Reduction of coupled equations for heavy ion reactions

Tanimura, O.

doi:10.1103/physrevc.35.1600

Cited by 37 publications

(30 citation statements)

References 5 publications

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“…The coupled-channels calculations that are performed make use of the so-called rotating frame [12,13] or isocentrifugal [14] approximation, which simplifies the calculations by reducing the number of channels considerably. The calculations use either the M3Y+rep potential [15] or the standard Woods-Saxon potential of Ref.…”

Section: Coupled-channels Calculationsmentioning

confidence: 99%

Fusion ofSi28+Si28,30: Different trends at

et al. 2014

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Background:The fusion excitation function of the system 28 Si + 28 Si at energies near and below the Coulomb barrier is known only down to ≃15 mb. This precludes any information on both coupling effects on sub-barrier cross sections and the possible appearance of hindrance. For 28 Si + 30 Si even if the fusion cross section was measured down to ≃50µb, the evidence of hindrance is marginal. Both systems have positive fusion Q-values. While 28 Si has a deformed oblate shape, 30 Si is spherical.Purpose: Investigating: 1) the possible influence of the different structure of the two Si isotopes on the fusion excitation functions in the deep sub-barrier region; 2) whether hindrance exists in the Si+Si systems and whether it is strong enough to generate an S factor maximum, thus allowing a comparison with lighter heavy-ion systems of astrophysical interest.Methods: 28 Si beams from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro were used. The set-up was based on an electrostatic beam separator, and fusion evaporation residues (ER) were detected at very forward angles. Angular distributions of ER were measured.Results: Fusion cross sections of 28 Si + 28 Si have been obtained down to ≃600 nb. The slope of the excitation function has a clear irregularity below the barrier but no indication of a S-factor maximum is found. For 28 Si + 30 Si the previous data have been confirmed and two smaller cross sections have been measured down to ≃4µb. The trend of the S-factor reinforces the previous weak evidence of hindrance. Conclusions:The sub-barrier cross sections for 28 Si + 28 Si are overestimated by coupled-channels calculations based on a standard Woods-Saxon potential, except for the lowest energies. Calculations using the M3Y+repulsion potential are adjusted to fit the 28 Si + 28 Si and the existing 30 Si + 30 Si data. An additional weak imaginary potential (probably simulating the effect of the oblate 28 Si deformation) is required to fit the low-energy trend of 28 Si + 28 Si. The parameters of these calculations are applied to predict the ion-ion potential for 28 Si + 30 Si. Its cross sections are well reproduced by including also one-and successive two-neutron transfer channels, besides the low-lying surface excitations.

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Section: Coupled-channels Calculationsmentioning

confidence: 99%

Fusion ofSi28+Si28,30: Different trends at

et al. 2014

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“…I, the validity of the iso-centrifugal approximation has been well tested for heavy-ion fusion reactions [18]. In contrast, it is known that the approximation fails to reproduce the exact result for scattering angular distributions in the presence of the long-range Coulomb force.…”

Section: Applicability Of the Iso-centrifugal Approximationmentioning

confidence: 99%

“…For a problem of heavyion fusion reactions, these equations are often solved in the iso-centrifugal approximation [25], where one replaces the angular momentum of the relative motion in each channel by the total angular momentum J (this approximation is also referred to as the rotating frame approximation or the no-Coriolis approximation in the literature). The iso-centrifugal approximation dramatically simplifies the angular momentum couplings, and reduces the dimension of the coupled-channels equations in a considerable way [13][14][15][16][17][18][19][20][21]. The coupledchannels equations in this approximation are given by…”

Section: Barrier Distribution For Multi-channel Systemsmentioning

confidence: 99%

“…And of course many experimental data also show welldefined barrier structures, which can be reproduced by coupled-channels calculations, even for systems where the excitation energies are large. However, although the validity of the isocentrifugal approximation has been shown to work well for fusion [18], its applicability for scattering processes in the presence of the long-range Coulomb interaction is less clear [17,[19][20][21]. We therefore re-examine its validity for the quasi-elastic barrier distribution.…”

Section: Introductionmentioning

confidence: 99%

“…III, we discuss the barrier distribution for coupled-channels systems. Theoretically, barrier distributions have a clear physical meaning only in the limit of zero angular momentum transfer (that is, in the isocentrifugal approximation [13][14][15][16][17][18][19][20][21]) with vanishing excitation energies for the intrinsic degrees of freedom. In this limit the barrier distribution representation may be derived analytically as a weighted sum of test functions.…”

Section: Introductionmentioning

confidence: 99%

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Large-angle scattering and quasielastic barrier distributions

2004

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We study in detail the barrier distributions extracted from large-angle quasi-elastic scattering of heavy ions at energies near the Coulomb barrier. Using a closed-form expression for scattering from a single barrier, we compare the quasi-elastic barrier distribution with the corresponding test function for fusion. We examine the isocentrifugal approximation in coupled-channels calculations of quasi-elastic scattering and find that for backward angles, it works well, justifying the concept of a barrier distribution for scattering processes. This method offers an interesting tool for investigating unstable nuclei. We illustrate this for the 32 Mg + 208 Pb reaction, where the quadrupole collectivity of the neutron-rich 32 Mg remains to be clarified experimentally.

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