The theory of multistep processes based upon the distorted-wave Born approximation as a leading term is investigated. Iterative procedures in which the many-body Green's operator for the complete system is replaced by a non-Hermitian or optical Green's operator are shown to have some unappealing features. Alternative procedures using a nonlinear form of the distorted transition matrix equation, corresponding to a dispersion-theory approach, are discussed and appear to provide a more consistent iterative procedure. A generalized optical theorem is derived and used to sum the multistep amplitudes which conserve energy. The summed result shows that the normal distorted-wave matrix element should be replaced by a modified leading term unless the absorption in initial and final states is weak. Difficulties with the theory involving multistep amplitudes off the energy shell and a new calculable form for two-step processes are suggested.

The differential cross section ($\frac{d\sigma }{\mathrm{dEd}{\Omega }^2}$) for the $\mathrm{D}\mathrm{}(p,2p)\mathrm{}$ reaction at proton laboratory energies of 20, 45, and 100 MeV is calculated in an exactly soluble model of the three-nucleon system. The model is essentially that of Aaron, Amado, and Yam with the exception that the spin-dependent $S$-wave separable two-nucleon scattering amplitude is modified to fit two-nucleon elastic scattering data at energies above 20 MeV. The coupled integral equations for the model three-nucleon system are solved iteratively, so that the Faddeev-Watson nuclear multiple-scattering series is generated. The multiple-scattering series, itself, is found to diverge at all energies below 100 MeV. The diagonal Padé approximates, which converge quite rapidly, are employed to sum the series. The results of the calculations are in reasonable agreement with experiment.

A critical consideration of the Bethe-Weizsacker relation shows that the surface tension term in it is not appropriate for determining the decrease in nuclear binding energy due to surface effects. The unsuitability of this term makes reconsideration of the expression for energy dependent on nuclear forces imperative and suggests a different approach for the purpose. The energy per nucleon in nuclear matter of different nuclei with an equal number of protons and neutrons and unaffected by Coulomb and asymmetry effects has been found to increase logarithmically with nucleon numbers It is considered that the increase in energy per nucleon with increasing nucleon number in such ideal nuclei is caused by increasing superposition effects of internucleonic forces and is determinable on statistical consideration. The energy in nuclear matter of different nuclei, thus obtained, actually measures the energy caused by nucleonic forces in the Bethe-Weizsacker relation, dependent on nucleon numbers only. The expression for ideal energy of nuclei, reduced by suitable expressions for the decrease in energy because of the different conditions of actual nuclei determines the corresponding expected values. These different amounts of reduction in energy are controlled by the internucleonic forces in ideal conditions and hence by ${\mathcal{E}}_N^0\mathrm{}\left(A\right)\mathrm{}$, the energy per nucleon in nuclear matter. The complete expression for the expected nucleonic energy, $-E_n\mathrm{}\left(A\right)\mathrm{}$, for optimum condition, isobaric nuclei, and different excited states in real nuclei is expressed as $-E_n\mathrm{}\left(A\right)=-{\mathcal{E}}_N^0\mathrm{}\left(A\right)[1-{\alpha }^0{e}^{{\beta }^0{\mathcal{E}}_N^0}-{\alpha }^{†}{e}^{{\beta }^{†}{\mathcal{E}}_N^0}(e^{{\sigma }^{†}{N}^{†}}-1)-{\alpha }^{*}{e}^{{\beta }^{*}{\mathcal{E}}_N^0}(1-e^{-{\sigma }^{*}{N}_i^{*}}\left)\right].\mathrm{}$ The experimental energy per nucleon in strongly bound nuclei of different nucleon number finds good agreement with only the first repulsive term.

The (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$) one-proton transfer reaction is investigated for $\mathrm{fp}$-shell targets ranging from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ to ${}_{}{}^{70}{}_{}{}^{}\mathrm{Zn}$, at incident energies $E\left({}_{}{}^{16}{}_{}{}^{}\mathrm{O}\right)=42.0,48.0\mathrm{}$, and 56.0 MeV. Angular distributions for the prominent transitions are presented. The results are discussed in a semiclassical model and are analyzed by finite-range distorted-wave Born-approximation (DWBA) calculations. With two sets of optical-model parameters, fixed for the whole region of nuclei, the extracted relative strengths of the transitions are consistent with those known from (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) reactions. The absolute strengths are found to be sensitive to the specific choice of the parameters used in the DWBA. A reexamination of the data that had been interpreted as indications of two-step processes in the (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$) reaction to final states in ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ leads to the conclusion that there is no evidence for such processes in this case at the incident energy employed.

The mass of the $N=Z$ nucleus ${}_{32}{}^{64}{}_{}{}^{}\mathrm{Ge}$ has been measured by determining the positron endpoint energy from the prominent decay to the 427-keV state in ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ga}$. The ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},2n){}_{}{}^{64}{}_{}{}^{}\mathrm{Ge}$ reaction was used to produce ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ge}$, at a bombarding energy of 36 MeV. Off-line ${\beta }^{+}-\gamma$ coincidences were studied, as well as the half-life of the 427-keV transition. The half-life was observed to be 70 ± 7 sec, in agreement with a previous measurement. The observed endpoint energy was 2.96 ± 0.25 MeV, leading to a total decay energy of 4.41 ± 0.25 MeV, and a mass excess of -54.43 ± 0.25 MeV for ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ge}$. Implications for nucleosynthesis and the solar system abundance of ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ are discussed.

Excited states of ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ which deexcite via $\gamma$-ray cascades through the 823-keV state were studied using the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({}_{}{}^3{}_{}{}^{}\mathrm{He},p)$ reaction at a beam energy of $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=2.88\mathrm{}$ MeV. Particle $\gamma$-ray angular correlations in a standard collinear geometry were obtained using NaI detectors for observing those $\gamma$ rays which were in coincidence with proton groups representing excited states up to 4.3 MeV excitation. The analysis of these data involved the simultaneous fitting of the correlations of all possible cascading $\gamma$ rays from the state under study and resulted in the measurement of spins, branching, and multipole mixing ratios for some excited states and their subsequent electromagnetic deexcitations. Coincident $\gamma$-ray spectra were also obtained with a Ge(Li) detector which provided additional information regarding the more complex decay schemes. Previously unreported lifetime information for the 1824- and 1972-keV states was obtained using the Doppler-shift-attenuation method and the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(t,n\gamma ){}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ reaction at a beam energy of $E_t\simeq 2.85$ MeV. These mean lifetimes are ≤ 65 fsec and ≥ 1.1 psec, respectively. The combined data for the 1824-keV state, as well as recently reported two-particle transfer data, suggest that the 823- and 1824-keV states are the $J^{\pi }=4^{+}$ and $5^{+}$ members, respectively, of the ground-state rotational band. Data obtained regarding the 1972-keV state suggest that this state has a $J^{\pi }=3^{-}$ assignment, while those for the 2195-keV state imply a $J^{\pi }=3^{+}$ assignment. The results of this experiment are compared with recently reported shell-model calculations.

The 8.65- and 8.69-MeV states in ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ have been studied with the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ reaction, with a resolution of 9 keV (full width at half maximum). Comparison of absolute spectroscopic strengths for this reaction and for the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}\mathrm{}(d,p)\mathrm{}{}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ reaction to the 9.19-MeV ($J^{\pi }={\frac{7}{2}}^{+}$) and 9.27-MeV ($J^{\pi }={\frac{5}{2}}^{+}$) states in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ shows unambiguously that the spin sequence in ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ is the same as in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$. An additional outcome of the present experiment is a measurement of the width of the 8.69-MeV state: ${\Gamma }_{\mathrm{TOTAL}}=15\mathrm{}\pm 1$ keV. The natural width of the 8.65-MeV state is considerably less than the experimental resolution width of 9 keV.

Angular distributions from the ($d,p$) reaction on ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ and ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ have been obtained with the 12-MeV deuteron beam of the Argonne tandem Van de Graaff. Excitation energies and $l$- transfer values have been obtained for a number of levels below 2 MeV excitation. The ground state of ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ga}$ is not excited with observable cross section in the ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}\mathrm{}(d,p)\mathrm{}{}_{}{}^{72}{}_{}{}^{}\mathrm{Ga}$ reaction. The first level excited with an appreciable cross section is the $1^{+}$ level at 161 keV in ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ga}$. The ($d,t$) reaction on ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ proceeds to the ground state of ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ga}$ and, over the energy range covered, excites most of the levels observed to have a strong $l=1\mathrm{}$ component in the ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}\mathrm{}(d,p)\mathrm{}{}_{}{}^{70}{}_{}{}^{}\mathrm{Ga}$ reaction. The excitation of the ground state of ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ga}$ via neutron pickup from ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ suggests that the neutron ground-state wave function of ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ga}$ has a large $\left(1\mathrm{}{g}_{\frac{9}{2}}\right)_{\frac{5}{2+}}^{}{}_{}{}^3$ component.

The reactions ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{46}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,t)\mathrm{}{}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ were studied simultaneously with a counter telescope at a beam energy of 41.65 MeV. Experimental resolution for the reaction products was 50 keV for tritons and 90 keV for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Angular distributions from 20 to 60° were obtained for 12 low-lying states in ${}_{}{}^{46}{}_{}{}^{}\mathrm{K}$, for 8 of their $T=4\mathrm{}$ analogs in ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$, and for 14 lower-lying ($T=3\mathrm{}$) states in ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$. Comparison of the angular distributions with those for known final states and with distorted-wave Born-approximation calculations allowed $L$ assignments for most of the observed transitions. The combination of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,t)\mathrm{}{}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ (analog) and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{46}{}_{}{}^{}\mathrm{K}$ results helped resolve some divergent $J^{\pi }$ suggestions for ${}_{}{}^{46}{}_{}{}^{}\mathrm{K}$ found in the literature. At least three ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ levels at the location of the unnatural-parity $T=4\mathrm{}$ analog states for ${}_{}{}^{46}{}_{}{}^{}\mathrm{K}$ were excited in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,t)\mathrm{}$ with about 10% of the strength of the neighboring natural parity $T=4\mathrm{}$ states. This seems to indicate that the familiar one-step zero-range interpretation of ($p,t$) transfers in this case is less reliable than usual. Another unexpected result was our failure to see a strong $0^{+}$ state in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{46}{}_{}{}^{}\mathrm{K}$.

A measurement of the $\beta$ spectrum of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$ was undertaken to resolve some discrepancies in recently reported values of the branching of the $\beta$ decay to the ground state of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$. Sources of mass-separated ${}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$, provided by the TRISTAN on-line isotope separator, were investigated with a high-resolution $\pi \sqrt{2}$ magnetic spectrometer. Using constraints based on previous $\gamma$-ray decay schemes, the measurement yielded a $Q$ value of 3.888 ± 0.007 MeV and a ground-state $\beta$ intensity of (30.5 ± 2.2)%. In addition, the intensity ratio for an unresolved $\gamma$-ray doublet at 2555 keV was independently determined on the basis of $\beta$-branch intensities to the levels at 2555 and 2960 keV.

Knockout of $\alpha$ particles by 156-MeV protons from ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$, and ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ has been used to investigate the $A$ dependence of $\alpha$ clustering in nuclei. Protons and $\alpha$ particles were detected in coincidence under conditions of quasifree scattering. Corresponding reaction cross sections were measured. Cross sections for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ were found to be about 2 orders of magnitude lower than for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. The cross section for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ was found to be about 3 times lower than that for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. Upper limits of the integrated cross sections for ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$ and ${}_{}{}^{232}{}_{}{}^{}\mathrm{U}$ are still compatible with a $A^{\frac{2}{3}}$ dependence of the $\alpha$ knockout process.

A Ge(Li) detector was used to measure $\gamma$-ray transitions in ${}_{}{}^{39}{}_{}{}^{}\mathrm{Cl}$ via proton-$\gamma$ coincidence studies in the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}(t,p\gamma ){}_{}{}^{39}{}_{}{}^{}\mathrm{Cl}$ reaction at $E_t=3.4\mathrm{}$ MeV. Measurements were carried out with the proton detector centered at 180° and the $\gamma$-ray detector at 90° and 0° to the beam. Excitation energies and $\gamma$-ray branching ratios were determined for the first 14 levels of ${}_{}{}^{39}{}_{}{}^{}\mathrm{Cl}$. The mean lives of these ${}_{}{}^{39}{}_{}{}^{}\mathrm{Cl}$ states were deduced from the Doppler-shift attenuations observed in the primary transitions. The excitation energies (in keV) and mean lives (in psec) resulting from these measurements are as follows: 396 (> 2.0), 1301 (> 3.0), 1695 (${1.1}_{-0.5\mathrm{}}^{+1.4\mathrm{}}$), 1722 (0.44 ± 0.09), 1745 (1.3 ± 0.4), 1786 (>2.0), 2061 (<0.05), 2238 (0.08 ± 0.04), 2424 (>1.8), 2490 (0.10 ± 0.05), 2586 (<0.3), 2835 (>1.8), 3116 (0.21 ± 0.06), and 3534 (<0.2).

Directional correlations were carried out with a NaI-Ge(Li) detector arrangement on three $2^{+}$ → $2^{+}$ cascades in ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$. The data yield the following $\delta$ values: -1.46(14), -0.14(4), and +0.29(5) for the 806-, 1261-, and 1745-keV transitions to the first excited $2^{+}$ level. The first two results confirm recent values from ($n,\gamma$) work but not the earlier ones from radioactivity studies. A new 2822-keV transition was observed from a level at that energy.

One-dimensional scattering from two mobile rectangular potential wells in a bound state is studied in order to investigate the contributions from the overlapping-potential region. The above model is used to compare the exact solution in the "fixed-scatterer" approximation with the corresponding ones obtained assuming non-overlapping potentials and additivity of phase shifts. The kinematics of the "fixed-scatterer" and "impulse" approximations are also examined, and the differences are found to be still significant at intermediate energies. For non-overlapping potentials the composite scattering is completely determined in terms of the individual scattering coefficients or on-shell information, and the solution is given by a linear system of coupled algebraic equations. Unfortunately, as far as scattering information is concerned the overlapping-potential region is the interesting one, since it offers the possibility of discriminating among phase-shift-equivalent potentials and of determining the short-range behavior of the wave function. Our results suggest that the predictions provided by the non-overlapping potentials or additivity of phase-shifts assumptions deviate sufficiently from the exact result to render ambiguous the extraction of the distribution function or two-body interaction from elastic intermediate-energy scattering in terms of either of these two models.

Projection of good angular momentum states has been performed for the deformed self-consistent solutions of even Ti, Cr, and Fe isotopes for the central Yukawa and Kuo-Brown interactions. The results from the two interactions are generally similar though striking dissimilarity in the level spacings is also observed in quite a few cases. The percentage composition of the different angular momentum states in a given deformed solution has been also calculated and compared for both the interactions. The energy spectra, when compared with the known experimental results, are found to agree qualitatively.

The reactions ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}(p,p^{\prime })$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}(\alpha ,{\alpha }^{\prime })$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$(${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$′), and ${}_{}{}^{48}{}_{}{}^{}V\left({\beta }^{+}\right)$ have been employed to measure excitation energies, lifetimes, and $\gamma$-decay branching ratios for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$ levels with $E_x<3.5\mathrm{}$ MeV. The results for excitation energies (in keV) and corresponding lifetimes (in psec) are: 983.35±0.10, 6.0±1.3; 2295.5±0.15, 2.4±0.6; 2420.3±0.15, 0.035±0.007; 2997.4±0.25, 0.160±0.032; 3223.5±0.20, ${0.042}_{-0.014\mathrm{}}^{+0.018\mathrm{}}$; 3239.7±0.35, ${0.044}_{-0.016\mathrm{}}^{+0.019\mathrm{}}$; 3358.7±0.65, 0.350±0.087; 3370.7±0.30, 0.018±0.007. Reduced electromagnetic-transition matrix elements have also been derived from the data. No evidence is found for a doublet at an energy of 3.224 MeV. The previous data on the 3.224-MeV level are reexamined in the light of the present results, and the tentative assignment $J^{\pi }=3^{+}$ is consistent with all data. A tentative assignment of $J^{\pi }=4^{+}$ is given to the level at 3.240 MeV. The present results are in reasonable agreement with the predictions of a model in which the valence nucleons are confined to the $f_{\frac{7}{2}}$ orbital.

Levels in ${}_{}{}^{25}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$ were populated via the ($p,t$) and ($p,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions with 27-MeV protons on a ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ target. Angular distributions of emitted tritons and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ were measured simultaneously with a detector telescope. Zero-range distorted-wave Born-approximation (DWBA) calculations with simple shell-model configurations for the two transferred nucleons provided satisfactory fits for several of the observed diffraction patterns. A sharp rise in cross section at forward angles was a good indication of the presence of $L=0\mathrm{}$ transfer even though transitions occurred with a mixture of $L$ values. Compound-nucleus calculations reproduced the smooth angular-distribution shapes observed for higher excited levels but predicted cross sections consistently larger than those observed. For the first ${\frac{1}{2}}^{+}$ levels neither DWBA, compound-nucleus, nor a direct two-step ($p,d$) ($d,t$) calculation were able to give a satisfactory description of the data.

Inelastic scattering experiments, using the ${}_{}{}^{84}{}_{}{}^{}\mathrm{Sr}(\alpha ,{\alpha }^{\prime })$, ${}_{}{}^{84}{}_{}{}^{}\mathrm{Sr}(\alpha ,{\alpha }^{\prime }\gamma )$, ${}_{}{}^{84}{}_{}{}^{}\mathrm{Sr}(p,p^{\prime })$, and ${}_{}{}^{84}{}_{}{}^{}\mathrm{Sr}(p,p^{\prime }\gamma )$ reactions, were performed on 82.2% enriched ${}_{}{}^{84}{}_{}{}^{}\mathrm{Sr}$ targets with solid-state detectors. The 18-MeV $\alpha$-particle inelastic scattering measurements resulted in the identification of excited states at 0.793, 1.454, 1.767, 2.07, 2.447, 2.62, 2.75, 2.81, 2.87, (3.01), 3.16, 3.24, 3.32, 3.46, 3.52, 3.65, 3.96, 4.25, 4.36, 4.55, 4.66, and 4.74 MeV, whereas the 13-MeV proton measurements resulted in identification of excited states at 0.793, 1.454, (1.502), 1.767, 2.07, 2.447, 2.76, (2.81), 2.88, (3.02), 3.18, (3.24), (3.34), 3.40, (3.48), and (3.53) MeV. Angular distributions of 13-MeV deuterons inelastically scattered from the 0.793- and 2.447- MeV states were measured with an Enge magnetic spectrograph and were fitted by $L=2\mathrm{}$ and $L=3\mathrm{}$ distorted-wave Born-approximation angular-momentum-transfer curves, respectively. Deformation parameters ${\beta }_2=0.150\mathrm{}$ and ${\beta }_3=0.129\mathrm{}$ were deduced.

The energy levels, static moments, and electromagnetic transition probabilities in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ are calculated from the projected multishell Hartree-Fock wave functions obtained with a realistic $\mathrm{NN}$ interaction. The modified Elliott interaction is employed as the realistic $\mathrm{NN}$ interaction. The results of these calculations are in good agreement with the experimental data. In particular, the magnetic moment of the ground state and the excitation energy of the first ${\frac{1}{2}}^{+}$ state in both the nuclei are predicted accurately. The computed $\mathrm{ft}$ values of the $\beta$ transitions to the states in the two nuclei are in semiquantitative agreement with the experimental data.

A study has been made of $\gamma$-ray deexcitations following the $\beta$ decays of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Kr}$ and ${}_{}{}^{89}{}_{}{}^{}\mathrm{Rb}$. The activities were produced from the TRISTAN on-line isotope-separator system. Measurements of $\gamma$-ray energies and intensities were made using Ge(Li) detectors. Level schemes have been constructed for ${}_{}{}^{89}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{89}{}_{}{}^{}\mathrm{Sr}$ with the aid of $\gamma -\gamma$ coincidence information, and $\beta$ branching was determined from equilibrium data and $\gamma$-intensity balances. The excited levels of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Sr}$ appear to be explained by single-particle states and the coupling of single-particle states to the vibration states of ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$. The ${}_{}{}^{89}{}_{}{}^{}\mathrm{Rb}$ nucleus is shown to have a complex level scheme and will require further studies to clarify the picture of its nuclear structure.