Second-order corrections to correlations in muon capture

Average polarization of 12B in polarized muon capture

Allowed partial transitions in muon capture by 28Si

Exploring the leptonic sector in frontier experiments is more of importance nowadays, since the conservation of lepton flavor and total lepton number are not guaranteed anymore in the Standard Model after the discovery of neutrino oscillations. $\mu^- + N(A,Z) \rightarrow e^+ + N(A,Z-2)$ conversion in a muonic atom is one of the most promising channels to investigate the lepton number violation process, and the measurement of this process is planned in future $\mu^--e^-$ conversion experiments with a muonic atom in a muon-stopping target. This paper discusses how to maximize the experimental sensitivity of the $\mu^--e^+$ conversion by introducing the new requirement of the mass relation of $M(A,Z-2)<M(A,Z-1)$, where $M(A,Z)$ is the mass of the muon-stopping target nucleus, to get rid of the background from radiative muon capture. The sensitivity of the $\mu^--e^+$ conversion is anticipated to have four orders of magnitude of improvement in forthcoming experiments using a proper target nucleus, which satisfies the mass relation. The most promising isotopes found are $^{40}$Ca and $^{32}$S.

An interesting relation $\ensuremath{\alpha}\ensuremath{-}2{P}_{L}=1$ is obtained between the asymmetry parameter $\ensuremath{\alpha}$ and the longitudinal polarization ${P}_{L}$ of the recoil nucleus in the reaction ${\ensuremath{\mu}}^{\ensuremath{-}}+A({{J}_{i}}^{{\ensuremath{\pi}}_{i}})\ensuremath{\rightarrow}B({{J}_{f}}^{{\ensuremath{\pi}}_{f}})+{\ensuremath{\nu}}_{\ensuremath{\mu}}$, in which the initial nuclear spin is zero. It is shown algebraically that this relation is independent of both the nuclear structure and the values of the coupling constants of the muon capture interaction with or without inclusion of second class current terms.

A generalized extraction procedure for magnetic interactions using effective Hamiltonians is presented that is applicable to systems with more than two sites featuring local spins Si ≥ 1. To this end, closed, nonrecursive expressions pertaining to chains of arbitrary equal spins are derived with the graphical method of angular momentum. The method is illustrated by extracting magnetic couplings from ab initio calculations on a [CaMn3(IV)O4] cubane. An extension to nonsequential coupling schemes proves conducive to expressing additional symmetries of certain spin Hamiltonians.

Advanced nuclear data for radiation damage calculations

The fluctuation theory based on the functional integration method is developed for a multimode Dicke‐Hamiltonian with arbitrary spins and with antiresonant terms included. The effective classical Hamiltonian of the fluctuations is deduced and the equilibrium phase transition, the existence of soft modes as well as the general equations of state are discussed in this unified approach. The consequences of the rotating‐wave approximation are clearly distinguished. The solid state phenomena of the cooperative Jahn‐Teller effect and of spin‐reorientation are implied in these considerations.

The separation of proton and deuteron spin-orbit distortions in the [formula omitted] reaction

Coupled tensorial forms of the second-order effective Hamiltonian for open-subshell atoms in jj-coupling

The cross sections of elastic scattering and fusion of identical heavy ions with arbitrary spin, s are derived. Applications to several light heavy ions at near-barrier energies are made. It is found that the transverse isotropy; namely, the flat angular distribution which sets in at a critical value of the energy, becomes less pronounced with higher values of the spin. The oscillations in energy in the fusion cross section was found to go as 1/(2s+1). A similar factor is found in the angle-oscillating term in the elastic-scattering cross section.

This technical paper of mathematical physics arose as an aftermath of the 2002 Cassini experiment (Bertotti et al 2003 Nature 425 374–6), in which the PPN parameter γ was measured with an accuracy σγ = 2.3 × 10−5 and found consistent with the prediction γ = 1 of general relativity. The Orbit Determination Program (ODP) of NASA's Jet Propulsion Laboratory, which was used in the data analysis, is based on an expression (8) for the gravitational delay Δt that differs from the standard formula (2); this difference is of second order in powers of m—the gravitational radius of the Sun—but in Cassini's case it was much larger than the expected order of magnitude m2/b, where b is the distance of the closest approach of the ray. Since the ODP does not take into account any other second-order terms, it is necessary, also in view of future more accurate experiments, to revisit the whole problem, to systematically evaluate higher order corrections and to determine which terms, and why, are larger than the expected value. We note that light propagation in a static spacetime is equivalent to a problem in ordinary geometrical optics; Fermat's action functional at its minimum is just the light-time between the two end points A and B. A new and powerful formulation is thus obtained. This method is closely connected with the much more general approach of Le Poncin-Lafitte et al (2004 Class. Quantum Grav. 21 4463–83), which is based on Synge's world function. Asymptotic power series are necessary to provide a safe and automatic way of selecting which terms to keep at each order. Higher order approximations to the required quantities, in particular the delay and the deflection, are easily obtained. We also show that in a close superior conjunction, when b is much smaller than the distances of A and B from the Sun, say of order R, the second-order correction has an enhanced part of order m2R/b2, which corresponds just to the second-order terms introduced in the ODP. Gravitational deflection of the image of a far away source when observed from a finite distance from the mass is obtained up to O(m2).

A general expression is obtained for the Raman scattering intensity in an ensemble of diatomic molecules for an arbitrary geometry of the experiment as a function of the anisotropy of angular distribution of molecular axes. In its derivation, the irreducible representation of the density matrix of molecules was used. It is shown that, in the Raman scattering experiments on the study of the anisotropy of molecular ensembles, a significant contribution to the signal is made, not only by the second-order terms 〈cos2θ〉, but also by the fourth-order terms proportional to 〈cos4θ〉, which should be taken into account to correctly interpret the experimental data. Convenient experimental geometries are proposed that allow the anisotropy of a molecular ensemble to be investigated.

A model that allows the authors to investigate the polarisation effects arising in elastic proton scattering by spin-1/2 nuclei is developed in the framework of multiple diffractive scattering theory. A general expression for the scattering operator is obtained, which contains terms describing the central spin-orbit and spin-spin proton-nucleus interactions. It is shown that in this case the complete experiment includes the measurement of eleven independent scattering angle functions of which the differential cross section, the analysing power of protons and recoil nuclei, two proton spin-flip functions and six other correlation coefficients are investigated. The available experimental data on 550 and 800 MeV elastic p-13C scattering have been analyzed.

We have examined (1) the elastic scattering of pions from the isodoublet /sup 3/He and /sup 3/H and (2) the single charge-exchange reaction /sup 3/H(..pi../sup +/,..pi../sup 0/)/sup 3/He using a formalism which incorporates the ..pi..-N multiple scattering to all orders. Emphasis is placed on numerical results which illustrate those features of the differential cross sections that are expected to be of interest to the experimentalist. Realistic nuclear densities corresponding to the form factors of elastic electron scattering were used. Charge-exchange cross sections are presented in terms of angular distributions for both the ..pi../sup 0/ and the recoil nucleus. In elastic scattering, Coulomb-nuclear interference effects are significant at incident pion kinetic energies of less than 100 MeV; form factor effects are apparent at large momentum transfer. Comparison of data and theory for ..pi../sup +/ - /sup 3/He with that for ..pi../sup -/ - /sup 3/He (or the conjugate ..pi../sup +/ - /sup 3/H) will provide a test of the convergence of the fixed scatterer, multiple-scattering formalism utilized in this report. 21 figures.

Study of deformation states in metals exposed to intense-pulsed-ion beams (IPIB)