Monochromatic 15.1 MeV plane-polarized photons have been scattered from seven additional targets having their $E1\mathrm{}$ giant resonances near 15 MeV. They are In, Sb, Nd, Hg, Pb, Th, and U. Photons scattered through 90° were observed in the planes both parallel and perpendicular to the plane of the polarization vector. The observation of photons scattered along the polarization vector by the spherical vibrators indicates that the giant resonance is coupled to the quadrupole oscillations of the nuclear surface. The agreement with the predictions of the dynamic collective model is not particularly striking though there is little doubt that the phenomenon is qualitatively understood.

NUCLEAR REACTIONS $\gamma ,\gamma$ and $\gamma ,{\gamma }^{\prime }$ using plane-polarized, monochromatic 15.1 MeV incident photons. New data reported for In, Sb, Hg, Pb, Th, and U.

The ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}(\alpha ,{}_{}{}^8{}_{}{}^{}\mathrm{He}){}_{}{}^{22}{}_{}{}^{}\mathrm{Mg}$ reaction was reinvestigated at a bombarding energy of 110.6 MeV with a magnetic spectrometer-multiwire proportional counter detection system, leading to an improved value for the mass excess of ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ of 31.57±0.03 MeV.

NUCLEAR REACTIONS ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}(\alpha ,{}_{}{}^8{}_{}{}^{}\mathrm{He})$, $E=110.6\mathrm{}$ MeV; ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ measured mass excess; compared mass predictions.

A $\overline{p}$-nucleus potential is constructed by folding a $\overline{p}N$ potential in the nuclear matter density. The strength of the $\overline{p}N$ potential is adjusted to the corresponding scattering lengths. The resulting $\overline{p}$-nucleus force consistently reproduces the antiprotonic atoms level shifts and widths.

A differential equation formulation of the multichannel coupled equations of Kouri and Levin describing rearrangement scattering is given. The different channels are linked together in these equations through the presence of the channel coupling array $W$. It is shown that the earlier results of Hahn, derived using the reduction method, follow directly from the multichannel coupled equations by making specific choices of the array $W$. These particular $W\text{'}\mathrm{s}$ guarantee that the iterated kernels of the coupled equations are connected in those channels which are explicitly considered, so that standard numerical techniques can be applied to their solution.

The coupled equations for $n$-body rearrangement collisions derived previously using the reduction method and the channel coupling array method are explicitly shown to be free of Federbush disease.

A simple and practical method is given for constructing a rapidly convergent separable expansion, with simple form factors, for the $t$ matrix of a local potential. The requirement of two-particle unitarity is maintained for approximations of any rank. Unlike commonly used methods, the calculation of eigenfunctions and eigenvalues of the kernel of the Lippmann-Schwinger equation is not required. The method is illustrated for the two of the commonly used nucleon-nucleon potentials and the results compared with the unitary pole expansion and the exact results. Also in these cases our method yields an excellent rank-one approximation to the $t$ matrix.

In the present paper we discuss photonuclear reactions for photon energies $E_{\gamma }>50\mathrm{}$ MeV. We show in detail how the different processes concerning the nucleon-nucleon interactions enter the transition matrix. Explanations are given for the similar behavior of ($\gamma , n$) and ($\gamma , p$) and for a strong relative suppression of the reactions ($\gamma , \mathrm{pp}$) and ($\gamma , \mathrm{nn}$) compared to ($\gamma , \mathrm{np}$). This solves the standing problems of photonuclear reactions at intermediate photon energies. We present numerical calculations for the reactions ($\gamma , p$) and ($\gamma , n$) on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ from 50 to 140 MeV photon energy and show in detail how the different physical processes numerically enter the total cross sections and angular distributions. Over-all good agreement with the experiments is achieved.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\gamma , p)$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\gamma , n)$ $E=50\mathrm{}-140$ MeV; calculated $\sigma$, $\sigma \left(\theta \right)$.

Using an approximate Bethe-Salpeter equation approximate values were obtained for the partial wave contributions of the two and three pion exchange ladder diagrams. With these results the region hypothesis of the two-nucleon force was tested for this model. No definite region structure was observed for the $S$ and part of the $P$ and $D$ waves (${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}D_3^{}{}_{}{}^{}$). A definite region structure was observed for other waves, but it was impossible to locate common (to all partial waves) radii for the outer and intermediate regions of this model of the two-nucleon interaction.

Differential cross sections and analyzing powers for polarized ($p,p^{\prime }$) scattering on ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ have been measured at an incident proton energy of 24.5 MeV, using the Saclay AVF cyclotron. Data have been taken for nine levels, up to 7.11 MeV excitation energy. The analysis has been carried out in the distorted wave Born approximation within the framework of the macroscopic and microscopic models. For the latter the available wave functions of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and an approximate description of the nucleon-nucleon interaction, derived from the Hamada-Johnston potential, have been used. The macroscopic model, with just a simple deformation parameter $\beta$, accounts reasonably well for some even-parity transitions, and also for the excitation of the $3^{-}$ level at 5.09 MeV. Furthermore, coupled-channel calculations support evidence for a rotational band based on the ground state and including the $2^{+}$ at 1.98 MeV and the $4^{+}$ at 7.11 MeV. The analysis also supports a collective character of the $3^{-}$ level at 5.09 MeV and accounts for the observed strong excitation of this state. Satisfactory fits are obtained for some levels within the microscopic model, even though the absolute values of the cross sections are usually underestimated and large normalization factors needed. The use of an imaginary form factor adds some structure to the calculated angular distributions and improves the agreement between theory and experiment for those transitions for which the real form factor is collective like, i.e., peaked at the nuclear surface.

NUCLEAR REACTIONS ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(p,p^{\prime }){}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, $E=24.5\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$ and analyzing power for nine levels. Macroscopic and microscopic DWBA calculations.

We have investigated high-spin states in ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{44}{}_{}{}^{}\mathrm{Sc}$ with the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({}_{}{}^{19}{}_{}{}^{}\mathrm{F}, p2n\gamma ){}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({}_{}{}^{19}{}_{}{}^{}\mathrm{F}, 2pn\gamma ){}_{}{}^{44}{}_{}{}^{}\mathrm{Sc}$ reactions at 45-55 MeV. Angular distribution, linear polarization, and $\gamma -\gamma$ coincidence data on the emitted $\gamma$ rays allowed us to construct decay schemes for states in ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{44}{}_{}{}^{}\mathrm{Sc}$, and to suggest likely spin and parity assignments for most of these states. In each case, positive parity levels with spins up to the maximum value permitted within a ${\left(f_{\frac{7}{2}}\right)}^4$ shell-model space were populated. Results of lifetime measurements for several of these states are given, and a comparison is presented of the level energies and some transition strengths to the predictions of shell-model calculations.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({}_{}{}^{19}{}_{}{}^{}\mathrm{F}, p2n\gamma \gamma \cdots )$, $E=45\mathrm{}-55$ MeV, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({}_{}{}^{19}{}_{}{}^{}\mathrm{F}, p2n\gamma \gamma \cdots )$, $E=45\mathrm{}-45$ MeV; measured $\gamma \gamma$ coin.; deduced levels in ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{44}{}_{}{}^{}\mathrm{Sc}$; measured $\sigma (E_{\gamma },\Theta )$ and $P_{\gamma }$; deduced $J^{\pi }$ for high-spin levels; measured recoil distance; deduced $T_{\frac{1}{2}}$, $B\left(E2\right)$, effective charges. Natural targets, Ge(Li) detectors.

A total of 40 states of ${}_{}{}^{31}{}_{}{}^{}\mathrm{Si}$ in the region of excitation from about 5 to 9 MeV have been studied using the reaction ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(d,p)$ at 10 MeV incident deuteron energy, and a biased quadrupole spectrometer. Fractionated single-particle states are identified via their forward-angle cross sections, using distorted-wave Born-approximation predictions with bound and resonance state form factors for the residual ${}_{}{}^{31}{}_{}{}^{}\mathrm{Si}$ system. Results are contrasted with what is known of the lower lying states, from large-basis shell-model calculations and earlier ($d,p$) experiments.

NUCLEAR REACTIONS ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(d,p)$, $E_d=10\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$. ${}_{}{}^{31}{}_{}{}^{}\mathrm{Si}$ deduced levels, $l$, $j$, $\pi$, spectroscopic factors. Enriched target.

High resolution measurements of the differential cross section for elastic proton scattering on ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ have been performed in the energy regions $E_p=1230\mathrm{}-1250, 1770-2170, 2440-2530, 2700-2800, \mathrm{and} 3000-3250$ keV. Thirty-six resonances were observed. For all resonances, the proton orbital angular momenta were determined and, in many cases, unique spin assignments were made. Partial proton widths are given for all resonances. Many of the observed $p_{\frac{1}{2}}$ and $p_{\frac{3}{2}}$ resonances are tentatively identified as the isobaric analogs of states in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ca}$. In addition to the elastic proton measurements, $\gamma$-ray spectra were obtained at the isobaric analog states corresponding to the 2041-keV ($J^{\pi }={\frac{3}{2}}^{-}$) and 2607-keV ($J^{\pi }={\frac{1}{2}}^{-}$) states in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ca}$. The results are compared with the predictions of a shell model calculation using the realistic Kuo-Brown interaction.

NUCLEAR REACTIONS ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}(p,p)$, $E=1.20\mathrm{}-3.23$ MeV; measured $\sigma (E,\theta )$; ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}(p,\gamma )$, $E=1.796\mathrm{} \mathrm{and} 1.822$ MeV; measured $E_{\gamma }$, $I_{\gamma }$; deduced $J$, $\pi$, $\Gamma$, level decay scheme; calculated $M1\mathrm{}$ rates.

A kaon-nucleus absorptive potential is derived by folding the $\overline{K}N$ finite range complex potential into the nuclear density distribution. The strengths of the $\overline{K}p$ and $\overline{K}n$ potentials have been adjusted to the corresponding scattering length values and the range of the $\overline{K}N$ forces has been obtained by fitting the $\overline{K}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering data. The resulting $\overline{K}N$ potential with no free parameters has been used to calculate kaonic atom level shifts and widths. Within the experimental uncertainties all kaonic data can be fitted in a consistent manner.

The ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ reaction has been studied at a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ bombarding energy of 18 MeV. The resulting angular distributions for states of probable ${\mathrm{}\left(\mathrm{sd}\right)\mathrm{}}^4$ configuration have been examined by the techniques of distorted-wave analysis, utilizing two-particle coefficients of fractional parentage obtained from recent shell-model calculations. Satisfactory agreement is found between theory and the present experiment.

NUCLEAR REACTIONS ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({}_{}{}^3{}_{}{}^{}\mathrm{He},p)$, $E=18.0\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; DWBA analysis with shell-model wave functions.

A method for constructing energy-dependent separable potentials of the form $V=\lambda \mathrm{}\left(E\right)\mathrm{}|v><v|\mathrm{}$ from (complex) elastic scattering phase shifts is presented. The energy-dependent coupling constant $\lambda \mathrm{}\left(E\right)\mathrm{}$ is shown to satisfy a dispersion relation as a consequence of the requirement of multichannel unitarity. It is this knowledge of the analytic properties of $\lambda \mathrm{}\left(E\right)\mathrm{}$ which makes it possible to solve the inverse problem. It is further demonstrated that in some cases the inverse problem can still be solved analytically even when the phase shift changes sign below the inelastic threshold.

Angular distributions were measured for particle groups populating low-lying levels in the reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{14}{}_{}{}^{}\mathrm{N},d){}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{14}{}_{}{}^{}\mathrm{N},p){}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{14}{}_{}{}^{}\mathrm{N},\alpha ){}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ at $E_{\mathrm{lab}}=20\mathrm{} \mathrm{and} 25$ MeV. Excitation functions were also measured for low-lying $\gamma$-ray transitions in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$, and ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ produced by ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ bombardment of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ at $E_{\mathrm{lab}}=14\mathrm{}-33$ MeV. The excellent agreement of Hauser-Feshbach statistical model predictions with these results indicates that the light particle production from the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ interaction reflects a dominant compound nuclear interaction mechanism.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ compound reactions, light particle emission and subsequent $\gamma$-ray decay, statistical model calculations. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{14}{}_{}{}^{}\mathrm{N},d)$, (${}_{}{}^{14}{}_{}{}^{}\mathrm{N},p$), (${}_{}{}^{14}{}_{}{}^{}\mathrm{N},\alpha$), $E_{\mathrm{lab}}=20, 25$ MeV, measured $\sigma \left(\theta \right)$; ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},\gamma )$, $E_{\mathrm{lab}}=14\mathrm{}-33$ MeV, measured $E_{\gamma }$, $\sigma \left(E_{\gamma }\right)$.

The ${}_{}{}^9{}_{}{}^{}\mathrm{Be}({}_{}{}^7{}_{}{}^{}\mathrm{Li},p){}_{}{}^{15}{}_{}{}^{}\mathrm{C}$ reaction has been studied at $E\left({}_{}{}^7{}_{}{}^{}\mathrm{Li}\right)=20\mathrm{}$ MeV using the Penn multiangle spectrograph. In addition to ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}*$(0.0, 0.74), proton groups are observed to at least 25 excited states with $E_x<12\mathrm{}$ MeV. Angular distributions are reported for many of these groups. $J^{\pi }=\left({\frac{1}{2}}^{-}\right) \mathrm{and} {\frac{5}{2}}^{-}$ are suggested for the states ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}*$(3.11) and ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}*$(4.22), respectively. It is concluded from the small reduced width for neutron decay of suggested 2p-1h neutron states in ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$ that the ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$(g.s.) has only a small 2p-2h neutron component.

NUCLEAR STRUCTURE ${}_{}{}^9{}_{}{}^{}\mathrm{Be}({}_{}{}^7{}_{}{}^{}\mathrm{Li},p)$, $E=20\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, $\Gamma$. ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$ levels deduced $J$, $\pi$. Calculated ${\Gamma }_n$ deduced $l_n$, $S$. Resolution 35 keV: $\theta =3.75\mathrm{}-168.75°$; $\Delta \theta =7.5\mathrm{}°$.

Excitation functions have been measured for inelastic proton scattering from the 1.78 MeV, $2^{+}$ first excited state of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ between 3.1 and 5.7 MeV. Two previously unidentified resonances corresponding to states in ${}_{}{}^{29}{}_{}{}^{}\mathrm{P}$ with excitation energies of 6.577 and 7.272 MeV have been observed. Triple angular correlations in the Goldfarb-Seyler geometry have been measured as a function of energy over all the resonances observed in the inelastic excitation function. Information obtained from the angular correlation data has been combined with previous information concerning these states to allow $J^{\pi }$ assignments for 9 of the 11 states observed.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(p,p_1)$, measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, $E=3.1\mathrm{}-5.7$ MeV. ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(p,p_1\gamma )$, measured $p-\gamma$ correlations, deduced $J^{\pi }$ of ${}_{}{}^{29}{}_{}{}^{}\mathrm{P}$ levels.

153 cross section data are presented for targets of carbon, oxygen, and nitrogen bombarded by protons, deuterons, and tritons in the 10 to 20 MeV region. The errors range from 1 to 2%. Comparisons are made with existing measurements, where available.

NUCLEAR REACTIONS $A(b,b)A$, $A={}_{}{}^{12}{}_{}{}^{}\mathrm{C}, {}_{}{}^{14}{}_{}{}^{}\mathrm{N}, {}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, $b=p,d,t$. $E=10\mathrm{}-20$ MeV, various angles. Measured $\sigma \left(\theta \right)$, $\Delta \sigma =1\mathrm{}-2$%.

$\gamma$ rays have been detected from 230-MeV negative pions incident on a water target. De-excitation $\gamma$ rays from ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ have been identified and cross sections for excitation of particular residual states determined. Where necessary, the cross sections have been corrected for $\gamma$ feeding from higher states. Decays from short lived nuclear states result in Doppler broadened peaks which yield nuclear recoil momenta.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({\pi }^{-},\gamma X)$, $E=230\mathrm{}$ MeV, measured relative $\gamma$ yields at $\theta =90\mathrm{}°$.