We derive an expression relating the photon-scattering cross section to the photoabsorption cross section, taking into account the underlying compound nuclear levels. This formalism provides for the first time a framework for the analysis of photon-scattering data that is valid for arbitrary width-to-level-spacing ratios of the compound nuclear levels. When applied to a giant resonance, the formalism leads to a ground-state photon branching ratio which is significantly different from that used to interpret recent Coulomb excitation experiments.

Results are presented from a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ photodisintegration experiment performed with quasimonochromatic photons using a large solid-angle detector. The tagged-bremsstrahlung technique gave a reliable absolute normalization. In addition, an unambiguous separation of the proton-triton channel from other photodisintegration channels was achieved. A total cross section of 218±8 μb was measured at a mean energy of 67±4 MeV and Legendre coefficients up to ${\mathit{a}}_5$ were extracted from the angular distributions.

The absolute p-d elastic-scattering differential cross sections were measured at 641.3 and 792.7 MeV beam energies over a range of c.m. angles from ∼35° to ∼115° and ∼35° to ∼140°, respectively. The longitudinally polarized (L-type) proton beam produced by the Lamb-shift ion source at LAMPF was used. The beam intensity was measured to high accuracy (∼0.1%) by a scintillator-beam particle-counting system designed and developed prior to the experiment. Typical uncertainties in the absolute cross sections were about 2–3% total, somewhat larger at back angles. The present results were compared with the existing measurements and the controversy about the previous data at 800 MeV was resolved. The present data can be fit with a relativistic multiple-scattering theory which uses off-mass-shell extrapolations of the nucleon-nucleon amplitudes suggested by the structure of derivative meson-nucleon couplings. Relativistic-impulse-approximation calculations do not fit these data at either energy.

Supersymmetric quantum mechanics links two Hamiltonians with the same scattering (phase equivalence) but different number of bound states. We examine the Green’s functions for these Hamiltonians as a prelude to embedding the two-body dynamics in a many-body system. We study the effect of the elimination of a two-body bound state near zero energy for the Efimov effect and Beg’s theorem.

A total of ten previously observed γ rays have been assigned to the N=Z+1 nucleus ${}_{}{}^{63}{}_{}{}^{}\mathrm{Ga}$; these provide the first information on excited states reported in this neutron-deficient system. ${}_{}{}^{63}{}_{}{}^{}\mathrm{Ga}$ has been populated using the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$${(}^{28}$Si, αp), ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$${(}^{32}$S, 2αp), and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$${(}^{29}$Si, αpn) reactions at beam energies of 80–100 MeV. Particle-γ coincidence techniques provide a definitive identification of γ transitions in ${}_{}{}^{63}{}_{}{}^{}\mathrm{Ga}$. An yrast-level scheme is proposed on the basis of charged-particle-γ, charged-particle-γ-γ, and neutron-γ-γ coincidences. Spin and parity assignments are based on neutron-gated γ-ray angular distributions, directional correlation with oriented nuclei ratios and systematics. Nine new energy levels are identified in addition to the previously known ground state, with the highest level at an excitation energy of 7.7 MeV. The results are interpreted in terms of the relevant single-particle orbitals and the systematics of the neighboring nuclei. In addition, a new determination has been made of the E2/M1 mixing ratio for the (5/$2^{\mathrm{-}}$${)}_1$→(3/$2^{\mathrm{-}}$${)}_1$ transition in ${}_{}{}^{65}{}_{}{}^{}\mathrm{Ga}$, resolving a disagreement between two previous measurements.

Measurements of electron conversion coefficients for high spin states of ${}_{}{}^{143,144}{}_{}{}^{}\mathrm{Nd}$ are reported. Parities are assigned for these states, and the results are used to test a weak-coupling model for ${}_{}{}^{143}{}_{}{}^{}\mathrm{Nd}$.

We report new cross-section and analyzing-power data for the excitation by 498-MeV protons of all narrow normal-parity states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ below 12.1-MeV excitation. In addition, spin-rotation measurements for elastic scattering and depolarization measurements for the $1_1^{\mathrm{-}}$, $2_1^{+}$, and $3_1^{\mathrm{-}}$ states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ have been performed. These data are used in conjunction with existing data for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ to study medium corrections to the effective interaction for nucleon-nucleus scattering at 500 MeV. Systematic differences between the data and nonrelativistic impulse approximation calculations based upon either the free t matrix or a recent density-dependent effective interaction are interpreted within the framework of the local-density approximation. An empirical effective interaction has been constructed which parametrizes the density dependence of the medium modifications in a simple form amenable to phenomenological analysis of data.

The parameters of the interaction are adjusted by fitting to data from many transitions simultaneously, including inelastic transitions sensitive to both the surface and the interior of the nucleus. We find that the empirical effective interaction provides a good description of both the fitted inelastic-scattering observables and elastic-scattering observables not included in the fit. Furthermore, we find that the empirical effective interaction fitted to inelastic-scattering data for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ provides an excellent description of both elastic- and inelastic-scattering data for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at 500 MeV. The most significant difference between the empirical interaction and the theoretical interaction is that absorption is enhanced at higher density, contrary to expectations based upon Pauli blocking. We find also that the empirical interaction has a stronger repulsive core than expected in nonrelativistic models of the effective interaction. Nevertheless, the optical potentials are very similar to the Schrödinger-equivalent potentials from a relativistic impulse approximation model, showing that the empirical density dependence is comparable to the equivalent density dependence due to elimination of lower components from this relativistic model of the nucleon-nucleus interaction. These results are also compared with global optical potentials from Dirac phenomenology, which suggest even stronger repulsion in the real central interaction.

The alpha-particle transfer reaction ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$${(}^7$Li,tγ${)}^{18}$O was used to study gamma deexcitation modes in ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ at a bombarding energy ${\mathit{E}}_{\mathit{L}}$=15 MeV. In this measurement 4×${10}^6$ triton-gamma coincidence events were collected. All natural parity states up to the alpha-particle threshold at 6.227 MeV were studied. These data together with our previously published study of states above threshold, using the α${+}^{14}$C radiative capture reaction, provide relatively complete spectroscopic information on states in ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ up to 8.3 MeV in excitation energy. Previously reported major gamma decay branching ratios were remeasured with higher accuracy and good agreement is found. Several new weak deexcitation modes are reported. Enhanced E1 decays, B(E1)≃${10}^{\mathrm{-}2}$ Weisskopf unit, were observed among the ${\mathit{J}}^{\mathrm{\pi }}$=$0_2^{+}$, $1_1^{\mathrm{-}}$, $1_2^{\mathrm{-}}$, $2_3^{+}$, and $3_3^{\mathrm{-}}$ states, representing some of the most enhanced E1’s found in even-even nuclei. A strong empirical correlation between enhanced E1 decays and cluster structure is established. These enhanced B(E1)’s suggest a selective deexcitation mode in which the states involved preferentially decay to cluster states. The cluster states are strongly populated in cluster transfer reactions and weakly populated in (t,p) reactions. Predictions of the vibron cluster model are compared with our data. The presence in our data of contaminant lines from ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$${(}^7$Li,α${)}^{17}$N allowed extraction of some information on ${}_{}{}^{17}{}_{}{}^{}\mathrm{N}$.

The quadrupole interaction of polarized ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$($8^{+}$,τ=0.29 μs) and ${}_{}{}^{93}{}_{}{}^{}\mathrm{Ru}$(21/$2^{+}$,τ=3.5 μs) isomers in a single crystal of Zr has been measured. The experiment utilizes the nuclear polarization induced by the tilted-multifoil interaction with separated isomer beams from a mass spectrometer. The magnitudes and signs of the quadrupole moments were deduced to be -0.33 and +0.04 b for ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$($8^{+}$) and ${}_{}{}^{93}{}_{}{}^{}\mathrm{Ru}$ (21/$2^{+}$), respectively. Together with previous work on the ${}_{}{}^{88,90}{}_{}{}^{}\mathrm{Zr}$($8^{+}$) isomers, this experiment sheds light on the particle-hole shell-model structure in the A=90 region. It also serves as a calibration of a recent experiment on parity mixing in the 17/$2^{\mathrm{-}}$-17/$2^{+}$ doublet in ${}_{}{}^{93}{}_{}{}^{}\mathrm{Tc}$. The induced nuclear polarization under the conditions of a separated reaction-product beam is found to be substantially higher than in previous in-beam experiments.

Form-factor measurements in the momentum-transfer range 0.6≤q≤2.7 ${\mathrm{fm}}^{\mathrm{-}1}$ are presented for the $1^{\mathrm{-}}$ levels in ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ at 4.46, 6.20, 7.62, and 8.04 MeV, the $3^{\mathrm{-}}$ levels at 5.10, 6.40, and 8.29 MeV, and the $5^{\mathrm{-}}$ levels at 7.86 and 8.13 MeV. These are the first measurements of the $5^{\mathrm{-}}$ states by inelastic scattering and the first electron-scattering measurements of the higher $1^{\mathrm{-}}$ and $3^{\mathrm{-}}$ states. A Rosenbluth separation of the longitudinal and transverse form factors was performed by fitting the data with a phenomenological polynomial-times-Gaussian parametrization motivated by the form of theoretical form factors when harmonic-oscillator wave functions are used. Comparisons are made with structure models. The Coulomb form factors of several levels indicate the significance of small admixtures of 3ħω components in the negative-parity wave functions.

Mean lifetimes of levels in the mirror nuclei ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{25}{}_{}{}^{}\mathrm{Al}$ have been measured using the Doppler-shift-attenuation (DSA) method and the reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${(}^{15}$N,pn${)}^{25}$Mg and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(p,γ${)}^{25}$Al, respectively. The lifetime values or limits were determined for 13 bound levels in ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$ below the excitation energy of 7 MeV and for the 1.61- and 1.79-MeV bound levels in ${}_{}{}^{25}{}_{}{}^{}\mathrm{Al}$. The lifetime values or limits of the 7.79, 8.02, and 9.00 MeV neutron unbound states in ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, and the 2.72-, 3.42-, and 4.03-MeV proton unbound states in ${}_{}{}^{25}{}_{}{}^{}\mathrm{Al}$ were also determined. The lifetimes of four levels in ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$ are reported for the first time. The targets were prepared by implanting ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ into Ta substrates, to ensure effective slowing down of the recoils. Computer simulations with the Monte Carlo method and experimental stopping power were used in the DSA analysis. Experimental transition matrix elements, based on the measured mean lifetime values, are compared with predictions of the universal sd-shell model.

For the first time an experiment has been performed to measure a magnetic monopole transition in inelastic electron scattering. In ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ the $0^{+}$→$0^{\mathrm{-}}$ transition to the level at ${\mathit{E}}_{\mathit{x}}$=10.957 MeV has been observed with a cross section of dσ/dΩ=(5.4±3.8)×${10}^{\mathrm{-}37}$ ${\mathrm{cm}}^{\mathrm{-}2}$/sr. Measurement of this transition is a direct signature of two-step contributions in electron scattering. Our measurement is in good agreement with the strength calculated for this transition.

Forward-angle cross sections and analyzing powers for the main $1^{+}$ T=1 and $1^{+}$ T=0 states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have been measured by proton inelastic scattering at 200, 400, and 600 MeV bombarding energy. The results are compared with microscopic distorted-wave impulse approximation (DWIA) calculations. The sensitivity to the optical potentials is pointed out. Two DWIA methods give compatible results for the ΔT=1 transition at 200 and 400 MeV, but differ strongly for the ΔT=0 transition at 200 MeV. For both the ΔT=0 and the ΔT=1 transitions no clear dependence on the incident energy can be ascertained for the ratio of the experimental to the theoretical cross section.

The odd-proton ${}_{}{}^{141}{}_{}{}^{}\mathrm{Eu}$ nucleus is studied with the ${}_{}{}^{110}{}_{}{}^{}\mathrm{Cd}$${(}^{35}$Cl,2p2nγ) reaction populating states in seven distinct bands. For the yrast band, high spin states are followed up to ${\mathit{I}}^{\mathrm{\pi }}$=43/$2^{\mathrm{-}}$ and a band crossing, due to the alignment of the second and third ${\mathit{h}}_{11/2}$ protons, is observed at a rotational frequency ħ${\mathrm{\omega }}_{\mathit{c}}$=0.37 MeV. For the positive-parity bands, only the three-quasiparticle configuration, namely, π${\mathit{g}}_{7/2}$⊗[π${\mathit{h}}_{11/2}$${]}^2$, is observed up to high spins. In addition, two ΔI=1 bands with no E2 crossovers are found in this nucleus. The cause of the relatively strong M1 transition bands can be explained by a drastic shape change due to the alignment of an ${\mathit{h}}_{11/2}$ neutron pair. A systematic comparison amongst the N=78 isotones, ${}_{}{}^{137}{}_{}{}^{}\mathrm{Pr}$, ${}_{}{}^{139}{}_{}{}^{}\mathrm{Pm}$, and ${}_{}{}^{141}{}_{}{}^{}\mathrm{Eu}$, is made.

The generator coordinate method for nuclear collective motion is studied in a simple model in which the dynamics is governed by the pairing interaction alone. A formula is derived for the overlap correlation length which exhibits the correct empirical dependence on nucleus mass number, pairing gap, and quadrupole deformation. The same analysis applied to the quadrupole inertia parameter provides an expression proportional to the square of the pairing gap, the same functional form as obtained from the cranking model. However, the simplified model differs numerically by a factor 2 to 4 from the results of a complete Hartree-Fock BCS calculation. The spectrum is well described by a hopping model based on the Hartree-Fock single-particle properties.

The even-mass Yb isotopes are studied in the boson-plus-fermion-pair model. The energy spectra of the ground-state bands, side bands, quasi-β bands, and quasi-γ bands can be reproduced quite well. It was found that the high-spin states between the second and the first backbends are mainly one-fermion-pair states while those states above the second backbends are mainly two-fermion-pair states. The effective moments of inertia and B(E2) values can be reproduced qualitatively. Some possible extensions of the model are discussed.

The Fermi energy ${\mathit{E}}_{\mathit{F}}$ is defined as the negative of the average between the separation energies of a nucleon from the (A+1)- and A-nucleon systems. In the independent-particle limit, ${\mathit{E}}_{\mathit{F}}$ is the average between the energies of the last occupied and of the first unoccupied shell-model orbits. For mass numbers 40≲A≲208, the experimental neutron Fermi energies ${\mathit{E}}_{\mathit{F}\mathit{n}}$ increase approximately linearly with increasing asymmetry parameter η=(N-Z)/A. In contrast, the experimental proton Fermi energies ${\mathit{E}}_{\mathit{F}\mathit{p}}$ are, on the average, nearly independent of η; when the average single-particle Coulomb energy ${\mathit{E}}_{\mathit{C}}$ is subtracted, the quantity ${\mathit{E}}_{\mathit{F}\mathit{p}}$-${\mathit{E}}_{\mathit{C}}$ decreases linearly with increasing η, with a slope whose modulus differs from that found for ${\mathit{E}}_{\mathit{F}\mathit{n}}$. These features are analyzed in the framework of two mean-field models; they both include an isoscalar and an isovector central component, as well as a Coulomb correction in the case of protons. From the comparison between the n${\mathrm{-}}^{208}$Pb and p${\mathrm{-}}^{208}$Pb mean fields, it is derived that the depth of the symmetry potential is nearly independent of energy in the domain 15≲E≲50 MeV, in close agreement with a recent phenomenological study of the global optical-model potential for nuclei with mass numbers 40≤A≤208.

In the vicinity of the Fermi energy, the isoscalar and isovector components are assumed to have Woods-Saxon radial shapes and linearly energy-dependent depths. In both models, the depth of the symmetry potential is taken equal to (23.2-0.46E) MeV. In the first model, all the parameters are extracted from a recent dispersion relation analysis of the mean fields felt by neutrons and protons in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$; then, the calculated neutron Fermi energies are in good agreement with the experimental values but the calculated proton Fermi energies are larger than the experimental values, except for the lead isotopes. The second model incorporates, in addition, information derived from dispersion relation analyses of the n${\mathrm{-}}^{40}$Ca and n${\mathrm{-}}^{90}$Zr potentials; its main characteristics are that the potential radius parameter ${\mathit{r}}_{\mathit{V}}$=${\mathit{R}}_{\mathit{V}}$${\mathit{A}}^{\mathrm{-}1/3}$ and the isoscalar depth both depend upon mass number; this second model yields satisfactory agreement with the experimental Fermi energies, not only on the average but also along isotope and isotone chains associated with a magic number of protons or of neutrons. The definition of the isovector potential adopted here is compared with prescriptions used in previous works. Some intrinsic limitations of a mean-field description are pointed out.

In this paper, stretching of nuclei is microscopically interpreted via the fermion dynamical symmetry model. A four-parameter energy formula with stretching for the yrast band of deformed nuclei is derived. This formula can account for the states in the yrast band below backbending and with the ratio ${\mathit{R}}_4$=E($4^{+}$)/E($2^{+}$)>0.32 in the rare earths and the actinides. It is also shown that stretching can improve the B(E2) fits in the rare earths as well. However, analyses of the fitted parameters reveal that the smooth increase of the moment of inertia and the enhancement of the B(E2)’s at low spins appear to be a more complicated phenomenon, thus suggesting the necessity to further microscopically understand these low-spin behaviors.

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the ${\mathit{v}}_2$ central interaction which is derived from Reid’s soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for the summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.

In recent years we have developed a mathematical treatment of large amplitude collective motion in the adiabatic limit and formulated a set of methods, collectively known as the generalized valley approximation, that were applied to the approximate solution of a series of simplified models. In this paper we report the application of one of our algorithms to the study of the nucleus ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, our first successful application to a realistic nuclear physics problem. We determine self-consistently a one-dimensional manifold of triaxial Slater determinants that connects the energy minimum of oblate deformation to the prolate minimum. Upon requantization of the implied collective Hamiltonian in the intrinsic frame, reasonable agreement with a shell-model calculation of the low-lying levels is achieved. Application of a theoretical criterion for assessing the quality of decoupling shows that a one-dimensional path is not sufficiently well decoupled in the model studied, thus suggesting one direction for future improvement. We compare our research with the only comparable previous work, that of Pelet and Letourneux.