States in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Ni}$ have been observed at excitations of 2.45 ± 0.01 and 3.00 ± 0.01 MeV using the ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{57}{}_{}{}^{}\mathrm{Ni}$ reaction, confirming previous indications of their existence from ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(\alpha ,n\gamma ){}_{}{}^{57}{}_{}{}^{}\mathrm{Ni}$ studies.

Additional data on neutron-proton bremsstrahlung measurements at 208-MeV neutron energy are presented. These are at $({\theta }_n,{\theta }_p)=({40}^{\circ },{30}^{\circ })$ and (45°, 30°). Also, the analysis of the symmetric-angle data reported earlier has been improved resulting in small changes in the cross sections.

The excitation function for all neutron groups leading to the formation of the 6.38-sec first excited state of ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ was measured for incident proton energies from 5.2 to 8.0 MeV by detecting the residual radioactivity. Resonances were observed corresponding to 19 levels in ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ ranging in excitation energy from 13.43 to 16.10 MeV. For the first four resonances, which are due to the $n_1$ group alone, neutron angular distributions were measured. $R$-matrix calculations produced fits to the excitation curve and angular distributions which permit spin and parity assignments of ${\frac{1}{2}}^{+}$, ${\frac{3}{2}}^{+}$, ${\frac{3}{2}}^{-}$, and ${\frac{5}{2}}^{+}$ to the levels of excitation energies 13.433, 13.703, 13.867, and 13.998 ± 0.015 MeV, respectively. Possible correspondence to isobaric analog states in ${}_{}{}^{27}{}_{}{}^{}\mathrm{Mg}$ is discussed.

In this paper we evaluate the radiative photon spectrum and the branching ratio $R$ of radiative-to-ordinary muon capture rate in ${\mathrm{Ca}}^{40}$, taking into account the nucleon-nucleon residual interaction by means of Migdal's quasiparticle model.

The most important effect of the residual interaction is to reduce both the ordinary and radiative rate about 40% lower than that obtained in the closure-harmonic-oscillator model. This result differs from that obtained by Fearing using the giant-dipole-resonance model, while it confirms the prediction of Rood and Tolhoek (RT) that the branching ratio $R$ would be nearly independent of the nuclear model. We also evaluate the circular polarization of the photons, $P_{\gamma }$. We find that our values of $P_{\gamma }$ are greater than the RT values by about 15% in the high-energy range. In the low-energy range, our values of $P_{\gamma }$ are in close agreement with those of RT. For the maximum energy of the photon spectrum, we obtain the average value $k_{max}=90.5\mathrm{}$ MeV, which is very close to the RT value.

Comparing our results with the experimental data of Conversi, Diebold, and Di Lella, we find that our calculation requires $g_P=(12.4\mathrm{}\pm 2.8)g_A$ to fit the experimental values, where $g_P$ is the induced pseudoscalar coupling constant and $g_A$ the axial-vector coupling constant.

Finally, we think that the disagreement between our result and the more currently accepted value of $g_P$ is not so great as to call into question the theoretical mechanism of the radiative capture, if one takes into account the large experimental uncertainties.

The levels of ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ up to an excitation energy of 7 MeV have been investigated by the ${}_{}{}^{86}{}_{}{}^{}\mathrm{Sr}\mathrm{}(t,p)\mathrm{}$ reaction with 15-MeV tritons. Proton spectra were measured by a $\Delta E-E$ counter telescope system with an over-all resolution of 35 keV, and close-lying peaks were resolved by additional measurements with a magnetic spectrograph. Angular distributions were measured from 12.5 to 90°, and comparisons with zero-range distorted-wave Born-approximation calculations permitted spin assignments of 32 of the 45 levels observed. Four excited $0^{+}$ states were observed. From a comparison of their cross sections with the ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}\mathrm{}(t,p)\mathrm{}{}_{}{}^{90}{}_{}{}^{}\mathrm{Sr}$ groundstate cross section, no one of them could be identified as the pairing vibration state; the strength of the latter appears to be fragmented. The data are compared with previous information on the ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ level structure.

The energies, spins, decay modes, and lifetimes of the first three excited states of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ have been determined. The results are: 3.832 MeV ($2^{+}$), 0.053 ± 0.024 psec; 4.284 MeV ($0^{+}$), 322 ± 16 psec; and 4.507 MeV ($3^{-}$), ${8.8}_{-2.8\mathrm{}}^{+5.5\mathrm{}}$ psec.

The presence of dynamical deformations in the ground-state charge distributions of the calcium isotopes provides a basis for understanding two well-known but very different effects observed in elastic electron scattering from these isotopes.

The first, seen at low momentum transfer, is the anomalous isotope dependence of the nuclear charge radius. It is shown that there is a deformation-dependent contribution to the rms radius, whose magnitude can be obtained from inelastic electron and $\alpha$-particle scattering via a sum rule and which leads to a prediction of the isotopic dependence in substantial agreement with experiment.

The second observed effect, visible at high momentum transfer, is the appearance of oscillations in the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ charge distributions, as revealed by fits to the elastic electron scattering data at 750 MeV. It is shown that an additional contribution of dynamical deformations to monopole elastic electron scattering, observable only at high momentum transfer, may be interpreted as due to an effective spherically symmetric "modulating charge" distribution superimposed upon the smoothly varying distribution obtained at lower energies. This modulating charge is calculated explicitly and exhibits an oscillatory behavior.

The penetrability is computed exactly for a fission barrier $V\left(\epsilon \right)$ defined in terms of two parabolic peaks connected smoothly with a third parabola forming the intermediate well. The potential is specified by the peak energies $E_1$ and $E_3$ and the minimum energy $E_2$ of the connecting curve, along with the constants $\hslash {\omega }_1$, $\hslash {\omega }_3$, and $\hslash {\omega }_2$ related to the curvatures of the three parabolas. For an incident wave of unit amplitude, the amplitude of the transmitted wave is determined by requiring that the wave functions (expressed exactly in terms of parabolic-cylinder functions) and their first derivatives match at the points where the parabolas are connected. The penetrability is then obtained from the amplitude of the transmitted wave. The transmission is essentially an increasing exponential function exhibiting narrow resonances at the positions of quasibound states in the intermediate well. The widths of these resonances are extremely small (∼10 eV) for the levels near the bottom of the well but increase dramatically as the energy increases. This trend continues in some cases above the top of the barrier, producing broad peaks in the penetrability function. The exact penetrabilities are accurately reproduced by the WKB approximation for energies well below the barrier tops, but for energies near the barrier tops the WKB approximation is found to overestimate the penetrability for the cases studied.

The $\alpha$ decay of ${}_{}{}^{255}{}_{}{}^{}\mathrm{No}$ and ${}_{}{}^{257}{}_{}{}^{}\mathrm{No}$ produced by ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},\alpha 2n){}_{}{}^{255}{}_{}{}^{}\mathrm{No}$ and ${}_{}{}^{248}{}_{}{}^{}\mathrm{Cm}({}_{}{}^{13}{}_{}{}^{}\mathrm{C},4n){}_{}{}^{257}{}_{}{}^{}\mathrm{No}$ reactions, respectively, has been studied. Five $\alpha$-particle groups with energies and intensities 8.30 (3%), 8.25 (6%), 8.11 (57%), 7.92 (19%), and 7.76 MeV (15%) were assigned to ${}_{}{}^{255}{}_{}{}^{}\mathrm{No}$; and three $\alpha$-particle groups with energies 8.32, 8.27, and 8.22 MeV to ${}_{}{}^{257}{}_{}{}^{}\mathrm{No}$. The half-lives of ${}_{}{}^{255}{}_{}{}^{}\mathrm{No}$ and ${}_{}{}^{257}{}_{}{}^{}\mathrm{No}$ were measured to be 200±10 and 26 ± 2 sec, respectively. The decay schemes of ${}_{}{}^{255}{}_{}{}^{}\mathrm{No}$ and ${}_{}{}^{257}{}_{}{}^{}\mathrm{No}$ are discussed.

Results are presented for the elastic scattering of 30.3-MeV polarized protons from targets of ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The angular region from 10 to 165° is covered with an absolute accuracy in the polarization measurements of about 0.01. The data, together with corresponding differential cross-section data previously reported, are analyzed using the optical model. Two forms of the model are used: (1) the standard version with independent geometries and ten parameters; and (2) the folding version of Greenlees, Pyle, and Tang with eight parameters. Good fits to the data are obtained, particularly for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Evidence is presented to support the suggestion that such models are most satisfactory for large nuclei (${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$), and that for smaller nuclei (${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$) second-order corrections ignored in the model are playing a nonnegligible role.

The analog of the ground state of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ was investigated by both the ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}\mathrm{}(p,n)\mathrm{}{}_{}{}^{209}{}_{}{}^{}\mathrm{Po}$ and the ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p,n\overline{p}){}_{}{}^{208}{}_{}{}^{}\mathrm{Bi}$ reactions. The Coulomb energy difference ${}_{}{}^{209}{}_{}{}^{}\mathrm{Po}$-${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ was determined as 18.92 ± 0.03 MeV, and the relative partial widths for proton decay into the $p_{\frac{1}{2}}$, $f_{\frac{5}{2}}$, and $p_{\frac{3}{2}}$ channels were determined. The total width of the analog state was found to be 380 ± 80 keV.

$\gamma$ rays emitted in 9.4-day ${\mathrm{Gd}}^{149}$ have been studied with Ge(Li) and NaI(Tl) detectors. $25\gamma$ rays have been attributed to the decay of ${\mathrm{Gd}}^{149}$ with energies and relative intensities of 149.6 (233), 214.5 (0.81), 252.3 (1.1), 260.5 (5.8), 272.0 (15), 298.5 (127), $346.5\left(\equiv 100\right)$, 405.5 (3.7), 430 (0.33), 459.9 (2.4), 478.7 (0.95), 496.4 (7.2), 516.4 (11), 534.2 (13), 645.2 (5.9), 663.3 (1.1), 666.2 (3.9), 748.2 (35), 788.6 (30), 812.4 (0.55), 863 (0.32), 875.8 (0.90), 933.3 (2.2), 939.1 (9.0), and 947.7 keV (3.7). On the basis of coincidence and anticoincidence experiments, relative intensities, and energy sums, states in ${\mathrm{Eu}}^{149}$ have been placed at 0, 149.6, 459.9, 496.2, 534.2, 666.0, 748.2, 794.8, 812.4, 875.8, 933.3, 939.1, and 1097.3 keV. The ${\mathrm{Eu}}^{149}$ x-ray intensity has also been measured. From our $\gamma$-transition intensities and published conversion-electron intensities, conversion coefficients were obtained for most of the electromagnetic transitions, thus allowing multipolarity assignments to be made for these transitions. These assignments, together with the $log\mathrm{ft}$ values, were then used for the placement of limits on the spins of the deduced levels. Our proposed decay scheme is compared with previously published decay schemes and is discussed in terms of current models.

The $g$ factors of the first and the second excited $2^{+}$ state in ${\mathrm{Pt}}^{192}$ have been measured by observing the integral rotation of the directional correlation pattern in the internal magnetic field acting on Pt nuclei implanted in an iron host. Both values, $g_{316}=0.27\mathrm{}\pm 0.02$ and $g_{612}={0.30}_{-0.04\mathrm{}}^{+0.06\mathrm{}}$, are higher than those predicted by the pairing-plus-quadrupole model of Kumar and Baranger.

An extensive study of ${}_{}{}^{90,91}{}_{}{}^{}\mathrm{Zr}\mathrm{}(d,p)\mathrm{}$ excitation functions has been carried out for deuteron energies from 5 to 11 MeV, in order to investigate the extent and systematic behavior of charge-exchange contributions to the ($d,p$) process. Nine residual states in ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$, up to excitations of 3.7 MeV, were involved, as well as three residual states of ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$, up to 1.5 MeV in excitation. In addition, deuteron elastic scattering from ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$ was measured from 5 to 11.0 MeV, and proton elastic scattering from 9.5 to 14.0 MeV. Energy-dependent optical potentials were extracted from the elastic scattering data, and distorted-wave Born approximation analyses were performed for the ($d,p$) data. An effort is made to demonstrate and summarize the various factors contributing to the manifestation of the charge-exchange threshold effect in ($d,p$). To provide the necessary perspective, a considerable amount of other data bearing on the nature of the effect is briefly described, including possible observation of charge-exchange effects with mass-50 targets, comparison of ($p,n\tilde{p}$) and ($d,n\tilde{p}$) excitation curves near threshold, and resonance behavior in ($p,p$) and ($d,p$), which can confuse the experimental and theoretical situation. The experimental evidence is concluded to be consistent with the Lane model of such processes, suggested by Zaidi and von Brentano.

Excitation functions for the ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}\mathrm{}(d,p)\mathrm{}{}_{}{}^{93}{}_{}{}^{}\mathrm{Zr}$ reaction to eight low-lying states in ${}_{}{}^{93}{}_{}{}^{}\mathrm{Zr}$ were measured from 4.2- to 11.2-MeV incident deuteron energy, a region including the ($d,n$) thresholds to the analogs of the observed states. Charge-exchange effects were observed for at least the $d_{\frac{5}{2}}$ ground state in ${}_{}{}^{93}{}_{}{}^{}\mathrm{Zr}$. Also, ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}\mathrm{}(d,d)\mathrm{}$ angular distributions were taken at 6.25, 7.5, and 11.0 MeV, in 5° steps from 40 to 165°, in order to obtain deuteron optical parameters. A ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}\mathrm{}(p,p)\mathrm{}$ angular distribution was taken at 10.75-MeV proton energy in order to obtain proton optical parameters. Orbital angular momenta and estimates of spectroscopic factors were obtained for three previously unreported states in ${}_{}{}^{93}{}_{}{}^{}\mathrm{Zr}$. The results of distorted-wave Born-approximation calculations for the excitation curves are discussed.