Application of <Emphasis Type="Italic">T</Emphasis>-Invariance Conditions in Selecting Mechanisms of Nuclear Reactions,Decays, and Fission

T-invariance conditions for the differential cross sections of multiparticle multistep nuclear reactions are found with allowance for spin orientations of particles in the initial channels of such reactions. It is shown that the asymmetry coefficients for different T-parities in the differential cross sections for original and time-reversed reactions are expressed in terms of unified scalar (pseudoscalar) functions that depend of the 3-momenta and spins of particles involved in the initial and final channels of the reactions under analysis. It is also shown that knowledge of the aforementioned functions for the asymmetries under analysis in the original reaction makes it possible to reconstruct the respective functions for the analogous asymmetries in the time-reversed reaction without studying it experimentally. By considering the example of T-even and T-odd asymmetries in reactions where oriented nuclei undergo binary and ternary fission induced by cold polarized neutrons, it is demonstrated that the T-invariance conditions in question can be used to select mechanisms behind the appearance of the above asymmetries—in particular, mechanisms associated with the presence of T-noninvariant interactions.     

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.     

<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.     

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.     

<Emphasis Type="Italic">T</Emphasis>-odd angular asymmetry in nuclear reactions involving sequential particle emission

A triple T-odd angular correlation is considered in the kinematically similar reactions ¹⁰B(n, αγ) and ²³³U(n, αf) induced by cold polarized neutrons. It is shown that, in the former reaction, this correlation is suppressed by the double parity-conservation selection rule due to the two-step character of the process; however, T invariance does not impose any specific constraints on this correlation. The mechanism through which the T-odd correlation found in ternary-fission reactions is formed seems to be closely related to a nearly simultaneous disintegration of the nucleus involved into two fission fragments and an alpha particle.     

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.     

Classification of <Emphasis Type="Italic">T</Emphasis>-odd asymmetries for prescission and evaporated light particles in ternary and quaternary nuclear fission induced by cold polarized neutrons

A unified mechanism of the emergence of T-odd ROT- and TRI-asymmetries is proposed for describing experimental T-odd asymmetry coefficients D(θ) in the angular distributions of prescission alphaparticles that are emitted in true ternary and quaternary nuclear fission reactions induced by cold polarized neutrons. The mechanism is related to the different ways in which the Coriolis interaction of the total spin of a polarized compound fissile nucleus with the orbital moment of alpha-particles affects even (for ROT-asymmetries) and odd (for TRI-asymmetries) components of the amplitude of an undisturbed angular distribution of emitted alpha-particles. Coefficients D_ROT(θ) and D_TRI(θ) derived with this mechanism for T-odd ROT- and TRI-asymmetries successfully describe the dependences of corresponding experimental coefficients for ²³⁵U and ²³⁹Pu nuclei over the range of angles θ, and for the ²³³U nucleus in the angular range of 60° < θ < 110°. It is explained why only ROT-type T-odd asymmetries emerge for evaporated neutrons and γ-quanta emitted by fission fragments in similar reactions if we allows for the Coriolis interaction of the total spin of the compound fissile nucleus with the orbital moments of the fission fragments and the wriggling vibrations of the above nucleus near its scission point.     

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.     

Determination of <Emphasis Type="Italic">T</Emphasis>-noninvariant amplitude for polarized-neutron interaction with polarized nuclei by the oscillating-field method

A solution for the T-noninvariant amplitude for polarized-neutron interaction with polarized nuclei in the region of the p-wave resonance is analyzed, this amplitude being extracted from two-dimensional neutron spectra obtained within Ramsey’s method. Here, the dimensionalities are the neutron energy and the radio-frequency phase at the instance of neutron entrance in an oscillating field. The spindensity-matrix formalism is used to derive an expression that describes the shape of the neutron spectrum and the corresponding expressions for the neutron-counting asymmetries both with respect to the direction of the P-odd field and with respect to the direction of the T-noninvariant field. It is shown that, for an appropriate choice of parameter values, there are exact solutions for the imaginary parts of the P-odd and T-noninvariant amplitudes and for their interference with the amplitude of strong spin-spin interaction.     

Mechanisms of excitation of <Emphasis Type="Italic">T</Emphasis>-odd correlations for prescission gamma rays and structure of these correlations

Conditions for the appearance and observation of prescission gamma rays emitted by a fissioning nucleus prior to its separation into fission fragments were investigated within quantum-mechanical fission theory. It is shown that these conditions are realizable in the gamma decay of isovector electric giant dipole resonances in a fissile nucleus that are excited because of nonadiabaticity of the collective deformation motion of the nucleus at the ultimate stages of its prefission evolution. Angular and energy distributions of prescission gamma rays emitted by unpolarized fissioning nuclei are analyzed. Features of T-odd correlations in angular distributions of gamma rays arising in the fission of unpolarized target nuclei that is induced by polarized cold neutrons are investigated, and it is shown that these correlations are similar in nature to T-odd ROT correlations discovered earlier for alpha particles emitted in the ternary fission of nuclei.     

<Emphasis Type="Italic">T</Emphasis>-odd asymmetries in the angular distributions of fragments originating from the ternary fission of nuclei

A version of a theoretical explanation is proposed for the recently discovered effect of T-odd correlation in ternary nuclear fission induced by polarized neutrons. It is shown that the inclusion of the Coriolis interaction between a third particle and the fissile-nucleus spin within the quantum theory of fission makes it possible to explain the experimental features of the effect and provides a correct estimate of its magnitude.     

Friedmann Cosmology with Matter Creation in Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f(R, T) (R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f(R, T)=R+2f(T) with “gamma-law” equation of state p = (γ?1)ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe.     

Spherical Symmetric Perfect Fluid Collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the frame work of f(R, T) modified theory of gravity. We proceed our work by considering the non-static spherically symmetric background in the interior and static spherically symmetric background in the exterior regions of the star. The junction conditions between exterior and interior regions are presented by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are to be constant, for a particular f(R, T) model. By inserting the solution of the field equations in junction conditions, we evaluate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is concluded that the term f(R ₀, T ₀) behaves as a source of repulsive force and that’s why it slowdowns the collapse of the matter.     

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.     

Polarization effects in rare <Emphasis Type="Italic">K</Emphasis> decays

We review some aspects of rare kaon decays with the polarization of outgoing muons that allows one to study a number of interesting CP-odd or T-odd observables.     

Violation of causality in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

In the standard formulation, the f(T) field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. Actually, even locally violation of causality can occur in this formulation of f(T) gravity. A locally Lorentz covariant f(T) gravity theory has been devised recently, and this local causality problem seems to have been overcome. The non-locality question, however, is left open. If gravitation is to be described by this covariant f(T) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality on non-local scale. Here, to look into the potentialities and difficulties of the covariant f(T) theories, we examine whether they admit Gödel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Gödel-type solution, which contains special solutions in which the essential parameter of Gödel-type geometries, \(m^2\), defines any class of homogeneous Gödel-type geometries. We show that solutions of the trigonometric and linear classes (\(m^2 < 0\) and \(m=0\)) are permitted only for the combined matter sources with an electromagnetic field matter component. We extended to the context of covariant f(T) gravity a theorem which ensures that any perfect-fluid homogeneous Gödel-type solution defines the same set of Gödel tetrads \(h_A^{~\mu }\) up to a Lorentz transformation. We also showed that the single massless scalar field generates Gödel-type solution with no closed time-like curves. Even though the covariant f(T) gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Gödel-type solutions makes apparent that the covariant formulation of f(T) gravity does not preclude non-local violation of causality in the form of closed time-like curves.     

Cosmic acceleration in non-flat <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) cosmology

We study f(T) cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial f(T) model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular f(T) models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-\(\sigma \) confidence level, emphasizing the fact that \(\Omega _{k0}\) turns out to be non-compatible with zero at least at 1\(\sigma \). Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the \(\Lambda \)CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the f(T) models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat f(T) cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial f(T) approach provides an effective de-Sitter phase, whereas the second f(T) framework shows analogous results compared with the \(\Lambda \)CDM predictions.     

Light Higgs boson in the two-doublet model featuring explicit <Emphasis Type="Italic">CP</Emphasis> violation

The most general form of an effective two-doublet Higgs potential whose parameters are complex-valued and whose CP invariance is violated explicitly in the minimal supersymmetric model caused by Higgs boson interaction with third-generation squarks is considered. Higgs boson states are obtained and their masses are calculated, along with the decay widths of the lightest Higgs boson and the cross section for its production, in the case of substantial mixing between the CP-even states h and H and the CP-odd state A.     

Interference effects in nuclear fission

Various interference effects governing the character of angular distributions of binary and ternary nuclear fission products and P-odd, P-even, and T-odd asymmetries in these angular distributions have been studied within the quantum theory of spontaneous and low-energy induced nuclear fission.