The alpha decay of deformed nuclei is studied in the framework of the shell model. It is found that the model is able to describe the clustering of the four nucleons that eventually constitute the alpha particle. The clustering process occurs on the deformed nuclear surface and it is induced by high-lying configurations. The absolute decay width of ${}_{}{}^{222}{}_{}{}^{}\mathrm{Rn}$ is calculated and good agreement with experimental data is obtained.

We calculate the magnetic moments of several hypernuclei using the σ-ω model with the addition of a tensor term to describe the ω-Λ coupling. We find that this change in the Λ coupling induces a modification in the structure of the hyperon sector of the baryonic current and has implications on the structure of the backflow current for finite nuclei. It manifests itself more dramatically in those cases where the Λ is sitting in s states which are precisely the states more likely to be measured experimentally. Our results indicate that, if no large deviations from the Schmidt values are observed experimentally, this might as well indicate a success and not a pitfall of the relativistic approach.

We comment on a recent paper from Adelseck and Saghai. We demonstrate that the data set chosen by these authors is insufficiently constraining to warrant a comparison between resulting models and SU(3) predictions for the coupling constants. Comments are also made on the signs of polarization observables calculated by these authors.

The most recent investigation of the photoactivation of isomeric nuclei reported by Krčmar et al. continues to contain a strong contribution from nonresonant channels. In this Comment we report that integrated cross sections for resonant photoactivation of isomeric levels in ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$, and ${}_{}{}^{113,115}{}_{}{}^{}\mathrm{In}$ have been calculated from recent nuclear structure data and compared to those experimental results which assert that nonresonant contributions are important. The latter have shown systematically smaller values and the amount of missing resonant strength can be correlated to the magnitude of nonresonant cross section found in these investigations. Monte Carlo simulations of realistic experimental geometries display important components in the photon fields, resulting from environmental Compton scattering, which have been omitted in previous analyses of experimental data. The strength and shape of this contribution as a function of the experimentally important parameters suggest that the data can be explained entirely on the basis of a resonant excitation mechanism without any need to introduce a nonresonant contribution.

This paper comments on the arguments of the paper by P. Halse [Phys. Rev. C 39, 1104 (1989)].

I reply to the preceding Comment.

In this paper we develop a practical ‘‘hybrid’’ numerical representation of the nucleon-nucleon T matrix. Part of the expression contains nonseparable terms which are easily calculated, and the rest consists of a separable representation of small rank in terms of Weinberg states. The method rests on the observation that when a set of positive-energy Weinberg states is used to obtain a separable representation of the potential V then the residue ΔV, due to the basis-set truncation, has very special properties: (1) The contribution ΔT to the T matrix due to ΔV is identical to the undistorted T matrix for ΔV alone, ${\mathit{T}}_{\mathrm{\Delta }}$, i.e., the usual Moeller distortion factors in the two-potential formula are unity in this case. (2) A perturbative-iterative treatment of ${\mathit{T}}_{\mathrm{\Delta }}$ in powers of ΔV is found to be equivalent to the finite-rank representation of operators of the type T, T-V, T-V-${\mathit{VG}}_0$V, and so on. This equivalence has both practical and theoretical implications. On the one hand, it provides a reliable method for calculating the T matrix and for analyzing the corresponding accuracy properties. On the other hand, a connection is established between each order of the quasiparticle method and the different variational principles which underlie the finite-rank representation of operators such as T, T-V, T-V-${\mathit{VG}}_0$V, etc. Numerical examples are provided for two different nucleon-nucleon singlet potentials (Reid soft core and Malfliet-Tjon). In the Malfliet-Tjon case, for instance, two Weinberg states are found to be sufficient in order to give an accuracy of 0.1% for the calculation of T-V-${\mathit{VG}}_0$V, while for T-V and T the same two states give an accuracy of 1% and 10%, respectively, in an interval of 6 ${\mathrm{fm}}^{\mathrm{-}1}$ around the on-shell point.

Relativistic effects on the relation between the root-mean-square radius ${\mathit{r}}_{\mathit{D}}$ of the bound state and the scattering length a are examined for models which simulate the triplet S state of the two-nucleon system. Two models are considered; one is based on the one-body Dirac equation and the other on the two-body Dirac equation. The relation is expressed as (${\mathit{r}}_{\mathit{D}}$/a${)}^2$=(${\mathit{c}}_0$+${\mathit{c}}_1$${\mathit{x}}^1$+${\mathit{c}}_2$${\mathit{x}}^2$+...)/8, where x==α${\mathit{r}}_0$; α is related to the binding energy and ${\mathit{r}}_0$ is the effective range. This expansion is compared with the corresponding expansion of the nonrelativistic Schrödinger case. The first three terms are shape independent. The ${\mathit{c}}_0$ (=1) and ${\mathit{c}}_1$ (=0) are the same as those of the nonrelativistic case but a relativistic correction appears in ${\mathit{c}}_2$.

An algorithm is developed by which two nucleon effective interactions are constructed to fit on- and off-shell t- and/or g-matrix elements. The effective interaction is defined as plane-wave matrix elements of local operators that may have explicit energy and medium dependences. It comprises central, tensor, spin-orbit, quadratic spin-orbit, and angular momentum square operators, all with Yukawa form factors. As examples, the Paris and Bonn potentials are used to construct t matrices for projection onto chosen forms of effective interactions.

Four-nucleon binding energies and Faddeev amplitudes are calculated in the integro-differential equation approach, which neglects all N-body correlations with N≥3, for realistic forces in the three-channel approximation. Good agreement is obtained with corresponding results recently obtained by means of the Faddeev-Yakubovsky equations. Thereby, the dominance of two-body correlations, even for realistic forces, is established. The effect of the inclusion of the hypercentral potential in the definition of the (modified) Faddeev amplitudes for realistic forces is investigated and found to be of less importance for realistic forces than for central spin-dependent forces. The three- and four-nucleon modified Faddeev amplitudes are also compared. We found that the D-state Faddeev amplitudes are less sensitive to the number of nucleons, to the inclusion of the hypercentral potential, and to the nucleon-nucleon force than the mixed symmetry S’-state amplitudes.

Angular distributions of the double-differential cross section ${\mathit{d}}^2$σ/dΩ dE(σ) and the spin-flip probability ${\mathit{S}}_{\mathit{n}\mathit{n}}$ have been measured for inclusive proton inelastic scattering from ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ at 290 MeV and from ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ at 318 MeV. Excitation energies up to about 50 MeV for ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ and 40 MeV for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ have been investigated over the laboratory angular ranges of 3° to 12° for ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ and 3° to 9° for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$. Multipole decompositions of angular distributions of both the spin-flip cross section σ${\mathit{S}}_{\mathit{n}\mathit{n}}$ and the estimated cross section for ΔS=0 transitions have been performed. Distributions of strengths were deduced for ΔL=1, ΔS=0 (the giant dipole), ΔL=2, ΔS=0 (the giant quadrupole), ΔL=0, ΔS=1 (the magnetic dipole), ΔL=1, ΔS=1 (the spin dipole), and ΔL=2, ΔS=1 (the spin quadrupole). The ΔS=0 summed strengths for ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ are lower than for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$. The spin-dipole summed strengths are found to be approximately independent of A. For ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, essentially all M1 strength observed was in the 10.23 MeV $1^{+}$ state; for ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$, M1 strength was observed to be fragmented over a range of 7 to 18 Mev.

Cross sections for proton-induced fission of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ have been measured at seven proton energies ranging from 3.0 to 4.45 MeV using a kinematic coincidence technique, and an upper limit established at an energy of 2.5 MeV. Contrary to recent findings of Ajitanand et al. Phys. Rev. Lett. 58, 1520 (1987), the present work indicates that the fission cross section decreases as expected at extreme sub-barrier energies down to a level of ≃20 pb at 3 MeV.

A simple three-body oscillator cluster shell model is proposed as an approximation for wave functions of neutron-rich nuclei, having a (core+2n) structure. The model is applied to the ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$ nucleus. With a few free parameters the model reproduces the experimental rms matter radius of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$, as well as the experimental transverse momentum distribution of the ${}_{}{}^9{}_{}{}^{}\mathrm{Li}$ nucleus resulting from ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$ fragmentation on a carbon target at an energy of 790 MeV/nucleon. The transverse momentum distributions of the neutrons from this reaction have also been calculated without any additional parameters. All geometric parameters of the ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$ nucleus are also calculated within the framework of this three-body model.

In view of new data on the ${}_{}{}^{10}{}_{}{}^{}\mathrm{C}$ superallowed Fermi β decay, the radiative corrections have been reevaluated. In particular we calculate and include the nuclear-structure-dependent part of the axial-vector-induced contribution to the O(α) radiative correction. The resulting ${\mathit{V}}_{\mathit{u}\mathit{d}}$ is appreciably larger than a value recently published, which was based on the same data.

The basic two-nucleon configurations which generate the structure of the nucleon spectral function at high values of momenta and removal energies are analyzed. A model spectral function expressed through a convolution integral of the momentum distributions describing the relative and center-of-mass motion of a correlated pair is suggested and shown to satisfactorily reproduce the spectral function of the three-body system and nuclear matter calculated in terms of realistic nucleon-nucleon interactions in a wide range of nucleon momenta and removal energies.

A method of minimal substitution is used to obtain the electromagnetic two-body interaction current operator associated with a relativistic separable interaction. The result is shown to satisfy a general restriction obtained from current conservation using the Ward-Takahashi identity within the Bethe-Salpeter formalism. It is shown that this two-body relativistic current operator can be reduced to an effective one-body form. Applications of this method to nuclear few-body systems, relativistic quark systems, and hadronic resonance processes are discussed. The numerical size of the interaction current for the pion charge form factor is estimated.