Gamma rays from the decays of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}_{}^m{}_{}{}^{}$, ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{47}{}_{}{}^{}\mathrm{K}$, produced by ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$+t reactions at $E_{\mathrm{t}}=3.2\mathrm{}$ MeV, were investigated with a Ge(Li) detector. A 3.5-MV Van de Graaff and a "rabbit" target-transfer system were used. Precision energy measurements resulted in the following $\gamma$-ray energies (in keV): ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}$, 523.792(18), 1121.124(5), and 1553.768(8); ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ca}$, 71.552(5), 256.894(10), 1519.300(20), and 1590.850(30). Relative $\gamma$-ray intensities were also measured and more accurate ${\beta }^{-}$ and $\gamma$-ray branches in the decay schemes of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{47}{}_{}{}^{}\mathrm{K}$ were obtained. Limits were set on unobserved branches and, in ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}$ decay, five new ${\beta }^{-}$ branches were found. By using a short timing cycle it was found that a possible ${\beta }^{-}$ branch from ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}_{}^m{}_{}{}^{}$ to the $2^{+}$ 1554-keV state of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ is <2.5%. An incidental result was a value of 520.436(15) keV for the lowest energy $\gamma$ ray in ${}_{}{}^{83}{}_{}{}^{}\mathrm{Rb}$ decay. The ${\beta }^{-}$ decay of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}$ is compared to shell-model predictions.

A phenomenological description of the ground state band energies of even-even nuclei, based on an anharmonic vibrational picture, is developed. The proposed model, with three adjustable parameters, gives excellent fits to the experimental spectra in the spherical, transitional, and deformed regions.

It is shown that nuclear mass relations should satisfy several criteria, the nature of which is either physical or mathematical. Simple examples demonstrate the significance of both the physical content and the mathematical stability required from an acceptable mass relation.

A hybrid quark-nucleon model of nuclei is developed in which nucleons merge into multiquark bags at short distances. This model is applied to calculate mass differences between ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and a number of other mirror nuclei. For light nuclei we obtain a reduction of the discrepancy between experiment and conventional theory. Probabilities for the formation of six-quark bags and nine-quark bags in these nuclei are evaluated, and the consequences of our results are discussed. In particular we comment on the compatibility of conventional and the hybrid quark-nucleon results.

The charge-exchange Hartree-Fock random-phase approximation theory is employed in the calculation of isovector spin excitations in nuclei with $N>Z$. Distributions of strength for all three $\Delta {\tau }_z=0,\pm 1$ components of $S=1\mathrm{}$, $L=0,1,2\mathrm{}$, $J=0^{-},1^{-},2^{-}, 1^{+}, 2^{+}, \mathrm{and} 3^{+}$ excitations are calculated. The results for isotopes of Ni and Zr are also presented.

Distortion effects in an assembly of clusters are studied by using a trial wave function in which—in addition to the intercluster separations—the size parameters of individual clusters appear as generator coordinates. An application to the nucleus ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, which is described as a bound alpha + deuteron system, shows that these new degrees of freedom, which can lead to compressional vibrations, are indeed important. We find that the deuteron cluster is compressed, whereas the size and the compressibility of the alpha cluster are unchanged with respect to the free case.

The use of Wick's theorem and angular momentum recoupling rules to construct perturbative algebraic expressions for the shell-model effective interaction is discussed. The problem is shown to reduce to the evaluation of certain configuration traces, which can be accomplished by techniques previously developed for use in trace-moment statistical spectroscopy. The use of the existing configuration-trace symbol-manipulation programs for automatic generation of complete sets of optimally simplified expressions is summarized. Examples are presented of expressions for fourth-order diagrams and of the simplifications achieved for third-order diagrams.

Shell-model calculations for ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ in an ${\mathrm{}\left(\mathrm{sd}\right)\mathrm{}}^4$-closed ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core basis predict significantly fewer than the observed number of levels below any given excitation energy. Calculations in a ${(p_{\frac{1}{2}}-s_{\frac{1}{2}}-d_{\frac{5}{2}})}^8$-closed ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ core basis predict more levels than the observed numbers. A simple weak-coupling extrapolation gives quite good agreement up to at least 7 MeV (75 levels).

The SU(3) limit of the $\mathrm{U}\left(\frac{6}{12}\right)$ boson-fermion symmetry has been studied in detail. By considering the single-particle structure of states, it has been possible to establish a one-to-one relation between bands in the symmetry scheme and those of the Nilsson model arising from the $2p_{\frac{1}{2}}$, $2p_{\frac{3}{2}}$, and $1f_{\frac{5}{2}}$ shell model states. The specific characteristics of the symmetry are shown to be evidenced empirically in the low lying bands of ${}_{}{}^{185}{}_{}{}^{}\mathrm{W}$. Moreover, it is shown that the $\mathrm{U}\left(\frac{6}{12}\right)$ SU(3) symmetry is able to account for the empirical fact of the fragmentation of single particle strength from the higher lying ½[501], $\frac{3}{2}\mathrm{}\left[501\right]\mathrm{}$, and $\frac{5}{2}\mathrm{}\left[503\right]\mathrm{}$ Nilsson bands. The results mentioned above, and also a comparison between the $B\left(E2\right)$ values predicted for the low lying bands in each model, confirm that the interacting boson-fermion approximation Hamiltonian employed incorporates the effects of Coriolis mixing in the Nilsson model. The question of supersymmetry is also discussed.

We present differential cross sections for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({\pi }^{+},{\pi }^{-}){}_{}{}^{13}{}_{}{}^{}\mathrm{O}(\mathrm{g}.\mathrm{s}.\mathrm{})$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({\pi }^{+},{\pi }^{-}){}_{}{}^{13}{}_{}{}^{}\mathrm{O}\left(4.21\mathrm{} \mathrm{MeV}\right)$ near the ${\Delta }_{33}$ resonance. The former exhibits a slowly varying angular distribution between 0° and 50°, but the excited state angular distribution shows diffractive features observed formerly only in $J^{\pi }=0^{+} \mathrm{to} 0^{+}$ non-analog double-charge-exchange reactions.

We have studied antiproton elastic scattering on Al, Cu, and Pb for two incident momenta: 514 and 633 MeV/c. The angular region covered extends from the forward Coulomb region to approximately 30 deg. The differential cross sections were analyzed using a nonrelativistic optical potential of the Woods-Saxon form, with the imaginary shape taken from electron scattering data. We obtained fits for the strengths of the real and imaginary parts of the potential, ($V_0$, $W_0$), of (51, 116) MeV for Al, (12, 71) MeV for Cu, and (12, 278) MeV for Pb.

The one-pion-exchange potential which depends on a single (cutoff) parameter is shown to provide an adequate description of most of the deuteron observables, provided that the parameter is adjusted to produce the correct binding energy. In particular, the tensor observables $\eta$ and $Q$ are within a few percent of their experimental values. Substituting this potential for the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ potential of a super-soft-core model in a Faddeev calculation of the ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ ground state increases the binding energy by only 0.1 MeV.

Microscopic calculations of the inelastic ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$,${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{\prime }{}_{}{}^{}$) reaction at $E_{\mathrm{lab}}=156\mathrm{}$ MeV are performed by considering knockout as the reaction mechanism. It is shown that such calculations explain the high energy parts of the spectra satisfactorily, but tend to underestimate significantly the low energy tail of the spectra.

We propose an electronic counter experiment for investigating both the existence of anomalous particle fragments and their characteristics. The experiment is based on triggering and isolating the secondary interaction fragments on a solid state multitarget device. This method uses the sensitivity of the anomalous particle fragment effect with respect to absorption experiments and permits us to solve the questions related to the anomalous particle fragment production cross section, their interaction cross section, and their lifetime.

The exchange effect for the alpha-nucleus potential has been computed by folding in the density matrices with a finite range effective interaction. The "effective" exchange interaction is both density and energy dependent. The potential agrees closely with phenomenology.

The coherent phonon state given by Haapakoski et al. is used to derive an analytic expression for the energy spectra valid over the entire range of deformation. An approximation is used to derive a simple expression for the energy spectra in the rotation-vibration region which is compared with the one obtained using Bohr-Mottelson's collective Hamiltonian.

Contrary to Gilmore et al., we show that second-order volume conservation in the liquid-drop model does not give rise to a constraint analogous to boson-number conservation in the interacting-boson model, but rather has only a minor effect on collective-model parameters.

We show that second order conservation of the time-averaged volume in a two-fluid modification of the liquid drop model gives rise to a constraint analogous to boson-number conservation in the interacting-boson model.

Low energy experimental data for the $\alpha -\alpha$ system are accurately described by an attractive local angular momentum and energy independent $\alpha -\alpha$ potential. The Woods-Saxon potential recently derived by Marquez is virtually identical to the Gaussian $\alpha -\alpha$ potential given by Buck et al. in 1977.

It is shown that Friedrich's comment is based on his subjective interpretation of what is new in my work.