We have studied ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-$p$ collisions at a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ incident momentum of 8.56 GeV/c using the 1 m Dubna bubble chamber. The $p$— ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering, the coherent $p+{}_{}{}^4{}_{}{}^{}\mathrm{He}\to N+{}_{}{}^4{}_{}{}^{}\mathrm{He}+\pi$ production and the breakup reaction $p+{}_{}{}^4{}_{}{}^{}\mathrm{He}\to p+{}_{}{}^3{}_{}{}^{}\mathrm{He}+n$ have been investigated. Cross sections and production features are presented. From the breakup reaction, subsamples of events in which a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ or a $n$ appear as spectators were selected. These events were used to study the virtual $\mathrm{pn}\to \mathrm{pn}$ and $p+{}_{}{}^3{}_{}{}^{}\mathrm{He}\to p+{}_{}{}^3{}_{}{}^{}\mathrm{He}$ scattering.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}(p, p)$, ($p, p{\pi }^0$), ($p, n{\pi }^{+}$), ($p, \mathrm{pn}$), $E=1.41\mathrm{}$ GeV; bubble chamber; measured $\sigma$; deduced $n(p, p)$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}(p, p)$.

A coupled-channel computer program has been used to calculate dispersion corrections to elastic and inelastic electron scattering from ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$ arising from the virtual excitation of some intermediate states in the ground state rotational band. Data from recent experiments on these nuclei have been analyzed using both phenomenological and Fourier-Bessel forms for the transition charge densities. The inclusion of dispersion corrections in the analysis was found to affect the extracted nuclear transition charge densities at a level comparable to other sources of uncertainty. These dispersion corrections did not remove the discrepancies existing between these experiments and the predictions of microscopic theories.

NUCLEAR REACTIONS ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}(e, e^{\prime })$, and ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}(e, e^{\prime })$ calculations, coupled-channels, $35 \mathrm{MeV}<E<\mathrm{}350\mathrm{} \mathrm{MeV}$. Dispersive effects on elastic and inelastic cross sections and on extracted nuclear shapes.

The 0° neutron spectra resulting from 800 MeV proton bombardment of targets of Al, Ti, Cu, W, Pb, and U have been measured for neutron momenta above 500 MeV/c. Integrated cross sections for the quasielastic charge exchange peaks and the broad pion associated peaks at lower momenta show a remarkably smooth dependence on atomic mass of the target, varying as $A^{\frac{2}{3}}$ and $A^{\frac{1}{2}}$, respectively.

NUCLEAR REACTIONS Al, Ti, Cu, W, Pb, U ($p, n$), $E=800\mathrm{}$ MeV; measured $\sigma$ (0°; $P_n$); deduced $A$ dependence of charge exchange and pion associated cross sections.

Cross sections for about two dozen radioactive spallation products have been measured for 50-, 100-, 190-, and 350-MeV ${\pi }^{\pm }$ and for 200- and 350-MeV proton interactions with copper. Sums of measured pion-induced cross sections at 50 and 350 MeV are about the same as for protons of 200 and 590 MeV, respectively. However, at 100 and 190 MeV, nearer to the (3,3) pion-nucleon resonance, these pion-induced cross section sums are 50 to 75% greater than those for protons of similar total energy. Ratios of the ${\pi }^{-}$ to ${\pi }^{+}$ cross sections are greater than unity for neutron-rich products and less than unity for neutron-deficient products at all four energies, indicating that pion absorption is a substantial reaction mode, even at 190 and 350 MeV. At 100 MeV, and especially at 50 MeV, absorption appears to dominate over inelastic scattering and the $\frac{{\sigma }_{\pi }^{-}}{{\sigma }_{\pi }^{+}}$ ratios are noticeably changed from those at the higher energies. The intranuclear cascade plus evaporation codes reproduce the proton cross sections fairly well. The pion version of the intranuclear cascade code reproduces the pion results quite well at 350 MeV, but it underestimates them significantly at 50 and 100 MeV.

NUCLEAR REACTIONS Cu (${\pi }^{\pm }$, spallation) and Cu ($p$, spallation), $E_{{\pi }^{\pm }}=50, 100, 190, 350$ MeV, $E_p=200, 350$ MeV. Production cross sections for radioactive residual nuclei. Comparison with intranuclear cascade plus evaporation calculations.

Angular distributions for the elastic and inelastic scattering of 0.8 GeV protons from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ have been measured. Reported are data for the ground, 4.4 MeV 2+, 7.6 MeV 0+, 9.6 MeV $3^{-}$, and 14.1 MeV 4+ states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; the ground, 3.1 MeV $\frac{1}{2^{+}}$, 3.7 MeV $\frac{3}{2^{-}}$, 6.9 MeV $\frac{5}{2^{+}}$, 7.6 MeV $\frac{5}{2^{-}}$, and 11.9 MeV (?) states of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$; and the ground, 2.6 MeV $3^{-}$, and 3.2 MeV $5^{-}$ states of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Analyses of the elastic angular distributions are made using the partial wave formalism and the Kerman-McManus-Thaler approach to the nucleon-nucleus optical potential; a realistic spin-orbit term is included. The inelastic transitions are analyzed within the framework of the distorted-wave Born-approximation, using transition strengths consistent with previous low-energy studies of inelastic scattering. A simple single-particle-plus-excited-core model is used for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$. In terms of this analysis, an assignment of $J^{\pi }={(\frac{5}{2}, \frac{7}{2})}^{+}$ is made for the 11.9 MeV state in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$.

NUCLEAR REACTIONS ${}_{}{}^{12,13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p^{\prime })$, $E=0.8\mathrm{}$ GeV; measured $\sigma \left(\theta \right)$; enriched targets; resolution ⩾ 80 keV, ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=2-40\mathrm{}°$, $\Delta \theta =0.2\mathrm{}°$. Optical potential analysis, DWBA, inelastic deformation lengths, ${\beta }_{l}R$.

The total isovector $M1\mathrm{}$ radiative width of the 16.6-16.9 MeV doublet in ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ to the broad first excited state has been measured via the ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha , \gamma )$ reaction to be 6.10±0.53 eV. Angular distributions at the 16.6 and 16.9 MeV resonances have been measured and determine the isovector $E2\mathrm{}$ to isovector $M1\mathrm{}$ mixing ratio to be $\delta \left[\right(\frac{E2, T=1)}{(M1, T=1)}]=0.19\mathrm{}\pm 0.03$. A comparison of these results with recent $\beta -\alpha$ angular correlation measurements of ${}_{}{}^8{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ is consistent with predictions of the conserved vector current theory and the absence of a second-class induced tensor form factor.

RADIOACTIVITY ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha , \gamma ){}_{}{}^8{}_{}{}^{}\mathrm{Be}_{}^{*}{}_{}{}^{}$. $E_{\alpha }=32-36\mathrm{}$ MeV, $\theta =90\mathrm{}°-135\mathrm{}°$, measured $\sigma (\theta , E)$. Model independent test of CVC and second-class currents.

The time distribution of neutrons from radiationless muonic transitions and muon capture has been measured for muonic ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{237}{}_{}{}^{}\mathrm{Np}$, ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$, and ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}$. Evidence is found for muon capture in fragments from prompt muon-induced fission. Muon-capture rates are deduced and compared to the prediction of the Goulard-Primakoff theory. Isotopic effects of the capture rate are found to be smaller than expected from the systematics. Ratios of $\frac{{\Gamma }_n}{{\Gamma }_f}$ are deduced for radiationless transitions. No clear evidence is found for isometric-state excitation in muonic cascade transitions.

RADIOACTIVITY Muonic atoms ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{235,238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{237}{}_{}{}^{}\mathrm{Np}$, ${}_{}{}^{239,242}{}_{}{}^{}\mathrm{Pu}$. Measured neutron-time distribution, deduced total muon-capture rates and isotopic effect, $\frac{{\Gamma }_n}{{\Gamma }_f}$ ratio for radiationless muonic transitions.

The decay scheme of neutron-rich ${}_{}{}^{126}{}_{}{}^{}\mathrm{Cd}$ is reported for the first time. Sources of mass-separated ${}_{}{}^{126}{}_{}{}^{}\mathrm{Cd}$ were produced using an in-beam target ion source combination. The ${}_{}{}^{126}{}_{}{}^{}\mathrm{Cd}$ half-life was measured to be 0.506±0.015 sec. Of 11 $\gamma$ rays observed, 10 were placed in a ${}_{}{}^{126}{}_{}{}^{}\mathrm{In}$ level scheme consisting of 6 excited states at 260, 308, 555, 585, 626, and 688 keV. The level density of low-spin excited states is less than that for ${}_{}{}^{124}{}_{}{}^{}\mathrm{In}$, and most of our levels are describable in terms of a single proton hole coupled to a single neutron hole. Surprisingly, most of the $\beta$ strength feeds one level in ${}_{}{}^{126}{}_{}{}^{}\mathrm{In}$ at 688 keV.

RADIOACTIVITY ${}_{}{}^{126}{}_{}{}^{}\mathrm{Cd}$ [from ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(n, f)$]; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$-coin, Ge(Li) detectors; ${}_{}{}^{126}{}_{}{}^{}\mathrm{In}$ deduced levels, $J$, $\pi$, $log\mathrm{ft}$. Mass separated ${}_{}{}^{126}{}_{}{}^{}\mathrm{Cd}$ activity.

A treatment of pairing correlation for high spin rotational states using the modified BCS approximation is given. The BCS gap equation and the number constraint equation is derived in the rotating frame. The gap parameter $\Delta$ and the Fermi level $\lambda$ is determined self-consistently. Numerical computations are performed for ${}_{}{}^{158}{}_{}{}^{}\mathrm{Dy}$ and ${}_{}{}^{160}{}_{}{}^{}\mathrm{Dy}$.

NUCLEAR STRUCTURE ${}_{}{}^{158,160}{}_{}{}^{}\mathrm{Dy}$, calculated properties at high spin, pairing interaction. Modified BCS approximation for rotating even-even nuclei.

Precision measurements, using a highly linear Ge(Li) spectrometer system, have been made of the muonic x-ray spectra of the ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ transitional nuclei. Equivalent Barrett nuclear charge radii for both of the isotopes have been determined. Generalized quadrupole moments of the charge distribution as probed by muonic atoms have been determined in a nearly model-independent way, and equivalent quadrupole radii for static and transitional quadrupole charge distributions of the 2+ states have been determined by comparison with Coulomb excitation data. The isomer shift of the 2+ state of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ was measured directly from the $K$ x rays, while that of ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ was determined from the observed nuclear $\gamma$ ray. A phenomenological rotation-vibration-interaction model provides a satisfactory explanation for the observed quadrupole moment and isomer shift of the 2+ state in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$.

NUCLEAR STRUCTURE ${}_{}{}^{150,152}{}_{}{}^{}\mathrm{Sm}$; measured muonic x-ray spectra; deduced monopole and quadrupole charge parameters, isotope and isomer shifts.

Results obtained with the $g$-matrix are compared in detail with variational calculations, by restricting both procedures to an oscillator basis consisting of the same maximum number of oscillator quanta. Three-body correlations are included in the $g$-matrix calculation by extending the basis of the hole states to include additional oscillator functions. The resulting formalism is similar to the Bethe-Faddeev equations, but the correlated wave function is presented in a way to make comparison with variational wave functions obvious. This comparison suggests a choice of potential in the particle states that yield a very small three-body correlation energy in ${}_{}{}^3{}_{}{}^{}\mathrm{H}$. Applications include the Sussex interaction, and a singular short-range repulsion.

NUCLEAR STRUCTURE $g$-matrix and variational calculations, ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, Sussex interaction, $\delta$-function potential.

A method is developed for correcting truncated harmonic oscillator basis calculations of one-body bound-state energies for the omitted matrix elements of the kinetic energy operator. The method is only applicable when the potential energy operator is accurately represented in the truncated space. As an example of the method, the Hartree-Fock potential for the oxygen nucleus is considered with the Tabakin nucleon-nucleon potential. In a very large space this potential has only one bound $s$ state, though solving the Schrödinger equation in coordinate space yields two. The method gives this second bound state's energy quite accurately.

NUCLEAR STRUCTURE Approximate eigenvalues, infinite matrix, truncated basis.

A relativistic nuclear Hamiltonian is constructed, from which the relativistic Hartree and Hartree-Fock equations are derived. Then the Hartree equations are applied to ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ nuclei taking as input different relativistic one-boson-exchange potentials as well as the effective interaction of Walecka, introduced in his theory of highly condensed matter. Single-particle energies turn out to be of the correct magnitude. In particular, it is possible to explain the magnitude of the spin-orbit splitting without any free parameter.

NUCLEAR STRUCTURE ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$; calculated single-particle binding energies. Relativistic Hartree-Fock method.

Previous studies of isospin mixing in reactions have been restricted to the case of overlapping levels, and have produced a variety of cross-section formula. We point out that, despite some differences, these formulas are in essential agreement; further that, by comparison with results in the case of isolated levels, one can naturally establish a general formula that is expected to be valid for all situations.

NUCLEAR REACTIONS Isospin mixing in nuclear reactions.

The systematics of the ground-state $\alpha$-cluster spectroscopic strengths for odd-$A$ nuclei from ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ to ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ deduced by finite-range distorted-wave Born-approximation calculations from the measurements of the (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, $d$) reaction are presented. This analysis shows the new result that the $\alpha$ spectroscopic strength increases abruptly in the middle of the $\mathrm{sd}$ shell with a maximum for ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ and a fall towards the end of the shell.

NUCLEAR REACTIONS (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, $d$) on odd-$A$ $2s-1d$ shell targets, finite range DWBA analysis; deduced systematics of ground state $\alpha$ spectroscopic strengths.

An earlier penetrability calculation through a triple-humped barrier for ${}_{}{}^{234}{}_{}{}^{}\mathrm{Th}$ nucleus by Sharma and Leboeuf failed to reproduce the right order of magnitude for penetrability. It is shown here that one can obtain the correct penetrability by assuming that Back et al. actually determined the parameters of the second saddle, third minimum, and the third saddle for ${}_{}{}^{234}{}_{}{}^{}\mathrm{Th}$ from an analysis of their ($t, \mathrm{pf}$) fission data. The height of the first barrier is assumed to be that given by microscopic calculations for this nucleus.

NUCLEAR REACTIONS, FISSION Fission penetrability calculated through triple-humped potential barrier in ${}_{}{}^{234}{}_{}{}^{}\mathrm{Th}$, quantitative resolution of thorium anomaly along the lines suggested by Möller and Nix.

When ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is treated as a bound system of three $\alpha$ particles interacting through the Ali-Bodmer $\alpha -\alpha$ force, as modified by Vallieres et al., we find using the Faddeev technique no 0+ excited state below the two-body threshold. When the $\alpha -\alpha$ force is made more attractive, a 0+ excited state eventually appears. It is not an Efimov state.

NUCLEAR STRUCTURE ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, examining 0+ excited state for Efimov characteristics through $\alpha -\alpha$ force.

Exact analytic expressions for the $S$-wave phase shifts and half-shell functions have been obtained in the case of exponential potentials with and without hard core. The same quantities have also been computed in the unitary pole approximation to the same potential. A comparison of the exact and unitary pole approximation values shows that the unitary pole approximation is a fairly good approximation at positive energies too, particularly when the potential has an infinitely repulsive core.

NUCLEAR STRUCTURE Unitary pole approximation, hard-core exponential potential, positive energies, half-shell function.

Three different procedures are generally adopted in the analysis of correlation observed between neutron and $\gamma$ widths in neutron capture experiments. We present a quantitative comparison of the three methods, the valence model, optical model, and shell model with an "exact" calculation including core excitation effects. The ${}_{}{}^{28}{}_{}{}^{}\mathrm{Sn}(n, \gamma )$ reaction is taken as an example which demonstrates that the approximation used for the single particle amplitudes and the omission of core excitation effects are possible sources of error in conventional calculations. Among the conventional procedures we conclude that because of possible external region contributions and its lack of sensitivity to the potential used, the optical model formulation of Lane and Mughabgab represent the most useful alternative.

NUCLEAR REACTIONS ($\eta , \gamma$) reaction, neutron and $\gamma$ width correlation.

The ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(d, {\alpha }_3){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reaction involves the spin-parity system 0+1+→0+$0^{-}$ and as such is important for absolute determination of deuteron vector analyzing powers. To aid in such uses I have measured $\frac{d\sigma }{d\Omega }$ at 17 angles for $6.7<\mathrm{}{E}_d<12.5\mathrm{}$ MeV. The new data identify a number of unnatural parity states in ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ and usually limit their $J^{\pi }$ assignments to one of two values.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(d, {\alpha }_3){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, $E_d=6.7-12.5\mathrm{}$ MeV; measured $\sigma (E, \theta )$ at 17 angles, $\Delta E_d=30\mathrm{}$ keV for $E_d<12.0\mathrm{}$ MeV; ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ deduced levels, $J$, $\pi$. Calculated coherence widths.