An accurate mass formula at finite temperature has been used to obtain a more precise estimation of temperature effects on fission barriers calculated within the liquid drop model.

NUCLEAR REACTIONS, FISSION Finite temperature effects.

Analytic expressions for the resonating group method (RGM) norm kernel of the nine-quark $\mathrm{NNN}$ system make it possible to examine the role of Pauli effects among quarks. The conclusion is that Pauli effects alone do not account for the central dip in the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ density, despite the fact that the RGM wave function for the nine-quark $\mathrm{NNN}$ system is dominated (70.3%) by states of [441] and [522] space symmetry and contains only 0.4% of the spatially totally symmetric state.

NUCLEAR STRUCTURE Nine-quark model of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.

The collision process is described by hydrodynamical equations. The escape of nucleons which do not take part in the thermal equilibrium is considered by including drain terms in these equations. The energy spectra of the escaped nucleons and of nucleons evaporated after the breakup of the fluid are compared.

NUCLEAR REACTIONS Relativistic heavy ion reactions, nuclear hydrodynamics, nucleon spectra.

This comment refers to the proton-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering differential cross section data in the energy range scanned by G. A. Moss et al. A comparison is made between the Moss et al. results and older results in the energy range $T_p=0.1-0.65\mathrm{}$ GeV. There is a short discussion about the concept of intermediate energies in the reaction considered here.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}(p, p){}_{}{}^4{}_{}{}^{}\mathrm{He}$, $E=0.2-0.5\mathrm{}$ GeV; compared $\sigma (E, \theta )$ with other results at $E=0.1-0.65\mathrm{}$ GeV; discussed intermediate energy range concept.

A response to the Comment on proton-${}_{}{}^4{}_{}{}^{}\mathrm{He}$elastic scattering at intermediate energies is presented.

Analytical expressions for the fusion barrier height and radius have been derived from a four-parameter empirical fusion cross section formula for heavy ions. The fusion barrier parameters calculated, using these expressions, are in good agreement with the literature values.

NUCLEAR REACTIONS Fusion cross section excitation functions, fusion barrier parameters.

Core-polarization effects on magnetic form factors of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ are investigated. The importance of the interaction range and the state dependence of the tensor contributions are demonstrated. The systematic reduction measured experimentally is not reproduced.

NUCLEAR REACTIONS ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}(e, e)$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(e, e^{\prime })$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(e, e)$; magnetic form factors, calculated first-order core-polarization effects.

We calculate binding energy difference between ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ using the exact hyperspherical harmonics method where Coulomb force is treated nonperturbatively. A variety of two-nucleon potentials with or without a two-pion-exchange three-body force (Fujita-Miyazawa type) has been used properly. We compare our results with the "hyperspherical formula" and previous calculations. Calculated Coulomb energy agrees roughly with the hyperspherical formula; but the significant difference indicates that the perturbative treatment is not sufficient.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, Coulomb energy, hyperspherical harmonics calculation.

The explicit expressions of Amado et al. for elastic scattering observables for protons at intermediate energies have been applied to data at 500 and 800 MeV. Analyses were performed using both the analytic form of the solutions and data-to-data relations. Good fits are obtained with few parameters; however, these seem to have only phenomenological significance.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, $E=500\mathrm{} or 800$ MeV; analyzed elastic $\sigma \left(\theta \right)$, $A_y\left(\theta \right)$, $Q\left(\theta \right)$.

The background of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(p, n)$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p, n)$ spectra has been calculated in a microscopic model for an incident proton energy of 160 MeV. The continuous parts of the spectra are reproduced within a factor of 1.3. It is shown that most of the background subtracted in the experimental analysis of the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p, n)$-Gamow-Teller resonance is actually Gamow-Teller strength. The calculations predict a strong $\Delta L=2\mathrm{}$ ($3^{+}$) resonance in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p, n)$ at 25 MeV excitation energy, but none in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$.

NUCLEAR REACTIONS ($p, n$) scattering: calculated background for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(p, n)$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p, n)$.

The assumptions underlying the liquid drop model and the interacting boson model are compared. These two models are inequivalent. However, only minor modifications in the original assumptions are required to make these models different representations of the same underlying physical processes.

NUCLEAR STRUCTURE Liquid drop model, interacting boson model, underlying Hilbert space, quantum-classical correspondence.

An inversion scheme proposed recently by the authors is successfully applied to various cases of neutron-nucleus scattering. The results are compared with those of other inversion methods.

NUCLEAR REACTIONS Inverse scattering problem at fixed energy, nonrational representation of scattering function; applied to complex nuclear potential.

New partial wave decompositions of nuclear and charge densities are utilized to improve the numerical reliability of realistic scattering calculations in momentum space.

NUCLEAR REACTIONS Nuclear densities, scattering, momentum space, numerical methods, partial wave decompositions.

Proton partial decay widths were measured from four of the members of the intermediate structure in ${}_{}{}^{41}{}_{}{}^{}\mathrm{Sc}$ at $E_x=7.2\mathrm{}$ MeV, using analyzing powers and spin-flip correlations to ascertain the relative $p_{\frac{1}{2}}$ and $p_{\frac{3}{2}}$ contributions to the structure. Two of the resonances at $E_x=7.27\mathrm{} \mathrm{and} 7.44$ MeV, respectively, are rather pure configurations of a $p_{\frac{1}{2}}$ proton coupled to the $3^{-}$, 3.73 MeV excited state in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ whereas at least one of the resonances at $E_x=7.37\mathrm{}$ MeV has some $p_{\frac{3}{2}}$ proton coupling to the same $3^{-}$ state in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(p, p^{\prime })$, measured $\sigma \left(\theta \right)$ at four energies. ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\overline{p}, p^{\prime }\gamma )$, measured analyzing powers, spin-flip correlations, and spin-flip asymmetries. Calculated partial proton decay widths.

Double differential cross sections for the inclusive production of neutrons, protons, and $\alpha$ particles from ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ and ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ bombarded with $\alpha$ particles of energies $E_{\alpha }=28\mathrm{} \mathrm{and} 32$ MeV, respectively, have been measured for several angles between 15° and 160°. Hybrid model calculations for the preequilibrium decay consistently yield initial exciton numbers $n_0=5\mathrm{}\left(4\right)\mathrm{}$ for both neutron and proton emission from $\alpha$+${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ ($\alpha$+${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$) if pairing effects are taken into account. The angular distributions of nucleons and $\alpha$ particles differ from those of the reactions $p$ + ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$,${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$; they are discussed in the framework of the generalized exciton model that distinguishes between multistep direct and multistep compound contributions.

NUCLEAR REACTIONS ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}(\alpha , xn)$, ($\alpha , \mathrm{xp}$), ($\alpha , x\alpha$), $E_{\alpha }=28-32\mathrm{}$ MeV; measured $\sigma (E_y, {\ominus }_y)$, deduced $\sigma \left(E_y\right)$, $y=n, p, \alpha$; calculated preequilibrium decay mode, deduced exciton configuration, entrance channel dependence.

Within the framework of the collective model, form factors are calculated for the inelastic excitation of quadrupole vibrational bands and the yrast band in deformed even-even nuclei. In the case of a "pure" vibrational band, analytical expressions are derived for a nuclear potential of exponential type. The general results include a numerical treatment of the vibration-rotation interaction; hence, the form factors should be useful in the intermediate spin region.

NUCLEAR REACTIONS HI coupled channels inelastic scattering. Form factors for quadrupole vibrational bands and the yrast band in deformed even-even nuclei.

High spin states in ${}_{}{}^{99}{}_{}{}^{}\mathrm{Rh}$ and ${}_{}{}^{101}{}_{}{}^{}\mathrm{Rh}$ have been populated via the ${}_{}{}^{96,98}{}_{}{}^{}\mathrm{Mo}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, 3n)$ reaction. Two cascades based on the ${\frac{1}{2}}^{-}$ ground state and the ${\frac{9}{2}}^{+}$ isomeric state are attributed to each nucleus on the basis of $\gamma -\gamma$ coincidence measurements. Excitation functions and angular distribution measurements were used to assign spin values and determine some multipole mixing ratios.

NUCLEAR REACTIONS ${}_{}{}^{96,98}{}_{}{}^{}\mathrm{Mo}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, 3n){}_{}{}^{99,101}{}_{}{}^{}\mathrm{Rh}$, $E=18-34\mathrm{}$ MeV; measured $E_{\gamma }$, $n-\gamma$, $\gamma -\gamma$ coincidences, $\gamma$-ray angular distributions; ${}_{}{}^{99}{}_{}{}^{}\mathrm{Rh}$, ${}_{}{}^{101}{}_{}{}^{}\mathrm{Rh}$ deduced levels, $J^{\pi }$; enriched targets, Ge(Li) detectors.

This paper discusses resonances of narrow width in the context of bound states embedded in the continuum spectrum of nonlocal potentials. Feshbach's theory of nuclear reactions leads directly to resonance theory, and we base our discussion here on the techniques he developed for shifting nuclear many-body aspects into effective single-particle nonlocal potentials. In our formulation, the many-body state of the compound nucleus is represented by a single-particle state. The basis for our discussion is a two channel model of a resonance of zero width, with a continuum bound state originating from the coupling of a bound state to the single-particle scattering state. We give a specific example of a model which leads to an arbitrarily narrow (nonzero width) resonance, and demonstrate that the width of the resonance produced by breaking the continuum bound state is proportional to ${(\Lambda -1)}^2$, where the parameter $\Lambda$ is such that $\Lambda =1\mathrm{}$ corresponds to the condition necessary for the existence of a continuum bound state.

NUCLEAR REACTIONS Compound nucleus resonances, coupled channels, nonlocal potentials, coutinuum bound states, Breit-Wigner formula.

The nucleons taking part in heavy ion reaction are considered as a three-component fluid. The first and second components correspond to the nucleons of the target and the projectile, while the thermalized nucleons produced in the course of the collision belong to the third component. Making use of the Boltzmann equation, hydrodynamical equations are derived. An equation of state for anisotropic nuclear matter obtained from a field theoretical model in mean field approximation is applied in a one dimensional version of the three-component fluid model. The speed of thermalization is analyzed and compared to the results of cascade and kinetic models.

NUCLEAR REACTIONS Relativistic heavy-ion reactions, hydrodynamic description.