We present a covariant optical model analysis of pion-nuclear elastic scattering at 1 GeV. Excellent agreement with experimental data is obtained without the introduction of any free parameters. Further, since we have calculated the scattering amplitudes from the pion-nucleus phase shifts, the application of our results is not limited to small angles. We stress that high-energy pion-nucleus elastic scattering can be regarded as an effective tool for investigation of nuclear properties. Some advantages over electron-nucleus and proton-nucleus scattering are discussed. The importance of using realistic matter distributions in the analysis of pion-nucleus scattering at high energies is emphasized.

NUCLEAR REACTIONS Covariant optical model analysis. Differential cross sections for pion scattering from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ at 1.12 GeV.

A semiclassical model for the observation of recoil protons in quasielastic pion scattering near the (3, 3) resonance is described. We show that the ${\pi }^{-}$ to ${\pi }^{+}$ ratio is enhanced by large factors at low proton energies by charge exchange of the recoil nucleon.

NUCLEAR REACTIONS Calculated recoil proton spectra, quasielastic pion scattering, (3, 3) resonance region. Dependence of $\frac{\sigma ({\pi }^{-},p)}{\sigma ({\pi }^{+},p)}$ on recoil nucleon charge exchange.

The decay of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$ (11.7 day) has been studied with Ge(Li) spectrometers and with a Ge(Li) $\gamma -\gamma$ coincidence system. Twelve $\gamma$ transitions and three levels in ${}_{}{}^{131}{}_{}{}^{}\mathrm{Cs}$ at 919, 1170, and 1342 keV have been identified which were not reported previously. Upper limits are given for the $\gamma$-ray intensities of previously reported transitions at 323 and 508 keV which were not observed in this experiment. The $Q$ value for the decay of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$ was determined from the $\frac{\left(\mathrm{electron}\mathrm{capture}\right)}{{\beta }^{+}}$ intensity ratio to be ${1372}_{-20\mathrm{}}^{+10\mathrm{}}$ keV. This value agrees with the latest atomic mass evaluation, but disagrees with the only previous measurement by 207 keV. Our $\frac{\left(\mathrm{electron}\mathrm{capture}\right)}{{\beta }^{+}}$ intensity ratio and the $Q$ value deduced from a reaction study suggest that the $\frac{\left(\mathrm{electron}\mathrm{capture}\right)}{{\beta }^{+}}$ ratio is not anomalous in contrast to some recent predictions. The ${}_{}{}^{131}{}_{}{}^{}\mathrm{Cs}$ level structure and $\gamma$ transition probabilities are compared to the results of an intermediate-coupling calculation.

RADIOACTIVITY ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coincidence; deduced $Q$ value, $log\mathrm{ft}$. ${}_{}{}^{131}{}_{}{}^{}\mathrm{Cs}$ deduced levels, $\gamma$ branching. Isotope separation, Ge(Li) detectors.

The level scheme of even-even ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$ has been studied from the decay of the ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ce}$ (75.9 h)→${}_{}{}^{134}{}_{}{}^{}\mathrm{La}$ (6.67 min) chain. Samples of ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ce}$ were produced by ∼800-MeV proton bombardment of Pr foils, followed by chemical and mass separation. $\gamma$-ray energy and intensity measurements were made using Ge(Li) and Si(Li) detectors. Identification of $\gamma$ rays as belonging to the ${}_{}{}^{134}{}_{}{}^{}\mathrm{La}$ decay was made in separate experiments using sources of ${}_{}{}^{134}{}_{}{}^{}\mathrm{La}$ milked from the parent ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ce}$ activity. In this manner, ∼99$\gamma$-ray transitions have been associated with the ${}_{}{}^{134}{}_{}{}^{}\mathrm{La}$ decay scheme. From these data and $\gamma -\gamma$ coincidence measurements, a comprehensive level scheme is proposed for ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$, consisting of ∼41 excited states. Further information on the energies of levels in ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$ was derived from a subsidiary series of $\gamma$-ray energy measurements using a source of ${}_{}{}^{134}{}_{}{}^{}\mathrm{Cs}$. For the ${}_{}{}^{134}{}_{}{}^{}\mathrm{La}$ decay, $log\mathrm{ft}$ values were obtained from relative x-ray, annihilation-quanta, and $\gamma$-ray intensities and using intensity-balance considerations for the individual levels in ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$. A comparison is made of the ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$ data with the predictions of several recent theoretical calculations dealing with even-even nuclei in this mass region.

RADIOACTIVITY ${}_{}{}^{134}{}_{}{}^{}\mathrm{La}$ from $\mathrm{Pr}\left[\right(p, \mathrm{spallation}\left)\right]$; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$; ${}_{}{}^{134}{}_{}{}^{}\mathrm{Cs}$ deduced levels, $J$, $\pi$, $log\mathrm{ft}$. Ge(Li) and Si(Li) detectors, chemical separation, isotope separations. ${}_{}{}^{134}{}_{}{}^{}\mathrm{Cs}$; measured $E_{\gamma }$.

The decay of 13.3-h ${}_{}{}^{123}{}_{}{}^{}\mathrm{I}$ to levels of ${}_{}{}^{123}{}_{}{}^{}\mathrm{Te}$ and the decay of 2.7-yr ${}_{}{}^{125}{}_{}{}^{}\mathrm{Sb}$ to levels of ${}_{}{}^{125}{}_{}{}^{}\mathrm{Te}$ have been studied. Forty-four $\gamma$ rays were attributed to the decay of ${}_{}{}^{123}{}_{}{}^{}\mathrm{I}$ and all but three were placed among 16 levels, 14 of which are also observed in ($p,t$) reaction studies and 11 in ($a,p$) reaction studies. Three previously unobserved low-intensity $E1\mathrm{}$ transitions and one new $M2\mathrm{}$ transition were observed in the decay of ${}_{}{}^{125}{}_{}{}^{}\mathrm{Sb}$. The detailed systematics of the odd-mass Te nuclei are compared to current particle-vibration and cluster models.

RADIOACTIVITY Measured $E_{\gamma }$, $I_{\gamma }$; deduced ${}_{}{}^{123}{}_{}{}^{}\mathrm{Te}$, ${}_{}{}^{125}{}_{}{}^{}\mathrm{Te}$ levels, $J^{\pi }$ values.

A density-dependent $\delta$ interaction is used to calculate pairing matrix elements for actinide proton and neutron orbitals. Tables of the matrix elements are given. The Seniority-one spectra of odd-mass actinides are analyzed in terms of these matrix elements. Several features of actinide spectra that cannot be understood with constant pairing matrix elements are explained with the density-dependent matrix elements.

NUCLEAR STRUCTURE Density-dependent $\delta$ interaction; pairing matrix elements; actinides; calculated single particle levels; deduced deformations.

Recent ($\mathrm{HI},\mathrm{xn}\gamma$) results on the levels of ${}_{}{}^{101,103,105}{}_{}{}^{}\mathrm{Pd}$ have been analyzed using the Nilsson model with Coriolis coupling at intermediate deformation ($\delta \simeq 0.12$). A variable moment of inertia treatment of the Nilsson basis was found to be necessary. With such a treatment the decoupled ${11/2}^{-}$ and ${7/2}^{+}$ bands of "favored states" are well reproduced for all three nuclei. In addition, the decoupled ($\Delta I=2\mathrm{}$) character of the ${5/2}^{+}$ ground-state band in ${}_{}{}^{101}{}_{}{}^{}\mathrm{Pd}$ is explained, as well as its transition to a conventional $\Delta I=1\mathrm{}$ band in ${}_{}{}^{105}{}_{}{}^{}\mathrm{Pd}$. Some of the other, "unfavored" states in these nuclei are also explained; and single-nucleon transfer spectroscopic factors and relative $\gamma$-ray branching are also discussed.

NUCLEAR STRUCTURE ${}_{}{}^{101,103,105}{}_{}{}^{}\mathrm{Pd}$; calculated energy levels ($d,p$) ($d,t$) spectroscopic factors, $\gamma$-ray branching. Nilsson model, Coriolis coupling, variable moment of inertia.

A general formalism is proposed for describing microscopically the asymmetric and symmetric rotors in both even and odd $A$ systems. It is shown that the quantum mechanical Hamiltonian for the rigid rotor can be uniquely determined from the classical Lagrangian independent of the quantization procedure, and it can be transformed to the one relevant to the rotating body-fixed frame of reference without introducing the angular velocity parameter. The Hartree-Fock-Bogoliubov equations are derived for this time-reversal invariant Hamiltonian. The microscopic operator form of the quantum number specifying the asymmetric rigid rotor state is provided by the previously proposed macroscopic model improved by taking into account the $D_2$ symmetry group and the consistency of the approximation. It is shown that the BCS approximation for the symmetric rotor in the even $A$ system predicts the disappearance of the pairing gap in the unique parity state at high spin.

NUCLEAR STRUCTURE Microscopic theory of the asymmetric rotor proposed. Constrained Hartree- Fock-Bogoliubov approximation.

The joint determination of the collective isoscalar monopole and quadrupole oscillations is studied in a self-consistent version of Suzuki's $l$-pole—$l$-pole interaction model with $l$ restricted to the values 0 and 2. The resulting variational problem leads to Suzuki's self-consistent monopole-monopole and quadrupole-quadrupole strengths, although with opposite sign in the case of the former. It is shown that the monopole and quadrupole pair excitations are decoupled with random-phase-approximation excitation energies $\sqrt{6}\hslash {\omega }_0$ and $\sqrt{2}\hslash {\omega }_0$, respectively.

NUCLEAR STRUCTURE Approximate many-body methods applied to solvable models.

We calculate several quantities of physical interest for an arbitrarily shaped diffuse-surface nuclear density distribution that is made diffuse by folding a short-range function over a uniform sharp-surface distribution of given shape. The quantities calculated include the moment of inertia about an arbitrary axis, generalized multipole moments, Coulomb and nuclear potentials, and Coulomb and nuclear energies. The expressions that are obtained in terms of volume integrals are converted into surface integrals by use of single and double divergence relations; these techniques are discussed for general functions. All of our methods and some of our results apply to arbitrary folding functions, although for definiteness most of our results are specialized to the case of a Yukawa folding function. The diffuseness of the nuclear surface increases the moment of inertia of light nuclei substantially, which increases the critical angular momentum at which compound nuclei can no longer be formed. The diffuseness correction to the Coulomb energy contains a term that is proportional to the surface area; this term increases the effective surface energy by approximately 2% for light nuclei and by approximately 1% for heavy nuclei.

NUCLEAR STRUCTURE Calculated quantities of physical interest for arbitrarily shaped diffuse-surface nuclear density distribution. Moment of inertia, generalized multipole moments, Coulomb and nuclear potentials, Coulomb and nuclear energies, Yukawa folding function, single and double divergence relations, applications to nuclear fission and heavy-ion reactions.

The intrashell quartet states proposed earlier on the basis of intrinsic multiconfiguration Hartree-Fock calculations are reexamined for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ in angular momentum projection formalism and supports in favor of the existence of such states are obtained. Quartet correlation in excited states of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ has also been investigated.

NUCLEAR STRUCTURE Intrashell quartet states, investigated in angular momentum projection formalism.

The difficulties which arise in the conventional development of the Jastrow method for fermions, from the failure to impose proper wave-function antisymmetry, are exhibited by an extension of the diagrammatic analysis of Pandharipande and Bethe. These problems are readily solved by the use of second quantization and a corresponding modification of the usual cluster expansion. A numerical example for a strong repulsive interaction shows that inaccurate treatment of the antisymmetrization can lead to very large errors in low-order estimates of the energy.

NUCLEAR STRUCTURE variational calculations, nuclear matter, Jastrow method, cluster expansion, antisymmetrization.

The branching ratio of the $1^{-}$ 2211-keV level of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ to the $3^{+}$ ground state has been measured to be (1.5 ± 0.2)%.

NUCLEAR REACTIONS ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(\alpha ,n)$, $E=5.5\mathrm{}$ MeV, measured branching ratio of 2211-keV level of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$.

Lehman and Gibson have recently derived an integral relation for $C_t$, the normalization of the $n-d$ tail of the triton wave function. We give (1) a concise alternative derivation of the Lehman-Gibson result, and (2) an explicit evaluation of $C_t$ in momentum space for the case in which the two-body interaction is not purely local or purely separable. This evaluation in general involves a five dimensional integration.

NUCLEAR REACTIONS Three-body problem; asymptotic normalization constant.

The $Q$ value for the reaction ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}(\alpha ,d){}_{}{}^{206}{}_{}{}^{}\mathrm{Bi}$ has been measured as $Q_0=-15798\mathrm{}\pm 11.6$ keV. This leads to a ${}_{}{}^{206}{}_{}{}^{}\mathrm{Bi}$ mass excess of -20 019 ± 13 keV which differs by 107 keV from the previously accepted value. Previously adopted mass values for ${}_{}{}^{210}{}_{}{}^{}\mathrm{At}$, ${}_{}{}^{214}{}_{}{}^{}\mathrm{Fr}$, ${}_{}{}^{218}{}_{}{}^{}\mathrm{Ac}$, and ${}_{}{}^{222}{}_{}{}^{}\mathrm{Pa}$ are also directly affected by a change in the ${}_{}{}^{206}{}_{}{}^{}\mathrm{Bi}$ mass.

NUCLEAR REACTIONS ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}(\alpha ,d)$, $E=48\mathrm{}$ MeV, measured $Q$ value relative to ${}_{}{}^{206,208}{}_{}{}^{}\mathrm{Pb}(\alpha ,d)$. Deduced ${}_{}{}^{206}{}_{}{}^{}\mathrm{Bi}$ g.s. mass.

The method of magnetic decoupling of hyperfine fields in free ions is used to estimate the magnetic moment of the lowest $3^{-}$ level of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ ($\tau =61\mathrm{}$ psec). The value $\mu =+0.56\mathrm{}\pm 0.13$ (where the sign is derived from an earlier measurement) confirms the basic nature of this state.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha ,{\alpha }^{\prime })$, $E=16.17\mathrm{}$ MeV; measured ($\alpha ,{\alpha }^{\prime }\gamma$) correlation vs decoupling field $H$ for free ion recoil. $3^{-}$ level ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ deduced magnetic moment $\mu$. Natural thin targets.

The magnetic dipole moment of the $6^{+}$ isomeric state of ${}_{}{}^{106}{}_{}{}^{}\mathrm{Ag}$ is determined by low temperature nuclear orientation, using the hyperfine field in an iron host, to be $\left|\mu \mathrm{}\right|=3.71\left(15\mathrm{}\right)\mathrm{}{\mu }_N$, in good agreement with that of ${}_{}{}^{110}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}$.

RADIOACTIVITY ${}_{}{}^{106}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}$, ${}_{}{}^{110}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}$; measured $I_{\gamma }\left(\theta \right)$ from polarized nuclei, deduced $\mu \left({}_{}{}^{106}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}\right)-{}_{}{}^3{}_{}{}^{}\mathrm{He}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ dilution refrigerator Ge(Li) detectors.

We present a comparison between the angular distributions calculated from the generalized exciton model and recent experimental material for the 45-MeV proton induced ($p,n$) reaction. A good description of the data is achieved.

NUCLEAR REACTIONS ($p,\mathrm{nx}$); $E=45\mathrm{}$ MeV; Calculations of the preequilibrium angular distributions and comparison with experiment.

We present some new developments in a treatment of exchange effects in radioactive decay published recently by us. By altering slightly the definition of the parent nucleus wave function in our expression for the radioactive decay width $\Gamma$, we find that the transformation of the volume integral expression for $\Gamma$ to the surface integral expression becomes rigorous. We discuss also how the optical model wave functions that appear in our expressions must be defined in a new manner which will lead to much larger predictions for $\Gamma$.

RADIOACTIVITY Width for radioactive decay by particle emission which includes effects of exchange symmetry is derived.

The $\gamma$-ray spectra of ${}_{}{}^{134}{}_{}{}^{}\mathrm{La}$ have been studied by $\gamma$-singles and $\gamma -\gamma$ Ge(Li) spectroscopy. The $\gamma$-ray decay of the low lying $0^{+}$ levels has been used to suggest that, because of softness toward $\gamma$ deformation, the lowest $0^{+}$ excited state in ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$, with $B(E2;0^{+}\to \frac{2_2^{+}}{0^{+}}\to 2_1^{+})=28\mathrm{}$, arises from the $N=3\mathrm{}$ phonon state. This is shown to be qualitatively consistent with calculations of transitional nuclei.

RADIOACTIVITY ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ce}$ → ${}_{}{}^{134}{}_{}{}^{}\mathrm{La}$, mass-separated, equilibrium sources, measured $E_{\gamma }$, $I_{\gamma }$, deduced ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$ levels.