Validity of the linear coupling approximation in heavy-ion fusion reactions at sub-barrier energies

Hagino, K.; Takigawa, N.; Dasgupta, M.; Hinde, David; Leigh, J.R.

doi:10.1103/physrevc.55.276

Cited by 82 publications

(89 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Contrary to the nuclear couplings, the higher order couplings of the Coulomb interaction have been shown to play a rather minor role [6]. The matrix elements are then given by …”

Section: /3mentioning

confidence: 99%

“…In the past, the coupledchannels calculations were often performed using the linear coupling approximation, where the coupling potential is expanded in powers of the deformation parameter, keeping only the linear term. It has been demonstrated that non-linear couplings significantly affect the shape of fusion barrier distributions and thus the linear coupling approximation is inadequate in quantitative comparison with the recent high quality data of fusion cross sections [6,7]. The program CCFULL includes the couplings to full order and thus it does not introduce the expansion of the coupling potential.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Hagino

Rowley

Kruppa

1999

Computer Physics Communications

Self Cite

903

828

View full text Add to dashboard Cite

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 ...

show abstract

“…Contrary to the nuclear couplings, the higher order couplings of the Coulomb interaction have been shown to play a rather minor role [6]. The matrix elements are then given by …”

Section: /3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Hagino

Rowley

Kruppa

1999

Computer Physics Communications

Self Cite

903

828

View full text Add to dashboard Cite

show abstract

“…However, it is difficult to judge the significance of the results because of the limited number of excitations that were included in the C. C. calculations. For example, the only excitation considered in the nickel isotopes is the one-phonon 2 + excitation, but it is well known that couplings to the 3 − state and higher-order couplings to two-phonon states are tremendously enhancing the heavy-ion fusion cross section [15,16].…”

Section: Introductionmentioning

confidence: 99%

Signature of shallow potentials in deep sub-barrier fusion reactions

2007

View full text Add to dashboard Cite

We extend a recent study that explained the steep falloff in the fusion cross section at energies far below the Coulomb barrier for the symmetric dinuclear system 64 Ni+ 64 Ni to another symmetric system, 58 Ni+ 58 Ni, and the asymmetric system 64 Ni+ 100 Mo. In this scheme the very sensitive dependence of the internal part of the nuclear potential on the nuclear equation of state determines a reduction of the classically allowed region for overlapping configurations and consequently a decrease in the fusion cross sections at bombarding energies far below the barrier. Within the coupled-channels method, including couplings to the low-lying 2 + and 3 − states in both target and projectile as well as mutual and two-phonon excitations of these states, we calculate and compare with the experimental fusion cross sections, S-factors, and logarithmic derivatives for the above mentioned systems and find good agreement with the data even at the lowest energies. We predict, in particular, a distinct double peaking in the S-factor for the far subbarrier fusion of 58 Ni+ 58 Ni which should be tested experimentally.

show abstract

“…The simplification is achieved by using one or more of the following approximations: i) the linear coupling approximation, where the nuclear coupling potential is assumed to be linear with respect to an excitation operator for intrinsic motions, ii) multi-phonon excitations are neglected, and iii) the eigenchannel approximation, where the intrinsic excitation energies are treated approximately. Since the effective coupling strength is approximately proportional to Z P Z T for a given value of deformation parameter [18], the shortcomings of these approximations become more severe for heavier systems.…”

Section: Coupled-channels Approach To Fusion Of Massive Systems Effecmentioning

confidence: 99%

Fusion dynamics around the Coulomb barrier

Hagino¹

2004

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

Abstract.We perform exact coupled-channels calculations, taking into account properly the effects of Coulomb coupling and the finite excitation energy of collective excitations in the colliding nuclei, for three Fm formation reactions, 37 Sc + 197 Au reactions, those calculations well reproduce the experimental total fission cross sections, and a part of the extra-push phenomena can be explained in terms of the Coulomb excitations to multi-phonon states. On the other hand, for the heaviest system, the deep-inelastic collisions become much more significant, and the fission cross sections are strongly overestimated. We also discuss the surprisingly large surface diffuseness parameters required to fit recent highprecision fusion data for medium-heavy systems, in connection with the fusion supression observed in massive systems.

show abstract

Validity of the linear coupling approximation in heavy-ion fusion reactions at sub-barrier energies

Cited by 82 publications

References 35 publications

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

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

Signature of shallow potentials in deep sub-barrier fusion reactions

Fusion dynamics around the Coulomb barrier

Contact Info

Product

Resources

About