Average volume integrals per nucleon of particle-particle collision probability in nuclear matter are evaluated using the preequilibrium exciton model. The results obtained are in quite reasonable accord with the volume integrals of optical model absorptive potentials.

NUCLEAR REACTIONS Exciton model evaluation of volume integrals of collision probabilities; comparison with optical model results.

The nucleus ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}$ has been studied by prompt and delayed $n-\gamma$ and $\gamma -\gamma$ coincidences in the bombardment of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ with 20-MeV $\alpha$ particles. A cascade of three $\gamma$ rays with energies of 114.7, 1094.0, and 1857.7 keV has been observed. The $\gamma$ cascade is emitted by an isomeric state of 3066.4-keV excitation energy; its mean life has been determined to be $\tau =810\mathrm{}\pm 50$ nsec. By measuring the relative intensities of the three $\gamma$ rays the sequence in the $\gamma$ decay has been established. The close resemblance of this $\gamma$ cascade to the one in the mirror nucleus ${}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}$ leads to the conclusion that the 3066.4-keV state in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}$ is an isomeric 19/$2^{-}$ state which has the decay scheme ${\frac{19}{2}}^{-}\underset{114.7}{\to }{\frac{15}{2}}^{-}\mathrm{}\left(2952.7\right)\mathrm{}\underset{1094.0}{\to }{\frac{11}{2}}^{-}\mathrm{}\left(1857.7\right)\mathrm{}\to {\frac{7}{2}}^{-}\mathrm{}\left(0\right)\mathrm{}$. This conclusion is in agreement with the results of measured excitation functions which show that the maximum yield of the 1857.7-keV $\gamma$ occurs at the lowest α energy and that of the 114.7-keV $\gamma$ at the highest. The $B\left(E2\mathrm{}\right)\mathrm{}$ value of the 19/$2^{-}$→15/$2^{-}$ transition in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}$ is larger by nearly a factor of 2 than the corresponding transition in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}$. The slightly lower excitation energy (56.9 keV) of the 19/$2^{-}$ state in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}$ with respect to the corresponding state in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}$ seems to be at least partially due to Coulomb shifts arising from the two valence protons in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}$.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha ,n\gamma )$; prompt and delayed $n-\gamma$ and $\gamma -\gamma$ coincidences with $E_{\alpha }=20\mathrm{}$ MeV. Singles $\gamma$-ray spectra: $\frac{d\sigma }{d\Omega }=f(E_{\alpha },E_{\gamma })$. Deduced for ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}:{\frac{19}{2}}^{-}\left(3066.4\mathrm{} \mathrm{keV}\right)\to {\frac{15}{2}}^{-} \left(2951.7\mathrm{} \mathrm{keV}\right)\to {\frac{11}{2}}^{-}\left(1857.7\mathrm{} \mathrm{keV}\right)\to {\frac{7}{2}}^{-}\mathrm{}\left(0\right)\mathrm{}$, ${\frac{19}{2}}^{-}$ state: $\tau =(810\mathrm{}\pm 50)$ nsec.

The ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha p){}_{}{}^{94}{}_{}{}^{}\mathrm{Y}$ and the ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha p){}_{}{}^{142}{}_{}{}^{}\mathrm{Pm}$ reactions studied at 39 MeV incident energy were used to investigate the proton decay of hole analog states. The $\alpha$ particles leading to these unbound levels in ${}_{}{}^{95}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{143}{}_{}{}^{}\mathrm{Sm}$ were detected near 0° in coincidence with the protons emitted from the $T_{>}$ hole states. In the case of the $2d_{\frac{5}{2}}$ hole analog state in ${}_{}{}^{143}{}_{}{}^{}\mathrm{Sm}$ only a mean value for the proton branching ratio has been determined from this study. Proton hole-neutron hole states have been observed in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Y}$ through the proton decay of the $2p_{\frac{1}{2}}$, $2p_{\frac{3}{2}}$, and $1f_{\frac{5}{2}}$ $T_{>}$ levels of ${}_{}{}^{95}{}_{}{}^{}\mathrm{Zr}$. Analysis of the $\alpha -p$ angular correlations has given inelastic proton widths, spins, and parities as well as shell model configurations of several of the observed residual states in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Y}$.

NUCLEAR REACTIONS ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha p)$, ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha p)$, $E=39\mathrm{}$ MeV; measured $\sigma (E_{\alpha },E_p,{\theta }_p)$. ${}_{}{}^{95}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{143}{}_{}{}^{}\mathrm{Sm}$ deduced IAS, proton branching. ${}_{}{}^{94}{}_{}{}^{}\mathrm{Y}$ deduced levels, $J$, $\pi$, ${\Gamma }_{p^{\prime }}$, spectroscopic factors. Enriched targets. 0° spectrometer.

A modification to the usual six-parameter Woods-Saxon parameterization of the optical model for the scattering of composite particles is proposed. This additional real term reflects the effect of coupling other channels to the elastic scattering. The analyses favor a repulsive interaction for this term, especially for $\alpha$ particles. It is found that the repulsive term, when combined with a Woods-Saxon term, yields potentials with central values and volume integrals similar to those found by uncoupled elastic scattering calculations. These values are $V(r=0\mathrm{})\mathrm{}\sim 125$ MeV and $\frac{J}{4A}\sim 300$ MeV ${\mathrm{fm}}^3$.

NUCLEAR REACTIONS Modification optical model, coupled-channel effects, intermediate energy composite particles, $\sigma \left(\theta \right)$ calculated.

The surface peaked modification to the conventional six-parameter representation of an $\alpha$ particle-nucleus interaction potential has been studied further. In particular we have used a nucleon-nucleus optical potential folded over the $\alpha$ particle to derive the central well depth, and it is found that constant geometry parameters can be used to fit the $A$ dependence and energy dependence of the optical model for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ from 40-140 MeV. It is further found that good quality fits to elastic scattering can be obtained for the entire energy range for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ with constant geometry for the Woods-Saxon imaginary well depth, resulting in a five search parameter potential and the geometrical parameters of the modification.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha ,\alpha )$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}(\alpha ,\alpha )$, $E=140\mathrm{}$ MeV; ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(\alpha ,\alpha )$, $E=40\mathrm{}-140$ MeV; modified optical model calculations, $\sigma \left(\theta \right)$.

The propagation of a deuteron through nuclear matter is examined in terms of a simple nonlocal but separable potential for the $n-p$ interaction. It is found that the binding energy of the deuteron in nuclear matter depends strongly on the relative orientation of the deuteron spin and center-of-mass momentum, when both the Pauli exclusion principle and the tensor force component in the neutron-proton interaction are included in the calculation. A thorough discussion of the physical mechanism involved is presented. It is shown that this effect is associated with the presence of a new type of spin dependent interaction of the $T_p$ type, in the deuteron-nucleus optical potential. The nuclear matter calculations are applied to the realistic case of a deuteron scattered by a heavy nucleus through a simple model which is valid for deuteron incident energies in excess of 100 MeV. The $T_p$ force thus produced is found to have a non-negligible strength over a wide range of high incident deuteron energies and to be very sensitive to high momentum components of the nucleon-nucleon interaction. The mechanism examined here is also expected to generate a $T_p$ force and a modified $T_R$ force at low energies.

NUCLEAR REACTIONS $d$ in nuclear matter, Pauli exclusion principle, $D$-state probability. $d$ optical potential, tensor force, $E_d<1\mathrm{}$ BeV, polarized $d$.

We present a technique for including the effects of nucleon-nucleon correlations in the optical phase shift ($\chi$) expansion of the nucleus-nucleus scattering amplitude and present the results for $\chi$ to second order. The total and inelastic cross sections are consistently higher than those obtained ignoring correlations, and are in better agreement with the data. Furthermore, the inclusion of correlations leads to second order phase shift functions which do not violate unitarity, in constrast to the case when correlations are ignored in very heavy nuclei ($A_1,A_2\gtrsim 200$). In elastic scattering differential cross sections, the effects of correlations can be quite large.

NUCLEAR REACTIONS Glauber approximation, high-energy scattering theory, short-range correlations, optical model, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{184}{}_{}{}^{}\mathrm{W}$, ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{U}$, projectiles, and targets, $E=0.87\mathrm{} \mathrm{and} 2.1$ GeV/ nucleon; calculated $\sigma$, ${\sigma }_{\mathrm{ine}1\mathrm{}}$, $\sigma \left(\theta \right)$.

A $T_{\frac{1}{2}}=18\mathrm{}$ ns isomer at $E_x=2986\mathrm{}$ keV has been found in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ and identified as the 19/$2^{+}$ member of the [$\left({}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\right)5^{-}\otimes h_{\frac{9}{2}}\left(\mathrm{proton}\right)$] weak coupling multiplet. The $g$ factor of the state has been determined to be $g=0.368\mathrm{}\pm 0.008$. Multipole mixing ratios have been determined for three transitions connecting the $i_{\frac{13}{2}}$ single particle state in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ with states of the [$\left({}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\right)3^{-}\otimes h_{\frac{9}{2}}\left(\mathrm{proton}\right)$] multiplet and with the ground state. In addition a 26%, 141 keV branch has been observed in the decay of the 15/$2^{+}$ member of the ($3^{-}\otimes h_{\frac{9}{2}}$) multiplet, resolving serious discrepancies between earlier Coulomb excitation work and theoretical expectations.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}({}_{}{}^7{}_{}{}^{}\mathrm{Li},{}_{}{}^4{}_{}{}^{}\mathrm{He}2n\gamma$; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $g$, $\gamma -\gamma$ coin, Ge(Li) detectors; ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ deduced levels, $J$, $\pi$.

Linear polarizations of $\gamma$ rays from the 11.86→8.12 →4.12 MeV decay in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ have been studied with a NaI polarimeter. The 11.86 MeV level was populated via the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha \gamma ){}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ reaction. The results are consistent with $J^{\pi }=8^{+}$ for the 11.86 MeV level and in agreement with earlier work, rule against a $6^{+}$ assignment with 85% confidence.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha \gamma )$, $E=42\mathrm{}$ MeV; measured linear polarization, $\alpha \gamma$ coincidence. Deduced $J^{\pi }$.

Fragment energy spectra from the 2.1- and 4.9-GeV proton irradiation of C, Al, Ag, and U targets were measured at several angles to the beam for products ranging from He up to Ar for the heavier targets. The fragments were detected in a telescope consisting of a gas $\Delta E$ counter and a silicon $E$ counter. The carbon target measurements are compared with previous data from projectile fragmentation studies. A Maxwellian type functional form which fits the energy spectra from all the targets is presented. The spectra were integrated to obtain values of the cross section as a function of atomic number.

NUCLEAR REACTIONS $\mathrm{C}(p,X)$, $E=2.1, 4.9$ GeV; measured $\sigma (E,\theta )$, $X=\mathrm{He} \mathrm{to} \mathrm{C}$. $\mathrm{Al}(p,X)$, $E=2.1, 4.9$ GeV; measured $\sigma (E,\theta )$, $X=\mathrm{He} \mathrm{to} \mathrm{Na}$. $\mathrm{Ag}(p,X)$, $E=4.9\mathrm{}$ GeV; measured $\sigma (E,90\mathrm{}°)$, $X=\mathrm{N} \mathrm{to} \mathrm{Ar}$. $\mathrm{U}(p,X)$, $E=4.9\mathrm{}$ GeV; measured $\sigma (E,\theta )$, $\sigma \mathrm{}\left(X\right)\mathrm{}$, $X=\mathrm{F} \mathrm{to} \mathrm{Ar}$. Spallation, fragmentation.

An intranuclear cascade model for reactions of pions and nucleons with complex nuclei that should cover the energy range from about 50 MeV to about 1000 GeV has been developed. The model includes the effect of a diffuse nuclear surface, the Fermi motion of the bound nucleons within the nucleus, the exclusion principle, a local potential for nucleons, a localized reduction in the density of the nucleus during the development of the cascade, and the sequencing of the events correctly with time. Theoretical results from the model are compared with experimental data over the energy range ∼ 3-1000 GeV. Within the cascade model, the equations that are used to represent the pion multiplicity from the reactions of nucleons and pions with the individual nucleons of the nucleus underestimates the number of shower particles produced by these individual nucleon interactions. In spite of this the predicted number of shower particles escaping from the nucleus, for 100-GeV nuclear interactions, is overestimated by about 25% for light nuclei to about 60% for heavy nuclei. The agreement for the number of escapes from the nucleus is somewhat better at lower interaction energies (∼ 10-20 GeV). Some of the major trends in the observed high energy data are predicted quite well. These include the energy independence of (a) the number of black tracks produced at interaction energies above 5 GeV, (b) the number of shower particles produced above 100 GeV, and (c) the radionuclides produced above 10 GeV. Other trends that are predicted fairly well are the small mass dependence of the shower particle multiplicity (factor of 2 increase predicted from carbon to lead; factor of 1.5 measured), and the change in the angular dependence of the multiplicity with mass. In absolute comparisons, the predicted total reaction cross sections are in good agreement with experimental data, and the cross sections for the production of radionuclides are in fair agreement.

NUCLEAR REACTIONS Theoretical, intranuclear cascade method, ${\sigma }_t\mathrm{}\left(A\right)\mathrm{}$ for $p$ and $\pi$, ${〈n〉}_{\mathrm{shower}}$ and ${〈n〉}_{\mathrm{black}}$ vs $E_{\pi }$, $\sigma \left({\theta }_{\pi }\right)\Delta {\theta }_{\pi }$ vs $A$, $\sigma (E_{\pi },E_p:\theta )$ for $p$ on Al, radiochemical $\sigma \text{'}\mathrm{s}$ for 11-and 300-GeV $p$ on ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$. All compared with experiment.

Differential cross sections for elastic scattering of positive pions on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ at 40.0 and 49.7 MeV were measured at about 10° intervals for laboratory angles from 25° to 160°. Relative uncertainties between angles are 3%, with the overall normalization known to 7% for each angular distribution. The angular distributions are similar in shape, being dominated by a minimum at about 60°. The differential cross sections are presented along with the results of a partial wave analysis which gives good fits at both 40.0 and 49.7 MeV. The data are also fitted by a simple phenomenological first-order Kisslinger nonlocal optical model calculation.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({\pi }^{+},{\pi }^{+}){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. $E=40.0, 49.7$ MeV, $\theta =25\mathrm{}-160°$, measured $\sigma (\theta ,E)$. Partial-wave and optical model analyses of $\sigma (\theta ,E)$.

Absolute differential cross sections have been measured for the ${\pi }^{+}+d\to p+p$ reaction at pion energies of 40, 50, and 60 MeV. The angular distributions are fitted with the functional form $C_0+C_2{cos}^2\theta +C_4{cos}^4\theta$.

NUCLEAR REACTIONS $d({\pi }^{+},pp)$, $E=40, 50, 60$ MeV; measured $\sigma (\theta ,E)$; deduced polynomial fits to fourth order.

We have produced the long-lived ground state of ${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}$ by irradiation of niobium foils with 14.8-MeV neutrons, and we have established its half-life from measurements of the disintegration rate and the neutron fluence together with the known ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}\mathrm{}(n,2n)\mathrm{}{}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}_{}^g{}_{}{}^{}$ cross section. On the basis of two separate experiments we obtain $t_{\frac{1}{2}}\left({}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}_{}^g{}_{}{}^{}\right)=(3.6\mathrm{}\pm 0.3)\times {10}^7$ yr.

RADIOACTIVITY ${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}_{}^g{}_{}{}^{}$; measured $T_{\frac{1}{2}}$.

A 41 cm double focusing mass spectrometer has been used to measure three closely spaced doublets ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_6^{}{}_{}{}^{}$ ${}_{}{}^2{}_{}{}^{}\mathrm{H}_6^{}{}_{}{}^{}$— ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}_6^{}{}_{}{}^{}$ ${}_{}{}^1{}_{}{}^{}\mathrm{H}_6^{}{}_{}{}^{}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_6^{}{}_{}{}^{}$ ${}_{}{}^1{}_{}{}^{}\mathrm{H}_{12}^{}{}_{}{}^{}$— ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_6^{}{}_{}{}^{}$ ${}_{}{}^2{}_{}{}^{}\mathrm{H}_6^{}{}_{}{}^{}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_6^{}{}_{}{}^{}$ ${}_{}{}^1{}_{}{}^{}\mathrm{H}_{12}^{}{}_{}{}^{}$— ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}_6^{}{}_{}{}^{}$ ${}_{}{}^1{}_{}{}^{}\mathrm{H}_6^{}{}_{}{}^{}$ in order to determine precisely the mass and the neutron separation energy of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$. The redetermination of the deuterium mass is included to allow a comparison with earlier work in this laboratory. The neutron separation energy for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ is then employed to calculate the ground-state $\gamma$-ray energy for the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(n,\gamma ){}_{}{}^{13}{}_{}{}^{}\mathrm{C}$.

NUCLEAR STRUCTURE ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ measured atomic mass, neutron separation energy. ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ remeasured atomic mass, neutron separation energy. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(n,\gamma ){}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ calculated $Q_{\gamma }$.

${}_{}{}^{164}{}_{}{}^{}\mathrm{Er}$ high-spin states were studied via the ${}_{}{}^{160}{}_{}{}^{}\mathrm{Gd}({}_{}{}^9{}_{}{}^{}\mathrm{Be},5n)$ reaction at 59-MeV beam energy. We find significant population of three new rotational bands in addition to higher-spin levels of the previously known $\gamma$-vibrational band. In most cases the spins of the levels were established by angular distribution measurements, and some parities were established by linear polarization measurements on interband transitions. Two odd-parity bands with both even- and odd-spin states begin with the previously reported $5^{-}$ (1664 keV) and $7^{-}$ (1985 keV) levels and extend to levels of spin 22 (5350 keV) and 13 (3351 keV), respectively. These two bands exhibit markedly different moments of inertia. The third band is of unknown parity and has a likely even-spin sequence extending from a level of spin 8 (2091 keV) to a possible spin-22 level (5678 keV). The even-spin sequence of the $\gamma$ band extends to a spin-14 level (3267 keV) and exhibits a backbend at the ${10}^{+}$ level to a new ${12}^{+}$' level of the previously established even-spin even-parity yrast band. The odd-spin sequence backbends at spin 13, and extends to a possible spin-19 level at 4588 keV, thereby providing evidence for an odd-spin even-parity yrast band some 500 keV higher in energy than its even-spin counterpart.

NUCLEAR STRUCTURE ${}_{}{}^{160}{}_{}{}^{}\mathrm{Gd}({}_{}{}^9{}_{}{}^{}\mathrm{Be},5n\gamma )$, $E=59\mathrm{}$ MeV; measured $I_{\gamma }$, $W{\left(\theta \right)}_{\gamma }$, linear $P$; deduced $\Lambda$, levels, $J$, $\pi$.

Energy levels arising from the 1p7h configuration of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ and the 1p5h configuration of ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$ are calculated with an effective interaction which previously has been shown to reproduce the energies of intruder states in mass 53-57 nuclei. Calculated energies for yrast levels of spin up to 11 agree closely with experimental values from ($\alpha ,2n\gamma$) reactions. An effective $M1\mathrm{}$ operator determined by a least-squares fit to data from $N=29\mathrm{}$ nuclei is used in the calculation of electromagnetic transition rates, and it is shown that only weak configuration mixing is required to account for transition rates which have been measured in ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$.

NUCLEAR STRUCTURE ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$; calculated 1p7h and 1p5h energy levels, effective $M1\mathrm{}$ operator, calculated $M1\mathrm{}$ and $E2\mathrm{}$ transition rates.

The muonic x rays from four highly deformed actinide nuclei, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$, have been measured. A four parameter Fermi charge distribution with distortion terms of the form ${\beta }_{2n}{Y}_{2n0}$, $n\le 2$, was used to characterize the nuclear charge distribution. A least squares fit was made to the energies of the $2p-1s$ and $3d-2p$ muonic x rays and their fine and hyperfine structure splitting. The $4f-3d$ and $5g-4f$ muonic x rays were measured for the four nuclei as well as the 5-3, 4-2, and 3-1 muonic transitions for ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. The intrinsic electric quadrupole moments were deduced. Our results are compared with those from earlier muonic experiments, as well as with proton, $\alpha$, and electron inelastic scattering.

NUCLEAR STRUCTURE Muonic ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$; measured transition energies and relative intensities; deduced nuclear charge parameters in distorted Fermi charge distribution; deduced intrinsic electric quadrupole moments.

The dynamical effect of the neutron-proton mass difference on charge asymmetry in the trinucleon system is investigated using perturbation theory and the Faddeev equations. The mixed symmetry components of the wave function play an unexpectedly critical role and reduce the effect by roughly a factor of 2 from simple estimates. A reduction rather than an enhancement occurs because the neutron-proton force is stronger than the neutron-neutron or proton-proton forces.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^3{}_{}{}^{}\mathrm{H}$ charge asymmetry, $n-p$ mass difference.

Bloch-Horowitz perturbation theory is applied to the calculation of approximate energies and model-space eigenvectors, for the solvable large-matrix Hamiltonian $H$ used by Pittel, Vincent, and Vergados. Two types of upper and lower bounds to the energies are discussed: moment-theory bounds, obtained by applying moment theory to the terms of perturbation theory, and norm bounds, derived from the expectation $\overline{E}$ and variance ${\sigma }^2$ of $H$ with respect to an eigenvector approximated by n th order perturbation theory ($n\le 6$). It is shown that lower bounds cannot be constructed unless some fourth-order quantity is known. The upper bounds are generally stricter than the lower bounds. All of the bounds apply even when back-door intruder states cause perturbation theory to diverge; but they lose their rigor and become "quasibounds" when there are physical intruders. The moment-theory and norm lower quasibounds always require estimation of a parameter. For the solvable Hamiltonians, it is shown that this can be done quite reliably, and that the resulting quasibounds are tight enough to have some practical utility. The energy-independent effective interaction V is constructed and its errors are displayed and discussed. Finally, a certain [1/2] pseudo-Padé approximant is empirically shown to give energies with a mean absolute error of less than 0.3 MeV in all cases.

NUCLEAR STRUCTURE Effective interactions, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. Perturbation theory for energies and bounds to them; used large solvable matrices, included intruder states. Padé approximants.