Coulomb Modified Glauber Model Research Articles

The effects of finite range of the NN force and in-medium NN cross-section on the proton–nucleus total reaction cross-section

The effects of the finite range of the NN force and medium modifications on the nucleon-nucleus total reaction cross sections are investigated in the framework of the Coulomb modified Glauber model (CMGM). Different models of the nuclear densities are used. Comparison with experiments is considered. It is found that the effects of finite range strongly increase the reaction cross section at low and intermediate energies. Medium modifications of the NN cross section reduced the reaction cross section at low and intermediate energies. Both effects are found to be important for a better description of the proton- and neutron-nucleus total reaction cross sections.

Deformation and orientation effects on reaction cross-sections at intermediate and high energies

The effects of deformation and orientation on the nucleus–nucleus and proton–nucleus reaction cross-sections are investigated at intermediate and high energies, in the framework of the Coulomb modified Glauber model. The matter density of the projectile is treated by a deformed Fermi shape with quadrupole and hexadecapole deformations. In-medium effects are included through a local density- and an energy-dependent effective nucleon–nucleon total cross-section. Calculations are performed for the deformed projectiles [Formula: see text] colliding by [Formula: see text] and by protons. It is found that the average of reaction cross-section over all directions of the symmetry axis of the deformed projectile differs by about 2[Formula: see text] compared with that calculated for a spherical projectile with the same rms matter radius as the deformed one. The difference between the cross-sections calculated with and without medium effects is of the order 2[Formula: see text] for both deformed and spherical cases. The integrated reaction cross-sections over all orientation angles provide a consistent explanation of the experimental data. The orientation of the heavy projectile can produce a difference in the calculated cross-section about 35[Formula: see text] for nucleus–nucleus and about 45[Formula: see text] for proton–nucleus. This study is also useful for experiments of polarized beams that have created opportunities to study oriented collisions of deformed nuclei. The method is applied to extract the rms radius of [Formula: see text] and it is found to be about 3.56 and 3.45[Formula: see text]fm when using deformation with and without in-medium effects.

Reaction Cross Section of Heavy Projectiles Using Coulomb Modified Glauber Model

We investigated reaction cross section and inelastic collisions of the wide number of projectile and target nuclei using the Coulomb Modified Glauber Model (CMGM). The total reaction cross sections were calculated with and without accounting for in-medium effect for various heavy projectiles such as 56Fe26, 84Kr36, 132Xe54, 197Au79 and 238U92 that interact with Nuclear Emulsion Detector’s (NED) nuclei at incident energies at around 1 GeV/n. The calculated average values of reaction cross section are compared with the corresponding experimental data.

Phase Shift Analysis of $^{6}$Li Elastic Scattering on $^{12}$C and $^{28}$Si at $E_{lab}$ = 318 MeV

We present a three-parameter phase shift model whose form is the same as that of Coulomb-modified Glauber model obtained from Gaussian nuclear densities. This model is applied to the $^{6}$Li + $^{12}$C and the $^{6}$Li + $^{28}$Si elastic scatterings at $E_{lab}$ = 318 MeV. The calculated differential cross sections provide quite a satisfactory account of the experimental data. The diffractive oscillatory structures observed at forward angles can be explained as being due to the strong interference between the near-side and the far-side scattering amplitudes. The optical potentials for two systems are predicted by using the method of inversion. The calculated inversion potentials are found to be in fairly good agreements with the results determined from the optical model analysis in the surface regions around the strong absorption radius. We also investigate the effects of parameters in the three-parameter phase shift model on the elastic scattering cross sections.

Analysis of Various Projectile Interactions with Nuclear Emulsion Detector Nuclei at ~1 GeV per Nucleon Using Coulomb Modified Glauber Model

The total nuclear reaction cross section is calculated considering the cases with and without medium effect by employing Coulomb modified Glauber model (CMGM) for interactions of projectiles 56Fe26, 84Kr36, 132Xe54, 197Au79, and 238U92 with nuclear emulsion detector (NED) nuclei at around 1 GeV per nucleon incident kinetic energy. These calculated nuclear reaction cross sections are correlated with the different target groups of the NED nuclei. The average value of various parameters is also calculated and compared with the corresponding experimental results. The number of shower particles emitted in an interaction is also calculated and showed good agreement with the experimental result. We observed that the total nuclear reaction cross section increases with increasing the target mass number in case of all the considered projectiles. In addition, it is shown that the average value of reaction cross section with nuclear medium effect is in good agreement with the experimental results for projectiles 56Fe, 84Kr, and 132Xe, although results of projectiles 197Au and 238U are not in agreement with the experimental observations. This study sheds some light on the energy dependence of the nuclear reaction cross section.

Study of p-4Hetotal reaction cross-section using Glauber and Coulomb-modified Glauber models

The total nuclear reaction cross-section σRfor p-4He in the energy range from 25 MeV to 1000 MeV is calculated within Glauber and Coulomb-modified Glauber models. The Coulomb-modified Glauber model (CMGM) is introduced via modification of the Coulomb trajectory of the projectile from a straight line, and calculation of the effective radius of interaction. The effects of in-medium nucleon–nucleon (NN) total cross-section, phase variation, high order momentum transfer component of nucleon–nucleon elastic scattering amplitude and Pauli blocking are studied. It is pointed out that the phase variation of the nucleon–nucleon amplitude plays a significant role in describing σRwith γ = -1.6 fm2at in-medium nuclear density ϱ = 0 and γ = -2 fm2at ϱ = 0.17 fm-3in the whole energy range. A remarkable fit to the available experimental data is obtained by invoking Pauli blocking and high order momentum transfer of nucleon–nucleon (NN) elastic scattering amplitude for Ep< 100 MeV.

ANALYSIS OF p-4, 6, 8He AND p-6, 9, 11Li SCATTERING

Using the Coulomb modified Glauber model, we analyze the elastic scattering of protons from He and Li isotopes at 60 MeV and 72 MeV. The calculations require two inputs; the nucleon–nucleon (NN) amplitude and the nucleon density distributions in target nuclei. The central part of the NN amplitude is taken from the available NN scattering observables. To find the spin-dependent part, we employ p-4 He scattering data to fix its parameter values. For target nuclei, we use nucleon density distributions available in the literature. The NN amplitude, as obtained in this work, is then used to study the sensitivity of the calculated differential cross-section and polarization for p-6, 8 He scattering on the density distributions used. It is found that both the differential cross-section and polarization could provide a test to know which is the better choice of nucleon (especially neutron) density distributions. We also present the differential cross-sections for p-6, 9, 11 Li scattering at 60 MeV and 72 MeV in order to assess the suitability of the obtained NN amplitude. It is found that the results are in reasonable agreement with the experiment up to only moderate scattering angles, leaving significant discrepancy at large scattering angles. Our calculations suggest the need of medium modifications in the NN amplitude, arising due to Pauli blocking.

Microscopic study of total reaction cross-sections for proton on deuteron, 3 He and 4 He at energy range 20 to 50 MeV

Working within the framework of Coulomb modified Galuber model and using harmonic oscillator shell model target density, the proton total reaction cross-sections on the deuteron, 3 He and 4 He have been analyzed in the beam energy range 20 to 50 MeV. A very satisfactory agreement with experimental data for p-deuteron and to some extent for p3 He have also been achieved. For p4 He, the calculated reaction cross-section becomes negative at lower energies which is absolutely unphysical. Keywords: Coulomb modified Glauber model; Microscopic analysis; Harmonic oscillator shell model density PACS: 25.40.Cm; 25.40.Dn; 24.10.Ht; 25.70Bc

Elastic α-Nucleus Scattering at 36 to 60 Mev/Nucleon

Working within the framework of the Coulomb modified Glauber model and using the optical limit approximation to evaluate the elastic S-matrix, we use a parameterized effective nucleon-nucleon phase shift function instead of the frequently applied Gaussian parameterization of the nucleon-nucleon scattering amplitude to compute elastic differential cross sections for alpha particles. Our phenomenological ansatz contains three parameters which are adjusted in order to reproduce the alpha nucleus elastic scattering data for one nucleus at each of three beam energies. It is found that once the nucleon-nucleon phase shift function is so calibrated, our model very nicely reproduces elastic alpha scattering data on other nuclei at the same energy.

Analysis of the 3He -nucleus total reaction cross-section

Working within the framework of the Coulomb-modified Glauber model, we analyze the total reaction cross-section ( $ \sigma_{{R}}^{}$ for 3He -particles from 9Be , 12C , 16O , 28Si , 40Ca , 58, 60Ni , 112, 116, 120, 124Sn , and 208Pb at 96.4, 137.8, and 167.3MeV. Our calculations i) involve the realistic form factors for the colliding nuclei, and ii) emphasize the parametrization of the basic (input) NN amplitude, which may be used for a wide range of angles. The results are found to provide quite a satisfactory account of the $ \sigma_{{R}}^{}$ data in all the cases. Moreover, we have also demonstrated the importance of the higher-momentum transfer components of the NN amplitude in providing a simultaneous description of the elastic angular distribution, covering large scattering angles, and the $ \sigma_{{R}}^{}$ data for 3He - and $ \alpha$ -nucleus systems in the considered energy range.

Eikonal phenomenology in the analysis of α–nucleus elastic-scattering data

Working within the framework of the Coulomb-modified Glauber model, we instead of conventionally using the Gaussian approximation to the basic input nucleon–nucleon (NN) amplitude, evaluate it from a three-parameter phenomenological NN phase shift function. At a given projectile energy the parameters of the NN phase shift function are varied to fit the α–nucleus elastic-scattering data. It is found that once the parameters of the NN phase shift function are fixed, it very nicely reproduces the available elastic α–scattering data on other nuclei at the same energy. By applying this procedure, a reasonably good account of elastic-scattering data for α–40–48Ca,58Ni,116Sn and 208Pb have been achieved in the energy range about 0.2 GeV–1.37 GeV.

$ \alpha$ -nucleus elastic scattering in the energy range 25-70 MeV/nucleon

Working within the framework of the Coulomb-modified Glauber model for nucleus-nucleus collisions, we analyse the elastic scattering of \( \alpha\) -particles on 4He at 25, 30, 35, 40, 50, and 70MeV/nucleon. Emphasis has been put on the parametrization of the basic (input) NN amplitude that preserves the low-q behavior at the desired energy, whereas the higher momentum transfer components are treated phenomenologically. The analysis also considers the medium modification of the NN amplitude due to Pauli blocking. Using the realistic form factors for colliding nuclei, it is found that the data are reproduced satisfactorily well up to the fairly large value of momentum transfer. We also discuss the suitability of the extracted NN amplitude for other target nuclei in the energy range under consideration. Our analysis suggests that the proper account of the higher momentum transfer components of the NN amplitude may push down the Glauber model to lower energies, and increase its validity in the region of relatively large momentum transfers.

A study of the energy dependence for the multiplicity of shower particles produced in a 16O–emulsion interaction in the framework of the Coulomb-modified Glauber model

The total reaction cross sections for the interaction of 16O with emulsion nuclei (16O–Em) at energies: 0.2, 2.1, 3.6, 14.6, 60.0, and 200.0A GeV have been calculated in the framework of the Coulomb-modified Glauber model. A similar calculation in case of proton–emulsion (p–Em) interactions is carried out at the same energies. For both types of interactions, the corresponding projectile and target participants beside the corresponding binary collisions have been calculated for the same energies. Then the averages of these quantities have been obtained. These averages have been used in the calculations of the corresponding average multiplicity of the shower particles (s-particles) in the case of the 16O–Em interaction. The agreement between the calculated total reaction cross sections and the corresponding experimental data is quite good. Also, a good agreement between the calculated average multiplicities of the shower particles and the corresponding experimental data has been obtained.PACS Nos.: 24.10.Cn, 24.10.Ht, 25.60.Dz

Nucleus–nucleus reaction cross sections for deformed nuclei

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 k=0, 2, 4. The reaction cross sections for 12C+27Al, 20Ne+27Al, 12C+64Zn, 12C+90Zr, 40Ar+238U and 20Ne+235U are studied at energy range (10–1000 MeV nucleon−1). The most significant effects in the intermediate energy range are the Coulomb field and in-medium effects that modified the trajectory of the incident beams. Introducing the deformation effect beside the Coulomb field and in-medium effects improves the agreement with the experimental data and two empirical parameterizations in the case of not finding experimental data. Moreover, it is shown that the enhancement of the reaction cross sections is attributed to fixed orientation in deformed nuclei.

Analysis of elasticα-nucleus scattering data at 240 MeV

Working within the framework of the Coulomb modified Glauber model we fit the elastic differential scattering cross section of 240 MeV $\ensuremath{\alpha}$ particle on $^{58}\mathrm{Ni}$ using the effective $N\text{\ensuremath{-}}\ensuremath{\alpha}$ amplitude with one adjustable parameter. It is found that once the effective amplitude is calibrated on $^{58}\mathrm{Ni}$ by varying the adjustable parameter, it very nicely reproduces the available elastic $\ensuremath{\alpha}$ scattering data on other nuclei at the same energy.

C12-C12elastic scattering at 1.016, 1.449, and 2.4 GeV and theNNamplitude

Working within the framework of the Coulomb modified Glauber model, we analyze the elastic angular distribution and reaction cross section for the $^{12}\mathrm{C}$-$^{12}\mathrm{C}$ system at 1.016, 1.449, and 2.4 GeV. The elastic $S$ matrix is evaluated using the effective profile function approach, and a correlation expansion for the Glauber amplitude is obtained. We emphasize the parametrization of the basic (input) $\mathit{NN}$ amplitude, which may be used for a wide range of angles. Retaining the first two terms of the correlation expansion and using the realistic densities for the colliding nuclei, we find that (i) the consideration of higher momentum transfer components, and hence the nondiffractive behavior, of the $\mathit{NN}$ amplitude provides a more satisfactory account of the data than does the conventional (one-term) Gaussian parametrization for the $\mathit{NN}$ amplitude, (ii) the in-medium effects seem to reduce the (free) $\mathit{NN}$ total cross section and influence the other parameters of the $\mathit{NN}$ amplitude as well, (iii) the phase of the $\mathit{NN}$ amplitude does not help in improving the theoretical situation, and (iv) the c.m. correlations play an important role at the energies considered. We also discuss the suitability of the effective profile function approach in the present context.

EIKONAL PHENOMENOLOGY FOR HEAVY-ION SCATTERING AT INTERMEDIATE ENERGIES

Working within the framework of the Coulomb modified Glauber model and the optical limit approximation, we propose a phenomenological method of analysis for heavy-ion elastic scattering data at intermediate energies. Instead of using the commonly employed Gaussian approximation for the input NN amplitude that is deficient in some respects at low intermediate energies, we evaluate it in terms of a three parameter phenomenological NN phase shift function. The application of the method to some 12 C -nucleus and 16 O -nucleus systems shows that a very good description of the elastic scattering data at several energies can be obtained in this way. In particular, the 12 C –12 C elastic scattering data at 200 MeV/nucleon is very well reproduced. We also calculate the effective NN potential using the phenomenological NN phase shift function by the method of inversion. The calculated potential shows the expected behavior and is found to vary smoothly with energy.

EFFECT OF COULOMB ENERGY SHIFT ON PROTON TOTAL REACTION CROSS-SECTION

In this work we study the effect of the Coulomb energy shift on proton total reaction cross-section (σ R ) at 25, 50, and 100 MeV for several nuclei in the mass region 12≤A≤208. The cross-sections are computed using the Coulomb modified Glauber model in the optical limit approximation, and the semi-phenomenological proton and neutron density distributions. We find that the Coulomb energy shift has a significant effect on the calculated σ R , and that it brings the theory quite close to the experiment.

Reaction cross-sections for carbon isotopes

The effects of the finite range of the NN force and medium modifications on the nucleon-nucleus total reaction cross sections are investigated in the framework of the Coulomb modified Glauber model (CMGM). Different models of the nuclear densities are used. Comparison with experiments is considered. It is found that the effects of finite range strongly increase the reaction cross section at low and intermediate energies. Medium modifications of the NN cross section reduced the reaction cross section at low and intermediate energies. Both effects are found to be important for a better description of the proton- and neutron-nucleus total reaction cross sections.

MASS DEPENDENCE OF p-NUCLEUS TOTAL REACTION CROSS SECTION AND GAMBHIR–PATIL NUCLEON DENSITY DISTRIBUTION

Total reaction cross sections for 50 and 100 MeV protons have been calculated for several nuclei using Gambhir–Patil semi-phenomenological nucleon density in the Coulomb modified Glauber model. It is shown that the semi-phenomenological nucleon density distribution provides quite satisfactory description of the observed A-dependence of the proton reaction cross sections.