The cross sections of ($p,2p$), ($p,pn$), and ($p,2n$) reactions at 300 MeV on the separated isotopes of tellurium were determined. The total ($p,pn$) cross sections, for those cases in which it was only possible to measure one of the isomeric states in the product, was calculated by assuming that the direct knockout mechanism was predominant. Both the total ($p,pn$) cross sections and the ($p,2n$) cross sections are directly proportional to the neutron skin thickness. This is consistent with the assumption that these reactions take place by direct knockout processes in the diffuse or peripheral region of the nucleus. The tellurium ($p,2p$) reactions were observed to be inversely proportional to the neutron skin thickness.

The $N=81\mathrm{}$ isomer ${\mathrm{Gd}}^{145m}$ is characterized as having a half-life of 85 ± 3 sec and an $M4\mathrm{}$ isomeric transition of 721.4 ± 0.4 keV. It also has a direct $\frac{{\beta }^{+}}{\epsilon }$ branch to the $h_{\frac{11}{2}}$ state at 716.1 keV in ${\mathrm{Eu}}^{145}$. The intensity of this branch is 4.7% of the decay, implying a $log\mathrm{ft}$ of 6.2. The $M4\mathrm{}$ transition probability is calculated and compared with the trends among other isomeric transitions in this region.

Calculation of electric monopole $X$ ratios in deformed nuclei using the higher-order shape deformations $Y_4$ and $Y_6$ yields much better agreement with measured values than is obtained when only pure quadrupole surfaces are assumed. Use was made of recently measured values of ${\beta }_4$, and ${\beta }_6$.

Elastic and inelastic scattering of monochromatic photons were used for studying nuclear energy levels in ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$; the photons were produced by thermal-neutron capture in titanium and iron. Two independent resonance lines at 6418 and 6760 keV were excited with the titanium $\gamma$ source, and three independent resonances at 6018, 7279, and 7632 keV were excited with the iron $\gamma$ source. Some 18 known low-lying levels were populated by deexcitation of these resonance levels. The angular distribution of some intense elastic and inelastic lines were measured and the following spin and parity determinations (keV, $J^{\pi }$) were made: 166, $\frac{5}{2}$; 1220, $\frac{5}{2}$, ($\frac{9}{2}$); 1384, $\frac{7}{2}$; 1419, $\frac{7}{2}$, ($\frac{11}{2}$); 1536, $\frac{7}{2}$; 1580, $\frac{9}{2}$; 2232, ($\frac{7}{2},\frac{11}{2}$); 6018, ${\frac{7}{2}}^{-}$; 6418, ${\frac{9}{2}}^{-}$; and 6760, $\frac{7}{2}$, where parentheses denote uncertainties. The parities of the 6018- and 6418-keV levels were directly determined using a Compton polarimeter. The total radiative widths of the 6018- and 6418-keV levels were measured and found to be ${\Gamma }_{\gamma }=0.051\mathrm{} \mathrm{and} 0.081$ eV, respectively. The ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ levels are compared with recent theoretical calculations.

Two new isotopes of californium have been identified through bombardments of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$ with ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ions from the Oak Ridge isochronous cyclotron. They decay with half-lives of 3.78 ± 0.70 and 1.06 ± 0.15 min and with the emission of $\alpha$ particles of 7.335 ± 0.005 and 7.590 ± 0.010 MeV, respectively. Analysis of the excitation functions for these $\alpha$ emitters favors the assignment of mass 241 to the former and mass 240 to the latter; also, the 7.335-MeV activity was shown to be chemically similar to californium. New values for the $\alpha$-particle energies of ${}_{}{}^{242}{}_{}{}^{}\mathrm{Cf}$ were obtained: 7.385 ± 0.004 and 7.351 ± 0.006 MeV, assigned, respectively, to $\alpha$-decay transitions to the ground and first excited states of ${}_{}{}^{238}{}_{}{}^{}\mathrm{Cm}$.

The average-resonance method of neutron-capture $\gamma$-ray spectroscopy is critically examined by means of measurements on stable isotopes of palladium, gadolinium, holmium, and erbium. A mathematical model of the capture process is developed. This model shows that the intensities of the lines in average-resonance-capture spectra can yield the parities and set narrow limits on the spins of states in almost all nuclides with $A>\mathrm{}100\mathrm{}$ if the $\gamma$-ray strength function is a smooth function of $\gamma$-ray energy and if the random fluctuations in intensity result only from the Porter-Thomas distribution of partial radiation widths. The measurements give extensive data for ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{158}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{166}{}_{}{}^{}\mathrm{Ho}$, and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$, and some for ${}_{}{}^{103}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{105}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{155}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{157}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{165}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$, and ${}_{}{}^{169}{}_{}{}^{}\mathrm{Er}$. These data are examined for information relating to the mechanisms of radiative capture. All of the data are consistent with the hypothesis that the radiation widths are a smooth function of $\gamma$-ray energy and that the random fluctuations in intensity are well described by the Porter-Thomas distribution. The intensities of $E1\mathrm{}$ transitions vary with $\gamma$-ray energy more rapidly than $E_{\gamma }^{}{}_{}{}^3$, as expected from a giant-resonance description of the radiative process. The intensity of $M1\mathrm{}$ radiation was measured over a 2-MeV range for ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$ and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$, and the reduced $M1\mathrm{}$ widths for ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$ form a giant-resonance-like curve that peaks at ∼7.8 MeV. Ratios of widths for $E1\mathrm{}$ and $M1\mathrm{}$ radiation and for $E1\mathrm{}$ and $E2\mathrm{}$ radiation are obtained for several nuclides. These properties of radiative capture are used to obtain spectroscopic information about final states. The most complete results are for ${}_{}{}^{166}{}_{}{}^{}\mathrm{Ho}$, for which 16 rotational bands are identified and interpreted in terms of the collective model. Similar but less extensive data are obtained for ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{158}{}_{}{}^{}\mathrm{Gd}$, and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$. The measurements on ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$ show that the shapes of the observed $\gamma$-ray lines may be used to determine the parities of final states.

The radiation widths of bound nuclear levels excited by ($\gamma ,{\gamma }^{\prime }$) reactions in nuclei ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$, ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{86}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{80}{}_{}{}^{}\mathrm{Se}$, and ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ have been measured. The present results together with results published by other authors using ($\gamma ,{\gamma }^{\prime }$) reactions are summarized and compared with similar results obtained in capture reactions of thermal and resonance neutrons. The expected properties of the nuclear levels obtained by extrapolation of the giant-dipole resonance to lower energies are compared with the present experimental data. The fluctuation in partial radiative widths from these bound levels is shown to be compatible with the Porter-Thomas distribution.

The 536-keV ($2^{+}$) first excited state of ${\mathrm{Xe}}^{130}$ has been investigated by means of nuclear-resonance-fluorescence scattering experiments. The use of a Ge(Li) detector allowed a good determination of the Rayleigh scattering contribution which amounted to about 30% of the resonant peak. The level width was found to be (5.2 ± 0.9) × ${10}^{-5\mathrm{}}$ eV, corresponding to a mean life of (1.3 ± 0.3) × ${10}^{-11\mathrm{}}$ sec and a ${B\left(E2\mathrm{}\right)\mathrm{}}_{\uparrow }$ of $(0.69\mathrm{}\pm 0.15)e^2\times {10}^{-48\mathrm{}}$ ${\mathrm{cm}}^4$. From this result and the relative transition probabilities determined previously in a Coulomb-excitation experiment by Pieper, Anderson, and Heydenburg, the absolute $B\left(E2\mathrm{}\right)\mathrm{}$ values for the first excited states of ${\mathrm{Xe}}^{128}$ and ${\mathrm{Xe}}^{132}$ were obtained.

Measurements of the relative thick-target yields of $\gamma$ rays deexciting the 2+ first excited states in ${}_{}{}^{112,116,118,120,122,124}{}_{}{}^{}\mathrm{Sn}$, following Coulomb excitation by $\alpha$ particles and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions, have been interpreted in terms of the relative static quadrupole moments of these states. The absolute static quadrupole moment of the 2+ state in ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$ was determined to be +(0.09 ± 0.10) b. With this value it was then possible to obtain the absolute static quadrupole moments for the 2+ state in the other even tin nuclei. The resulting values are closer to the vibrational-model prediction (static quadrupole moment of zero) than to values predicted by the rotational model. A set of absolute $B(E2,0\mathrm{}\to 2)$ values was also obtained with assigned errors between 2 and 3%.

A charge-exchange threshold cusp is observed in the summed 160° excitation curve for ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}\mathrm{}(d,p)\mathrm{}{}_{}{}^{94}{}_{}{}^{}\mathrm{Nb}(6^{+},\mathrm{g}.\mathrm{s}.-2^{+},0.31\mathrm{} \mathrm{MeV})$ at ∼7.1 MeV, the threshold of the analogous ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}\mathrm{}(d,n)\mathrm{}{}_{}{}^{94}{}_{}{}^{}\mathrm{Mo}_{}^A{}_{}{}^{}(6^{+},13.2\mathrm{} \mathrm{M}\mathrm{e}\mathrm{V}-2^{+},13.5\mathrm{} \mathrm{MeV})$ reaction. As predicted by theory, it is essentially identical in shape to the excitation curve previously measured for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}\mathrm{}(d,p)\mathrm{}{}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}(d_{\frac{5}{2}},\mathrm{g}.\mathrm{s}.\mathrm{})$ in the same energy region.

Using new information concerning the decay modes of the 460-, 557-, and 559-keV levels in ${\mathrm{Ir}}^{193}$, previous resonance-fluorescence data have been reevaluated in terms of the mean lives of these levels.

An improved search for the $K$-capture branch in ${\mathrm{In}}^{113m}$ has established a new upper limit for this decay mode of 0.0036%, from which one may conclude $log\mathrm{ft}>\mathrm{}6.5\mathrm{}$ for this first-forbidden transition.

Computer calculations of Coulomb-distortion effects are presented for inelastic electron scattering inducing $M2\mathrm{}$ transitions in light nuclei. The distortion effect is presented over $1<Z<\mathrm{}20\mathrm{}$, $40 \mathrm{MeV}<E_0<140\mathrm{}$ MeV, $10<k<\mathrm{}19\mathrm{}$ MeV, and for two large angles of scatter. The dependence of the calculation on the assumed nuclear transition current is displayed.

Low-energy $\gamma$ rays following slow-neutron capture in thulium have been used to check the angular-momentum assignments of the neutron resonances. A previous discrepancy in the spin of the 17.5-eV resonance has been resolved. The correlation between reaction widths noted in previous work has been recalculated and found to be substantially unchanged. An isomeric state at 183.2 keV has been investigated by measuring the delay in the low-energy transitions involving this state, and a half-life of 3.2 ± 0.3 μsec is obtained, in fair agreement with previous work.

Previously reported helium recoil energy distributions produced by neutron elastic scattering from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in a gaseous scintillator have been modified to provide cross-section data suitable for use in current phenomenological investigations of the nucleon-helium interaction.

The $R$ matrix of Wigner and Eisenbud is a function of a set of parameters (channel radii, boundary numbers, etc.) as well as of the energy of the incoming particle. Invariant imbedding techniques have been applied, which give the variation of the $R$ matrix with respect to changes of the parameters entering into the theory. A generalization of various formulas, derived originally by Wigner and Teichmann and Wigner, to the multichannel case has been obtained. Our general results apply also to deformations of the nucleus other than spherical. An application of the invariant imbedding technique is also shown concerning Robson's theory of the isobaric spin analogs.

The effects of central, spin-orbit, and tensor components of the Sussex interaction on various ground-state properties of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ nuclei are studied. It is observed that a major contribution to the binding energy comes from the central part of the interaction alone. In the case of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, almost all of the $1p_{\frac{1}{2}}-1p_{\frac{3}{2}}$ splitting comes from the spin-orbit component. However, in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, the tensor part of the interaction also provides large splitting, but its contribution is of the wrong sign.

The experimental cross sections for production of the Li, Be, and B isotopes and their isotopic ratios have been determined for interactions produced by 70-MeV $\alpha$ particles with the carbon and nitrogen nuclei of a nuclear emulsion. The cross-section values as well as the isotopic ratios have been fitted with the help of Rudstam's formula; there is good agreement for the carbon target and poor agreement for the nitrogen target.

The new method of Truelove and Nicholls for obtaining reaction matrix elements for nuclear-structure calculations is discussed. In this method, the Bethe-Goldstone wave function is expanded in terms of eigenfunctions of two interacting nucleons bound in a common potential well. The Bethe-Goldstone equation, which is written in terms of an expansion over noninteracting two-particle states, is then solved iteratively. In practice, the method is most easily applied when a harmonic-oscillator basis is used; the Pauli operator $Q$ can then be treated exactly. The convergence of the Truelove-Nicholls iteration scheme and of the above two expansions is investigated. It is shown that the original method is incorrect for nucleon-nucleon potentials with an infinite hard core. A simple way of correcting the method is presented.

Slater determinants used in a standard Hartree-Fock calculation and built with parity-mixed single-particle orbitals do not have a definite parity; a parity projection after the variation is needed, in general. A different solution is investigated here, in which the projection is performed before the variation. Conditions are studied for the case where the solution is still a Slater determinant. The results of explicit calculations for both methods are compared in the case of a three-nucleon system. A larger binding energy is obtained in the case of projection before variation, and in the corresponding solution (which is not a Slater determinant) considerable parity mixing in single-particle wave functions is allowed.