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.     

Interference of fission amplitudes of neutron resonances and <Emphasis Type="Italic">T</Emphasis>-odd asymmetry for various prescission third particles in the ternary fission of nuclei

Differential cross sections for reactions of the true ternary fission of nuclei that was induced by cold polarized neutrons were constructed with allowance of the effect that Coriolis interaction and the interference between fission amplitudes of neutron resonances excited in fissile nuclei upon incidentneutron capture by target nuclei exerted on angular distributions of prescission third particles (alpha particles, neutrons, or photons). It is shown that T -odd TRI- and ROT-type asymmetries for prescission alpha particles are associated with, respectively, the odd and even components of the Coriolis interaction-perturbed amplitude of angular distributions of particles belonging to the types indicated above. These asymmetries have angular distributions differing from each other and stemming from a nontrivial dependence of these components on the neutron-resonance spins J _s and their projections K _s onto the symmetry axis of the nucleus involved. It is shown that angular distributions of prescission photons and neutrons from reactions of the ternary fission of nuclei that is induced by cold polarized neutrons are determined by the effect of Coriolis forces exclusively. Therefore, the emerging T-odd asymmetries have a character of a ROT-type asymmetry and are universal for all target nuclei.     

<Emphasis Type="Italic">T</Emphasis>-odd angular correlations in the emission of prompt gamma rays and neutrons in nuclear fission induced by polarized neutrons

Study of the T-odd three-vector correlation in the emission of prompt neutrons from ²³⁵U fission by polarized cold neutrons has been continued at the facility MEPHISTO of the FRM II reactor (Technical University of Munich). The sought correlation was not found within experimental error of 2.3 × 10⁻⁵. The upper limit for the asymmetry coefficient has been set to |D _n | < 6 × 10⁻⁵ at 99% confidence level, whereas for ternary fission correlation coefficient D _α = (170±20) × 10⁻⁵. This limit casts doubt on a model that explains the three-vector correlation in ternary fission by the Coriolis mechanism. At the same time, five-vector correlation in the emission of prompt fission neutrons has been measured, which describes the rotation of the fissioning nucleus at the moment it breaks (ROT effect). At the angle 22.5° to the fission axis, the correlation coefficient was found to be (1.57 ± 0.20) × 10⁻⁴, while at the angle of 67.5° it is zero within the experimental uncertainty. The existence of ROT effect in the emission of prompt fission neutrons can be explained by the anisotropy of neutron emission in the rest frame of the fragment (fission fragments are aligned with respect to the axis of deformation of the fissioning nucleus), similar to the mechanism of ROT effect in the emission of prompt γ-rays.     

<Emphasis Type="Italic">T</Emphasis>-odd correlation in polarized neutron decay

T-odd correlation [p_e, p_ν]η appears in the lowest order radiative correction to the polarized-neutron decay width, where δ is the polarization vector of a neutron. It appears as a consequence of the final-state interaction and should not be confused with real CP violation of the Standard Model. The asymmetry has the order of 10^?5. Final-state interaction in the decay of an unpolarized neutron causes the appearance of transverse polarization of a recoil proton and electron. Explicit expressions are given.     

<Emphasis Type="Italic">P</Emphasis>-even correlations in binary and ternary nuclear fission induced by polarized neutrons

The evolution of a fissile nucleus from transition fission states specified at the saddle point of the deformation potential to fission states associated with prescission configurations of this nucleus and characterized by a pearlike shape of the nucleus is studied within the quantum-mechanical theory of fission processes that is based on the time-independent formalism. The coefficients of P-even asymmetries in the angular distributions of a light fragment and a third particle are calculated on the basis of the idea of the one-step mechanism of the production of a third particle and two fragments from the ternary fission of nuclei that is induced by polarized thermal neutrons. In order to confirm the developed concepts, it is proposed to repeat, at a higher level of statistical accuracy, experiments devoted to observing left-right asymmetries in the angular distributions of alpha particles from 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.     

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.     

Search for <Emphasis Type="Italic">P</Emphasis>-odd asymmetry of prompt neutron emission in <Superscript>235</Superscript>U fission induced by cold polarized neutrons

The preliminary result of the P-odd asymmetry of prompt neutron emission in ²³⁵U fission induced by polarized cold neutrons is a=(2.7±0.8)×10^?5. Only scission neutrons can show such asymmetry, whereas neutrons emitted by excited fragments are the unavoidable background, which suppress the sought asymmetry. The P-odd asymmetry of light fragment emission for ²³⁵U is equal to (8.4±0.6)×10^?5. Assuming that the last figure defines the parity mixture of the fissile nucleus, then the suppression factor is equal approximately to 3.     

<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.     

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 correlations in the decay of scalar fermions

We define a CP-sensitive asymmetry in the sfermion decays , based on triple product correlations between the momenta of the outgoing fermions. We study this asymmetry in the MSSM with complex parameters. We show that the asymmetry is sensitive to the phases of the parameters and M₁. The leading contribution stems from the decay chain , for which we obtain analytic formulae for the amplitude squared. The asymmetry can go up to for , and up to for . We also estimate the rates necessary to measure the asymmetry.Received: 2 July 2003, Revised: 7 November 2003, Published online: 13 February 2004     

New static solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) theory

We consider the equations of motion of an anisotropic space-time in f(T) theory, where T is the torsion. New spherically symmetric solutions of black holes and wormholes are obtained with a constant torsion and for the cases for which the radial pressure is proportional to a real constant, to some algebraic functions f(T) and their derivatives f _T (T), or vanishes identically.     

Static anisotropic solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) theory

In previous work, we undertook to study static and anisotropic content in f(T) theory and obtained new spherically symmetric solutions considering a constant torsion and some particular conditions for the pressure. In this paper, still in the framework of f(T) theory, new spherically symmetric solutions are obtained, first considering the general case of an isotropic fluid and later the anisotropic content case in which the generalized conditions for the matter content are considered such that the energy density, the radial and tangential pressures depend on the algebraic f(T) and its derivative f _T (T). Moreover, we obtain the algebraic function f(T) through the reconstruction method for two cases and also study a polytropic model for the stellar structure.     

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.     

Searches for <Emphasis Type="Italic">T</Emphasis>-odd correlations in the emission of prompt neutrons in the polarized-neutron-induced fission of <Superscript>235</Superscript>U nuclei

The results of an experiment aimed at searches for formally T-odd correlations in the angular distribution of prompt neutrons from the fission of ²³⁵U nuclei are presented. The experiment was performed in the MEPHISTO polarized cold-neutron beam from the Munich FRMII reactor. The correlation coefficient proved to be (−3.5 ± 3.4) × 10⁻⁵ for a three-vector correlation (TRI effect) and (−5.0 ± 3.4) × 10⁻⁵ for a five-vector correlation (ROT effect). This means that no significant effects were discovered within the measurement errors. A comparison with the analogous effects in the ternary fission of ²³⁵U nuclei was performed. The values of the corresponding correlations in the angular distribution of prompt fission gamma rays were refined.     

Accelerating universe from <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

It is shown that the acceleration of the universe can be understood by considering a F(T) gravity models. For these F(T) gravity models, a variant of the accelerating cosmology reconstruction program is developed. Some explicit examples of F(T) are reconstructed from the background FRW expansion history.     

New types of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

Recently f(T) theories based on modifications of teleparallel gravity, where torsion is the geometric object describing gravity instead of curvature, have been proposed to explain the present cosmic accelerating expansion. The field equations are always second order, remarkably simpler than f(R) theories. In analogy to the f(R) theory, we consider here three types of f(T) gravity, and find that all of them can give rise to cosmic acceleration with interesting features, respectively.     

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.     

Reconstruction of some cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) cosmology

In this paper, we reconstruct cosmological models in the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We show that the dust fluid reproduces ΛCDM, phantom–non-phantom era and phantom cosmology. Further, we reconstruct different cosmological models, including the Chaplygin gas, and scalar field with some specific forms of f(R,T). Our numerical simulation for the Hubble parameter shows good agreement with the BAO observational data for low redshifts, z<2.     

Hypersurface-homogeneous Universe filled with perfect fluid in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) theory of gravity

The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of f(R, T) theory of gravity (Harko et al, Phys. Rev. D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.