Introducing a suitable cutoff parameter $r_0$ for the effective potential in the three-body subsystem, we show that the number of four-body bound states is roughly $k\ln \left[\epsilon a\right(r_0\left)\right]$, where $\epsilon$ is a momentum cutoff and $\frac{2}{3\pi }\le k\le \frac{1}{3}$, if the scattering length $a\left(r_0\right)$ for a two-body bound state and a third particle tends to infinity. In a numerical calculation we found that the value $r_0\approx 1.82$ fm, which provides a sufficiently resonant effective interaction in the three-body subsystem, is independent of the applied two-body potentials within the numerical accuracy.

NUCLEAR REACTIONS Efimov effect.

A method for the description of spin-isospin phase transitions in nuclear matter is developed. It allows a complete description of the pion condensation phase transition in the framework of the Landau-Migdal Fermi liquid theory. The equation of the order parameter is derived and the condensation energy is calculated. We study the influence of pion condensation on the nuclear equation of state and the temperature dependence of pion condensation.

NUCLEAR STRUCTURE Description of pion-condensed ground state by Green's function technique.

The $K$-harmonics method is used to determine the $\Lambda$ separation energy $B_{\Lambda }$ for the hypertriton and the $\Lambda \Lambda$ separation energy $B_{\Lambda \Lambda }$ for ${}_{\Lambda \Lambda }{}^6{}_{}{}^{}\mathrm{He}$. $B_{\Lambda }$ is calculated by retaining twelve harmonics and using $\Lambda -N$ and $N-N$ local potentials of the Volkov type fitted to Nagel's meson theoretic (model B) values of the scattering lengths and effective ranges. It gets reduced from 0.33 to 0.13 MeV by the addition of suitable repulsive terms. Retaining only nine harmonics, a convergent result for $B_{\Lambda \Lambda }$ is obtained with Tang and Herndon's $\alpha -\Lambda$ potential and a two-term $\Lambda -\Lambda$ potential of the Volkov type. The experimental $B_{\Lambda \Lambda }$ value of 10.8 MeV can be reproduced with a $\Lambda -\Lambda$ potential that gives rise to the scattering length of - 2.23 fm and an effective range of 3.31 fm.

NUCLEAR STRUCTURE Short-range repulsion, $K$ harmonics, ${}_{\Lambda }{}^3{}_{}{}^{}\mathrm{H}$, $\Lambda$ separation energy, ${}_{\Lambda \Lambda }{}^6{}_{}{}^{}\mathrm{He}$, $\Lambda \Lambda$ separation energy, scattering length, effective range.

It is shown by relating the transition amplitude of radiative muon capture to that of radiative pion capture, that the transition amplitude of radiative muon capture proposed recently by Hwang and Primakoff differs from the others mainly by Low's counter terms. Despite the fact that the "original" transition amplitude does not violate seriously the conservation of the hadronic electromagnetic current, Low's counter terms, as introduced via Low's prescription to secure the presence of small conservation-of-hadronic-electromagnetic-current-breaking terms, are confirmed to be of numerical importance. Further, it is found in the "elementary-particle" treatment of radiative muon capture that the uncertainty arising from the nuclear structure can be reduced to become negligible. Therefore, an exclusive radiative muon capture experiment can in principle differentiate the Hwang-Primakoff theory from the others and yet provide a comprehensive test of partial conservation of axial-vector current.

RADIOACTIVITY Theories of radiative muon capture, linearity hypothesis versus Low's prescription; nuclear structure and PCAC.

The decay of ${}_{}{}^{100}{}_{}{}^{}\mathrm{Ag}_{}^{g,m}{}_{}{}^{}$ has been studied using $\beta$ and $\gamma$ spectrometers in singles and coincidence modes. Two isomers were identified: one decaying with 2.00±0.10 min half-life, tentatively assigned to ${}_{}{}^{100}{}_{}{}^{}\mathrm{Ag}_{}^{\mathrm{}\left(g\right)\mathrm{}}{}_{}{}^{}$ ($5^{+}$) and the other with 2.30±0.15 min half-life, corresponding to ${}_{}{}^{100}{}_{}{}^{}\mathrm{Ag}_{}^{\mathrm{}\left(m\right)\mathrm{}}{}_{}{}^{}$ ($2^{+}$). Separate decay schemes were proposed.

RADIOACTIVITY ${}_{}{}^{100}{}_{}{}^{}\mathrm{Ag}_{}^{g,m}{}_{}{}^{}$ [from ${}_{}{}^{102}{}_{}{}^{}\mathrm{Pb}(p, 3n)$ enriched ${}_{}{}^{102}{}_{}{}^{}\mathrm{Pd}$]; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$, $E_{\beta }$, $\beta -\gamma$, deduced $log\mathrm{ft}$, ${}_{}{}^{100}{}_{}{}^{}\mathrm{Pd}$ levels.

Angular-correlation measurements were made on ten direct cascades and four skip cascades in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Sr}$ and on nine direct cascades in ${}_{}{}^{96}{}_{}{}^{}\mathrm{Sr}$. These nuclei were populated by beta decay of isotopically pure ${}_{}{}^{94}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{96}{}_{}{}^{}\mathrm{Rb}$ ion beams produced by fission and on-line mass separation. Correlations were measured for most of the intense transitions in coincidence with the $2^{+}$→$0^{+}$ ground-state transition in both nuclei and two additional transitions in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Sr}$. Five levels in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Sr}$ are given definite spin assignments and four levels tentative assignments. In ${}_{}{}^{96}{}_{}{}^{}\mathrm{Sr}$ definite spin assignments are made for four levels and tentative assignments for five levels. Values are listed for angular-correlation coefficients and, where applicable, multipole mixing ratios. Level systematics of neutron-rich even mass Sr isotopes are discussed within the context of assignments made here.

RADIOACTIVITY ${}_{}{}^{94}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Rb}$; measured $\gamma -\gamma \left(\theta \right)$ ${}_{}{}^{94}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Sr}$ deduced $J$, $\Pi$. Mass-separated ${}_{}{}^{94}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Rb}$ activity.

Precise ratios of elastic electron scattering cross sections for the nuclei ${}_{}{}^{54,56,58}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58,60,62,64}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{64,66,68,70}{}_{}{}^{}\mathrm{Zn}$ have been measured in the momentum-transfer region $0.6 {\mathrm{fm}}^{-1\mathrm{}}\le q\le 2.3 {\mathrm{fm}}^{-1\mathrm{}}$. The data were analyzed with a Fourier-Bessel parametrization of the charge distribution. Charge distribution differences were determined nearly model independently for the $\Delta A=2\mathrm{}$ isotope and isotone pairs. The $\Delta Z=2\mathrm{}$ isotone charge distribution differences show a strong shell effect, if one compares the Ni-Fe charge distribution differences, where the two added protons close the $1f_{\frac{7}{2}}$ shell, and the Zn-Ni charge distribution differences, where the two added protons start to fill the $2p_{\frac{3}{2}}$ shell. For the $\Delta N=2\mathrm{}$ isotopes we observe a nearly constant increase of the "half density radius" in the investigated region of the $2p_{\frac{3}{2}}$, $1f_{\frac{5}{2}}$, and $2p_{\frac{1}{2}}$ neutron shells. However, the skin thickness of the charge distribution increases strongly at the beginning (${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$-${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$) and decreases at the end (${}_{}{}^{70}{}_{}{}^{}\mathrm{Zn}$-${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$) of these shells by adding two neutrons. The rms radii differences deduced from a combined analysis of the electron scattering data and present muonic x-ray data show the same trend. These differences, determined model independently with a typical accuracy of some ${10}^{-3\mathrm{}}$ fm, decrease nearly linearly with increasing neutron number in the investigated region $28\le N\le 40$. These isotope shifts are nearly independent of the proton configuration of the involved nuclei, which indicates that the added neutrons interact primarily with the proton core rather than with the valence protons. Recent calculations, which include ground state correlations, show that the observed isotope shifts reflect deformation changes caused by changes of the amplitude of the zero-point quadrupole surface oscillations. A comparison of the experimental charge distribution differences with results of density dependent Hartree-Fock calculations also indicates the importance of deformation changes. The core rearrangement due to added protons, deduced from the measured isotone charge distribution differences, and the core rearrangements due to added neutrons, directly measured by the isotope shifts, are similar. The last two nucleons of both the $1f_{\frac{7}{2}}$ neutron and proton shell cause core polarizations, resulting in a smaller charge core radius.

NUCLEAR STRUCTURE ${}_{}{}^{54,56,58}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58,60,62,64}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{64,66,68,70}{}_{}{}^{}\mathrm{Zn}$; elastic electron scattering differential cross sections $\frac{d\sigma }{d\Omega (E, \theta )}$ and ratios at $E=100, 150, 275$ MeV; model-independent charge distribution differences for isotones and isotopes; model-independent radial moments ${〈{\mathcal{r}}^k〉}^{\frac{1}{k}}$ and $\Delta {〈{\mathcal{r}}^k〉}^{\frac{1}{k}}$, deduced from a combined elastic electron and muonic x-ray data analysis; charge distribution differences, compared with Hartree-Fock calculations, and calculations considering ground state correlations.

A recently proposed method for $t$ matrix Lippmann-Schwinger-type equations is reexamined and is investigated numerically. The method relies on the introduction of an auxillary equation containing an arbitrary function, whose kernel is free from the fixed point singularity of the original equation. In the present work we rewrite the final result of the method in such a way that it has all the important features of a related method by Kowalski and Noyes and is simple to use in practice. With special choices of the arbitrary function the present method can be considered as an off-shell extension of methods of Bolsterli, of Kowalski, and of Sasakawa. The method also readily gives a practical way of calculating $K$ matrix elements. Using the iterative solution of the auxiliary equation the method is tested numerically to compute off-shell $t$ matrix elements for three commonly used nucleon-nucleon potentials for various choices of the arbitrary function.

NUCLEAR REACTIONS Singular scattering equations, nonsingular auxiliary equations, off-shell $t$ matrix elements and phase shifts computed.

The Faddeev equations in $N$ space dimensions for three identical spinless particles in their ground state interacting via harmonic oscillator, two-body potentials is solved analytically. Unlike the well-known Schrödinger solution, the individual Faddeev amplitudes may be negative and contain a long-range component of arbitrary strength. Upon symmetrizing to obtain the full wave function, this component vanishes and the Schrödinger solution results. Three-dimensional plots of the various wave functions are presented.

NUCLEAR STRUCTURE Faddeev calc., configuration space, harmonic oscillator.

A refined version of the Brillouin-Wigner perturbation method is employed to calculate the binding energies of the deuteron and triton with the Reid soft core potential. The method is shown, analytically, to yield an exact treatment of the strong short ranged components of the force. A primary advantage of the procedure is that it yields a variational upper bound on the energy eigenvalue. A formal comparison is made with the $g$ matrix method. It is found that this perturbation procedure is equivalent to seeking an optimum $g$ matrix, which yields the lowest upper bound when two-body correlations are included in the variational wave function. In order to retain the variational property some multiparticle terms are included in the energy series.

NUCLEAR STRUCTURE Brillouin-Wigner perturbation method. Reid soft core potential.

The consequences of assuming different radial dependences for the multipole residual interaction are explored, using macroscopic and microscopic arguments. Calculations are done both for schematic and realistic cases.

NUCLEAR STRUCTURE Radial dependence of multipole forces in RPA.

We explore the concept of the pseudopotential, introduced in a previous paper, within the context of the exact boundary condition for a system of fermions interacting through a pair-wise, hard-core potential, in the thermodynamic limit. We discuss several Ansätze for the Lagrange multipliers that allow the inclusion of the boundary conditions into the variational principle. It is found that under a given Ansatz, a dynamical, microscopic interpretation of the pseudopotential can be put forward. A comparison between this situation and the coherent approximation induced by the use of the correlation function is also presented.

NUCLEAR STRUCTURE Hard-core interactions, boundary condition, variational principle constrained Hartree-Fock problem; Ansatz, structure of the pseudopotential, state dependence.

In the procedure of fitting of the rotational spectra in high spins of even-even nuclei the assumption that there is equal uncertainty in the energy levels, overall, leads to more reasonable results than the assumption that each energy level should be weighted by the square of its inverse.

NUCLEAR STRUCTURE Rotational spectra, VMI models, properties of ${}_{}{}^{158,160}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{162,164}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{168}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{172,174,176}{}_{}{}^{}\mathrm{Hf}$.

This comment refers to a recent work by Raphael, Tandy, and Tobocman. The danger of incorporating cluster approximation in many-body Lippmann-Schwinger equations is emphasized. A certain type of antisymmetrization of Lippmann-Schwinger equations may lead to continuum spurious spectra. In particular it is pointed out that the cluster model equations introduced by these authors have highly suppressed (unphysical) incoming and outgoing waves. Contrary to claims made by these authors, it is stressed that Lippmann's identity is true.

NUCLEAR REACTIONS Many-body Lippmann-Schwinger equations; cluster model of Raphael, Tandy, and Tobocman; spurious continuum spectra.

It is shown that abnormal occupation, as found in a previous paper, does not occur if one allows for two-body correlations.

NUCLEAR STRUCTURE Plane-wave Hartree-Fock; nuclear matter.

The ($p, t$) reaction on ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$ at a bombarding energy at 89 MeV shows a broad feature similar to the one observed at lower bombarding energy. The excitation energies and widths were consistent with those observed in the earlier experiment. Angular distributions are in good agreement with distorted-wave Born approximation calculations in which two neutrons are assumed to have been picked up from deeply bound orbits.

NUCLEAR REACTIONS ${}_{}{}^{120,122,124}{}_{}{}^{}\mathrm{Sn}(p, t)$, $E=89\mathrm{}$ MeV; measured levels, $\Gamma$, $\sigma (\ominus )$. Enriched targets. DWBA analysis.

The wave function of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ which is totally antisymmetric under the Coulomb interaction and the neutronproton mass difference is presented. The generalized Faddeev equation recently proposed by us is applied to this wave function.

NUCLEAR STRUCTURE Totally antisymmetric ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ wave function. Involving the Coulomb force and the $n-p$ mass difference. The generalized Faddeev equation.

Fission isomers in ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ have been populated in ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(d, p){}_{}{}^{236}{}_{}{}^{}\mathrm{U}_{}^m{}_{}{}^{}$, ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}(d, pn){}_{}{}^{236}{}_{}{}^{}\mathrm{U}_{}^m{}_{}{}^{}$, and the ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(d, pn){}_{}{}^{238}{}_{}{}^{}\mathrm{U}_{}^m{}_{}{}^{}$ reactions. Time spectra of fission fragments with respect to the cyclotron beam pulses have been measured. From these measurements the isomeric-to-prompt fission ratios are derived for deuteron energies ranging from 17 to 25 MeV. The isomeric-to-prompt ratios show a distinct maximum around 20 MeV for the ($d, \mathrm{pn}$) reactions, whereas a monotonic decrease is observed for the ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(d, p){}_{}{}^{236}{}_{}{}^{}\mathrm{U}_{}^m{}_{}{}^{}$ reaction.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(d, pf)$ and ${}_{}{}^{236,238}{}_{}{}^{}\mathrm{U}(d, pnf)$, measured delayed fission fragment time spectra, deduced isomeric-to-prompt fission ratios.

Neutron capture $\gamma$-ray spectra have been measured from the 7.76-keV $s$-wave and the 9.48-, 11.2-, and 14.4-keV $p$-wave resonances in ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$. The 7.76-keV resonance spectrum is in excellent agreement with valence model predictions.

NUCLEAR REACTIONS ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(n, \gamma )$, $E_n=1-18\mathrm{}$ keV, measured $E_{\gamma }$, $I_{\gamma }$. ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ deduced resonances, levels, $J$, $\pi$, neutron separation energy. Enriched target, Ge(Li) detector. Comparison with valence model predictions.

Elastic scattering cross sections extracted for 412, 468, and 662 keV $\gamma$ rays scattering by uranium, platinum, tungsten, barium, cadmium, and silver are reported at scattering angles from 30° to 130° using a Ge-Li detector. The results are compared with theoretical cross sections obtained from the Dirac-Hartree-Fock-Slater form-factor approximation and correction factors evaluated by interpolation techniques from recent second order perturbation scattering amplitude calculations. Good agreement between the measurements and theory exists when both the $K$ and $L$ shell contributions to Rayleigh scattering are included.

NUCLEAR REACTIONS Elastic scattering; U, Pt, W, Ba, Cd, Ag ($\gamma , \gamma$); $E=412, 468, \mathrm{and} 662$ keV; $\theta$ from 30° to 130°; deduced theoretical Rayleigh scattering amplitudes; measured $\sigma (E_{\gamma }, \theta )$; natural targets.