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Recent years have seen the accumulation of a considerable amount of new information, both experimental and theoretical, pertaining to the location and character of the excited states in the light nuclei. We have attempted in the following sections to summarize the pertinent facts appearing in the literature and to present this material in a systematic way. To a large extend the organization of the present article follows the pattern of the two previous papers on this subject.(1,2) The present article contains a summary of the most important information appearing in the earlier papers and is intended to supersede them entirely.

In a recent paper, we considered the possibility of dynamical enhancement of SU(3) symmetry breaking in baryon couplings. It was found that certain patterns of symmetry breaking are enhanced and tend to dominate; the results were presented and compared with experiment. In the present companion paper, we explain in detail the methods by which these conclusions were obtained and give a more complete summery of the numerical results.

This paper reviews various results related to the single-particle structure in spherical and deformed nuclei, discussed from the viewpoint of the so-called shell-correction method. This method stresses the importance of large-scale nonuniformities in the energy distribution of the individual particles especially near the Fermi energy. The way in which these nonuniformities affect in an essential way many nuclear properties, such as the shape stiffness, the spatial density distribution, the total mass of the nucleus, the mass and inertia of the nuclear shape variations, etc. is also discussed. Against this background, the behavior of the nuclear deformation energy is described, in particular for larger distortions relevant to the fission process. In this connection, some qualitative singularities of the phenomenological liquid-drop deformation energy at large shape distortions are pointed out, and their possible implications for fission are discussed. As the problems considered cover a wide range of nuclear properties, this paper is not a review in the narrow sense of the word. Comparison with other approaches as well as historic references are given mainly to clarify specific points, because a complete review would be a monumental undertaking.

The present paper aims to deal only with a limited portion of the subject, the evaluation of the so-called atomic constants: e the electronic charge, m the electronic mass, and h Planck's constant of action together with certain auxiliary constants intimately associated with them. A number of useful physical constants which can be computed from the above data will also be evaluated.

In most recoilless gamma-ray resonance experiments the magnetic-dipole and electric-quadrupole hyperfine interaction do not cause any shift of the center of gravity of the velocity spectrum. This is usually related to the fact that the trace of the hyperfine-interaction Hamiltonian is zero. Nevertheless a large shift can be caused under proper conditions by a magnetic hyperfine interaction in second order, the so-called "pseudoquadrupole" interaction.(1) This paper reports the first observation of the pseudoquadrupole shift of gamma lines.(2)

The possibility that certain patterns of SU(3) symmetry breaking are dynamically enhanced in baryon-meson couplings is studied by bootstrap methods. For the strong couplings, a single dominant enhancement is found. It produces very large symmetry-breaking terms, transforming like an octet, as often conjectured. Experimental consequences are listed, such as a reduction of K-baryon couplings relative to π-baryon couplings which is in accord with the experimental weakness of K relative to π production in many circumstances, such as photoproduction and multi-BeV cosmic-ray collisions. For parity-violating nonleptonic couplings, a dominant octet enhancement is again found, as mentioned in a previous paper, which leads to an excellent fit with experiment. For parity-conserving nonleptonic couplings, on the other hand, several different enhancements compete, and the only conclusion we can draw is that terms with the "abnormal" transformation properties brought in by strong symmetry-breaking corrections are present. Our work provides a dynamical derivation of various phenomenological facts associated with SU(6), such as the dominance of the 35 representation in parity-violating nonleptonic decays.

Calculations of many physical processes according to the SU(12) theories(1) can be facilitated by the use of appropriate subgroups of SU(12). Direct calculations are difficult because of the complexity of the group and the present lack of available Clebsch-Gordan coefficients. Tables of SU(6) Clebsch-Gordan coefficients do exist,(2) however, and have been used for calculations of non-relativistic processes. In this paper we present SU(6) subgroups which differ from the conventional SU(6) by the replacement of ordinary spin by different SU(2) subgroups of SU(12).

In this paper we report methods of computation which have been developed to provide a theoretical understanding of the RR Lyrae and Cepheid type pulsating stars. The results reported are intended to illuminate the methods of calculation and to provide insight into the physical processes in these stars. A survey of pulsation in RR Lyrae models using these methods has also been carried out and will be reported soon in another journal. A survey of pulsation in Cepheid models has been initiated and will be continued.

Spectra of stripped atoms, sodium to chlorine.—Grating spectrograms of order three to eight have been obtained of the hot-spark spectra of these elements, which have yielded more accurate values for the (3p2-3p1), (3s-3p2) and (3p1-3d) terms of AlIII, SiIV, PV and SVI, and have enabled the identification and determination within about 5 frequency units (1) of 18 series lines of PV, and thence of the 14 most important term values (3s to 6f′′), (2) of 11 series lines of SVI, and 10 corresponding term values (3s to 5f′), and (3) of the first doublet of the principal series of ClVII at 800.70 and 813.00 A. The position of this doublet was first predicted by use of the method developed in a previous paper(1), based on observed regularities in these spectra. Further evidence is presented for the fact that both the regular and the irregular doublet laws of x-ray spectra, hold also throughout the field of optics. A plot of sqrt[ν/R] for the stripped atom levels as a function of atomic number gives approximately straight lines (Moseley law), those for the 3s, 3p and 3d terms and for the 4s, 4p, 4d and 4f terms being approximately parallel (irregular doublet law). The doublet separations d1d2, however, do not fit well into the relativity doublet law, the ratio of observed to theoretical values decreasing from about .8 for SVI to less than .2 for SiIV, while AlIII and MgII are anomalous, d1 having a greater frequency than d2. The general similarity of the spectra of all these elements is strikingly shown in spectrograms on which appear the "D" doublet of Na and the corresponding "D" doublets of the stripped atoms of Mg, Al, Si, P, S, and Cl in the second, third, fourth, fifth, sixth and seventh ordelrs, respectively, all near 5600 A, that for Na being farthest from the mean position. The frequencies of all the known terms found for the stripped atoms of Na to S, are collected in a table. Ionization potentials of PV and SiVI, computed from the 3s levels of PV and SVI, come out 64.7 and 87.6 volts.

The invited speakers have done an excellent job of describing the various topics within the field of weak interactions. The contributed papers have presented many fascinating results. Furthermore, what is rare these days at a physics conference, there has been plenty of discussion, which has brought out, I think, every point that was overlooked in the speeches. Evidently, there is no need for a summary. A few words about what appear to me to be the principal questions that we would like to have answered in the future are given in the following.

Series spectra of three-valence-electron atoms of P, S and Cl.—By the methods of the preceding paper, 21 lines of PIII have been identified, 20 lines of SIV and 10 lines of ClV, including a pp′ group for each; also 10 term values of PIII have been determined and 10 term values of SIV, including the x level. Screening constants for one, two, and three valence electron systems are collected in a table for Na to Cl. The values increase regularly with the number of valence electrons and decrease with the atomic number, the difference decreasing as the atomic number increases.

The problem of the dynamical structure and definition of energy for the classical general theory of relativity is considered on a formal level. As in a previous paper, the technique used is the Schwinger action principle. Starting with the full Einstein Lagrangian in first order Palatini form, an action integral is derived in which the algebraic constraint variables have been eliminated. This action possesses a "Hamiltonian" density which, however, vanishes due to the differential constraints. If the differential constraints are then substituted into the action, the true, nonvanishing Hamiltonian of the theory emerges. From an analysis of the equations of motion and the constraint equations, the two pairs of dynamical variables which represent the two independent degrees of freedom of the gravitational field are explicitly exhibited. Four other variables remain in theory; these may be arbitrarily specified, any such specification representing a choice of coordinate frame. It is shown that it is possible to obtain truly canonical pairs of variables in terms of the dynamical and arbitrary variables. Thus a statement of the dynamics is meaningful only after a set of coordinate conditions have been chosen. In general, the true Hamiltonian will be time dependent even for an isolated gravitational field. There thus arises the notion of a preferred coordinate frame, i.e., that frame in which the Hamiltonian is conserved. In this special frame, on physical grounds, the Hamiltonian may be taken to define the energy of the field. In these respects the situation in general relativity is analogous to the parametric form of Hamilton's principle in particle mechanics.