Regular Series


Vol. 11 (1980), No. 8, pp. 579 – 648


Plebański Classification of the Tensor of Matter

abstract

This work presents a unified approach to the Plebański classification of the tensor of matter by showing how all the polynomial, tensorial, and spinorial objects used by Plebański arise from the study of a single linear operator, a derivation, on the real Clifford–Dirac algebra. In particular, we show that the classification of the tensor of matter is equivalent to the Petrov–Penrose classification of the conformal Weyl tensor, by way of the principal correlation which exists between them, which gives a positive answer to Plebański’s question of whether such a correlation exists. A new interpretation of spinors as elements of a complex projective plane of bivectors emerges. Our approach makes extensive use of the method of simplicial and multivector differentiation, and this method is explained in a series of appendices.


Anomalous Dimension and Infrared Behavior for High Energy QED

abstract

The generalization of the Sudakov results for real photons is obtained. It allows one to calculate the anomalous dimensions for the Coulomb and the electron–electron scattering. The formulas \({\mit \Delta }E = E \exp (-\eta (E/m))\) for the Coulomb case and \({\mit \Delta }E = E \sqrt {s} \exp (-\eta (s/m^2))\) for the electron–electron case are given. These formulas give anomalous dimensions which depend on the energy. This dependence, which comes from the Sudakov double logarithmic behavior of QED, disappears for semi-inclusive scattering. These results can be extended to other models of QFT like scalar QED or QCD and they partially justify the eikonal approximation.


Coherent Production on Nuclei and Measurements of Total Cross Sections for Unstable Particles

abstract

The Kölbig–Margolis formula is fitted to some explicitly nonperturbative models of diffractive production. It is shown that, in spite of the fact that the standard procedure of fitting the integrated cross sections may give acceptable fits, thus obtained “cross sections of unstable particles”, \(\sigma _2\), grossly disagree with the “true” cross sections known exactly from the models.


Relativistic Calculation of Polarized Nuclear Matter

abstract

The binding energy of nuclear matter with excess of neutrons, of spin-up neutrons, and spin-up protons (characterized by the corresponding parameters, \(\alpha _{\tau } = (N-Z)/A\), \(\alpha _{\rm n}(N\)\(\uparrow - N\)\(\downarrow \)\(/A\), and \(\alpha _{\rm p} = (Z\)\(\uparrow - Z\)\(\downarrow \)\(/A\)), contains three symmetry energies: the isospin symmetry energy \(\varepsilon _{\tau }\), the spin symmetry energy \(\varepsilon _{\sigma }\), and the spin–isospin symmetry energy \(\varepsilon _{\sigma \tau }\). Relativistic correction to the non-relativistic Skyrme effective interaction to order 1/\(c^2\) is used in order to calculate the relativistic corrections for the binding energy of polarized nuclear matter. The relativistic corrections to \(\varepsilon _{\tau }\), \(\varepsilon _{\sigma }\), and \(\varepsilon _{\sigma \tau }\) are found to be \(-2.06\), \(-2.6\) and \(-0.89\) MeV respectively. The relativistic correction to the compression modulus is \(-10.8\) MeV.


\(\mu ^+\) Decay from Muonium

abstract

The decay rate of muonium is calculated, taking into account the presence of the bound electron. The corresponding correction involved in the high precision \(\mu \)SR and magnetic resonance experiments is discussed. The angular distribution is also calculated, and the initial polarization of the muon is separately studied. The decay rate of a muon decaying from muonium is found to be 0.004% greater than when it decays from the free state and this enhancement is not negligible.


all authors

L. Jarczyk, B. Kamys, K. Seliger, Z. Wróbel, J. Lang, R. Müller, C.M. Schweizer-Teodorescu

Investigation of Nucleon-Unbound States in \(^{29}\)5i and \(^{29}\)P by the Reaction \(^{28}\)Si (d,pn)

abstract

Stripping reactions leading to unbound states of \(^{29}\)Si and \(^{29}\)P nuclei were investigated by measuring proton–neutron correlations in \(^{28}\)Si (d,p)\(^{29}\)Si(n) \(^{28}\)Si and \(^{28}\)Si(d,n) \(^{29}\)P(p) \(^{28}\)Si reactions at \(E_{\rm lab} = 11\) MeV. Twenty three states of 29Si were observed in the excitation energy range from 9.00 MeV to 13.43 MeV, and seventeen states of \(^{29}\)P in the energy range from 5.48 MeV to 9.81 MeV. For most of them spin, parity and partial width were derived.


top

ver. 2024.03.17 • we use cookies and MathJax