The derivation of nuclear neutron distributions from hadron-nucleus scattering data is critically examined. Using the Glauber model, we investigate how the total and differential cross sections depend on specific properties of the radial nucleon densities ${\rho }_N\mathrm{}\left(r\right)\mathrm{}$ of the target nucleus. Emphasis is placed on the interpretation of hadron-nucleus total cross sections. As to the deduction of r.m.s radii from total cross-section measurements only, we find that a large systematic error arises from the a priori unknown shape of ${\rho }_N\mathrm{}\left(r\right)\mathrm{}$. This error can be reduced if physically justified constraints are imposed on ${\rho }_N\mathrm{}\left(r\right)\mathrm{}$. In many published analyses, however, the constraint on ${\rho }_N\mathrm{}\left(r\right)\mathrm{}$ has been of mathematical origin since only density distributions of a certain shape (e.g., Fermi distributions) have been used. As an example, our findings are applied to two recent pion-nucleus total cross section experiments. It is also shown that earlier attempts to avoid a mathematical constraint on ${\rho }_N\mathrm{}\left(r\right)\mathrm{}$ must be viewed with reservations.

NUCLEAR STRUCTURE Hadron-nucleus scattering, deduction of matter radius, model dependence.

A once-subtracted form of the Low equation for the pion-nucleon scattering amplitude is derived, with partial conservation of axial-vector current used to define the amplitude when one pion is off the mass shell. The static approximation is not made and both the seagull terms and the antinucleon contribution ($z$ graphs) are retained. The theory is applied to calculate the $S$-wave amplitudes in the elastic scattering region. Good agreement is found with the phase shift fits to the data when we use $\left|g_{\pi }\right(4\mathrm{}{M}^2\left)\right|=11.69\mathrm{} \mathrm{and} 25.5$ MeV for the $\pi N\sigma$ commutator. The implications of this work for the analysis of low-energy elastic scattering of pions from nuclei are discussed. In particular, we point out how this work establishes the presence of a Laplacian term in the pion-nucleus optical potential with a magnitude that is fixed from the value of the $\sigma$ commutator.

NUCLEAR REACTIONS Pion nucleon scattering, off-shell amplitude, $\sigma$ commutator, Laplacian in pion-nucleus optical potential.

The theory of $\alpha$ particle scattering at high energies (in the GeV region) is reviewed and compared with the recent Saclay experiments. It is shown that the optical model of Czyz and Maximon has to be improved, some of the omitted multiple scattering terms being large. The effect of long or short range correlations is also examined and found to be less important than the previous corrections. These features are very likely to occur also for the scattering of two heavy nuclei, and the measurement of the elastic scattering of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ or heavier double closed shell nuclei at energies above 300 MeV per nucleon is suggested.

NUCLEAR REACTIONS $\mathrm{Ca}(\alpha ,\alpha )$, $\mathrm{Ca}(\alpha ,{\alpha }^{\prime })$, $E=1.4\mathrm{}$ GeV calculated $\sigma \left(\theta \right)$.

Cross sections for neutrino scattering on ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ to specific nuclear states are calculated. The ratio of the isovector neutral to charged current events is found to be independent of the nuclear models and sufficiently sensitive to permit discrimination among various fashionable models of neutral currents. Low energy neutrino elastic cross sections for $p$-shell nuclei are predicted to be of the order of ${10}^{-39\mathrm{}}$ ${\mathrm{cm}}^2$.

RADIOACTIVITY Neutral and charged currents. CVC. Elastic and inelastic neutrino reactions. Gauge theory models. Shell model. Structure of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$.

The decay of mass-separated ${}_{}{}^{122}{}_{}{}^{}\mathrm{Ag}$ to levels in ${}_{}{}^{122}{}_{}{}^{}\mathrm{Cd}$ has been studied. The half-life was measured to be 0.48 ± 0.08 sec in disagreement with earlier work. Of six $\gamma$ rays observed, five were placed in a ${}_{}{}^{122}{}_{}{}^{}\mathrm{Cd}$ level scheme with excited states at 569, 1329, 1368, and 1979 keV. The results are compared with the systematics of other even-even Cd nuclei and predictions from a rotation-vibration model.

RADIOACTIVITY ${}_{}{}^{122}{}_{}{}^{}\mathrm{Ag}$ [from ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}\mathrm{}(n,f)\mathrm{}$]; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$-coin Ge(Li) detectors; ${}_{}{}^{122}{}_{}{}^{}\mathrm{Cd}$ deduced levels, $J$, $\pi$, $log\mathrm{ft}$. Mass-separated ${}_{}{}^{122}{}_{}{}^{}\mathrm{Ag}$ activity.

The amounts of excess ${}_{}{}^{128}{}_{}{}^{}\mathrm{Xe}$ and ${}_{}{}^{130}{}_{}{}^{}\mathrm{Xe}$ in xenon which had been extracted by stepwise heating of an old telluride ore from the Mattagami Lake area, Quebec, indicate that the $\beta \beta$-decay half-life of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Xe}$ exceeds that of ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$ by a factor of (1.57 ± 0.10) × ${10}^3$. These results agree with the relative half-lives reported earlier for ${}_{}{}^{128}{}_{}{}^{}\mathrm{Te}$ and ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$ in tellurides from Kalgoorlie, Western Australia.

RADIOACTIVITY $\beta \beta$ decay ${}_{}{}^{128}{}_{}{}^{}\mathrm{Te}$ and ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$; measured excess ${}_{}{}^{128}{}_{}{}^{}\mathrm{Xe}$ and ${}_{}{}^{130}{}_{}{}^{}\mathrm{Xe}$; deduced relative $T_{\frac{1}{2}}$ values.

For the ground-state bands of nonmagic even-even nuclei, the variable moment-of-inertia law defines an effective moment of inertia $\mathfrak{g}\mathrm{}\left(J\right)\mathrm{}$, using only the energies of the $2^{+}$ and $4^{+}$ states. From the definition, $\mathfrak{g}\mathrm{}\left(J\right)\mathrm{}$ is never negative. The "average" moment of inertia ${\mathfrak{g}}_{02}\equiv \frac{1}{2}\left[\mathfrak{g}\mathrm{}\right(0)+\mathfrak{g}\mathrm{}(2\left)\right]$ may then be related to the transition quadrupole moment $Q_{02}$. $\mathfrak{g}\mathrm{}\left(Q\right)\mathrm{}$ is well described by a continuous function ranging over almost two orders of magnitude in both quantities. This function is linear for small values of $Q(\lesssim 4 e\mathrm{b})$, quadratic for intermediate values ($4\lesssim Q\lesssim 11$ e b), and essentially constant for larger values ($11\le Q\le 13$ e b). The linear section pertains to all nuclei which deviate by not more than two pairs from being singly magic. In this group are both light deformed nuclei (e.g., ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$) and heavier spherical nuclei ranging from $30\lesssim A\lesssim 200$. The values of $\mathfrak{g}$ and $Q$ in this region are (within ± 50%) those that would be obtained if the nucleus were replaced by a dumbbell with length equal to the nuclear diameter and an $\alpha$ particle at either end. The quadratic relation has a simple interpretation in a picture of the nucleus as a droplet composed of two fluids, a superfluid which does not contribute to the angular momentum, and an inertial or rigidly rotating component which forms a fixed fraction $f$ of the mass density at each point in the nucleus. The fraction $f$, computed according to a simple rule from the degree of deformation of the droplet, vanishes if the droplet is spherical. The constancy of $\mathfrak{g}$ at the largest $Q$ values (associated with spontaneously fissioning nuclei) may be due to a slight proton excess at the poles of the nucleus.

NUCLEAR STRUCTURE Quadrupole moments, VMI model, moments of inertia.

A simple microscopic derivation of the kinetic energy in the collective model is presented with no restriction to small vibrations. The result gives a small correction to the Bohr-Mottelson expression.

NUCLEAR STRUCTURE Kinetic energy found in generalization of Bohr model.

X-ray spectra were observed from proton-induced excitation of monazite inclusions possessing both normal and giant pleochroic halos at $E_p=4.7\mathrm{} \mathrm{and} 5.7$ MeV. A complete elemental analysis of these spectra is reported for elements with $Z\ge 26$. Weak photopeaks are observed from monazite inclusions possessing giant halos which are absent from inclusions with normal halos, although limitations in spatial resolution of the proton beam prevented accumulation of statistically definitive data. Because of energy, width, and intensity anomalies, some of these weak photopeaks are not readily interpretable as x rays or $\gamma$ rays of known elements. Proposed evidence for superheavy elements is carefully examined.

NUCLEAR STRUCTURE, Elemental analysis, measured proton-induced x-ray spectra from monazite inclusions with pleochroic halos, $E_p=4.7\mathrm{} \mathrm{and} 5.7$ MeV.

Relations among the masses of neighboring nuclei provide an accurate and convenient method for the estimation of unknown masses. A set of such relations is "derived" and their structure as partial difference equations is discussed. These considerations lead to a set of mass equations (solutions of the difference equations) that can be ordered such that each successive member gives a potentially more nearly accurate representation of nuclear ground-state energies as functions of $N$ and $Z$. The first two members of this ordered set are the mass equations considered originally by Garvey et al. The results obtained by fitting the third member of this set to the known masses are discussed in this paper. This third mass equation is shown to satisfy the principle of charge symmetry to a good approximation. As a consequence, it gives predictions for the masses of proton-rich nuclei.

NUCLEAR STRUCTURE Relations among ground-state energies of neighboring nuclei.

A comparison of two two-term separable $\Lambda -N$ potentials which have been used in three-body calculations of the hypertriton binding energy is reported. The potentials compared are approximately on-shell $T$ matrix equivalent, but yield quite different values for the hypertriton binding energy. It is shown that the radial wave function for one of the potentials has an extra node due to a spurious state. The comparison is based on a Fredholm determinant approach to the radial wave equation for a nonlocal potential.

NUCLEAR STRUCTURE Two-term separable $\Lambda -N$ potentials, Fredholm determinants, spurious states, extra nodes and separable potential three-body calculations.

Energy-level calculations are performed for the odd-mass Pd isotopes using a simple model in which valence neutrons in the $d_{\frac{5}{2}}$, $g_{\frac{7}{2}}$, and $h_{\frac{11}{2}}$ orbitals are coupled to a weakly deformed soft core. The softness is simulated by a variable moment-of-inertia representation for the core. A spherical basis is used throughout so that all basis states are eigenstates of good $J$, $R$, and $I$. The Hamiltonian is treated in the BCS approximation, and the deformation for each level is determined by an energy minimization condition. In general, calculated intraband energies are in good agreement with experiment; bandhead positions are much more difficult to fit, especially for ${}_{}{}^{105}{}_{}{}^{}\mathrm{Pd}$.

NUCLEAR STRUCTURE ${}_{}{}^{101,103,105}{}_{}{}^{}\mathrm{Pd}$; calculated levels and deformations. Spherical basis bandmixing calculation with energy minimization with respect to deformation.

We describe the rich variety of nuclear phenomena in the odd-mass indium isotopes by taking into account the coupling of both single-hole and one-particle two-hole configurations (seniority $v=1\mathrm{}$ and $v=3\mathrm{}$) with the quadrupole and octupole vibrations of the underlying core (Sn) nucleus. To fully test the calculations, we have performed detailed spectroscopic studies of the ${}_{}{}^{113}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{115}{}_{}{}^{}\mathrm{Cd}_{}^m{}_{}{}^{}$, and ${}_{}{}^{115}{}_{}{}^{}\mathrm{Cd}_{}^g{}_{}{}^{}$ decays. Energy spectra, spectroscopic factors for stripping and pickup reactions, and electromagnetic properties are calculated and compared with the experimental results for ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$. We compare our model with earlier calculations for the odd-mass In isotopes and with band-mixing calculations using a deformed basis (Nilsson model) for all odd-mass In isotopes ($107\le A\le 119$). The equivalence of the unified-model description with a rotational interpretation is discussed in some detail.

NUCLEAR STRUCTURE, RADIOACTIVITY Unified-model calculation; chemically separated sources; measured $E_{\gamma }$, $I_{\gamma }$; deduced ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$ and ${}_{}{}^{113}{}_{}{}^{}\mathrm{In}$ levels; Compton suppression.

The Thomas-Fermi approximation is used in order to study nuclear deformation at high angular momenta. A great similarity between our results and the liquid drop results is found.

NUCLEAR STRUCTURE ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$; shape at high angular momenta; Thomas-Fermi method.

The equations of motion along a large amplitude collective path $\left|q\mathrm{}\right(t),p\mathrm{}(t)\mathrm{}〉$ are shown to require, in general, complex parameters $q$ and $p$. It is shown, however, that real values are sufficient if $|q,p〉$ is constructed by Hartree-Fock with coordinate and momentum constraint. In addition, the motion along the particular paths suggested by the adiabatic time-dependent Hartree-Fock theory and by the local harmonic approach is proved to be stable against small imaginary displacements.

NUCLEAR STRUCTURE Classical motion, collective path, constrained Hartree-Fock, adiabatic time-dependent Hartree-Fock, local harmonic approach, large amplitude collective motion, complex generator coordinates.

It is pointed out that because of the omission of residue terms from the basic Green's function, the two hole-line approximation to the ground state energy of infinite nuclear matter with self-consistent intermediate state energies for hole lines only differs from the corresponding physical energy in a completely uncontrolled manner. This interpretation is in contrast to that of Wong.

NUCLEAR STRUCTURE Ground-state energy nuclear matter correctness 2 methods calculation assessed.

Recent data for the reaction ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{29}{}_{}{}^{}\mathrm{P}$ at 25.0 MeV have been analyzed with an unbound stripping code. Resulting spectroscopic factors are in good agreement with those extracted from the original analysis using a modified bound-state calculation, and with spectroscopic factors calculated from measure proton widths.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({}_{}{}^3{}_{}{}^{}\mathrm{He},d)$, $E=25.0\mathrm{}$ MeV; DWBA analysis of published data for unbound final states; deduced $S_p$, $\frac{{\Gamma }_{p_0}}{{\Gamma }_{\mathrm{s}.\mathrm{p}.\mathrm{}}}$.

Angular distributions have been measured for neutron energies of 8 and 12 MeV for the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(n,{\gamma }_0){}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ reaction. The extracted $a_2$ coefficients are in good agreement with recent direct-semidirect calculations. The behavior of $a_2$ is examined in light of recent results from polarized proton capture measurements on ${}_{}{}^{54,56,58}{}_{}{}^{}\mathrm{Fe}$.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(n,{\gamma }_0)$, measured $\sigma \left(\theta \right)$, $E_n=8.0, 12.0$ MeV. Compared to direct-semidirect model predictions.

The excitation function for the inelastic scattering reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ($2^{+}$, 4.43 MeV) has been measured from $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=15.4\mathrm{}-30.9$ MeV in 214 keV steps. A series of broad resonances is observed in striking correlation with structures previously seen in the fusion channel. The positions of the observed resonances correlate closely with the calculated energies of the $n=0\mathrm{}$ molecular shape resonances and have widths which approach the single particle widths.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ * (4.43); $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=15.4\mathrm{}-30.9$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$; deduced evidence for shape resonances; compared with structure in fusion excitation function.

The branching ratio of $\gamma$ rays depopulating the 682 keV ($7^{+}$) level in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Y}$ leading to $3^{-}$ and $2^{-}$ levels is remeasured. The deduced transition probability $B(E5,7^{+}\to 2^{-})=(3.7\mathrm{}\pm 0.3)\times {10}^5$ ${\mathit{e}}^2$${\mathrm{fm}}^{10}$ compares favorably with a previously reported value of (4.24±0.85) × ${10}^5$${\mathit{e}}^2$${\mathrm{fm}}^{10}$.

RADIOACTIVITY ${}_{}{}^{90}{}_{}{}^{}\mathrm{Y}_{}^m{}_{}{}^{}$; ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}(\alpha ,n)$ measured $\frac{I_{\gamma }\left(682\mathrm{} \mathrm{keV}\right)}{I_{\gamma }\left(480\mathrm{} \mathrm{keV}\right)}$; deduced $B(E5,7^{+}\to 2^{-})$.