Characteristics of potential-resonance elastic scattering of slow electrons by calcium atoms

The characteristics of elastic scattering of electrons by atomic systems are described by the potential resonance method in terms of the energy dependence of integral-type cross section S taken using a hypocycloidal electron spectrometer. The effect of ² D shape resonance on the run of the curve S(E) is demonstrated with scattering of slow (of energy no higher than 2 eV) electrons by calcium atoms. The energy and width of the resonance are derived from the extrema (minimum and maximum) of the experimental curve S(E). This dependence also serves to find the electron scattering differential cross sections. Two slightly differing scattering angles are taken into account. The differential cross sections derived from the experimental data qualitatively agree with theoretical results, albeit being somewhat lower.     

Final-state interactions in (e,e′p) reactions with polarized nuclei

The cross section for coincidence, quasielastic proton knock-out by electrons from a polarized ³⁹K nucleus is computed in DWIA using an optical potential in describing the wave function of the ejected nucleon. The dependence of the FSI on the initial polarization angles of the nucleus is analyzed and explained in a new, semi-classical picture of the reaction in which the nuclear transparency decreases as a function of the amount of nuclear matter that the proton has to cross, thus providing a method for obtaining detailed information on its mean free path in finite nuclei. We propose a procedure to find the best initial kinematical conditions for minimizing the FSI which will be useful as a guide for future experiments with polarized nuclei.     

Quasielastic magnetic scattering of neutrons by heavy-fermion systems

A theory of quasielastic scattering by a spin liquid with resonating valence bonds is constructed. It is demonstrated that the dependence of the scattering cross section of the spin liquid on the energy transfer has the same shape as the quasielastic peak observed experimentally in heavy-fermion systems. It is shown that a consequence of fact that the excitations of the spin-liquid state obey Fermi statistics is that the total quasielastic scattering cross section oscillates as a function of the momentum transfer. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 480–485 (25 September 1998)     

Elastic scattering of slow electrons by calcium atoms into an angular range depending on the collision energy

The use of trochoidal and hypocycloidal spectrometers that are applied in modern experimental techniques for studying processes of electron scattering by atoms, ions, and surfaces is considered in some detail. The angular range of the collection of scattered electrons is determined by the operation mode of the spectrometer and depends on the collision energy. To analyze the structure of the measured energy dependence S(E), an analytical formalism reflecting both resonance and nonresonance features of low-energy scattering was used. A theoretical analysis of elastic scattering of slow (to 2 eV) electrons by Ca atoms permitted the interpretation of the observed structure of S(E) as a manifestation of the ² D shape resonance. A comparison of the theoretical values of the S(E) function with the total and differential scattering cross sections was performed.     

Formation of positive and negative ions of thymine molecules under the action of slow electrons

The formation of positive and negative molecules of thymine—a base of nucleic acids—under the action of slow electrons is investigated by the method of crossed electron and molecular beams. The method developed makes it possible to measure the molecular beam intensity and determine the energy dependences and absolute values of total cross sections for the formation of positive and negative ions of thymine molecules. It is found that the maximal cross section for the formation of positive ions is reached at an energy of 95 eV and its absolute value is, accordingly, 1.4 × 10^?15 cm². The total cross section for the formation of negative ions is 8.2 × 10^–18 cm² at an energy of 1.1 eV. The mass spectra of thymine molecules are measured and the cross sections of dissociative ionization are determined.     

Photodisintegration of He

Total and differential cross sections for the reaction ³He(γ, d)¹H have been measured from 13 MeV to 45 MeV using a magnetic spectrometer and solid-state detectors. The results agree well with some of the previous measurements. A systematic study of the energy and the angular dependence of the cross sections shows that the E2 cross section increases with increasing energy indicating relative importance of the higher-order multipole transitions in the disintegration process. The isotropic terms in the angular distribution also increase with energy, suggesting the importance of D-state in the ground state of ³He. Comparison of our experimental data with the available theoretical calculations is also presented.     

Multiple scattering effects for quasifree scattering in 3He(d,dd)1H breakup reaction

The differential cross sections for the ³He(d, dd)¹H breakup reaction have been measured in the kinematical region corresponding to quasifree scattering (QFS). The angular dependence of the cross section at the minimum laboratory energy of the unobserved proton has been obtained. The shapes of energy spectra are approximately reproduced by a calculation in the plane-wave impulse approximation (PWIA). As for the angular dependence of the cross section and for the absolute values, the calculation fails to reproduce the experimental results. A calculation with multiple scattering effects reproduces the experimental data well, not only for the shape of the energy spectra but also for the angular dependence. For the absolute cross sections, the ratio of the experimental values to the calculated ones with multiple scattering effects is 0.7 and this value is improved compared with the value of 0.3 obtained by the PWIA calculation.     

The elastic scattering of low energy electrons from Xenon

Calculations are presented of angular distributions for electrons elastically scattered from xenon in the energy range 5.5 to 10 eV. The potential describing the xenon atom is determined by the X_α-approximation. The relative dependence with energy of the differential cross section at 30° scattering angle has been calculated in the range 30 to 200 eV. The theoretical results are in very good agreement with experimental data.     

Muonic atoms in the neighbourhood of lead

In a previous paper the electroexcitation of various giant multipole resonances in heavy nuclei has been discussed in Born approximation. This has given only the qualitative features of the cross section, since the electron wave functions in heavy nuclei are considerably distorted by the nuclear charge. Therefore we derive in this paper the corresponding cross sections using a phase shift analysis for the electron wave functions. Moreover, the coupling between giant resonances and surface oscillations has been taken into account. This leads to transitions not only to the several giant resonances itself but also to their “satellites” (i.e. giant resonance plus surface oscillations). Since the giant resonances have rather large widths, the calculated differential cross sections have been folded using a Lorentz shape and plotted against excitation energy. It is shown that the quadrupole giant resonance levels should be observed very clearly at scattering angles of the electron of about 40° (primary energy of the electrons about 200 MeV). It seems, however, unlikely to observe the monopole giant resonance as a distinct peak of the electron cross section because of the relatively large damping to be expected.     

Experimental confirmation of the EPES sampling depth paradox for overlayer/substrate systems

Elastic-peak electron spectroscopy (EPES) has been one of the main tools for obtaining the inelastic mean free path of electrons in solids. Recently it has become clear that, if this type of experiment is done using an energetic electron beam (20-40 keV) and large scattering angles, then the recoil energies of the elastic scattering event for different elements can be resolved. This recoil energy is mass dependent and this fact makes it possible to separate the elastic-peak contributions due to electrons scattered from light and heavy elements. Here we use this energy separation to determine experimentally the sampling depth for an overlayer/substrate system. The sampling depth for a (high-Z) Au overlayer on a (low-Z) C substrate is found to be about two orders of magnitude smaller than for a C overlayer on a Au substrate, whereas the inelastic mean free path of electrons in both materials differ much less. This effect is shown to be a consequence the strong Z dependence of the elastic scattering cross section. The dependence of the spectra on the electron kinetic energy and sample rotation is also dramatically different for both sample geometries.     

Proton yields from quasielastic pion scattering on 27Al and 208Pb

A singles measurement of the quasielastic scattering of 255 MeV pions by ²⁷Al and ²⁰⁸Pb has been made. The measured values for the ratio R of π⁺ and π^? induced cross section, averaged over all measured angles of 2.2 ± 0.2 and 1.5 ± 0.1 for ²⁷Al and ²⁰⁸Pb respectively are substantially below the classical impulse approximation value of 11. A semiclassical nucleon charge exchange model is described for singles and coincidence measurements and is compared with the measured proton spectra. The comparison indicates that the singles proton spectra are dominated by events other than the quasielastic process whereas the coincidence data reported earlier and compared with the present calculations support the quasielastic interpretation. A strongly decreasing dependence of R on A for coincidence measurements may be interpreted as supporting the view that recoil nucleon charge exchange plays an important role in the quasielastic knockout process.     

Distorted wave theory of scattering of nucleons with intermediate energies on nuclei

In the context of nonrelativistic theory in the distorted wave approximation, a three-dimensional form of analytical expression for the differential cross section of scattering of nucleons with intermediate energies on atomic nuclei is derived. In the context of this theory, the main parameters of elastic scattering of protons with incident energy of 1 GeV on the ²⁰⁸Pb nucleus are determined. For inelastic scattering of protons with nuclear surface vibrations, giant multipole resonances in the excited nucleus are investigated for the collective nucleus model. The energy losses of the scattered proton are calculated together with the energies of giant dipole and quadrupole resonances and nuclear surface vibration energy. This allows the deformation parameter of the excited nucleus to be calculated.     

The reaction mechanism in the system132Xe+56Fe at 5.73 MeV/u: Evidence for a new type of strongly damped collisions

We present data for the¹³²Xe+⁵⁶Fe-system at 5.73 MeV/u laboratory energy. Due to inverted kinematics, where Xe is the projectile, we were able to measure energy spectra as well as angular distributions for reaction products with 20≦Z≦60 with unitZ-resolution; i.e. target- and projectile-like fragments have been investigated. The reaction shows a well focussed quasielastic component, where charge transfer from the light to the heavy collision partner dominates. This apparent tendency towards more asymmetric fragmentation is explained by a potential energy surface which favours such charge transfer in order to minimize the asymmetry energy of the liquid drop. The strongly damped component which constitutes the major part of the reaction cross section exhibits characteristics of a fusion-fission reaction with typical fission fragment kinetic energies and 1/sinΘ _c.m. angular distributions. The maximum cross section is found for the symmetric fragmentation, no clear indication is observed for a diffusion process leading to target- and projectile-like fragments. Our data are difficult to reconcile either with the standard diffusion models or with an equilibrated compound nucleus fission picture. We tentatively conclude that an essential part of the fully damped cross section originates from partial waves for which the compound nucleus has no fission barrier.     

Low-energy vibrational excitation cross section of multilayers of CO molecules on graphite using electron scattering

This paper presents a low-energy study of the vibrational excitation cross section of 50 layers of CO molecules on graphite at 23 K using the electron energy loss spectroscopy technique. The vibrational excitation cross section or the excitation curve is presented for two different scattering angles. The results show an energy dependence of the vibrational excitation cross section, at both angles, which indicates the formation of negative ion resonance in this adsorbed phase of CO on graphite. The data show an oscillatory structure in the region between 0.5 and 3 eV that is associated with the excitation of the ²Π state.     

Comparative analysis of characteristic electron energy loss spectra and inelastic scattering cross-section spectra of Fe

The inelastic electron scattering cross section spectra of Fe have been calculated based on experimental spectra of characteristic reflection electron energy loss as dependences of the product of the inelastic mean free path by the differential inelastic electron scattering cross section on the electron energy loss. It has been shown that the inelastic electron scattering cross-section spectra have certain advantages over the electron energy loss spectra in the analysis of the interaction of electrons with substance. The peaks of energy loss in the spectra of characteristic electron energy loss and inelastic electron scattering cross sections have been determined from the integral and differential spectra. It has been shown that the energy of the bulk plasmon is practically independent of the energy of primary electrons in the characteristic electron energy loss spectra and monotonically increases with increasing energy of primary electrons in the inelastic electron scattering cross-section spectra. The variation in the maximum energy of the inelastic electron scattering cross-section spectra is caused by the redistribution of intensities over the peaks of losses due to various excitations. The inelastic electron scattering cross-section spectra have been analyzed using the decomposition of the spectra into peaks of the energy loss. This method has been used for the quantitative estimation of the contributions from different energy loss processes to the inelastic electron scattering cross-section spectra of Fe and for the determination of the nature of the energy loss peaks.     

Partial differential cross section of inelastic magnetic neutron scattering in the paramagnetic phase of LaCoO3

The partial differential cross section of inelastic magnetic neutron scattering from the compound LaCoO₃ in the paramagnetic phase is studied theoretically. The contribution to scattering from the high-spin state of an ion in zero magnetic field and the modification of this contribution upon application of a magnetic field are calculated using the effective Hamiltonian for the ⁵ D term. The amplitude of the peak in the dependence of the scattering cross section on the energy of scattered neutrons, which corresponds to the transition from the low-spin to the intermediate-spin state, is estimated.     

Optoelectrical investigations on MOS-sandwiches at low temperatures

MOS-structures are irradiated with light of energy from 1.5 to 6 eV at different temperatures (300, 77, 12 K) while the resulting photocurrent is measured. At high photon energies (hv>4 eV) the threshold energy and the scattering mean free path for electrons at the Si — SiO₂-interface are determined. They are independent from temperature. At low photon energies (hv<3 eV) electrons are released from traps with energy levels 1.2 and 1.9 eV below the Si-conduction band. The trap concentration is 4.8 10¹³ cm^–3. The capture cross section is measured in a rather direct way. The temperature and electrical field dependence of this cross section is explained by a trapping model.     

Cross sections for the photofission of <Superscript>243</Superscript>Cm, <Superscript>245</Superscript>Cm, <Superscript>249</Superscript>Bk,and <Superscript>249</Superscript>Cf isotopes in the energy range from the threshold to 10–12 MeV

The relative method was used to measure the photofission cross sections for ²⁴³Cm and ²⁴⁹Cf isotopes in the energy range from 6 to 12 MeV, for ²⁴⁵Cm in the energy range from 5 to 10 MeV, and for ²⁴⁹Bk in the energy range from 5.5 to 10 MeV. The measurements were performed with an energy step of 50 to 200 keV by using the microtron installed at the Institute of Physics and Power Engineering (Obninsk). The cross section for ²³⁸U photofission was used as a reference in these measurements. Data on the cross sections for ²⁴³Cm, ²⁴⁵Cm, and ²⁴⁹Bk photofission were obtained for the first time, while data on the cross section for ²⁴⁹Cf photofission were obtained for the first time only in the energyregion E<10 MeV. The data on the ²⁴⁵Cm nucleus suggest that, in the energy region around 6 MeV, the cross section for its photofission has a maximum, which is likely to be due to the low-energy resonance structure of the dipole-photoabsorption cross section. For ²⁴⁹Cf, an anomalously large value of the photo fission cross section is observed in the region of the first maximum of the giant dipole resonance (E≈11 MeV). By comparing the energy dependences obtained for the fissilities of the ²⁴³Cm and ²⁴⁹Bk isotopes from photofission data with the fissilities from direct-reaction data, it is found that the observed fission thresholds agree and that there is a plateau-like dependence at energies above 7.5 MeV. For the ²⁴⁵Cm and ²⁴⁹Cf nuclei, there are no similar data for performing such a comparison. Data on the fissilities as obtained from the present series of relative measurements that employ the microtron bremsstrahlung spectrum are analyzed.     

Deconvolution of inelastic background signal from XPS spectra of homogeneous solids

For noble and transition metals, the product of the inelastic electron mean free path and the differential inelastic scattering cross section is a weak function of both the particular metal and the electron energy. It is demonstrated that this property can be useful in the removal of inelastically scattered electrons from XPS spectra of homogeneous solids.     

Low-energy radiative captures with gauge independence and the MCAS description

We describe radiative-capture reactions at low energies within the nuclear coupled-channel approach denoted MCAS (multi-channel algebraic scattering). The amplitude of single-photon emission is constructed via a generalization of the Siegert theorem in an explicit gauge-independent way, without any multipole decomposition of the electromagnetic (e.m.) current operator. As a first test application, we calculate the ³He(α, γ)⁷Be reaction cross section at astrophysical energies using a simplified two-cluster model. The energy dependence of the calculated astrophysical factor reproduces the experimental situation fairly well, though the cross-section normalization turns out to be overestimated.