Partial-wave dispersion relations for the coupled $\alpha +n$ and $t+d$ channels of the $Z=2\mathrm{}$ five-nucleon system have been solved by the matrix $\frac{N}{D}$ technique. Driving terms have been constructed from one- and two-cluster exchange graphs with parameters of vertex functions taken from studies of $A\le 4$ subsystems. Accurate solutions to the coupled $N$ and $D$ equations have been obtained by a Pagels approximation based on [$N,N-1\mathrm{}$] Padé approximants. Coulomb forces in charged-fragment channels were incorporated via the repeated $\frac{N}{D}$ scheme of Kinoshita and Kugler. No proper treatment has been given of the anomalous threshold of the $t+d\to \alpha +n$ proton-exchange graph. Calculated $\alpha +n$ scattering phase shifts lack uniqueness, due to strong sensitivity to the inaccurately known vertex parameters used as input, but display the basic features of repulsion in the $s$ wave, occurrence of resonances in the $p$ waves, and existence of the small ${3/2}^{+}$, $d$-wave resonance just above the $t+d$ threshold. Failure of the calculation to produce the width of the $p$-wave resonances is attributed to the improper treatment of the anomalous threshold. Differential cross sections for $t+d\to \alpha +n$ show reasonable agreement with experiment in both the forward and backward directions but lack details of the observed structure at medium angles. The latter again occurs for the calculated $t+d$ elastic scattering cross sections which moreover are unsatisfactory at forward angles. A comparison with other coupled-channel calculations of light systems is attmpted.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(n,n)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$, $E=0\mathrm{}-40$ MeV; calculated $S_{\frac{1}{2}}$ through $D_{\frac{3}{2}}$ phase shifts; ${}_{}{}^3{}_{}{}^{}\mathrm{H}\mathrm{}(d,n)\mathrm{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{H}\mathrm{}(d,d)\mathrm{}$, $E=6\mathrm{} \mathrm{and} 14.2$ MeV; calculated $\sigma \left(\theta \right)$. Dispersion-relation method.

In the generator-coordinate formalism we calculate the phase shifts for $\alpha -\alpha$ scattering by solving the Hill-Wheeler equation in the continuum. The Pauli principle is exactly taken into account for the nuclear potential term. The Coulomb interaction is introduced under a long-range assumption. The results are compared to the experimental values.

NUCLEAR REACTIONS $\alpha -\alpha$ elastic scattering. Calculated phase shifts.

The Sasakawa theory of scattering in its various generalized forms is reviewed in detail with particular emphasis on Austern's extension of the method to the iterative solution of coupled differential and integral equations. The relevance of these methods to physical applications is explained. Coester's convergence proof for the Sasakawa series is generalized to include distorted waves and coupled equations, and the convergence of the related Austern series is investigated. A numerical comparison between the Austern and Born series is made for elastic scattering from a central potential. In a model coupled-channel calculation of nuclear inelastic scattering, the Austern method is shown to be a very practical method of solution.

The ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}\mathrm{}(d,p)\mathrm{}{}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ reaction has been reinvestigated with special emphasis on the weak states. The structure of all states below 4.2 MeV is reviewed and compared with ${\left(sd\right)}^4$ and open-core shell-model calculations.

NUCLEAR REACTIONS ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}\mathrm{}(d,p)\mathrm{}$, $E=12.0\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$, DWBA analysis, comparison with shell model.

Differences between results from earlier measurements of the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(p,n_0){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ differential cross section have prevented use of the neutron spectrum from this reaction as a standard of neutron intensity. Differential excitation curves for the reaction were obtained at 17 angles for proton energies between 2.1 and 3.8 MeV. A pulsed proton beam incident upon a thick lithium metal target produced continuous neutron spectra which were measured by time of flight. The data were corrected for neutron scattering from the target. The neutron detector efficiency was determined through a simultaneous normalization of the measured angular distributions to the known total cross section at all proton energies. The efficiency determination was judged to be uncertain to about 5%. Resultant differential excitation curves have uncertainties between 5 and 8%. The zero degree differential cross section ($E_p=1.89\mathrm{} \mathrm{to} 3.8$ MeV), and the excitation functions and Legendre coefficients ($E_p=2.09\mathrm{} \mathrm{to} 3.80$ MeV), are presented in 10-keV increments and compared with other measurements.

NUCLEAR REACTIONS ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(p,n_0)$, $E=\mathrm{threshold}\mathrm{to} 3.8$ MeV; time of flight, plastic scintillator, deduced efficiency; measured $\sigma \left(\theta \right)$. Natural target.

The cross section for the photodisintegration reaction $\gamma +{}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +p+n$ has been calculated for photon energies from threshold ($E_{\gamma }=3.70\mathrm{}$ MeV) up to $E_{\gamma }=16\mathrm{}$ MeV utilizing dispersion theory methods. In this energy region, the dominant contribution to the transition amplitude results from diagrams characterized by the virtual breakups ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +d$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to p\left(n\right)+{}_{}{}^5{}_{}{}^{}\mathrm{He}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}\left({}_{}{}^5{}_{}{}^{}\mathrm{Li}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}\right)$, and rescattering corrections. In the calculation, the coupling constant for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +d$, vertex is obtained from an analysis of quasielastic cross sections for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\mathrm{}(p,pd)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$. The ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to p+{}_{}{}^5{}_{}{}^{}\mathrm{He}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ coupling constant is determined from an analysis of quasielastic cross section for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\mathrm{}(p,2p)\mathrm{}{}_{}{}^5{}_{}{}^{}\mathrm{He}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$. The predicted $\sigma (\gamma ,n)$ cross section agrees both in shape and magnitude with the experimental results. The calculated cross section integrated up to the ${}_{}{}^3{}_{}{}^{}\mathrm{H}$-${}_{}{}^3{}_{}{}^{}\mathrm{He}$ threshold is 13.0 MeV mb, while experimentally it is found to be 12.4-14.6 MeV mb.

NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(\gamma ,n)$, calculated $\sigma \left(E_{\gamma }\right)$, $E_{\gamma }=3.70\mathrm{}-15.8$ MeV, dispersion theory.

The width of the first excited state of ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ has been studied through high resolution ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,\gamma ){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ measurements. Extracted values of this quantity were found to have wide variations when the data were analyzed with different assumptions concerning backgrounds and reaction theories. A previous suggestion that existing data show statistically significant difference in this width when observed in different reactions is not supported by these studies. Width values for the second and third excited states of ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ have also been extracted from the (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) measurements.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,\gamma )$, $E_p=600\mathrm{}$ keV, thick target; measured yield $E_{\gamma }$. ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$, deduced ${\Gamma }_1$. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},d)$, $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=12\mathrm{}-15$ MeV; measured yield $E_d$. ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$, deduced ${\Gamma }_{1,2,3}$. Alternative analyses compared.

From a survey of the heavy-ion systems measured until now two conditions can be deduced empirically which must be fulfilled in order to find correlated resonances of the type measured in the low-energy excitation functions of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction. With both conditions one is able to explain simultaneously the lack and the existence of correlated resonances in all measured reactions. The conditions are: (1) the level density of the corresponding compound nuclei and the number of open channels must be small, and (2) both nuclei in the entrance channel must be $\alpha$-particle nuclei. The latter condition seems reasonable because experimental evidence exists for the assumption that these resonances are due to $\alpha$-particle doorway states.

NUCLEAR REACTIONS Several heavy-ion reactions, energies in the vicinity of the Coulomb barrier, measured $\sigma (E,\theta )$, deduced explanation explanation for the occurrence of correlated resonances.

Nuclear properties of several ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ states in the region of 4-MeV excitation were obtained using the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}\mathrm{}(t,p)\mathrm{}{}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ reaction at a bombarding energy of $E_t=2.9\mathrm{}$ MeV. Angular correlations of $\gamma$ rays in time coincidence with protons detected in an annular particle detector positioned near 180° were obtained using an array of five NaI(T1) counters. Doppler-shift-attenuation measurements were also performed using a 20-${\mathrm{cm}}^3$ Ge(Li) counter for the detection of $\gamma$ rays. Analyses of these data yielded lifetime, excitation energy, and branching ratio information for some ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ excited states. A unique spin assignment of $J=2\mathrm{}$ was found for the 4.31-MeV state and the mixing ratio for the 4.31 → 1.56-MeV transition was found to be $\delta =-0.26\mathrm{}\pm 0.17$. Some of the measured excitation energies (keV) and lifetimes (psec) are: (3869.9 ± 2.3, ${0.60}_{-0.20\mathrm{}}^{+0.45\mathrm{}}$); (4150.4 ± 6.3, not measured); (4179.2 ± 4.2, ≤ 0.30); and (4310.7 ± 3.0, < 0.08).

NUCLEAR REACTIONS ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}\mathrm{}(t,p)\mathrm{}$, $E_t\mathrm{}(t,p)\mathrm{}$ MeV; measured $\sigma (E_{\gamma },{\theta }_{\gamma })$, $E_{\gamma }$, $t_{\frac{1}{2}}$, $\delta$, $\Gamma$, deduced $J$, $\pi$ for ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ levels.

The ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(p,t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reaction has been studied at 20 MeV. Relative cross sections to the ground ($0^{+}$), 6.05 MeV ($0^{+}$), 6.92 MeV ($2^{+},K=0\mathrm{}$), and 9.85 MeV ($2^{+},K=2\mathrm{}$) states have been compared with standard distorted-wave Born-approximation (DWBA) calculations using ${\mathrm{SU}}_3$ parentage factors and the nuclear coexistence model. The agreement is good for the $0^{+}$ states but poor for the $2^{+}$ states, given the uncertainties inherent in the DWBA calculation itself. The presence of competing second-order processes is indicated by the relatively strong population of the 8.88 MeV $2^{-}$ level.

NUCLEAR REACTIONS, STRUCTURE ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(p,t) E=20\mathrm{}$ MeV; measured $d\sigma \left(\theta \right)$; resolution 25 keV. DWBA calculation of $d\sigma \left(\theta \right)$. Nuclear coexistence model.

We report on recent $\alpha$-scattering experiments at 141.7 MeV using ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ targets. The results are compared with previous experiments on other nuclides at approximately the same energy and are used to illustrate phenomena occurring in intermediate-energy $\alpha$ scattering to which we have given the name "refractive behavior." All the elastic scattering differential cross sections exhibit the exponential-like falloff at large angles characteristic of nuclear rainbow scattering. The variation in the rainbow angle with $A$ is found to be approximately linear. In each instance it is shown that, consistent with earlier predictions, it is the data beyond the rainbow angle which make possible the elimination of the discrete ambiguities in the optical potential: For each nucleus studied, only a single family of Woods-Saxon optical potentials is found to fit the data. The real parts of the extracted potentials are characterized by well depths ranging from 108 to 118 MeV and volume integrals $\frac{J}{4A}$ ranging from 297 to 352 MeV ${\mathrm{fm}}^3$; hence they are more nearly three times the strength of nucleon-nucleus potentials at 1/4 the incident energy, rather than 4 times, as is frequently assumed. Systematic variations of the optical potentials with $A$ occur primarily in the imaginary part of the potential and are greatest for the lighter nuclei; as $A$ decreases, $W$ and $a^{\prime }$ decrease, $r_0^{}{}_{}{}^{\prime }$ increases, and the volume integral of the real part of the potential increases.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(\alpha ,\alpha )$, $E=141.7\mathrm{}$; enriched targets; measured $\sigma \left(\theta \right)$; deduced optical-model parameters, nuclear rainbow angles; results compared with those from ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.

The levels of ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ with $E_x\le 2.51$ MeV have been studied with the ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ reaction at $E\left({}_{}{}^7{}_{}{}^{}\mathrm{Li}\right)=34\mathrm{}$ MeV to test the usefulness of this reaction as a spectroscopic tool. Elastic scattering data were taken for the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ + ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ + ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ systems and optical model parameters were extracted so that finite range distorted-wave Born-approximation (DWBA) calculations could be performed. The DWBA differential cross sections well reproduce the shapes of the data. The absolute spectroscopic factors are in excellent over-all agreement with previously published light-ion studies, indicating that the extracted ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ optical parameters are a reasonable approximation for the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ optical parameters and that the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}\to {}_{}{}^6{}_{}{}^{}\mathrm{He}+p$ spectroscopic factor is in good agreement with the theoretical value of Cohen and Kurath. In addition, this reaction permits a clear distinction between $p_{\frac{3}{2}}$ and $p_{\frac{1}{2}}$ final-state configurations when very forward angle data are taken.

NUCLEAR REACTIONS ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$), (${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$) $E=34.0\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; deduced optical model parameters; deduced $S$, from finite range DWBA analysis. ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$) $E=28.1, 30.1, 32.1$ MeV; measured $\sigma \left(\theta \right)$; deduced optical model parameters.

Energy levels in ${}_{}{}^{62}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ have been investigated via the ($p,t$) reaction at 35 MeV. Many new levels are reported up to an excitation energy of 5.3 MeV, with spin and parity assignments determined for most levels, including the $0^{+}$ member of the two phonon triplet in ${}_{}{}^{62}{}_{}{}^{}\mathrm{Zn}$ at 2.33 MeV. A comparison between the states populated in these two reactions is made. Standard distorted-wave calculations give reasonable agreement with the data. However, $3^{-}$ and $4^{+}$ states cannot be unambiguously distinguished.

NUCLEAR REACTIONS ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}\mathrm{}(p,t)\mathrm{}{}_{}{}^{62}{}_{}{}^{}\mathrm{Zn}$, $E=35\mathrm{}$ MeV, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}\mathrm{}(p,t)\mathrm{}{}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$, $E=35\mathrm{}$ MeV; measured $\sigma (E_t,\theta )$; ${}_{}{}^{62}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$, deduced levels, $J$, $\pi$.

We describe a method for the calculation of the leading term of a previously proposed low-density expansion for the self-energy of nucleons in nuclear matter. We compute the single-particle complex potential energy, the average binding energy per nucleon, the complex symmetry potential, and the symmetry energy. We use Reid's hard core nucleon-nucleon interaction and take a Fermi momentum $k_F=1.4\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$. The calculated single-particle potential energy is compared with the phenomenological values of the optical-model potential in the inner region of a nucleus. The real part of our theoretical value is given by $56-0.3E$ (MeV) below $E=150\mathrm{}$ MeV, and changes sign at 200 MeV. The imaginary part rises from 2 MeV at low energy to about 20 MeV at $E=200\mathrm{}$ MeV. These features are in good agreement with experimental evidence. The average binding energy $B$ per nucleon calculated with a self-consistent potential energy for the particle states above $k_F$ is equal to -11 MeV. In the standard approach, with no potential energy for intermediate particle states above $k_F$, one finds -8.65 MeV. We also calculate the symmetry potential. At low energy, its real part is equal to $14 \frac{(N-Z)}{A}$ (MeV); it changes sign at 110 MeV. Its imaginary part is equal to $3.5\frac{(N-Z)}{A}$ (MeV) at low energy, and rises to $8.5\frac{(N-Z)}{A}$ (MeV) at 200 MeV. The symmetry energy is equal to 27.8 MeV.

NUCLEAR REACTIONS Calculated complex optical-model potential, symmetry potential, average binding energy and symmetry energy for nucleons in nuclear matter, for a Fermi momentum equal to 1.4 ${\mathrm{fm}}^{-1\mathrm{}}$, from Reid's hard core nucleon-nucleon interaction, in the frame of Brueckner's theory.

The fission-neutron multiplicity $\overline{\nu }$ and the total prompt $\gamma$-ray energy have been studied for the resolved resonances in ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ between 10 and 170 eV. There was a weak correlation found between $\overline{\nu }$ and the spin of the resonances. There was a significant correlation between the total $\gamma$-ray energy and the spin of the resonance. These correlations can be explained by competition of the ($n,\gamma f$) reaction with the ($n,f$) reaction in the $J=1\mathrm{}$ resonances which have a narrow fission width.

NUCLEAR REACTIONS neutrons per fission and total prompt $\gamma$ energy from ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ resonance fission, $E_n=10\mathrm{}-170$ eV. Correlation with ${\Gamma }_f$ due to ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}(n,\gamma f)$.

The decay properties of the levels in ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ up to 1720.12 keV have been carefully investigated via the ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}(p,n\gamma ){}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ reaction at 7.3 MeV, using a Ge(Li)-NaI(Tl) anti-Compton spectrometer. Three new weak transitions from well established levels were observed. Using the Doppler-shift attenuation method the values of ${0.48}_{-0.15\mathrm{}}^{+0.32\mathrm{}}$, ≥ 1.1, ${0.11}_{-0.02\mathrm{}}^{+0.03\mathrm{}}$, ${0.63}_{-0.18\mathrm{}}^{+0.36\mathrm{}}$, ${0.35}_{-0.03\mathrm{}}^{+0.05\mathrm{}}$, ≥ 0.6, and ${0.49}_{-0.17\mathrm{}}^{+0.51\mathrm{}}$ psec were obtained for the lifetimes of the 576.47-, 829.60-, 970.25-, 1009.11-, 1114.48-, 1450.62-, and 1720.12-keV levels, respectively. The value of the stopping power of Ni, previously calibrated for Cu ions, was used for the stopping of Co ions in Fe in order to extract the lifetimes from the measured centroid shifts obtained in singles experiments. Limits for the $B\left(E2\mathrm{}\right)\mathrm{}$ and $B\left(M1\mathrm{}\right)\mathrm{}$ values of many transitions were deduced from the present lifetimes and branching ratios using previously reported limits for the multipole mixing ratios $\delta \left(\frac{E2\mathrm{}}{M1\mathrm{}}\right)$. The results are compared with recent shell model calculations and good agreement is observed.

NUCLEAR REACTIONS ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}(p,n\gamma )$, $E_p=7.3\mathrm{}$ MeV, enriched targets; measured $E_{\gamma }$, $I_{\gamma }$, $I_{\gamma }\left(\theta \right)$, $\Delta E_{\gamma }\left(\tau \right)$; confirmed ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ levels; deduced branching ratios, $\tau$, $B\left(E2\mathrm{}\right)\mathrm{}$ and $B\left(M1\mathrm{}\right)\mathrm{}$ values.

In order to study the core polarization effects in medium heavy spherical nuclei the mean lives and $g$ factors of the ${11/2}^{-}$ states in ${}_{}{}^{111}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{113}{}_{}{}^{}\mathrm{Sn}$ have been measured. The isomeric states were populated by the ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}(\alpha ,2n){}_{}{}^{113}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{107,109}{}_{}{}^{}\mathrm{Ag}({}_{}{}^7{}_{}{}^{}\mathrm{Li},3n){}_{}{}^{111,113}{}_{}{}^{}\mathrm{Sn}$ reactions with pulsed $\alpha$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ beams. The nuclear spin precession in the 60 kG field of an on-line superconducting magnet was observed time differentially. The following values were obtained: ${}_{}{}^{111}{}_{}{}^{}\mathrm{Sn}$ ${(11/2\mathrm{}}^{-}$, 979.6 keV): $\tau =13.3\mathrm{}\left(15\right)\mathrm{}$ ns, $g=-0.23\mathrm{}\left(2\right)\mathrm{}$; ${}_{}{}^{113}{}_{}{}^{}\mathrm{Sn}$ ${(11/2\mathrm{}}^{-}$, 740 keV): $\tau =118.5\mathrm{}\left(25\right)\mathrm{}$ ns, $g=-0.235\mathrm{}\left(4\right)\mathrm{}$. The magnetic moments of the ${11/2}^{-}$ states in ${}_{}{}^{111,113,115,119}{}_{}{}^{}\mathrm{Sn}$ and their near constancy as a function of mass number are reproduced by a first order $M1\mathrm{}$ core polarization calculation using pairing model wave functions, experimentally determined energy denominators, and occupancy parameters. The strong reduction of the $M2\mathrm{}$ rates for the $h_{\frac{11}{2}}\to g_{\frac{7}{2}}$ transition as compared to the single particle estimate shows the destructive effect of the spin-isospin $M2\mathrm{}$ core polarization.

NUCLEAR REACTIONS ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}(\alpha ,2n)$, ${}_{}{}^{107,109}{}_{}{}^{}\mathrm{Ag}({}_{}{}^7{}_{}{}^{}\mathrm{Li},3n)$, $E_{\alpha }=21\mathrm{}$ MeV, $E_{\mathrm{Li}}=30\mathrm{}$ MeV; measured $\tau$ and $\mu$ (${\frac{11}{2}}^{-}$ states in ${}_{}{}^{111,113}{}_{}{}^{}\mathrm{Sn}$). Isotopic and natural metal targets.

The ($d,\alpha$) reactions on ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ have been studied using the 80 MeV incident deuteron beam of the Orsay synchrocyclotron. It was found that satisfactory distorted wave Born approximation fits can be obtained. The experimental angular distributions were structured and thus provide minimal ambiguity in the determination of the angular momentum transfer. The angular momentum matching conditions greatly favored large values for the angular momentum transfer. Together with the selectivity of the ($d,\alpha$) reactions, it allowed the identification of $7^{+}$ states in ${}_{}{}^{38,42,46}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$. The observation of $7^{+}$ levels in ${}_{}{}^{38,42,46}{}_{}{}^{}\mathrm{K}$ gives a measure of the $f_{\frac{7}{2}}$ proton occupation number in the ground state of the target nuclei ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}$. An apparent enhancement of certain of the $3^{+}$ states at high excitation energy was observed in ${}_{}{}^{46}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ and the relative $3^{+}$, $7^{+}$ separation was in qualitative agreement with a simple shell-model picture.

NUCLEAR REACTIONS ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}(d,\alpha )$ and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}(d,\alpha )$, $E=80.2\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; enriched targets, microscopic DWBA analysis, deduced $J$, $\pi$, $S$.

A ${100-\mathrm{\mu }\mathrm{g}/\mathrm{c}\mathrm{m}}^2$ thick ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ target was bombarded with 72.2-MeV ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ ions accelerated in the Oak Ridge isochronous cyclotron. Reaction products were detected at the focal plane of an Elbek spectrograph using a 60-cm long position-sensitive proportional counter. In addition to determining the position of the detected particle along the focal plane, the energy loss in the counter helped to identify the particle type. Angular distributions were measured for all four possible single-nucleon transfer reaction products, i.e., ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$. These reactions were found to excite single-particle or single-hole states in the heavy residual nuclei, though some groups corresponding to the light ions being left in excited states were also identified. A finite-range distorted-wave Born-approximation analysis including exactly the effects due to recoil was made of these differential cross sections with particular attention being paid to various uncertainties. The major uncertainties arise from the choice of potentials (especially in the exit channels) and of form factors for the bound nucleon before and after transfer. Except for the (${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$) reactions, which suffer from an unfavorable matching between incoming and outgoing orbits, the predicted angular distributions were in good agreement with the data, with extracted spectroscopic factors close to expected values and to those obtained in other light- and heavy-ion experiments. The indication then is that these reactions are predominantly one-step processes, though there is some evidence of the need for other effects to be considered.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$), ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$), ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$), ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$), $E_L=72.2\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; optical model and DWBA analyses; deduced spectroscopic factors. Enriched target.