A scheme based on variation after approximate angular momentum projection from a triaxially symmetric intrinsic wave function has been developed and applied to the study of ground-state band and $\gamma$ band of ${}_{}{}^{188}{}_{}{}^{}\mathrm{Os}$ and ${}_{}{}^{188}{}_{}{}^{}\mathrm{Pt}$ nuclei. The intrinsic calculation has been performed in the framework of Hartree-BCS theory employing the pairing $+Q·Q$ interaction of Baranger and Kumar. The calculated level energies, $B\left(E2\mathrm{}\right)\mathrm{}$ values and electromagnetic moments compare quite well with the available experimental values. The position of the $K=4^{+}$ band, many $B\left(E2\mathrm{}\right)\mathrm{}$ values and electromagnetic moments have been predicted. This study predicts relatively more rigid triaxial shapes for these nuclei than have been usually believed.

NUCLEAR STRUCTURE Variation after angular momentum projection with triaxial symmetry, ${}_{}{}^{188}{}_{}{}^{}\mathrm{Os}$ and ${}_{}{}^{188}{}_{}{}^{}\mathrm{Pt}$; level energies, $B\left(E2\mathrm{}\right)\mathrm{}$ values, electromagnetic moments of ground and $\gamma$ band, pairing $+Q·Q$ interaction.

Low-lying spectra of ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$, and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Yb}$ are studied in the framework of the pseudo SU(3) model allowing natural parity neutrons alone to be active. Various interband and intraband $B\left(E2\mathrm{}\right)\mathrm{}$ values are predicted and compared with experimental results and other model calculations. The agreement is quite reasonable. We predict a different level structure for the $2^{+}$ quasirotational band in ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$ and $3^{+}$ quasirotational band in ${}_{}{}^{168}{}_{}{}^{}\mathrm{Yb}$. The present calculation shows that the enlargement of the natural parity neutron space will improve the predictions considerably.

NUCLEAR STRUCTURE ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{168}{}_{}{}^{}\mathrm{Yb}$, Pseudo SU(3) model, only natural parity neutrons, $\tilde{Q}$. $\tilde{Q}$ Interaction, calculated levels, $B\left(E2\mathrm{}\right)\mathrm{}$, ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$-$I_{\gamma }$, compared with experiment and other models.

$\alpha$-transfer spectroscopic factors computed from shell-model wave functions for ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ generated in the full $\mathrm{sd}$-shell model space with the Chung-Wildenthal interaction are in good agreement with experimental ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$,$d$)${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ results, contrary to previous SU(3)-type calculations.

NUCLEAR STRUCTURE ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$; Calculation of $\alpha$ spectroscopic factors in full $\mathrm{sd}$ basis; comparison with experiment and SU(3).

We show that the number of particles within a subvolume of a finite Fermi system has a variance that scales with the number of particles as $N^{\frac{2}{3}}logN$. This contrasts with the naive classical model, which gives a scaling proportional to $N$. It also contrasts with a certain collective model that produces a variance that scales as $N^{\frac{2}{3}}$.

NUCLEAR STRUCTURE, NUCLEAR REACTIONS nuclear matter, bulk matter and collective aspects of heavy-ion reactions, general properties of fission.

We have examined the contribution of the ($p$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$t$) two-step process to the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$($p$,$t$) reaction leading to unnatural parity $T=4\mathrm{}$ states in ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$. We find that the two-step cross section is more than an order of magnitude smaller than the experimental data. Possible reasons for this discrepancy are discussed.

NUCLEAR REACTIONS ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$($p$,$t$)${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$, $E_p=41.7\mathrm{}$ MeV; calculated ($p$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) (${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$t$) two-step contribution.

The spin and parity of the 398 eV resonance in the capture of neutrons by ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$ has been determined by the method of particle-$\gamma$ directional correlations. The resonance is shown to have a spin and parity of $2^{-}$ and the process proceeds predominantly with the channel spin 2.

NUCLEAR REACTIONS Slow neutron capture, spin and parity 398 eV resonance, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$; directional correlation of neutrons, $\gamma$ rays.

The earlier calculations of Goode and Barrett are repeated using the super-soft-core potential of Gogny, Pires, and de Tourreil. The particular third-order folded diagram which they calculated now converges in its intermediate-state energy summation, because of the suppression of the strong short-range repulsive effects present in earlier calculations.

NUCLEAR STRUCTURE Theory, effective interaction in mass-18, convergence intermediate-state summation in third order to $26\hslash \omega$; effects of super-soft-core versus hard-core nucleon-nucleon potentials.

The effective coupling constant of the Coriolis term in a rotational nucleus is treated by applying the renormalization group method to the interaction of the intruder nucleon with the nucleons composing the rotor. The attenuation of the Coriolis term and the phase transition from rotational to vibrational-like behavior can be explained by the change of the coupling as an analytic function of the energy and the cutoff energy varying over the isotopes.

NUCLEAR STRUCTURE Renormalized Coriolis coupling, phase transition and attenuation factor.

The ($d$,$p$) stripping pattern for excitation of the 7064-keV level in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ is best described by $l=2\mathrm{}$ which implies $J^{\pi }=1^{-}$. This implies that electromagnetic deexcitation would take place by $E1$ radiation rather than $M1$ as had been previously suggested.

NUCLEAR REACTIONS ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ ($d$,$p$), $E=26.2\mathrm{}$ MeV; measured $\sigma (E_p, \theta )$; deduced levels, $J$,$\pi$.

The Hamiltonian in a body-fixed frame for odd mass nuclei or for the decoupled band of even-even nuclei is derived in the same method of quantization previously applied to the ground band of even-even nuclei. The resulting form coincides with that given by classical mechanics.

NUCLEAR STRUCTURE Quantized rotation, triaxial decoupled rotor.

A drastic limitation of the high-spin selectivity of heavy-ion compound reactions is shown to be introduced by the angular momentum cutoff $J_{max}$ in the composite system. However, for final spins near $J_{max}$ a strong shape dependence of the angular distributions (being peaked at 90°) arises as result of a strong decrease of the alignment of the final nucleus and can be used for high spin spectroscopy.

NUCLEAR REACTIONS: Statistical model calculations-critical angular momentum effects.

A simple unitarity relation is derived for the elastic projectile-nucleus scattering amplitude. This result provides an alternative interpretation and justification for the ordinary distorted wave impulse approximation, and thus may serve to correct a misapprehension concerning this approximation which might erroneously be obtained from recent trends in the literature.

NUCLEAR REACTIONS unitarity, optical potential, knock-out reactions, DWIA.

Three neutron-hole states—$1i_{\frac{13}{2}}$, $2f_{\frac{7}{2}}$, and $1h_{\frac{9}{2}}$—in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ are found to be affected strongly due to the coupling of these states with the $3^{-}$, $5^{-}$, $2^{+}$, $4^{+}$, and $6^{+}$ vibration states of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The unperturbed shell model energies of these states are found at 2.00, 3.00, and 3.90 MeV, respectively. The fragmentations of $1i_{\frac{13}{2}}$, $1h_{\frac{9}{2}}$, and $1h_{\frac{11}{2}}$ states, as observed in a recent ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ (${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$\alpha$) reaction, can be quantitatively accounted for in terms of these altered level positions together with the hole-core coupling scheme.

NUCLEAR STRUCTURE Deduced shell model energies of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$.

We apply Myers's technique to calculate sum rule values of the moments ${\sigma }_2$ and ${\sigma }_3$ for the triton photoeffect. We find that ${\sigma }_2$ agrees within 10% with the value found from Myers's cross sections. The disagreement found between values of ${\sigma }_3$ from sum rules and Myers's cross sections seems due to the sensitivity of the latter to inaccuracies in the high energy cross section.

NUCLEAR REACTIONS Triton-photoeffect; hyperspherical harmonics; Sum rules.

From a coincidence study of the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$\mathrm{np}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction we obtain branching ratios of (9.6±1.4)% and (16.4±3.6)% respectively for the isospin forbidden proton decays of the lowest $T=\frac{3}{2}$ level of ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ to negative parity levels of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at 9.64 and 10.84 MeV. The reduced widths for these $s$- or $d$-wave decays are much larger than those for the $p$-wave decays to the lower lying positive parity levels of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. This establishes the importance of ${\left(2s1d\right)}^{2}1p^7$ configurations in the isospin impurity in ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$($T=\frac{3}{2}$). We argue that isospin impurities containing pairs of particles excited into higher shells are a widespread phenomenon and present a qualitative explanation of this effect which has been ignored in essentially all isospin mixing calculations.

NUCLEAR REACTIONS ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$\mathrm{np}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=7.0\mathrm{}$ MeV; ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$($T=\frac{3}{2}$) proton decays; isospin mixing

Energy-averaged angular distributions have been measured for the reaction ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$→$\alpha$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, covering the c.m. bombarding-energy range 12.86-14.53 MeV in 40 equal steps. Angular distributions are approximately symmetric about 90° and are qualitatively reproduced by Hauser-Feshbach calculations.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$\alpha$), $E=22.5-25.5\mathrm{}$ MeV; ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$,$\alpha$), $E=30-34\mathrm{}$ MeV. Measured $\sigma (E_{\alpha },\theta )$. Energy-averaged angular distributions. Hauser-Feshbach calculations.

We have measured the differential cross-section and the analyzing power (polarization) for $p$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering at incident kinetic energies of 0.56, 0.80, 1.03, 1.24, and 1.73 GeV. The experiment used a polarized proton beam incident on a liquid helium target and a single arm magnetic spectrometer to detect elastic scattering. Both the differential cross sections and the analyzing power show structure near $-t=0.25\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ which decreases in magnitude with increasing energy. Both multiple scattering and optical model interpretations of the data are discussed.

NUCLEAR REACTIONS elastic scattering, $p$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$; GeV energies; measured differential cross section; measured polarization; comparison with theory.

Allowed partial transition rates are calculated for muon capture by nuclei with $A=6-14\mathrm{}$. The nuclear 1p shell model is used and the corrections to the impulse approximation due to exchange currents are estimated with the one-pion exchange model. Whereas the capture rates themselves are strongly dependent on the wave functions, similar amount of exchange current corrections are obtained with all nuclear shell model variants. These percentages vary in a smooth way with the mass number from ≈ -2% for $A=6\mathrm{} \mathrm{to} \approx -20\%$ for $A=14\mathrm{}$. It is found that the scalar and tensor parts of the current are responsible for the main contributions to the corrections.

NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{10,11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12,13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (${\mu }^{-}$, ${\nu }_{\mu }$). Calculated partial capture rates. $1p$ shell model. One pion exchange currents.

We analyze $\pi$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ elastic scattering at pion energies between 40 and 340 MeV. An excellent fit to the data follows from the inclusion of a second-order optical potential. The parameters specifying the second-order potential are found to exhibit marked resonance behavior. The magnitude and the energy dependence of the parameters of the second-order potential obtained for pion-oxygen scattering are, in the main, very similar to that determined for pion-carbon scattering. This result indicates that a universal parametrization of the second-order pion-nucleus optical potential may be possible.

NUCLEAR REACTIONS Pion-oxygen scattering at 40, 49.7, 50, 79.3, 114.3, 162.6, 240.2, and 342.6 MeV. Parameters of second-order optical potential.

We have measured the inclusive production spectra of protons, deuterons and $\alpha$ particles following negative pion capture from rest in carbon, calcium, indium, and bismuth from low energies up to 55 MeV for protons and deuterons, and 30 MeV for $\alpha$ particles. The proton and deuteron spectra separate into contributions from direct processes and from evaporation. The integrated production rates are in agreement with previous results. The data are compared with various theoretical models.

NUCLEAR REACTION ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, measured spectra of $p$, $d$, $\alpha$ following ${\pi }^{-}$ absorption.