It is shown that the large class of exchange currents in electron-nucleus elastic scattering compensates the effects of deviation from the mass shell in the nucleon form factor. The approximation which utilizes this compensation and which minimizes the first order corrections is derived. The $e$-nucleus amplitude is found to be factorized in this approximation into an $e-N$ on-shell scattering amplitude and a nuclear body form factor.

NUCLEAR REACTIONS Electron-nucleus scattering, impulse approximation, exchange currents, optimal approximation, on-shell form factor, factorization.

A theory of nuclear reactions induced by pions is presented, which includes scattering and absorption on an equal footing. The theory is consistent with a quantum field theory of mesons, but is developed in an effective Schrödinger equation formulation, to be consistent with conventional multiple scattering methods which are here extended. Methods of application to practical calculations are discussed.

NUCLEAR REACTIONS Theory of pion scattering and absorption in coupled channel formulation.

General features are calculated for excitation of non-normal parity states in pion scattering on $1p$-shell targets. Detailed distorted-wave impulse approximation results are given for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and related to effects of nuclear structure. Approximate formulas are deduced and applied to the region of excitation energy from 10 to 23 MeV. Calculations for ($e, e^{\prime }$) in this region are included.

NUCLEAR REACTIONS, NUCLEAR STRUCTURE ($\pi , {\pi }^{\prime }$) $E_{\pi }\approx 160$ MeV; $\frac{d\sigma }{d\Omega }$ for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ based on DWIA in momentum space; comparison of calculated ($e, e^{\prime }$) and ($\pi , {\pi }^{\prime }$); effects of nuclear structure.

The problem of nucleon final-state interaction in inclusive electromagnetic reactions is discussed within an optical potential description for the outgoing nucleon. The formalism accounts for both the loss of flux in the primary one-nucleon removal channel and the excitation of the multinucleon ones. Thereby a crucial difficulty encountered in the distorted-wave Born-approximation treatments of inclusive processes is eliminated. The calculation has been applied to the ($e, e^{\prime }$) reaction at the Stanford kinematics of 500 MeV incident energy and 60° scattering angle. As a result of nucleon final-state interaction, the peak intensities are reduced by 5-10%; about half of the ($e, e^{\prime }$) reaction is found to correspond to multinucleon removal. In contrast to the good agreement of the calculation with the Stanford data, severe discrepancies are obtained if applied to the recent Saclay data for incident energies around 400 MeV. The limitations of our approach are explored by considering processes at relatively low momentum transfers: low-energy electron scattering and radiative pion capture.

NUCLEAR REACTIONS Inclusive electron scattering. Radiative pion capture. Green's function approach. DWBA. Targets $4<~A<~58$. Electron energy 100-500 MeV, $\theta =60\mathrm{}°$; stopped pion.

We present the results of an experimental study of allowed Gamow-Teller ${\beta }^{+}$ and electron-capture decays of ${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{33}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{34}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{41}{}_{}{}^{}\mathrm{Sc}$. Thirteen new branches have been found and the precision has been increased, or upper limits reduced, on the intensities of more than 50 others.

RADIO ACTIVITY ${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{33}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{34}{}_{}{}^{}\mathrm{Cl}_{}^m{}_{}{}^{}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{41}{}_{}{}^{}\mathrm{Sc}$ measured $I_{\gamma }$; ${}_{}{}^{26}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{34}{}_{}{}^{}\mathrm{Cl}_{}^m{}_{}{}^{}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ca}$ measured $T_{\frac{1}{2}}$.

The highly proton-rich nucleus ${}_{}{}^{24}{}_{}{}^{}\mathrm{Si}$ has been produced via the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He}, 3n)$ reaction. The half-life of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Si}$ was found to be 103(42) ms, and the energy of the protons de-exciting the $T=2\mathrm{}$ state in the daughter, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$, has been measured as 3912.7(37) keV. From detailed consideration of masses in the $A=24\mathrm{}$ isobaric quintet (recently completed), it is concluded that this quintet constitutes a test of the isobaric multiplet mass equation as precise as the mass 9 quartet and that there is, in this case, no significant departure from the equation.

RADIOACTIVITY ${}_{}{}^{24}{}_{}{}^{}\mathrm{Si}$; from ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He}, 3n)$; measured $T_{\frac{1}{2}}$, $E_p$ ($\beta$-delayed protons).

Phase diagrams for bulk nuclear matter at finite temperatures and variable proton concentrations are presented and discussed. This binary system exhibits a line of critical points, a line of equal concentrations, and a line of maximum temperatures. the phenomenon of retrograde condensation is also possible.

NUCLEAR STRUCTURE Phase diagrams of nuclear matter, equation of state.

Energy spectra and $E2\mathrm{}$ matrix elements have been calculated by means of the interacting boson fermion model for ${}_{}{}^{79,81,83}{}_{}{}^{}\mathrm{Rb}$. A more schematic description obtained by assuming that the extra proton which is coupled to an even-even Kr core is in a pure $g_{\frac{9}{2}}$ particle state has been compared with calculations within a larger model space including the $d_{\frac{5}{2}}$ and $g_{\frac{7}{2}}$ particle states. We find that it is possible to achieve excellent agreement for both the schematic and the more detailed calculation as far as only level energies are concerned. However, the choice of the model space turns out to have a strong influence on the model parameters. Moreover, we find that $B\left(E2\mathrm{}\right)\mathrm{}$ values differ considerably in both descriptions. We conclude that even if there is a large separation between shells, the mixing due to the strong core-particle quadrupole force does not allow for restricting the model space to a single $j$ shell.

NUCLEAR STRUCTURE Interacting boson fermion model, ${}_{}{}^{79,81,83}{}_{}{}^{}\mathrm{Rb}$.

An effective $\mathrm{NN}$ interaction is constructed in the framework of noncovariant perturbation theory, containing a one-boson exchange part and explicitly the noniterative $2\pi$ exchange terms involving nucleon intermediate states. The one-boson exchange parameters are adjusted to fit $\mathrm{NN}$-scattering phase shifts and the data of the deuteron. The resulting interaction is used in Brueckner-Hartree-Fock calculations for nuclear matter and finite nuclei. The contributions of the so-called stretched-box and crossed-box terms to the binding energy are investigated. Special attention is paid to the many-body effects which quench the contribution of the noniterative $2\pi$ exchange terms in the nuclear medium.

NUCLEAR STRUCTURE Brueckner-Hartree-Fock, nuclear matter, light nuclei, nucleon-nucleon interaction, mesonic degrees of freedom, noniterative $\pi$ exchange.

Isoscalar monopole, quadrupole, and octopole states are calculated in closed shell nuclei. A delta interaction is used, its strength determined by the multipole condition, namely that the mean single-particle-single-hole potential energy difference is equal to the corresponding kinetic energy difference. This interaction is used to obtain particle-hole matrix elements appropriate for a random-phase approximation calculation. The strengths given by the different multipole conditions are different but (except for $L=0\mathrm{}$) they appear to approach each other as the mass number $A$ becomes large. The monopole mode has already collapsed somewhat before the strength implied by the quadrupole condition is reached. Some of the calculations were repeated using a zero-range Skyrme interaction. We observe a very high degeneracy in our calculation which we are able to explain in terms of $L-S$ coupling and the fact that the particle-hole matrix element of a delta interaction is of the form $\int f_{P_A{H}_A}\mathrm{}\left(r\right)\mathrm{}{f}_{P_B{H}_B}\mathrm{}\left(r\right)\mathrm{}{r}^2\mathrm{dr}$.

NUCLEAR STRUCTURE Closed shell nuclei, $0^{+}$, $2^{+}$, $3^{-}$ $T=0\mathrm{}$ states, delta interaction with multipole condition, RPA calculations.

The interacting boson approximation Hamiltonian for $s$ and $d$ bosons is renormalized in lowest order for the effects of the $g$ boson using second-order perturbation theory in a single $j$ shell approximation. In this paper only the correction term which renormalizes the single-boson energy is investigated in detail, with a specific application to the Ba isotopes. In the evaluation of this correction, the general form of the matrix elements of two-body quadrupole operators, taken between paired-fermion states, is obtained. Our numerical results for Ba indicate that the effects of the $g$ boson on the single-boson energy are of the correct sign and magnitude and that a perturbative approach to including these effects appears to be appropriate.

NUCLEAR STRUCTURE Interacting boson approximation, perturbation theory of $g$ boson, calculated $2^{+}$ - $0^{+}$ splittings in Ba.

We investigate the accuracy of the energy-dependent pole expansion for the (3 + 1) and (2 + 2) subamplitudes in the calculation of the binding energy of the $\alpha$ particle, $E_{\alpha }$, for separable $\mathrm{NN}$ potentials with tensor components. We employ the truncated $t$-matrix ($t_{00}$) approximation and compare our results for $E_{\alpha }$ to those obtained, independent of any separable expansion, by Gibson and Lehman and to the results for $E_{\alpha }$ obtained with the Hilbert-Schmidt expansion of the subamplitudes. It is shown that the energy-dependent pole expansion is both more economical and converges faster than the Hilbert-Schmidt expansion, even one term of the energy-dependent pole approximation already being accurate to better than 1.5%.

NUCLEAR STRUCTURE Accuracy of energy-dependent pole expansion for calculation of $\alpha$-particle binding energy, compared to Hilbert-Schmidt expansion. Separable nucleon-nucleon potentials with tensor forces. Truncated $t$-matrix approximation.

A model of nuclear matter composed of nucleons interacting with neutral scalar mesons and neutral vector mesons, which Walecka has shown in the classical field approximation to reproduce the nuclear saturation property, is studied. The Fermi gas state for the system is shown to be unstable, resulting in the equidistant multilayer structure, a new phase of the system in which nucleons are distributed in multiple layers spaced equidistantly. In this structure, the energy per nucleon is $\frac{E}{N}=-24\mathrm{}$ MeV and the nucleon density is $\rho =0.02\mathrm{}{\rho }_0$ with the normal nucleon density ${\rho }_0$. It is pointed out that the saturation property of a nucleon system, as well as the exchange term for nuclear interactions should be of considerable consequence in the discussion of the instability of nuclear states.

NUCLEAR STRUCTURE Instability of Fermi gas state and stable phase in nuclear matter. Saturation and antisymmetrization considered.

The measured beta branching ratio of <0.1% to the 2.03 MeV ($\frac{1}{2^{+}}$) state in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ from the $\frac{1}{2^{+}}$ state of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Tl}$ indicates the validity of the $n$-selection rule leading to near equality of the $n-p$ radius parameters.

RADIOACTIVITY ${}_{}{}^{209}{}_{}{}^{}\mathrm{Tl}$; $\beta$ branching ratio to levels in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$; deduced near equality of $n-p$ radius parameters.

The scattering of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ at 236 MeV has been measured with sufficient energy resolution to separate elastic from inelastic scattering. The results demonstrate the importance of long-range absorption due to strong Coulomb interaction and are well reproduced by appropriate theoretical calculations.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$), ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$′), $E=236\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$, optical model analysis with dynamic polarization potential, semiclassical analysis of inelastic scattering. Enriched target.

From a joint analysis of electrofission- and photofission-fragment angular distribution data for ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, limits can be set on the uncertainties of the $E2\mathrm{}$ virtual-photon spectra calculated in the distorted-wave Born approximation that are no larger than ±20%.

NUCLEAR REACTIONS ${}_{}{}^{236,238}{}_{}{}^{}\mathrm{U}(e, f)$ angular distributions; virtual-photon spectra; distorted-wave Born approximation.

By employing a system for three bound identical bosons, a simple connection is made between Faddeev's and the $K$-harmonic approaches.

NUCLEAR STRUCTURE Quantum few-body problem.

Volume integrals of the imaginary part of $d$, $t$, and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ optical potentials are obtained from existing phenomenological analyses over the range of target mass numbers $A=50-208\mathrm{}$. Comparison of these values with those for nucleons shows that the volume integrals for nulceon, deuteron, and mass-3 projectiles, averaged over this $A$ range, are in the ratio of 1:2:3. The present results are thus in good agreement with predictions of the simple folding model.

NUCLEAR REACTIONS Systematics—volume integrals of imaginary part of nucleon, deuteron, and mass-3 optical potentials.

An exact Fourier-Bessel impact parameter amplitude $S_F\mathrm{}\left(b\right)\mathrm{}$ is given in the form of a quadrature for the case of nonrelativistic scattering by a $\frac{1}{r^2}$ potential. The only other potential for which $S_F\mathrm{}\left(b\right)\mathrm{}$ is known is the Coulomb potential. An asymptotic expansion of the exact $S_F\mathrm{}\left(b\right)\mathrm{}$ is not correctly represented by the eikonal expansion series due to the $\frac{1}{r^2}$ singularity of the potential. Perturbation theory results are also presented.

NUCLEAR REACTIONS Scattering theory, Fourier-Bessel amplitudes, eikonal approximation.

The ratio of near-resonance inclusive ${\pi }^{\pm }$ scattering cross sections from the isotopic pair ${}_{}{}^{16,18}{}_{}{}^{}\mathrm{O}$ is shown to be consistent with an isospin dependence of the $\Delta$-spreading potential determined by intermediate coupling to the pion absorption channel.

NUCLEAR REACTIONS ${}_{}{}^{16,18}{}_{}{}^{}\mathrm{O}({\pi }^{\pm }, {{\pi }^{\pm }}^{\prime })$ inclusive scattering; test isospin dependence of $\Delta$-nucleus interaction.