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.

Prompt high-energy $\gamma$ rays resulting from neutron capture at thermal energies and in the resonances of ${\mathrm{Sb}}^{121}$ and ${\mathrm{Sb}}^{123}$ have been studied with the high flux beam reactor fast chopper using high-resolution Ge(Li) detectors. The binding energy $B_n$ of the last neutron in ${\mathrm{Sb}}^{122}$ and ${\mathrm{Sb}}^{124}$ has been determined to be 6807 ± 2 and 6468 ± 2 keV, respectively. Based on prompt capture $\gamma$-ray data, we have assigned a spin of 4 to the 21.6-eV resonance of ${\mathrm{Sb}}^{123}$. Energy levels populated by the neutron-capture $\gamma$ rays are given up to an excitation energy of 2475 keV in ${\mathrm{Sb}}^{122}$ and up to 2221 keV in ${\mathrm{Sb}}^{124}$. These data are compared with the existing ($d,p$) data on ${\mathrm{Sb}}^{121}$ and ${\mathrm{Sb}}^{123}$. We have also studied the low-energy (<511 keV) $\gamma$ rays originating in neutron capture in the different resonances. For ${\mathrm{Sb}}^{121}$, the observed spectra are found to fall into two classes, each having its own characteristic intensity distribution depending on the spin of the capturing state. By comparing these spectra with those originating from the 6.24-eV resonance ($3^{+}$) and the 15.4-eV resonance ($2^{+}$), we have assigned the following spins to the resonances in ${\mathrm{Sb}}^{121}$: 29.7 eV (3), 53.5 eV (2), 64.5 eV (3), 73.8 eV (2), 111.4 eV (2), and 126.8 eV (3). Similar, but more tentative, spin assignments are made for resonances in ${\mathrm{Sb}}^{123}$.

The low-energy spectra have also been used to measure the half-life of the 61.6-keV isomeric state in ${\mathrm{Sb}}^{122}$ by a new method. This experimental procedure is described. The half-life of the isomeric state is found to be 2.3 ± 0.6 μsec.

The intensities of the high-energy $\gamma$ rays in the 2.1-day decay of ${}_{}{}^{238}{}_{}{}^{}\mathrm{Np}$ to ${}_{}{}^{238}{}_{}{}^{}\mathrm{Pu}$ are measured using a high-resolution Ge(Li) detector (full width at half maximum of 1.7 keV at 1333 keV). The branching ratios for the transitions from the $\gamma$-vibrational band are found to be consistent with values of (26.5 ± 7.8) × ${10}^{-3\mathrm{}}$ for $z$, the band-mixing parameter for the ground-state rotational and $\gamma$-vibrational bands, and $\approx -7\mathrm{}\times {10}^{-3\mathrm{}}$ for $z_{\beta \gamma }$, the parameter for the mixing of $\beta$- and $\gamma$-vibrational bands.

The ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}(\gamma ,n)$ cross section was measured from threshold to 24 MeV with a photon beam produced by the in-flight annihilation of positrons. The photon beam resolution was determined to be 1.2% (full width at half maximum) by elastically scattering the $\gamma$ rays from the 15.1-MeV level in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The ($\gamma ,n$) cross section was found to have a maximum value of ∼348 mb and an integrated value up to 24 MeV of 1.72 ± 0.16 MeV b. Within the statistics and the photon resolution of the measurement, the results indicate that there is no structure in the cross section, with the possible exception of a weak bump at approximately 17.5 MeV. The results are compared with previous measurements and with theory; the latter comparison indicates that the widths of states in the dynamic collective theory should be considerably broader than those which have been typically used.

The spins of the four lowest neutron resonances in ${\mathrm{Er}}^{167}$ have been determined by measuring the transmission of polarized neutrons through a sample of polarized erbium nuclei. The determination of the spins depends solely on the transmission effect and is independent of any assumption about the sign of the nuclear magnetic moment or the direction of the effective field at the target nuclei. The spins were found to be $J=I+\frac{1}{2}=4\mathrm{}$ for the 0.460-eV resonance and $J=I-\frac{1}{2}=3\mathrm{}$ for the resonances at 0.584, 6.10, and 9.6 eV. The nuclear polarization of the sample, obtained as function of the sample temperature at a fixed energy, was fitted to a theoretical curve, using the magnetic and electric hyperfine splitting constants as fitting parameters. The values found for the magnetic and electric hfs constants are, respectively, $\frac{A}{k}=-0.085\mathrm{}\pm 0.0005$°K and $\frac{P}{k}=-0.005\mathrm{}\pm 0.001$°K. Taking the nuclear magnetic moment of ${\mathrm{Er}}^{167}$ to be $-0.56\mathrm{}{\mu }_N$, the corresponding effective magnetic field at the nucleus is 7.26 × ${10}^6$Oe.

Monochromatic photons obtained from thermal-neutron capture in iron were used for exciting nuclear levels in the energy region between 6 and 9 MeV. Angular distribution of the elastically scattered radiation was carried out for the determination of the spins of the resonance levels. Total and ground-state radiation widths of ten resonance levels in various isotopes were measured using self-absorption, temperature variation, and absolute scattering cross-section measurements. The parity of six resonance levels was measured using a Compton polarimeter, and strong $M1\mathrm{}$ transitions were found in ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$; the character of four transitions was found to be $E1\mathrm{}$. The observed total radiation widths ${\Gamma }_{\gamma }$ of these bound levels were found to have the same magnitude as those of unbound levels obtained in neutron resonances, which indicate that ${\Gamma }_{\gamma }$ is continuous across the ($\gamma ,n$) threshold.

A four-parameter correlation experiment which measured neutron emission in "long-range alpha" (LRA) fission is described. The energies of both the fission fragments and of the $\alpha$ particle as well as the time of flight of the neutron were recorded. The experimental data were analyzed with the aid of a computer, and the method of analysis is described.

Some of the results of the present experiment have already been published. In this paper we discuss the pre-neutron-emission mass distribution of LRA fission as well as some properties of the neutrons as a function of $\alpha$-particle energy. In addition, the neutron kinetic energy as a function of fragment mass is given. The probability of $\alpha$-particle emission as a function of the fission-fragment mass ratio is also discussed.

Lane and Robson have given a stationary-principle formulation of an approximation theory for resonance reactions. They stated a paradox in the stationary principle, which is resolved here in support of the approximation method.

It is shown that the Tabakin potential apparently predicts a deuteron quadrupole moment which is smaller than that previously assumed by a factor of 3. This discrepancy arises from the original use of an inaccurate formula relating the quadrupole moment of the deuteron to the threshold slope of the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ coupling parameter ${\epsilon }_1$. The new value indicates a corresponding Tabakin tensor force which is considerably weaker than is required. Also, the small $D$-wave spin-orbit splitting given by the Tabakin potential at 142 MeV is found to be different from the small experimental value.

The expansion developed previously for the derivation of the relation between the transmission coefficient and the ratio of the average width to the average spacing is reexamined. By rewriting the series in a more convenient form, not only is the objection raised against the expansion removed, but also an estimate of the smallness of the terms which are usually thrown out can be easily made.

In continuation of previous study of the impact-parameter representations of potential scattering amplitudes at large angles, we have numerically evaluated and compared various approximate forms of the impact phases along the trajectories parallel to the initial, final, and average momenta. The necessity of phase averaging in the symmetric forms of the amplitudes is pointed out. None of the presently available approximations seems to be sufficiently accurate to reliably replace the phase-shift analysis at large angles.