On some tests of the basic properties of the neutral weak interaction. II. With massive neutrinos

Assuming a general nonderivative point interaction, and Born approximation, the angular distributions for neutrino scatterings by electrons are written, using only simple considerations, allowing all leptons to have nonzero mass. Our distributions have been previously obtained for some special cases, from general considerations by Bell et al., or in the results of explicit calculations. Applications to (i) determination of the Lorentz structure of the neutral weak interaction, and (ii) tests of lepton locality are considered. For illustration, two explicit calculations are given; one of these could hold for heavy lepton production, and the other for scattering of very low energy cosmic neutrinos.     

Interference maxima in the backward excitation curve of α-particle elastic scattering on medium-weight nuclei

Excitation functions for the elastic scattering of α-particles from Ni, Co and Cu at θ_lab = 179° were measured in the lab energy range 22.75–28.40 MeV, as well as some angular distributions for Co(α, α). Broad maxima with a width of about 2.5 MeV were found in the excitation functions. It is shown that a simple four-parameter optical model of the interaction is able to reproduce the angular distributions as well as the excitation functions. Examination of the Argand diagrams leads to the conclusion that the maxima in the excitation curves are formed as a result of a coherent superposition of a number of partial waves, none of which behaves in itself in a resonance-like manner.     

A Spinor Approach to the SU(2) Clebsch-Gordan Coefficients *

We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two independent angular momentum vector operators. Utilizing the spinor algebra, we are able to develop a simple way for calculating the SU(2) Clebsch-Gordan (CG) coefficients. The explicit expression for the SU(2) CG coefficients is worked out, and some simple physical examples are presented to illustrate the spinor approach.     

Quantum nature of ROT and TRI asymmetries in the ternary fission of nuclei

Effects of T-odd asymmetry in ternary-nuclear-fission reactions induced by polarized cold neutrons are considered within quantum theory. It is shown that the asymmetry coefficient can be expressed in terms of experimental angular distributions of third particles in reactions induced by unpolarized neutrons. The explicit form of this coefficient makes it possible to explain the difference in the magnitudes and signs of the TRI and ROT effects observed experimentally for different targets.     

General relations between neutrino and antineutrino scattering

Assuming Born approximation and that the neutrino covariants in the interaction are nonderivative, we obtain some simple relations between neutrino and antineutrino scattering on any target: the scattering may be elastic, inelastic or deeply inelastic. Some of these relations have been noted already in some special cases by making stronger assumptions and sometimes only by explicit calculation. Our derivations rest only on simple general considerations.     

Messung der Winkelverteilung der α-Teilchen der Kern-Reaktion11B (p, α1)8Be (2,9 MeV)

It is not possible to measure the angular distribution of the α-particles from¹¹B(p, α₁)⁸Be*(2,9 MeV) with a simple one-detector arrangement, because the back-ground α-particle spectrum from⁸Be* will change shape and contents with angle. Therefore a coincidence method is employed. Two detectors are arranged in such a way that with any angle in thelaboratory system the angle between the detectors is 180 degrees in the center ofmass system. By this method angular correlations are eliminated and the angular distribution of α₁ can be measured as long as the two coincident lines, recorded by each detector, are separable. Since this is not always the case the angular distributions are determined only for reactions proceeding through the two excited states in¹²C that are reached with 1.39 and 2.64 MeV proton energy. Angular distributions of the α_o radiation have been remeasured.     

The Angular Distributions of intermediate Mass Fragments Emittsd in 30 MeV/u 40Ar+58,64Ni and 115In Reactions

The angular distributions of intermediate mass fragments with Z=3-19 emitted in 30 MeV/u ⁴⁰Ar+^58,64Ni and ¹¹⁵In reactions over an angular range of 5°—140°have been measured.Exponential distribution function: dσ/dΩ=N·exp(-θ/a) was used tO fit the measured angular distributions.We have extracted the decay factor a that can be connected with the interaction time τ, and the factor N that is related to the intensity of the emission source.The relationships of a(Z) with Z and N(Z) with Z for different reaction systems and different angular ranges have been discussed. The dependence of angular distributions on isospin and the symmetry of reaction system have also been discussed.     

Target-fragment angular distributions for the interaction of 86 MeV/A12C with 197Au

Target-fragment angular distributions were measured using radiochemical techniques for 69 different fragments (44 ? A ? 196) from the interaction of 86 MeV/A¹²C with ¹⁹⁷Au. The angular distributions in the laboratory system are forward-peaked with some distributions also showing a backward peaking. The shapes of the laboratory system distributions were compared with the predictions of the nuclear firestreak model. The measured angular distributions differed markedly from the predictions of the firestreak model in most cases. This discrepancy could be due, in part, to overestimation of the transferred longitudinal momentum by the firestreak model, the assumption of isotropic angular distributions for fission and particle emission in the moving frame and incorrect assumptions about how the lightest (A < 60) fragments are produced. No evidence was found for any significant number of target fragments moving sidewise to the beam direction in apparent contradiction to the expectation of hydrodynamical-model calculations. The laboratory-frame angular distributions were transformed into the moving frame using various assumptions about the moving frame velocity. The resulting light-fragment distributions showed an asymmetry in the moving frame indicative of their production in a fast process without the establishment of statistical equilibrium. No evidence was found for any production of the light fragments by a very asymmetric fission mechanism. The fission-fragment distributions were compared to standard formulas and an average fissioning-system angular momentum of $\text{J = 40?50}\text{h}\text{?}$ was deduced. It was not possible to find a moving frame in which the heavy (A > 145) fragment distributions were symmetric about 90°.     

Parametrization of woods-saxon potential for heavy-ion systems

Several elastic scattering angular distributions of ~(12)C from target nuclei of A ≥39 are analyzed to extract the Woods-Saxon potential parameters with the fixed imaginary potential and Coulomb radius parameters.Using the best fitted diffuseness parameters,the correlations of the real part parameters with A_1~(1/3)+ A_2~(1/3) and incident energy are revealed, and the systematic Woods-Saxon potential parameters are presented for nucleus-nucleus interaction.The proposed potential parameters can reproduce not only the elastic scattering angular distributions induced by ~(12)C,but also many elastic scattering angular distributions induced by the projectiles other than ~(12)C,thus providing important inputs for the study of nuclear reactions of heavy-ion systems.     

The uncertainty relation expressed by means of a new entropic function

In this article we use a new entropic function, derived from an f-divergence between two probability distributions, for the construction of an alternative entropic uncertainty relation. After a brief review of some existing f-divergences, a new f-divergence and the corresponding entropic function, derived from it, is introduced and its useful characteristics are presented. This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics. An explicit expression for such an uncertainty relation is found for the case of two observables which are the x- and z-components of the angular momentum of the spin-1/2 system.      

One- and two-particle angular distributions of central collisions induced by 1.88 GeV/nucleon Fe nuclei

Metal-sandwiched emulsion chambers containing Al, Cu and W targets were exposed to 1.88 GeV/nucleon Fe beams at Bevalac. It is found that one- and two-particle angular distributions of fast particles from central collisions are well reproduced by the simple thermal model, but that neither a simple idea of the thermal model nor that of hydrodynamical model can explain the two-particle angular correlation among the fast particles.     

Cross sections and dynamical properties of a emitters produced in interactions of 12C at 86 MeV/n on medium and heavy targets

Cross sections, mean recoil ranges and angular distributions of radioactive a emitters produced in ¹²C, induced reactions at 1 GeV on medium and heavy targets are presented. A new on-line electrostatic collection device is used. A wide spectrum of heavy residues corresponding to various mass losses away from the target between D to 60 a.m.u. has been observed. A phenomenological analysis based on the statistical decay of possible precursors gives some information on the properties of the primary interaction. Losses of 10 to 30 nucleons can be partly fitted by the intranuclear cascade model. For greater mass losses, more collective primary interaction is needed. The abrasion-ablation model can produce such residues but in its clean cuts approximation the predicted excitation energy is too low.     

On neutrino and antineutrino scattering by electrons,and by partons

Assuming a non-derivative point interaction, and Born approximation, there are some simple relations between neutrino and antineutrino scattering on electrons or partons. They have been observed already, for some special cases, in the results of explicit calculations. Here they are obtained from simple general considerations.     

Two-particle kinematic distributions from new physics at an electron–positron collider with polarized beams

The kinematic distributions in two-particle inclusive processes at an e⁺e^- collider arising from standard-model s-channel exchange of a virtual γ or Z and the interference of the standard-model contribution with contributions from physics beyond the standard model involving s-channel exchanges are derived entirely in terms of the space-time signature of such new physics. Transverse as well as longitudinal polarizations of the electron and positron beams are taken into account. We show how these model-independent distributions can be used to deduce some general properties of the nature of the interaction. We then specialize to two specific two-particle final states, viz., ZH, where H is one of the Higgs bosons in a model with an extended Higgs sector, and ff̄, where f, f̄ are a pair of conjugate charged fermions, wherein distributions of two (of the possibly several) decay products are measured. We show how some of the properties of the distributions have been realized in the analysis of physics beyond the standard model in earlier work which made use of two-particle angular distributions.     

Quasi-free inclusive processes in the two-particle splitting of tritons by deuterons with an energy of 37 MeV

The d + t → d + d + n reaction was experimentally and theoretically investigated at an incident deuteron energy of 36.9 MeV. The experiment was performed on the U-240 isochronous cyclotron at the Institute for Nuclear Research, National Academy of Sciences of Ukraine. Inclusive spectra of deuterons and their angular distributions in the range of 15° ≤ θ_d ≤ 52° were measured. Experimental spectra and angular distributions of the final deuterons from the d + t → d + d + n reaction are satisfactorily described in a diffraction approximation that considers interaction in the final state and the correct asymptotic of the wave function of colliding nuclei. The scattered deuterons are the main contributors to the cross section (up to 70–90%), while the deuterons from tritons can be seen well only at low and high energies, at the edges of the spectra.     

Angular distributions of fragments originating from the spontaneous fission of oriented nuclei and problem of the conservation of the spin projection onto the symmetry axis of a fissile nucleus

The concept of transition fission states, which was successfully used to describe the angular distributions of fragments for the spontaneous and low-energy induced fission of axisymmetric nuclei, proves to be correct if the spin projection onto the symmetry axis of a fissile nucleus is an integral of the motion for the external region from the descent of the fissile nucleus from the external fission barrier to the scission point. Upon heating a fissile nucleus in this region to temperatures of T ≈ 1 MeV (this is predicted by many theoretical models of the fission process), the Coriolis interaction uniformly mixes the possible projections of the fissile-nucleus spin for the case of low spin values, this leading to the loss of memory about transition fission states in the asymptotic region where the angular distributions of fragments are formed. Within quantum-mechanical fission theory, which takes into account deviations from A. Bohr’s formula, the angular distributions of fragments are calculated for spontaneously fissile nuclei aligned by an external magnetic field at ultralow temperatures, and it is shown that an analysis of experimental angular distributions of fragments would make it possible to solve the problem of spin-projection conservation for fissile nuclei in the external region.     

Angular distributions of penning electrons

Angular distributions of electrons ejected in thermal collisions of He(2¹ S, 2³ S)-metastables with Ar, Kr, Xe, Hg, CO, N₂ are measured with respect to the vector of relative velocity of the colliding particles. Except for preliminary results on the He(2₁S, 2³ S)-/Ar-system, these are the first such distributions reported. They are found to be strongly anisotropic and asymmetric in some cases, and approximately isotropic in those cases where the interaction potential between the metastable- and the target particle is strong. For the cases of weak interaction potential, the connection between the “internal” angular distribution in the frame fixed to the internuclear axis and the laboratory angular distribution, has been derived. Calculations of laboratory angular distributions involving an assumed “internal” distribution and the kinematics of a hard core collision show good qualitative agreement with the experimental results.