Fusion cross sections were measured for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ bombardments of ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ from 32 to 151 MeV by detecting the evaporation residues from the compound nucleus decay with gas counter telescopes. Charge, energy, and angular distributions of projectilelike fragments from the deeply inelastic collisions were also measured at 151 MeV. The fusion excitation function was analyzed through the barrier penetration model and compared to the predictions of the statistical yrast line model. The critical angular momentum and the grazing angular momentum deduced from the fusion and elastic scattering data were used in the interpretation of the kinetic energies of the deeply inelastic fragments in terms of a rotating dinuclear model.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, $E=32.5\mathrm{} \mathrm{to} 151$ MeV; measured evaporation residue $\sigma (E, \theta )$; deduced $\sigma \mathrm{}\left(E\right)\mathrm{}$ total fusion excitation function; barrier and critical parameters. $E=55.7, 63, 125, 151$ MeV; measured elastic scattering $\sigma \left(\theta \right)$; deduced optical potentials; reaction cross sections ${\sigma }_R$. $E=151\mathrm{}$ MeV; measured charge, energy, and angular distributions for $4\le Z\le 12$ fragments. Natural target. Gas ionization and Si detectors.

Inclusive $\gamma$ spectra from the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ interaction have been measured using from 45 up to 105 MeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ beams. Experimental mass and charge spectra are compared with statistical model calculations. Total reaction and fusion cross sections are extracted. The optical, Glas and Mosel, and Bass model calculations are presented and compared with the data. The limitation of the fusion cross section by the statistical yrast line is also discussed.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $E_{\mathrm{lab}}=45, 55, 60, 70, 80, 85, 105$ MeV; measured mass spectra for $12\le A\le 44$, charge spectra for $6\le Z\le 22$; measured total reaction and fusion cross sections ${\sigma }_R$, ${\sigma }_f$; deduced critical angular momentum and radius $l_f$ and $r_{\mathrm{cr}}$.

Compound nuclear processes should in fact exhibit all the resonances of the underlying compound nucleus. In intermediate resolution experiments where the energy resolution $\Delta E$ is considerably large compared to the width and spacing of compound nuclear states but small compared to those of optical model shape resonances, one observes the well-known intermediate structure. In the case of compound elastic processes a dynamically reasonable account of intermediate structure resonances was developed by various authors, where one assumes the existence of a doorway state through which the incident (or the final) state couples to the compound nuclear states. An energy average of the resultant amplitude exhibits intermediate structure. In the case of compound inelastic reactions the incident and the final states are different and the doorway states that relate the final state to the compound nuclear states will in general be different from the doorway states which relate the incident state to the compound nuclear states. The former doorway states will be referred to as the exit doorway states and the latter as the entrance doorway states. A dynamical theory is developed acknowledging the notion of these two kinds of doorway states. The energy averaged transition amplitude shows two sets of intermediate structure resonances corresponding to these two kinds of doorway states. It is expected that one of these sets of resonances will usually dominate a reaction in an energy domain. The present formulation can possibly explain the different sets of intermediate structure resonances observed in different exit channels of a nuclear reaction, for example, those observed in various exit channels of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ system.

NUCLEAR REACTIONS Intermediate structure resonances, entrance and exit doorway states, inelastic compound nuclear processes.

A variational principle, based on microscopic trial wave functions to calculate corrections to the Born amplitude, is described. The case of high multiplicity final channels is considered. It is shown that the transition amplitude for exclusive processes can always be estimated.

NUCLEAR REACTIONS Variational principle gives microscopic transition amplitudes for heavy ion fragmentation.

For the fission of ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ induced by fast neutrons from a ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ critical assembly, we have determined the mass-yield distribution and measured independent fission yields and one isomer ratio. The mass-yield distribution curve was constructed from the results for 29 total chain yields which were derived from measurements of fission products ranging from ${}_{}{}^{91}{}_{}{}^{}\mathrm{Y}$ to ${}_{}{}^{161}{}_{}{}^{}\mathrm{Tb}$. Absolute fission yields were obtained with an accuracy of 4% by the requirement of unit total yield in each half of the mass-yield distribution curve and by use of the ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(n, f)$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(n, f)$ monitor reactions. The peak-to-valley ratio is about 60. Several independent fractional chain yields were measured. Values of $Z_p$, the most probable charge for a given mass number, inferred from these measurements are in good agreement with those estimated from independent-yield systematics.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}(n, f)$, $E=\mathrm{d}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{d}\mathrm{f}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}-\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{m}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$; measured fission yields, deduced fission mass distribution. Measured independent fractional chain yields; measured isomer ratio.

Absolute yields have been determined for 47 gamma rays emitted in the decay of 37 fission products representing 25 mass chains created during thermal-neutron fission of ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$. Using a Ge(Li) detector, spectra were obtained of gamma rays emitted between 15 min and 0.4 yr after very short irradiations by thermal neutrons of a 15-μg sample of ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$. On the basis of measured gamma-ray yields and known nuclear data, yields for cumulative production of 37 fission products were deduced. The absolute overall normalization uncertainty is <8%. The results are compared with fission-product yields previously measured, with generally good agreement. On this basis, and using other measurements for masses not observed in the present experiment, a complete mass distribution for $A$ between 76 and 152 was deduced. The measured $A$-chain cumulative yields from the present program make up 84% of the total light-mass ($A\le 115$) yield and 77% of the total heavy-mass yield. The data were analyzed to obtain values of most-probable charge ($Z_p$) and charge-dispersion ($\sigma$) parameters. Based upon insight gained from study of similar data obtained for thermalneutron fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, we postulate a simple functional dependence $\sigma =\sigma \left(Z_p\right)$, and using this dependence obtain values of $Z_p\mathrm{}\left(A\right)\mathrm{}$ for 15 mass chains created during fission of ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$. Values of $Z_p\mathrm{}\left(A\right)\mathrm{}$ were estimated for other mass chains based upon results of a recent study of $Z_p\mathrm{}\left(A\right)\mathrm{}$. Charge distributions determined using the deduced mass distribution and the deduced sets of $Z_p\mathrm{}\left(A\right)\mathrm{}$ and $\sigma \left(Z_p\right)$ are in very good agreement with recent measurements, exhibiting a pronounced even-odd effect in elemental yields. These results may be used to predict unmeasured yields for ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$ fission.

NUCLEAR REACTIONS Fission ${}_{}{}^{209}{}_{}{}^{}\mathrm{Th}(n_{\mathrm{th}}, f)$, measured fission product gamma-ray yields; deduced fission-product yields and element and mass yields.

In view of relativistic three-body calculations we have investigated several quasipotential approximations to the Bethe-Salpeter equation assuming separable kernels with Yamaguchi-type form factors. In particular we have calculated $\pi -N$ and $N-N$ phase shifts with $l=0, 1$. As a result it is shown that the choice of a symmetric or unsymmetric reduction of the Bethe-Salpeter equation for $\pi N$ or $\mathrm{NN}$ scattering is less important in comparison to the choice of the analytic form of the pole. The quasiparticle equation proposed by Erkelenz and Holinde has turned out to be superior to other quasiparticle equations which have also been considered. As a consequence we present parameters for a separable potential to determine $\pi -N$ and $N-N$ phase shifts.

NUCLEAR REACTIONS Separable Bethe-Salpeter kernels reduced to six different quasipotential equations; application to pion-nucleon and nucleon-nucleon phase shifts; $E=0-300\mathrm{}$ MeV; $l=0, 1$.

The mass of ${}_{}{}^{16}{}_{}{}^{}\mathrm{Ne}$ has been measured using the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{He}$)${}_{}{}^{16}{}_{}{}^{}\mathrm{Ne}$ reaction. The $Q$ value of the reaction was determined to be -60.197±0.023 MeV, which corresponds to a mass excess of 23.984±0.024 MeV. The weighted average of this result with two previous measurements yields a mass excess of 23.994±0.020 MeV. This value is in reasonable agreement with the quadratic isobaric multiplet mass equation. The four parameter isobaric multiplet mass equation suggests a cubic or quartic coefficient of 4±3 keV for the $A=16\mathrm{}$ multiplet.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{He}$)${}_{}{}^{16}{}_{}{}^{}\mathrm{Ne}$. Measured ${}_{}{}^{16}{}_{}{}^{}\mathrm{Ne}$ mass. Deduced coefficients of the isobaric multiplet mass equation for the $A=16\mathrm{}$ quintet.

The angular distribution for elastic pion double charge exchange on ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ at 164 MeV is studied. Delta motion and delta-nucleus charge exchange interactions are included and found to be important, but the cross section is not satisfactorily reproduced. Some of our results are consistent with the single datum point for the single charge exchange reaction on ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$.

NUCLEAR REACTIONS Elastic (${\pi }^{+}, {\pi }^{-}$) and (${\pi }^{+}, {\pi }^0$) cross sections calculated and compared with experiment: $E_{\pi }=164\mathrm{}$ MeV.

Differential cross sections $\sigma \left(\theta \right)$ and analyzing powers $A\left(\theta \right)$ for $\mathrm{pp}$ elastic scattering have been measured in the Coulomb-nuclear interference region at 800 MeV. The measurements, which extend down to 0.5 deg in the laboratory, have been analyzed to deduce the zero-degree $\mathrm{pp}$ scattering amplitudes. The ratio $\rho$ of the real to imaginary parts of the spin-independent amplitude was found to be -0.04±0.04; the contribution of the double-spin-flip amplitudes to $\sigma \mathrm{}\left(0\right)\mathrm{}$ was found to be 0.16±0.03 times that of the spin-independent amplitude; while the ratios of the imaginary and real parts of the single spin-flip amplitude to $sin\theta$ were found to be 0.74±0.04 and -0.03±0.08 fm, respectively. Except for the last, these experimental values agree with the predictions of forward dispersion relations and phase shift analyses.

NUCLEAR REACTIONS ${}_{}{}^1{}_{}{}^{}\mathrm{H}(p, p){}_{}{}^1{}_{}{}^{}\mathrm{H}$, $E=800\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$ and $A\left(\theta \right)$. Deduced zero-degree scattering amplitudes.

The incident energy dependence of recoil ranges of ${}_{}{}^{32}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$, and ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ar}$ formed in thorium and uranium by 0.6-24 GeV protons has been studied by the thick-target-thick-catcher technique. While the range of ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$ and ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ar}$ produced in thorium decreases noticeably between 1 and 24 GeV, that of ${}_{}{}^{32}{}_{}{}^{}\mathrm{P}$ produced in the same target decreases slightly between 0.6 and 21 GeV. The constancy of range over this energy interval is interpreted as fragmentation, while a marked decrease is considered to be characteristic of deep spallation. Fragmentation and deep spallation are interpreted as collective interaction mechanisms, for which the role of the impact parameter of the initial collision (proton-target nucleus) is emphasized.

NUCLEAR REACTIONS Measurement of $2W(F+B)\mathrm{}$ of ${}_{}{}^{32}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$, and ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ar}$ formed in thorium and uranium by 0.6-24 GeV protons.

To focus on the nature of the short range part of the $\mathrm{NN}$ interaction, the intrinsically nonlocal interaction among the quark constituents of colorless nucleons is converted to an equivalent local potential using resonating group kernels which can be evaluated in analytic form. The WKB approximation based on the Wigner transform of the nonlocal kernels has been used to construct the equivalent potentials without recourse to the long range part of the $\mathrm{NN}$ interaction. The relative importance of the various components of the exchange kernels can be examined: The results indicate the importance of the color magnetic part of the exchange kernel for the repulsive part in the $\mathrm{}\left(\mathrm{ST}\right)=\left(10\right), \mathrm{}\left(01\right)\mathrm{}$ channels, in particular since the energy dependence of the effective local potentials seems to be set by this term. Large cancellations of color Coulombic and quark confining contributions, together with the kinetic energy and norm exchange terms, indicate that the exact nature of the equivalent local potential may be sensitive to the details of the parametrization of the underlying quark-quark interaction. The equivalent local potentials show some of the characteristics of the phenomenological short range terms of the Paris potential.

NUCLEAR REACTIONS Short range part of $\mathrm{NN}$ interaction, six-quark model, RGM quark exchange kernels, equivalent local potentials via WKB and Wigner transforms.

Momentum spectra of protons in the reactions of $\gamma +\mathrm{Be}\to p+\mathrm{anything}$ and $\gamma +\mathrm{C}\to p+\mathrm{anything}$ were measured in the photon energy range from 180 to 420 MeV for beryllium and from 340 to 580 MeV for carbon by use of a tagged photon beam. The spectrum obtained shows two peaks which are interpreted to be due to the protons in the reactions $\gamma +``N\text{'}\text{'}\to p+\pi$ and $\gamma +``pn\text{'}\text{'}\to p+n$, where "$N$" and "$\mathrm{pn}$" are the quasifree nucleons and proton-neutron systems in the target nuclei.

NUCLEAR REACTIONS ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(\gamma , p)$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\gamma , p)$, $E=180-580\mathrm{}$ MeV; measured $\sigma (E;E_p)$.

We discuss the scattering theory pertaining to the coupled $\pi NN-NN$ system and approach the problem in two independent ways. The first one starts from a Hamiltonian formalism and coupled Schrödinger equations, whereas the second one employs an off-mass-shell relativistic theory of classifying perturbation diagrams. Both ways lead to connected equations among transition operators in which $\pi \mathrm{NN}$ vertices, as well as nucleon propagators, are completely dressed and renormalized. Furthermore, the physical amplitudes obey two- and three-body unitarity relations. The resultant equations form a sound theoretical basis for subsequent numerical calculations leading to the evaluation of physical observables in the reactions $\pi +d\to \pi +d$, $\pi +d\leftrightarrow N+N$, and $N+N+\to N+N$.

NUCLEAR REACTIONS Coupled $\pi NN-NN$ equations, Hamiltonian approach, off-mass-shell approach, dressed vertex and propagator, last cut lemma.

Gamma-ray energies and intensities in the alpha decay of ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$ were precisely determined using a high-resolution Ge detector. Twenty new gamma rays were observed whereas 16 gamma rays earlier reported could not be observed. A modified energy level diagram for ${}_{}{}^{225}{}_{}{}^{}\mathrm{Ra}$ is proposed using the present results.

RADIOACTIVITY ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$; measured $E_{\gamma }$, $I_{\gamma }$. Ge detector. ${}_{}{}^{225}{}_{}{}^{}\mathrm{Ra}$ deduced levels. Radiochemistry.

It is shown in the hybrid quark-two-baryon model of a $\Lambda N$ cluster in nuclei that the short distance, six-quark part dominates the nonmesonic decay. For a six-quark probability of 15% for a nuclear cluster the nonmesonic lifetime is ${\tau }_{\Lambda }^{\mathrm{NM}}\approx \frac{1}{3}{\tau }^{\mathrm{free}}$, which is consistent with present experiment.

NUCLEAR STRUCTURE Hypernuclear structure. Calculation of lifetime of $\Lambda$ in hypernuclei. Hybrid pion-six quark model of $\Delta s=1\mathrm{}$ weak nuclear interactions. Quark structure of nuclei and hypernuclei.

In order for a boson-expansion theory to be useful for practical purposes, it must satisfy at least two requirements: It must be in the form of a linked-cluster expansion, and the pure (ideal) boson states must be usable as basis states. Previously, we constructed such a boson theory and used it successfully for many realistic calculations. This construction, however, lacked mathematical rigor. In the present paper, we develop an entirely new approach, which results in the same boson expansions obtained earlier, but now in a mathematically rigorous fashion. The achievement of the new formalism goes beyond this. Its framework is much more general and flexible than was that of the earlier formalism, and it allows us to extend the calculations beyond what had been done in the past.

NUCLEAR STRUCTURE Boson expansion theories, commutator method, Marumori-Yamamura-Tokunaga method, fermion system, norm matrix, linked-cluster expansion, ideal-boson state, physical boson state, even-even nucleus, odd-$A$ nucleus, nuclear collectivity.

The $J=0\mathrm{}$, $T=1\mathrm{}$ charge-independent pairing Hamiltonian is treated by means of the equations of motion for pair creation operators. Exact equations for the seniority-zero states of $N$ nucleons are derived. It is shown that these equations can be solved by a stepby-step procedure which consists of progressively adding pairs of nucleons to a core. A method is given which removes the spurious effects arising from the redundancy of the set of basis vectors. The theory can be applied at several levels of approximation depending on the number of core states which are chosen to build up the basis vectors. Of special interest are the lowest orders of approximation, which are very simple in application. To assess the practical value of the present work, a three-level model calculation is performed using the first-order theory, wherein the core states are restricted to the lowest energy state for each value of the total isospin. Comparison shows that the energies, occupation probabilities, and two-nucleon transfer amplitudes for the lowest states of natural isospin are in very good agreement with the exact results for all values of $N$.

NUCLEAR STRUCTURE Equations-of-motion treatment of neutron-proton pairing correlations.

The one-hole states of $A=41-43\mathrm{}$ nuclei are calculated with a model space spanning the ${\left(f_{\frac{7}{2}}{p}_{\frac{3}{2}}\right)}^n{\left(d_{\frac{3}{2}}{s}_{\frac{1}{2}}\right)}^{-1\mathrm{}}$ configurations. The two-body effective interaction is assumed to be the modified surface-delta type. Energy spectra and spectroscopic factors are calculated and compared with the observed values. Satisfactory results are obtained.

NUCLEAR STRUCTURE $A=41-43\mathrm{}$, calculated effective interaction, energy spectra, spectroscopic factors.

The nucleus ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ is studied assuming a three-body model—two neutrons outside an inert core of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$—and solving the Faddeev equations. The calculated spectrum is in good agreement with experiment.

NUCLEAR STRUCTURE ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$; three-body calculation of binding energies. Separable interactions.