The strength of the $\Delta$-nucleus potential is calculated from the many-body Hamiltonian for $\pi$, $N$, and $\Delta$ constructed by Betz and Lee. The results are compared to the empirical values of the $\Delta$-hole doorway model. It is found that the calculated strength of the central potential reproduces the empirical one to a large extent. However, the calculated spin-orbit potential is much smaller than that of of the $\Delta$-hole model. It is also shown that the pion absorption through the $N\Delta S$ wave only accounts for about half of the total absorption. The sums of other $N\Delta$ partial waves are found to be equally important.

NUCLEAR REACTIONS A model of interactions between $\pi$, $N$, and $\Delta$ in nuclear matter. Calculation of the $\Delta$-nucleus potential.

We measured the energy spectra and yields of neutrons above 1.2 MeV from nuclear capture of negative pions slowing down and stopping in C, N, O, Al, Cu, Ta, and Pb targets. Each neutron spectrum was decomposed into an evaporation portion and a direct portion. The number of direct neutrons per stopped pion is substantially constant for all the targets with a mean value of 1.74±0.28, whereas the yield of evaporation neutrons increases by an order of magnitude from about 0.7 for carbon to about 7 for lead. The total kinetic energy carried away by the neutrons is substantially constant also for all the targets with a mean value of 76.7±2.0 MeV. The kinetic energy carried away by evaporation neutrons increases with mass number with an associated decrease in the kinetic energy carried away by direct neutrons. We obtained the nuclear temperature (in MeV) of the first residual nucleus formed in the evaporation process for each target: Pb (1.4), Ta (1.4), Cu (1.9), A1 (2.3), O (2.2), N (2.2), and C (2.1). The spectrum from a light target displays a shoulder in the region around 60 MeV which is consistent with a two-nucleon absorption mechanism. The direct neutron spectra are characterized by a rising yield as the neutron energy decreases in the region from 30 MeV down to about 10 MeV. The data are compared with previous measurements and with the predictions of intranuclear cascade and preequilibrium calculations.

NUCLEAR REACTIONS C, N, O, Al, Cu, Ta, Pb (${\pi }^{-}$,$\mathrm{xn}$), $E_{{\pi }^{-}}\approx 0$ MeV. Measured differential energy spectra and yields. Deduced nuclear temperature. Compared results to intranuclear cascade and preequilibrium model calculations.

The coalescence approach to light fragment formation is applied to light ion induced reactions at intermediate energies. These reactions show evidence of a transition between the snowball model for fragment formation in noncomposite particle induced reactions, and the traditional coalescence model of heavy ion reactions. Possible experiments which could be done to better test these ideas are suggested.

NUCLEAR REACTIONS Coalescence models, inclusive reactions, light fragment production, nucleon and light ion induced reactions.

Double $K$-hole creation has been studied in the electron-capture decay of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Cs}$ by measuring hypersatellite $K$ x rays emitted when the double vacancies of the $K$ shell are filled. The complex $K$ lines observed with a two-Ge-detector coincidence spectrometer show evidence of the hypersatellite $K\alpha$ and $K\beta$ lines. The double $K$-hole creation probability is determined: (1.4±0.1)×${10}^{-5\mathrm{}}$ per $K$-capture event. This value, which does not agree with theoretical predictions, is discussed in detail. The intensity ratio of the $K{\alpha }_1$ to $K{\alpha }_2$ hypersatellites is found to be 1.5±0.2. The intensity of internal bremsstrahlung photons accompanying the $K$-electron capture decay has also been reevaluated.

RADIOACTIVITY ${}_{}{}^{131}{}_{}{}^{}\mathrm{Cs}$ (EC) ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$; $\left(K \mathrm{x}\mathrm{ray}\right) \otimes \left(K \mathrm{x}\mathrm{ray}\right)$ coincidences measured by Ge detectors, double $K$-hole creation probability, hypersatellite energy shift, ratio $\frac{K{\alpha }_1^K}{K{\alpha }_2^H}$, associated internal bremsstrahlung intensity.

The new isotopes ${}_{72}{}^{163}{}_{}{}^{}\mathrm{Hf}$ [$T_{\frac{1}{2}}=40.0\mathrm{}\left(6\right)\mathrm{}$ s] and ${}_{72}{}^{162}{}_{}{}^{}\mathrm{Hf}$ [$T_{\frac{1}{2}}=37.6\mathrm{}\left(8\right)\mathrm{}$ s] were produced in ${}_{60}{}^{142}{}_{}{}^{}\mathrm{Nd}$ (${}_{12}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $\mathrm{xn}$) reactions and transported to a measuring station by use of the He-jet technique. Decay properties were observed with $\alpha$, $\gamma$, and $\gamma -\gamma$ spectroscopy. The $Z$ assignment of the new isotopes was based on a cross bombardment, ${}_{12}{}^{24}{}_{}{}^{}\mathrm{Mg}$+${}_{59}{}^{141}{}_{}{}^{}\mathrm{Pr}$, and on results of $\gamma$-x-ray coincidence measurements. The mass assignment was deduced from measured excitation functions. Beta-delayed $\gamma$ rays were identified, 11 for ${}_{}{}^{163}{}_{}{}^{}\mathrm{Hf}$ and 3 for ${}_{}{}^{162}{}_{}{}^{}\mathrm{Hf}$, and level schemes for ${}_{71}{}^{163}{}_{}{}^{}\mathrm{Lu}$ and ${}_{71}{}^{162}{}_{}{}^{}\mathrm{Lu}$ are proposed based on the results of intensity and $\gamma -\gamma$ coincidence measurements. A small $\alpha$ branch [$I_{\alpha }={0.0087 }_{(-37\mathrm{}}^{+17)}$%] with a decay energy of $E_{\alpha }=4308\mathrm{}$ (10) keV was found in the decay of ${}_{}{}^{162}{}_{}{}^{}\mathrm{Hf}$. The reduced $\alpha$ width $W_{\alpha }={2.6}_{(-1.2\mathrm{}}^{+0.6)}$ for ${}_{}{}^{162}{}_{}{}^{}\mathrm{Hf}$ is in accordance with those for neighboring nuclei. With the new ${}_{}{}^{162}{}_{}{}^{}\mathrm{Hf}$ $\alpha$-decay energy, mass values were derived for ${}_{72}{}^{162}{}_{}{}^{}\mathrm{Hf}$, ${}_{74}{}^{166}{}_{}{}^{}\mathrm{W}$, ${}_{76}{}^{170}{}_{}{}^{}\mathrm{Os}$, ${}_{78}{}^{174}{}_{}{}^{}\mathrm{Pt}$, and ${}_{80}{}^{178}{}_{}{}^{}\mathrm{Hg}$. The new masses as well as values deduced for two-proton binding energies are compared with predictions of current mass formulas.

RADIOACTIVITY ${}_{}{}^{163,162}{}_{}{}^{}\mathrm{Hf}$ from ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}$(${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$,$\mathrm{xn}$); measured $E_{\gamma }$, $I_{\gamma }$, $E_{\alpha }$, $I_{\alpha }$, and $T_{\frac{1}{2}}$; ${}_{}{}^{163,162}{}_{}{}^{}\mathrm{Lu}$ deduced level schemes; deduced reduced $\alpha$ width for ${}_{}{}^{162}{}_{}{}^{}\mathrm{Hf}$; deduced mass values for ${}_{}{}^{162}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{166}{}_{}{}^{}\mathrm{W}$, ${}_{}{}^{170}{}_{}{}^{}\mathrm{Os}$, ${}_{}{}^{174}{}_{}{}^{}\mathrm{Pt}$, and ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hg}$. He-jet technique; Ge(HP), Ge(Li), and Si surface-barrier detectors.

The previously unreported decay of ${}_{}{}^{36}{}_{}{}^{}\mathrm{P}$ to levels in ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ has been studied from activity generated by the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$($n$,$2p$)${}_{}{}^{36}{}_{}{}^{}\mathrm{P}$ reaction using neutrons produced through the stopping of 70-MeV deuterons in a Be target. The half-life for ${}_{}{}^{36}{}_{}{}^{}\mathrm{P}$ was measured to be 5.9±0.4 s. From $\gamma$ singles and coincidence measurements excited states in ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ at 3290.7($2^{+}$), 4192.7($3^{-}$), and 5830.8($4^{-}$,$5^{-}$) keV were established. The ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ levels are compared with results from ($d$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) and ($t$,$p$) reactions and shell-model calculations, and the nature of the negative-parity states is discussed.

RADIOACTIVITY ${}_{}{}^{36}{}_{}{}^{}\mathrm{P}$ [from ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$($n$,$2p$)], neutrons from 70-MeV deuterons; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coin. Ge(Li) detectors; ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ deduced levels, $J$, $\pi$, $log\mathrm{ft}$. Natural target.

The elastic model, which successfully explains the isoscalar giant resonances, is now applied to study the isovector giant resonances. In solving the Lamé equation, we employ the boundary condition that the displacement shall vanish at the surface. The results are compared with those obtained under the contrasting boundary condition that the stresses shall be absent at the surface. It was found that the results are dependent on the type of boundary conditions. Future experimental data will allow the assessment of the correct choice of boundary conditions.

NUCLEAR STRUCTURE Nuclear giant resonances, isovector vibrational nodes. Electric and magnetic multipoles.

A recently developed relativistic many-body theory which has been used to explain the saturation properties of nuclear matter is applied to the study of the interaction between relativistic quasiparticles. Specifically, we calculate the scattering amplitude for two quasiparticles at the Fermi surface. From a calculation of the forward scattering amplitude we may extract the Landau-Migdal parameters of the interaction. We compare our results with the parameters determined in extensive phenomenological studies of the properties of finite nuclei. In the relativistic theory the Landau-Migdal parameter $F_0$ exhibits a very strong density dependence. Recently, phenomenological studies have indicated that this parameter is about ten times larger in the less dense regions of the nuclear surface than in the interior of a large nucleus. From our work we see that this large reduction of $F_0$ with increasing density (found in phenomenological studies) may be a relativistic effect closely related to the mechanism giving rise to nuclear saturation in the relativistic theory. In addition, if we contrast the results of the relativistic model with those of the nonrelativistic model, we find that the parameter $F_1$ is a larger (negative) number in the relativistic theory. (In turn this implies that the effective mass parameter, $m^{*}$, is somewhat smaller.) The parameters $F_1$ and $m^{*}$ exhibit a stronger density dependence in the relativistic theory. The physical basis for the increased magnitude of $F_1$ in the relativistic analysis and the strong density dependence of $F_0$ are discussed.

NUCLEAR STRUCTURE Relativistic theory of the effective interaction in nuclei; calculation of the Landau-Migdal parameters.

The strength function for deep-lying hole states in an optical potential is studied by the method of Green's functions. The role of isospin is emphasized. It is shown that, while the main trends of the experimental data on hole states in isotopes of Sn and Pd can be described by an energy independent optical potential, intermediate structures in these data indicate the specific nuclear polarization effects have to be included. This is done by introducing doorway states of good isospin into the optical model potential. Such states consist of neutron hole plus proton core vibrations as well as more complicated excitations that are analog states of proton hole plus neutron core vibrations of the parent nuclear system. Specific calculations for ${}_{}{}^{115}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{103}{}_{}{}^{}\mathrm{Pd}$ give satisfactory fits to the strength function data using optical model and doorway state parameters that are reasonable on physical grounds.

NUCLEAR STRUCTURE ${}_{}{}^{115}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{103}{}_{}{}^{}\mathrm{Pd}$; calculated single hole strength functions. Green's function method for optical potential, intermediate structure doorway states. Good isospin.

The effect on the ground-state $A=6\mathrm{}$ three-body binding energies of representing the $S_{\frac{1}{2}}$ $\alpha -N$ interaction by a repulsive potential compared to an attractive, excluded-bound-state potential is examined. The theory underlying construction of an attractive, excluded-bound-state potential is reviewed and then applied in the construction of an $S_{\frac{1}{2}}$ $\alpha -N$ interaction. The role of Levinson's theorem from potential theory as opposed to its modified form for composite-particle scattering is stressed in comparing the repulsive and attractive-excluded-bound-state interactions. The $A=6\mathrm{}$ three-body equations are generalized to accommodate an attractive $S_{\frac{1}{2}}$ $\alpha -N$ interaction with a forbidden bound state and it is shown that the limit to exclude the forbidden state leads to a set of well-defined three-body equations containing no spurious, deeply-bound solutions. Results for the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ binding energies suggest that the attractive, excluded-bound-state interaction gives a better representation of Pauli-exclusion effects in the $S_{\frac{1}{2}}$ $\alpha -N$ interaction than the repulsive form, based on the marked improvement in the predicted ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ binding energy compared to experiment with essentially no degradation in the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ value. This conclusion can be further tested by using the new wave functions to calculate the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +d$ momentum distribution which is sensitive to the components in the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ wave function that are present solely due to the $S_{\frac{1}{2}}$ $\alpha -N$ interactions.

NUCLEAR STRUCTURE ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, Pauli-exclusion effects, three-body calculations, Levinson's theorem.

The equilibrium deformations of nuclei in the rare earth and transition region ($146\le A\le 192$) are studied with the self-consistent quadrupole plus pairing interaction model, by considering all the nucleons in the nucleus explicitly in the configuration space of the first seven major oscillator shells for both protons and neutrons. The present results are in agreement with those obtained earlier by assuming an inert core and employing the renormalized strengths for the quadrupole and pairing interactions. The experimental $B\left(E2\right)$ values are correctly reproduced by employing bare nucleon charges in large configuration space.

NUCLEAR STRUCTURE Equilibrium deformations, rare earth and transition nuclei, self-consistent $Q+P$ model, $B\left(E2\right)$ values.

Starting from a simplified model, treating proton two-particle two-hole excitations in interaction with low-lying quadrupole vibrational configurations, we calculate the low-lying levels in even-even ${}_{}{}^{112,114}{}_{}{}^{}\mathrm{Cd}$. We also present configuration mixing calculations within the framework of the interacting boson model. Both approaches give a good description of the quintuplet of levels occurring below $E_x\cong 1.5$ MeV in ${}_{}{}^{112,114}{}_{}{}^{}\mathrm{Cd}$ (energy spectra and a detailed account of $E2$ and $E0$ decay properties). Finally, we point out some similarities between both approaches and try to interpret the interacting boson model mixing parameters in terms of shell-model quantities (two-body matrix elements and single-particle energies).

NUCLEAR STRUCTURE Collective excitations in ${}_{}{}^{112,114}{}_{}{}^{}\mathrm{Cd}$; shellmodel intruder states; interacting boson model configuration mixing.

Using the procedure of Ewart and de Takacsy to obtain expressions for the energy of angular momentum projected yrast states coming from coherent phonon intrinsic states, the energy expressions are then minimized with respect to the phonon structure coefficients and for each individual level the calculation is made self-consistent with an amended Bardeen-Cooper-Schrieffer number equation. The pairing plus quadrupole Hamiltonian is used and quite good results are obtained for the low spin yrast states of even xenon isotopes. The proton gap was found to vanish at $J=10\mathrm{} or 12$.

NUCLEAR STRUCTURE Even xenon isotopes, calculated yrast states, coherent phonon model, pairing plus quadrupole interaction, boson expansion theory, static moments, $B\left(E2\right)$.

Precision measurements of high energy $\gamma$ rays from thermal ($n$,$\gamma$) reactions with twelve nuclides as targets have been performed with an energy scale based upon the neutron separation energy of ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$. The final nuclides and the deduced neutron separation energies (in keV) with absolute errors are ${}_{}{}^{143}{}_{}{}^{}\mathrm{Nd}$ (6123.62±0.13), ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}$ (7817.11±0.12), ${}_{}{}^{146}{}_{}{}^{}\mathrm{Nd}$ (7565.28±0.14), ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$ (8536.39±0.12), ${}_{}{}^{158}{}_{}{}^{}\mathrm{Gd}$ (7937.39±0.12), ${}_{}{}^{162}{}_{}{}^{}\mathrm{Dy}$ (8196.99±0.12), ${}_{}{}^{163}{}_{}{}^{}\mathrm{Dy}$ (6270.98±0.11), ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$ (7658.11±0.12), ${}_{}{}^{165}{}_{}{}^{}\mathrm{Dy}$ (5715.96±0.11), ${}_{}{}^{166}{}_{}{}^{}\mathrm{Ho}$ (6243.69±0.11), ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$ (7464.63±0.11), and ${}_{}{}^{175}{}_{}{}^{}\mathrm{Yb}$ (5822.35±0.12).

NUCLEAR REACTIONS ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}$($n$,$\gamma$), ${}_{}{}^{143}{}_{}{}^{}\mathrm{Nd}$($n$,$\gamma$), ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$($n$,$\gamma$), ${}_{}{}^{155}{}_{}{}^{}\mathrm{Gd}$($n$,$\gamma$), ${}_{}{}^{157}{}_{}{}^{}\mathrm{Gd}$($n$,$\gamma$), ${}_{}{}^{161}{}_{}{}^{}\mathrm{Dy}$($n$,$\gamma$), ${}_{}{}^{162}{}_{}{}^{}\mathrm{Dy}$($n$,$\gamma$), ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$($n$,$\gamma$), ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$($n$,$\gamma$), ${}_{}{}^{173}{}_{}{}^{}\mathrm{Yb}$($n$,$\gamma$); ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$($n$,$\gamma$), thermal; measured $E_{\gamma }$; deduced $\mathrm{Qn}$.

An apparent ambiguity was recently reported in coupling either pairs of identical fermions or hole pairs. This is explained here as being due to a Hamiltonian whose lowest eigenstates do not have the structure prescribed by generalized seniority. It is shown that generalized seniority eigenstates can be equivalently constructed from correlated $J=0\mathrm{}$ and $J=2\mathrm{}$ pair states of either particles or holes. The interacting boson model parameters recently calculated can be unambiguously interpreted and then are of real interest to the shell model basis of the interacting boson model.

NUCLEAR STRUCTURE Shell model description of interacting boson model; particle-hole equivalence in generalized seniority.

Detailed calculations of electromagnetic transition rates ($E2$, $M1$, $M2$) have been carried out for ${}_{}{}^{134}{}_{}{}^{}\mathrm{Te}$ and compared with the results of detailed measurements on the gamma decay properties of this nucleus. The need for a small, but nonzero, contribution from the tensor $M1$ operator is pointed out.

NUCLEAR STRUCTURE Shell model calculations; electromagnetic transition rates; influence of tensor $M1$ operator.

The shapes of continuum angular distributions have previously been described using the energy of the emitted particle as the principal parameter, but phenomenological methods are here found to be unable to distinguish conclusively between this and other related energy parameters. This points to the need for more theoretical work. Slight evidence for a shift by the ejectile binding energy is noted.

NUCLEAR REACTIONS Investigated alternate energy parameters for describing shapes of continuum angular distributions.

Angular distributions of protons from the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction are discussed for low-spin states of the residual nucleus. It is suggested that the oscillating patterns observed experimentally could be explained assuming the emission of a proton from the strongly deformed ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ system followed by fusion of the remaining nucleons.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$p$), $E=29.5, 30.0, 30.5$ MeV; $\sigma (E,\theta )$ and $\overline{\sigma }\left(\theta \right)$ studied, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ levels deduced prefusion $\sigma$.

Small-angle inelastic $\alpha$ scattering data for ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ at 129 MeV have been reanalyzed with the giant resonance peak parameters suggested by Bertrand et al. The two components of the giant resonance peak, assumed by them to correspond to $L=0\mathrm{}$ and $L=2\mathrm{}$, respectively, are found to have similar angular distributions between 0°-8° where large differences between these multipolarities should exist. This is not in agreement with their interpretation of ($p$,$p^{\prime }$) and large-angle ($\alpha$,${\alpha }^{\prime }$) data wherein a concentration of $L=0\mathrm{}$ strength was suggested at 20 MeV in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$. Their data for the assumed $L=0\mathrm{}$ component are shown in our analysis to be consistent with an $L=2\mathrm{}$ transfer.

NUCLEAR REACTIONS ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$($\alpha$,${\alpha }^{\prime }$); $E_{\alpha }=129\mathrm{}$ MeV. Measured $E_x$, $\sigma \left(\theta \right)$, giant resonances; deduced $L$.

Problems arising in viscous nuclear fluid dynamical models of high-energy heavy-ion collisions are discussed. The importance of an accurate treatment of the transport properties of the hot and dense nuclear matter is pointed out.

NUCLEAR REACTIONS Heavy-ion reaction, nuclear hydrodynamics, viscosity.