Narrow Results

In this paper, a simultaneous analysis of the elastic scattering data of the ¹⁶O+¹⁶O system for the energy range 5–10 MeV/nucleon is performed theoretically within the framework of the optical model formalism, by using the α–α double folding cluster potential. The α–α double folding cluster potential is evaluated by using the α-cluster distribution densities in the usual nucleon–nucleon double folding process with an effective α–α interaction potential. The results of the α–α double folding cluster potential analysis are compared with the findings of the phenomenological Woods–Saxon squared and nucleon–nucleon double folding potentials. All potentials have exhibited a very good agreement with the experimental measurements for the elastic scattering angular distributions. Furthermore, it is shown that, the α–α double folding cluster potential and nucleon–nucleon double folding potential calculations provide very consistent results with each other. Thus, the ¹⁶O+¹⁶O system has been described by optical potentials having a deep real potential part and a weak absorptive imaginary potential part.

We investigate the dynamic polarization potential (DPP) contribution to the bare potential obtained by using double-folding model (DFM) within the framework of the Optical Model (OM) for the different density distributions of ⁶He nucleus scattered from ²⁰⁸Pb target at 22 MeV. The final results are in agreement with the experimental data. We are proposing a new parametrization of the DPP that could be very useful in other weakly bound projectile studies.

The elastic scattering cross-sections of ${}^{28}$Si projectile by ${}^{27}$Al, ${}^{28}$Si, ${}^{58}$Ni, ${}^{64}$Ni and ${}^{208}$Pb targets are analyzed using the double folding model based on the effective M3Y interaction which is known as the most popular density independent form. In the calculations of the double folding model, 16 different density distributions of ${}^{28}$Si nucleus are examined. A very good agreement between experimental data and theoretical results is obtained, and also the literature results support our results. In addition, dependence on incident energy, target atomic number and target mass number of the imaginary potential depth is studied, and new and global equations are proposed.

Since it was reported that several radioisotopes might be advantageous for different medical uses in diagnostics and therapeutics, they have gained significance. Theoretical and experimental researches on such radioisotopes have contributed to the literature on a wide variety of topics, including production route research, getting activation and yield values, optimum production method analysis, clinical effects and production cross-section calculations. This study was motivated by the studies described in this domain as well as those published in the literature. The primary purpose of this study is to investigate the effects of deuteron optical model potentials in various reactions where ${}^{66\text{-}68}\mathrm{\text{Ga}}$ radioisotopes, which are known to be medically important, have been generated with deuteron induced particles on ${}^{\mathrm{\text{nat}}}\mathrm{\text{Zn}}$ and ${}^{\mathrm{\text{nat}}}\mathrm{\text{Ge}}$ targets. The experimental data from the literature and the calculation results generated using the five deuteron optical model potentials accessible in the TALYS code (version 1.95) were compared in line with the objective of this study. The experimental results in the literature and the data obtained as an outcome of the computations are graphically illustrated in order to comprehend these comparisons. Furthermore, to perform a numerical assessment, mean weighted deviation and relative variance calculations were also performed.

Studying nuclear reactions near the Coulomb barrier shows a number of problems which have remained unsolved for a long time: The out-of-phase problem between theoretical predictions and experimental data; the reproductions of the oscillatory structure near the Coulomb barrier; the consistent description of angular distributions together with the excitation functions data are just some of these problems. In order to address and overcome these problems, by considering a comparative study of the shallow and deep optical potentials, the elastic scattering angular distributions and excitation functions data of the ¹²C+²⁴Mg reaction have been analyzed within the framework of the optical model over a wide energy range. The potential depths near the Coulomb barrier according to the increasing energy and threshold anomaly are discussed in terms of the shallow and deep potentials. Excellent agreement between theoretical results and measured data is obtained by using the optical model.

This paper comprises the first detailed application of the microscopic potentials for a simultaneous analysis of the elastic scattering and fusion cross-section data of the ¹²C+²⁴Mg system from 16.0 MeV to 24.0 MeV. We use the microscopic nucleon-nucleon double folding and α-α double folding cluster potentials within the framework of the optical model and coupled-channels formalism. We compare our microscopic potential results with the findings of the phenomenological deep and shallow potentials. All potentials provide a very good agreement with the experimental data for the elastic scattering angular distributions. However, only deep phenomenological, the microscopic nucleon-nucleon and α-α double folding cluster potentials provide a consistent description of the angular distributions and fusion cross-section data simultaneously.

Elastic scattering of the two-neutron halo nucleus, ⁶He, on ¹²C target at 38.3 and 41.6 MeV/nucleon has been analyzed in the framework of the double-folding optical model. Real double-folded potentials based on the realistic density-dependent DDM3Y and JLM effective nucleon–nucleon interactions are generated using different forms of the nuclear matter density distribution of ⁶He. The imaginary optical potentials are taken in the conventional Woods–Saxon form. The bare (unnormalized) real folded potentials derived from the JLM interaction are more successful in reproducing the data at both energies than those derived from the DDM3Y interaction. The effect of contribution of the dynamic polarization potential is also studied. A semimicroscopic approximation is proposed to simulate this potential by introducing a repulsive real part extracted from the generated folded potential. Fits to data have been slightly improved by considering this approximation.

Microscopic local optical potentials from two sources were calculated by folding the numerical g-matrices over point proton and neutron RMF densities of target nuclei. The hard-core Hamada–Johnston and the soft-core Urbana v-14 local inter-nucleon potentials have been used to generate numerical g-matrices by solving Bethe–Goldstone integral equation. The calculated potentials have been used to analyze successfully both the proton and neutron differential elastic scattering and polarization data at 65 MeV over a wide mass region of targets: ¹²C–²⁰⁸Pb. Comparison of the present results with a phenomenological optical model analyzes is also presented. Mass number dependence of the mean square radii of the two microscopic potentials are in close agreement with each other as well as with empirical results.

Total reaction cross-sections of the two neutron halo nuclei ¹¹Li and ²²C elastic scattering from ¹²C target at E = 30–1000 MeV/nucleon have been analyzed using the eikonal phase shift based, for the first time, on the semi-phenomenological nucleon density. The obtained results reasonably agree with those of previous theoretical calculations as well as the corresponding experimental data.

This paper includes the experimental measurements for the angular distributions of ¹⁶O ion beam elastically scattered by ¹⁶O nuclei at energies 20, 24 and 28 MeV. The experimental results were analyzed within the framework of both the optical model using different complex potential and the double folding (DF) potential obtained with different density-dependent nucleon–nucleon interactions which give the corresponding values of the nuclear incompressibility K in the Hartree–Fock calculation of nuclear matter. The agreement between the experimental results and the theoretical predictions in the whole angular range is fairly good. In DF calculations, the obtained normalization coefficient N_r is in the range 0.833–1.07.

The vector analyzing power and differential cross-section for the elastic scattering of ⁸He nucleus from polarized protons at 71 MeV/nucleon have been analyzed in the framework of the optical model potentials. Microscopic single folding (SF) optical potentials (OP) have been constructed based upon two different effective nucleon–nucleon (NN) interactions, namely Jeukenne–Lejeune–Mahaux (JLM) and BDM3Y1 effective interactions. The effect of ⁸He nuclear structure has been tested through two different choices of the nuclear density distribution. It is concluded that the nucleus ⁸He may be considered as a thick skin exotic nucleus. In order to investigate the vector analyzing power data, besides the Thomas phenomenological representation, three different forms of the spin–orbit (SO) part of the OP have been considered. These forms are based directly or indirectly upon the density distribution of ⁸He nucleus. It is found that SO potentials of larger root mean square radii are able to successfully describe the vector analyzing power data more than those of shorter radii.

The elastic scattering of deuterons, ³He and ⁴He on ⁶Li at different incident energies have been analyzed in the framework of the optical model (OM) using ECIS88 as well as SPI GENOA codes. The optical potential parameters were extracted in the phenomenological treatment. A good agreement between theoretical and experimental differential cross-sections was obtained in whole angular range. Parameters for real part of potential have been also calculated microscopically with double-folding model for the d, ³He and ⁴He scattering, respectively, using DFPOT code. The elastic transfer mechanism has been studied by coupled reaction channel (CRC) method using FRESCO code. Spectroscopic amplitudes of ⁶Li ≡ t + ³He and ⁶Li ≡ α + d configurations have been extracted from d, ³He and ⁴He scattering on ⁶Li at wide energy range. A comparison between spectroscopic amplitudes obtained from deuteron and α elastically scattering from ⁶Li has been made. The extracted spectroscopic amplitudes of ⁶Li ≡ ⁴He + d(SF = SA²) from ⁶Li(d, ⁶Li)d and ⁶Li(α, ⁶Li)α are not the same as expected theoretically.

We have measured the angular distributions for ¹⁶O elastically scattered on ¹²C nuclei at energy 28 MeV and also for ¹²C ion beam elastically scattered on ¹¹B target nuclei at energy 18 MeV. These measurements were performed in the cyclotron DC-60 INP NNC RK. Calculations were performed using both empirical Woods–Saxon and double folding optical model potentials. Both elastic scattering and transfer reaction were taken into consideration. We have extracted the spectroscopic factors for the configurations ¹⁶O → ¹²C + α and ¹²C → ¹¹B + p and compared them with other calculated or extracted values at different energies from literature. The extracted spectroscopic factor for the configuration ¹²C → ¹¹B + p from the current work is in the range 2.7–3.1, which is very close to Cohen–Kurath prediction. While for the configuration ¹⁶O → ¹²C + α, spectroscopic factors show fluctuation with energy which could be due to the well-known resonant-like behavior observed in ¹⁶O + ¹²C excitation function.

The alpha (α) elastic scattering from different targets potential over the energy range 10–240 MeV has been analyzed in the framework of the single-folding (SF) optical model. Four targets are considered, namely, ²⁴Mg, ²⁸Si, ³²S and ⁴⁰Ca. The SF calculations for the real central part of the nuclear optical potential are performed by folding an effective α–α interaction with the α-cluster distribution density in the target nucleus. The imaginary part of the optical potential is expressed in the phenomenological Woods–Saxon (WS) form. The calculated angular distributions of the elastic scattering differential cross-section using the derived semimicroscopic potentials successfully reproduce 36 sets of data all over the measured angular ranges. The obtained results confirm the validity of the α-cluster structure of the considered nuclei. For the sake of comparison, the same sets of data are reanalyzed using microscopic double-folded optical potentials based upon the density-dependent Jeukenne–Lejeune–Mahaux (JLM) effective nucleon–nucleon interaction.

The angular distribution measurements for ¹⁶O ion beam elastically scattered from ¹¹B target of thickness 32.9μg/cm² at energy 22.4 MeV had been performed in the cyclotron DC-60 INP NNC RK. The previous measurements for ¹⁶O+¹¹B nuclear system at energies 27, 30, 32.5 and 35 MeV showed an increase in the differential cross-section at backward angles due to the contribution of cluster transfer. Such transfer process could not be described in terms of optical model (OM); it could be described within the framework of distorted wave Born approximation method implemented in FRESCO code. Both one (⁵Li) and two-step transfer (proton transfer followed by Alpha transfer) were taken into considerations. We have extracted the spectroscopic amplitude (SA) for the configuration ¹⁶O→¹¹B+⁵Li.

Elastic and inelastic scattering of $\alpha$-particles at 48.1MeV and ³He at 60MeV on ${}^{16}$O nuclei has been measured with excitation of states at 6.05 (0${}^{+}$)–6.13 (3${}^{-}$)MeV, 6.92 (2${}^{+}$)–7.12 (1${}^{-}$)MeV and 8.87 (2${}^{-}$)MeV. The center-of-mass beam momenta are the same for these two strongly absorbed particles. Analysis of angular distributions was performed in the frameworks of the optical model, the coupled channels method and the Distorted Wave Born Approximation (DWBA). A good description of experimental data was obtained over the full angular range without taking into account the spin-orbit interaction and the cluster transfer mechanism with real potentials that have volume integrals of about 400MeV fm³. Collective and microscopic models were used in the analysis of the inelastic scattering. The values of the octupole deformation lengths were extracted. It is shown that nuclear rainbow effects appear not only in the elastic, but also in the inelastic scattering with excitation of the 3${}^{-}$ state of ${}^{16}$O.

Differential cross-sections for the elastic and inelastic scattering of $\alpha$-particles had been measured at the energy of 48.8MeV with excitation of low-lying states of the ${}^{20}\mathrm{\text{Ne}}$ nucleus. The data for transitions to the ground $(0^{+})$ and excited $(E_x=1.63\mathrm{\text{MeV}}(2^{+})$, $E_x=4.25\mathrm{\text{MeV}}(4^{+}))$ states relating to the ground state band were analyzed in the framework of the optical model and the coupled-channel method based on the rotational model. It is shown that the analysis is sensitive not only to the magnitude, but also to the sign of the quadrupole and hexadecapole deformations. The extracted values of the parameters ${\beta }_2=+0.54\pm 0.14$ and ${\beta }_4=+0.17\pm 0.06$ are in good agreement with the results of other experiments on the scattering of protons, ${}^3\mathrm{\text{He}}$ and $\alpha$-particles and correspond to the data known from the electron scattering and Coulomb excitation.

In the present study, two different density distributions of oxygen isotopes (${}^{16\text{–}18}$O) that consist of the harmonic oscillator single-particle wave functions (SDHO) and the relativistic mean-field (RMF) approaches are investigated for the availability of elastic scattering cross-sections. For this purpose, the elastic scattering angular distributions of nuclear reactions with 13 target nuclei, four target nuclei and nine target nuclei are calculated for ${}^{16}$O, ${}^{17}$O and ${}^{18}$O, respectively. For these calculations, the double folding model based on the optical model is used. The optical potential parameters, volume integrals and cross-sections for all the nuclear reactions are given in this study. The comparison of theoretical results and experimental data shows very good agreement. The imaginary potential depth expressions, which will be new and more practical terms to explain the nuclear interactions of ${}^{16}$O, ${}^{17}$O and ${}^{18}$O with different nuclei, for each oxygen isotope are proposed.

The elastic and inelastic scatterings of $\alpha$-particles were investigated at an energy of 40MeV with excitation of low-lying states of the ${}^{11}$B nucleus [0.0 (3/2${}^{-}$), 4.445 (5/2${}^{-}$), 6.74 (7/2${}^{-}$), 2.125 (1/2${}^{-}$) and 5.02MeV (3/2${}^{-}$)]. The analysis of the experimental angular distributions was carried out via the coupled channels method within the framework of the collective model. The value of the quadrupole deformation parameter ${\beta }_2=0.545$ was extracted. Calculations indicate a preference for a negative sign for deformation. It is shown that the exchange mechanism with the transfer of the heavy ⁷Li cluster does not play an important role in the scattering of $\alpha$-particles on ${}^{11}$B nuclei at an energy of 40MeV.

Angular distribution of the ${}^{10}\mathrm{\text{B}}+{}^{12}\mathrm{\text{C}}$ elastic scattering was measured at $E_{\mathrm{\text{lab}}}({}^{10}\mathrm{\text{B}})=41.3$MeV. Experimental data showed a significant increase in differential cross-sections at backward angles. The optical model with phenomenological potentials reproduces well the experimental cross-sections in the region of the angles of the forward hemisphere, but is not able to explain the increase in cross-sections at large angles. The distorted wave Born approximation method was used to reproduce the experimental data at large angles $(>90^{\circ })$ by taking into consideration a deuteron transfer. Spectroscopic amplitude has been extracted for the configuration ${}^{12}$C${\to }^{10}$B + $d$ from the analysis.