It is argued that Coulomb corrections to the $K^{-}p$ scattering length may affect the latter significantly and reduce the strong-interaction effects in kaonic hydrogen to below the observable level.

NUCLEAR REACTIONS kaon-baryon interactions.

The giant-resonance region of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ was studied using $\alpha$ beams of energies between 100 and 172 MeV. Relative to the excitation of the giant quadrupole resonance located at $E_x=10.9\mathrm{}$ MeV the new resonance at $E_x=13.8\mathrm{}$ MeV was found to be more strongly excited at higher incident energies. This yields a new piece of evidence for the monopole character of this new resonance.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$($\alpha$,${\alpha }^{\prime }$), $E_{\alpha }=100-172\mathrm{}$ MeV. Measured $\sigma (\ominus ,E)$ for giant-resonance excitations. Calculated cross section for $L=0\mathrm{}$ and $L=2\mathrm{}$. Deduced $E0\mathrm{}$ strength from energy dependence.

The total cross sections relative to photoproduction off the proton have been measured for the reactions ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($\gamma$,${\pi }^{+}$)${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$($\gamma$,${\pi }^{+}$)${}_{}{}^9{}_{}{}^{}\mathrm{Li}$ over the energy region from the production threshold up to 12 MeV over threshold. A distorted wave impulse approximation calculation has been performed for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($\gamma$,${\pi }^{+}$)${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ reaction and is seen to be ≃ 30% higher than the observed cross section from threshold to 10 MeV. The ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$($\gamma$,${\pi }^{+}$)${}_{}{}^9{}_{}{}^{}\mathrm{Li}$ reaction represents the first ($\gamma$,${\pi }^{+}$) measurement near threshold in which the cross section is not dominated by the $\overrightarrow{\sigma }·\overrightarrow{\epsilon }$ term in the production Hamiltonian.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($\gamma$,${\pi }^{+}$)${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$($\gamma$,${\pi }^{+}$)${}_{}{}^9{}_{}{}^{}\mathrm{Li}$, bremsstrahlung end point energies to 175 MeV, measured $\sigma \mathrm{}\left(E\right)\mathrm{}$; calculated $\sigma \mathrm{}\left(E\right)\mathrm{}$, DWIA.

In a collision between relativistic heavy ions the projectile (target) nucleons encounter an effective number of target (projectile) nucleons. We calculate these numbers by allowing the nucleons to move on bent trajectories. A comparison is made with the result obtained from the usual straight-line (eikonal) assumption. The implications for one-nucleon inclusive spectra are discussed.

NUCLEAR REACTIONS Relativistic heavy ions, effective nucleon numbers, calculated from Fresnel multiple scattering theory.

The binding energy of a $\Lambda$ particle in nuclear matter $B_{\Lambda }$ is calculated with the models $D$ and $F$ of the NIjmegen baryon-baryon interaction. The result $B_{\Lambda }=30.6\mathrm{}$ MeV obtained for model $F$ agrees with semiempirical value of $B_{\Lambda }$. and shows that suppression of $\Lambda \Sigma$ conversion in nuclear matter solves the hypernuclear overbinding problem.

NUCLEAR STRUCTURE Binding energy of $\Lambda$ particle in nuclear matter, $\Lambda N$ interaction with $\Lambda \Sigma$ coupling.

General expression are derived for all possible even and odd order tensor orientations of recoil nuclei, recoiling into the forward (or backward) hemisphere in the reaction ${\mu }^{-}+A(J_i=0)\to B(J_f\ge 1)+{\nu }_{\mu }$. Numerical results are presented for the case of muon capture by ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$.

NUCLEAR REACTIONS Muon capture, recoil nucleus, orientations, all orders.

High spin states in ${}_{}{}^{178}{}_{}{}^{}\mathrm{W}$ have been studied using the ${}_{}{}^{170}{}_{}{}^{}\mathrm{Er}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$4n$) reaction and $\gamma$-ray techniques. The yrast band in ${}_{}{}^{178}{}_{}{}^{}\mathrm{W}$ has been identified to spin 18. At this spin the moment of inertia curve shows backbending. The systematics of backbending in the tungsten isotopes is discussed.

NUCLEAR REACTION ${}_{}{}^{170}{}_{}{}^{}\mathrm{Er}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$4n$), $E=66\mathrm{}$ MeV; measured $\gamma -\gamma$ coinc. $E_{\gamma }\gamma \left(\theta \right)$: ${}_{}{}^{178}{}_{}{}^{}\mathrm{W}$ deduced yrast levels; backbending systematics.

${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ elastic scattering angular distributions have been measured between $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.50\mathrm{} \mathrm{and} 7.05$ MeV at intervals of 0.05 MeV. Resonances were observed in these yields at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.64\mathrm{} \mathrm{and} 6.83$ MeV. A phase shift analysis of these data was carried out which resulted in assignments of $J^{\pi }=2^{+}$ ($E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.64\mathrm{}$ MeV) and $J^{\pi }=4^{+}$ ($E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.83\mathrm{}$ MeV) for the resonances. Carbon partial widths were determined by parametrizing the deduced phase shifts in terms of isolated Breit-Wigner resonances. The results, ${\Gamma }_c={29}_{-9\mathrm{}}^{+6\mathrm{}}$ keV at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.64\mathrm{}$ MeV and ${\Gamma }_c=11\mathrm{}\pm 3$ keV at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.83\mathrm{}$ MeV, demonstrate unambiguously the quasimolecular nature of the resonances.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, $E=13.0-14.1\mathrm{}$ MeV; measured $\sigma (E;\theta )$; kinematic coincidence. Deduced phase shift parameters; deduced spins and carbon widths for resonances.

We use fireball geometry and a statistical model to calculate charged particle associated multiplicity in relativistic heavy ion reactions. General expressions for multiplicity distributions based upon this model are derived. The constraints of charge and baryon number conservation are shown to lead to modified Poisson distributions. The expressions developed are applicable to all nonstrange particles and composites. Comparison is made with existing data.

NUCLEAR REACTIONS Relativistic heavy ion collisions; charge multiplicity; Fireball; statistical model.

Total fusion-evaporation cross sections for the systems ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ + ${}_{}{}^{16,18}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{\mathrm{nat}}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{16,18}{}_{}{}^{}\mathrm{O}$ have been measured in the energy range $34 \mathrm{MeV}\le E_{\mathrm{lab}}\le 81 \mathrm{MeV}$ by detecting the evaporation residues in a time-of-flight spectrometer. The fusion cross sections for all systems were found to saturate at 1150-1200 mb. Fusion barriers have been deduced with the parametrization of Glas and Mosel. The data have also been discussed in terms of the Bass model.

NUCLEAR REACTIONS ${}_{}{}^{16,18}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{16,18}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{\mathrm{nat}}{}_{}{}^{}\mathrm{Si}$; $E_{\mathrm{lab}}=34-81\mathrm{}$ MeV; measured ${\sigma }_{\mathrm{fusion}}$; deduced fusion barriers.

The traditional formulation of the exact-finite-range calculation is demonstrated to have a procedural flaw which impeded unnecessarily the computational time. A revised method is shown to be in principle significantly more efficient than currently existing approaches. When the exact calculation is applied to the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ reaction, the spin-orbit potential predictions are found to disagree with recently published norecoil approximation analyses.

NUCLEAR REACTION ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$, $E=60\mathrm{}$ MeV; calculated $\sigma \left(\theta \right)$; full recoil; exact-finite-range spin-orbit DWBA and CCBA.

${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ elastic scattering angular distributions have been measured at twenty-three bombarding energies over a range $19 \mathrm{MeV}\le E_{\mathrm{lab}}\le 48 \mathrm{MeV}$. At energies below 30 MeV the angular distributions are smooth and can be reproduced with a wide variety of optical potentials; similarly, above 40 MeV the angular distributions exhibit diffraction oscillations which optical potentials can rather easily reproduce. Irregular structure is observed in the cross sections for angles larger than 50° in the bombarding energy range 30-40 MeV. No optical potential has been found to give a good account of all the data; the best potential is a surface transparent Woods-Saxon potential which has energy dependences for both real and imaginary well depths. Examination of potentials which give reasonably good fits to the 36 MeV data shows that, although these potentials agree on a real well depth at a reasonable "strong absorption radius," they can have quite different Argand diagrams—even in the range of the most sensitive partial waves. A Regge analysis finds several equally good families of Regge parameters for the same choice of background potential, but larger angle data might allow this ambiguity to be lifted. A Breit-Wigner analysis gives results which are at least partially consistent with the resonance parameters reported by Ost et al. Coupled-channel calculations with a 20% reduction of real and imaginary optical model well depths give a good account of inelastic scattering to the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ $2^{+}$ state while leaving the elastic scattering essentially unchanged from the predictions of the unmodified one-channel optical model. In the energy range of this study the grazing partial wave is found to be the same as the most important exit channel partial wave of the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ ground state transition.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, measured $\sigma (E,\theta )$ $E=19-48\mathrm{}$ MeV deduced optical model parameters.

Fragment-energy and specific-luminescence spectra from the fission of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ were measured by a two-dimensional display of coincident signals from a solid state detector and a thin-film organic scintillator detector. Symmetric-to-asymmetric fission ratios and peak-to-valley ratios were determined as a function of bombarding energy. Discontinuities in the ratio curves, observed in some previous experiments but not in others, were mapped out in detail. The major discontinuities were found to occur near fission thresholds.

NUCLEAR REACTIONS: FISSION ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$($p$,$f$), ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$($p$,$f$), $E=9.5-17.0\mathrm{}$ MeV; measured $E$, specific luminescence spectra of single fragments; Si detector coin thin-film plastic scintillator detector; deduced symmetric-to-asymmetric mass ratio trends, competing reaction thresholds.

Photofission yield measurements on ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and${}_{}{}^{235,236,238}{}_{}{}^{}\mathrm{U}$, showing the "shelf effect," have been analyzed in terms of a double-humped fission barrier. From the characteristic of the shelf it was possible to evaluate the excitation energy $E_{\mathrm{II}}$ of the shape isomer. In the framework of the double-humped barrier, with the competition between $\gamma$ decay to the shape isomer and tunneling through the outer barrier of a compound state in the second well, it was possible to deduce fission branching ratios in agreement with those known in the literature. In particular for ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ a three-humped fission barrier is proposed, the second deep minimum causing the shelf effect and the third one the narrow resonances detected in this isotope.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{235,236,238}{}_{}{}^{}\mathrm{U}$ photofission yields measurements analyzed in the frame of a double-humped fission barrier model. Excitation energies and fission branching ratios for shape isomers deduced. A three-humped fission barrier proposed for ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$.

The elastic scattering of pions from finite nuclei is examined theoretically within the context of the impulse approximation to the optical potential for the relativistic Schrödinger and Klein-Gordon equations. The kinematical relationships between potentials and wave functions are specified by considerations similar to those discussed by Cammarata and Banerjee. We find: (1) At low energy ($T_{\pi }\lesssim 50$ MeV) there is a large difference between the solutions of the two equations. (2) At low energy there is a strong sensitivity to the range of the pion-nucleon interaction, the Klein-Gordon equation being dramatically sensitive. (3) Near the (3-3) resonance there are small differences between the solutions of the two equations and there is only a moderate sensitivity to the range of the interaction. The low energy results are explained in terms of the interaction of pions with nuclear matter. The resonance energy results are explained in simple geometric terms. The large differences between wave functions near the resonance region found by Siciliano and Thaler are not found if one uses the relationships proposed here, although we do find significant differences at lower energies.

NUCLEAR REACTIONS Compared relativistic Schrödinger (RSE) and Klein-Gordon equations (KGE) for pion scattering; KGE very sensitive to form factor at low energy; both moderately sensitive at (3-3) resonance energy; simple explanations of sensitivity proposed.

The possible existence of density isomers in nuclear matter, induced by pion condensation, is discussed; the nuclear equation of state is treated within the framework of the $\sigma$ model. Repulsive short-range baryon-baryon correlations, the admixture of $\Delta \mathrm{}\left(1232\right)\mathrm{}$ isobars and finite-range pion-baryon vertex form factors are taken into account. The strong dependence of density isomerism on the high density extrapolation of the equation of state for normal nuclear matter is also investigated. We find that, once finite range pion-baryon vertices are introduced, the appearance of density isomers becomes unlikely.

NUCLEAR STRUCTURE Nuclear matter, pion condensation, density isomers

Inclusive spectra for outgoing particles believed not to arise from a single-collision process are presented and analyzed as though a single-collision description, "quasi-two-body scaling," were applicable. The characteristic momentum of the momentary distribution $k_0$ is of order 60 MeV/c and is approximately $A$ independent. An alternative analysis in terms of nuclear temperature is made, suggesting a correlation between the value of $k_0$ and the nuclear temperature of a "hot spot."

NUCLEAR REACTIONS 90 MeV proton, 140 MeV alpha induced reactions. $p$, $d$, $t$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and alpha energy spectra interpreted by "quasi-two-body-scaling" and "hot spot"; deduced characteristic parameter.

The role of the inelastic pion channels of the nucleon-nucleon interaction at large momentum transfers is examined in view of recent experiments on nucleon transfer and pion production reactions. At energies below the pion production threshold the excitation functions of proton elastic back scattering from ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are characteristic of a simple nucleon exchange mechanism. The high energy region can be understood in terms of pion exchange contributions as expressed by triangle diagrams with the subprocesses $\mathrm{pp}\to {}_{}{}^2{}_{}{}^{}\mathrm{H}\pi$, $p{}_{}{}^2{}_{}{}^{}\mathrm{H}\to {}_{}{}^3{}_{}{}^{}\mathrm{H}\pi$, and $p{}_{}{}^3{}_{}{}^{}\mathrm{He}\to {}_{}{}^4{}_{}{}^{}\mathrm{He}\pi$, respectively. Similarly, "hidden" pion exchange effects are suggested as an explanation for the excitation functions of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$($p$,$d$)${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$($p$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^2{}_{}{}^{}\mathrm{H}$, invoking the proton backscattering reactions $p{}_{}{}^2{}_{}{}^{}\mathrm{H}\to {}_{}{}^2{}_{}{}^{}\mathrm{H}p$ and $p{}_{}{}^3{}_{}{}^{}\mathrm{He}\to {}_{}{}^3{}_{}{}^{}\mathrm{He}p$ as subprocesses.

NUCLEAR REACTIONS ($p$,$p$) backscattering from ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$($p$,$d$)${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$($p$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^2{}_{}{}^{}\mathrm{H}$ for $T_p\approx 100-700$ MeV; excitation functions of $\frac{d\sigma }{d\Omega }$ (${\theta }_0$,$T$) analyzed in terms of nucleon exchange and pion exchange supported reaction mechanisms.

Relative yields of 11 selected products (${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{43,44,46,47,48}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{55,56,57,58,60}{}_{}{}^{}\mathrm{Co}$) have been measured for the interaction of 0.6- and 0.9-GeV negative pions with Cu. In addition, the yields of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Co}$ from Cu have been measured for 12-GeV ${\pi }^{-}$. Results at the two lower energies which correspond to the first two isospin $T=\frac{1}{2}$ pion-nucleon resonances are compared with earlier studies of Cu spallation by ${\pi }^{-}$ at energies across the first $T=\frac{3}{2}$ resonance, i.e., 50 to 350 MeV. The 12-GeV ${\pi }^{-}$ results are compared with similar investigations in which both energetic protons and heavy ions were used. For $E_{\pi }\ge 0.5$ GeV no evidence of strong resonance effects can be found in the pattern of the spallation yields. As the pion energy is raised a smooth trend of enhanced yields of deep spallation products to near-target yields closely parallels the same trend observed for both high-energy proton and heavy-ion spallation of Cu. These results indicate that at high energy, pi-mesic spallation exhibits the same features of limiting fragmentation and factorization of the isotopic yields that have been observed previously in hadron induced spallation.

NUCLEAR REACTIONS Cu(${\pi }^{-}$, spallation), $E_{\pi -}=0.6, 0.9, \mathrm{and} 12$ GeV, measured relative $\sigma \mathrm{}(A,Z)\mathrm{}$, 11 selected products ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$-${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$. Comparison with high-energy proton and heavy-ion spallation of Cu. Natural targets, Ge(Li) detectors.