Optimal sum-rule inequalities for spin-12 compton scattering

A formalism appropriate for model-independent dispersion theoretical investigations of the (not necessarily forward) Compton scattering off $\text{spin}\text{-}\text{1}\text{2}$ hadronic targets, which fully exploits the analyticity properties of the amplitudes (to lowest order in electromagnetism) in ν² at fixed t ($\text{ν =}\text{1}\text{4}\text{(s ? u); s, t}$, u = Mandelstam variables), is developed. It relies on methods which are specific to boundary-value problems for analytic matrix-valued functions. An analytic factorization of the positive definite hermitian matrix associated with the bilinear expression of the unpolarized differential cross section (u.d.c.s.) in terms of the Bardeen-Tung (B.T.) invariant amplitudes is explicitly obtained. For t in a specified portion of the physical region, six new amplitudes describing the process are thereby constructed which have the same good analyticity structure in ν² as the (crossing symmetrized) B.T. amplitudes, while their connection with the usual helicity amplitudes is given by a matrix which is unitary on the unitarity cut. A bound on a certain integral over the u.d.c.s. above the first inelastic threshold, established in terms of the target's charge and anomalous magnetic moment, improves a previous weaker result, being now optimal under the information accepted as known.     

Approaches to the gravitational spin-32 axial anomaly

The $\text{spin}\text{-}\text{3}\text{2}$ axial anomaly is discussed from various points of view. Two consistent theories for a $\text{spin}\text{-}\text{3}\text{2}$ field interacting with gravity are considered: supergravity and a real quantized $\text{spin}\text{-}\text{3}\text{2}$ field in a classical gravitational background. The Feynman graph method, the zeta function regularization method, the point splitting method and the topological method all yield the same result for the latter theory, in agreement with that first found by Christensen and Duff.     

Construction of a unitary analytic amplitude for the scattering of spin-12 particles

We study the existence, the uniqueness and the construction of unitary analytic amplitudes for $\text{spin}\text{1}\text{2}\text{?}\text{1}\text{2}$ scattering, in the framework previously introduced by Atkinson-Mahoux-Ynduráin for spin 0-0, and $\text{spin}\text{0?}\text{1}\text{2}$ scattering.     

Spin-12 particles in the field of monopoles

The equations of motion of a $\text{spin}\text{-}\text{1}\text{2}$ particle in the field of a point-like (Abelian and non-Abelian) monopole are solved; helicity states and scattering solutions are constructed. The motion in an extended monopole and dyon source is discussed: charge-exchange scattering amplitudes are computed in the distorted-wave Born approximation. By the introduction of suitable spinors, the separation of variables is accomplished for any value of isospin. The non-existence of fermion zero modes in the field of an SU(2) monopole when $\text{T > 1, J >}\text{1}\text{2}$ is shown.     

Quasipotential approach to the Coulomb bound state problem for spin-0 and spin-12 particles

A recently proposed local quasipotential equation is reviewed and applied to the electromagnetic interaction of a spin-0 and a $\text{spin}\text{-}\text{1}\text{2}$ particle. The Dirac particle is treated in a covariant two-component formalism in the neighbourhood of the mass shell. The fine structure of the bound state energy levels and the main part of the Lamb shift (of order α⁵ ln(1/α)) are evaluated with full account of relativistic recoil effects (without using any inverse mass expansion). Possible relevance of the techniques developed in this paper to fine structure calculations for meso-atomic systems is pointed out.     

Relativistic transport equation for spin 12 particles

For the model of positive energy Dirac particles with short range interaction a transport equation for the one- particle Wigner function is obtained. This transport equation is a generalization of the non-relativistic Walsmann- Snider equation for spin particles.     

On spin-52 gauge fields

We present and discuss the theory of free, massless gauge fields with spin $\text{5}\text{2}$.     

NMR relaxation at low temperature in one dimensional antiferromagnets: Comparison between S = 12 and S = 52

The proton spin-lattice relaxation time T₁ has been measured at low temperatures in spin $\text{5}\text{2}$ (CH₃)₄NMnCl₃ (TMMC) and spin $\text{1}\text{2}$ CuCl₂2NC₅H₅ (CuPC). The two systems have very different temperature dependences which we attribute to the different spin values.     

Two-nucleon pick-up from spin-12 targets (II). 89Y

The angular distributions for the ⁸⁹Y(p, t), (p, τ), and (d, α) reactions are compared to DWBA predictions and to the data for the ⁹⁰Zr(p, t) and (d, α) reactions. Several new spins are assigned to levels of ⁸⁷Y. A weak coupling model is tested by the comparison between the reactions on ⁸⁹Y and ⁹⁰Zr, and found to fail. The (d, α) reaction is found to populate strongly levels at excitation energies of 2.70 MeV and 3.07 MeV in ⁸⁷Sr, corresponding roughly in Q-value and strength to states formed in ths ⁸⁸Sr(d, α)⁸⁶Rb reaction.     

Origin of 1ƒ noise

$\text{1}\text{?}$ noise dependence on temperature for both n- and p-type silicon has been measured. The formula for calculation of $\text{1}\text{?}$ noise is presented. The formula has been derived by presumption that only lattice scattering gives $\text{1}\text{?}$ noise. A good agreement between calculations and experimental results is found.     

The axial and trace anomalies for spin 32

The axial and trace anomalies for a real spin $\text{3}\text{2}$ field interacting with a background gravitational field, as in simple supergravity, is computed. The axial anomaly result differs from that of Van Nieuwenhuizen and Vermaseren.     

Structures in pp → ππ

A Barrelet-zero analysis is presented of data on $\text{p}\text{p}\text{→ π π}$ in the momentum range 1 to 2 GeV/c. With π^?π⁺ data alone, the slope for ambiguity is very large, but the addition of π⁰π⁰ information enables the number of solutions to be reduced to just a few. Although the alternative solutions differ considerably, they significant common features, in particular, with plausible extra assumptions, all solutions appear to be dominated by resonances in all spin states from J = 1 to 5.     

Comparison of pp and pp interactions at s = 53 GeV

Results are presented from the first p$\text{p}$ colliding beam runs at the CERN ISR, using the UA5 streamer chamber detector. p$\text{p}$ interactions at $\text{s}\text{= 53}\text{GeV}$ are compared with pp data taken in the same experiment. The results are in good agreement with extrapolations of low-energy p$\text{p}$ data.     

Scattering of solitons with fermion number ±12

In a model of a Dirac field coupled to a sine-Gordon system, we have soliton solutions with half-integral fermion number. Scattering problems of such solitons are investigated. For soliton-soliton and soliton-antisoliton solutions, we find explicit solutions to the Dirac equations which are localized at the position of the (anti-)solitons. It is shown that the fermion number is generally transferred between the soliton and the (anti-)soliton in the scattering process.     

Energies of the n2S12 and n2D32,52 states of Cs

Using the technique of Doppler-free two-photon spectroscopy the energies of the n²S_{$\text{1}\text{2}$} (12 ? n ? 35) and n²D_{$\text{3}\text{2}$,$\text{5}\text{2}$} (11 ? n ? 48) states of CsI have been measured with a thermionic detector. The absorption spectrum of molecular iodine was used as a reference giving us a total estimated accuracy of about 2 × 10^-7. Taking also into account the energies of the 7–11 ²S_{$\text{1}\text{2}$} and 5 and 6 ²D_{$\text{3}\text{2}$,$\text{5}\text{2}$} states measured by other authors and using an extended Ritz-formula we found the ionization limit to be E_i = 31406.468 ± 0.006 cm^-1.     

Integral representation for the spin 12 Ising ferromagnet

A simpler derivation is given for a recently discovered integral representation for the spin $\text{1}\text{2}$ Ising ferromagnet.     

The spin 12 gravitational anomalous magnetic moment

The gravitational anomalous magnetic moment of a spin $\text{1}\text{2}$ particle is calculated and compared with an earlier dimensional regularization result. The answers disagree although both agree the answer is finite. It is argued that this quantity is not uniquely determined by physical requirements. The methods used are shown to respect the gravitational and electromagnetic gauge invariances. In addition, a physical interpretation of the regularization method employed is offered.     

Quark-tadpole origin of the ΔI = 12 rule

In the context of a two-quark field picture of current quarks and renormalized constituent quarks, we show that an s-d current-quark tadpole generated by the weak Cabbibo-GIM current appears in the current-quark nonleptonic ΔY = 1 hamiltonian. Then we demonstrate that this $\text{ΔI =}\text{1}\text{2}$ operator in fact sets the observed scale of the K_s→ππ decays without recourse to any fitted parameters.     

Phonon observations from 1ƒ noise measurements

From mobility fluctuation $\text{1}\text{?}$ noise parameter measurements five phononic energies corresponding to LO, TO vibrational modes as well as TA + S₂ or O, TO + TA, TO + O combined modes were identified. They stand for phonon replicas of non-radiative recombination processes. It is thus demonstrated that the carrier-phonon interaction is the source of $\text{1}\text{?}$ noise in semiconductors.     

Q gravity

The geometrical structure of an extended theory of gravitation incorporating the quaternion field is investigated. A lagrangian is constructed and shown to be pure real as a consequence of the geometrical structure. The structure of spacetime becomes nonabelian; however, the base manifold in which physics takes place, remains real and n-dimensional.