions on the complexity of the programThe program is best suited for systems where the number of channels which strongly couple to the ground state is relatively small and where multi-nucleon transfer reactions play less important role compared with inelastic channels. It also relies on an assumption that the fusion process is predominantly governed by quantum tunneling over the Coulomb 2 barrier. This assumption restricts a system which the program can handle to that where the sum of the charge of the projectile and the target nuclei Z p + Z T is larger than around 12 and the charge product Z p Z T less than around 1800. For most of experimental data which were measured to aim to extract fusion barrier distributions, this condition is well ...

Hot fusion-evaporation cross sections ofSc45-induced reactions with lanthanide targets

“…The microscopic shell correction is adopted from the tabulated data of Möller et al [45]. Average values of l CN were calculated using the coupled-channel code CCFULL [53], but only small impact parameters and thus small angular momenta should contribute to the EvR cross sections because the higher partial waves result in almost certain fission during the de-excitation cascade.…”

In-beam spectroscopy with intense ion beams: Evidence for a rotational structure in246Fm

“…However, the effects of coupling to excited states of the target and projectile can give rise to a distribution of Coulomb barriers with, in particular, some barrier "weight" at lower energies. With no coupling, the peak in the distribution of angular momenta occurs for L ≈ 8h, with a partial cross section of σ L ≈ 10 µb [33]. Coupled-channels calculations using the program CCFULL [33] figure 6(b) and the barrier distribution D = dT 0 /dE is shown in 6(c).…”

“…With no coupling, the peak in the distribution of angular momenta occurs for L ≈ 8h, with a partial cross section of σ L ≈ 10 µb [33]. Coupled-channels calculations using the program CCFULL [33] figure 6(b) and the barrier distribution D = dT 0 /dE is shown in 6(c). We now see that the lowest barrier occurs at about 154.7 MeV, now below our incident energy.…”

Theoretical study of fusion reactions 32S + 94,96Zr and 40Ca + 94,96Zr and quadrupole deformation of 94Zr

“…Broglia et al [29,30] suggested that the coupling to transfer channels with positive Q values is needed to explain the enhancement of fusion data for the Ni + Ni systems. Large enhancements of subbarrier fusion cross sections have been also observed in many other reaction systems with positive Q-value neutron transfer (PQNT) channels, such as the reaction systems 32 S + A Pd (A = 104-106, 108, and 110) [36], 40 Ca + 44,48 Ca [37], 40 Ca + 94,96 Zr [38,39], and 32 S + 94,96 Zr [40,41]. For some of these systems, the fusion excitation functions have been measured in sufficiently small energy steps, which can be used to extract the underlying barrier distributions to study the contribution from transfer channels.…”

“…Thus, the influence of the PQNT channels on fusion is accompanied by and depends on the change of nuclear deformations. In the quantum coupled channel (QCC) model [48], the coupling to PQNT channels is treated approximately by using a macroscopic form factor. Within the microscopic dynamics models, such as the quantum molecular dynamic model [49][50][51][52][53][54] and the time-dependent HartreeFock method [55][56][57][58][59][60][61], the effects of surface excitations as well as nucleon transfer can be automatically included.…”