It is shown that stable collective particle hole excitations are possible in a generalized Hartree-Fock basis which describes a ground state that has less symmetry than the Hamiltonian. It appears that these collective states remain stable also for strong attractive interaction.

[NUCLEAR STRUCTURE Nuclear matter density fluctuations, generalized random phase approximation.]

A cluster expansion of the three-body problem is constructed from an asymmetric choice of the Alt-Grassberger-Sandhas operator equations. The Karlsson-Zeiger approach is shown to lead to one choice of the effective interaction. In a model three-boson problem it is found that no numerical advantage is gained by solving the cluster expansion corresponding to the Karlsson-Zeiger choice of operators.

Density matrices and dyadic operators are systematically introduced in the definition of a $T$-matrix element and the square modulus of that element. This use of the density matrices and dyadic operators provides two new variational functionals in addition to the Kohn-Schwinger type functional. An equivalence between the evaluation of the inverse of an operator and a diagonalization procedure for practical calculations is also established.

We have investigated the possibility of describing nuclear one-body densities as a sum of step functions. The results show that a relatively limited number of bins is sufficient to fit the form factor up to 2-3 ${\mathrm{fm}}^{-1\mathrm{}}$. Such approximate nuclear densities are useful to calculate various contributions in multiple scattering problems; two examples are presented.

Interband $B\left(E2\mathrm{}\right)\mathrm{}$ values from dynamic deformation theory using the $P+Q·Q$ interaction reproduce recent accurate data from Doppler shift recoil experiment contrary to recent claims.

[NUCLEAR STRUCTURE $B\left(E2\mathrm{}\right)\mathrm{}$ values in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Gd}$, dynamic deformation theory.]

It is suggested that the de-averaged 180° excitation function of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, recently considered by Frahn and Kaufmann, is strongly model dependent. Within a multistep $\alpha$-transfer description of the back-angle anomaly, we obtain a de-averaged 180° excitation function that exhibits a more regular gross structure.

Differential cross section data for inelastic proton and neutron scattering to the first $2^{+}$ states in ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ at several energies in the 11-26 MeV range have been analyzed using a microscopic distorted-wave Born approximation model. The entrance- and exit-channel optical potentials and the transition form factors were calculated consistently in a folding model using a density-dependent interaction obtained from nuclear matter calculations based upon a free nucleon-nucleon interaction. These microscopic calculations yield reasonable agreement with the data. The model was used to determine the ratio of neutron and proton transition matrix elements $\frac{M_{\mathrm{n}}}{M_{\mathrm{p}}}$ for these excitations.

The rotation, ${\phi }_{\mathrm{pnc}}$, of a neutron beam polarization vector due to parity nonconserving forces is measured in a lanthanum target. It is found that $\frac{{\phi }_{\mathrm{pnc}}}{l}=-(21.9\mathrm{}\pm 2.9)\times {10}^{-5\mathrm{}}$ rad/cm, where the negative sign corresponds to a left-handed rotation of the neutron spin about its momentum.

Quasielastic pickup and stripping reactions have been measured for the reaction ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$+${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ at 695 MeV with a magnetic spectrometer. The angular distributions observed for single neutron pickup are analyzed with the distorted-wave Born approximation, which accounts well for the absolute differential cross sections. Quasielastic transfer reactions account for about 20% of the total reaction cross section.

Previous measurements have shown that pion double-charge-exchange angular distributions between nonanalog $J^{\pi }=0^{+}$ states at $T_{\pi }=164\mathrm{}$ MeV are consistent with simple diffractive scattering, whereas angular distributions between analog $J^{\pi }=0^{+}$ states at $T_{\pi }=164\mathrm{}$ MeV are not. We present measurements of angular distributions for the nonanalog reaction ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({\pi }^{+},{\pi }^{-}){}_{}{}^{16}{}_{}{}^{}\mathrm{Ne}$(g.s.) at two additional energies and compare the energy dependence with that expected for diffractive scattering.

The bremsstrahlung-induced fission cross section of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ was measured in the energy region of the giant dipole resonance. The data analysis, performed in terms of the bremsstrahlung spectrum calculated in the Davies-Bethe-Maximon approximation, shows that the photofission cross section measured at Livermore is more compatible with our results than the ($\gamma ,f$) data from Saclay.

Inclusive mass, energy, and angular distributions of all fragments with $A\ge 6$ have been measured for alpha-particle-induced reactions on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at five energies between 49 and 159 MeV. From these data the evolution of the dominant reaction mechanisms with energy is characterized. Based on analysis of the mean value of the mass distribution, it appears that linear momentum transfer from projectile to target initially increases with beam energy and reaches a maximum at about 30-40 MeV/nucleon. The low-energy data are consistent with compound nucleus formation and simple transfer processes. At higher energies the growth of forward-peaked angular distributions, continuum energy spectra, and the disappearance of two-body states demonstrate the increasing importance of nucleon-nucleon collisions and multibody breakup mechanisms as the velocity of the projectile exceeds the Fermi velocity. The observed total reaction cross section decreases with increasing bombarding energy. Inclusion of these new data into the excitation functions for $6\le A\le 11$, which are required for nucleosynthesis calculations relevant to the origin of the elements Li, Be, and B, does not significantly alter conclusions based on previously available data.

Mass, energy, and angular distribution data for fragments with $A\ge 6$ produced in intermediate-energy proton- and alpha-particle-induced reactions on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ nuclei are compared with the results of an intranuclear cascade calculation followed by deexcitation of the residual nuclei via a Fermi breakup mechanism. In this latter step all possible particle-stable exit-channel states are included in the phase space available for decay. The shapes of the angular distributions are reproduced successfully by the calculation, even at relatively low bombarding energies (e.g., $E_{\alpha }=60\mathrm{}$ MeV). The energy spectra are also reproduced qualitatively. The isobaric cross sections of fragments heavier than the target nucleus are underpredicted for alpha-particle-induced reactions, whereas the yields of fragments with $A=6-8\mathrm{}$ are overpredicted. The former discrepancy is attributed to the importance of alpha-particle breakup during the cascade while the latter may serve as a measure of the relative importance of statistical multibody breakup mechanisms.

[NUCLEAR REACTIONS Intranuclear cascade, Fermi breakup model, evaporation model; calculated $\sigma (E,\theta ,A)$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\alpha ,\mathrm{HI})$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(p,HI), ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(p,HI); HI: $A=6-19\mathrm{}$.]

The possibility of a nucleus being excited during pair production has been investigated. Total cross sections for both $E1\mathrm{}$ and $M1\mathrm{}$ transitions have been evaluated as a function of photon energy and differential cross sections expressed as a function of the outgoing electron energy are also calculated.

The validity of the triad of one inhomogeneous and two homogeneous Lippmann-Schwinger equations as a means to determine three-particle scattering states uniquely is reconfirmed. This is done by studying the on-spectrum limits of resolvent equations and by relating the properties of the triad to the characteristic features of any multichannel system. In this way it is made clear that recent objections against the existence and the necessity of the homogeneous equations not only contradict rigorous proofs concerning the relevant $\epsilon$ limits, but also disagree with the basic structure of multichannel collision theory. The origin of the erroneous claims is exhibited in detailed error analyses.

This paper is mainly concerned with the construction and various properties of a new class of antisymmetric, two-fragment, elastic scattering optical potentials. The construction is based directly on the wave function formulation of $N$-particle collision theories, which are antisymmetrized herein using the method of Adhikari and Glöckle. Those theories which are label transforming are considered first. For such theories, the resulting optical potentials are asymmetric but nevertheless real for energies below the inelastic threshold $E_{\mathrm{inel}}$, and are asymmetric and absorptive for $E\ge E_{\mathrm{inel}}$. This unusual feature of asymmetry is a consequence of working directly with $N$-particle collision theories, almost all of which are expressed in non-Hermitian matrix form, and arguments are presented as to why asymmetry is not a practical problem. Not only are the new class of optical potentials asymmetric, it is also found that exchange effects generally enter them in an extremely simple fashion. These latter two features distinguish the members of the new class from the optical potential developed recently by Goldflam and Kowalski. Examples of label-transforming theories producing such potentials are the extended Faddeev theory of Levin, the precursor form of the Bencze, Redish, Sloan theory, and the wave function component theory of L'Huillier, Redish, and Tandy. Their existence establishes that formalisms other than those based on the Alt, Grassberger, Sandhas transition operator lead to symmetrized optical potentials free of elastic unitarity cuts, albeit potentials which are not Hermitian analytic. In addition to the above theories, a new, symmetrized form of the equations of the channel permuting array theory is developed.

The extension of Siegert's theorem for the retarded electric multipole field is constructed. Analogously, a form of the electric current is developed which is manifestly conserved. Isolation of those components of the Fourier transform of the current which are constrained by current conservation is shown to be unique. In the new form of the electric multipole fields, the current enters only in the combination $\overrightarrow{\mu }\left(\overrightarrow{\mathrm{x}}\right)=\frac{1}{2}\overrightarrow{\mathrm{x}}\times \overrightarrow{\mathrm{J}}\left(\overrightarrow{\mathrm{x}}\right)$.

The ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$(p,p) and ($\mathrm{p},{\alpha }_0$) differential cross sections were measured in the range $E_{\mathrm{p}}=0.92\mathrm{} \mathrm{to} 1.85$ MeV with an overall resolution of 350 to 400 eV (full width at half maximum.) Resonance parameters were extracted for 31 resonances with a multilevel, multichannel, $R$-matrix analysis code; these parameters include resonance energy, total angular momentum, partial elastic and inelastic widths, and channel spin and orbital angular momentum mixing ratios. Eleven analog states were identified, and the Coulomb displacement energies and spectroscopic factors were calculated. For the $2^{+}$ resonance at $E_{\mathrm{p}}=1.37\mathrm{}$ MeV the entrance orbital angular momentum mixing ratio was determined. The relevance of this mixing ratio to a previous test of time reversal invariance is discussed.

The electromagnetic form factors for the stronger transitions to negative parity states in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ were measured for electron energies 90-280 MeV and scattering angles of 90° and 160°. The iso-scalar $K^{\pi }=0^{-} \mathrm{and} 3^{-}$ bands show form factors in agreement with open-shell random-phase approximation calculations, even though the parentages of these two bands are radically different. For the isovector negative parity states, a quenching of magnetic strength is observed; its origins are discussed.

Measurements of the Coulomb excitation probability of the first $2^{+}$ state of ${}_{}{}^{136}{}_{}{}^{}\mathrm{Ba}$ were carried out using back-scattered ions of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The static quadrupole moment $Q_{2^{+}}$ and the reduced transition probability $B(E2;0^{+}\to 2^{+})$ have been determined using the reorientation effect. It is found that $Q_{2^{+}}=+0.01\mathrm{}\pm 0.05e\mathrm{b} (+0.25\mathrm{}\pm 0.05e\mathrm{b})$ for the positive (negative) sign of the $2^{+}$′ interference term, and $B(E2;0^{+}\to 2^{+})=0.399\mathrm{}\pm 0.003e^2{\mathrm{b}}^2$.