Differential Cross Sections For Reaction Research Articles

Differential cross sections of the deuteron reactions on beryllium at energies and angles suitable for nuclear reaction analysis

The differential cross sections of the 9Be(d,p0)10Be, 9Be(d,p1)10Be, 9Be(d,a0)7Li and 9Be(d,a1)7Li reactions with deuterons in the energy range 1.0 – 2.2 MeV and at the detection angles of 120°, 140°, 150°, 160° and 170° were measured. These differential cross sections are appropriate for nuclear reaction analysis, a non-destructive technique to detect and quantify light elements. The determination of the differential cross sections was performed using the deuteron elastic scattering differential cross section of the natural silicon. The results were validated using a bulk beryllium target and the difference between the simulation and the experimental spectra does not exceed 10%.

$${T}$$-Invariance Conditions for Differential Cross Sections for Binary Nuclear Reactions Involving Spin-Oriented Particles and Nuclei

By employing the $$T$$ -invariance condition for the amplitudes describing arbitrary binary nuclear reactions that involve spin-oriented particles and the respective time-reversed reactions, a relation between the differential cross sections for these reactions is obtained for the first time. These cross sections are determined with the aid of sets of potentials simulating the interaction between particles of the initial and final reaction channels and not including any of spin–orbit interactions. The resulting relation covers the case corresponding to the implementation of the previously known detailed-balance principle. This relation is used to derive equalities between the components appearing in the cross sections under analysis via a unified mechanism and possessing identical $$P$$ and $$T$$ parities. These equalities make it possible to prove the existence of a number of components in the cross section that vanish upon taking into account $$T$$ invariance, and this opens new possibilities in studying $$T$$ -noninvariant interactions in nuclear reactions.

Study of Inelastic $$\boldsymbol{A}$$($$\boldsymbol{p,p^{\prime}}$$)$$\boldsymbol{X}$$ Reaction with $${}^{\mathbf{9}}$$Be and $${}^{\mathbf{90}}$$Zr Nuclei at 1 GeV

The secondary proton polarization and differential cross sections of the ( $$p,p^{\prime}$$ ) inelastic reaction on nuclei $${}^{9}$$ Be and $${}^{90}$$ Zr at the initial proton energy of 1 GeV were measured over a wide range of the scattered proton momenta at a laboratory angle of $$\Theta=21^{\circ}$$ . Scattered protons were detected by means of the magnetic spectrometer equipped with a polarimeter based on multiwire proportional chambers and carbon analyzer. A structure in the polarization and cross section data, related probably to the quasielastic scattering off nucleon correlations in the $${}^{9}$$ Be and $${}^{90}$$ Zr nuclei, was observed as earlier in the same data for the $${}^{12}$$ C, $${}^{28}$$ Si, $${}^{40}$$ Ca and $${}^{56}$$ Fe nuclei. A difference in the momentum distributions of the scattering cross section ratios for the $${}^{90}$$ Zr and $${}^{12}$$ C nuclei and for the $${}^{90}$$ Zr and $${}^{9}$$ Be nuclei was observed.

Mechanism analysis of reaction based on the quantum state-to-state dynamics**Project supported by the National Natural Science Foundation of China (Grant No. 11674198), the Taishan Scholar Project of Shandong Province, China (Grant No. ts201511025), and the Science Fund from the Shandong Provincial Laboratory of Biophysics.

We present a state-to-state dynamical calculation on the reaction S++H2→ SH+ + H based on an accurate X2A″ potential surface. Some reaction properties, such as reaction probability, integral cross sections, product distribution, etc., are found to be those with characteristics of an indirect reaction. The oscillating structures appearing in reaction probability versus collision energy are considered to be the consequence of the deep potential well in the reaction. The comparison of the present total integral cross sections with the previous quasi-classical trajectory results shows that the quantum effect is more important at low collision energies. In addition, the quantum number inversion in the rotational distribution of the product is regarded as the result of the heavy–light–light mass combination, which is not effective for the vibrational excitation. For the collision energies considered, the product differential cross sections of the title reaction are mainly concentrated in the forward and backward regions, which suggests that there is a long-life intermediate complex in the reaction process.

Study of the Mechanism of the 27Al(α, p)30Si Reaction at Eα = 30.3 MeV

The results from measuring the angular dependence of the 27Al(α, p)30Si reaction differential cross sections at 30.3 MeV α-particle energy with the formation of the final nucleus in the ground (0+) and first excited (2+; 2.235 MeV) states are presented. The experimental results are compared to calculated ones obtained by assuming there is both a mechanism of triton cluster stripping in a collective model and one of compound nucleus formation. The amplitudes of spectroscopic factors for the virtual decay of 30Si → 27Al + t are obtained using a shell model with wave functions of the 1d–2s shell nuclei in the Nilsson model, allowing for nuclear deformation and the spin–orbit interaction of nucleons. Comparison of the results from calculations and experiments shows that mechanism of triton stripping used in the FRESCO code with the obtained spectroscopic amplitudes mainly describes both the shape of angular distributions and the absolute values of the differential cross sections. The contribution from the mechanism of compound nucleus formation is notable only at large angles of proton emission.

The $D_{03}(2380)$ dibaryon resonance excitation in the $pd\to pd\pi\pi$ reaction.

The recent ANKE@COSY data on the differential cross section of reaction pd \to pd\pi\pipd→pdππ demonstrate a peak at invariant mass of the final d\pi\pidππ system 2.38~GeV2.38GeV, that corresponds to the isoscalar J^P = 3^+JP=3+ dibaryon D_{03}D03, and the enhancement in the distribution over the invariant mass of two final pions. The two-resonance model involving the tt-channel \sigmaσ-meson exchange between the proton and deuteron in the subprocess pd\to pD_{03}pd→pD03 and the sequential decays D_{03}\to D_{12}+\piD03→D12+π and D_{12}\to d +\piD12→d+π was applied to describe the shapes of these distributions with the lowest orbital angular momenta in the corresponding vertices. A possible role of higher orbital momenta in those vertices is studied here.

Possibility to study the pentaquark states Pc(4312) , Pc(4440) , and Pc(4457) in the reaction γp→J/ψp

Inspired by the observation of the pentaquark states $P_{c}(4312),P_{c}(4440)$ and $P_{c}(4457)$ at LHCb, photoproduction of these three $P_{c}$ states via the interaction $\gamma p\rightarrow J/\psi p$ is investigated in an effective Lagrangian approach. The $t$-channel Pomeron exchange diffractive process is considered as the main background for the $J/\psi $ photoproduction. The numerical results show that the theoretical cross section, which is calculated by assuming a branching ratio $Br[P_{c}\rightarrow J/\psi p]\simeq 3\%$, is consistent with the existing experimental data of the $ \gamma p\rightarrow J/\psi p$ process. With such a branching ratio, if experimental precision reaches 0.1 nb within a bin of 100 MeV for photon energy, two peaks are expected to be obviously observed in the $J/\psi $ photoproduction. To observe the two-peak structure from $P_{c}(4440)$ and $ P_{c}(4457)$, higher precision, about 0.1nb/10 MeV, is required to distinguish two close pentaquarks. If the physical branching ratio is larger, the requirement of experimental precision will be reduced. The differential cross sections for reaction $\gamma p\rightarrow J/\psi p$ are also present. It is found that the $t$-channel Pomeron exchange provides a sharp increase at extreme forward angles and gives a sizable contribution at most energy points, while the contributions from the $s$-channel $P_{c}$ exchanges play important roles at threshold energies. The experimental measurement of the $\gamma p\rightarrow J/\psi p$ process in the near-threshold energy region around $E_{\gamma }\simeq 9.4-10.5$ GeV is suggested, and is accessible at CEBAF@JLab and COMPASS.

Critical Comments on the T-Null Theorem and New Approach to Searches for T-Invariance Violation in Quantum Systems

for nuclear reactions that are two-body ones in the initial and final channels and which involve polarized particles, the T-null theorem stating the absence of vanishing observables in such reactions was proven in a number of studies by means of concepts of reaction \({\cal T}\) matrices that take into account general conservation laws along with T-invariance conditions in the “dynamically independent” approach. Not only does this approach focus on known mechanisms of such reactions, but it may also be applicable to their as-yet unknown mechanisms. By employing T-invariance conditions, the selection rules for specific mechanisms that make it possible to describe observables of a → b many-particle multistep nuclear reactions involving polarized particles are analyzed in the present study. It is shown that, in the differential cross sections for the initial nuclear reactions a → b and for \(\overline b \to \overline a \) reactions that are time-reversed with respect to them, the components characterized by specific P and T parities and related by T-invariance conditions are associated with unified mechanisms of their appearance and can be expressed in terms of unified scalar functions differing for a → b and \(\overline b \to \overline a \) reactions by the interchange of the channels and by the sign reversal for the momenta and spins of particles involved in these reactions. First, this permits selecting only one mechanism among all possible T-invariant mechanisms that describes simultaneously the features of the components considered for a → b and \(\overline b \to \overline a \) reactions and discarding all of the remaining mechanisms. Second, this enables one to obtain, in a number of cases, zero values for some components of the differential cross sections for the reactions in question. The latter constrains the applicability region of the aforementioned T-null theorem and makes it possible to use these components in the cross section for the initial reaction a → b to study the nature of T-noninvariant interactions.

Rainbows, supernumerary rainbows and interference effects in the angular scattering of chemical reactions: effect of varying the modulus of the S matrix in the context of Heisenberg’s S matrix programme

We investigate the existence of primary rainbows, supernumerary rainbows and diffraction interference effects in the product differential cross sections (DCSs) of state-to-state chemical reactions. The rainbows can be ‘pronounced’ or ‘hidden’. Our theoretical approach uses a ‘weak’ version of Heisenberg’s scattering matrix programme (wHSMP) introduced by Shan and Connor 2011 Phys. Chem. Chem. Phys. 13 8392. This wHSMP uses four general physical principles for chemical reactions to suggest simple parametrised forms for the S matrix; it does not employ a potential energy surface. We use a realistic parametrization in which the modulus of the S matrix is the sum of a smooth-step function and a gaussian function; both are functions of the total angular momentum quantum number, J. We then vary the parameters in the modulus. The phase of the S matrix is a cubic polynomial in J, which is held fixed. We demonstrate for a Legendre partial wave series (PWS) the existence of primary rainbows and supernumerary rainbows (both pronounced and hidden) as well as diffraction interference effects, in reactive DCSs. We find that reactive rainbows can be complicated in their structure. We also analyse for five examples, the angular scattering using nearside–farside (NF) PWS theory, including resummations of the PWS. In addition, we apply full and NF asymptotic (semiclassical) rainbow theories to the PWS—in particular, the uniform Airy and transitional Airy approximations for the farside scattering. This lets us prove that structures in the DCSs are indeed primary rainbows, supernumerary rainbows as well as diffraction interference effects. Our calculations complement and extend those in an earlier paper by Shan et al 2018 Phys. Chem. Chem. Phys. 20 819, in which the modulus of the S matrix is held fixed, whilst the phase is varied.

Elastic scattering of one-proton halo nucleus 17F on different mass targets using semi microscopic potentials

The elastic scattering of 17F have been studied for different mass targets (e.g. 12C, 14N, 58Ni, 208Pb) at different energies. We used the double folding optical model potential based on the density-dependent DDM3Y effective nucleon-nucleon interaction. Both version of the density distribution of the one-proton halo 17F nucleus has been taken into account in the above mentioned potential. The data for angular distributions of the elastic scattering differential cross section and reaction cross sections has been successfully reproduced at different energies using the above potentials. The energy dependence and the target mass number dependence of scattering in the imaginary volume integrals and the total reaction cross sections has also been studied.

Asymptotic theory of charged particle transfer reactions at low energies and nuclear astrophysics

An asymptotic theory is proposed for the peripheral transfer [Formula: see text] reaction at low energies within the three-body ([Formula: see text], [Formula: see text] and [Formula: see text]) model by combining the dispersion theory and DWBA, where [Formula: see text], [Formula: see text] and [Formula: see text] is a transferred particle. The contribution of the three-body ([Formula: see text], [Formula: see text] and [Formula: see text]) Coulomb dynamics of the transfer mechanism both to the peripheral partial amplitudes for the partial wave [Formula: see text] and to the DWBA amplitude is investigated. The results of the analysis of the differential cross sections of the specific proton transfer reactions at above-barrier energies are presented. New estimates and their uncertainties are obtained for values of the asymptotic normalization coefficients for [Formula: see text] and [Formula: see text] as well as for the direct astrophysical [Formula: see text] factors at stellar energy of the radiative capture [Formula: see text] and [Formula: see text] reactions.

An ab initio-based global potential energy surface for the SH3 system and full-dimensional state-to-state quantum dynamics study for the H2 + HS → H2 S + H reaction.

An accurate potential energy surface for the ground electronic state of SH3 system has been constructed with 41,882 high level ab initio energy points and the neural network fitting method. The time-dependent wave packet method has been used to calculate the first state-to-state differential cross sections for the title reaction up to 1.2 eV in full dimensions, based on the reactant-product decoupling scheme. It is found that the majority of H2 S are produced in the ground vibrational state, with a large fraction of available energy for the reaction ending up as product translational motion. The differential cross sections at the threshold energy are dominated by a very narrow peak in the backward direction. With the increase of collision energy, the width of the angular distribution increases considerably, which is a typical feature of a direct reaction via abstract mechanism, similar to the H2 + OH → H2 O + H reaction. © 2018 Wiley Periodicals, Inc.

Application of T-Invariance Conditions in Selecting Mechanisms of Nuclear Reactions, Decays, and Fission

T-invariance conditions for the differential cross sections of multiparticle multistep nuclear reactions are found with allowance for spin orientations of particles in the initial channels of such reactions. It is shown that the asymmetry coefficients for different T-parities in the differential cross sections for original and time-reversed reactions are expressed in terms of unified scalar (pseudoscalar) functions that depend of the 3-momenta and spins of particles involved in the initial and final channels of the reactions under analysis. It is also shown that knowledge of the aforementioned functions for the asymmetries under analysis in the original reaction makes it possible to reconstruct the respective functions for the analogous asymmetries in the time-reversed reaction without studying it experimentally. By considering the example of T-even and T-odd asymmetries in reactions where oriented nuclei undergo binary and ternary fission induced by cold polarized neutrons, it is demonstrated that the T-invariance conditions in question can be used to select mechanisms behind the appearance of the above asymmetries—in particular, mechanisms associated with the presence of T-noninvariant interactions.

Contribution from Mechanisms of Direct Nucleon Transfer to Proton Spectra in the 15N (α, p)18O Reaction

The differential cross section for the (α, p)18O reaction at an α-particle energy of 30 MeV is analyzed in the context of direct reaction mechanisms and the compound nucleus model. Spectroscopic amplitudes are calculated at the vertices of the diagrams illustrating triton and 14С cluster transfer reactions, including cases of mixed configurations of 1p–2d shells. The OP parameters of α–15N and p–18O interaction are found that provide the best agreement between the calculated and experimental data at an energy of ~30 MeV. It is shown that the main contribution to the production of protons comes from direct triton cluster transfer. The role of the heavy 14С cluster transfer mechanism and the compound nucleus mechanism is notable in the region of angles greater than 90°.

Study of Inelastic A(p, p′)X Reaction with Nuclei at 1 GeV

The secondary-proton polarization and differential cross sections for the (p, p') inelastic reaction on 28Si and 56Fe nuclei at the initial proton energy of 1 GeV were measured over a wide range of the scattered-proton momenta at a laboratory angle of Θ = 21◦. Scattered protons were detected by means of a magnetic spectrometer equipped with a polarimeter based on multiwire proportional chambers and a carbon analyzer. A structure in the polarization and cross section data, which is probably related to quasielastic scattering off nucleon correlations in the 28Si and 56Fe nuclei, was observed as earlier in the analogous data for 12C and 40Ca nuclei. Momentum intervals within which cross-section ratios for nuclei did not depend on the scattered-proton momentum were found.

A benchmarking procedure for PIGE related differential cross-sections

Abstract The application of standard-less PIGE requires the a priori knowledge of the differential cross section of the reaction used for the quantification of each detected light element. Towards this end, a lot of datasets have been published the last few years from several laboratories around the world. The discrepancies often found between different measured cross sections can be resolved by applying a rigorous benchmarking procedure through the measurement of thick target yields. Such a procedure is proposed in the present paper and is applied in the case of the 19F( p, p ′ γ )19F reaction.

Neutron-rich nuclei produced at zero degrees in damped collisions induced by a beam of 18O on a 238U target

Cross sections and corresponding momentum distributions have been measured for the first time at zero degrees for the exotic nuclei obtained from a beam of 18O at 8.5 MeV/A impinging on a 1 mg/cm2238U target. Sizable cross sections were found for the production of exotic species arising from the neutron transfer and proton removal from the projectile. Comparisons of experimental results with calculations based on deep-inelastic reaction models, taking into account the particle evaporation process, indicate that zero degree is a scattering angle at which the differential reaction cross section for production of exotic nuclei is at its maximum. This result is important in view of the new generation of zero degrees spectrometers under construction, such as the S3 separator at GANIL, for example.

Rainbows, supernumerary rainbows and interference effects in the angular scattering of chemical reactions: an investigation using Heisenberg's S matrix programme.

In earlier research, we have demonstrated that broad "hidden" rainbows can occur in the product differential cross sections (DCSs) of state-to-state chemical reactions. Here we ask the question: can pronounced and localized rainbows, rather than broad hidden ones, occur in reactive DCSs? Further motivation comes from recent measurements by H. Pan and K. Liu, J. Phys. Chem. A, 2016, 120, 6712, of a "bulge" in a reactive DCS, which they conjecture is a rainbow. Our theoretical approach uses a "weak" version of Heisenberg's scattering matrix program (wHSMP) introduced by X. Shan and J. N. L. Connor, Phys. Chem. Chem. Phys., 2011, 13, 8392. This wHSMP uses four general physical principles for chemical reactions to suggest simple parameterized forms for the S matrix; it does not employ a potential energy surface. We use a parameterization in which the modulus of the S matrix is a smooth-step function of the total angular momentum quantum number, J, and (importantly) its phase is a cubic polynomial in J. We demonstrate for a Legendre partial wave series (PWS) the existence of pronounced rainbows, supernumerary rainbows, and other interference effects, in reactive DCSs. We find that reactive rainbows can be more complicated in their structure than the familiar rainbows of elastic scattering. We also analyse the angular scattering using Nearside-Farside (NF) PWS theory and NF PWS Local Angular Momentum (LAM) theory, including resummations of the PWS. In addition, we apply full and NF asymptotic (semiclassical) rainbow theories to the PWS - in particular, the uniform Airy and transitional Airy approximations for the farside scattering. This lets us prove that structure in the DCSs are indeed rainbows, supernumerary rainbows as well as other interference effects.

Experimental Study of Three-nucleon Dynamics in Proton--Deuteron Breakup Reaction

Proton-deuteron breakup reaction can serve as a tool to test state-of- the-art descriptions of nuclear interactions. At intermediate energies, below the threshold for pion production, comparison of the data with exact theoretical calculations is possible and subtle effects of the dynamics beyond the pairwise nucleon-nucleon interaction, namely the three-nucleon force (3NF), are significant. Beside 3NF, Coulomb interaction or relativistic effects are also important to precisely describe the differential cross section of the breakup reaction. The data analysis and preliminary results of the measurement of proton-induced deuteron breakup at the Cyclotron Center Bronowice, Institute of Nuclear Physics, Polish Academy of Sciences in Krakow are presented.

The H2+ + He proton transfer reaction: quantum reactive differential cross sections to be linked with future velocity mapping experiments

We construct the velocity map images of the proton transfer reaction between helium and molecular hydrogen ion . We perform simulations of imaging experiments at one representative total collision energy taking into account the inherent aberrations of the velocity mapping in order to explore the feasibility of direct comparisons between theory and future experiments planned in our laboratory. The asymptotic angular distributions of the fragments in a 3D velocity space is determined from the quantum state-to-state differential reactive cross sections and reaction probabilities which are computed by using the time-independent coupled channel hyperspherical coordinate method. The calculations employ an earlier ab initio potential energy surface computed at the FCI/cc-pVQZ level of theory. The present simulations indicate that the planned experiments would be selective enough to differentiate between product distributions resulting from different initial internal states of the reactants.