Differential cross sections for the elastic scattering and inelastic scattering to the low-lying states in ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ have been measured using 50-MeV $\alpha$-particle and 30-MeV proton beams from the Texas A&M variable-energy cyclotron. Spin and parity assignments are checked and transition strengths measured for states at 1.66, 1.81, and 2.19 MeV. A $2^{+}$ assignment is made for a state at 2.45±0.02 MeV. The angular distributions are analyzed in the distorted-wave Born approximation, employing collective-model form factors. The present results are compared with previous experimental data and with recent theoretical calculations of the states in ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$.

Elastic and inelastic scattering of monochromatic photons were used for studying nuclear energy levels in ${}_{}{}^{112}{}_{}{}^{}\mathrm{Cd}$; the photons were produced by thermal-neutron capture in iron. The energy of the resonance level was 7632 keV; it was found to decay to 19 known low-lying energy levels in ${}_{}{}^{112}{}_{}{}^{}\mathrm{Cd}$. The angular distributions of the elastic and inelastic lines were measured and the following spin-parity determinations were made (energy in keV, $J^{\pi }$): 617, $2^{+}$; 1223, $0^{+}$; 1429, $0^{+}$; 1468, $2^{+}$; 1869, $0^{+}$; 2832, $0^{+}$; 2850, $2^{+}$; 3110, 2; 3193, 2; 3247, 0; and 7632, $1^{-}$. The parity of the last level was directly determined by polarization measurements, while the parities of the other levels were inferred from the radiation strength of the corresponding high-energy transitions. The $\frac{M2\mathrm{}}{E1\mathrm{}}$ mixing ratio for one primary transition was found to be about 3 orders of magnitude higher than that predicted by the simple theory. The results of statistical analysis of the data are given.

The decay of a three-quasiparticle isomeric state at 1355 keV in ${}_{}{}^{177}{}_{}{}^{}\mathrm{Ta}$ was studied using in-beam $\gamma$-ray spectroscopic techniques. Tantalum isotopes were produced by the ${}_{}{}^{175,176}{}_{}{}^{}\mathrm{L}\mathrm{u}-(\alpha ,xn)$ reactions with $\alpha$-particle energies between 24 and 48 MeV. The half-life of the isomer was measured to be $t_{\frac{1}{2}}\left(1355\mathrm{} \mathrm{keV}\right)=5.02\mathrm{}\pm 0.20$ μsec, and its spin and parity were determined to be $I^{\pi }={\frac{21}{2}}^{-}$. The $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratios and the rotational-model parameters $\frac{{(g_K-g_R)}^2}{{Q_0}^2}$ were deduced for five $\Delta I=1\mathrm{}$ transitions between members of the rotational band based on the $\frac{9}{2}\mathrm{}\left[514\right]\mathrm{}$ state.

The ${}_{}{}^{134}{}_{}{}^{}\mathrm{Cs}$ and ${}_{}{}^{115}{}_{}{}^{}\mathrm{Cd}$ isomer ratios have been measured for the following cases of charged-particle-induced fission: ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(35-\mathrm{MeV} \alpha ,f)$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}(20-\mathrm{MeV} d,f)$, ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}(19-\mathrm{MeV} d,f)$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(35-\mathrm{MeV} \alpha ,f)$. The values of the ${}_{}{}^{134}{}_{}{}^{}\mathrm{Cs}$ isomer ratio were 0.52 ± 0.02, 0.64 ± 0.01, and 0.20 ± 0.05 for the fission of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, and ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}$, respectively. The ${}_{}{}^{115}{}_{}{}^{}\mathrm{Cd}$ isomer ratios were 0.090 ± 0.006, 0.059 ± 0.007, 0.90 ± 0.12, and 0.9 ± 0.2 for the fission of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, respectively. The low values of the ${}_{}{}^{115}{}_{}{}^{}\mathrm{Cd}$ isomer ratios for the fission of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ are attributed to decay-scheme effects. The average initial fragment angular momentum was deduced from the isomer-ratio values using the Vandenbosch-Huizenga formalism. The values obtained were $(11\mathrm{}\pm 1)\hslash$, $(13\mathrm{}\pm 1)\hslash$, and $(7\mathrm{}\pm 2)\hslash$ for the ${}_{}{}^{134}{}_{}{}^{}\mathrm{Cs}$ fragment in the fission of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, and ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}$, respectively. Values of $>(15\mathrm{}\pm 4)\hslash$ and $>(13\mathrm{}\pm 4)\hslash$ for the ${}_{}{}^{115}{}_{}{}^{}\mathrm{Cd}$ fragment in the fission of ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ were obtained. These results are discussed in terms of current theories about the origin of the fragment angular momentum in fission.

Neutron-deuteron and proton-deuteron coincidence spectra in the reaction $d+d\to d+p+n$ were measured simultaneously for $E_d=6.0-13.0\mathrm{}$ MeV and ${\theta }_1=-{\theta }_2={20}^{\circ }$. The results are discussed in terms of nucleon-deuteron quasifree scattering.

The $J$ dependence for $L=2\mathrm{}$ transfer has been studied at $E_{\alpha }=28.8\mathrm{}$ MeV for the ($\alpha ,p$) reactions on ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$. The results are compared with previous ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(\alpha ,p){}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ data where no $J$ dependence is observed for $L=2\mathrm{}$ transfer.

Differential cross sections for elastic scattering of protons by deuterium have been measured at laboratory energies of 14.9, 15.5, 16.2, 17.1, 18.5, 19.0, 19.6, and 19.9 MeV. 17 angles between 21.8 and 150.9° c.m. were included in each distribution. Nine of the angles represent the zeros of the Legendre polynomials through $l=4\mathrm{}$. Relative errors were about 0.8% on the average, and absolute errors were about 1.8%. In addition, relative angular distributions were taken at 16.2, 17.1, 18.5, and 19.1 MeV, including 51 angles between 9.8 and 167.0° c.m. These were normalized to the absolute data at c.m. angles between 30 and 54° and are in good agreement at the remaining angles. Smooth curves can be drawn through the data and no indications of strong resonant behavior are found in this energy range.

An angular distribution for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\alpha ,\alpha ){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ near the center of a resonance can be fitted with any value for the real part of the resonating nuclear phase shift. This surprising result is in agreement with resonance theory and occurs because the elastic width of the resonance is ½ of the total width. In general, in a phase-shift analysis the real part of the nuclear phase shift will be indeterminate whenever the inelastic parameter is zero.

We verify the validity of the low-energy theorem for emission of soft photons in the case of two particles which interact via an exchange potential. To lowest order in $K$, the photon momentum, we define the amplitude for emission from exchange currents, and show that it cancels part of the amplitude arising from internal nucleon lines. Comparison is made with the definition of exchange currents made by other authors.

The method of $\beta -\gamma -\gamma$ and $\gamma -\gamma -\gamma$ angular correlation is used to determine the sign of $\delta$ (the amplitude mixing ratio in $\gamma$-ray transitions independent of phase conventions).

The giant resonance of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ has been investigated by means of inelastic electron scattering. The incident energies and scattering angles employed were 77.0 MeV (75°), 106.0 MeV (75°), 55.4 MeV (145.7°), and 81.0 MeV (145.7°). The data show a distinct splitting of the resonance into two large peaks near 20.5 and 24.5 MeV. Some fine structure is observed which correlates well with the position of excitations calculated by Easlea. Considerable strength is observed in the region of 14-MeV excitation which may correspond to the "pygmy" resonance seen in the photonuclear work of Cook. Data were also taken consecutively on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The form factors for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ are compared. The presence of the extra neutron in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ results in a major restructuring of the giant-resonance strength. The possibility of an isotopic splitting in the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ giant resonance is discussed.

Measurements of total cross sections for ${}_{}{}^3{}_{}{}^{}\mathrm{He}({}_{}{}^3{}_{}{}^{}\mathrm{He},2p){}_{}{}^4{}_{}{}^{}\mathrm{He}$ have been made for center-of-momentum energies between 80 keV and 1.1 MeV. A continuously recirculating differentially pumped gas target system was employed to minimize uncertainties in energy loss and straggling. A calorimetric device was used to integrate the beam current within the target gas. Proton angular distributions were measured at seven energies. The measured cross-section factor, $S\left(E\right)\mathrm{}$, was fitted to a linear function of energy for $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}<500\mathrm{}$ keV: $S\left(E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\right)=S_0+{S_0}^{\prime }{E}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$, where $S_0=\left({5.0}_{-0.4\mathrm{}}^{+0.6\mathrm{}}\right)$ MeVb and ${S_0}^{\prime }=(-1.8\mathrm{}\pm 0.5)$ b. The formula $S\left(E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\right)=S_0+{S_0}^{\prime }{E}_{\mathrm{c}.\mathrm{m}.\mathrm{}}+\frac{1}{2}{S_0}^{\prime \prime }{E}_{\mathrm{c}.\mathrm{m}.\mathrm{}}^2$, with $S_0=5.2\mathrm{}$ MeVb, ${S_0}^{\prime }=-2.8\mathrm{}$ b, and ${S_0}^{\prime \prime }=2.4\mathrm{}$ b Me${\mathrm{V}}^{-1\mathrm{}}$ gives a good representation of $S\left(E\right)\mathrm{}$ over the entire range of energies studied here.

We have measured the proton-proton bremsstrahlung cross section, $\frac{d\sigma }{d{\Omega }_{1}d{\Omega }_2}$, with 20-MeV incident proton energy, detecting coincident protons at 25° and at 30° on either side of the beam. In addition, we have determined the photon angular distributions, $\frac{d\sigma }{d{\Omega }_{1}d{\Omega }_{2}d{\theta }_{\gamma }}$. The value measured for $\frac{d\sigma }{d{\Omega }_{1}d{\Omega }_2}$ for proton angles of 25° is 0.68 ± 0.07 ${\mathrm{\mu }\mathrm{b}/\mathrm{s}\mathrm{r}}^2$ while that for 30° is 0.69 ± 0.07 ${\mathrm{\mu }\mathrm{b}/\mathrm{s}\mathrm{r}}^2$. These results are for coplanar geometry and are determined from the data using the azimuthal angular dependence for the cross section predicted by Drechsel and Maximon. The results agree with the predictions of Marker and Signell, when Coulomb corrections are included.

Negative pions produced by the National Aeronautics and Space Administration Space Radiation Effects Laboratory cyclotron were stopped in water and the nuclear deexcitation $\gamma$ rays observed. $\gamma$ rays from ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ were identified, and yields to particular states in these nuclei obtained. A prominent $\gamma$-ray peak in our spectra was from the 3.945-MeV $1^{+}$ state in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ which was formed with a rate of 1.8% per stopped pion. The Doppler-broadened line shape of the decay $\gamma$ ray for this state was analyzed to obtain the momentum distribution of the recoiling ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ nucleus. This momentum distribution is compared with momentum distributions obtained by related experiments, and to theoretical predictions. Yields to various states are presented and discussed.

A theory of correlated wave functions for finite systems is developed which systematically neglects the contribution from three-body cluster terms. The approximation made leads to a derivation of a Bethe-Goldstone equation for finite systems which includes modified occupation probabilities and self-consistent potentials for occupied states. The absence of potentials in unoccupied states follows from the neglect of three-body cluster terms. It is also shown that a careful treatment of the Pauli principle and occupation probabilities allows the application of variational techniques.

The angular variation of the ghost anomaly is found to be identical to that of the ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ ground state for the reaction ${}_{}{}^9{}_{}{}^{}\mathrm{Be}\mathrm{}(d,t)\mathrm{}{}_{}{}^8{}_{}{}^{}\mathrm{Be}$ at $E_d=2.5\mathrm{}$ MeV. The anomaly is absent from deuteron spectra of the reaction ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(\alpha ,d){}_{}{}^8{}_{}{}^{}\mathrm{Be}$, but present in spectra from the reactions ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(\alpha ,t){}_{}{}^8{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^9{}_{}{}^{}\mathrm{Be}\mathrm{}(p,d)\mathrm{}{}_{}{}^8{}_{}{}^{}\mathrm{Be}$. End points of possible three-particle reactions lie close to the observed anomaly so the interpretation is doubtful.

A new version of a method due originally to Marumori for the representation of fermion pair operators as expansions in boson variables is developed and applied to nucleons confined to a single $j$ shell. In the present formulation, a seniority basis of good angular momentum states is imaged in a subspace of the boson space — the physical boson space — characterized by the same quantum numbers. This transformation has the following properties, only the first of which is shared with previous work: (i) Pauli-principle restrictions are satisfied. (ii) The fermion pair operators approach the leading terms of their expansions as $j\to \infty$. (iii) For fixed $j$ one can identify maximal subspaces of the physical boson space in which the boson expansions converge and which define the maximum extent to which the model physical system can exhibit vibrational behavior. An extension appropriate to systems with an odd number of nucleons is also described. By consideration of the direct product, the method described here should be useful for shell-model calculations of a restricted set of states for large particle number.

Taking into account the final-state density of the leptons, a single resonance model for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}+\alpha 1^{-}$ scattering amplitude predicts a markedly asymmetric peak in the $\alpha$ spectrum following ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}\beta$ decay into continuum states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The observed peak is nearly symmetric and it is shown that this symmetry can arise from destructive interference from the subthreshold $1^{-}$ state (7.12 MeV) and/or a background from states of ∼17-MeV excitation in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. It is shown that the $\alpha$ width of the 7.12-MeV state must be an order of magnitude smaller than that of the $1^{-}$ state (9.58 MeV).