Differential Excitation Functions Research Articles

Negative ion resonances in the autoionizing region of zinc: excitation of the 4s4p3P0,1,2 states

Temporary negative ion resonances above the ionization threshold of zinc atoms have been observed in angular differential electron excitation functions and photon excitation functions of the lowest optically forbidden 3P state. These resonances involve the opening of the 3d-shell or double excitation from the outermost 4s-shell and provide a sensitive test for channel coupling and electron correlation effects.

Precompound Monte-Carlo model for cluster induced reactions

We present an algorithm for Monte-Carlo selection of exciton energies for reactions induced by clusters. Reaction mechanisms are addressed that involve a dissolution of the cluster into its constituent nucleons followed by the initiation of a preequilibrium cascade. Calculated single differential spectra and excitation functions for ${}^{93}\mathrm{Nb}(\ensuremath{\alpha},xn)$ reactions are compared with experimental results to illustrate use of this method. Some advantages of exclusive computational techniques over analytic inclusive methods are summarized.

Stereodynamics of the Reaction O(1D2) + H2(v=0) → OH(X2Πi;v‘=0,N‘,f) + H: State-Resolved Linear and Rotational Angular Momentum Distributions

The product-state-specific stereodynamics of the photon-initiated reaction of O(1D2) with H2 has been investigated by polarized Doppler-resolved laser-induced fluorescence, under room-temperature bulb conditions. Product-state-resolved differential cross sections, excitation functions, and rotational angular momentum alignments are reported for the channels leading to OH(2Π3/2(A‘/A‘‘);v‘=0,N‘=5) and OH(2Π1/2(A‘);v‘=0,N‘=14) at a mean collision energy of ∼12 kJ mol-1. The data are compared with (state-resolved) quasi-classical trajectory (QCT) calculations of the linear and angular momentum distributions and excitation functions conducted on the Schinke−Lester (SL1) ab initio ground-state potential energy surface, under similar conditions as the experiments. Overall, excellent agreement is obtained between the QCT calculated and experimentally determined stereodynamical features. The results are discussed in light of other recent work on this prototypical insertion reaction and on the related systems O(1D2) + HD and CH4.

State‐Resolved Stereodynamics of an Insertion Reaction O(1D2) + H2(v = 0, j) → OH(X2Πi; v′, N′, f′) + H

AbstractThe product state‐resolved stereodynamics of the reaction of O(1D2) with H2 have been studied at 300 K at a mean collision energy of ca. 12 kJ mol−1, using polarized, Doppler‐resolved laser‐induced fluorescence to probe the scattered products, OH(X2Πi; v′ = 0, N′, f′), and polarized photodissociation of N2O to provide the reagent O(1D2) atoms. Product state‐resolved differential cross sections, rotational polarizations, and excitation functions are in very good qualitative agreement with the results of quasi‐classical trajectory (QCT) calculations, conducted on the Schinke‐Lester, SL1 ab initio potential energy surface (PES) for the ground electronic state of the collision complex. The experimental and computational results are compared with those obtained in a complementary study of the reaction of O(1D2) with CH4 and remarkable parallels have been exposed. The linear and angular momentum vector correlations are all consistent with an “insertion” mechanism, proceeding over an attractive PES, which presents no entrance barrier.

Measurement of fast-neutron activation cross sections for copper, europium, hafnium, iron, nickel, silver, terbium and titanium at 10.0 and 14.7 MeV and for the Be( d, n) thick-target spectrum

Several fast-neutron activation reactions for copper, europium, hafnium, iron, nickel, silver, terbium and titanium that are important to fusion energy have been investigated in three distinct neutron fields generated by accelerators at Argonne National Laboratory (ANL) and Los Alamos National Laboratory (LANL), U.S.A., and Japan Atomic Energy Research Institute (JAERI), Tokai, Japan. The experimental data acquired from this collaboration, which has been organized by the International Atomic Energy Agency, include both differential cross sections at 10.0 and 14.7 MeV and integral cross sections for the Be( d, n) thick-target spectrum produced by 7-MeV deuterons. 58Ni( n, p) 58 g + m Co and 93Nb ( n,2 n) 92 m Nb were used as neutron fluence standards, and the 238U( n, f) cross section was measured at 10.0 MeV to validate the experimental techniques. Measured differential cross sections are compared with corresponding experimental data from the literature and with values obtained from nuclear model calculations and evaluations. Measured integral cross sections are compared with some earlier experimental results from ANL and with calculated values based on available differential cross-section excitation functions and various representations of the Be( d, n) neutron spectrum. Reasonably good agreement is observed in many of these comparisons.

High-energy pion-induced double charge exchange and isovector renormalization

The (${\mathrm{\ensuremath{\pi}}}^{+}$,${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$) double-charge-exchange reaction for pion energies of 200 to 1400 MeV is calculated with a zero-parameter Glauber theory that includes spin flip and pion absorption. Differential cross sections and excitation functions are obtained for $^{14}\mathrm{C}$ and $^{18}\mathrm{O}$ targets. Results for ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}$=300--525 MeV are compared with recent experimental results and suggest a new quenching process. We have calculated effects of medium polarization on the isovector pion operator and find a strong reduction in good agreement with data. A pronounced dip in the cross section near ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}$=1300 MeV offers a unique testing ground for unconventional mechanisms.

A new technique for collecting excitation functions for electron spectrometers fitted with a position sensitive detector

A new experimental method has been used for measuring electron impact differential excitation functions when using a spectrometer fitted with a position sensitive detector. This technique can be easily implemented and results in a large increase in sensitivity, with no loss of information. A general derivation is given which facilitates calculation of the gain in sensitivity independent of the type of dispersive elements used or the exact nature of the spectroscopy being performed. The technique helps to reduce space charge problems associated with preparation of the incident electron beam.

The 63Cu(α, p) 66Zn cross section and the corresponding thermonuclear reaction rate

Differential cross sections and excitation functions for the reaction 63Cu(α, p) 66Zn have been measured over the energy range E α = 6–10 MeV. Results of statistical model calculations are compared to the excitation functions for individual proton groups and are found to give good representations to within about a factor of two. The data and the calculated cross sections are used to determine the thermonuclear reaction rates for temperatures of astrophysical interest.

Pion scattering by6Li

Differential cross sections, excitation functions, and vector (and tensor) polarisations have been calculated for pion elastic and inelastic scattering off 6Li near the Delta 33-resonance energy. A momentum-space coupled-channel formalism has been used. It contains the usual first-order term and a phenomenological rho 2 term, the parameters of which were determined earlier from pi -12C experimental data. Cluster and phenomenological shell-model wavefunctions of the Li nuclear states are shown to produce quantitatively different results for the vector polarisation. At the same time the differential cross sections corresponding to the two nuclear models differ at moderate momentum transfers mainly in their absolute values.

Kinematics and dynamical effects in the total and differential excitation functions. A variational transition state theory analysis

A variational transition state theory, previously developed to account for the kinetic energy dependence of the reaction cross section, has been extended to include the effect of the curvature of the reaction coordinate as well as to calculate the energy disposal of elementary reactions. A systematic study of the influence of kinematics and dynamical factors in the kinetic energy dependence of both the energy disposal and reaction cross section has been made. The theory was applied to ideal systems with different mass combinations as well as to the M + RX → MX + R reaction family (M = Na, K, Rb; R = CH 3; X = Cl, Br, I). One of the most important findings of the present study is that for a given potential energy surface there is a correlation between the energy disposal as well as the excitation function, with the actual location of the maximum in the curvature of the reaction coordinate. Those systems for which the location of the maximum of the curvature along the reaction coordinate lies close to that of maximum gradient in the potential energy showed a clear non-adiabatic behaviour, i.e. there is a significant flux between the (translational) energy along the reaction coordinate and the (vibrational) energy perpendicular to it. Therefore they showed the higher fraction in vibrational energy of the products as well as the higher collision energy dependence of the reaction cross section (i.e. higher slope of σ R versus E T.

Microanalysis of Flourine by nuclear reactions: I. [formula omitted] reactions

The quantitative determination and depth profiling of fluorine in the surface region of various substrates using nuclear reaction microanalysis was studied. Differential cross sections and excitation functions for the reaction 19F(p, α 0) 16O and 19F(p, αγ) 16O were investigated in great detail, especially in the vicinity of resonances, where automatic energy scanning was used. Resonance widths and positions were measured precisely, in particular for the narrow resonances of 19F(p, αγ) 16O. A very narrow, τ = 150 ± 50 eV, resonance was found at 1088 keV. The excitation curves shown for various resonances allow one to carry out the computer calculations required for converting yield curves into depth profiles. The paper discusses how to choose among the nuclear reactions and resonances available to achieve best sensitivity, selectivity, depth resolution, ease of operation or speed of measurements, according to the problem considered, and to define the corresponding optimal experimental conditions. It appears that, in addition to the strong 872 keV, τ = 4.2 keV resonance of 19F(p, αγ) 16O, the 340 keV, τ = 2.4 keV resonance may be especially useful. The results are also of interest for hydrogen depth profiling when using the reverse reaction 1 H( 19 F, αγ) 16 O .

Influence of the He-resonances in the post-collision interaction process

The negative ion resonances involved in electron collisions with helium in the 57-60 eV autoionisation region are studied with recent data obtained from electron scattering measurements. The decay processes into the available channels are discussed in relation to the 'post-collision interaction' (PCI). By means of systematic measurements of differential excitation functions of the n=2 to 8 bound states, new data are obtained on the strengths of the decay into these channels. Least-squares fits carried out with these data show that a good account is given for the direct decay of the 57.19 eV 2P resonance into the single-excitation channels by the empirical relation S(n)=S0ekn2/, where S is the strength, n the quantum number and S0 and k are parameters. Assuming that such a law should hold for the 58.29 eV 2D resonance also, arguments are presented to show that for the features in n=4 channels, the PCI mechanism should proceed via negative-ion formation.

On the mechanism of the reactions24,25,26Mg(n,?)21,22,23Ne at neutron energies near 14 MeV

Differential cross sections of the reactions24Mg(n,α)21Ne,25Mg(n,α)22Ne, and26Mg(n,α)23Ne have been measured at neutron energies of 13.19,13.93 and 14.33 MeV, at 13.93 and 14.33 MeV, and at 13.47 and 13.93 MeV, respectively. In forward direction, differential excitation functions of those reactions have been measured at energies between 12.67 and 16.05 MeV. The results are analysed in terms of direct-reaction and compound-nucleus theories.

A study of the (α, t) reaction on 19F, 27Al, 51V and 59Co

The angular distributions of tritons from the (α, t) reaction on 19F, 27Al, 51V and 59Co nuclei corresponding to the (0 +) ground states and (2 +) excited states in the final nuclei have been measured in the angular range between 15° and 170° at α-particle energies of 25 MeV. For reactions on 27Al and 51V nuclei, the differential excitation functions have also been obtained at different angles of outgoing tritons at E α from 20 to 25 MeV. The experimental angular distributions are analysed by the DWBA approximation on the assumption of a nucleon stripping mechanism. The analyses of the present results and the data obtained earlier for the ( α, t) reaction on the 1 p shell nuclei, A ≲ 30, reveal that the distinguishing feature of the reaction under study is the presence of backward angle peaks in the reaction cross section, which appear to be associated with exchange processes. For the ( α, t) reaction on the heavier nuclei ( A > 30), the dominant mechanism is nucleon stripping.

Electroexcitation of Xe I energy levels in the 18-24 eV autoionization region

An electron energy-loss spectrum and five differential excitation functions of bound states of Xe I have been measured in the autoionization region, 18 to 24 eV. An attempt is made to interpret the numerous peaks of the spectrum and the perturbations present in the excitation functions. Singly and doubly excited neutral states and temporary negative-ion states are involved. The results obtained by electron spectrometry are compared with those obtained by photoabsorption and transmission spectroscopies.

Resonances in the differential electron excitation cross section of bound states of krypton in the autoionization region

The observations of resonances is reported for inelastic electron scattering by krypton in the autoionization region. The differential excitation functions of the states 5s, 5s', 5p and 6s+4d have been measured in the forward direction by means of a high-resolution electron spectrometer with a static gas target. Numerous features are detected and compared with the observations performed in the transmission and electroionization spectroscopies. Interpretations are proposed in terms of Feshbach resonances and Wigner cusps. The energy calibration is achieved by means of the lower-lying resonances 4s24p55s2(2P1+or-12/) which appear, in this energy range, in the channel 6s+4d via multiple scattering effects. These secondary processes are also investigated in other rare gases, and the expected pressure dependence is shown.

Resonances in the differential excitation functions of five electronic states of Ne in the autoionization region

We have observed many resonances by electron spectrometry in the differential excitation functions of the states $3s$, $3{s}^{\ensuremath{'}}$, $3{p}^{\ensuremath{'}}$, $4{s}^{\ensuremath{'}}$, and $3d$ of neon in the autoionization region. These measurements are compared to the data obtained by other spectroscopic methods and their interpretation is discussed. For the main resonances, the energies and natural widths are determined. Moreover, their effective strengths and profile indices are presented for the various decay channels in comparison with the data obtained in the ionization channel.

Proton scattering from 9Be between 6 and 30 MeV and the structure of 9Be

Differential cross-section excitation functions at lab scattering angles 86.9°, 120.0°, 140.0° and 160.0° were measured for 9Be(p, p o) 9Be, 9Be(p, p 2) 9Be and 9Be(p, d 0) 8Be at proton lab energies from 6 to 15 MeV in 100 keV steps. A broad anomaly was observed in the 9Be(p, p 0) 9Be excitation functions. Differential cross-section angular distributions were measured for 9Be(p, p 0) 9Be and 9Be(p, p 2) 9Be at lab energies of 13.0, 14.0, 15.0, 21.35 and 30.3 MeV and for 9Be(p, d 0) 8Be at 13.0, 14.0, 15.0 and 21.35 MeV. Angular distributions of polarization analysing powers for 9Be( p ,p 0) 9Be, 9Be(p, p 2) 9Be and 9Be( p , d 0) 8Be were measured at 8.0, 11.0, 12.0, 13.0 and 15.0 MeV. A spherical optical-model (SOM) analysis of the elastic scattering angular distribution data from 13.0 to 30.3 MeV showed that an energy dependence of only V R and W s (volume real and surface imaginary depths) is sufficient to reproduce the measurements. Coupled-channels (CC) analyses were made with a quadrupole-deformed optical-model potential and strong coupling of 3 2 − , 5 2 − and 7 2 − levels of a K = 3 2 ground-state rotational band of 9Be. The 9Be(p, p 0) 9Be and 9Be(p, p 2) 9Be data from 13.0 to 30.3 MeV were analyzed simultaneously at each energy, varying only V R and W s with energy, for a potential deformation of β = 1.1. Both SOM and CC analyses indicated the same energy dependence in V R, while W s averaged 3.5 MeV lower in CC than in SOM, with both energy dependences consistent with previous analyses of nucleon scattering from 1p shell nuclei.

The Mechanism of the Reactions Mg24 (d, p.) Mg23 and Mg26 (d, p.) Mg27 in the Deuteron Energy Range 1.3‐2.5 MeV

AbstractThe differential excitation functions of the low lying levels for the reactions Mg24 (d, p) Mg25 and Mg26 (d, p.) Mg27 have been measured in steps of 10 KeV in a deuteron energy range 1.3‐2.5 MeV and at angles 20°–160y in steps of 20°. Thin isotopic targets (0.45 μ gm/cm2) on Ni backing (0.5 micron) were used. Auto‐correlations, angular and group crosscorrelations, and probability distributions were calculated in terms of ERIOSON's theory of statistical fluctuations. The mean coherence width Γ for both reactions was found to be equal to 32 KeV which corresponds to a life time τ = 2.1 × 10−20 sec. of the compound nucleus formation.

A shell-model calculation for the reaction 15N(p,n) 15O

The unified theory of Feshbach is applied to the reaction 15N(p,n) 15O. Two open channels for the elastically scattered proton and the inelastically scattered neutron are explicitly included. The open channels are coupled by the optical isospin-dependent potential of Lane. The closed channel Hamiltonian is diagonalized in a restricted shell-model basis of one-particle-one-hole negative-parity states; the positions and widths of the resonances in 16O due to the closed channels are compared with experiment. The total neutron cross section and angular distributions are also compared with experiment. Some differential excitation functions are presented for the elastically scattered proton.