Asymmetries of various <Emphasis Type="Italic">P</Emphasis>- and <Emphasis Type="Italic">T</Emphasis>-parities in angular distributions of products of cold-polarized-neutron-induced binary and ternary fission of oriented nuclei and <Emphasis Type="Italic">T</Emphasis>-invariance

It is shown that a quantum system whose Hamiltonian is independent of time is T -invariant if this Hamiltonian contains only those terms that do not change sign upon time reversal. It is also shown that the coincidence of the amplitudes for multistep direct and statistical nuclear reactions with the timereversed amplitudes for the reactions being studied is a condition that ensures the T -invariance of the amplitudes in question, the transition from the original amplitudes to their time-reversed counterparts being accomplished, first, upon introducing the inverse-reactionmatrices T instead of the original-reaction matrix T and, second, upon replacing the wave functions for the initial, final, and intermediate states of the system by the respective time-reversed functions. It is found that the T -even (T -odd) asymmetries in cross sections for nuclear reactions stem from the interference between the amplitudes characterizing these reactions and having identical (opposite) T -parities. It is shown that the T -invariance condition for the above T -even (T -odd) asymmetries is related to the conservation of (change in) the sign of these asymmetries upon going over from original to inverse nuclear reactions. Mechanisms underlying the appearance of possible T -even and T-odd asymmetries in the cross sections for the cold-polarizedneutron- induced binary and ternary fission of oriented target nuclei are analyzed for the case of employing T -invariant Hamiltonians for the systems under study. It is also shown that the asymmetries in question satisfy the T -invariance condition if the reactions being considered have a sequential multistep statistical character. It is concluded that T -invariance is violated in the limiting case where, in ternary nuclear fission, the emission of a light third particle froma fissile compound nucleus formed upon incident-neutron capture by a target nucleus and its separation to two fission fragments are simultaneous events.     

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.     

Current status of research on <Emphasis Type="Italic">T</Emphasis> invariance in neutron-nuclear reactions

In this work, the current state of research on T invariance in neutron-nuclear reactions is considered. The promising character of investigations in this field related to possible enhancement of T-invariance violation in compound states of medium and heavy nuclei is underlined. Progress in preparation of experimental tests of T invariance using three-and five-vector correlations in cross sections of interaction of polarized neutrons with aligned nuclei is described in detail. T-invariance tests in reactions of radiative neutron capture and in coherent scattering of polarized neutrons on crystals are also considered.     

Effects of electric dipole,anapole, and neutral weak magnetic moments of a proton in the polarized electron-proton electroweak scattering

We have derived and investigated analytical expressions for the cross sections and spin asymmetries in the elastic electromagnetic and electroweak scattering of unpolarized/longitudinally polarized electrons on a polarized/unpolarized proton target with allowance for the C-, P-, and T/CP-invariance violating anapole and electric dipole moments, as well as the neutral weak electric, magnetic, and axial form factors of the proton. The dependence of the spin asymmetries on the energy and form-factor parameters is studied.     

The Reliability of Cross Sections of Partial Photoneutron Reactions for <Superscript>98</Superscript>Mo

The cross sections of partial photoneutron reactions for ⁹⁸Mo were evaluated. These cross sections are free from the shortcomings of various methods for neutron multiplicity determination used at the beams of quasimonoenergetic annihilation photons and bremsstrahlung radiation. New data on the cross sections of reactions (γ, 1n), (γ, 2n), and (γ, 3n) were obtained using the experimental–theoretical method for evaluation of cross sections of partial reactions satisfying the introduced physical reliability criteria. It is demonstrated that considerable deviations of the experimental cross sections from the evaluated ones result from an inaccurate sorting of neutrons between channels with a multiplicity of 1, 2, and 3.     

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.     

Unified Mechanism behind the Appearance of <Emphasis Type="Italic">T</Emphasis>-Odd TRI and ROT Asymmetries in Actinide Fission Induced by Cold Polarized Neutrons

Some shortcomings of the approaches that are used to describe T-odd ROT and TRI asymmetries in true ternary fission via reactions involving the emission of prescission alpha particles and which are based on employing the classical method of trajectory calculations are analyzed. These shortcomings are caused by the disregard of the interference between the fission widths of different sJ_s neutron resonance states formed in the first well of the deformation potential of fissile compound nuclei. It is shown that the method used in some studies to determine T-odd TRI-asymmetries for prescission alpha particles is at odds with basic concepts of the generalizedmodel of the nucleus and approaches to constructing collective (for example, bending) vibrations of a fissile compound nucleus. Quantum-mechanical fission theory is generalized via employing a unified mechanism of formation of T-odd TRI and ROT asymmetries for prescission alpha particles and evaporated photons (neutrons). The proposed mechanism takes correctly into account the effect of quantum rotation of a fissile compound nucleus on the angular distributions of fission fragments and alpha particles for true ternary fission, as well as on the angular distribution of prompt photons (neutrons) emitted by fragments originating from the delayed fission of the aforementioned nuclei.     

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.     

Single and double spin asymmetries in the elastic <Emphasis Type="Italic">e</Emphasis>-<Emphasis Type="Italic">d</Emphasis> scattering and their dependence on the deuteron wave function

Single and double spin asymmetries in the elastic electron-deuteron (e-d ) scattering were investigated. The tensor-deuteron asymmetries T_2i(i = 0, 1, 2) and the beam-vector-deuteron asymmetries T ^e _1i(i = 0, 1) were calculated and compared with the available experimental data. The sensitivity of the results for these spin asymmetries to the deuteron wave function has been investigated. The predicted asymmetries were found to be agree with one another and with experiment. It was found that, the double spin asymmetry T ^e ₁₀ is much smaller than the T ^e ₁₁-asymmetry. Therefore, in addition to the single tensor-deuteron asymmetry T₂₀, the doubly beam-vector-deuteron asymmetry T ^e ₁₁ can be used as an another tool for extracting the deuteron electromagnetic form factors.     

Evaluation of Reliable Cross Sections of Partial and Total Photoneutron Reactions for the <Superscript>139</Superscript>La Nucleus

Cross sections of partial photoneutron reactions free of the shortcomings of different ways of determining the multiplicity of neutrons used on beams of quasi-monoenergetic annihilation photons are evaluated for ¹³⁹La. The experimental-theoretical method of evaluation of partial reaction cross sections satisfying proposed data reliability criteria is used to obtain new data on the cross sections of reactions (γ, 1n), (γ, 2n), and (γ, 3n). It is shown that noticeable deviations of experimental cross sections from evaluated values are due to the unreliable sorting of neutrons between channels with multiplicities of 1, 2, and 3.     

<Emphasis Type="Italic">T</Emphasis>-invariance conditions for sequential multistep statistical nuclear reactions

A generalized version of the R-matrix theory is used to determine the amplitudes of sequential n-step statistical nuclear reactions. T-invariance conditions for these amplitudes are analyzed. Within the scope of the unified theory, integral formulas are constructed for the decay amplitudes of the intermediate states of compound nuclei via the matrix elements QHP of the system Hamiltonian H, where Q and P operators perform projections onto resonance and energy-continuous states of the system, respectively.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Data on photoneutron reactions from various experiments for <Superscript>133</Superscript>Cs, <Superscript>138</Superscript>Ba and <Superscript>209</Superscript>Bi nuclei

Basic methods for determining cross sections for photoneutron partial reactions are examined. They are obtained directly in experiments with quasimonoeneregetic annihilation photons or from the cross section for the (γ, xn) = (γ, 1n) + 2(γ, 2n) + 3(γ, 3n) +... neutron-yield reaction in experiments with bremsstrahlung photons by introducing corrections based on statistical nuclear-reaction theory. The difference in the conditions of these experiments, which leads to discrepancies between their results because of sizable systematic errors, is analyzed. Physical criteria are used to study the reliability of data on the photodisintegration of ¹³³Cs, ¹³⁸Ba, and ²⁰⁹Bi nuclei. The cross sections for partial and total reactions satisfying the reliability criteria are evaluated within the experimental–theoretical method (σ^eval(γ, in) = F_i^theor × σ^expt(γ, xn)) on the basis of the experimental cross sections σ^expt(γ, xn) and the results of the calculations within the combined model of photonuclear reactions.     

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.     

Test of <Emphasis Type="Italic">T</Emphasis>-invariance in <Emphasis Type="Italic">pd</Emphasis> scattering with double polarization

A formalism of the invariant spin amplitudes of the pd-scattering process in the Madison frame of reference is developed. The condition for T invariance with conservation of P-parity is formulated in terms of these amplitudes, and the relationships between differential spin observables that follow from this condition, are derived. The relative efficiency of the method for testing T-invariance on the basis of these relationships is compared to the method based on recording a null-test signal in an experiment with a polarized proton beam and the deuteron target.     

Anregungsfunktionen für die (d,p)-, (d,n)-und (d,2n)-Reaktionen an Ce142 bis 11,8 MeV

Total cross sections and excitation functions up to 11·8 MeV have been measured for the Ce¹⁴²(d,p), -(d,n) and -(d, 2n) reactions by the activation method. The cross sections found forE _d=11·8 MeV are 187mb, 54 mb and 535 mb, respectively. By comparing these results with cross sections calculated from the statistical theory of nuclear reactions it can be shown that the (d,p)-reaction and nearly the whole (d,n) -reaction proceed by stripping mechanism.     

Evaluated Cross Sections of Photoneutron Reactions on the Isotope <Superscript>116</Superscript>Sn and Spectra of Neutrons Originating from These Reactions

With the aid of the results obtained by evaluating cross sections of partial photoneutron reactions on the isotope ¹¹⁶Sn and the energy spectra of neutrons originating from these reactions, the possible reasons for the well-known discrepancies between the results of different photonuclear experiments were studied on the basis of a combinedmodel of photonuclear reactions. On the basis of physical criteria of data reliability and an experimental–theoretical method for evaluating cross sections of partial reactions, it was found that these discrepancies were due to unreliably redistributing neutrons between (γ, 1n), (γ, 2n), and (γ, 3n) reactions because of nontrivial correlations between the experimentally measured energy of neutrons and their multiplicity.     

Bestimmung des Kompoundkern- und Stripping-Anteils der (d,p)- und (d,n)-Reaktionen an Zr94 und Zr96

An experiment has been accomplished which gives information on the reaction mechanism of the (Zr^94,96+d)-reactions. Total cross sections and excitation functions up to 11,8 MeV have been measured for the reactions Zr⁹⁴ (d, p), Zr⁹⁴ (d, n), Zr⁹⁶(d, p), Zr⁹⁶(d, n) and Zr⁹⁶(d, 2n) by the activation method. The results are compared with cross sections calculated according to the statistical theory of nuclear reactions. It is shown that the (d, p) -reactions proceed almost completely by the stripping-mechanism. The (d, n)- and (d, 2n)-excitation functions on the other hand are in good agreement with the predictions of the statistical theory and one can conclude that the compound nucleus mechanism is the dominating process.     

Isospin purity of the isobaric analogue resonances for several open channels

The isospin purity of the full and of the doorway state scattering functions in the internal region is investigated, under the assumption of no internal mixing. When several channels are open, it is shown that the isospin is pure at an energyE _> (slightly larger then the resonance energy) only under a restrictive condition, namely that the reduced widths of the analogue state vanish in all channels but one. This may happen either because of isospin selection rules (for the neutron channels) or for reasons of nuclear structure (for some of the proton channels). Then, the corresponding (p, n) and (p, p′) cross sections vanish atE _>. If several channels with non-vanishing reduced widths are open, the isospin of both the full and doorway state wave function is no longer pure atE _>. If two proton channels are open, the doorway state contains three different types of admixtures in the internal region. Two, one of isospinT _> and one of isospinT _<, are excited according to a simple Breit-Wigner probability law. They are both independent of the entrance channel. The third one has isospinT _<, depends upon the entrance channel and is excited according to an asymmetric enhancement factor identical toRobson's.     

Dipole resonances in the electroexcitation of the <Superscript>24</Superscript>Mg nucleus

The wave functions and form factors of E1 excited states of the deformed nucleus ²⁴Mg are obtained within the particle-core coupling version of the shell model by using spectroscopic data on direct nucleon-pickup reactions. A comparison of the calculated E1-strength distributions with experimental cross sections shows the validity of the theoretical approach used, which is based on connections between direct and resonance nuclear reactions.