Channel Calculations Research Articles

Investigation of the one-neutron transfer in C13+Si28 at Elab=30 and 34 MeV

Background: Neutron transfer measurements for the $^{18}$O + $^{28}$Si system have shown that the experimental one-neutron and two-neutron transfer cross sections are well reproduced with spectroscopic amplitudes from two different shell model interactions for the Si isotopes: \textit{psdmod} for the two-neutron transfer, and \textit{psdmwkpn} for the one-neutron transfer. Purpose: The origin of this ambiguity can be related to a more complex mechanism in the one-neutron transfer that requires the unpairing of neutrons prior to its transfer in the ($^{18}$O,$^{17}$O) reaction. Studying a nucleus where this characteristic is absent ($^{13}$C) should help to elucidate this question. Method: One-neutron transfer cross sections were measured for the $^{13}$C + $^{28}$Si at E$_{lab}$ = 30, and 34 MeV, and compared with coupled reaction channel calculations using spectroscopic amplitudes derived from the \textit{psdmod} and \textit{psdmwkpn} shell model interactions. Results: The spectroscopic amplitudes from the \textit{psdmod} interaction for the relevant states in $^{29}$Si provide a good description of the experimental data and the corresponding values agree with previous estimates obtained from the (d,p) reaction. Conclusions: The experimental data for the one-neutron transfer to $^{28}$Si induced by ($^{13}$C,$^{12}$C) reaction is well reproduced using spectroscopic amplitudes from the \textit{psdmod}.

Approximate technique for calculation the celerity of long wave in channels with complex cross section

Dynamic processes in rivers are always associated with long waves of a different type. The celerity of the waves is main property for calculating their propagation, and the shape of channels cross section is one of the factors affecting the celerity. Previously, the approach based on the principles of the theory of energy motion was used to study the dynamics of the waves. Several analytical solutions for the celerity were obtained for the channels with simple geometry of cross section such as rectangular, triangular, and trapezoidal ones. Developing the approach for similar calculations in natural channels, which cross sections have complex shape, the approximate technique is proposed in the paper. The technique needs information on the geometric properties of the stream and channel. Obtained solutions were compared with some field measurements of tidal bores in natural channels. Aim of the paper is to further develop the approach, which is based on principles of energy motion, to the analysis of unsteady fluid flow.

Li-like carbon Auger KLL measurements of mixed-state C4+(1s2 1S, 1s2s 3S) ions in 6-15 MeV collisions with He and comparison to 3eAOCC calculations

SynopsisNew state-resolved Li-like carbon Auger KLL measurements of mixed-state C4+(1s2 1S, 1s2s 3S) ions in 6-15 MeV collisions with He are presented. Results of three-electron semiclassical atomic orbital AOCC coupled channel (3eAOCC) calculations are also presented and compared.

Quasi-elastic scattering measurements of the 28Si + 142Nd system at back-angle

The barrier distribution of a system can be extracted from excitation function data obtained either through fusion reaction or through quasi-elastic scattering measurement. In the present work, the quasi-elastic excitation function has precisely been measured at back angle for the 28Si + 142Nd system at energies around the Coulomb barrier and the corresponding experimental barrier distribution has been extracted. The experimental data has been interpreted in the frame work of the coupled channel calculations which include couplings to different possible modes of excitations of the interacting target-projectile combination. The possible effect of the nature of projectile excitations on the derived barrier distribution has been presented.

Coupled channels calculation of fusion reaction for selected medium systems

This study focuses on using a semi-classical and quantum mechanical approach based originally on the theory of Winther and Alder that is used to explain the Coulomb excitation. This approach is called the coupled channels with continuum-discretised (CCCD), where the semi-classical and quantum models were used to investigate the channel coupling effects on the determination of the cross section for fusion σfus (mb) and the distribution of the fusion barrier Dfus (mb/MeV) for systems 14N+59Co, 16O+64Ni and 18O+64Ni. The comparison between the results of the semi-classical and quantum mechanical models along with the corresponding experimental data shows clearly that the adopted semi-classical model is very competitive to the quantum mechanical model and can be considered as efficient approach to study the properties of the fusion reactions.

Electron correlation in simultaneous electron transfer and excitation: results of new 2eAOCC calculations and comparison to experiment in 50-500 keV He+ + H/H2 collisions

SynopsisNew two-electron semiclassical atomic orbital coupled channel calculations (2eAOCC) are compared to experiment and to older coupled channel calculations. Progress in these type of calculations is assessed in an effort to investigate the effect of electron correlations in this fundamental collision system.

Reaction channel contributions to the helion optical potential

Background: The well-established coupled channel and coupled reaction channel processes contributing to direct reactions make particular contributions to elastic scattering that are absent from local density folding models. Very little has been established concerning the contribution of these processes to the optical model potentials (OMPs) for $^{3}\mathrm{He}$ scattering. For studying such processes, spin-saturated closed shell nuclei such as $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ are particularly suitable target nuclei and the ($^{3}\mathrm{He}$, $^{4}\mathrm{He}$) reaction is easily handled within conventional reaction theory because it avoids complications such as breakup.Purpose: To establish and characterize the contribution to the $^{3}\mathrm{He}$-nucleus interaction generated by coupling to neutron pickup (outgoing $^{4}\mathrm{He}$) channels; also to study the contribution of collective states and identify effects of dynamical nonlocality from these couplings.Methods: Coupled reaction channel (CRC) calculations, including coupling to collective states, will provide the elastic channel $S$-matrix ${S}_{lj}$ resulting from the included processes. Inversion of ${S}_{lj}$ will produce the local potential that yields, in a single channel calculation, the elastic scattering observables from the coupled channel calculation. Subtracting the bare potential from the CRC calculations yields a local and $l$-independent representation of the dynamical polarization potential (DPP). From the DPPs, because of a range of combinations of channel couplings, the influence of dynamically generated nonlocality can be identified.Results: Coupling to $^{4}\mathrm{He}$ channels systematically induces repulsion and absorption in the $^{3}\mathrm{He}$ OMP and also a reduction in the rms radius of the real part. The repulsion and absorption is less for $^{208}\mathrm{Pb}$ than for the lighter target nuclei although the qualitative effects, including the general undularity of the DPPs, are similar for all cases; therefore coupling to these channels cannot be represented by renormalizing folding model potentials. Evidence is presented for substantial dynamical nonlocality of the induced DPPs; for $^{40}\mathrm{Ca}$ this modifies direct reaction angular distributions. The local equivalent DPPs for individual couplings cannot be added to give the overall DPP for the complete set of couplings. For the $^{208}\mathrm{Pb}$ case, channel coupling reduces the reaction cross section although it increases it for $^{16}\mathrm{O}$, with $^{40}\mathrm{Ca}$ an intermediate case.Conclusions: The DPPs established here strongly challenge the notion that folding models, in particular local density models, provide a satisfactory description of elastic scattering of $^{3}\mathrm{He}$ from nuclei. Coupling to neutron pickup channels induces dynamical nonlocality in the $^{3}\mathrm{He}$ OMP with implications for direct reactions involving $^{3}\mathrm{He}$. Departures from a smooth radial form for the $^{3}\mathrm{He}$ OMP should be apparent in good fits to suitable elastic scattering data.

Systematic of fusion incompleteness in reactions induced by α cluster projectiles

In order to investigate the systematic of fusion incompleteness in reactions induced by $\ensuremath{\alpha}$ cluster projectiles, a detailed study was carried out using the $^{20}\mathrm{Ne}+^{165}\mathrm{Ho}$ system at energies above the barrier. Measurements of the excitation function (EF) of the observed evaporation residues (ERs) were carried out by employing the offline characteristic $\ensuremath{\gamma}$-ray detection method. The EFs of the ERs populated through $xn/pxn$ channels were found to be in good agreement with the prediction of the statistical model code pace4, whereas the EF of the ERs populated through the $\ensuremath{\alpha}$ emitting channels shows an enhancement over the pace4 prediction. The degree of fusion incompleteness in the $^{20}\mathrm{Ne}+^{165}\mathrm{Ho}$ reaction is estimated by comparing the fusion EF with coupled channels calculations and the extracted fusion function with the universal fusion function. The influence of input angular momentum on fusion reaction dynamics is explored in light of the sum-rule model. An attempt has also been made to examine the dependence of incomplete fusion probability on various entrance channel parameters.

Peculiarities of 6Li +12C elastic scattering

Using the phenomenological optical potential and two different semi-microscopic potentials, namely double folding and cluster folding (CF), the available experimental data for 6Li elastically scattered from [Formula: see text]C nucleus at energies 50–600[Formula: see text]MeV are reanalyzed. On the basis of the well-known cluster structure of 6Li as a composite nucleus consisting of a core “alpha” with a valence particle “deuteron” orbiting this core, special attention was paid to the CF potential. Elastic scattering data for 6Li+[Formula: see text]C system plotted as a function of momentum transfer showed that the real Coulomb nuclear interference region is independent of the bombarding energy. The aforementioned structural behavior for the data could be used to define the potential with some certainty. In addition to a Woods–Saxon imaginary potential of fixed radius, the real part of the potential derived from the cluster structure of 6Li was successful in reproducing the experimental data in the whole angular range. Coupled channel (CC) calculation effects are also performed by coupling to 6Li resonant state ([Formula: see text], [Formula: see text][Formula: see text]MeV).

Strong neutron-transfer coupling effects in the reaction mechanism of the O18+Zn64 system at energies near the Coulomb barrier

The precise quasielastic excitation function for the $^{18}\mathrm{O}+^{64}\mathrm{Zn}$ system was measured at energies near and below the Coulomb barrier at ${\ensuremath{\theta}}_{\mathrm{lab}}={161}^{\ensuremath{\circ}}$, from which its correlated quasielastic barrier distribution was derived. The excitation functions for the two-neutron, $\ensuremath{\alpha}$, and tritium transfer reactions have also been measured at the same conditions. These data were well described by the coupled channel and coupled reaction channel calculations. The comparison of the data with theoretical calculations shows the strong influence of three inelastic channels in the coupling process: the quadrupole and octupole vibrational states of $^{64}\mathrm{Zn}$, ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$, and the quadrupole vibrational state of $^{18}\mathrm{O}$, ${2}_{1}^{+}$. In addition, theoretical calculations indicate that the two-neutron stripping is mostly due to a one-step process, which has a striking effect on the reaction mechanism of this system.

Fusion reactions in the Be9 + Au197 system above the Coulomb barrier

The cross sections of complete fusion and incomplete fusion for the $ ^{9} $Be + $ ^{197} $Au system, at energies not too much above the Coulomb barrier, were measured for the first time. The online activation followed by offline $\gamma$-ray spectroscopy method was used for the derivation of the cross sections. A slightly higher value of ICF/TF ratio has been observed, compared to other systems reported in the literature with $ ^{9} $Be beam. The experimental data were compared with coupled channel calculations without taking into account the coupling of the breakup channel, and experimental data of other reaction systems with weakly bound projectiles. A complete fusion suppression of about 40\% was found for the $ ^{9} $Be + $ ^{197} $Au system, at energies above the barrier, whereas the total fusion cross sections are in agreement with the calculations.

Scattering of O16,18 beams on Cu63,65 targets: A systematic study of different reaction channels

Precise quasielastic experimental excitation function for the $^{18}\mathrm{O}+^{65}\mathrm{Cu}$ system has been measured and its barrier distribution has been derived. Several reaction channels have been observed on the experimental spectra, revealing the presence of two-neutron and $\ensuremath{\alpha}$-stripping processes, as well as the proton pickup transfer, for which excitation functions were also measured. Extensive coupled channel and coupled reaction channel calculations have been performed to describe the experimental data. The inelastic couplings of target and projectile, and the ground state reorientation of the target, were important to the proper description of data. The transfer data were well described by calculations; however, it was shown that they almost do not affect the excitation function of $^{18}\mathrm{O}+^{65}\mathrm{Cu}$ quasielastic scattering. Whenever possible, structure shell model calculations have been performed to obtain the spectroscopic amplitudes of projectile and target overlaps. The two-neutron and $\ensuremath{\alpha}$-transfer reactions have been calculated considering the transferred particle as a cluster with spin 0.

Reaffirmation of probe dependence of the mass deformation length for low-lying excitations in Sn112,116,118,120,122,124 isotopes

Background: A transparent approach for the study of nuclear shapes and sizes in excited states requires knowledge about dynamic deformations of both neutron and proton distributions, by means of their independent excitations at the same energy. Heavy-ion scattering could be a reliable approach, facilitating a simultaneous study of deformations of charge and matter densities in nuclei.Purpose: Measurement of angular distributions of the inelastic scattering cross sections for excitations to low-lying ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in $^{112,116,118,120,122,124}\mathrm{Sn}$ nuclei using $^{12}\mathrm{C}$ beam as a probe at ${E}_{\mathrm{lab}}=60\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, and determination of neutron and proton transition matrix elements involved in each excitation.Methods: Projectilelike fragments have been detected using ten sets of Si-surface barrier detector telescopes to measure the cross sections for elastic and inelastic scattering channels. Coupled reaction channels calculations are performed to understand the measured differential cross sections.Results: Homogeneous nature of surface vibrations (similar deformation for proton and neutron distributions) for the ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in Sn isotopes is observed.Conclusions: A comparison with recent results using $^{7}\mathrm{Li}$ projectile at similar ${E}_{\mathrm{c}.\mathrm{m}.}/{V}_{\mathrm{B}}$, which showed damped neutron vibrations particularly for the ${3}_{1}^{\ensuremath{-}}$ state, confirms that such measurements are probe dependent. Intrinsic transition matrix elements of nuclei can be deduced by removing the effects of finite projectile size in the extraction of nuclear shapes.

Imitation modeling of antenna of a hydroacoustic communication channel

The energy calculation of the hydroacoustic communication channel is divided into a number of interrelated stages: the choice of the operating frequency of the communication line; selection of sonar antennas; determination of the acoustic power of the signal. Experimental studies of hydroacoustic systems require significant financial costs. Therefore, recently, in order to reduce these costs, simulation models of individual nodes or even of the entire hydroacoustic system as a whole are resorted to. This work is devoted to the simulation modeling of a hydroacoustic channel antenna. A schematic diagram of the SKOL-2000R hydroacoustic antenna model is given, and the operating parameters of this model are chosen so that the resonant frequency of the model coincides with the resonant frequency of the original 29.6 kHz.

Role of target shell structure in direct reactions involving weakly bound Li7

The effect of the shell structure of the target nuclei ($^{89}\mathrm{Y}$ and $^{93}\mathrm{Nb}$) on reaction mechanisms involving the weakly bound $^{7}\mathrm{Li}$ projectile has been investigated via a comparative study of different processes. Measurements of direct breakup, nucleon transfer leading to the ejectile in bound as well as unbound states, and elastic scattering have been carried out for the $^{7}\mathrm{Li}+^{89}\mathrm{Y}$ system at three different energies near the Coulomb barrier. An extensive analysis of this comprehensive data set was carried out using coupled channel calculations and compared with a previous similar study for the $^{7}\mathrm{Li}+^{93}\mathrm{Nb}$ system. The observed cross sections at low target excitations for nucleon transfer reactions correlate with the vacancies in the valance orbitals.

Impact of pharmaceutical companies upon the economy and public finance in Poland: The Sanofi case study

The paper discusses a two-channel impact of pharmaceutical companies upon the economy and public finance. Firstly, pharmaceutical companies predominantly impact the net value added, employment, income of people employed by their suppliers and customers as well as public finance revenue in the countries where they are based. The mechanisms of such an influence are presented in the input-output matrix (input-output analysis) that shows how output from one industrial sector in the economy may become an input to another industrial sector. The input-output model was developed by Leontief and earned him the Nobel Prize. This kind of influence upon the Polish economy has been illustrated with the case study of the Sanofi company. Secondly, pharmaceutical products improve the effectiveness of medical treatment, by which they contribute to the higher standard of living and economic growth.In this part of investigation into the impact of pharmaceutical companies upon the economy the key method consists in calculating indirect costs, that is, the lost productivity (lost GDP). Non-generated GDP as well as the negative impact of diseases and the treatment thereof on public finance can be significantly reduced by using more effective pharmaceutical products. This second channel through which pharmaceutical companies exert influence on the economy has been illustrated with an example of economic consequences calculated from the social viewpoint for three gynaecological–oncology diseases. Our calculations for both channels in this exercise have led us to conclude that a pharmaceutical company positively influences its business partners and the economy while by improving the health of the population it exerts a positive impact upon the economy and public finance.

Elastic and inelastic scattering of O16 on Al27 and Si28 at 240 MeV

The nuclear scattering at energies well above the Coulomb barrier allows for a fairly sensitive examination of the parameters of the optical potential when the relevant couplings are included into the calculations. In this work we present experimental angular distribution data for the elastic and inelastic scatterings of $^{16}\mathrm{O}$ impinging on $^{27}\mathrm{Al}$ and $^{28}\mathrm{Si}$ target nuclei at ${E}_{\mathrm{lab}}=240\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. The experimental data were measured at ${7}^{\ifmmode^\circ\else\textdegree\fi{}}<{\ensuremath{\theta}}_{\text{c.m.}}<{16}^{\ifmmode^\circ\else\textdegree\fi{}}$ with good angular resolution. Experimental data are compared with coupled channel calculations with the inclusion of couplings to excited states in the target and projectile. We show that the shape of angular distributions are sensitive to the mass diffuseness parameter and the best agreement is achieved for $a=0.62\phantom{\rule{0.28em}{0ex}}\mathrm{fm}$.

Nuclear potentials model for heavy-ion reactions

Here, we present a nuclear potential model for heavy- ion reactions consisting of four central, spin, iso-spin and Iτ terms. The potential model presented here, predicts more accurate values for the barrier height of 6Li+24Mg→30P* and 7Li+24Mg→31P* reactions compared to the other potential models such as Proximity potential (Prox.77 and Prox.88) and Age Wither potential model (AW 95). A detailed comparative study of the fusion excitation functions of 6Li+24Mg and 7Li+24Mg reactions has been performed in 1–25 MeV energy interval. For energies below the Coulomb barrier and above the 15 MeV, our proposed potential model exhibits a better agreement with the experimental data than the above-mentioned potential models and leads to about 10 to 20 percent improvement in the previous results. Also, the analysis of S factor and the logarithmic derivatives showed that the coupled channel calculation based on our purposed potential is in good agreement with the corresponding experimental data at these energy ranges.

Spin-orbit effects in the 8Li+58Ni elastic scattering

In this work we present an elastic scattering angular distribution for the 8Li+58Ni system measured at Elab = 26.1 MeV. The 8Li beam was produced in the Radioactive Ion Beams in Brasil (RIBRAS) facility using the 7Li primary beam delivered by the 8-UD Pelletron accelerator. The angular distribution covers the angular range from 20 to 85 degrees in the center of mass frame. The data have been analysed by optical model and coupled channels calculations, including couplings to low-lying states in 8Li and the spin-orbit interaction. Our results indicate that the inclusion of the spin-orbit interaction in the calculations is important to describe the data at backward angles.

Elastic scattering of the B12+Ni58 system at near-barrier energies

Elastic scattering of a radioactive neutron-rich boron isotope, $^{12}\mathrm{B}$, has been measured for the first time. Angular distributions for the elastic scattering of $^{12}\mathrm{B}+^{58}\mathrm{Ni}$ have been measured at ${\mathit{E}}_{\mathrm{Lab}}=30.0$ and 33.0 MeV, which are just above the Coulomb barrier (${\mathit{V}}_{\mathrm{B}}=24$ MeV). The obtained angular distributions were analyzed in terms of the large-scale coupled channel (CC) and coupled reaction channel (CRC) calculations, where several inelastic transitions for the target, as well as the most relevant transfer reactions, have been included in the coupling matrix elements. The roles of the spin reorientation and spin-orbit interaction in the reaction mechanism were also investigated. The one-neutron transfer reaction through a coupled reaction calculation had some effect on the elastic scattering of the system studied.