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

Abstract

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 ...

The behavior of reaction cross-section at low and intermediate energies by considering in-medium effects in σNN for light and heavy target nuclei

“…The root mean square radius of the nucleus A correct parameterization of the crosssection between two free nucleons is given by Charagi and Gupta [1]. It depends on the incident nucleon energy in laboratory system as ... (6) where In-medium effects modify the free space crosssection in the following way, for two similar nucleons, for two different nucleons ... (7) The multiplicative factors which take medium effects into consideration are given by [9], ... (8) In using the last equations, the correct treatment of ρ-dependence is to take the density ρ as the sum of the projectile and target densities in each volume element dr v…”

“…Another approach to consider approximate medium effects is to evaluate ( , ) n n p χ at constant global density which is usually equal to the value of saturated nuclear matter density. In case of neglecting in-medium effects in calculating σ R we use equations ( 6) for σ NN instead of equations (7,8). In the present work the reaction cross-section is calculated for the light and heavy target pairs 12 C-12 C and 12 C-208 Pb at different values of incident energy per projectile nucleon in the range (10-1000 MeV/nucleon).…”

“…[6], the effective rms radii of nucleon distribution of B, Be and He isotopes had been deduced by comparing the experimental data for the reaction cross-section by theoretical calculations based on Glauber theory. The optical limit to Glauber theory is usually used with appreciable success to describe the reaction cross section between complex nuclei 2,3,8 . The inputs to these calculations are the nucleon-nucleon (NN) reaction cross-section, σ NN , and the density distribution of the interacting nuclei.…”

“…The inputs to these calculations are the nucleon-nucleon (NN) reaction cross-section, σ NN , and the density distribution of the interacting nuclei. Recently, this method has been used to determine the rms radii of the interacting nuclei and to study halo nuclei 3,6,8,9 . The value of σ R for a pair of interacting nuclei calculated in the frame work of the optical limit of Glauber theory is affected by different factors.…”

“…σ R is usually calculated by assuming the zero-rang force [3] of the interacting nucleons and the NN reaction crosssection is considered through different approaches [ 1,5,9]. First, σ NN is taken directly as free NN crosssection, f NN σ [8], without density dependence or evaluated at constant density usually assumed to be equal to saturation nuclear matter density ( ρ=0.17 fm -3 ) [1,9].This approach in treating inmedium effects permits extracting σ NN out of integrations since, in this case, it has constant value. Moreover for constant value of σ NN and assuming Gaussian shapes for the density distribution, most of the integrals in calculating σ R can be performed analytically which means that the evaluation of σ R is numerically very simple.…”