The longstanding disagreement between the predictions of Faddeev and variational calculations on the existence of the trineutron is shown to arise from the potentials used and is not attributable to the difference in approach.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}n$; confirmed nonexistence. Faddeev-UPE method.

For $E_p=18-20\mathrm{}$ MeV, the $Q$ effects in ($p$,$t$) cross sections on rare-earth nuclei completely mask most of the differences expected from nuclear structure models.

NUCLEAR REACTION Sm, Gd, Dy, Er, Yb, Hf ($p$,$t$); $E_p=18, 19$ MeV. DWBA calculations. Investigated $Q$, $Z$, $A$ dependence.

The ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$($t$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^{100}{}_{}{}^{}\mathrm{Nb}$ reaction has been used to determine the mass and the energy levels of ${}_{}{}^{100}{}_{}{}^{}\mathrm{Nb}$. A mass excess of - 79480±30 keV is obtained for ${}_{}{}^{100}{}_{}{}^{}\mathrm{Nb}$, in substantial disagreement with $\beta$-decay results. Twentytwo excited states of ${}_{}{}^{100}{}_{}{}^{}\mathrm{Nb}$ with $E_x<1.3\mathrm{}$ MeV have been observed.

NUCLEAR REACTION ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$($t$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$), $E=23.0\mathrm{}$ MeV; measured $\sigma (E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}},\theta )$. ${}_{}{}^{100}{}_{}{}^{}\mathrm{Nb}$ deduced levels. New mass of ${}_{}{}^{100}{}_{}{}^{}\mathrm{Nb}$.

The extraction of rotational contributions to the energies of deep-inelastic fragments from light systems is discussed. It is concluded that the data are consistent with the occurrence of scission at the critical radius as well as at the large radii previously suggested.

NUCLEAR REACTIONS ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$ + ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, Calculated deep-inelastic fragment energies, extracted rotational contribution.

Elastic and inelastic scattering excitation functions for ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$ and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ by ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ have been measured. The inelastic data associated with ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ on common targets are very different. Optical model and distorted-wave Born approximation calculations indicate that multistep processes involving the projectile states are responsible.

NUCLEAR REACTIONS ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$), (${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$), $E=30-42\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$. DWBA analysis, deduced optical parameters, $B\left(E2\mathrm{}\right)\mathrm{}$, ${\beta }_n$.

Levels of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Xe}$ populated by the decays of $1^{+}$ ${}_{}{}^{128}{}_{}{}^{}\mathrm{Cs}$ and $1^{+}$ ${}_{}{}^{128}{}_{}{}^{}\mathrm{I}$ were studied by $\gamma \gamma$ angular correlations and Compton-suppressed $\gamma$-ray spectroscopy. $0^{+}$ states were established in ${}_{}{}^{128}{}_{}{}^{}\mathrm{Xe}$ at 1582 and 2598 keV. Experimental branching ratios were compared with those calculated from a fit to the levels of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Xe}$ and ${}_{}{}^{130}{}_{}{}^{}\mathrm{Xe}$ by an interacting boson approximation.

RADIOACTIVITY ${}_{}{}^{128}{}_{}{}^{}\mathrm{Cs}$ [from ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$($d$,$7n$)${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$ decay], and ${}_{}{}^{128}{}_{}{}^{}\mathrm{I}$ [from ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$($n$,$\gamma$)]; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma \left(\theta \right)$; deduced $A_{22}$, $A_{44}$, ${}_{}{}^{128}{}_{}{}^{}\mathrm{Xe}$ deduced levels, $J$, $\pi$, $log\mathrm{ft}$. Ge(Li) detectors, Compton suppression.

Liquid scintillator solutions based on the solvent phenethyl alcohol are loaded with the salt indium trifluoroacetate to concentrations as high as 200 g In/1. Using a scintillator solution loaded with 51 g In/1 in a low background chamber with muon anticoincidence and Pb walls 20 cm thick, a ${\beta }^{-}$ decay spectrum from ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$ is obtained and fitted with a sixth order polynomial in $\frac{(E_{\mathrm{endpoint}}-E)}{E_{\mathrm{endpoint}})}$. From these data we find $T_{\frac{1}{2}}\left({}_{}{}^{115}{}_{}{}^{}\mathrm{In}\right)=4.41\mathrm{}\left(25\right)\mathrm{}\times {10}^{14}$ yr and $E_{\mathrm{endpoint}}\left({}_{}{}^{115}{}_{}{}^{}\mathrm{In}\right)=482\mathrm{}\left(15\right)\mathrm{}$ keV. These low background experiments also show that indium loaded liquid scintillators are excellent neutron detectors. Their sensitivity for epithermal neutrons in particular is excellent. It is expected that these results will be useful in designing a solar neutrino capture detector of the type suggested by Raghavan.

RADIOACTIVITY ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$; measured $T_{\frac{1}{2}}$, $E_{\beta }$. In-loaded liquid scintillator, 90 keV FWHM at 390 keV.

Approximate probabilities of electron excitation (shakeup/shakeoff) from various atomic states during nuclear $\mathrm{ns}$ electron capture have been calculated in the sudden approximation, using Hartree-Fock wave functions. Total excitation probabilities are much lower than during inner-shell ionization by photons or electrons, and $\mathrm{ns}$ states are more likely to be excited than $\mathrm{np}$ states. This latter result is borne out by $K\alpha$ x-ray satellite spectra.

RADIOACTIVITY Atomic electron excitation (shakeup/shakeoff) during nuclear electron capture, calculated form Hartree-Fock wave functions.

The probability $P_{\mathrm{KK}}\left(\mathrm{IC}\right)$ of double $K$-shell vacancy creation per $K$ internal conversion of the 88 keV $E3\mathrm{}$ transition in the decay of ${}_{}{}^{109}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}$ has been determined by means of a $K\alpha$-x-ray—$K$-x-ray coincidence experiment on ${}_{}{}^{109}{}_{}{}^{}\mathrm{Pd}$:$P_{\mathrm{KK}}\left(\mathrm{IC}\right)=(13.0\mathrm{}\pm 1.1)\times {10}^{-5\mathrm{}}$. From $P_{\mathrm{KK}}\left(\mathrm{IC}\right)$ and a similar experiment on ${}_{}{}^{109}{}_{}{}^{}\mathrm{Cd}$ the probability $P_{\mathrm{KK}}\left(\mathrm{EC}\right)$ of double $K$-shell vacancy production per $K$-electron capture decay of ${}_{}{}^{109}{}_{}{}^{}\mathrm{Cd}$ has been determined as well: $P_{\mathrm{KK}}\left(\mathrm{EC}\right)=(1.02\mathrm{}\pm 0.36)\times {10}^{-5\mathrm{}}$. The energy shift of the hypersatellite Ag $K{\alpha }_1^H$-x-ray line was found to be 532 ± 6 eV.

RADIOACTIVITY ${}_{}{}^{109}{}_{}{}^{}\mathrm{Pd}$ and ${}_{}{}^{109}{}_{}{}^{}\mathrm{Cd}$; measured $K\alpha$-x-ray—$K$-x-ray coincidences, deduced double $K$-shell vacancy production probabilities of 88 keV $E3\mathrm{}$ transition and EC decay, and hypersatellite $K{\alpha }_1$-x-ray shift.

The spectrum of the internal bremsstrahlung accompanying the $K$-capture decay of ${}_{}{}^{204}{}_{}{}^{}\mathrm{Tl}$ was measured. The intensity of the spectrum in the range from 103 keV to the end point was found to be (2.17±0.26) × ${10}^{-5\mathrm{}}$ photons per $K$ capture, 4.3 times lower than the intensity predicted by the theory of Zon. The Coulomb-free version of the theory is in better agreement with the data.

RADIOACTIVITY ${}_{}{}^{204}{}_{}{}^{}\mathrm{Tl}$; measured IB x-ray coin; deduced $I_{\mathrm{IB}}$, $Q$.

Magnetic moments of single-particle and single-hole states in the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ region are calculated in a large shell model space taking into account the core polarization and meson exchange effects to a high order of perturbation.

NUCLEAR STRUCTURE ${}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$; magnetic dipole moments; core polarization; meson exchange currents.

We carry out an extended study of the Vary-Sauer-Wong effect on the second-order core-polarization diagrams $G_{3\mathrm{p}1\mathrm{h}}$ and $G_{3\mathrm{p}1\mathrm{h}}^T$ in the effective interaction between two valence nucleons. As in Vary-Sauer-Wong, we first calculate $G_{3\mathrm{p}1\mathrm{h}}$ using a harmonic oscillator propagator for the intermediate particle states $p$, including particle-hole excitations with energies up to $22\hslash \omega$. Results are in close agreement with those of Vary-Sauer-Wong. We then calculate $G_{3\mathrm{p}1\mathrm{h}}^T$ where a free particle propagator for $p$ is used. This is obtained by including the $-U$, the oscillator one-body potential, insertions of all orders to $p$ of $G_{3\mathrm{p}1\mathrm{h}}$. Although the resulting matrix elements are generally smaller in magnitude than those of Vary-Sauer-Wong, the qualitative feature of the Vary-Sauer-Wong effect is clearly maintained. Namely there are strong cancellations between the contributions from the low and high energy $p$ states. This makes the net effect from the core polarization diagrams significantly weaker than from $G_{3\mathrm{p}1\mathrm{h}}$ calculated with $2\hslash \omega$ excitations alone. We also study some intermediate choices for the propagator of $p$, where the free particle propagator is used only for high energy valence states. The Brueckner reaction matrix elements in a mixed representation where one particle is in a harmonic oscillator state and the other in a plane wave state are needed in our calculations. By using the vector transformation brackets of Wong and Clement and of Balian and Brezin and the Tsai-Kuo treatment of the Pauli exclusion operator, we have developed a technique for accurately calculating these matrix elements.

NUCLEAR STRUCTURE Contributions to effective interaction for $A=18\mathrm{}$ nuclei calculated from converged values of lowest order core polarization diagrams as function of intermediate state propagator using new momentum space techniques.

The Hartree-Fock theory for many fermions with plane-wave orbitals but with abnormal occupation is studied. A one-dimensional problem with an interparticle interaction of finite range which saturates the $N$ body system at a fixed density and finite binding energy is solved explicitly. A direct variation of the resulting Hartree-Fock energy with respect to the additional variational parameters introduced is carried out numerically and results reminiscent of a gas-to-liquid phase transition are found.

NUCLEAR STRUCTURE plane-wave Hartree-Fock; model calculation; nuclear matter.

The WKB approximation, in conjunction with the Poisson sum rule, is proposed as an alternative to Hartree-Fock for self-consistent determination of spatial density and energy. To illustrate, self-consistent WKB and extended Thomas-Fermi calculations are performed with a Skyrme-type interaction in a model one-dimensional nucleus.

NUCLEAR STRUCTURE Semiclassical calculations of model nucleus.

We show that by exploiting the resonance pole, one can give an unambiguous definition for the amplitude or wave function of a resonance in a bound state. The amplitude is of the standard form of vertex over on-shell energy denominator, but not subject to normalization constraints.

NUCLEAR STRUCTURE Definition for the wave function of a resonance in a bound state.

$\alpha$ particle spectroscopic factors have been calculated in the $f_{\frac{5}{2^{\prime }}}{p}_{\frac{3}{2^{\prime }}}{p}_{\frac{1}{2}}$ shell model space for transitions from the Ni isotopes to states in ${}_{}{}^{62,64,66,68}{}_{}{}^{}\mathrm{Zn}$. The Zn ground states are found to be described well by weak-coupling ${}_{}{}^{60}{}_{}{}^{}\mathrm{Z}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ to the corresponding Ni ground state.

NUCLEAR STRUCTURE Calculated $\alpha$ spectroscopic factors in shell model for even Ni+$\alpha$→Zn, compared with Ni(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$,$d$)Zn $S$ values.

A microscopic justification of the experimental observation of shape coexistence in ${}_{}{}^{151}{}_{}{}^{}\mathrm{Gd}$ is given. The potential energy as a function of nuclear deformation in $\beta -\gamma$ space is calculated. The Hartree-Bogoliubov method is used with the usual pairing-plus-quadrupole schematic interaction. The location of the potential minimum is strongly dependent on which single particle state the odd neutron occupies. Three distinct nuclear shapes are predicted in agreement with the data. The stability of these shapes is tested by a dynamic calculation.

NUCLEAR STRUCTURE ${}_{}{}^{151}{}_{}{}^{}\mathrm{Gd}$; calculated potential energy of shape; calculated shape stability.

Simple wave functions for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ from Gerace and Green and for ${}_{}{}^{42,44}{}_{}{}^{}\mathrm{Ca}$ derived from ($d$,$p$) data give a remarkably good fit to recently measured $E0\mathrm{}$ matrix elements in ${}_{}{}^{40,42,44}{}_{}{}^{}\mathrm{Ca}$.

NUCLEAR STRUCTURE ${}_{}{}^{40,42,44}{}_{}{}^{}\mathrm{Ca}$. Calculated $E0\mathrm{}$ matrix elements in the three-component model.