On the accuracy of multipole expansion of deformed density distribution

Ismail, M.; Seif, W. M.; Ellithi, A. Y.; Salah, F.

doi:10.1088/0954-3899/35/7/075101

Cited by 21 publications

(17 citation statements)

References 25 publications

(63 reference statements)

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“…A similar study had been made in Ref. 17 for different ranges of the NN force. In this study the authors assumed the existence of quadruple and hexadecapole deformations and they found 17 that the accuracy of the three terms expansion increases with increasing both the range of NN force and the mass number of the incident projectile.…”

Section: The Accuracy Of Multipole Expansion In Calculating Hi-potentsupporting

confidence: 52%

“…According to Table 1, the maximum error in the six terms is 11% for 40 Ca and 7% for 208 Pb which is still large. In fact when we use finite range NN force like Michigan 3-range Yukawa (M3Y)-interacting [15][16][17] (consists of two finite range terms and a zero range one) to calculate the Coulomb barrier parameters for spherical-deformed interacting pair, we expect that the error in the barrier parameters due to the six terms will be more smaller than the above values. This is because the barrier is combination of the finite range Coulomb interaction and the nuclear part which is derived from finite range and zero range terms.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…17 We include both quadrupole and octupole deformations and also limit ourselves to the interaction potential between spherical projectile (P) and deformed target (T). In the double folding model the real part of the interaction potential can be written as…”

Section: The Accuracy Of Multipole Expansion In Calculating Hi-potentmentioning

confidence: 99%

“…15 Each term is the product of spherical harmonic and radial part. 15,17 This method is useful and reduces the amount of calculations and can be used for the most of the widely used types of NN forces. The aim of the present work is to estimate the error produced in HI potential when multipole expansion is used.…”

Section: Introductionmentioning

confidence: 99%

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Accuracy of the Multipole Expansion of Density Distribution in the Presence of Octupole Deformation

Ismail

Botros

Wheida³

2011

Int. J. Mod. Phys. E

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The accuracy of multipole expansion of density distribution for deformed nuclei is tested. The interaction potential for a deformed-spherical pair of nuclei was calculated using the folding model derived from zero-range nucleon-nucleon (NN) interaction. We considered two spherical projectiles Ca 40 and Pb 208 scattered on U 238 deformed target nucleus. The error in the heavy ion (HI) potential resulting from using a truncated multipole density expansion is evaluated for each case in the presence of octupole deformation δ 3 besides quadrupole δ 2 . We are interested in the value of error for R ≥ R T (touching distance). We found that for values of |δ 3 | ≤ 0.1 the error at R = R T reaches reasonable values when six terms expansion is used. For |δ 3 | = 0.2, we calculated the Coulomb barrier parameters using realistic NN force and found that the large error present in six terms for zero range force decreases strongly to less than 1% when the zero range is added to finite range forces and Coulomb interaction to form the Coulomb barrier. It is noted that the negative value of octupole deformation parameters δ 3 = −0.1 produce error at orientation angle θ equal in value to that produced at angle (180 • − θ) for the positive values δ 3 = 0.1. We also found that the error decreases as the mass number of the projectile nucleus increases.

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Section: The Accuracy Of Multipole Expansion In Calculating Hi-potentsupporting

confidence: 52%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: The Accuracy Of Multipole Expansion In Calculating Hi-potentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Accuracy of the Multipole Expansion of Density Distribution in the Presence of Octupole Deformation

Ismail

Botros

Wheida³

2011

Int. J. Mod. Phys. E

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“…To simplify the complications coming from the finite range of the proton-proton Coulomb force, the density multipole expansion of the deformed daughter has been used to calculate the Coulomb direct part [27,28]. If the ground states spin-parity of parent ( ) and daughter ( ) are not identical, we have then unfavored decay mode.…”

Section: Theoretical Formalismmentioning

confidence: 99%

Preformation probability inside α emitters having different ground state spin-parity than their daughters

2015

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ABSTRACT:The ground-state spin and parity of a formed daughter in the radioactive -emitter is expected to influence the preformation probability of the  and daughter clusters inside it. We investigate the  and daughter preformation probability inside odd-A and doubly-odd radioactive nuclei when the daughter and parent are of different spin and/or parity. We consider only the ground-state to ground-state unfavored decays. This is to extract precise information about the effect of the difference in the ground states spin-parity of the involved nuclei far away any influences from the excitation energy if the decays are coming from isomeric states. The calculations are done for 161 -emitters, with and , in the framework of the extended cluster model, with WKB penetrability and assault frequency. We used a Hamiltonian energy density scheme based on Skyrme-SLy4 interaction to compute the interaction potential. The  plus cluster preformation probability is extracted from the calculated decay width and the experimental half-life time. We discussed in detailed steps the effect of angular momentum of the emitted -particle on the various physical quantities involved in the unfavored decay process and how it is finally increases the half-life time. We found that if the ground states spin and/or parity of parent and daughter nuclei are different, then the preformation probability of the -cluster inside parent is less than it would be if they have similar spin-parity. We modified the formula that gives the preformation probability in terms of the numbers of protons and neutrons outside the shell closures of parent, to account for this hindrance in the preformation probability for the unfavored decays between ground states.2

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Investigation of deformation effects on the decay properties of12C+αCluster states in 16 O

et al. 2018

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We have analyzed the elastic scattering angular distributions data of the α+ 12 C reaction over a wide energy range (E lab =28.2 to 35.5 MeV) within the framework of the Optical Model formalism. A double folding (DF) type real potential was used with a phenomenological Woods-Saxon-squared (WS2) type imaginary potential. Good agreement between the calculations and experimental data was obtained. By using the real DF potential we have calculated the properties of the α-cluster states in 16 O by using the Gamow code as well as the α-decay widths by using the WKB method. We implemented a 12 C+α cluster framework for the calculation of the excitation energies and decay widths of 16 O as a function of the orientation of the planar 12 C nucleus with respect to the α-particle. These calculations showed strong sensitivity of the widths and excitation energies to the orientation. Branching ratios were also calculated and though less sensitive to the 12 C orientation, it was found that 12 C gs +α structure, with the α-particle orbiting the 12 C in its ground state, is dominant. This work demonstrates that deformation, and the orientation, of 12 C at plays a crucial role in the understanding the nature of the α-cluster states in 16 O.

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On the accuracy of multipole expansion of deformed density distribution

Cited by 21 publications

References 25 publications

Accuracy of the Multipole Expansion of Density Distribution in the Presence of Octupole Deformation

Accuracy of the Multipole Expansion of Density Distribution in the Presence of Octupole Deformation

Preformation probability inside α emitters having different ground state spin-parity than their daughters

Investigation of deformation effects on the decay properties of12C+αCluster states in 16 O

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