Pairing forces connected with the \(R_3\) group and quadrupole forces with the \(SU_3\) group were taken together to generate the common symmetry group. It has been proved that the resulting group is the symplectic group in \((N+1)(N+2)\) dimension, where \(N\) is the major shell number. The special case of \(Sp(6)\) for \(N = 1\) is discussed in detail.
It is shown that the standard expression for the total mass \(M\) of a closed static system in the form of the volume integral of canonical energy-momentum complex using the covariant quantity \(R\) as Lagrangian leads to the equality \(M = M_{\rm s}/2\), where \(M_{\rm s}\) — Schwarzschild mass of the system. It follows that either the expression for the complex is inconsistent with the field equations or the “total” mass of the system is different from Schwarzschild mass, or \(M=0\). There are some ideas given here that favour the possibility of \(M=0\).
The fixed u continuous moment sum rules for meson–nucleon scattering were derived and applied to the analysis of \(Kp\) scattering amplitude. It was found that sum rules are compatible with the hypothesis of \({\mit \Lambda }_{\alpha }\)–\({\mit \Lambda }_{\gamma }\) exchange-degenerate trajectory dominance.
It is shown that the \(S\)-operator cannot exist, but it is possible to define probabilities in momentum space by a careful transition to the limit. Our construction is quite independent of any asymptotic conditions upon the ingoing and outgoing fields.
The quark model predictions for the decay distributions of resonances photoproduced in the reactions \(\gamma B \to PB^*\), \(\gamma B \to VB\) and \(\gamma B \to VB^*\) are given. The numbers of relations predicted for the three reactions are: three, three and sixty respectively.
The principal properties of the transversity amplitudes (i.e. amplitudes with spins projected on the normal to the reaction plane) are presented. The properties which are important for applications, as the simplicity of crossing relations and the behaviour under spatial reflections are discussed in detail. The applications to the study of behaviour of scattering amplitudes at thresholds and pseudothresholds and to the description of spin correlations in decay distributions are also presented. Finally many other applications (including those proposed by other authors) are shortly discussed.
In a study of the decay of 15\(^{\rm min}\) \(^{65}\)Ga, about eight new gamma rays were found, and in all twenty-five gamma transitions were observed. A level scheme has been constructed. Levels not reported earlier in the decay studies of \(^{65}\)Ga are found at 910 keV and 2419 keV. Gamma-ray energy- and intensity values are given, and branching ratios for the \(\beta ^+\) — decay and EC-processes are deduced. Corresponding log ft values have also been calculated.
An explicit mapping procedure is used to determine an approximate off zero-momentum transfer-squared symmetry group for the inelastic binary connected part.
The optical theorem for partially polarized particles is derived in its most general form. It is shown that it can be used to determine experimentally the imaginary part of all spin amplitudes nonvanishing in the forward direction.
