Absolute cross sections of electron attachment to molecular clusters: Part I. Formation of (CO2) N −

A procedure of determining absolute cross section σ^? of electron attachment to (CO₂)_N clusters at pair collisions in crossed beams is suggested. The cross section is measured as a function of energy (E = 0.1–50 eV) and of cluster mean size N in a beam $(\bar N = 2 - 4000 molecules)$ . It is found that, even at $\bar N > 200$ and E ≤ 3 eV, σ^? is equal to, or larger than, 7 × 10^?13 cm², i.e., by more than one order of magnitude exceeds the maximal cross section of CO₂ ionization by electron impact. The dependences σ^? $(\bar N,E)$ have two wide continua at E ≤ 5.2 eV and E ≥ 6.9 eV, which correlate well with known functions of CO₂ electron-impact-induced excitation. These continua are attributed largely to formation of (CO₂) _N ^? ions during electron thermalization and solvation in the clusters. At E → 0, the polarization capture of an incident electron by the cluster leads to a sharp increase in cross section σ^?(E). From the dependences σ^? $(\bar N,E)$ measured, the thermalization and sovation probabilities for electrons with E ≤ 0.8 eV and the rate of electron energy loss in the cluster are found.     

Total photonuclear absorption cross section for Pb and for heavy nuclei in the Δ-resonance region

The partial sum σ⁽²⁾(E_γ) = Σ_i?2 σ(γ, in…), representing the inclusive cross section for all reaction channels in which at least two neutrons are emitted, has been measured with a quasimonochromatic photon beam obtained by the in-flight annihilation of monoenergetic positrons, and neutron multiplicity counting. These experimental results, taken with photon energies E_γ from 145 up to 440 MeV for Pb and with photon energies E_γ= 235 MeV and 330 MeV for Al, Cu, Zr, Sn, Ho, Ta and U, are subsequently used to determine the total photonuclear absorption cross section σ(tot: E_γ) and to study the dependence upon the mass number A of the normalized cross section σ(tot: E_γ)/A. These results are then compared with other information on the total photonuclear absorption cross section.     

The shape of the giant dipole resonance for light nuclei

A complete spectrum of the giant dipole resonance is calculated taking into account the finite depth of the single particle potential. The mixing of the one particle-one hole excitations because of residual interactions is treated in the time-dependent Hartree-Fock approximation. If the interaction is approximated by a separable potential a general formula can be derived, which gives the total dipole excitation cross section σ(E) in terms of the simple shell-model cross section σ₀(E). Numerical results are given for O¹⁶ and C¹² by evaluating σ₀(E) in a square well potential.     

Scattering of charged particles by atoms

A closed variant of the Born approximation for calculating differential scattering cross sections in ion-atom collisions is developed. An expression in terms of the matrix elements J _ij with respect to the single-electron states of the atom is found for the matrix element describing the target atom in the formula for the differential cross section. The matrix elements J _ij are averaged over the relative orientation of the momentum transferred in the collision and the symmetry axis of the electronic orbitals of the target atom, using the single-electron Rutaan-Hartree-Fock wave functions. The algebraic representation of the matrix elements J _ij makes it possible to perform calculations for atoms with any value of Z. The model developed is used to calculate the cross sections σ_Σ and characteristic scattering angles θ_c for the process of electron loss by H^? ions with energy E = 0.1–100 MeV in targets consisting of atoms with Z = 2–54. It is shown that σ_Σ ∝ E ^?1 and θ_c ∝ E ^?1/2 for all Z, and for fixed E the behavior of σ_Σ(Z) and θ_c(Z) is determined by the order of filling of the electronic shells of the target atoms (the ionization potential). The computational results are analyzed and compared with the experimental data and the results of other calculations.     

Spinaustauschstreuung von Kalium an Caesium

The differential spin exchange cross sectionI _ex(?, E) for the system K-Cs has been measured as a function of angle for 2°???40° and collision energy for 1.2 · 10^?13 erg ?E?2.1 · 10^?13erg. Confirming previous experiments it exhibits a maximum neargj≈10°. The angular position of maximum changes with collision energy. Increasing the energy lowers the maximum angle. The analysis of the cross section with regard to information about the interaction of the collision partners turns out to be very complicated. A first few model calculations are presented and discussed. The most obvious, qualitative relations between the singlet and triplet interaction potentials,V ₀ andV ₁, and the differential spin exchange cross sectionI _ex(?) appear to be: 1. The average magnitude ofI _ex is markedly different below and above the rainbow angle \(\vartheta _{R_1 }\) of the shallow triplet potential V₁. From the observed intensity drop towards large angles we estimate a lower bound for the triplet potential well depth? ₁?1.4 · 10^?14 erg. 2. The expected relation between the integral spin exchange cross sectionσ _ex and the difference potentialΔV(R)=V ₁-V ₀ at large distances is also borne out by the differential spin exchange cross section I_ex(?) below \(\vartheta _{R_1 }\) . Relative to the intensity beyond \(\vartheta _{R_1 }\) the cross section increases if range and strength ofΔV is increased.     

Reliability of the data on the cross sections of the partial photoneutron reaction for <Superscript>63,65</Superscript>Cu and <Superscript>80</Superscript>Se nuclei

The cross sections of partial photoneutron reactions are evaluated for the ^63,65Cu and ⁸⁰Se isotopes. The cross sections are free of systematic uncertainties from shortcomings of the experimental methods for neutron multiplicity sorting based on measurements of neutron energy used in experiments with quasimonoenergetic annihilation photon beams. An experimental-theoretical method is used to evaluate cross sections σ^eval(γ, in)= F_i^theor σ^exp(γ, xn), where ratios F_i^theor = σ^theor(γ, in)/σ^theor(γ, xn) = σ^theor(γ, in)/σ^theor[(γ, 1n) + 2(γ, 2n) + …] are calculated using a combined model of photonuclear reactions, and σ^exp(γ, xn) is the experimental cross section of the neutron yield reaction free from neutron multiplicity sorting problems. The cross sections are evaluated for reactions (γ, 1n) and (γ, 2n) for the ^63,65Cu and ⁸⁰Se isotopes, and for the total photoneutron reaction σ(γ, Sn) = σ[(γ, 1n) + (γ, 2n) + …]. It is shown that noticeable deviations of the experimental cross sections from the evaluated values result from the unreliable sorting of neutrons between the channels with multiplicities 1 and 2.     

Absolute cross section of the3He(α,γ)7Be reaction

The absolute cross section σ(E) of the³He(α, γ)⁷Be reaction has been measured fromE _c.m. =195 to 686 keV. The studies employed both a supersonic jet gas target and an extended gas target, and were carried out by the observation of the prompt capture γ-ray transitions as well as the⁷Be residual nuclei. The absolute cross sections deduced from the capture γ-rays are in good agreement with most previous work and remove a discrepancy with other earlier work. In comparison, the σ(E) values obtained from the⁷Be residual nuclei are systematically higher, suggesting a small production of additional⁷Be by contaminant reactions.     

Relaxationserscheinungen im 63 P 2-Zustand des Quecksilber-Isotops199Hg bei Stößen mit Quecksilberatomen im Grundzustand

The decay ofrf resonance signals (Δm _F =± 1, ΔF=0) in the hfs-states (F=3/2, 5/2) of the 6³ P ₂-state of¹⁹⁹Hg has been observed by means of a sampling method. By comparing the relaxation times to those of the even isotopes, the cross section σ₂(F) for the destruction of an alignment in the hfs-states by collisions with ground state Hg-atoms could be measured. The following ratios were obtained: σ₂(F=3/2)/σ₂=1.04±0.06 and σ₂(F=5/2)/σ₂=0.90± 0.03. The cross section σ₂ for the even isotopes was found to be (2.620±0.265) 10^?14cm². Assuming total decoupling of nuclear spinI and electronic angular momentumJ during the collision, the cross sections for the destruction of an orientation (σ₁) and an “octupolarisation” (σ₃) could be calculated. For the even isotopes the following ratios were derived: σ₁/σ₂=0.76 ± 0.07 and σ₃/σ₂=1.08 ± 0.09.     

The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

Cross sections of the photoneutron reaction for <Superscript>141</Superscript>Pr and <Superscript>186</Superscript>W nuclei,estimated from physical criteria of data reliability

Using objective physical criteria for data reliability, cross sections of partial photoneutron reactions (γ, 1n), (γ, 2n) and (γ, 3n) that are free of the shortcomings of neutron multiplicity sorting methods used on beams of quasimonoenergetic annihilation photons are obtained for ¹⁴¹Pr and ¹⁸⁶W nuclei. Evaluation is performed using the experimental–theoretical method (ETM), based on the experimental cross section of neutron yield reaction σ^exp(γ, xn) = σ^exp(γ, 1n) + 2 σ^exp(γ, 2ⁿ) + 3 σexp(γ, 3n) + … and ratios F _i ^theor= σ^theor(γ, in)/σ^theor(γ, xn) calculated within the combined model (CM) of photonuclear reactions, which stipulates that σ^eval(γ, in) = F _i ^theor σ^exp(γ, xn). It is found that for ¹⁴¹Pr and ¹⁸⁶W, ratios F ^exp _i do not contradict the data reliability criteria only at energies up to ~21 and ~22 MeV, respectively. At the same time, there are notable discrepancies between F _i ^theor and F ^exp _i, and thus between the evaluated and experimental cross sections of reactions. It is shown that the discrepancies between the evaluated and experimental cross sections are due to the assumed unreliable experimental distribution of neutrons in the channels with multiplicities 1, 2, and 3.     

Temperature dependence of the radiation-stimulated conductivity of CsI crystals upon picosecond excitation by electron beams

The temperature dependence of the pulse conductivity for CsI crystals upon excitation with an electron beam (0.2 MeV, 50 ps, 400 A/cm²) at a time resolution of 150 ps is investigated. Under experimental conditions, the time of bimolecular recombination of electrons and holes (V _k centers) is directly measured in the temperature range 100–300 K. This made it possible to calculate the temperature dependence of the effective recombination cross section S(T)=7.9×10^?8 T² cm². The temperature dependence of the conductivity σ(T) is interpreted within the model of the separation of genetically bound electron-hole pairs. The activation energy of this process is found to be E _G =0.07 eV.     

Cross section and resonance strengths of the 19 F(p, αγ)16 O reaction in the energy range E p = 0.8–3.6 MeV

An excitation function of the ¹⁹ F(p, αγ)¹⁶ O reaction has been measured over the proton beam energy range E_p=0.8–3.6 MeV using a 4π NaI summing spectrometer. The absolute efficiency of this spectrometer was determined by Monte Carlo simulations. The results from the efficiency calculations have been experimentally confirmed by measuring known resonances of three nuclear reactions. The properties EinR, ГinR, σinR and ωγ have been extracted for ten narrow resonances (Г ≤ 20 keV) by analysing the excitation function and taking into account all the involved effects such as target thickness, beam energy distribution and energy straggling. Total cross section vs. proton energy has been obtained for the rest of the excitation curve, where the thickness and stoichiometry of the targets was determined by using three nuclear analytical techniques.     

Zum Kernphotoeffekt am Ar40 und Ar38

Liquid Argon was irradiated with bremsstrahlung from 18 to 31 MeV endpoint energy in steps of 2 MeV. The yields of the reactions Ar⁴⁰(γ, n)+(γ, p) and Ar³⁸(γ, n) were measured by detecting the 269a and the 35d rest activity with a low-level-counter. Cross section curves for the (γ, n)-processes could be found from the yield values, and they allowed together withσ _N, σ(γ, p) andσ(γ, np) a determination ofσ(γ, 2n) and σ_γabs for Ar⁴⁰. The integrated cross section forσ(γ, n) from threshold to 33 MeV yields (200±40) MeVmb for Ar⁴⁰ and (210±40) MeVmb for Ar³⁸, the corresponding value for σ_γabs being (450±60) MeVmb for Ar⁴⁰.     

Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

Investigation of the 6Li(d, α)4He reaction between 1.5 and 11.5 MeV

The differential cross section σ₀(θ) and the analysing powers T₁₁(θ), T₂₀(θ), T₂₁(θ) and T₂₂(θ) of the reaction ⁶Li(d, α)⁴He have been measured for twelve energies between 1.5 and 11.5 MeV at c.m. angles between 3.5° and 90°. The results were fitted with Legendre polynomials. The energy dependence of the resulting coefficients indicates resonance-like behaviour at several energies corresponding to excitation between 22 and 32 MeV in ⁸Be. The reaction ⁶Li(d, α)⁴He shows excellent features as an analyser for deuteron vector and tensor polarization over the whole energy range investigated.     

Calculation of the energy dependence of the fusion cross section and total cross sections for peripheral reactions on the basis of an analysis of data on elastic heavy-ion scattering: Strongly bound ions

A method is proposed for calculating the energy dependence of the fusion cross section (in general, the sum of the cross sections for complete and incomplete fusion, quasifission, and reactions of deep-inelastic scattering) σ _F (E) and the total cross section for peripheral (or quasielastic) reactions, σ _D (E). The method is based on an analysis of a limited set of angular distributions for the elastic scattering in a given pair of nuclei. The predictive power of the method is illustrated by considering the ¹⁶O + ²⁰⁸Pb, ¹⁶O + ⁴⁰Ca, and ¹⁶O + ²⁸Si systems. For each of these systems, the calculations were performed at energies in the range extending from subbarrier values to those exceeding the barrier height substantially. The results of the calculations are found to be in good agreement with relevant experimental data, whereby the reliability of the method is confirmed. By virtue of this, it is proposed to employ the method to study the energy dependences σ _F (E) and σ _D (E) in collisions involving unstable nuclei, for which it is difficult to determine experimentally the above dependences because of a low intensity of secondary beams.     

Influence of relativistic effects on electron-loss cross sections of heavy and superheavy ions colliding with neutral atoms

The influence of relativistic effects, such as relativistic interaction and relativistic wave functions, on the electron-loss cross sections of heavy and superheavy atoms and ions (atomic number Z ? 92) colliding with neutral atoms is investigated using a newly created RICODE-M computer program. It is found that the use of relativistic wave functions changes the electron-loss cross section values by about 20–30% around the cross-section maximum compared to those calculated with nonrelativistic wave functions. At relativistic energies E ≥ 200 MeV/u, the relativistic interaction between colliding particles leads to a quasiconstant behavior of the loss cross sections σ _EL ^rel ～ const, to be compared with the Born asymptotic law σ _EL ^B ～ lnE/E.     

Lifetime measurements on the compound nucleus 236U by means of the shadow effect

The lifetime of the ²³⁶U nucleus is measured in the range of excitation energies E_x = 6.7–11.5 MeV by a method based on the shadow (blocking) effect. The results obtained, as well as those of an earlier measurement of the lifetime for the ²³⁹U nucleus in the range E_x = 6.4–9.1 MeV, are compared with the results of calculations based on the level density ρ(E_x) in the Fermi-gas model and on the empirical level density ρ(E)_x) calculated as a result of an analysis of(n, γ) and (n, n') cross sections. An increase of excitation energy produces a substantial reduction in the rate of decrease of the lifetime at E_x ? 7.5 MeV for both compound nuclei as compared to the theoretical dependence τ(e_x).     

E2 component in subcoulomb breakup of 8B

We calculate the angular distribution and total cross section of the ⁷Be fragment emitted in the break up reaction of ⁸B on ⁵⁸Ni and ²⁰⁸Pb targets at the subcoulomb beam energy of 25.8 MeV, within the non-relativistic theory of Coulomb excitation with proper three-body kinematics. The relative contributions of the E1, E2 and M1 multipolarities to the cross sections are determined. The E2 component makes up about 65% and 40% of the ⁷Be total cross section for the ⁵⁸Ni and ²⁰⁸Pb targets respectively. We find that the extraction of the astrophysical S-factor, S₁₇(0), for the ⁷Be(p,γ)⁸B reaction at solar energies from the measurements of the cross sections of the ⁷Be fragment in the Coulomb dissociation of ⁸B at sub-Coulomb energies is still not free from the uncertainties of the E2 component.