We examine the role of Galilean invariance in a nonrelativistic theory of pions and nucleons. We define a nonrelativistic pion-nucleon interaction $h$ as one which in perturbation theory gives the same matrix for a physical reaction as the limit of small nucleon velocities of the relativistic matrix. The latter matrices are always Galilean invariant, but this does not require that $h$ be Galilean invariant. If pion emission or absorption occurs from a nucleon moving in a potential, then the Galilean correction term can be shown to be ambiguously of order $\frac{v}{c}$ or of order $\frac{v^2}{c^2}$. We show that $h$ cannot always reproduce the nonrelativistic limit of a relativistic matrix. Finally, we suggest that pion production by nucleons on nuclei with excitation of giant dipole and quadrupole states may be particularly sensitive to the presence of a Galilean correction term in the production matrix.

NUCLEAR REACTIONS Nonrelativistic form of pion-nucleon interaction.

Coulomb effects in high energy charged hadron-nucleus collisions are studied in a formalism which is exact within the framework of multiple diffraction theory and takes into account the extended charge effects of the incident hadron and the bound protons. Several more approximate but simpler formulas are also considered and their accuracy discussed. Results are extended to include heavy-ion collisions in the optical limit of the Glauber theory and in the Chou-Yang model. Applications are made to the proton-deuteron elastic and elastic plus quasielastic scattering measurements below 70 GeV to extract the ratio of real to imaginary part and the slope parameter of the proton-neutron elastic scattering amplitude. The results are compared with those from dispersion relation calculations and from earlier analyses. Approximate analytic formulas derived for $p-d$ scattering give results almost identical to the more exact expressions. For nucleus-nucleus collisions the Coulomb effects are found to be important over a rather wide range of momentum transfers.

NUCLEAR REACTIONS $d(p, p)$, $E=10-70\mathrm{}$ GeV; calculated $\sigma (E, \theta )$ in Coulomb-nuclear interference region; deduced $p-n$ scattering amplitude parameters. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p)$, $E=1.04\mathrm{}$ GeV, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$), $E=2.1\mathrm{}$ GeV/nucleon; Coulomb effects, calculated $\sigma \left(\theta \right)$.

Quasifree proton-proton and proton-deuteron scattering cross sections on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ have been measured and compared with theoretical calculations in the distorted wave impulse approximation. Information on the low components for the proton and deuteron momentum distributions in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are deduced.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}(p, 2p)$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}(p, pd)$, $E=156\mathrm{}$ MeV; measured $\sigma (E_1, E_2, {\theta }_1, {\theta }_2)$; proton and deuteron momentum distributions in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ deduced.

The differential cross section for the proton ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering at 156 MeV was measured in the angular range from 10° to 168°. An optical potential analysis with an exchange term is performed and extended to the 100 and 85 MeV data. Some of the impulse approximations are tested and a comparison is performed with a Glauber calculation.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}(p, p)$, $E=156\mathrm{}$ MeV measured $\sigma \left(\theta \right)$; optical potential analysis, impulse approximations tested.

The energy dependence of the angular correlation of the cascade $2^{-}$(723 keV $\beta$ particle)-$2^{+}$(1260 keV $\gamma$ ray)$0^{+}$ in the decay of ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sb}$ is measured and found to agree with the reports of Raghavan et al. and Yamada et al. Nuclear matrix elements governing the 723 keV $\beta$ transition are extracted using the available experimental data on this transition. Buhring's formulas that are simplified by simms are used in the analysis. It is observed that the contribution of the nondiagonal elements to the Coulomb Hamiltonian is significant.

RADIOACTIVITY ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sb}$; measured $\beta \gamma \left(\theta \right)$; deduced $\beta$ decay nuclear matrix elements.

The nuclear spectroscopy of ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$ has been studied by means of $\gamma$-ray and charged-particle spectroscopy. Information on ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$ levels was obtained via the decay of ${}_{}{}^{145}{}_{}{}^{}\mathrm{Pr}$ and the ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}(n, \gamma )$ reaction with thermal neutrons. From the $\gamma$-ray spectroscopy ≈ 20 energy levels were assigned to ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$, and 43 $\gamma$ rays could be placed in the decay scheme. The charged-particle spectroscopy of ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$ consisted of the ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}(d, p)$ reaction at $E_d=33.3\mathrm{}$ MeV, the ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}(\alpha , {}_{}{}^3{}_{}{}^{}\mathrm{He})$ reaction at $E_{\alpha }=66.2\mathrm{}$ MeV, and the ${}_{}{}^{146}{}_{}{}^{}\mathrm{Nd}(p, d)$ reaction at $E_p=31\mathrm{}$ MeV. Differential cross sections for the charged particle reactions were measured over the range of ∼7° to ∼37° lab for ≈ 40 excited states. These angular distributions are compared with distorted-wave Born approximation calculations to extract $l$ values and spectroscopic factors.

RADIOACTIVITY ${}_{}{}^{145}{}_{}{}^{}\mathrm{Pr}$; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coin ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$ deduced levels, $log\mathrm{ft}$, $J^{\pi }$.

NUCLEAR REACTIONS ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}(n, \gamma )$, $E=\mathrm{thermal}$; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coin ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}(d, p)$, $E=33.3\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; $\theta =7.5-32.5\mathrm{}°$. ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}(\alpha , {}_{}{}^3{}_{}{}^{}\mathrm{He})$, $E=66.2\mathrm{}$ MeV; measured $\sigma \left(15\mathrm{}°\right)$. ${}_{}{}^{146}{}_{}{}^{}\mathrm{Nd}(p, d)$, $E=31\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; $\theta =7.5-32.5\mathrm{}°$. DWBA analysis, resolution 25 keV. ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$ deduced levels, $l$, $J^{\pi }$, $S$, $Q$.

The concept of rearrangement energy in nuclear particle removal is carefully defined by specifying several energies associated with the process and its analysis. Connection is made between the present definition and closely related concepts apt to be confused with "rearrangement energy" so defined. Remarks are made concerning the implications of rearrangement to analysis and interpretation of experimental data.

NUCLEAR STRUCTURE Nuclear rearrangement energy theoretically defined and differentiated from related energies. Reaction theories examined regarding rearrangement.

The various transitions induced by muon capture are described and classified in the framework of the shell model. The influence of the muon amplitude overlap with the initial nucleus on the distribution of the multipole transitions is considered, after which the interplay of those various excitations is analyzed to obtain information on the over-all trend of the mean excitation energy of the final nucleus.

NUCLEAR REACTIONS Shell model effects in muon capture calculations.

The effect of the parity nonconserving nuclear force on the 501-keV $\gamma$ transition of ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$ has been confirmed by a remeasurement of the angular distribution asymmetry of the radiation emitted by ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}_{}^m{}_{}{}^{}$ polarized at temperatures down to 16 mK. A difference of 1% was observed between the $\gamma$-ray intensities parallel and antiparallel to the nuclear polarization direction. When the results of the present study are averaged with previous nuclear polarization experiments and compared with the results of circular polarization experiments, It is deduced that the parity mixing can be uniquely assigned to an irregular $\tilde{E}2$ multiple, rather than to a higher order irregular multiple such as $\tilde{M}3$. Assuming a vanishing $\tilde{M}3$ component, the present study yields $\epsilon =\frac{〈\tilde{E}2〉}{〈M2\mathrm{}〉}=-0.026\mathrm{}\pm 0.002$, and the global average from all measurements is $\epsilon =-0.030\mathrm{}\pm 0.002$.

NUCLEAR STRUCTURE ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$; 501-keV transition, parity mixing.

The disagreement that currently exists regarding the calculated and experimental values of the triton binding energy ($E_T$) and the doublet scattering length (${}_{}{}^2{}_{}{}^{}a$) is analyzed in considerable detail. Using the unitary pole approximation, which has previously been tested with great success, we have calculated $E_T$ and ${}_{}{}^2{}_{}{}^{}a$ for a large class of realistic potentials. The results show that the one-boson-exchange potentials (OBEP) give in general ∼1 MeV more binding for ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and correspondingly smaller ${}_{}{}^2{}_{}{}^{}a$ than the local hard- and soft-core potentials. This difference is shown to be partly due to the fact that the OBEP have in general smaller deuteron $D$-state probability, and partly due to the fact that they fit the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ $n-p$ rather than the $p-p$ data. Finally, we demonstrate that the correlation between $E_T$ and ${}_{}{}^2{}_{}{}^{}a$, predicted by Phillips on the basis of separable potential calculations, has validity for the more realistic interactions.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{H}$; calculated binding energy, doublet scattering length. Faddeev approach, realistic $N-N$ interactions.

A method recently proposed for treating recoil effects in electron scattering is shown to be incorrect. The appropriate recoil correction factors are given for the extraction for both radiative decay widths and integrated photoabsorption cross sections from electron scattering.

NUCLEAR REACTIONS Electron scattering theory, recoil effects, center-of-mass $\sigma$, relationship with $\gamma$ absorption, $\gamma$ decay.

$B\left(E2\mathrm{}\right)\mathrm{}$ transition rates in $A=42\mathrm{}$ and $A=43\mathrm{}$ nuclei have been calculated in ${\mathrm{}\left(\mathrm{pf}\right)\mathrm{}}^n$ model spaces using an effective interaction and effective charges obtained by summing the diagrams of the Tamm-Dancoff approximation for screened particle-hole vertices. Good agreement with measured $B\left(E2\mathrm{}\right)\mathrm{}$ rates are obtained for transitions between high-spin states. The results are further very similar to those obtained by parametrizing the effective charges.

NUCLEAR STRUCTURE $B\left(E2\mathrm{}\right)\mathrm{}$ transition rates in $A=42, 43$ nuclei, calculated with ${\mathrm{}\left(\mathrm{pf}\right)\mathrm{}}^n$ wave functions and realistic effective interaction and charges.

In an attempt to clear up discrepancies between lifetimes measured by the nuclear resonance fluorescence method and by the Doppler shift attenuation method, the results of a further resonance fluorescence experiment are reported for the 720, 1237, 1409, 1662, and 2092 keV levels in ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}$.

NUCLEAR REACTIONS ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}(\gamma , \gamma )$, bremsstrahlung $0.8<\mathrm{}{E}_e<2.2\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, deduced $\tau \text{'}\mathrm{s}$.

The branching ratio $\frac{[{}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}\to {}_{}{}^{19}{}_{}{}^{}\mathrm{F}_{}^{*}{}_{}{}^{}(1554\mathrm{} \mathrm{keV})+e^{+}+\nu ]}{[{}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}\to {}_{}{}^{19}{}_{}{}^{}\mathrm{F}+e^{+}+\nu ]}$ as inferred from observing a subsequent $\gamma$ transition in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ is found to be (8.2±2.0) × ${10}^{-6\mathrm{}}$. Uncertainties about possible ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ contamination lead to the conservative interpretation of this result as an upper limit for the branching ratio. The implications for a recently suggested study of inelastic neutrino scattering from ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ are discussed.

RADIOACTIVITY ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$; measured $\beta$ decay branching ratio to 1554 keV level.

The half-life of the ground state of ${}_{}{}^{212}{}_{}{}^{}\mathrm{Po}$ in the decay of ${}_{}{}^{212}{}_{}{}^{}\mathrm{Bi}$ has been measured by recording $\beta \alpha$-delayed coincidences. The decay curve analyzed by the slope method gave the half-life $T_{\frac{1}{2}}\left({}_{}{}^{212}{}_{}{}^{}\mathrm{Po} \mathrm{ground}\mathrm{state}\right)=296\mathrm{}\pm 2$ ns.

RADIOACTIVITY ${}_{}{}^{212}{}_{}{}^{}\mathrm{Po}$; measured $T_{\frac{1}{2}}$.

It is shown by means of an example that a multiple-scattering series for neutron-deuteron scattering, based on the Alt-Grassberger-Sandhas version of the Faddeev equations, can be made to converge by subtracting out the deuteron pole in the two-nucleon $T$ matrix. The subtraction is carried out by means of Kowalski's generalized Sasakawa method. The interactions between the nucleons are rank one separable potentials with Gaussian form factors.

NUCLEAR REACTIONS Scattering theory, neutron-deuteron scattering below breakup threshold.

Energy levels and spectroscopic factors for the low-lying levels in ${}_{}{}^{99}{}_{}{}^{}\mathrm{Mo}$ are calculated within the framework of the quasiparticle-vibration coupling approach in the unified nuclear model. The calculated results are in very good agreement with the experimental data. Nuclear moments for the ground and first excited states are also predicted.

NUCLEAR STRUCTURE ${}_{}{}^{99}{}_{}{}^{}\mathrm{Mo}$; calculated levels, $J$, $\pi$, and spectroscopic factors; $\mu$ and $q$ for the ground and first excited states. Compared with experiments.

Distorted wave impulse approximation calculations of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(e, e^{\prime }p)$ cross sections show no sensitivity to short range correlations in the range of recoil momenta covered by the data. For this result, which is in contrast to previous calculations, it is crucial to use correlated wave functions of correct rms radii on which the quality of the fit depends critically.

NUCLEAR REACTION ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(e, e^{\prime }p)$; $E=500\mathrm{}$ MeV; DWIA calculation.

Inelastic electron scattering 180° cross sections for the excitation of the 2.523 MeV ${\mathrm{½}}^{+}$ first excited state in ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ have been determined to be predominantly $E2\mathrm{}$, and from them an upper limit of ${\Gamma }_{\gamma }\mathrm{}\left(M1\mathrm{}\right)\mathrm{}\le 0.1$ meV for an $l$-forbidden $M1\mathrm{}$ component has been extracted. This disagrees with other results for this state that imply an $M1\mathrm{}$ width comparable to the $E2\mathrm{}$ width.

NUCLEAR REACTIONS ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}(e, e^{\prime })$, $E=50.98, 60.65$ MeV; measured $\sigma (E, E^{\prime })$ at ${\theta }_{\mathrm{lab}}=180\mathrm{}°$. Deduced partial width $\Gamma \mathrm{}\left(M1\mathrm{}\right)\mathrm{}$. Natural ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ target.

New measurements have been made with the ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}(p, t)$ reaction to excite the $K^{\pi }=2^{-}$ rotational band in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. Coupled-channel Born approximation calculations fail to account for the angular distribution of the transition to the $4^{-}$ member of this band, although they describe well that for the transition to the $2^{-}$ member. Particularly significant is the failure of the cross section for the $4^{-}$ transition to decrease at forward angles. This behavior is in dis-agreement with that expected for unnatural parity transitions in ($p, t$) reactions which proceed through multistep processes involving inelastic excitations. The implications of these results for the reaction mechanism are discussed.

NUCLEAR REACTIONS ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}(p, t)$, $E=40\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$ for $E_{\mathrm{exc}}=4.97\mathrm{} \left(2^{-}\right), 5.63 \left(3^{-}\right), \mathrm{and} 7.01 \left(4^{-}\right)$ MeV. Compared to CCBA calculations.