Effect of in-medium NN cross section and finite range force on the reaction cross section for a deformed target nucleus

Ismail, M.; Osman, M. M.; Gebaly, H. El; Salah, F.; Seif, W. M.

doi:10.1103/physrevc.69.014606

Cited by 7 publications

(11 citation statements)

References 14 publications

(20 reference statements)

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“…interaction at energy range from 10 to 1000 MeV/nucl, using the prolate quadrupole deformation parameter 2  =0.219 (see Fig.4 and table [5]). Nearly, we get the same results as reaction and the spherical reaction cross-section lies between them as given in [29]. [5,22].…”

Section: [3] Calculations and Resultssupporting

confidence: 52%

“…In the Glauber model, the nuclear phase shift of nucleus-nucleus collision is the sum of nucleon-nucleon phase shift of nucleons in the two nuclei [1]. The nuclear phase shift is considered for the two colliding nuclei, such that one of them is deformed [27][28][29][30]. In the present work the quadrupole deformation and modified Glauber model are studied with fixed orientations to calculate the reaction crosssections.…”

Section: [2] Theorymentioning

confidence: 99%

See 1 more Smart Citation

Nucleus–nucleus reaction cross sections for deformed nuclei

Hassan¹,

Farag²,

Abul-Magd³

et al. 2008

Phys. Scr.

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Reaction cross-sections are calculated using the Coulomb modified Glauber model for deformed target nuclei. The deformed nuclear matter density of the target is expanded into multipoles of order are studied at energy range (10-1000 MeV/nucleon). The most significant effects in the intermediate energy range are the Coulomb field and in-medium effect that modified the trajectory of the incident beams. Introducing the deformation effect beside the Coulomb field and in-medium effect improves the agreement with the experimental data and two empirical parameterizations in the case of not finding experimental data. Moreover it is indicated that the enhancement of the reaction cross-sections is attributed with fixed orientation in deformed nuclei.

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Section: [3] Calculations and Resultssupporting

confidence: 52%

Section: [2] Theorymentioning

confidence: 99%

Nucleus–nucleus reaction cross sections for deformed nuclei

Hassan¹,

Farag²,

Abul-Magd³

et al. 2008

Phys. Scr.

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“…For the reactions induced by stable nuclei, the results of the Glauber theory agree with the experimental data well. Considering the total cross section of the reaction medium effect and limited range interaction, Ismail calculated the total cross section of 12 C+ 238 U by using the optical limit of the Glauber theory [3]; the results agree with the experimental data excellently. Rashdan investigated the shape, deforma-tion, and orientation dependence as well as in-medium effects for the reaction cross sections of 16,19 C+C systems within the optical limit of the Glauber theory [4].…”

Section: Introductionmentioning

confidence: 57%

Study of the total reaction cross section via QMD

Yang¹,

Guo²,

Zhang³

et al. 2013

Chinese Phys. C

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This paper presents a new empirical formula to calculate the average nucleon-nucleon (N-N) collision number for the total reaction cross sections (σR). Based on the initial average N-N collision number calculated by quantum molecular dynamics (QMD), quantum correction and Coulomb correction are taken into account within it. The average N-N collision number is calculated by this empirical formula. The total reaction cross sections are obtained within the framework of the Glauber theory. σR of 23Al+12C, 24Al+12C, 25 Al+12C, 26Al+12C and 27Al+12C are calculated in the range of low energy. We also calculate the σR of 27Al+12C with different incident energies. The calculated σR are compared with the experimental data and the results of Glauber theory including the σR of both spherical nuclear and deformed nuclear. It is seen that the calculated σR are larger than σR of spherical nuclear and smaller than σR of deformed nuclear, whereas the results agree well with the experimental data in low-energy range.

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“…Later, Warner et al [7] introduced the local matter density in σ NN for each volume element of the nuclear overlap region; as a result the value of σ R is reduced by a relatively small percentage compared with that obtained using free NN cross section σ f NN . The effect of the finite range force [8] is found to increase σ R by about 5% compared to the zero range force for the reaction 238 U + 12 C.…”

mentioning

confidence: 88%

Effect of finite range of theNNforce andNNcross section on reaction cross section for neutron rich nuclei

2005

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The reaction cross section (σ R ) is calculated using the optical limit of the Glauber theory. A density-dependent effective nucleon-nucleon (NN) cross section σ NN is considered. Finite and zero range NN interactions are studied. The effect of finite range and an appropriate local density can increase σ R up to 20% compared to the zero range at constant density (0.16 fm −3 ), while a zero range calculation with free NN cross section increases σ R up to 13%. These factors affect the values of the rms radii for neutron rich nuclei extracted from σ R . PACS number(s): 24.10. Ht, 25.60.Dz, Recently, the optical limit to Glauber theory [1] has been used with considerable success to describe the nucleus-nucleus reaction cross section σ R [2]. The inputs to these calculations are the NN cross section σ NN and the density distribution of the interacting nuclei. The cross section σ R is usually calculated by assuming a zero range force of the interacting nucleons, and σ NN is considered through different approaches. First, σ NN is taken directly as a free NN cross section σ f NN without density dependence [3,4], and Cai Xiangzhou et al.[5] developed a density-dependent formula (in medium) averaged over the isospin of the interacting nucleiσ NN . In this approach, σ NN is usually evaluated at a constant global density ρ = 0.17 fm −3 [2,5].The method of calculating σ R is improved by using the density-dependent σ NN derived in Ref. [5]. One of these attempts [6] showed the effects of the in-medium NN cross section on σ R , using zero range NN force and the isospin averaged constant density-dependent NN cross section. Later, Warner et al. [7] introduced the local matter density in σ NN for each volume element of the nuclear overlap region; as a result the value of σ R is reduced by a relatively small percentage compared with that obtained using free NN cross section σ f NN . The effect of the finite range force [8] is found to increase σ R by about 5% compared to the zero range force for the reaction 238 U + 12 C.The main in-medium effect in the NN cross section at low and intermediate energies is due to Pauli blocking; this prevents the scattered nucleons from going into occupied states in binary collisions between the projectile and target nucleons. The accurate treatment of Pauli blocking is the geometric approach [9], which requires numerical calculation of a fivefold integral to get the in-medium NN cross section. Due to this complexity, many authors simplified the effect of Pauli blocking by making different approximations [7,[9][10][11].Although most of the recent calculations of σ R use the density dependence parametrization of Ref.[5] to include inmedium effects in σ NN , it is interesting to compare this method with the one obtained by the geometrical approach for Pauli blocking [9], when either finite or zero range NN interaction is assumed.In the optical limit of the Glauber theory, the calculation of σ R is known to be affected by the in-medium effects of σ NN , the finite range of the NN force, and the root ...

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Effect of in-medium NN cross section and finite range force on the reaction cross section for a deformed target nucleus

Cited by 7 publications

References 14 publications

Nucleus–nucleus reaction cross sections for deformed nuclei

Nucleus–nucleus reaction cross sections for deformed nuclei

Study of the total reaction cross section via QMD

Effect of finite range of theNNforce andNNcross section on reaction cross section for neutron rich nuclei

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