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.

Thick Target Neutron Production on Aluminum and Copper by 40 MeV Deuterons**Supported by the Project of China Academy of Engineering Physics under Grant No 2013B0103015.

The thick target neutron yields (TTNYs) of deuteron-induced reaction on Al and Cu isotopes are analyzed by combining the improved nuclear models and particle transport effects. The modified Glauber model is employed mainly to produce the peak of double differential cross section for the breakup process, and the exciton model and the Hauser–Feshbach theory are used for the statistical processes. The thin-layer accumulation method is used to calculate the TTNYs considering the neutron attenuation effects in the target. The calculated results are compared with the existing experimental data, and the analysis method can predict the TTNY data well at the deuteron energy of 40 MeV.

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.

Capture cross sections of 15N(n, γ)16N at astrophysical energies**Support given by National Natural Science Foundation of China (11447236, 11505002, 11247001) and Foundation of Anhui University of Science and Technology (11130, 12608)

We have reanalyzed reaction cross sections of 16N on a 12C target. The nucleon density distribution of 16N, especially surface density distribution, was extracted using the modified Glauber model. On the basis of dilute surface densities, the 15N(n, γ)16N reaction is discussed within the framework of the direct capture reaction mechanism. The calculations agree quite well with the experimental data.

Fermi-motion effect on the intermediate energy nucleus–nucleus collision

The Glauber model is modified with the Fermi-motion effect in the calculation of elastic differential cross-sections and momentum distributions of a fragment from mother nucleus. Different reaction systems at low energies are calculated with the modified Glauber model. It is found that calculations including the Fermi-motion provide a better prescription relating the model to a proper nuclear density distribution by comparing with the experimental data. On the basis of the studies, the influence of the correction on the extracted nuclear radius is quantified. The results further confirm the importance of the Fermi-motion in the nucleus–nucleus collision reactions at low energies.

Centrality and multiparticle production in ultrarelativistic nuclear collisions

A critical analysis of methods for selecting central events in high-energy proton–nucleus (pA) and nucleus–nucleus (AA) collisions is presented. A sample of event classes in which background fluctuations associated with the dispersion of the impact parameter of each event or the number of participant nucleons are minimal is examined. At the SPS and LHC energies, the numbers of nucleon–nucleon collisions are estimated with the aid of the Monte Carlo event generators HIJING and AMPT, which take into account energy–momentum conservation, and on the basis of a non-Glauber model involving string fusion and a modified Glauber model. The results obtained in this way demonstrate the need for revising the extensively used application of the Glauber model in normalizing multiplicity yields in experimental data on pA and AA collisions in the soft region of the spectrum.

Density distribution ofLi8and8Band capture reaction at low energy

Reaction cross sections of Li8 on stable targets were measured at intermediate energies. With the existing experimental data of interaction cross sections at 790 MeV/nucleon the nucleon density distribution of Li8 was extracted by the use of the modified Glauber model. Meanwhile, the existing data of 8B have been also reanalyzed. Structures of Li8 and 8B were compared through the density. On the basis of dilute surface densities, the discussion of 7Li(n,γ)8Li and 7Be(p,γ)8B capture reactions was performed within the framework of the direct capture reaction mechanism. The calculations agreed quite well with the experimental data as well as other analyses.Received 14 November 2014Revised 10 January 2015DOI:https://doi.org/10.1103/PhysRevC.91.014614©2015 American Physical Society

Nonlinear relativistic mean-field theory studies on He isotopes

The ground state properties of He isotopes are studied in the nonlinear relativistic mean-field (RMF) theory with force parameters NL-SH and TM2. The modified Glauber model is introduced as a gatekeeper to check the calculations. The investigation shows that the RMF theory provides a good description on the properties of He isotopes. The many-body space information of 4He + neutrons is obtained reliably. As a product, the calculation gives strong evidence for a neutron halo in 5He.

Structure ofLi8from a reaction cross-section measurement

We have precisely measured reaction cross sections (σR) for Li8 using Be9, 12C, Al27, and proton targets at intermediate energies by the transmission method. From the energy dependence of the σR including the high energy data, the density distribution of Li8 was deduced through a modified Glauber model. It is shown that Li8 has a shorter tail structure in the density as compared with that of 8B and the matter radius of Li8 is similar to those of the other nonhalo Li isotopes. The result is consistent with the previous experiments that there is a tendency for Li8 to be a skin nucleus.Received 7 July 2014Revised 4 September 2014DOI:https://doi.org/10.1103/PhysRevC.90.044321©2014 American Physical Society

Big deformation in 17C

Reaction and interaction cross sections of 17C on a carbon target have been re-analyzed using the modified Glauber model. The analysis with a deformed Woods-Saxon density/potential suggests a big deformation structure for 17C. The existence of a tail in the density distribution supports the possibility of it being a one-neutron halo structure. Under a deformed core plus a single-particle assumption, analysis shows a dominant d-wave of the valence neutron in 17C.

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 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.

One-Proton Halo Structure in 23Al

The Glauber theory is used to investigate the reaction cross section ofproton-rich nucleus 23Al. A core plus a proton structure is assumedfor 23Al. HO-type density distribution is used for the core whilethe density distribution for the valence proton is calculated by solvingthe eigenvalue problem of Woods–Saxon potential. The transparencyfunction in an analytical expression is obtained by adoptingmulti-Gaussian expansion for the density distribution. Coulombcorrection and finite-range interaction are introduced. This modifiedGlauber model is suitable for halo nuclei. A dominate s-wave issuggested for the last proton in 23Al from our analysis which ispossible in the calculation of relativistic mean-field theory.

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.