Elastic Deuteron Scattering on the <Superscript>12</Superscript>C Nucleus within a Three-Body Model

The formalism developed earlier for elastic pd scattering on the basis of Glauber theory with allowance for a total spin dependence is modified by replacing pN amplitudes by amplitudes for N¹²C scattering and is applied to elastic deuteron scattering on the ¹²C nucleus. The amplitudes for elastic N¹²C scattering are obtained within the optical model. Respective numerical calculations performed at the kinetic deuteron-beam energy of 270 MeV lead to results that agree well with data on the differential cross section for d¹²C scattering into the forward hemisphere, but the calculated spin observable A _y ^d agrees with experimental data only qualitatively.     

Meson-baryon scattering with SU (3) invariant interactions

The static model invariant under SU₃ is discussed. The baryons and mesons are assigned according to the “eightfold way”, and the Low equation for the scattering matrix is derived. The scattering matric has been diagonalized for arbitrary mixing ofF- andD-type coupling and the crossing matrix has been calculated. To determine the mixing of the two couplings photoproduction cross sections have been calculated. From the comparison of theK ⁺ Λ andK ⁺ Σ0 production cross sections with experiment it follows that α=D/F=3.5. For this value of α the model predicts the 3/2 decublet resonance in very good agreement with the experimental situation.     

<Emphasis Type="Italic">η</Emphasis><Superscript>7</Superscript>Li Scattering in the <Emphasis Type="Italic">αt</Emphasis>-Cluster Model

The cross sections for elastic and inelastic η-meson scattering on ⁷Li nuclei are obtained on the basis of the αt-cluster representation of the target nucleus. The experimentally known values of the parameters of elastic ηα and αt scattering are used in exactly solving three-body Faddeev equations with separable two-body potentials. The η⁷Li elastic-scattering scattering length found from respective calculations is a_η7Li = ?0.310 ? i0.198 fm.     

Evaluation ofk ± p forward dispersion relations

Kaon-nucleon forward scattering amplitudes have been calculated from dispersion relations using recent experimental data on the total cross sections. In the unphysical region the analytical continuation of theK ^? p effective range theory has been done and for the asymptotic behaviour of the total cross sections a parametrization, suggested by the Regge-pole models, has been used. The calculated real parts of the scattering amplitude are compared with the existing experimental values, as found by the optical theorem and the extrapolation of the angular distribution to the forward direction.     

Elastic and inelastic scattering of 800-MeV protons on <Superscript>16</Superscript>O and <Superscript>20</Superscript>Ne nuclei

Differential cross sections and polarization observables for the elastic and inelastic scattering of 800-MeV protons on ¹⁶O and ²⁰Ne nuclei are calculated on the basis of the theory of multiple diffractive scattering and the α-cluster model involving dispersion. The single-particle nucleon-density distributions obtained within the α-cluster model involving dispersion are used in the calculations. The differential cross sections and polarization calculated for elastic and inelastic p¹⁶O and p²⁰Ne scattering are compatible with available experimental data. The spin-rotation functions calculated for elastic p¹⁶O and p²⁰Ne scattering within the independent-nucleon model differ qualitatively from their counterparts calculated within the α-cluster model involving dispersion.     

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.     

Analysis of experimental data on neutron-proton scattering in the energy range between 0 and 150 keV

Experimental data on neutron-proton scattering in the energy range between 0 and 150 keV are analyzed by using various sets of effective-range parameters. It is shown that, in contrast to the parameters corresponding to the phase shifts of a Nijmegen group, the parameters corresponding to the experimental phase shifts reported by a group from George Washington University (GWU group) lead to very good agreement between the calculated cross sections and their experimental counterparts in the energy region under consideration. On the basis of the experimental value of the cross section for neutron—proton scattering at an energy of 2 keV, the total cross section for neutron-proton scattering at zero energy was found to be σ ₀ = 20.428(16) b, which is in very good agreement with a value of σ ₀ = 20.423(9) b, which was obtained as the weighted mean of the cross sections presented by Houke and Hurst. It is shown that, in the energy region around several tens of keV units, the effective-range parameters matched with Dilg’s cross-section value of σ ₀ = 20.491(14) b lead to calculated cross sections whose values are in excess of their experimental counterparts.     

Neutron scattering in argon and <Emphasis Type="Italic">ne</Emphasis> interaction

As a preparation for the new experiment to measure the ne scattering length a_ne the total neutron cross section of gaseous argon has been obtained by the time-of-flight method at the Dubna booster IBR-30 in the energy range from ～5 eV to ～30 keV. A combined one-level analysis of the newly obtained and other known data on cross sections of Ar and ³⁶Ar has made it possible to improve some neutron parameters and calculate the scattering cross section σ_s and the scattering length a separately for ³⁶Ar and ⁴⁰Ar at any energy.     

<Emphasis Type="Italic">K</Emphasis><Superscript>±</Superscript><Emphasis Type="Italic">p</Emphasis> elastic scattering in the QCD inspired eikonalized model

Based on our previous study of the QCD inspired eikonalized model for describing vector meson photoproduction, pp, and \(\bar p\) p elastic scattering at high energies, we apply the mode to high energy K ^± p elastic scattering. The total cross section σ _tot(s), differential cross section dσ/dt, the ratio of the real part to imaginary part of the forward scattering amplitude ρ(s), and nuclear slope parameter function β(s) are calculated in the model. Our results show that the theoretical prediction for σ _tot(s) is in a good agreement with the experimental data within error bars of the data. For the other theoretical predictions there are no data to test the predictive power of the model. We need the corresponding experimental data to examinate the validity of our QCD inspired eikonalized model. However, our calculations clearly show that the Odderon exchange in the process makes a significant contribution to the observable of ρ(s) and β(s). Therefore, we may conclude that there is a good opportunity to find the QCD Odderon in the K ^± p elastic scattering at high energies.     

Modern status of photonuclear data

The reliability of experimental cross sections obtained for (γ, 1n), (γ, 2n), and (γ, 3n) partial photoneutron reactions using beams of quasimonoenergetic annihilation photons and bremsstrahlung is analyzed by employing data for a large number of medium-heavy and heavy nuclei, including those of ^63,65Cu, ⁸⁰Se, ^90,91,94Zr, ¹¹⁵In, ^112?124Sn, ¹³³Cs, ¹³⁸Ba, ¹⁵⁹Tb, ¹⁸¹Ta, ^186?192Os, ¹⁹⁷Au, ²⁰⁸Pb, and ²⁰⁹Bi. The ratios of the cross sections of definite partial reactions to the cross section of the neutron-yield reaction, F _i = σ(γ, in)/σ(γ, xn), are used as criteria of experimental-data reliability. By definition, positive values of these ratios should not exceed the upper limits of 1.00, 0.50, 0.33,... for i = 1, 2, 3,..., respectively. For many nuclei, unreliable values of the above ratios were found to correlate clearly in various photon-energy regions F _i with physically forbidden negative values of cross sections of partial reactions. On this basis, one can conclude that correspondent experimental data are unreliable. Significant systematic uncertainties of the methods used to determine photoneutron multiplicity are shown to be the main reason for this. New partial-reaction cross sections that satisfy the above data-reliability criteria were evaluated within an experimental–theoretical method [σ ^eval(γ, in) = F _i ^theor (γ, in) × σ ^expt(γ, xn)] by employing the ratios F _i ^theor (γ, in) calculated on the basis of a combined photonuclear-reaction model. It was obtained that cross sections evaluated in this way deviate substantially from the results of many experiments performed via neutron-multiplicity sorting, but, at the same time, agree with the results of alternative activation experiments. Prospects of employing methods that would provide, without recourse to photoneutron-multiplicity sorting, reliable data on cross sections of partial photoneutron reactions are discussed.     

Theoretical study of photoionization of the isoelectronic sequence Rb<Superscript>+</Superscript>, Sr<Superscript>2+</Superscript>, and Y<Superscript>3+</Superscript>

The photoionization cross sections for the 4p shell of ions of the Kr isoelectronic sequence Rb⁺, Sr²⁺, and Y³⁺ are calculated. The configuration interaction theory and the perturbation theory are used to describe the many-electron effects. The relativistic effects are taken into account in the Pauli-Fock approximation. The calculated resonance structure of photoionization cross sections for the 4p shell in the region below the 4s threshold associated with the autoionization of the 4s-np singly excited states and the 4p4p-nln′l′ doubly excited states reproduces the results of recent measurements of total photoabsorption cross sections for the Rb⁺, Sr²⁺, and Y³⁺ ions. It is found that, as the nuclear charge in the isoelectronic sequence increases, the ratio between the direct and correlation parts of amplitudes of the 4s-(n/?)p transition changes and, as the consequence, the minimum of the photoionization cross section of the 4s shell shifts from the continuous spectrum to the region of states of discrete spectrum. This accounts for the strong changes in the shape of the 4s-np resonances in the photoionization cross sections for the 4p shell of Rb⁺, Sr²⁺, and Y³⁺, as well as the distinction between the shapes of the 4s-6p _1/2 mirror resonance in the partial 4p _1/2 and 4p _3/2 photoionization cross sections for the Y³⁺ ion which do not suppress each other in the total photoionization cross section, as is the case for similar resonances in Rb⁺ and Sr²⁺.     

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.     

Atom-Atom-Streuexperimente: Geschwindigkeitsabhängigkeit einiger totaler Streuquerschnitte

The velocity dependence of total cross sections for the collision partners Cs-Hg, K-Hg, Xe, Kr, Ar has been measured in crossed beams. Except for Cs-Hg glory scattering oscillations were resolved. Invariably good agreement with theoretical predictions is found for the extrema velocities assumingn-6 potentials with 8≦n≦16 or exp-6 potentials with 10≦α≦18, for the amplitudes of the oscillations no fit is obtained. K-Hg, probably also K-Xe and K-Kr appear to deviate from theν ^?2/5 average velocity dependence expected for dipole-dipole interaction at large distances.     

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.     

Analysis of <Emphasis Type="Italic">p</Emphasis><Superscript>10</Superscript>B scattering within Glauber theory

The differential cross sections for p ¹⁰B scattering are calculated at the energies of 197, 600, and 1000 MeV within Glauber theory. The contributions of single and double collisions are taken into account in the multiple-scattering operator. The contributions of proton collisions with nucleons belonging to various (1s, 1p) shells are estimated in the single-scattering cross sections. A comparison with experimental data and with the result of calculations in the distorted-wave Born approximation (DWBA) at 197 MeV showed that the differential cross sections for p ¹⁰B scattering are adequately described in the region forward scattering angles.     

The Elusive p-air cross section

For the \(\bar pp\) and pp systems, we have used all of the extensive data of the Particle Data Group [K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66, 010001 (2002)]. We then subject these data to a screening process, the “Sieve” algorithm [M. M. Block, physics/0506010], in order to eliminate “ outliers” that can skew a χ² fit. With the “Sieve” algorithm, a robust fit using a Lorentzian distribution is first made to all of the data to sieve out abnormally high Δχ _i ² , the individual i^th point’s contribution to the total χ². The χ² fits are then made to the sieved data. We demonstrate that we cleanly discriminate between asymptotic ln s and ln² s behavior of total hadronic cross sections when we require that these amplitudes also describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to the “sieved” high energy measurements of \(\bar pp\) and pp total cross sections and ρ-values for \(\sqrt s \) ≥ GeV, while requiring that their asymptotic fits smoothly join the the σ _pp and σ_pp total cross sections at \(\sqrt s \) = 4.0 GeV—again both in magnitude and slope. Our results strongly favor a high energy ln² s fit, basically excluding a ln s fit. Finally, we make a screened Glauber fit for the p-air cross section, using as input our precisely-determined pp cross sections at cosmic ray energies.     

Application of a folding-model optical potential to analyzing inelastic pion–nucleus scattering and the in-medium effect on a pion–nucleon amplitude

The folding-model optical potential is generalized in such a way as to apply it to calculating the cross sections for inelastic scattering of π ^±-mesons on ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, and ²⁰⁸Pb nuclei at the energies of 162, 180, 226, and 291 MeV leading to the excitation of the 2⁺ and 3^? collective states. In doing this, use is made of known nucleon-density distributions in nuclei and the pion–nucleon scattering amplitude whose parameters were obtained previously by fitting the elastic scattering cross sections for the same nuclei. Thus, the values of quadrupole (β ₂) and octupole (β ₃) deformations of nuclei appear here as the only adjustable parameters. The scattering cross section is calculated by solving the relativistic wave equation, whereby effects of relativization and distortion in the entrance and exit scattering channels are taken exactly into account. The cross sections calculated in this way for inelastic scattering are in good agreement with respective experimental data. The importance of the inclusion of in-medium effects in choosing parameters of the pion–nucleon amplitude is emphasized.     

Physical criteria for the reliability of data on the photodisintegration of the <Superscript>89</Superscript>Y nucleus

Experimental photonuclear reaction cross sections obtained in experiments using quasimonoenergetic annihilation, monoenergetic tagged photons, and bremsstrahlung γ-radiation are analyzed using physical criteria for the reliability of data on the ⁸⁹Y nucleus. It is found that the reliability of data on the cross sections of partial reactions (γ, 1n) and (γ, 2n), obtained by means of photoneutron multiplicity sorting, is highly doubtful. Reliable cross sections of reactions (γ, 1n) and (γ, 2n) are obtained using the experimental–theoretical method (ETM) for evaluating using both experimental cross sections of neutron yield reaction σ^exp(γ, xn) that are free of neutron multiplicity problems, and theoretically calculated F _i ^theor ratios of the cross sections of definite (i) partial reactions to cross section σ^theor(γ, xn). It is shown that the evaluated cross sections differ noticeably from the experimental data.     

Structure of the antiproton-proton elastic scattering amplitude

It is found that the simple expression [(πcq)/sinh(πcq)][J ₁(Rq)/(Rq)] for the elastic scattering amplitude makes it possible to well describe differential cross sections over a broad range of energies from 100 MeV to \(\sqrt s \) = 1800 GeV. This parametrization can be used to calculate antiproton-nucleus and antinucleus-nucleus amplitudes and cross sections, which are necessary in accelerator experiments and in cosmic ray physics. The generalization of the wavelet expansion to the case of functions defined on a semi-infinite interval is also proposed.