For low energy neutron-induced fission in the thermal and epithermal range, the momentum transferred in forming the compound nucleus is small enough that the compound nucleus may remain bound in the lattice until it decays. Phonons, therefore, may be emitted or absorbed in the neutron absorption process changing the energy of the compound nucleus from that which would be derived simply from measuring the incoming neutron energy. The probability and influence of phonon transfer to and from the lattice is calculated at energies below 1 eV and is shown to have a small but significant effect on the observed cross section. The magnitude of the effect is temperature dependent and ranges in size from a few tenths of 1% for ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ fission at thermal to 5% for ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ fission at the 0.3 eV resonance. Some of the effect can be accounted for by applying the usual Doppler broadening approximation in the thermal range.

[NUCLEAR REACTIONS FISSION Capture, Doppler effect, phonon exchange; temperature dependence.]

The proton spectrum resulting from 794-MeV neutron bombardment of deuterium was measured at several angles. The angular distribution of the integral of the quasielastic charge exchange peak is fitted very well by the two exponential form $\frac{d\sigma }{\mathrm{dt}}={\alpha }_1{e}^{{\beta }_{1}t}+{\alpha }_2{e}^{{\beta }_{2}t}$ as has previously been found for the $\mathrm{np}$ elastic case. The ratio of the two cross sections at $t=0\mathrm{}$ is 0.56±0.04. A modified impulse approximation calculation accounts for most features of the observed angular distribution.

[NUCLEAR REACTION $n{}_{}{}^2{}_{}{}^{}\mathrm{H}\to \mathrm{pnn}$, $E=794\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$. Calculated $\sigma \left(\theta \right)$ with modified PWIA.]

The cross section for elastic scattering of 794-MeV neutrons by deuterium has been measured for neutron center of mass angles from 139° to 179°. The angular distribution is fitted very well both by an empirical function $\alpha e^{\beta (\mu -{\mu }_{{180}^{\circ }})}$ and by a calculation that uses the one parameter Craigie-Wilkin triangle diagram technique.

[NUCLEAR REACTION $n{}_{}{}^2{}_{}{}^{}\mathrm{H}\to {}_{}{}^2{}_{}{}^{}\mathrm{H}n$, $E=794\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$. Calculated $\sigma \left(\theta \right)$ with triangle diagram techniques.]

The inclusive scattering of $K^{+}$ mesons on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is calculated in the plane wave impulse approximation. The momentum distribution employed for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and different reaction mechanism approaches are checked by a comparison with data of a calculation of the inclusive scattering of electrons on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.

[NUCLEAR REACTIONS Quasifree scattering of kaons and electrons, PWIA, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(e,e^{\prime })$ at $E_{\mathrm{lab}}=500\mathrm{}$ MeV, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(K^{+},K^{+\prime })$ at $E_{\mathrm{lab}}=300\mathrm{}$ MeV.]

The differential cross section for scattering of pions on deuterons was measured at LAMPF at laboratory momenta of 343, 441, 539, and 637 $\frac{\mathrm{MeV}}{c}$, using an $E-\Delta E$ method to identify the recoil deuterons. Angles ranged from 40° to 160° in the center of mass system. The momentum resolution was $\sigma =\pm 3.5\%$ and the angular resolution was ± 1.70° in the laboratory system. The experimental method is discussed, and results are presented and compared with other experimental data as well as with various theoretical calculations.

[NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\pi ,\pi )$; $E=230,323,417,512\mathrm{}$ MeV. ${\mathrm{D}}_2$O, C${\mathrm{D}}_2$ targets. Measured $\sigma \left(\theta \right)$, $\theta ={40}^{\circ }-{160}^{\circ }$, $\Delta \theta ={1.7}^{\circ }$, $\frac{\Delta p}{p}=3.5\%$.]

Recent measurements of high energy inclusive cross sections in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, close to the elastic limit, allow for experimental verification of the "coherent recoil" postulate of "quasi-two-body scaling." Theoretical arguments for the dominance of coherent recoil up to internal nucleon momenta $k\simeq 1.2 \frac{\mathrm{GeV}}{c}$ are presented, along with a new "derivation" of the relationship between quasi-two-body scaling and an "effective" ground state momentum distribution. A possible relationship between inclusive and elastic cross sections is explored.

[NUCLEAR REACTIONS Quasi-two-body scaling, "effective" momentum distributions.]

We calculate the total cross section for the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\gamma ,{\pi }^{-}){}_{}{}^{12}{}_{}{}^{}\mathrm{N}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ and study its energy dependence in the threshold region. Contrary to previous theoretical analyses, we find agreement between theory and experiment using a $\overrightarrow{\sigma }·\overrightarrow{\epsilon }$ interaction. Our results depend strongly on the inclusion of all pion partial waves and a correct treatment of the isospin dependent terms in the pion-nucleus optical potential.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\gamma ,{\pi }^{-}){}_{}{}^{12}{}_{}{}^{}\mathrm{N}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$; photon lab. energy 0-10 MeV above threshold; realistic pion optical potential; shell model wave functions; $\overrightarrow{\sigma }·\overrightarrow{\epsilon }$ interaction. Calculated total cross section.]

The decay of mass-separated ${}_{}{}^{143}{}_{}{}^{}\mathrm{Ba}$ to levels in ${}_{}{}^{143}{}_{}{}^{}\mathrm{La}$ has been investigated using $\gamma$-ray spectroscopy in both the singles and coincidence modes. Of 69 $\gamma$ rays ascribed to the decay of ${}_{}{}^{143}{}_{}{}^{}\mathrm{Ba}$, 59 were placed in a level scheme which represents the first information on excited states in ${}_{}{}^{143}{}_{}{}^{}\mathrm{La}$. A total of 19 levels up to a maximum energy of 2347 keV were observed. The resulting level scheme is compared with that of ${}_{}{}^{141}{}_{}{}^{}\mathrm{La}$ and systematics of odd- $A$ La isotopes are discussed.

[RADIOACTIVITY ${}_{}{}^{143}{}_{}{}^{}\mathrm{Ba}$ [from ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}\mathrm{}(n,f)\mathrm{}$]; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$-coin Ge(Li) detectors; ${}_{}{}^{143}{}_{}{}^{}\mathrm{La}$ deduced levels, $J$, $\pi$. Mass-separated ${}_{}{}^{143}{}_{}{}^{}\mathrm{Ba}$ activity.]

In this study the decay of ${}_{}{}^{143}{}_{}{}^{}\mathrm{Gd}_{}^{g+m}{}_{}{}^{}$ by positron emission and electron capture and the isomeric decay of ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}_{}^m{}_{}{}^{}$ were investigated. $\gamma$ rays associated with ${}_{}{}^{143}{}_{}{}^{}\mathrm{Gd}_{}^{g+m}{}_{}{}^{}$ were placed on the basis of excitation functions, half-life, and $\gamma -\gamma$ coincidence information. We assigned 61 $\gamma$ rays deexciting 33 levels in ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$ from the decay of 112±2 sec ${}_{}{}^{143}{}_{}{}^{}\mathrm{Gd}_{}^m{}_{}{}^{}$. Another 7 $\gamma$ rays deexcite an additional 6 levels in ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$ from 39±2 sec ${}_{}{}^{143}{}_{}{}^{}\mathrm{Gd}_{}^g{}_{}{}^{}$ decay. A small delayed $p$ or $\alpha$ branch associated with ${}_{}{}^{143}{}_{}{}^{}\mathrm{Gd}$ decay was observed with an upper limit of 1 × ${10}^{-5\mathrm{}}$. The half-life of the ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}_{}^m{}_{}{}^{}$ isomer at 389.47 keV was found to be 50.0±0.5 μ sec. The resulting level structure observed in ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$ is explained quite satisfactorily in terms of a triaxial weak-coupling model.

[RADIOACTIVITY ${}_{}{}^{143}{}_{}{}^{}\mathrm{Gd}_{}^{g+m}{}_{}{}^{}$, ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}_{}^m{}_{}{}^{}$, measured $T_{\frac{1}{2}}$, delayed $p+\alpha$, $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coin, $\sigma \mathrm{}\left(E\right)\mathrm{}$; deduced $log\mathrm{ft}$, $Q$. ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$ deduced levels, $J$, $\pi$. NUCLEAR STRUCTURE ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$; calculated levels, $J$, $\pi$. Triaxial weak-coupling model.]

The shape of the $\beta$-ray spectrum of ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ has been investigated as a test of the weak magnetism prediction of the conserved vector current theory. Using the radiative width of the analog $M1\mathrm{}$ decay in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ to determine the magnetic form factor we calculate, from conserved vector current theory, a deviation of the $\beta$ spectrum from the allowed shape of +1.23±0.03% Me${\mathrm{V}}^{-1\mathrm{}}$. Higher order terms reduce the slope to 0.94% Me${\mathrm{V}}^{-1\mathrm{}}$. The spectrum was measured with an iron-free intermediate-image magnetic spectrometer and the deviation was found to +0.4±0.5% Me${\mathrm{V}}^{-1\mathrm{}}$ or somewhat smaller than the conserved vector current prediction.

[RADIOACTIVITY ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$: measured $\beta$-spectrum shape; compared with CVC prediction.]

A theoretical estimate has been made of the probability of electron-positron pairs being produced in the $\alpha$ decay process. The results are in agreement with the experimental value observed in the decay of ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$, which is the only experimental result currently available. Estimates of the probabilities of pair production in other possible $\alpha$ decays are also given.

[RADIOACTIVITY Calculation of internal pair formation in $\alpha$ decay.]

Separable-potential three-body ($\alpha \mathrm{np}$) models of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground state are examined. Different separable-potential fits to the $\alpha -n$ phase shifts and the low-energy ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ two-nucleon parameters are reviewed, after which integral equations are derived for the spectator functions of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground-state wave function assuming $S_{\frac{1}{2}}$, $P_{\frac{1}{2}}$, and $P_{\frac{3}{2}}$ components in the $\alpha -n$ interaction. These equations are solved to determine the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ binding energy and investigate its sensitivity to the ${}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ component of the two-nucleon interaction, its variation upon neglecting different components of the $\alpha -n$ interaction, and its dependence on different analytical forms for the $P$-wave $\alpha -n$ interactions. For two wave functions derived from the same set of $\alpha -n$ interactions, but with the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ two-nucleon interaction producing 0% and 4% $d$-wave components in the deuteron, respectively, the spectator functions are given and the contributions to the ground-state normalization of the various components are calculated. The latter two wave functions correspond to three-body ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ binding energies of 4.446 MeV (0%) and 4.070 MeV (4%) compared with the Coulomb-adjusted experimental value of 4.53 MeV.

[NUCLEAR STRUCTURE ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$; binding energy, wave function, wave function components, normalization. Three-body, separable-potential model.]

An algebraic approach, within a framework using equations of motion, is applied to the study of vibrational collective motion in exactly soluble shell models with symmetry R(5) and R(5) × R(5). The latter exhibits two phonon branches, permitting the study of the effect of the noncollective on the collective branch. The results of this method, including the splitting of the two-phonon degeneracy, agree satisfactorily with exact results for a range of parameters well into the transition region between vibrational and rotational motion.

[NUCLEAR STRUCTURE Approximate many-body methods applied to a solvable model. Vibrational spectrum. Equations of motion method.]

Recently a semiclassical approximation was applied by Jennings et al. for a system of noninteracting fermions in a local one body potential. This is a way to calculate shell corrections alternative to the Strutinski method. We have generalized this method to a spherical but a momentum dependent potential of the form $V\left(r\right)+\frac{1}{2}\left[p^{ 2}W\right(r)+W(r\left)\mathrm{}{p}^{ 2}\right]$. Explicit expressions are developed for the number of particles and the smoothed sum of single particle energies in terms of the Fermi energy and the one body potential and its first two derivatives. They are calculated for selected values of the parameters and compared with the sum of single particle energies obtained by numerical solution of the Schrödinger equation. The difference between the two is essentially the shell correction. The shell correction can be roughly estimated using a simple modification of the isotropic harmonic oscillator model.

[NUCLEAR STRUCTURE Shell corrections, momentum dependent potentials.]

Effective interactions for $N=50\mathrm{}$ and $N=28\mathrm{}$ isotones are obtained by fitting the low-lying excited levels. Coulomb displacements and separation energies are deduced directly from the difference of observed and calculated binding energies.

[NUCLEAR STRUCTURE $N=50\mathrm{}$ and $N=28\mathrm{}$; calculated effective interactions, deduced Coulomb displacements and separation energies.

The precision attainable in the numerical treatment of the Griffin-Hill-Wheeler equation is studied in a solvable model. Truncation errors related to the generator coordinate kinematics are exhibited and briefly discussed.

[NUCLEAR STRUCTURE Numerical treatment of the generator coordinate method. Comparison with exact solutions.

Several commonly made approximations in microscopic effective interaction calculations have been found to result in serious inaccuracies. Recent improved second-order calculations for $A=18\mathrm{}$ nuclei suggested somewhat better order by order convergence in the reaction matrix $G$ than indicated previously. A selected third-order term has been calculated to study further this possibility. The convergence of the intermediate-state summation was also investigated for this diagram. Our improved calculational technique results in a greater reduction of the third-order term than the reduction found earlier for the second-order term. The outlook for the (asymptotic) convergence of the expansion is much improved, but the prospects for a complete third-order calculation of the effective interaction are dim due to the difficulties of the calculation.

[NUCLEAR STRUCTURE Effective interaction, theory; convergence of the intermediate-state sums; convergence of the diagram series through third-order in the nuclear reaction matrix; shell-model matrix elements in the $\mathrm{sd}$ shell.]

A detailed nuclear matter calculation with a charge-dependent realistic $N-N$ potential has been made under the Brueckner formalism. The binding energy, compressibility, and wound integrals are evaluated and compared with results of other potentials. The influence of charge dependence of the nuclear potential on the infinite nuclear matter binding energy from the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ states is studied in detail.

[NUCLEAR STRUCTURE Infinite nuclear matter, Brueckner formalism, compared with HF approximation results. Calculated binding energy, wound integrals, HPWC, compressibility, charge dependence. Charge-dependent realistic finite potential.]

Using the effective Yale interaction the Lipkin-Nogami version of the spherical BCS method is applied to study the ground-state properties of Ni, Zn, and Ge isotopes. Calculations are performed using three different conditions to determine the parameter ${\lambda }_2$ of the Lipkin-Nogami method. Neutron-pair separation energies are compared with the experimental values.

[NUCLEAR STRUCTURE Lipkin-Nogami method applied to the Ni, Zn, and Ge isotopes. Effective Yale interaction.]

Whenever the residual potential is repulsive the introduction of Padé approximants into the BrillouinWigner perturbation expansion generates lower bounds to the exact eigenvalues. The method is extended to perturbation from a subspace and to singular repulsions.

[NUCLEAR STRUCTURE Padé approximants replace the Brillouin-Wigner (BW) equation by an equation whose solutions are lower bounds to the BW solutions.]