Test of the proximity theorem for deformed nuclei

Seiwert, M.; Greiner, Walter; Oberacker, V. E.

doi:10.1103/physrevc.29.477

Cited by 37 publications

(31 citation statements)

References 14 publications

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“…To cope with this problem the observation was made in [34,35] that, whereas any theory of heavy-ion potentials is expected to reduce to the double-folding model in the limit of large ion-ion separations and vanishing density overlap, the compound system resulting from fusing the two ions is accurately described by the liquid-drop energy E LDM . To interpolate between these two extremes the nuclear deformation energy was written as…”

Section: Simulations Of a Repulsive Corementioning

confidence: 99%

Signature of shallow potentials in deep sub-barrier fusion reactions

2007

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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.

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Section: Simulations Of a Repulsive Corementioning

confidence: 99%

Signature of shallow potentials in deep sub-barrier fusion reactions

2007

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“…While asymptotically such potentials are determined from Coulomb and centrifugal interactions, the short distance behavior strongly depends on the nuclear surface properties and the readjustments of the combined nuclear system, resulting in potential pockets, which determine the characteristics of the compound nuclear system.Among the various approaches for calculating ion-ion potentials are: 1) Phenomenological models such as the Bass model [1,2], the proximity potential [3,4,5,6], and potentials obtained via the double-folding method [7,8,9,10]. Some of these potentials have been fitted to experimental fusion barrier heights and have been remarkably successful in describing scattering data.…”

mentioning

confidence: 99%

“…1 are two widely used phenomenological potentials, the standard proximity potential for two spherical nuclei [3,4,5] and the double-folding potential with M3Y effective NN interaction [7,8,9,10]. We evaluate the double-folding integral for the strong nuclear and Coulomb interaction in momentum space [10].…”

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confidence: 99%

Heavy-ion interaction potential deduced from density-constrained time-dependent Hartree-Fock calculation

2006

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We present a new method for calculating the heavy-ion interaction potential from a densityconstrained time-dependent Hartree-Fock calculation.PACS numbers: 21.60.Jz,25.60.Pj, The study of internuclear potentials for heavy-ion collisions is of fundamental importance for the formation of superheavy elements and nuclei far from stability. While asymptotically such potentials are determined from Coulomb and centrifugal interactions, the short distance behavior strongly depends on the nuclear surface properties and the readjustments of the combined nuclear system, resulting in potential pockets, which determine the characteristics of the compound nuclear system.Among the various approaches for calculating ion-ion potentials are: 1) Phenomenological models such as the Bass model [1,2], the proximity potential [3,4,5,6], and potentials obtained via the double-folding method [7,8,9,10]. Some of these potentials have been fitted to experimental fusion barrier heights and have been remarkably successful in describing scattering data. 2) Semi-microscopic and full microscopic calculations such as the macroscopic-microscopic method [11,12,13], the asymmetric two-center shell-model [14], constrained Hartree-Fock (CHF) with a constraint on the quadrupole moment or some other definition of the internuclear distance [15,16], and other mean-field based calculations [17,18,19].One common physical assumption used in many of the semi-microscopic calculations is the use of the frozen density or the sudden approximation. As the name suggests, in this approximation the nuclear densities are unchanged during the computation of the ion-ion potential as a function of the internuclear distance. On the other hand, the microscopic calculations follow a minimum energy path and allow for the rearrangement of the nuclear densities as the relevant collective parameter changes. As it was pointed out in Ref. [12], CHF calculations seldom produce the correct saddle-point since the system can follow any one of the minimum potential valleys in the multidimensional potential energy surface. In this paper, we shall call this the static adiabatic approximation since a real adiabatic calculation would involve a fully dynamical calculation, thus also including the effects of dynamical rearrangements.One conclusion that may be reached from the discussion above is that ultimately we would like to have an approach for calculating internuclear potentials which is time-dependent and is unrestricted in the choice of collective variables. In this paper we provide such an approach in which time-dependent Hartree-Fock (TDHF) is used for the nuclear dynamics and the potential energy is calculated by constraining the time-dependent density.The density constraint is a novel numerical method that was developed in the mid 1980's [20,21] and was used to provide a microscopic description of the formation of shape resonances in light systems [21]. In this approach the TDHF time-evolution takes place with no restrictions. At certain times during the evolution the instantan...

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“…The 238U nucleus has flat surface areas due to the existence of hexadecapole deformation. For a certain orientation, two flat areas face each other and in this case, the number of nucleons which come into nuclear contact is considerably increased compared to the situation of two curved surfaces [20]. This explains the dependence of the pocket depth on the relative orientation of the 23sU nuclei.…”

Section: Numerical Calculations and Discussionmentioning

confidence: 89%

The effect of deformation on the nucleus-nucleus optical model potential and how it produces pockets

Ismail

Rashdan

Faessler

et al. 1986

Z. Physik A - Atomic Nuclei

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A recently derived nucleon-nucleon interaction has been used to calculate both the real and imaginary parts of the optical-model potential for the two nuclear pairs Pb + U and U+U. Three different bombarding energies per projectile nucleon (6MeV, 11.8 MeV and 20.9 MeV) have been considered. We found a dramatic dependence of both the real and imaginary parts of the optical-model potential on relative orientation of the colliding nuclei. For the two considered pairs we predicted pockets whose depths depend strongly on orientation.

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Test of the proximity theorem for deformed nuclei

Cited by 37 publications

References 14 publications

Signature of shallow potentials in deep sub-barrier fusion reactions

Signature of shallow potentials in deep sub-barrier fusion reactions

Heavy-ion interaction potential deduced from density-constrained time-dependent Hartree-Fock calculation

The effect of deformation on the nucleus-nucleus optical model potential and how it produces pockets

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