Energy-dependent renormalization coefficients of folding-model description of 32S+40Ca elastic scattering

Baeza, A.; Bilwes, B.; Bilwes, R.; Dı́az, J.; Ferrero, J.L.

doi:10.1016/0375-9474(84)90401-9

Cited by 89 publications

(34 citation statements)

References 24 publications

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“…Secondly, the fusion potential is found to exhibit the threshold anomaly, as was observed for tightly bound projectiles [20,21,22], but the DR potential does not show a rapid energy variation, i.e., the threshold anomaly. Thirdly, at the strong absorption radius, the magnitude of the fusion potential was found to be much smaller than that of the DR potential.…”

Section: Introductionmentioning

confidence: 66%

Extended optical model analyses of elastic scattering and fusion cross sections for theLi6+Pb208system at near-Coulom

Udagawa

Kim

et al. 2007

Phys. Rev. C

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Based on the extended optical model approach in which the polarization potential is decomposed into direct reaction (DR) and fusion parts, simultaneous χ 2 analyses are performed for elastic scattering and fusion cross section data for the 6 Li+ 208 Pb system at near-Coulomb-barrier energies. A folding potential is used as the bare potential. It is found that the real part of the resultant DR part of the polarization potential is repulsive, which is consistent with the results from the Continuum Discretized Coupled Channel (CDCC) calculations and the normalization factors needed for the folding potentials. Further, it is found that both DR and fusion parts of the polarization potential satisfy separately the dispersion relation.

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Section: Introductionmentioning

confidence: 66%

Extended optical model analyses of elastic scattering and fusion cross sections for theLi6+Pb208system at near-Coulom

Udagawa

Kim

et al. 2007

Phys. Rev. C

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“…A finite-range interaction term [20] v nn EX (r) = 4631.8 e −4r 4r + 1787.13 e −2.5r 2.5r + 7.8474 e −0.7027r 0.7027r (7) has been adopted to calculate the exchange contribution in the potential. The effect of density dependence, though not so prominent for extremely peripheral collisions, is included as an exponentially varying multiplicative factor…”

Section: The Interactionmentioning

confidence: 99%

“…These couplings, on the one hand, dynamically polarize the real potential inducing a marked energy dependence of its strength around the Coulomb barrier energies and, on the other hand, contribute significantly to the absorptive potential for elastic scattering at large distances. The extraordinary energy dependence of the real potential, the so-called threshold anomaly, was experimentally observed [7][8][9][10] and was demonstrated to be dispersively connected with an increase with the energy of the imaginary potential accounting for the increasing number of open reaction channels absorbing the incident flux [11,12].…”

Section: Introductionmentioning

confidence: 97%

Coupled channel description of 16O+142,144,146Nd scattering around the Coulomb barrier using a complex microscopic potential

et al. 2003

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Angular distributions of elastic scattering and inelastic scattering from 2 + 1 state are measured for 16 O + 142,144,146 Nd systems at several energies in the vicinity of the Coulomb barrier. The angular distributions are systematically analyzed in coupled channel framework. Renormalized double folded real optical and coupling potentials with DDM3Y interaction have been used in the calculation. Relevant nuclear densities needed to generate the potentials are derived from shell model wavefunctions. A truncated shell model calculation has been performed and the calculated energy levels are compared with the experimental ones. To simulate the absorption, a 'hybrid' approach is adopted. The contribution to the imaginary potential of couplings to the inelastic channels, other than the 2 + 1 target excitation channel, is calculated in the Feshbach formalism. This calculated imaginary potential along with a short ranged volume Woods-Saxon potential to simulate the absorption in fusion channel reproduces the angular distributions for 16 O + 146 Nd quite well.

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“…It ~s shown thai the non-central potentmls should exhibit an energ5 dependence at energies m the vicinity of the Coulomb barrier Th~s energy dependence is, however, different from that of the elastkc optical potenual, occurring at lower energies It ff further shown thai there are correctmns to the tradmonal collectwc model such that. ff the trans~tmn potential ~s expressed as the derivative of the optical potential, the corresponding deformation length will be complex and energy-dependent Simple model calculauons are presented Durmg recent years, evidence of the energy-dependence of the real (the threshold anomaly) and imaginary parts of nucleus-nucleus optical potentials has been found by careful analyses of the elastxc scattering at energies m the vtcmlty of the Coulomb barrter [1][2][3][4][5] This energy dependence has been attributed to the couphng of non-clasttc channels to the elastic channel tn this energy region [6.7]. The threshold anomaly has also been related to the rapid mcrease of the surface imaginary potential as the energy ts mcreased above the Coulomb barrier and the consequent correction to the real potential through a dispersion relation [8][9][10].…”

mentioning

confidence: 99%

“…Durmg recent years, evidence of the energy-dependence of the real (the threshold anomaly) and imaginary parts of nucleus-nucleus optical potentials has been found by careful analyses of the elastxc scattering at energies m the vtcmlty of the Coulomb barrter [1][2][3][4][5] This energy dependence has been attributed to the couphng of non-clasttc channels to the elastic channel tn this energy region [6.7]. The threshold anomaly has also been related to the rapid mcrease of the surface imaginary potential as the energy ts mcreased above the Coulomb barrier and the consequent correction to the real potential through a dispersion relation [8][9][10].…”

mentioning

confidence: 99%

Threshold anomaly in non-central forces

Gómez‐Camacho

Nagarajan

1993

Physics Letters B

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The behavmur of the threshold anomaly for non-central potentials, wh,ch account for collectwe excltat,ons m heavy-~on colhs~ons. ~s investigated. It ~s shown thai the non-central potentmls should exhibit an energ5 dependence at energies m the vicinity of the Coulomb barrier Th~s energy dependence is, however, different from that of the elastkc optical potenual, occurring at lower energies It ff further shown thai there are correctmns to the tradmonal collectwc model such that. ff the trans~tmn potential ~s expressed as the derivative of the optical potential, the corresponding deformation length will be complex and energy-dependent Simple model calculauons are presented Durmg recent years, evidence of the energy-dependence of the real (the threshold anomaly) and imaginary parts of nucleus-nucleus optical potentials has been found by careful analyses of the elastxc scattering at energies m the vtcmlty of the Coulomb barrter [1][2][3][4][5] This energy dependence has been attributed to the couphng of non-clasttc channels to the elastic channel tn this energy region [6.7]. The threshold anomaly has also been related to the rapid mcrease of the surface imaginary potential as the energy ts mcreased above the Coulomb barrier and the consequent correction to the real potential through a dispersion relation [8][9][10]. The optical potential can thus be written aswhere go is an energy-independent potential (double-folded potential, for example), I,I'(E) ts the tmagmary potential and the dispersive real potenual AI'(E) ts defined aswhere P denotes a prmclpal value mtegral. Generahzlng this to the case of a set of strong-coupled channels, it was suggested by Satchler [ 1 1 ] that Permanent address SERC Daresbury Laborator3., Daresburs, Warrmgton WA4 4AD, UK each element of the potential matrix, which defines the coupled channels equation, should be expected to exhtbtt a threshold anomaly. In such a case, the energy dependence of the different diagonal and off-diagonal elements of the potenttal matrix will be attributed to couphngs to other channels not mcluded m the subset of coupled channels. However. a priori, there ts no reason for all the terms of the potential matrix to have the same energy dependence. Satchler [ 1 1 ] argued that, m the case of collective excitations, one would expect a similar energy dependence m the coupling mteractlon (transition potential) and the elastic optical potenttal, though one could expect a shift m the threshold of the coupling potential by approxtmatel,, half of the excitation energy. He further concludes that tfone uses an optical potential that ts consistent with the dispersion relatton but still needs an energy-dependent deformation length, then either the optical model itself or the nuclear structure model. or both, are madequateThe excitation functions of the first excited 3 -state of 2°8Pb by ~60 at energies around the Coulomb barrter have been measured and analysed [ 12,13] and more recently detailed angular dtstrtbutions for the same system were measured at energies from above t...

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Energy-dependent renormalization coefficients of folding-model description of 32S+40Ca elastic scattering

Cited by 89 publications

References 24 publications

Extended optical model analyses of elastic scattering and fusion cross sections for theLi6+Pb208system at near-Coulom

Extended optical model analyses of elastic scattering and fusion cross sections for theLi6+Pb208system at near-Coulom

Coupled channel description of 16O+142,144,146Nd scattering around the Coulomb barrier using a complex microscopic potential

Threshold anomaly in non-central forces

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