We have searched for the $\beta$-decay branch from the ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$ ground state to the 1.837 MeV level in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$. Since both states are $J^{\pi }=0^{+}$, $T=1\mathrm{}$, this decay is an example of a non-analog Fermi decay which could occur by reason of some mixing of the analog ground states into the lowest excited ${\mathrm{O}}^{+}$ state in both ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$ and ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$. As a signal for this branch, we looked for a subsequent cascade $\gamma$ ray with a Ge(Li) detector-rabbit arrangement. We found a branching ratio of (2.2 ± 1.7) × ${10}^{-5\mathrm{}}$ relative to the superallowed ground state to ground state decay. Interpreted as an upper limit, this corresponds to a branching ratio < 3.9 × ${10}^{-5\mathrm{}}$ at the 84% confidence level. This result is at the lower bound of what present theory can predict with a Coulomb force mixing calculation.

RADIOACTIVITY ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$ (g.s.); measured upper limit on $\beta$-decay branching ratio to the 1.837 MeV level in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ relative to the ground state.

The new isotope ${}_{}{}^{57}{}_{}{}^{}\mathrm{Cr}$ was produced via the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}({}_{}{}^{11}{}_{}{}^{}\mathrm{B},pn){}_{}{}^{57}{}_{}{}^{}\mathrm{Cr}$ reaction at $E\left({}_{}{}^{11}{}_{}{}^{}\mathrm{B}\right)=21\mathrm{}$ MeV. Delayed singles $\gamma$ spectra, and $\gamma -\gamma$ and $\beta -\gamma$ coincidences were measured, using large Ge(Li) detectors and a plastic scintillator. The half-life of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Cr}$ was measured to be 21.1 ± 1.0 s, and its ground-state spin and parity have been assigned as 3/$2^{-}$. Spin restrictions have been placed on a number of levels in the daughter nucleus ${}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$. The mass excess of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Cr}$ was determined to be -52.39 ± 0.10 MeV. The measured ${}_{}{}^{57}{}_{}{}^{}\mathrm{Cr}$ mass excess is compared with various predictions.

RADIOACTIVITY ${}_{}{}^{57}{}_{}{}^{}\mathrm{Cr}$ [from ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}({}_{}{}^{11}{}_{}{}^{}\mathrm{B},pn)$]; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coin, $E_{\beta }$, $\beta -\gamma$ coin; deduced decay scheme, $log\mathrm{ft}$ values, $J^{\pi }$, mass excess. ${}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ deduced levels, $J^{\pi }$ restrictions. Enriched targets, multiple rabbit, helium jet, Ge(Li) and plastic detectors.

The decay of ${}_{}{}^{61}{}_{}{}^{}\mathrm{Cu}$ to levels of ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}$ and the decay of ${}_{}{}^{67}{}_{}{}^{}\mathrm{Cu}$ and ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ga}$ to levels of ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ have been studied in detail. The half-life of ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ga}$ is measured to be 3.261 ± 0.001 days. Also, absolute intensities are reported for the $\gamma$ rays from the decay of ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ga}$. Transition probabilities are calculated for ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}$ using a shell model and a modified surface $\delta$ interaction.

RADIOACTIVITY Chemically separated sources; measured $E_{\gamma }$, $I_{\gamma }$, deduced ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ levels $J$, $\pi$; Compton suppression.

In the hydrodynamical model, the nuclear spin and isospin symmetry energies and the speeds of spin sound and isospin sound are pertinent to the determination of the static and dynamic properties of finite nuclei. We examine these quantities with a generalized Skyrme interaction. From the explicit expressions we obtain for these quantities, we find an interesting algebraic relation connecting the symmetry energies and likewise the sound speeds. Relevant collective vibrational energies of various types and different multipolarities are evaluated with the known sets of Skyrme interactions, in order to provide information for future amendments or selections among the sets of interactions and for the confrontation of the hydrodynamical model with experiment. We further investigate the dispersion of sound waves due to the range of the nuclear interaction. In particular, the "plasma oscillation" arising from the long-range Coulomb interaction is found to lead to a simple modification of the energies of the isoscalar and isovector collective vibrational states. When applied to the nuclear giant dipole and monopole resonances, the inclusion of the plasma oscillation gives an improved agreement between the hydrodynamical and the experimental giant dipole state energies and modifies the nuclear incompressibility extracted from measured giant monopole energies by as much as 15%.

NUCLEAR STRUCTURE Nuclear hydrodynamical model. Symmetry energies, and their algebraic relations. Speeds of different sound waves, and their algebraic relations. Giant multipole resonances in the hydrodynamical model. Plasma oscillations in finite nuclei. Energy of nuclear giant dipole states. Energy of giant monopole states. Nuclear incompressibility.

A particular third-order diagram which contributes to the effective two-body interaction in mass-18 nuclei is computed up to intermediate excitations of $26\hslash \omega$. We find that our results have not converged by $26\hslash \omega$ and that the slow decrease in the higher-lying contributions is mainly due to the strong short-range repulsion in the central components of the nucleon-nucleon force.

NUCLEAR STRUCTURE Theory, effective interaction mass-18; convergence intermediate-state summation in third order to $26\hslash \omega$; effects of tensor and hard-core components of nuclear force.

The angular distributions of cross section and of analyzing power for the ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}(\overrightarrow{p},{\gamma }_0){}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ reaction have been measured throughout the giant dipole resonance region of ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$. In addition, the 90° yield curve has been measured for $E_p$ from 5.8 to 16.5 MeV. The data are analyzed to deduce the amplitudes and phases of the $T$ matrix elements involved. Comparison of the results is made to both the dynamic collective model calculation of Ligensa and Greiner and to a direct-semidirect model calculation. The direct-semidirect calculation indicates that the reaction proceeds predominantly via the radiative capture of $d_{\frac{5}{2}}$ protons. Isospin splitting is also discussed.

NUCLEAR REACTIONS ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}(\overrightarrow{p},{\gamma }_0)$; measured $\sigma \left(\theta \right)$ and $A\left(\theta \right)$ $E_p=6.8\mathrm{}-12.8$ MeV. ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}(p,{\gamma }_0)$ measured $\sigma \left(90\mathrm{}°\right)$, $E_p=5.8\mathrm{}-16.5$. Deduced $T$-matrix amplitudes and phases. Compared to model calculations.

The isotope shifts of atomic $K$ x rays were measured for pairs of the six mercury isotopes with $A=198, 199, 200, 201, 202, \mathrm{and} 204$, using a curved crystal spectrometer. The changes of the nuclear charge radii were derived in terms of $\delta 〈r^2〉$ and $\delta R_k$ and compared with optical and muonic isotope shift data. From our results, a renormalization of the optical data was obtained.

NUCLEAR STRUCTURE x rays, ${}_{}{}^{198,199,200,201,202,204}{}_{}{}^{}\mathrm{Hg}$; measure $K$ x-ray isotope shifts enriched targets; derived $\delta 〈r^2〉$, $\delta R_k$.

Based on the conventional particle-hole representation of the random-phase-approximation eigenvalue equation, it is shown that the coordinate-space formalism can be derived directly and is valid generally for rotation and time-reversal invariant interactions. Explicit expressions are given for the interaction strengths and transformation coefficients in the case of Skyrme interactions.

NUCLEAR STRUCTURE Random-phase approximation, coordinate-space formalism. General and Skyrme interactions.

The physical and mathematical differences of several formulations for preequilibrium decay are discussed. Mathematical models and examples are presented or referred to in order to illustrate what the author believes to be errors in the exciton formulation as being due to improper inclusion of spectator effects. An earlier work of Gadioli et al. is reinterpreted, and quotations therein to work of the present author are corrected.

NUCLEAR REACTIONS Preequilibrium decay formulations; compositions and comments.

It is shown that a double-folding model potential based on a realistic nucleon-nucleon $G$ matrix yields a real ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ optical potential extremely similar to that found empirically by Michel and Vanderpoorten. With only a 7% renormalization this folded potential, combined with the imaginary potential of Michel and Vanderpoorten, provides a good description of ${}_{}{}^{40}{}_{}{}^{}\mathrm{He}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ scattering over the full angular range.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$), $E=29\mathrm{}$ MeV, calculated $\sigma \left(\theta \right)$.

The statistical-theory predictions of the average spin of fission products, the dependence of spin on the bombarding energy, and the distribution of spin with respect to the fragment mass are compared with experimental results. Good agreement is obtained. The last one provides direct evidence that asymmetric fission is associated with higher density of quantum states and thus offers direct experimental proof of the statistical-theory explanation of asymmetric fission.

NUCLEAR REACTIONS, FISSION Spin distribution, statistical theory.

The deuteron sepctra from ($n,d$) reactions at 800 MeV near 0° are characterized by a high energy quasielastic scattering peak, and at lower momentum, a quasifree scattering peak. The ratio of the quasifree to quasielastic cross sections is approximately 10:1. Both cross sections exhibit an $A^{\frac{1}{3}}$ mass dependence over the range of target nuclei studied. Comparisons are made with corresponding proton-induced quasielastic and quasifree deuteron production.

NUCLEAR REACTIONS $n+X\to d$. $E_{\mathrm{lab}}=800\mathrm{}$ MeV. Measured deuteron quasielastic and quasifree cross sections near 0°.

The $1g_{\frac{9}{2}}$ analog state in ${}_{}{}^{55}{}_{}{}^{}\mathrm{Co}$ is investigated through the ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(p,\gamma ){}_{}{}^{55}{}_{}{}^{}\mathrm{Co}$ reaction. At $E_p=3462\mathrm{}\pm 2$ keV and $E_p=3473\mathrm{}\pm 2$ keV two resonances are found corresponding to states in ${}_{}{}^{55}{}_{}{}^{}\mathrm{Co}$ at $E_x=8470\mathrm{}$ keV and $E_x=8480\mathrm{}$ keV, respectively. These resonances combined with another one as seen through a ($p,p^{\prime }\gamma$) experiment are identified as the fragments of the $1g_{\frac{9}{2}}$ analog state in ${}_{}{}^{55}{}_{}{}^{}\mathrm{Co}$.

NUCLEAR REACTIONS ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(p,\gamma )$, $E=3450\mathrm{}-3480$ keV; measured $E_{\gamma }$, $I_{\gamma }$. ${}_{}{}^{55}{}_{}{}^{}\mathrm{Co}$ deduced $g_{\frac{9}{2}}$ analog resonances. Enriched target.

The neutron cross section of ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ up to 1 MeV was calculated by the coupled channels method, using a simple vibrational model. It was found that intermediate structure observed in $s$-wave scattering from ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ may be accounted for by this model. By modifying the coupled channels code to calculate bound states, it was also found that the general features of the measured distributions of spectroscopic factors are accounted for by this model.

NUCLEAR REACTIONS ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}\mathrm{}(n,n)\mathrm{}$; $E=0\mathrm{}-1.0$ MeV; calculated $J_t\mathrm{}\left(E\right)\mathrm{}$.

It is shown that direct absorption cannot explain the measured ratio of $\mathrm{nn}$ to $\mathrm{np}$ emission following a negative $2p$-bound pion absorption in light nuclei. For ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, we show that this problem can be solved by introducing $p$-wave rescattering terms with a reasonable cutoff range parameter.

NUCLEAR REACTIONS Pion absorption; initial and final state correlations, final nucleon-nucleus correlations, $p$- and $s$-wave rescattering.

A high velocity Doppler shift attenuation experiment was performed using an inverse reaction with a ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ ion beam on a deuteron target. The mean lives of the two first 3/$2^{-}$ levels at 1943 and 2462 keV have been determined as 0.79±0.10 and 6.7±0.8 psec, respectively. Concurrently, the lifetime of the 2670 keV level was found to be 4.5±1.3 psec. An empirical electric quadrupole charge is extracted for the neutron from the $1943\left({\frac{3}{2}}^{-}\right)\to \mathrm{g}.\mathrm{s}\left({\frac{7}{2}}^{-}\right)$ $\gamma$-ray transition probability using a shell model wave function in the $\mathrm{fp}$ space.

NUCLEAR REACTION ${}_{}{}^2{}_{}{}^{}\mathrm{H}({}_{}{}^{40}{}_{}{}^{}\mathrm{Ca},p\gamma )$ $E=60\mathrm{}$ MeV; measured $\gamma$-ray doppler patterns. ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ levels, deduced ${\tau }_m$.

The energy dependence of two-step distorted-wave Born approximation calculations is studied for unnaturalparity state excitations by the ($p,t$) reaction involving ($p,p^{\prime },t$), ($p,t,t^{\prime }$), and ($p,d,t$) processes. The calculations which provide rapidly decreasing cross sections with an increase in the incident energy are found to be quite consistent with the observed results for the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(p,t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ (8.88 MeV, $2^{-}$) reaction at the energy range of $E_p=20\mathrm{}-45$ MeV. The remarkable difference of kinematical features between one-step and twostep processes is pointed out and the importance of higher-order effects for one-step allowed transitions is apparently indicated.

NUCLEAR REACTIONS Energy dependence of second-order DWBA cross sections, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(p,t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ (8.88 MeV, $2^{-}$) and (9.85 MeV, $2^{+}$) $E=20.0\mathrm{}-43.6$ MeV.

We measured the tensor analyzing power $T_{20}$ for the reaction ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}(\overrightarrow{d},\alpha ){}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ for $E_x\left({}_{}{}^{18}{}_{}{}^{}\mathrm{F}\right)\le 6.48$ MeV at ${\theta }_{\mathrm{lab}}=176.3\mathrm{}°$ and for incident energies of $10.5\le E_d\le 12.0$ MeV in steps of 0.25 MeV. Comparison of the measured $T_{20}$ values with theoretical predictions leads to assignments of natural or unnatural parity to about 30 levels in ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$. Combining the present results with published spectroscopic information leads to new unambiguous $J^{\pi }$ and isospin assignments for some levels and the confirmation of previously determined values for others.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}(\overrightarrow{d},\alpha )$, $10.5\le E_d\le 12.0$ MeV; $\Delta E_d=0.25\mathrm{}$ MeV; measured $T_{20}(E,E_{\alpha },176.3\mathrm{}°)$. ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ deduced levels, natural target.

A study of the ($t,p$) reactions on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ has been carried out using 23 MeV tritons and an Elbek-type spectrograph using photographic emulsions as detectors. A total of 71 states of ${}_{}{}^6{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{B}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been studied. Some of the states had not been previously reported. In other cases new values of excitation energies and widths are proposed. Attempts have been made to fit the 62 angular distributions we obtained with the distorted-wave Born approcimation: no systematic analysis was possible except in the case of $L=0\mathrm{}$ distributions.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(t,p)$, $E=23\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$. ${}_{}{}^6{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ deduced levels, $J^{\pi }$, ${\Gamma }_{\mathrm{c}.\mathrm{m}.\mathrm{}}$.