The suggested failure of the model independent energy sum rule of Koltun in a recent ($e, e^{\prime }p$) experiment is studied in light of current Hartree-Fock theory. It is shown that the use of (i) density dependent forces or (ii) partial occupation probabilities compensates for the restricted momentum and energy range of the experimental proton spectral function, and can explain the sum rule violation.

NUCLEAR STRUCTURE Correction to Koltun's energy sum rule calculated for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ using effective density dependent or three-body forces.

We study the isospin splitting of the giant resonance of $T=\frac{1}{2}$ nuclei with sum rules. The particular isospin geometry involved in this case permits a number of simplifications in the isospin sum rules and several largely model independent relations are obtained and discussed. It turns out that for several light isodoublets the "symmetry" energy $U$ tends to be smaller that $60(T+1\mathrm{})\mathrm{}{A}^{-1\mathrm{}}$ MeV.

NUCLEAR STRUCTURE $T=\frac{1}{2}$ nuclei; calculated isospin splitting of $E1\mathrm{}$ resonance with sum rules, model independent results discussed.

The mixed derivatives that appear in the three-body Schrödinger equation (when written in terms of interparticle distances) are treated as a perturbation. The following results are obtained: (a) $B_3\ge 3B_2$, where $B_n$ is the $n$ body binding energy. (b) For the harmonic oscillator potential, the calculated binding energy falls within 3% of the exact one. Numerical results for attractive square well and exponential potentials are presented.

NUCLEAR STRUCTURE Three body, Schrödinger equation, perturbation theory, binding energy.

A recent study of the ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}(d, p){}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ reaction reopened the question of the Spin of the 4744 keV level of ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$. In an effort to determine this spin, the 4744 keV level has been excited using bremsstrahlung. The observed angular distribution of the resonant $\gamma$ radiation is compatible only with the assignment of spin 1. With a branching ratio $\frac{{\Gamma }_0}{\Gamma }=1\mathrm{}$, the observed yield corresponds to a total width $\Gamma \mathrm{}\left(4744\right)=(95\mathrm{}\pm 20)$ meV.

NUCLEAR REACTIONS ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(\gamma , \gamma )$, $E<\mathrm{}5\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, deduced $J$, $\Gamma$; natural target.

Results for the matrix elements of the effective interaction between particles in the $d_{\frac{5}{2}}$ and $g_{\frac{9}{2}}$ orbits are modified in view of a new spin identification by Metzger.

NUCLEAR REACTIONS ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}(d, p)$, $E=12\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, deduced level energies, $J^{\pi }$, deduced revised two-body matrix elements.

A previous result of Gibson and Lehman for the binding energy of ${}_{\Lambda }{}^3{}_{}{}^{}\mathrm{H}$ using a single-term nonlocal separable potential representation of a meson-theoretic $\Lambda N$ potential is shown to be significantly modified when a two-term separable $\Lambda N$ potential is used instead.

NUCLEAR STRUCTURE ${}_{\Lambda }{}^3{}_{}{}^{}\mathrm{H}$, $\mathrm{YN}$ potentials, separable potential three-body calculation, $B_{\Lambda }$.

We argue on the basis of model calculations that the introduction of short-range repulsion and $\Lambda -\Sigma$ coupling into the separable potential approximation to meson-theoretic potentials will not alter the conclusions previously obtained. In addition, it is shown that the introduction of the tensor force into the $N-N$ triplet interaction, which produces a larger effect than either of the other two modifications, will not alter the conclusions.

NUCLEAR STRUCTURE ${}_{\Lambda }{}^3{}_{}{}^{}\mathrm{H}$, $Y-N$ potentials, separable potential three-body calculation, $B_{\Lambda }$.

The recent results of Kouri and Levin on the properties of the single-channel two-particle off-shell transition amplitude which follow from off-shell unitarity are shown to be readily obtainable from results in the published literature. It is also pointed out that the use of the damping (or Heitler) equation as a realization of off-shell unitarity leads to no new information except on the off-shell structure of the $K$-matrix amplitude. Finally, the implications of off-shell unitarity in some (two-particle) multichannel situations are deduced, thereby extending the results of previous investigations.

NUCLEAR REACTIONS Off-shell structure of two-particle scattering amplitudes.

A measurement was made of the angular distribution of neutrons from the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(p, n){}_{}{}^{13}{}_{}{}^{}\mathrm{N}(\mathrm{g}.\mathrm{s}.\mathrm{})$ from which the total cross section leading to the ground state of ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ was determined. At the same time, the determination of the ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ activity was made. The ratio of the reaction cross sections at 22.8 MeV determined from ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ activation to the yield of the ground state neutron group is 1.06±0.07. Thus there is no significant competition in the decay of excited states by $\gamma$ emission with particle emission. This result implies that the reaction can be used as a convenient fast neutron calibration source.

NUCLEAR REACTIONS $\frac{d\sigma }{d\Omega }$ ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(p, n){}_{}{}^{13}{}_{}{}^{}\mathrm{N}(\mathrm{g}.\mathrm{s}.\mathrm{})$, $E=16.3, 22.8$ MeV. Comparison of neutron yield and ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ activity.

The ${\alpha }_K$ coefficient of the 65-keV $M4\mathrm{}$ transition in ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$ was measured. The result is ${\alpha }_K=1610\mathrm{}\pm 82$ which shows a 3% deviation from the theoretical value of Hager and Seltzer. This deviation agrees with the systematic behavior of $E3\mathrm{}$ and $M4\mathrm{}$ conversion coefficients.

RADIOACTIVITY ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}_{}^m{}_{}{}^{}$; measured $I_{\mathrm{X}}$ and $I_{\gamma }$. ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$ deduced ${\alpha }_K$.

The six interaction potentials defined in a distorted-wave Born-approximation calculation are considered for multinucleon transfer heavy-ion reactions. In order to get the necessary post-prior equivalence, all terms must be included; however, at this time the most reasonable solution is to include the normally neglected Coulomb potentials in post-representation calculations.

NUCLEAR REACTIONS DWBA theory, multinucleon transfer interaction potentials.

The yrast levels of ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ were investigated via the in-beam study of $\gamma$ rays from the 30-40-MeV ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ bombardment of enriched ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ targets. Present results show that the 5.086 MeV → 3.285 MeV ($6^{+}$) → 2.283 MeV($4^{+}$) → 1.157 MeV($2^{+}$) → g.s.($0^{+}$) cascade is the principal deexcitation path for the high-lying states populated via the ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, 2p\gamma ){}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ reaction. The $\gamma -\gamma$ coincidence measurements are consistent with the 5.086 MeV → 3.285 MeV transition being an 8 → 6 stretched quadrupole transition.

NUCLEAR REACTIONS ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, 2p\gamma )$, $E_{{}_{}{}^{16}{}_{}{}^{}\mathrm{O}}=30-40\mathrm{}$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coincidence; deduced ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ levels.

Cross sections for the formation of a number of iodine, tellurium, and cadmium nuclides in the interaction of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ with 300- and 11.5-GeV protons have been determined. Including previously obtained results on cesium and barium nuclides we obtain a weighted average value of 0.92 ± 0.14 for $\frac{{\sigma }_{300}}{{\sigma }_{11.5}}$ based on 34 values for nuclides in the $A=110-140\mathrm{}$ region. The cross section ratios show little dependence on $Z_A-Z$.

NUCLEAR REACTIONS Measured $\sigma$ of 28 Cd, Te, and I nuclides from 300- and 11.5-GeV proton bombardment of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$.

The ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(\alpha , {}_{}{}^8{}_{}{}^{}\mathrm{He}){}_{}{}^{14}{}_{}{}^{}\mathrm{O}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ reaction has been observed at $E_{\alpha }=58\mathrm{}$ MeV. The measured cross section is 40 ± 15 nb/sr at ${\theta }_{\mathrm{lab}}=8\mathrm{}°$. The mass excess of ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ was determined to be 31 600 ± 25 keV. Possible reaction mechanisms are discussed.

NUCLEAR REACTIONS ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{He}$), $E=58\mathrm{}$ MeV. Measured $\sigma (E_f, 8°)$. Deduced $Q_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ and mass excess for ${}_{}{}^8{}_{}{}^{}\mathrm{He}$. Magnetic spectrometer.

We explore the effects of including the $D$-state part of the deuteron wave function in a previous distorted-wave impulse-approximation calculation applied to the reaction $\mathrm{pd}\to t\pi$ in the resonance region. We find that the $D$-state component tends to increase the cross section at large angles by amounts ranging from 15% at 470 MeV to a factor of 3 at 1050 MeV. Results are however sensitive to the short range details of both $S$ and $D$ parts of the deuteron wave function.

NUCLEAR REACTIONS ($p, \pi$), ${}_{}{}^2{}_{}{}^{}\mathrm{H}(p, \pi ){}_{}{}^3{}_{}{}^{}\mathrm{H}$, calculated effect of deuteron $D$ state on $\sigma \left(\theta \right)$ at $E=470, 590, 1050$ MeV. Used distorted-wave impulse approximation.

Cross sections for evaporation residues following complete fusion have been measured for the bombardment of ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ with 81-, 105-, 126-, and 168-MeV ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, 138- and 210-MeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, and 336-MeV ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$. The results were obtained using a counter telescope and, in some cases, differ considerably from previous work with mica track detectors. The experimental critical angular momenta for fusion are in good agreement with recent theoretical calculations for the O and Ne bombardments. Our data suggest parameters for the critical distance of approach which are significantly smaller than previously reported values.

NUCLEAR REACTIONS, COMPLETE FUSION ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}$*), $E=81, 105, 126, 168$ MeV; ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$(${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{47}{}_{}{}^{}\mathrm{V}$*), $E=138, 210$ MeV; ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$(${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Cu}$*), $E=336\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, $\sigma$ for evaporation residues, deduced $l_{\mathrm{cr}}$.

The elastic and inelastic scatterings of ${\pi }^{-}$ by ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are calculated from the $\pi$-nucleon scattering matrix of the Chew model which fits the $\pi$-nucleon $P_{33}$ phase shift data up to about 200 MeV. The results are compared with those calculated from the Kisslinger and Landau-Tabakin models to study the off-shell dependence of the $\pi$-nucleus scattering.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\pi , \pi )$, $E=120-230\mathrm{}$ MeV; calculated $\sigma \left(\theta \right)$, $\sigma$ with various models of $\pi$-nucleon interaction.

The problem of the Coulomb corrections to inelastic electron scattering cross sections is treated in the distorted wave Born approximation (DWBA) using electron wave functions evaluated in the second Born approximation. The formalism is developed for magnetic multipole transitions in a manner analogous to the method developed by Cutler for Coulomb transitions, in which the nuclear and electron physics are represented by separate factors in the integrand of a double integral expression for the cross section. Since the nuclear factor turns out to be simply the inelastic form factor in the first Born approximation, the usual problem of having to specify the transition current density is avoided. The Coulomb correction is considered in detail for $M1\mathrm{}$ transitions, and numerical comparison with "exact" DWBA results is presented.

NUCLEAR REACTIONS Coulomb corrections to $M\lambda$ inelastic electron scattering. Calculated in DWBA using 2nd BA wave functions.

Excitation functions and angular distributions of the reactions ${}_{}{}^{20,22}{}_{}{}^{}\mathrm{Ne}(\alpha , {\gamma }_0)$ were used to study the distribution of $E2\mathrm{}$ strength in the energy regions 14-22 MeV of ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$, as well as to probe the importance of isospin in the decay of the $E1\mathrm{}$ giant resonance in these nuclei. It was found that the $E2\mathrm{}$ strength in the ($\gamma , {\alpha }_0$) channel is rather uniformly distributed and accounts for about 10% of the energy weighted sum rule in each nucleus. Together with the $E2\mathrm{}$ strength observed in lower resonances, about 45% of the sum rule is accounted for. No evidence for a compact $E2\mathrm{}$ resonance is found. A comparison of the $E1\mathrm{}$ distribution and total strength in the ($\gamma , {\alpha }_0$) channel of the giant dipole resonances in ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$ indicates that isospin conservation may be important in these reactions. Information was also obtained on the reactions ${}_{}{}^{20,22}{}_{}{}^{}\mathrm{Ne}(\alpha , {\gamma }_1)$.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}(\alpha , \gamma )$, $E=2.5-20\mathrm{}$ MeV; ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}(\alpha , \gamma )$, $E=4.5-16\mathrm{}$ MeV; measured $\sigma (E, E_{\gamma }, {\theta }_{\gamma })$. ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$ deduced $E1\mathrm{}$, $E2\mathrm{}$ strength. Enriched targets.

To describe elastic and inelastic scattering, Glauber theory has been used often at an energy higher than 1 GeV with considerable success. It is also interesting to apply this model to scattering at lower energies to define its limits of validity. Cross sections and polarization values for proton scattering are calculated at 75, 155, 315, and 1040 MeV. The results for optical potentials in an exact solution or in the eikonal approximation are compared. First order corrections due to Wallace are also included. These improve the fit at small momentum transfers.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p)$, $E=75-1000\mathrm{}$ MeV; used Glauber model, calculated $\sigma \left(\theta \right)$, $P$ eikonal approximation and phase additivity effects.