Semileptonic Weak Interactions Research Articles

Evolution of Hot and Dense Stellar Interiors: The Role of the Weak Interaction Processes

The evolution of the hot and dense interior of massive stars has aroused the intense interest of researchers the last more than three decades. In this article, the role of the semi-leptonic weak interaction processes of leptons (involving neutrinos) with nucleons and nuclei in the late stages of stellar evolution, as well as in the relevant terrestrial neutrino detection experiments, is reviewed. Such processes play crucial role for the massive stars’ evolution in the final stages of their life, and specifically in the core-collapse supernova leading to the supernova explosion phenomenon. We start by mainly focusing on the neutrino producing charged-lepton capture, like the electron-capture and the muon-capture on nuclei and, then, we discuss the neutrino absorbing reactions which are essential in the neutrino-driven explosive nucleo-synthesis. These processes are also significant in many ongoing and planned worldwide underground sensitive experiments aiming to detect astrophysical neutrinos which rely on the interactions of neutrinos with the bound nucleons inside atomic nuclei.

Precision frontier in semileptonic weak interactions: theory

Recent advances in experimental physics have opened a new frontier for the precision measurements in low energy weak interactions. In this note we discuss the theoretical basis for the analysis of such experiments and their implications for the standard model.

SevenOperators, a Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactions

Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order | p → | / M , where p → and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q 2 , where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summary Program title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2227 No. of bytes in distributed program, including test data, etc.: 19 382 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer running Mathematica; tested on Mac OS X PowerPC (32-bit) running Mathematica 6.0.0 Operating system: Any running Mathematica RAM: Memory requirements determined by Mathematica; 512 MB or greater RAM and hard drive space of at least 3.0 GB recommended Classification: 17.16, 17.19 Nature of problem: Algebraic evaluation of harmonic oscillator nuclear matrix elements for the one-body multipole operators governing semi-leptonic weak interactions, such as charged- or neutral-current neutrino scattering off nuclei. Solution method: Mathematica evaluation of associated angular momentum algebra and spherical Bessel function radial integrals. Running time: Depends on the complexity of the one-body density matrix employed, but times of a few seconds are typical.

Semileptonic weak interactions in nuclei within continuum RPA

Semileptonic weak reactions in nuclei at low and intermediate energies play an important role both in accelerator-based experiments in Neutrino Physics and in Neutrino Astrophysics. Theoretical estimates of such reaction rates are needed either to compare with the data or, in case they have not been measured, as input to astrophysical simulations. We show how weak observables can be calculated within Continuum RPA theory and present the most relevant applications.

Strength of spin-isospin transitions in A = 28 nuclei

The relations between the strengths of spin-isospin transition operators extracted from direct nuclear reactions, magnetic scattering of electrons and processes of semi-leptonic weak interactions are discussed.

Chiral perturbation theory with virtual photons and leptons

We construct a low-energy effective field theory which allows the full treatment of isospin-breaking effects in semileptonic weak interactions. To this end, we enlarge the particle spectrum of chiral perturbation theory with virtual photons by including also the light leptons as dynamical degrees of freedom. Using super-heat-kernel techniques, we determine the additional one-loop divergences generated by the presence of virtual leptons and give the full list of associated local counterterms. We illustrate the use of our effective theory by applying it to the decays pi -> l nu_{l} and K -> l nu_{l}.

Chiral perturbation theory

The main elements and methods of chiral perturbation theory, the effective field theory of the Standard Model below the scale of spontaneous chiral symmetry breaking, are summarized. Applications to the interactions of mesons and baryons at low energies are reviewed, with special emphasis on developments of the last three years. Among the topics covered are the strong, electromagnetic and semileptonic weak interactions of mesons at and beyond next-to-leading order in the chiral expansion, nonleptonic weak interactions of mesons, virtual photon corrections and the meson-baryon system. The discussion is limited to processes at zero temperature, for infinite volume and with at most one baryon.

On T-violation in muon capture by oxygen

Possible CP- and T-violation in muon capture are analyzed. With thehelp of the first forbidden nuclear muon capture bith T-violating semileptonic weak interaction and T-violating nuvlear forces can be investigated. As follows from our calculations only one phase of possible T-violating nuclear forces is important in muon capture by O 16.

Symmetry tests with highly charged ions

We summarize the present status of testing the standard model of parity nonconservation in neutral atoms, emphasizing the success in understanding the semileptonic weak interactions. There is good agreement for the nuclear spin independent contributions, especially in cesium. There is some evidence of nuclear spin dependent terms, probably due to hadronic weak interactions. There is no evidence of leptonic weak interactions. The lessons learned from atomic physics are discussed, together with strategies for parity experiments using highly charged ions.

Relativistic multipole operators for semileptonic weak and electromagnetic nuclear reactions.

We discuss multipole operators that arise in a relativistic analysis of semileptonic weak and electromagnetic interactions with nuclei. These single-particle operators are evaluated between relativistic nucleon bound states that are solutions to the Dirac equation with potentials of the form produced by the \ensuremath{\sigma}-\ensuremath{\omega} model. The reduced matrix elements are given in terms of easily programmable radial integrals and can be applied to a number of reactions such as elastic and inelastic electron scattering, real photon processes, \ensuremath{\beta} decay, and charged lepton capture as well as more exotic interactions such as charged and neutral current neutrino reactions. As a specific example, we calculate the elastic and inelastic magnetic form factors of p-shell nuclei.

Chiral perturbation theory — Strong and semileptonic weak interactions

Recent work on the low energy structure of S-matrix elements and Green functions is reviewed, emphasizing the theoretical foundations. Some of the results are confronted with the data and problems occuring in the theoretical analysis as well as inconsistencies in the data are pointed out.

Semileptonic weak interactions in nuclei: A relativistic analysis

We use a consistent relativistic formalism, with relativistic Hartree wave functions and a covariant effective current operator with all the properties of the standard model, to study semileptonic weak processes in nuclei. Results are obtained for β-decay, μ- capture, charge-changing v-reactions and neutral v-scattering involving the isodoublet systems 17F 17O and 3H 3He.

Limit on second class polar vector couplings in semileptonic weak interactions

Although a great deal of experimental work has succeeded in limiting a possible second class axial coupling to about ten percent of the size of weak magnetism, published limits on the size of a possible second class polar vector current are one order of magnitude less sensitive. We summarize the present situation and demonstrate that muon capture provides the strictest present limit.

Induced scalar effects in semileptonic weak interactions

The size of an induced scalar coupling in semileptonic weak processes arising from quark mass differences, impulse-approximation results, and charged-Higgs-boson exchange is estimated. Although the predicted size of the effect is non-negligible it is apparently below present experimental capability to detect.

Semileptonic weak and electromagnetic interactions in nuclei: Recoil polarization in muon capture

An analysis of the polarization of the recoiling nucleus following the capture of polarized muons by nuclei is performed. New general expressions for abitrary nuclear spin are obtained in terms of the same reduced matrix elements which govern inelastic electron scattering and β -decay. As an application we consider the A = 12 system and study uncertainties in the nuclear structure by using different sets of one-body density matrices. With the canonical values of the weak form factors (i.e. absence of second-class currents) we achieve a fairly good agreement with the experimental data including the inelastic form factor at high momentum transfers and the recently measured average 12B polarization. Implications Of the new corrected value of the average polarization on weak form factors and nuclear structure are discussed.

Semileptonic weak and electromagnetic interactions with nuclei: Parity violations in electron scattering and abnormal-parity admixtures in nuclear states

We derive an expression for the difference in the differential cross section for the scattering of right- and left-handed longitudinally polarized electrons from nuclei. Our result is applicable to scattering between any two nuclear levels and includes contributions from both the parity-nonconserving weak-electromagnetic interference and from abnormal-parity admixtures in the nuclear states. It is written in terms of the same nuclear matrix elements that govern all semileptonic transitions between the two levels and these matrix elements are examined using a recently developed one-body density matrix analysis of weak and electromagnetic interactions with nuclei. By exploiting the different momentum transfer dependence of the admixture and interference contributions, we find that, for the general cases considered here, the two contributions can be observed independently. In inelastic transitions in even-even nuclei, the admixture terms dominate at low-momentum transfers allowing for a determination of the scale of the parity admixing and a check of other parity-violation experiments. In this limit the contributions from the abnormal-parity admixtures can be investigated by appealing to the long-wavelength limit of the nuclear multipole matrix elements and by specifying the nuclear-state admixing with one overall scale parameter, which may become large in cases of favorable admixing. At higher momentum transfers, the interference terms dominate, permitting an investigation of the weak neutral-current interaction. In elastic scattering, current conservation implies that the leading term of the abnormal-parity nuclear matrix element vanishes; hence, the weak-electromagnetic interference is highly dominant in these cases. These results are illustrated by two examples using a simple parity-violating nucleon-nucleon potential derived from one-pion exchange. We use previously determined one-body transition densities to calculate the asymmetry in the 0 +0 → 1 +1 (15.11 MeV) transition in 12C, and perform a new calculation of the asymmetry in elastic scattering from 13C, determining the one-body transition densities from electron scattering data.

Semileptonic weak and electromagnetic interactions with nuclei: Nuclear current operators through order (v/c)nucleon2

We use a previously developed procedure for generating the multipole operators of the weak and electromagnetic nuclear current from single-nucleon matrix elements. The analysis is extended through O(( v / c ) nucleon 2 ) by including relativistic corrections in the matrix elements. We neglect explicit exchange currents and treat ambiguities arising from the off-mass-shell behavior of the nucleons in a consistent fashion using two alternative methods of calculation. One method equates the energy transfer to the energy difference between single-nucleon states, the other uses the lepton energy loss; our results agree with similar calculations done previously. We also prove a theorem indicating the circumstances under which these ambiguities are absent. In explicit calculations in the A = 6 and A = 12 systems using previously determined nuclear parameters, we find that second-order corrections are small when second-class currents are absent. When second-class currents are included, their effects on β-decay are ambiguous; however in processes involving large momentum transfers (e.g. neutrino scattering), their effects may be large and are insensitive to the treatment of the off-shell behavior of the nucleons.

Semi-leptonic weak and electromagnetic interactions in nuclei:: Parity violations in electron scattering and weak neutral currents

A general result for the difference in differential cross sections for electron scattering between any two nuclear levels with incident longitudinally polarized right- and left-handed electrons is derived. This difference must involve the parity-violating weak interaction at least linearly and can be used to study weak neutral currents as pointed out by Feinberg. A V — A structure for the weak neutral currents is assumed with a semi-leptonic current-current interaction, and the electromagnetic interaction is treated in the one-photon-exchange approximation. The result is expressed in terms of the same set of reduced matrix elements of the multipoles of the nuclear currents which govern all electromagnetic and weak transitions between these levels. A previously developed unified analysis of semi-leptonic weak and electromagnetic interactions in nuclei which determines one-body transition densities, including their spin and spatial dependences, through electron scattering provides nuclear transitions to serve as known analyzers in testing the structure of this part of the weak interaction. Examples are given using Weinberg's model of the weak neutral currents. Feinberg's result for elastic scattering from spin-0 nuclei is rederived and two new examples using previously determined one-body densities are discussed : the 1 +0 → 0 +1 (3.56 MeV) transition in 6Li and the 0 +0 → 1 + 1(15.1 MeV) transition in 12C.

Semi-leptonic weak and electromagnetic interactions with nuclei: Isoelastic processes

A one-body density matrix formalism is presented for studies of isoelastic processes, that is, for semi-leptonic weak and electromagnetic interactions involving the members of a nuclear ground-state isospin doublet. Relationships involving density matrices are given for the general case and then specialized to the systems 3H- 3He and 11B- 11C, where data on conventional electromagnetic and weak interactions provide stringent constraints on the form of the density matrix. Predictions are then given for charge-changing and neutral current neutrino reactions. The effects of changes in the weak coupling constants and of second-class tensor currents on these processes are discussed.

Semi-leptonic weak and electromagnetic interactions with nuclei: Muon capture to discrete nuclear levels from hyperfine states

We derive a general expression for the muon-capture rate to discrete nuclear levels from hyperfine states of the initial μ-nucleus system, in terms of the same few reduced nuclear matrix elements which govern all electromagnetic and weak semi-leptonic transitions involving these nuclear levels. We discuss a recently developed unified analysis of these matrix elements. Three examples are given : two simply demonstrate the relation of the present approach to previous work in this area, and one is a full, new calculation for the process μ − + 6 Li → ν μ + 6 He(g.s.) from the two initial hyperfine states F = 1 2 , 3 2 using one-body densities for this system previously determined through electromagnetic interactions by Donnelly and Walecka. As has been emphasized in the past by other authors, knowledge of muon capture from the hyperfine levels can give us invaluable information about the fundamental nature of the weak interactions and about nuclear structure.