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.     

Messungen der Geschwindigkeitsabhängigkeit totaler Streuquerschnitte für Atom-Atom-Stöße im Energiebereich zwischen 6 und 1000 eV

The velocity dependence of the total scattering cross sectionQ(v) for fast Cs, K, and Na beams scattered by Xe, Kr, and Ar has been measured for energies of 6 to 1000 eV. In all cases, the transition region between thev ^?2/5-dependence ofQ(v) (where the cross section is predominantly influenced by the attractive part of the potential) and the high energy behaviour (where the cross section is determined by the repulsive part of the potential) is observed. Values for the product?r _m of the potential well depth? and the equilibrium distancer _m are determined by comparing the measurements with calculations for a five parameter potential model.     

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.     

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.     

Magnetic-field-induced slowing-down of molecular rotation in C<Subscript>60</Subscript> crystals

The molecular dynamics of C₆₀ crystals was studied by inelastic neutron scattering at T=290 K, i.e., above the first-order phase transition temperature (T_C≈260 K), in the region of free C₆₀-spheroid rotation in the lattice. The energy broadening of the original neutron spectrum 2Γ₀≈0.1 meV for a momentum transfer q=2 Å^?1 is in agreement with NMR data on the rotational relaxation time of the molecule τ～10^?11 s～ ?Γ₀. This effect was observed to decrease in magnetic fields H=2.5–4.5 kOe applied along the scattering vector: Γ_H=0.7Γ₀. The slowing-down of the molecular rotation is discussed in connection with the interaction of a magnetic field with the molecular currents, which fluctuate when the C₆₀ cage rotates.     

<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.     

Calculation of the Cross Sections for Neutron Scattering at Spin Waves in Helimagnets

An analytical dependence of the cross section for the small-angle scattering of polarized neutrons at spin waves in helimagnets formed because of Dzyaloshinskii—Moriya interaction in cubic crystals without an inversion center (the space group is P2₁3) is obtained. It is assumed that the dispersion of spin waves in helimagnets with the wave vector k _s polarized by a magnetic field is larger than the critical field H_C2 of the transition to the ferromagnetic phase and has the form E _q = A(q ? k _s ) + gμ_B(H ? H_С2). It is shown that the cross section for neutron scattering at the two-dimensional map of angles (θ _x , θ _y ) is two circles of the radii θ_C with the centers ±θ _S , corresponding to the Bragg angle of diffraction by a helix oriented along the applied magnetic field H. The radii of these two circles θ_C are directly related to the stiffness of spin waves A of the magnetic system and depends on the applied magnetic field: \(\theta _C^2 = \theta _0^2 - \frac{{g{\mu _B}H}}{{{E_n}}}{\theta _0}\), where \({\theta _0} = \frac{{{h^2}}}{{2A{m_n}}}\) and E _n and m _n are the neutron energy and mass. It is shown that the scattering cross section depends on the neutron polarization, which is evidence of the chiral character of spin waves in the Dzyaloshinskii—Moriya helimagnets even in the completely polarized phase. The cases of neutron scattering at magnons where θ₀ ≤ θ _S and θ _S ≥ θ₀ are considered. The case of neutron scattering at spin waves in helimagnets is compared with analogous scattering at ferromagnets where θ _S → 0.     

Neutron optics of strongly absorbing media and interaction of long-wave neutrons with gadolinium films

The modern state of neutron optics of absorbing media is briefly surveyed. In all probability, there are no physics arguments that would constrain, in the case of strong absorption, the applicability of the commonly accepted Fermi-Foldy dispersion law for neutron waves. In accord with previously known results, it is found that the coefficient of reflection of neutrons from the boundary of a strongly absorbing medium tends to unity with decreasing velocity of neutrons incident on this medium. At low neutron energies peculiar to the case of ultracold neutrons, the complex scattering length for neutron-nucleus interaction proves to be constant, whence it follows that the cross section for neutron capture by a free nucleus obeys the 1/v law. The cross section for the analogous process on nuclei within a medium is described by the 1/v′ law, where v′=?k′/m, with k′ being the real part of the neutron wave number in the medium. As the incident-neutron velocity v decreases, the velocity v′ in a medium tends to some limiting value. From the coefficient of reflection of cold neutrons that is measured as a function of the wavelength and the angle of incidence, a refined value is found for the real part of the scattering length for neutron interaction with gadolinium nuclei. An experiment was performed where ultracold neutrons were transmitted through thin samples containing natural gadolinium. In analyzing the results of this experiment, use was made of the value found here for the real part of the neutron-nucleus scattering length. The experiment indicates that the imaginary part of the scattering length is a constant or, what is the same, that, for neutron velocities ranging from 4 to about 120 m/s, the 1/v law for the cross section for neutron capture by a free nucleus is valid to within 6%.     

Study of the heavy-fermion compound CeRu<Subscript>2</Subscript>Si<Subscript>2</Subscript> by the small-angle neutron scattering method

In order to directly observe neutron scattering by heavy fermion quasiparticles at low temperatures, a CeRu₂Si₂ single crystal has been studied by the small-angle neutron scattering method. In the experiment, neutron scattering is observed at T = 0.85 K for momentum transfers q ≤ 0.04 Å^?1, which is treated as the orbital component of magnetic scattering by heavy fermion quasiparticles. It has been found that the application of a magnetic field H = 1 T leads to both an increase in the observed scattering and its anisotropy with respect to the field direction. Moreover, measurements in the magnetic field reveal additional scattering for q > 0.04 Å^?1, which is well described by a Lorentzian and is interpreted as neutron magnetic scattering by spin-density fluctuations with a correlation radius R_c ≈ 30 Å.     

Formfaktor des π-Mesons und Struktur der Nukleonen

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsG _e ^v andG _m ^v are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useG _e ^s (s)≈G _e ^v (s) andG _m ^s (s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionF _π in terms of the scattering lengtha ₁ and the effective ranger ₁ of the π-π-scattering in the stateL=T=1.a ₁ is roughly known from pion production by pions. With this value and a suitabler ₁,F _π has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π⁺?π^? cross section with neglect of other states thanL=T=1. Under this assumption the π?π cross section has a resonance for low energy-momentum transfer.     

Correlation between the properties of the deuteron and the low-energy triplet parameters of neutron-proton scattering

The correlation between the asymptotic normalization constant for the deuteron, A_S, and the neutron-proton scattering length for the triplet case, a_t, is investigated. It is found that 99.7% of the asymptotic constant A_S is determined by the scattering length a_t. It is shown that the linear correlation between the quantities A _S ^?2 and 1/a_t provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant A_S and for the root-mean-square deuteron radius r_d, the results obtained with the experimental value recommended at present for the triplet scattering length a_t are exaggerated with respect to their experimental counterparts. By using the latest experimental data obtained for phase shifts by the group headed by Arndt, it proved to be possible to derive, for the low-energy parameters of scattering (a_t, r_t, P_t) and for the properties of the deuteron (A_S, r_d) results that comply well with experimental data.     

The electromagnetic effects in <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">e</Emphasis>4</Subscript> decay

The final-state interaction of pions in K _e4 decay allows to obtain the value of the isospin and angular-momentum-zero ππ scattering length a ₀ ⁰ .We take into account the electromagnetic interaction of pions and isospin-symmetry-breaking effects caused by different masses of neutral and charged pions and estimate the impact of these effects on the procedure of scattering-length extraction from K _e4 decays.     

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.     

<Emphasis Type="Italic">nd</Emphasis> scattering at low energies in the two-body potential model

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k²/k ₀ ² )^?1(?1/α+C₂k²+C₄k⁴) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C₂ and C₄ are obtained from our previous calculations of the asymptotic normalization parameter function C _t ² (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.     

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.     

Behavior of the Elastic-Scattering Cross Section <Emphasis Type="Italic">σ</Emphasis>(<Emphasis Type="Italic">E</Emphasis>) in the Vicinity of Two Overlapping Levels with Equal Resonance Energies

The elastic-scattering process proceeding through two resonance levels that have the same spin j and equal resonance energies, (E₁ = E₂), but different widths (Γ₁ ≠ Γ₂) is considered. It is shown that the energy dependence of the total scattering cross section has two equal maxima at the points E₁ ± (1/2) \(\sqrt {{\Gamma _1}{\Gamma _2}} \), the cross-section value at the maxima being 4π (2j + 1)?², where ? is the wavelength of the incident particle in the c.m. frame, and that, at the energy E₁, the cross section vanishes, σ (E₁) = 0. The cross section is symmetric with respect to the point E₁.     

<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.     

The reactions N14(n, α)B11 and N14(n,t)C12 observed with a gridded ionization chamber

The cross sections for the reactions N¹⁴(n, α)B¹¹ and N¹⁴(n, t)C¹² have been measured in the neutron energy range 4.0 to 6.4 MeV and at 2.5 MeV. Mono-energetic neutrons were produced in the D(d, n) He³ reaction using a gas target. The (n, α) and (n, t) disintegrations were detected in a gridded ionization chamber filled with an argonnitrogen mixture. The response of the chamber under different operation conditions is described. The excitation functions, measured with a neutron energy resolution of 40 to 50 keV, are given for theα ₀ group from the N¹⁴(n,α)B¹¹ reaction over the entire neutron energy range and for theα ₁ group and the t₀ group from N¹⁴(n, t) C¹² for neutron energies above 4.3 and 5.6 MeV, respectively.     

Relationship between <Emphasis Type="Italic">T</Emphasis>-invariance and formation mechanisms for <Emphasis Type="Italic">T</Emphasis>-odd and <Emphasis Type="Italic">T</Emphasis>-even asymmetries in the angular distributions of fission fragments of oriented nuclei

The T-invariance condition was analyzed for the amplitude T _b,a of multiparticle multistep elastic or inelastic a → b nuclear reactions. This condition leads to the equality of the amplitude T _b,a to the amplitude \({\tilde T_{\bar a,\bar b}}\) of \(\bar b \to \bar a\) time-reversed reaction, for which the reaction operator \(\tilde T\) coincides with the inverse-reaction (b → a) operator. It is shown that, in the case where the original, inverse, and time-reversed reactions are governed by a common T-invariant mechanism, the coefficients D of asymmetries appearing in the differential cross sections for these reactions can be represented in the form of a unified scalar (pseudoscalar) function of arguments equal to the momentum and spin vectors of particles of the initial and final channels of the reactions under analysis. It is also shown that the use of the T-invariance condition for the coefficients D of asymmetries in the differential cross section for the original nuclear reaction that are different in P- and T-parity makes it possible to separate mechanisms leading to nonzero coefficients D for a number of the asymmetries under analysis from the remaining mechanisms leading to zero coefficients D of these asymmetries. It is proven that there exist such asymmetries in the differential cross section for the original reaction whose coefficients vanish for all possible T-invariant mechanisms of their appearance, so that, upon proving experimentally the appearance of nonzero coefficients of these asymmetries in the differential cross section for the original reaction, this fact can be used to assess features of T-noninvariant interactions in nuclear systems.     

Four-particle problem using Feynman diagrams

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin singlet state, with corresponding scattering length a. We recover exactly the previously known result a _B = 0.60a, where a _B is the dimer-dimer scattering length. A detailed discussion of how one can “sum all the diagrams” in this case is presented. Applications to the study of 4-particle bound states of various complexes in 2D are briefly presented.