Isotopic effects of the N(2D) + H2 → NH + H reaction: a quantum time-dependent wave packet investigation

Based on the potential energy surface reported by Li and co-workers (J. Comput. Chem. 34 1686–1696 (2013)), the dynamics calculations of N(²D)?+?H₂(v ₀?=?0, j ₀?=?0) reaction and its isotopic variants HD and D₂ are studied using time-dependent wave packet method in the collision energy range of 0.01–1.0?eV. Dynamics properties such as reaction probability, differential cross section, and integral cross section are studied at state-to-state level of theory. Present values are compared with available theoretical and experimental results. The results indicate that the integral cross sections of N(²D)?+?D₂ reaction are in general good agreement with the experimental data at collision energy below 0.15?eV. The rotational state-resolved integral cross sections of N(²D)?+?H₂/HD/D₂ reactions are compared with experimental values for the first time, with the obtained values being in good agreement with the experimental data.     

Low-energy antimony implantation in silicon

Abstract

Antimony is known to be a donor in silicon, Low-energy implantations of Sb in Si produce very shallow profiles which have many device applications. Gibbons et al. ¹ calulated the projected ranges of Sb ion-implanted in Si, using the LSS (Lindhard, Scharff, and Schiott) method. Oetzmann et al. ² measured projected ranges and range straggling for several heavy ions in Si, Al, and Ge, using high-resolution backscattering; in the energy region of interest to us, e = 10^?2 to 10^?1, their results were about 30% higher than those reported by Gibbons et al. In the study reported here, we implanted 5 × 10¹⁴ Sb/cm² in Si at 5–60 keV, measured the resulting depth distribution by secondary ion mass spectrometry, and checked the measurements by backscattering. Our results showed the experimental projected ranges to be about halfway between those reported in the earlier studies. The discrepancies between theoretical calculations and experimental results are due not to the electronic stopping cross section, which is negligible in the range of interest here, but to the nuclear stopping power. Using a modified nuclear scattering potential given by Wilson et al.,³ we calculated the projected range distribution according to the method described by Winterbon.⁴ Our results are in very good agreement with the experimental measurements.     

The reactions of 12C with 12C AT 293 MeV

Energy spectra, angular distributions, and elemental yield distributions have been measured for products Z = 1?9 produced in the reactions of ¹²C on ¹²C. A total reaction cross section 1170_?100⁺¹⁷⁰ mb was determined from the measured elemental cross sections and the principle of charge conservation. This total reaction cross section is about 250 mb less than the geometric cross section and agrees with the Glauber-model calculations of DeVries and Peng. The experimental energy spectra, angular distributions, and yield distributions were compared with those from model calculations for the statistical decay of the products of fusion and of incomplete fusion reactions. For both types of calculations, a modified version of the code LILITA was used. By comparing the data to model calculations, an upper limit of 75 mb for the fusion cross section was determined. That limit corresponds to an upper limit of L_crit for fusion of 10? in the sharp-cutoff approximation. The dominant reaction mechanisms appear to be incomplete fusion processes.     

Dynamics studies of O+ + D2 reaction using the time-dependent wave packet method

Based on the potential energy surface (PES) reported by Li et al. (Phys. Chem. Chem. Phys. 20, 1039 (2018)), the initial state dynamics calculation of O⁺?+?D₂ (v?=?0, j?=?0) reaction was conducted using the time-dependent wave packet method with a second order split operator. Dynamics properties such as reaction probability, integral cross section, differential cross section, and distribution of products were calculated and compared with available experimental and theoretical results. The present integral cross section values were in good agreement with experimental results. In addition, the differential cross section indicates that the mechanism of the complex-formation reaction plays a dominant role during the reaction.     

Positron scattering from hydrocarbons

The total cross sections for positron impact on hydrocarbons have been calculated using the additivity rule in which the total cross section for a molecule is the sum of the total cross section for the constituent atoms. The energy range considered is from a few eV to several thousand eV. The total cross sections for positron impact on an atom are calculated by employing a complex spherical potential which comprises of a static, polarization and an absorption potential. We have good agreement with the experimental results for hydrocarbons for positron energy ⩾100 eV. Our results also agree with the available calculations for CH₄ and C₂H₂ which employed full molecular wavefunctions beyond 100 eV. Our absorption cross sections also agree with molecular wave-function calculations for C₂H₂ and CH₄ beyond 100 eV. We have shown the Bethe plots fore ⁺−C ande ⁺−H scattering systems and Bethe parameters have been extracted. We have fitted the cross section for positron impact on hydrocarbons in the formσ _t(C _n H _m )=naE ⁻ b+mcE ⁻ d in the energy range 300–5000 eV wherea=195.0543,b=0.7986,c=371.1757 andd=1.1379 withE in eV andσ _t in 10⁻¹⁶ cm².     

Neutron-neutron quasifree scattering in the 2H(n,nn)p reaction at En = 14.1 MeV

Neutron-neutron quasifree scattering has been studied in the deuteron break-up reaction ²H(n, nn)p at E_n = 14.1 MeV. Two coplanar and symmetric configurations have been investigated in a kinematically complete experiment where the detection of the spectator particle was not possible. The experimental cross sections are compared with “exact” calculations derived from Faddeev-type equations solved with S- and P-wave nucleon-nucleon separable interactions. These calculations agree both in shape and magnitude with the differential cross section for the θ₁ = ? θ₂ = 40° configuration (E_p^min = 0). At θ₁ = ? θ₂ = 30° (E_p^min = 180 keV). however, the absolute value of the measured cross section is too high and an observed structure in the shape of the differential cross section is in sharp conflict with the now available “exact” calculations.     

Investigation of the reaction D(e, pp)e′ π − on a tensorpolarized deuterium target at high proton momenta

The differential cross section of the reaction D(e,pp)e′ π ⁻ is measured in the range of proton momenta 300–720 MeV/c and proton emergence angles 64–83° for invariant masses of the pp system ranging from 2m _p to 2220 MeV/c ². The measured values of the cross section are found to differ substantially from single-particle model calculations. The components of the analyzing power for this reaction are measured. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 10, 730–736 (25 May 1998) Deceased.     

Three-body calculation of neutron-deuteron elastic scattering in the energy region from 2.5 MeV up to 50 MeV

The three-body Faddeev equations for neutron-deuteron scattering are solved in the energy region from 2.5 MeV to 50 MeV of the incident neutron energy with small energy steps. Higher-rank separable potentials are used in the¹ s ₀ wave and in the³ s ₁—³ d ₁ waves, while rank-1 separable potentials are used in¹ p ₁,³ p _0,1,2 ¹ d ₂ ³ d _2,3 waves. The calculation is compared with experiments for the total cross section, the total break-up cross section, the differential cross section and the analyzing power of neutron-deuteron scattering. The improvements in the agreement as compared to previous calculations are impressive in many cases. Especially, the calculated total cross section agrees with the experiment below 30 MeV within the error bars, which are as small as 1%. A discussion on the numerical accuracy is given. General aspects of the calculated cross section are discussed. It is pointed out that thes-wave asymptotic normalization of the deuteron wave function (A _s ) is important.     

A two-scale model from the point of view of the small-slope approximation

Abstract

General results for the scattering cross section following from the small-slope approximation (SSA) are applied to the case of two-scale surface roughness which can be represented as a superposition of small-scale and large-scale components. The purpose of the paper is to obtain analytically tractable results with obvious physical meaning which can be used for estimates prior to undertaking extensive numerical calculations according to exact unambiguous expressions of the SSA. The general case of vector (electromagnetic) or scalar (sound) waves is considered. The statistics of small-scale roughness is not assumed to be Gaussian (in any sense) or space-homogeneous, and the possible dependence of the statistics of small-scale roughness on a large-scale undulating surface is taken into account. As a result, a modified local spectrum of small-scale components of roughness enters into corresponding expressions for the scattering cross section. It is demonstrated that under appropriate conditions, the resulting formulae for the scattering cross section reduce to the conventional two-scale model.     

Theoretical calculation of of B-like ions： photoionization cross sections N^2＋, O^3＋ and F^4＋

There can be found some notable discrepancies with regard to the resonance structures when R-matrix calculations from the Opacity Project and other sources are compared with recent absolute experimental measurements of Bizau et al [Astron.Astrophts.439 387(2005)] for B-like ions N2+,O3+ and F4+.We performed close-coupling calculations based on the R-matrix formalism for the photoionizations of ions mentioned above both for the ground states and first excited states in the near threshold regions.The present results are compared with experimental ones given by Bizau et al and earlier theoretical ones.Excellent agreement is obtained between our theoretical results and the experimental photoionization cross sections.The present calculations show a significant improvement over the previous theoretical results.     

Elastic scattering of low-energy electrons by cadmium atoms

Experimental results on the differential cross sections of 180° elastic electron scattering and the total cross section of electron scattering by cadmium atoms in the energy range 0–6 eV are reported for the first time. Distinct shape resonances with the (5s ²5p)² P ⁰ and 5s5p ² configurations are revealed in the near-threshold range and at E≈4 eV. In the range 3.0–3.7 eV, the differential cross section exhibits extra singularities that are probably related to the d-wave shape resonance. The resonance contribution to the backscattering cross section near 4 eV is found to be about 20%.     

In-plane vibrations of circular rings

Except in a few cases rings have been treated one-dimensionally as curved beams in analyses to determine their frequencies of vibration. Consequently, for thick rings there are large discrepancies between theoretical and experimental results. In this paper an analysis is carried out in which account is taken of the warping of the cross section. The displacement v in the circumferential direction is assumed to be of the form v₀ + v₁y + v₃y³ + v₅y⁵, where the v_i are functions of the angular co-ordinate θ. The frequencies of free vibration are determined by using the principle of minimum total potential energy. Numerical calculations are made for a ring of rectangular cross section. Results are in good agreement with experimental ones.     

Total reaction and fusion cross sections at sub- and near-barrier energies for the system 7Li + 28Si

Fusion cross sections are extracted for the ⁷Li$ + $²⁸Si system, via reaction cross section and transfer measurements at sub- and near-barrier energies ( E _lab = 5.7 to 14MeV). The energy evolution of transfer to reaction cross section ratios is determined with the aid of CDCC calculations, which subsequently allows the deduction of fusion cross sections at sub- and near-barrier energies. It is shown that fusion can be well represented in a BPM context. Fusion cross sections are compared for the systems ⁷Li$ + $²⁸Si and ⁶Li$ + $²⁸Si, the latter studied previously, and are found to exhibit different strengths. Last, the direct channels determined at 13MeV, are found to be dominated by a 2n -transfer mechanism.     

Cross section for the production of compound nuclei in <Emphasis Type="Italic">p</Emphasis>Bi interaction at energies in the range 20–100 MeV

A method for determining the cross section for compound-nucleus formation, σ _CN, in nuclear reactions initiated by protons of energy in the range 20–100 MeV is proposed. The method is based on measuring cross sections for the yield of isotopes maximally remote from the target nucleus. The applicability of the method is illustrated by applying it to the reaction ²⁰⁹Bi(p, xn), which is considered by way of example. Data obtained for the cross section σ _CN are compared with the results of calculations performed on the basis of the intranuclear-cascade model.     

Capture cross sections for very heavy systems

In intermediate-mass systems, collective excitations of the target and projectile can greatly enhance the subbarrier capture cross section σ _cap by giving rise to a distribution of Coulomb barriers. For such systems, capture essentially leads directly to fusion [formation of a compound nucleus (CN)], which then decays through the emission of light particles (neutrons, protons, and alpha particles). Thus, the evaporation-residue (ER) cross section is essentially equal to σ _cap. For heavier systems, the experimental situation is significantly more complicated owing to the presence of quasifission (QF) (rapid separation into two fragments before the CN is formed) and by fusion-fission (FF) of the CN itself. Thus, three cross sections need to be measured in order to evaluate σ _cap. Although the ER essentially recoil along the beam direction, QF and FF fragments are scattered to all angles and require the measurement of angular distributions in order to obtain the excitation function and barrier distribution for capture. Two other approaches to this problem exist. If QF is not important, one can still measure just the ER cross section and try to reconstruct the corresponding σ _cap through use of an evaporation-model code that takes account of the FF degree of freedom. Some earlier results on σ _cap obtained in this way will be reanalyzed with detailed coupled-channels calculations, and the “extra-push” phenomenon discussed. One may also try to obtain σ _cap by exploiting unitarity, that is, by measuring instead the flux of particles corresponding to quasielastic (QE) scattering from the Coulomb barrier. Some new QE results obtained for the ⁸⁶Kr + ²⁰⁸Pb system at iThemba LABS in South Africa will be presented. The text was submitted by the authors in English.     

The reaction mechanism of heavy ion scattering at intermediate energies

The contribution to the real and imaginary nucleus-nucleus (N-N) optical potential from nucleon-nucleon scattering in the medium is calculated in a local density approximation from a two Fermi sphere nuclear matter picture for the N-N collision. This reaction mechanism is shown to be dominant for ¹²C + ¹²C scattering at all considered energies (160 MeV < E_lab < 2250 MeV) giving a weakly energy dependent reaction cross section of about 900 mb. Inclusion of the collective 2⁺, 3^? excitations in a coupled channel calculations gives good agreement for both the measured elastic and inelastic 2⁺ cross section at E_lab = 1016 MeV. This fully microscopic parameter free calculation indicates that the energy dependence of the reaction cross section for this system is mostly due to the decrease of the collective contribution with increasing energy contrary to current theoretical models.     

Cross section measurements and thermonuclear reaction rates for 48Ca(p, γ)49Sc and 48Ca(p,n)48Sc

Absolute cross sections have been measured for the reaction ⁴⁸Ca(p, γ)⁴⁹Sc for 0.579 MeV ≦ E_{p, lab} ≦ 2.670 MeV and for the reaction ⁴⁸Ca(p, n)⁴⁸Sc for 0.956 MeV ≦ E_{p, lab} ≦ 2.670 MeV. Substantial competition effects in the cross section for ⁴⁸Ca(p, γ)⁴⁹Sc were observed at the thresholds for neutron emission to the 623 keV (3⁺), 1143 keV (2⁺) and 1402 keV (2^?) excited states of ⁴⁸Sc. Thermonuclear reaction rates were calculated from the measured cross sections for 0.1 ≦ T₉ ≦ 10.0. The new rates differ considerably from those used in earlier calculations of the production of the rare, neutron-rich intermediate mass nuclides during explosive carbon burning. In particular, the new rates may change the predicted abundances for ⁴⁸Ca, ^{49, 50}Ti and ⁵⁰V substantially. The good agreement between current global Hauser-Feshbach models and the experimental data indicates that Hauser-Feshbach calculations can provide sufficiently reliable rates for astrophysical calculations in cases where experimental data are non-existent.     

Investigation of cross sections for the formation and destruction of negative boron ions

The electron loss and electron capture cross sections σ _i,i+m and σ _i,i−m for boron ions and atoms traveling at the velocities V=1.19 and 1.83 a.u. in H₂, He, N₂, Ne, Ar, and Xe are measured. The known experimental data on these cross sections at velocities near the cross-section maximum are analyzed. It is found that the electron loss cross sections can be described by a formula which was previously derived in the free-collision approximation and takes into account features of both the ions and the ambient atoms. As the nuclear charge Z _t of the ambient atoms increases, the cross sections vary nonmonotonically, increasing on average as Zt _t ^1/2 . A formula based on the model of independent electrons is proposed for electron capture by ions with small values of the charge i. It describes the dependence of the electron capture cross section σ _i,i−1 on the mean binding energy of an electron in an ion with the charge i−1. The total electron capture cross section σ _i,i−1 is proportional to the number of vacancies in the unfilled electron shell nearest the nucleus. The cross sections 0σ _i,i−1 exhibit substantially nonmonotonic variation with Z _t, increasing on average as Z _t ^1/3 . Zh. éksp. Teor. Fiz. 116, 1539–1550 (November 1999)     

Proton-Induced Deuteron Breakup at E lab P = 65 MeV in Quasi-Free Scattering Configurations

The proton-deuteron breakup cross sections and analyzing powers A _y for three kinematically complete configurations in a quasi-free-scattering geometry have been measured at E ^lab _P = 65 MeV. The data are compared with predictions of rigorous Faddeev calculations using the Argonne AV14, Bonn-B, Nijmegen-78, and Paris potentials. A satisfactory agreement between theory and experimental data, both for cross sections and analyzing powers, has been found. Received January 16, 1995; accepted in final form March 13, 1995     

Optical nutation at a Raman-active transition

Optical nutation at the Raman-active transition 6P _1/2−6P _3/2 of thallium atoms (ω _R /2πc=7793 cm ⁻¹) under resonant Raman excitation by a biharmonic picosecond pulsed field, giving rise to substantial motion of the population, is detected. Optical nutation appears as an oscillatory behavior of the energy of the anti-Stokes scattering of probe pulses, which follow with a fixed delay, as a function of the product of the energies of the excitation pulses. As a result of the dynamic Stark effect, which decreases the frequency of the transition under study, resonance excitation conditions are satisfied for negative initial detunings of the Raman excitation frequency from resonance. The Raman scattering cross section for the transition under study is estimated by comparing the experimental data with the calculations. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 1, 7–12 (10 July 1999)