The electric-dipole radiative capture reaction of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ by $\alpha$, leading to the ground and first excited states of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$, is considered. The wave functions used are the result of a single-channel ${}_{}{}^3{}_{}{}^{}\mathrm{He}+\alpha$ resonating-group calculation which yields not only correct ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ separation energies in both of these ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ bound states, but also a satisfactory description of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}+\alpha$ scattering angular distributions in the low-energy region. As in our previous ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ charge-form-factor study, the present investigation is entirely microscopic and has the following important characteristics: (i) totally antisymmetric wave functions are used, (ii) the c.m. motion is correctly accounted for, (iii) bound-state and continuum wave functions are obtained in a unified manner, and (iv) the wave functions used have correct asymptotic behavior. With no adjustable parameters, it is found that quite reasonable agreement with experiment can be obtained. In particular, the behavior of the branching ratio is satisfactorily reproduced. The only discrepancy is that the calculated total capture cross section is about 20-30% too large, which is very likely related to the fact that, for simplicity, only the dominant ${}_{}{}^3{}_{}{}^{}\mathrm{He}+\alpha$ cluster configuration has been included in the calculation.

[NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\alpha ,\gamma )$, $E=0.1\mathrm{}-4.0$ MeV; calculated capture cross section and branching ratio with resonating-group wave functions.]

We use the formalism of hyperspherical harmonics to calculate several moments for the triton photoeffect, for a Volkov spin-independent potential. First, we improve the accuracy of Maleki's calculations of the moments ${\sigma }_2$ and ${\sigma }_3$ by including more terms in the hyperspherical expansion. We also calculate moments ${\sigma }_0$ and ${\sigma }_1$ for a Serber mixture. We find reasonable agreement between our moments found by sum rules and those found from the cross sections calculated by Fang et al. and Levinger-Fitzgibbon. We then develop a technique of inversion of a finite number of moments by making the assumption that the cross section can be written as a sum of several Laguerre polynomials multiplied by a decreasing exponential. We test our inversion technique successfully on several model potentials. We then modify it and apply it to the five moments (${\sigma }_{-1\mathrm{}} \mathrm{to} {\sigma }_3$) for a force without exchange, and find fair agreement with Fang's values of the cross section. Finally, we apply the inversion technique to our three moments (${\sigma }_{-1\mathrm{}},{\sigma }_0,\mathrm{and} {\sigma }_1$) for a Serber mixture, and find reasonable agreement with Gorbunov's measurements of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ photoeffect.

NUCLEAR REACTIONS Triton photoeffects, hyperspherical harmonics, moments of photoeffect, inversion of moments.

Using the realistic $\mathrm{NN}$ interaction we study the influence of the axial meson exchange current effects on the cross sections and spectra in the weak neutral and charged disintegration of deuterons. In the hard pion approach we estimate these effects to be ≅8%. We suggest that an accurate experimental study of the problem may reveal the existence of the axial meson exchange current effects and the isobar configurations in nuclear physics.

NUCLEAR REACTIONS $d({\overline{\nu }}_e,{\nu }_e^{\prime })np$, (${\overline{\nu }}_e,e$), reactor antineutrinos. Calculated cross sections and spectra. Hard pion approach to exchange currents.

High resolution neutron total cross-section measurements on the separated isotope ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ have been made in energy range of few eV to about 370 keV using a pulsed neutron time-of-flight technique with a nominal resolution of 0.07 ns/m. We have analyzed the cross section data up to 370 keV using a multilevel multichannel computer code and obtained values of the resonance parameters ($E_0,J^{\pi },g{\Gamma }_n$). From these results we obtain the following values for the average properties of the resonance parameters: ${〈D〉}_{l=0\mathrm{}}=(3.59\mathrm{}\pm 0.16)$ keV, $S_0(\times {10}^4)=1.89\mathrm{}\pm 0.26$, and $S_1(\times {10}^4)=0.59\mathrm{}\pm 0.06$. We have also investigated the neutron width and nearest neighbor spacing distributions for 103 $s$-wave resonances up to 370 keV. The neutron width distribution follows a chi-squared distribution with $\nu =1.15\mathrm{}\pm 0.30$. We have determined values for Dyson-Mehta's ${\Delta }_3$ statistic for $s$-wave levels up to 300 keV as a function of energy. These are found to be in excellent agreement with the predicted values as explained in Table V. Similarly the linear coefficient of correlation between nearest neighbor spacings gives a value of $\rho =-0.35\mathrm{}$ in agreement with the predicted value of the random matrix model. The value for the mean $p$-wave level spacing is larger than expected from the ($2J+1$) density law, indicative of missed $p$-wave levels.

NUCLEAR REACTIONS ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}\mathrm{}(n,n)\mathrm{}$, $E=\mathrm{few}$ eV to ∼370 keV. Measured ${\sigma }_t$ vs $E_n$, deduced resonance parameters. Resonance energies $E_{\lambda }$, $J^{\pi }$, ${\Gamma }_n^0$, ${\Gamma }_n^1$, $S_0$, $S_1$, ${〈D〉}_{l=0\mathrm{}}$, ${〈D〉}_{l=1\mathrm{}}$.

Total neutron capture cross section measurements of the separated isotope of ${}_{30}{}^{64}{}_{}{}^{}\mathrm{Zn}$ have been made in the energy interval of 2.5-900 keV. These were made using time-of-flight techniques and a total energy $\gamma$-ray detector system with a nominal resolution of about 0.12 ns/m. Resonance energies and capture areas were determined for 191 resonances up to 131 keV. Values of the radiation widths and neutron widths for many resonances have been determined making use of the results available from transmission measurements. From these results mean values of $〈{\Gamma }_{\gamma }〉=(726\mathrm{}\pm 60)$ meV for $s$-wave and $〈{\Gamma }_{\gamma }〉=(272\mathrm{}\pm 30)$ meV for $p$-wave resonances have been determined. A value for the $p$-wave strength functions $S_1=(0.75\mathrm{}\pm 0.08)\times {10}^{-4\mathrm{}}$ ${\mathrm{eV}}^{-1/2\mathrm{}}$ was obtained for neutron energy up to 130 keV. Bayes' theorem for conditional probability was used to identify $d$-wave levels and from these resonances a lower limiting value for $d$-wave strength function $S_2=(0.78\mathrm{}\pm 0.12)\times {10}^{-4\mathrm{}}$ ${\mathrm{eV}}^{-1/2\mathrm{}}$ was obtained. The values for the $p$-wave mean level spacing for all resonances observed up to 130 keV, and after elimination of $d$-wave resonances, were found to be (0.68±0.04) and (1.10±0.07) keV, respectively. An analysis of the linear correlation coefficient ($\rho$) between ${\Gamma }_n^0$ and ${\Gamma }_{\gamma }$ gave a value of (0.47±0.08) at a confidence level of 99.7%.

NUCLEAR REACTIONS ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}(n,\gamma ){}_{}{}^{65}{}_{}{}^{}\mathrm{Zn}$, $E=2.5\mathrm{}-900$ keV; measured ${\sigma }_{n,\gamma }\mathrm{}\left(E\right)\mathrm{}$, deduced resonance parameters; $E_0$, $\frac{g{\Gamma }_n{\Gamma }_{\gamma }}{\Gamma }$, ${\Gamma }_n$, $\left({\Gamma }_{\gamma }\right)l$, $S_l$, ${〈D〉}_{l=1\mathrm{}}$, $\rho ({\Gamma }_n^0,{\Gamma }_{\gamma })$.

An experimental study on the nuclear excitation process of ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ by positron annihilation has been made. After irradiation of a natural lutecium foil by positrons from ${}_{}{}^{64}{}_{}{}^{}\mathrm{Cu}$, the 88.35-keV $\gamma$ rays from ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}_{}^m{}_{}{}^{}$ were observed by the Ge(Li) detector. The cross section of the annihilation-excitation process has been evaluated to be (9.0 ± 3.2) × ${10}^{-22\mathrm{}}$ ${\mathrm{cm}}^2$. The result is compared with the theoretical value in the two-step model and possible reasons for the discrepancy between theory and experiment are discussed.

NUCLEAR REACTIONS ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$; evaluated excitation cross section by positron annihilation with $K$-shell electrons.

Charged-particle emission cross sections, spectra, and angular distributions have been measured for targets of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, and ${}_{}{}^{92,94,95,96}{}_{}{}^{}\mathrm{Mo}$ bombarded with 14.8-MeV neutrons. A magnetic quadrupole spectrometer served to detect the charged particles. Evidence for both statistical and pre-equilibrium reaction mechanisms was found in the proton, deuteron, and alpha-particle emission. The cross sections and spectra are compared with calculations based on these reaction models.

NUCLEAR REACTIONS ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{92,94,95,96}{}_{}{}^{}\mathrm{Mo}$. ($n,p$), ($n,d$), ($n,\alpha$), $E=14.8\mathrm{}$ MeV; measured $\sigma (E_p,\theta )$, $\sigma (E_d,\theta )$, $\sigma (E_{\alpha },\theta )$, enriched targets. Hauser-Feshbach and hybrid pre-equilibrium analysis, deduced reaction mechanisms.

High-spin states have been populated in ${}_{}{}^{102}{}_{}{}^{}\mathrm{Pd}$ by ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}({}_{}{}^{13}{}_{}{}^{}\mathrm{C},3n\gamma ){}_{}{}^{102}{}_{}{}^{}\mathrm{Pd}$ with $E_{\mathrm{lab}}=56\mathrm{}$ MeV and in ${}_{}{}^{100}{}_{}{}^{}\mathrm{Pd}$ by ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},3n\gamma ){}_{}{}^{100}{}_{}{}^{}\mathrm{Pd}$ with $E_{\mathrm{lab}}=63\mathrm{}$ MeV. We find in each nuclide a ground state band $\Delta J=2\mathrm{}$ of positive parity extending to $J^{\pi }={14}^{+}$, as well as two negative parity bands $\Delta J=2\mathrm{}$, one of odd spin and one of even spin. For ${}_{}{}^{100}{}_{}{}^{}\mathrm{Pd}$, the present level scheme represents the first definitive study of excited states in this nuclide. For ${}_{}{}^{102}{}_{}{}^{}\mathrm{Pd}$ the present data include the first measurement of the $\gamma$-ray linear polarizations. The level energies are compared to the variable moment of inertia model, the interacting boson approximation model, and to the results of a quasiparticle calculation. NUCLEAR REACTIONS, NUCLEAR STRUCTURE ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}({}_{}{}^{13}{}_{}{}^{}\mathrm{C},3n\gamma ){}_{}{}^{102}{}_{}{}^{}\mathrm{Pd}$, $E=56\mathrm{}$ MeV, ${}_{}{}^{94}{}_{}{}^{}\mathrm{Zr}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},4n\gamma ){}_{}{}^{102}{}_{}{}^{}\mathrm{Pd}$, $E=69\mathrm{}$ MeV, ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},3n\gamma ){}_{}{}^{100}{}_{}{}^{}\mathrm{Pd}$, $E=56, 63$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \left(\theta \right)$, $\gamma \mathrm{}\left(t\right)\mathrm{}$, $\gamma \mathrm{}\left(E\right)\mathrm{}$, $\gamma -\gamma$ coin, linear polarizations. ${}_{}{}^{102,100}{}_{}{}^{}\mathrm{Pd}$ deduced levels, $\gamma$ branching, $J$, $\pi$, $\delta$, $t_{\frac{1}{2}}$ limits. Enriched ${}_{}{}^{91,92,94}{}_{}{}^{}\mathrm{Zr}$ targets, Ge(Li) detectors, Ge(Li) Compton polarimeter. Variable moment of inertia model, interacting boson approximation model, rotation alignment model.

Collective features of odd-$N$ ${}_{}{}^{117,119,121}{}_{}{}^{}\mathrm{Xe}$ have been investigated via ${}_{}{}^{106,110}{}_{}{}^{}\mathrm{Cd}({}_{}{}^{14}{}_{}{}^{}\mathrm{N},p2n){}_{}{}^{117,121}{}_{}{}^{}\mathrm{Xe}$ and ${}_{}{}^{106}{}_{}{}^{}\mathrm{Cd}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},2pn){}_{}{}^{119}{}_{}{}^{}\mathrm{Xe}$ reactions. In-beam $\gamma$-ray excitation, $\gamma -\gamma$ coincidence, and $\gamma -W\left(\theta \right)$ measurements were performed to establish decay schemes, $\gamma$-ray multipolarities, and $J^{\pi }$ assignments. Strong $\Delta J=2\mathrm{}$ band structures, associated with the $1h_{\frac{1}{2}}$ quasi-neutron band, were observed on ${11/2}^{-}$ states in the ${}_{}{}^{117,119,121}{}_{}{}^{}\mathrm{Xe}$ nuclei. The unfavored $\Delta J=2\mathrm{}$ sidebands, which crossover in energy at the $N=64\mathrm{}$ subshell (${}_{}{}^{119}{}_{}{}^{}\mathrm{Xe}$ core), were weakly observed down to the ${9/2}^{-}$ member in all three nuclei. Systematics of these $1h_{\frac{1}{2}}$ band structures in odd-Xe nuclei are presented and discussed in terms of the current theoretical models. A second collective feature, a $\Delta J=1\mathrm{}$ band structure built on $1g_{\frac{1}{2}}$ quasi-neutron-hole states, was observed in the ${}_{}{}^{119,121}{}_{}{}^{}\mathrm{Xe}$ nuclei.

NUCLEAR REACTIONS ${}_{}{}^{106,110}{}_{}{}^{}\mathrm{Cd}({}_{}{}^{14}{}_{}{}^{}\mathrm{N},p2n){}_{}{}^{117,121}{}_{}{}^{}\mathrm{Xe}$, ${}_{}{}^{106}{}_{}{}^{}\mathrm{Cd}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},2pn){}_{}{}^{119}{}_{}{}^{}\mathrm{Xe}$, measured $\gamma -\gamma$ coincidences, $\gamma (E,\theta )$; ${}_{}{}^{117,119,121}{}_{}{}^{}\mathrm{Xe}$ deduced levels, $\gamma$ multipolarities, $J^{\pi }$. Enriched targets, Ge(Li) detectors.

NUCLEAR STRUCTURE Odd-$N$ ${}_{}{}^{117,119,121}{}_{}{}^{}\mathrm{Xe}$, calculated ${\frac{11}{2}}^{-}\Delta J=2\mathrm{}$ rotational bands.

The reaction ${}_{}{}^{50}{}_{}{}^{}\mathrm{Cr}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^{51}{}_{}{}^{}\mathrm{Mn}$ was investigated at extreme forward angles, $1.6°\le \theta \le 12°$, in order to study the $j$ dependence for the (${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,${}_{}{}^6{}_{}{}^{}\mathrm{He}$) reaction at 28 MeV. The ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ ejectiles were detected with a position-sensitive (helix) counter in the focal plane of an Enge-split-pole spectrograph. A total energy resolution of about 30 keV was obtained. The angular distributions for seven low-lying states in ${}_{}{}^{51}{}_{}{}^{}\mathrm{Mn}$ show a pronounced $j$ dependence for angles below 7° and the expected $l$ dependence at angles $\theta \ge 9°$. Finite-range distorted-wave Born approximation calculations which include recoil effects reproduce the $j$-dependent angular distributions very well and permit a clear distinction between $p_{\frac{3}{2}}$, $p_{\frac{1}{2}}$, $f_{\frac{7}{2}}$, and $f_{\frac{5}{2}}$ final state angular momenta. The relative spectroscopic factors deduced were in reasonable agreement with those obtained in a recent ${}_{}{}^{50}{}_{}{}^{}\mathrm{Cr}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{51}{}_{}{}^{}\mathrm{Mn}$ reaction study.

NUCLEAR REACTIONS ${}_{}{}^{50}{}_{}{}^{}\mathrm{Cr}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^{51}{}_{}{}^{}\mathrm{Mn}$, $E_{\mathrm{Li}}$ MeV; measured $E_{{}_{}{}^6{}_{}{}^{}\mathrm{He}}$ and $\sigma (\theta ,E_{{}_{}{}^6{}_{}{}^{}\mathrm{He}})$ in split pole spectrograph with 30 keV resolution. Finite-range-DWBA analysis, deduced $j_{\mathrm{transfer}}$, spectroscopic factors.

States of ${}_{}{}^{200}{}_{}{}^{}\mathrm{Tl}$, populated through the ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}({}_{}{}^6{}_{}{}^{}\mathrm{Li},4n)$ reaction at $E=30\mathrm{} \mathrm{to} 40$ MeV, were studied using in-beam $\gamma$-ray spectroscopy techniques. An almost completely new level scheme is presented comprising the $\tilde{\pi }{h}_{\frac{9}{2}}\otimes \tilde{\nu }{i}_{\frac{13}{2}}$ two-quasiparticle band which in this case is built on an $I^{\pi }=7^{-}$ isomeric state ($T_{\frac{1}{2}}=4.8\mathrm{}\pm 0.2$ ns) in contrast to $I^{\pi }=8^{-}$ for all the lighter doubly odd Tl isotopes studied up to now. The systematic variation of the odd-even staggering present in these bands offers arguments to support the interpretation that this phenomenon is related to the signature dependence of the Coriolis interaction.

NUCLEAR REACTIONS ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}({}_{}{}^6{}_{}{}^{}\mathrm{Li},4n)$, $E=30\mathrm{}-40$ MeV, measured $E_{\gamma }$, $I_{\gamma }$, $\sigma (E_{{}_{}{}^6{}_{}{}^{}\mathrm{Li}},E_{\gamma },{\theta }_{\gamma })\gamma -\gamma$ coin. ${}_{}{}^{200}{}_{}{}^{}\mathrm{Tl}$ deduced levels, $J$, $\pi$, $T_{\frac{1}{2}}°$. Ge(Li) detectors, enriched target.

A phase-shift analysis of the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) elastic scattering angular distributions measured between 0 and 180° c.m. shows that the backward rise of the angular distributions is due to small statistical fluctuations of the scattering matrix elements.

NUCLEAR REACTIONS Phase-shift analysis of heavy ion elastic scattering. Statistical fluctuations of the scattering matrix.

We use a classical dynamical theory with shape degrees of freedom to describe deep inelastic scattering of heavy ions, and include thermal fluctuations by means of the Fokker-Planck equation. The degrees of freedom allow for neck formation, mass transfer, and stretching of the two-nucleus system. Inertias are calculated for these degrees of freedom, and dissipative and conservative forces are used. Fluctuations are calculated by considering the second moments of the distribution and determining a temperature from the excitation energy at each time. We calculate distributions in final energy, angle, charge, and mass, including some double differential cross sections. Results are in good agreement with data.

NUCLEAR REACTIONS Classical dynamical model, shape degrees of freedom, Fokker-Planck equation, thermal fluctuations; angular, energy, mass, and charge distributions are calculated for the reactions ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ + ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ + ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$, and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ + ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$.

Coincidence measurement was made in the reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},{}_{}{}^{16}{}_{}{}^{}\mathrm{O}\alpha )$ at 260 MeV incident energy, and the experimental results were analyzed in terms of the projectile breakup scheme. The reaction can be conveniently classified into the elastic- and inelastic-breakup processes. Comparison of the present results to those of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$-singles measurement indicates the importance of the process in which the breakup is followed by the fusion process. Theoretical analysis shows that the main aspects of the present experimental results are explained.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},{}_{}{}^{16}{}_{}{}^{}\mathrm{O}\alpha )$ $E=260\mathrm{}$ MeV measured coincidence energy and angular correlations. Deduce reaction mechanisms. Calculations of elastic breakup and breakup-fusion processes.

The real part of the optical potential for heavy ion elastic scattering is obtained by double folding of the nuclear densities with a density-dependent nucleon-nucleon effective interaction which was successful in describing the binding, size, and nucleon separation energies in spherical nuclei. A simple analytical form is found to differ from the resulting potential considerably less than 1% all through the important region. This analytical potential is used so that only few points of the folding need to be computed. With an imaginary part of the Woods-Saxon type, this potential predicts the elastic scattering angular distribution in very good agreement with experimental data, and little renormalization (unity in most cases) is needed.

NUCLEAR REACTIONS Optical model for nucleus-nucleus, double folding model, nucleon-nucleon effective interaction.

We present a simple, exact numerical method of obtaining the complex, $l$-dependent potentials $\Delta U_l\mathrm{}\left(r\right)\mathrm{}$ induced in the elastic channel by coupling to inelastic channels. For ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ at 72 MeV, we consider pure Coulomb coupling and find that a simple power law absorption or the imaginary $l$-dependent polarization potentials of Baltz et al. gives good agreement with coupled channel cross sections out to 100°. For larger angles a more accurate representation of the polarization potentials for the low partial waves is required, both real and imaginary parts being significant. We also examine the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ system at 68 MeV including a number of excited levels in both projectile and target. Here, nuclear coupling is dominant. The strength of the imaginary part of $\Delta U_l$ is found to vary quadratically with deformation length and inversely with excitation energy for excitations above about 5 MeV. The states above 8 MeV lead to a real potential of strength comparable to the imaginary in the surface region. The effect on the cross sections is discussed.

NUCLEAR REACTIONS ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\prime$), $E=72\mathrm{}$ MeV; ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}\prime$), $E=68\mathrm{}$ MeV; coupled channel analysis; deduced effective elastic optical potential.

The possibility of using secondary reactions as a tool to produce new isotopes is considered. This question is renewed with the emergence of intense beams of energetic heavy ions in the range of 20 to 100 MeV/nucleon. Three different methods are considered. They involve either the in situ production of a secondary radioactive target, which interacts with the primary beam, or the production of a radioactive secondary beam by an inverse fusion or a fragmentation process. Very heavy or very neutron deficient isotopes can be produced by these methods.

NUCLEAR REACTIONS Investigation of possibilities for new isotope production in secondary reactions.

A theoretical study documenting the probing sensitivity of the $K^{+}$ meson to the neutron distribution is reported for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ isotopes. Combining Hartee-Fock and phenomenological neutron densities with two independent empirical sets of kaon-nucleon amplitudes, different first-order microscopic kaon-nucleus optical potentials are constructed and compared. The sensitivity of predicted elastic cross sections to choice in potential is found to be significant and is dominated by the uncertainty in the $K^{+}$-neutron interaction. For relative cross section differences between Ca isotopes, however, the sensitivity to the neutron distribution is roughly comparable to the uncertainty introduced by the $\mathrm{KN}$ interaction, suggesting that preliminary $K^{+}$-nucleus measurements may provide improved neutron information about isotopic density differences. Conditions and prescriptions for extracting such information are discussed.

NUCLEAR REACTIONS Kaon-nucleus elastic scattering. Calculated $\sigma (\theta ,E)$ for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$. First-order multiple scattering optical potential and impulse approximation. Hartree-Fock and empirical neutron densities. Neutron distribution sensitivity study.

A momentum space coupled-channel formalism is proposed for the study of pion-nucleus single-charge-exchange reactions at medium energies. Formal elimination of certain reaction channels leads to a reduced set of coupled equations with a complex and energy-dependent interaction. A nonperturbative method based upon unitarity considerations is then used to construct each order of this effective pion-nucleus interaction. Our analysis thus leads to a second-order pion-nucleus interaction with analytical properties very different from those obtained from multiple-scattering theory. The theory is applied to the study of pion-${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ elastic scattering and the single-charge-exchange reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({\pi }^{+},{\pi }^0){}_{}{}^{13}{}_{}{}^{}\mathrm{N}(\mathrm{g}.\mathrm{s})$. Included in our calculations are the first- and second-order pion-nucleus strong interactions, and the pion-nucleus Coulomb interaction. We have calculated the first-order interaction using a covariant, nonstatic theory and have evaluated contributions to the second-order interaction arising from two-nucleon processes related to true pion absorption and to the scattering of pions from a nucleon pair. We present a general relation connecting the second-order pion-nucleus strong interaction potentials of nuclei whose structure do not differ appreciably. Theoretical results for $\pi {}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ elastic scattering predicted by our theory are found to be in good agreement with the data. The calculated excitation function of the single-charge-exchange reaction exhibits a high sensitivity to the type of two-nucleon processes considered. Pion-nucleus single-charge-exchange reactions therefore have promise as a tool for investigating pion-nucleus reaction mechanisms.

NUCLEAR REACTIONS Coupled-channel theory, pion-nucleus single-charge-exchange reactions, pion absorption, nucleon-nucleon correlations, $\pi {}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ elastic cross sections at 50 and 180 MeV, excitation function of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({\pi }^{+},{\pi }^0){}_{}{}^{13}{}_{}{}^{}\mathrm{N}(\mathrm{g}.\mathrm{s})$ between 30 and 260 MeV.

New and/or corrected 800 MeV $p+{}_{}{}^{40,42,44,48}{}_{}{}^{}\mathrm{Ca}$ elastic angular distributions are presented. The data, together with analyzing power measurements, are analyzed to investigate the isotopic neutron and matter density differences between these four calcium isotopes. The analysis employs a local, spin-dependent form of the second order Kerman, McManus, and Thaler optical potential in which approximately model-independent forms for the neutron densities are assumed. Nucleon-nucleon amplitude uncertainties which occur at 800 MeV are taken into account in determining the empirical isotopic density differences. The deduced neutron and matter density differences are compared to the results of other intermediate energy proton and alpha particle scattering analyses and to Hartree-Fock predictions. The various empirical results are generally in good agreement with each other and with the Hartree-Fock predictions, except for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ where the results obtained here and elsewhere suggest that the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ neutron excess is not distributed at quite as large a radius as predicted by Hartree-Fock theory.

NUCLEAR REACTIONS Proton elastic scattering cross sections; targets, ${}_{}{}^{40,42,44,48}{}_{}{}^{}\mathrm{Ca}$; $E_{\mathrm{lab}}=800\mathrm{}$ MeV; second order Kerman, McManus, and Thaler optical potential; neutron and matter isotopic density differences.