$\gamma$ rays emitted in the radioactive decay of 15.2 day ${}_{}{}^{156}{}_{}{}^{}\mathrm{Eu}$ have been studied with large volume Ge(Li) detectors in both singles and coincidence modes. A total of 95 $\gamma$-ray transitions were observed in the ${}_{}{}^{156}{}_{}{}^{}\mathrm{Eu}$ decay and 84 of these are placed in the ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$ level scheme which consists of 26 excited states. Seven of these levels are assigned here for the first time. Many of the inconsistencies that have complicated the interpretation of previous work have been resolved in these studies. In particular, it has been possible in the extensive coincidence measurements to resolve several multiplets in the $\gamma$-ray spectrum and, therefore, to obtain accurate branching intensities for members of both the $\gamma$-vibrational band and two $K^{\pi }=0^{+}$ excited bands.

RADIOACTIVITY ${}_{}{}^{156}{}_{}{}^{}\mathrm{Eu}$ (from $n$ capture on ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$); measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coin; deduced $log\mathrm{ft}$. ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$ deduced levels, $J$, $\pi$, ICC. Enriched ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ target, Ge(Li) detectors.

The internal conversion coefficients (ICC) of 18 transitions in the decay of ${}_{}{}^{140}{}_{}{}^{}\mathrm{Xe}$ have been measured by the normalized electron-to-$\gamma$-ray ratio method using Si(Li) and Ge(Li) detectors. Mass-separated sources of ${}_{}{}^{140}{}_{}{}^{}\mathrm{Xe}$ were obtained from the TRISTAN on-line isotope separator facility. The ICC were used to deduce the multipolarities of the transitions. Tentative spin-parity assignments have been made for 14 levels in ${}_{}{}^{140}{}_{}{}^{}\mathrm{Cs}$ from consideration of the transition multipolarities and $log\mathrm{ft}$ values deduced from the results of a previous $\gamma$-ray decay study.

RADIOACTIVITY ${}_{}{}^{140}{}_{}{}^{}\mathrm{Xe}$ [from ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}\mathrm{}(n,f)\mathrm{}$]; measured $E_{\gamma }$, $I_{\gamma }$ for low-energy $\gamma \text{'}\mathrm{s}$, ce spectrum; Ge(Li) and Si(Li) detectors; deduced ICC, $I_{\beta }$, $log\mathrm{ft}$, $J^{\pi }$ for ${}_{}{}^{140}{}_{}{}^{}\mathrm{Cs}$ levels; mass-separated ${}_{}{}^{140}{}_{}{}^{}\mathrm{Xe}$ activity.

Directional correlations of $\gamma -\gamma$ cascades from polarized ${}_{}{}^{169,175}{}_{}{}^{}\mathrm{Yb}$ were measured and a difference technique used to search for time-reversal-invariance violating (TRIV) asymmetries. For the 198-110 keV cascade in ${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}$ a TRIV asymmetry ${\mathcal{a}}^{\mathrm{TRIV}}=(-18\mathrm{}\pm 15)\times {10}^{-4\mathrm{}}$ was determined, corresponding to a phase angle between the $E2\mathrm{}$ and $M1\mathrm{}$ multipole matrix elements of the 198 keV radiation given by $sin\eta =+0.15\mathrm{}\pm 0.12$ with $T$-odd components of the $E2\mathrm{}$ and $M1\mathrm{}$ matrix elements equal to + (1.8 ± 1.5) × ${10}^{-4\mathrm{}}$ and -(6.2 ± 5.0) × ${10}^{-3\mathrm{}}$ of the Weisskopf estimates, respectively. Hypothetical interpretation of TRIV as a result of state mixing is discussed, giving the expectation value of the TRIV part of the interaction Hamiltonian as +1.0 ± 0.8 keV. For the 283-114 keV cascade in ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}$, ${\mathcal{a}}^{\mathrm{TRIV}}=(+1.9\mathrm{}\pm 5.8)\times {10}^{-4\mathrm{}}$ was measured, with corresponding $\frac{M2\mathrm{}}{E1\mathrm{}}$ phase angle given by $sin\eta =-0.17\mathrm{}\pm 0.5$ and $T$-odd matrix elements equal to -0.05 ± 0.16 and + (2 ± 7) × ${10}^{-4\mathrm{}}$ Weisskopf units for the $M2\mathrm{}$ and $E1\mathrm{}$ components, respectively. Similar measurements on the 177-131 keV cascade in ${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}$ yielded uncertain results due in part to a large precessional perturbation. However, treatment of TRIV in the 283 keV $\gamma$ ray assumed due to state mixing is shown to result in the conclusion that a modestly sensitive measurement of the phase angle of the $E2\mathrm{}$ with respect to the $M1\mathrm{}$ matrix element would give a good test of the magnitude of the TRIV component of the relevant interaction potential.

RADIOACTIVITY ${}_{}{}^{169,175}{}_{}{}^{}\mathrm{Yb}$; $\gamma -\gamma$ directional correlations, time-reversal-symmetry tests; deduced mixing ratio phase angles, 198-, 177-, and 283-keV $\gamma$ rays; estimated $T$-odd component, Hamiltonian.

The spectrum of $\gamma$ rays following the $\beta$ decay of ${}_{}{}^{49}{}_{}{}^{}\mathrm{Cr}$ has been measured with a 65 ${\mathrm{cm}}^3$ Ge(Li) detector. $\beta$-decay branches to the following states in ${}_{}{}^{49}{}_{}{}^{}\mathrm{V}$ were observed $log\mathrm{ft}$ values in parentheses): ground state (5.6), 91 keV (4.9), 153 keV (4.7), 1514 keV (5.7), 1661 keV (6.0), 2182 keV (6.9), 2235 keV (6.6), and 2309 keV (7.1). $\beta$-decay branches to the last three states have not been previously reported. In contrast to an earlier $\beta$-decay experiment, $\beta$ branches to the 748 (3/$2^{+}$), 1021 (11/$2^{-}$), and 1140 (5/$2^{+}$) keV states were not observed.

RADIOACTIVITY ${}_{}{}^{49}{}_{}{}^{}\mathrm{Cr}$ [from ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}(\alpha ,n)$]; measured $E_{\gamma }$, $I_{\gamma }$; deduced $log\mathrm{ft}$. ${}_{}{}^{49}{}_{}{}^{}\mathrm{V}$ deduced levels, $J$, $\pi$. Enriched targets, Ge(Li) detector.

Nuclei of ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ and ${}_{}{}^{255}{}_{}{}^{}\mathrm{Fm}$ were oriented in single crystals of neodymium ethylsulfate at temperatures down to 11 mK. Orientation was detected by $\alpha$-particle angular distributions. The temperature dependences of these distributions were consistent with the lowest electronic states of these two actinide ions in the ethylsulfate lattice being similar to those of the corresponding lanthanide ions. Thus quadrupole orientation was observed in ${\mathrm{Am}}^{3+}$ ($5f^6$), as in ${\mathrm{Eu}}^{3+}$ ($4f^6$). In ${\mathrm{Fm}}^{3+}$ ($5f^{11}$) the orientation was magnetic and equatorial ($\mathrm{}\left|B\right|>\left|A\right|\mathrm{}$), as would be expected from the hyperfine interaction in ${\mathrm{Er}}^{3+}$ ($4f^{11}$). For ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ we report $P=-0.0033\mathrm{}\left(6\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and for ${}_{}{}^{255}{}_{}{}^{}\mathrm{Fm}$, $\mathrm{}\left|B\right|=0.035\mathrm{}\left(7\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The ${\mathrm{Am}}^{3+}$ data are consistent with an antishielding constant of ${\gamma }_{\infty }\approx {-10\mathrm{}}^2$, in good agreement with theory, and a shielding factor ${\sigma }_2=0.7\mathrm{}$, similar to the value for ${\mathrm{Eu}}^{3+}$. The nuclear results showed that the $s$ and $d$ $\alpha$-particle partial waves are in phase for the favored $\alpha$-decay branch in each case. The relative phase of the $g$ wave could not be determined.

RADIOACTIVITY ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$, ${}_{}{}^{255}{}_{}{}^{}\mathrm{Fm}$; measured $W(\theta ,\frac{1}{T})$, nuclear orientation; deduced hyperfine coupling constants, $\alpha$ partial wave phases.

We have assumed the $T=0\mathrm{} \mathrm{and} 1$ negative-parity quartets of levels in $A=14\mathrm{}$ nuclei, as well as the $T=1\mathrm{}$ negative-parity quartet in $A=16\mathrm{}$ nuclei, to represent pure configurations. Linear relationships between the energies of these groups of levels produce results which are consistent with the relevant part of the single-particle energy spectrum in this region. From the given $A=14\mathrm{}$ energy values conclusions are made concerning the low positive-parity levels in $A=15\mathrm{}$. Due consideration is given to the necessary Coulomb corrections in all the calculations.

NUCLEAR STRUCTURE $A=12\mathrm{}-16$; calculated Coulomb energies, single-particle energies. $A=16\mathrm{}$ negative-parity states and $A=15\mathrm{}$ positive-parity states; deduced level positions.

The diagrammatic expansion of the two-body density $\rho ({\overrightarrow{\mathrm{r}}}_1,{\overrightarrow{\mathrm{r}}}_2)$ in the nuclear ground state is given through second order in the reaction matrix. The second-order diagrams are grouped into sets and all diagrams of a given set have to be computed together in order to preserve its normalization $\int d^3{r}_1{d}^3{r}_2\rho ({\overrightarrow{\mathrm{r}}}_1,{\overrightarrow{\mathrm{r}}}_2)=1\mathrm{}$. Microscopic calculations of nuclear correlations have usually violated this normalization constraint.

A Coriolis-coupling model extended to include a residual pairing type interaction is applied to investigate the energy levels of low lying states of the odd nuclei of the $1g_{\frac{9}{2}}$ shell $73<A<\mathrm{}87\mathrm{}$. This deformed rotational treatment includes spectra of both parities originating from overlapping states of the $N=4\mathrm{}$ and $N=3\mathrm{}$ positive and negative parity shells. Single particle energy levels and wave functions throughout a shell are computed using spin-orbit and well-flattening parameters $C=-0.26\mathrm{}\hslash {\omega }_0$ and $D_{N=4,3\mathrm{}}=-0.040\mathrm{}\hslash {\omega }_0$ $-0.053\mathrm{}\hslash {\omega }_0$, respectively, the latter values being consistent with $d_{\frac{5}{2}}$ parentage states of ${}_{}{}^{79}{}_{}{}^{}\mathrm{Se}$ (positive parity) and $f_{\frac{5}{2}}$ states of ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$ (negative parity). Inclusion of an extracore pairing interaction primarily introduces a multiplicative effective overlap which serves as a quenching factor to the strength of off-diagonal Coriolis coupling terms. All parameters in the analysis are taken from available experimental considerations. The rotational constant $A$ and deformation $\beta$, in particular, are derived from the location of the first excited $2^{+}$ state of the neighboring even-even nucleus and its observed $E2\mathrm{}$ transition rate to the ground state. For each set of parameters both a single particle and a Coriolis coupling diagonalization are performed over an entire shell of 10 or 15 Nilsson states to obtain final negative or positive parity spectra and wave functions. The results of this essentially fixed parameter model are presented and compared with experimental determinations with which they are in substantial agreement. In general, the model favors a prolate description for the nuclei in this region. Energy excitation spectra are all in general agreement, and in particular: (a) ground state spins and lowest lying opposite parity spins are always correctly predicted; (b) many otherwise anomalous low lying and often ground state ${7/2}^{+}$, ${5/2}^{+}$ spins are well predicted. The systematic reproduction of experimental spectra provided by the model points to the validity of a statically deformed interpretation of the odd neutron nuclei of the $1g_{\frac{9}{2}}$ shell, in contrast to the purely spherical and vibrational approaches to which the region has been restricted in the past.

NUCLEAR STRUCTURE ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{75,77,79,81}{}_{}{}^{}\mathrm{Se}$, ${}_{}{}^{83,85}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$; calculated levels, $I$ $\pi$. Deformed Coriolis coupling treatment with pairing. Both parties.

A discussion is presented of the interaction between rotations and vibrations in nuclei, based on the generator coordinate method. As an example, a solvable model due to Moszkowski is studied. It is shown that the generator coordinate method describes adequately the dynamics of this type of motion, not only in the deformed zone, but also in the transition region, due to the softness of the system against deformations and to the Coriolis effect.

Utilizing the ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}({}_{}{}^3{}_{}{}^{}\mathrm{He},n)$ reaction the lowest $0^{+}$ $T=2\mathrm{}$ state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ has been located at 27.611 ± 0.020 MeV. The result agrees with earlier ($p,t$) measurements on ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$. The $T=2,1,0$ splitting of 2p-2h, $0^{+}$ states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is discussed.

NUCLEAR STRUCTURE ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; measured ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}({}_{}{}^3{}_{}{}^{}\mathrm{He},n)$; deduced $E_x$ of $J^{\pi }=0^{+}$, $T=2\mathrm{}$ state; isospin splitting of $0^{+}$ states discussed.

The phenomenological single-particle Hamiltonian of Meldner is rederived as a renormalized single-particle $K$ matrix and is used to calculate the propreties of ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ on the fission path from the ground state to scission into asymmetric fragments. Substantial radial density fluctuations or "bubble configurations" are observed as well as a displacement of the neutron center of mass relative to that of the protons. It is also found that the presence of a deep minimum and saddle near the touching point can be observed for one of the parameter sets of the interaction. The parameters of our deformation and atomic number independent model were obtained by fitting to the experimental properties of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and nuclear matter. The present results illustrate the importance of using a nonorthogonal two-oscillator basis as well as taking into account the properties of nuclear matter.

NUCLEAR STRUCTURE, FISSION ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$; calculated fission path, shape asymmetry, static total energy, single particle energies. Self-consistent Brueckner-Hartree-Fock method.

It has been shown that in the evaluation of the $M2\mathrm{}$ transition from the $J^{\pi }=\frac{11}{2}_{}^{-}{}_{\mathrm{}\left(1\right)\mathrm{}}{}^{}$ to the $J^{\pi }=\frac{7}{2}_{}^{+}{}_{\mathrm{}\left(1\right)\mathrm{}}{}^{}$ state in the odd-proton $N=82\mathrm{}$ isotones, the three-quasiparticle admixtures in the transition moment, are not negligible.

NUCLEAR STRUCTURE ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$; $B(M2;1\mathrm{}{h}_{\frac{11}{2}}\to 1g_{\frac{7}{2}})$, $B(E3;1\mathrm{}{h}_{\frac{11}{2}}\to 1d_{\frac{5}{2}})$ and the gyromagnetic ratio $g_{1h_{\frac{11}{2}}}$ Quasi-Tamm-Dancoff Approximation. Comparison theory experiment.

We comment on the present theoretical status of the distant-neighbor spacing distributions in view of recent experimental results. In particular, we stress that both the Gaussian orthogonal and the two-body random Hamiltonian ensembles predict essentially identical spacing distributions for the highly excited part of the spectrum; this is true also for the other available measures. Thus the statistical analysis of spectrum fluctuations does not inform us about the two-body or multibody nature of the interaction. We point out also that, when due attention is paid to the variation of level density with excitation, the fluctuation pattern observed in the slow-neutron domain is found to extend throughout the entire spectrum.

A total of 112 $\gamma$ rays of the reaction ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}(n,\gamma ){}_{}{}^{233}{}_{}{}^{}\mathrm{Th}$ have been observed with the Fribourg pair spectrometer in the energy range $2.48<\mathrm{}{E}_{\gamma }<4.8\mathrm{}$ MeV. The level scheme proposed in previous works has been extended. A value of 4786.35 ± 0.25 keV has been determined for the neutron binding energy in ${}_{}{}^{233}{}_{}{}^{}\mathrm{Th}$.

NUCLEAR REACTION ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}(n,\gamma )$, $E_n=th$; measured $E_{\gamma }$, $I_{\gamma }$; deduced $Q$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ deduced levels.

The $p,n$ reaction on targets of ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, and ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ has been studied to obtain the widths, reaction $Q$ values, and selected cross sections of the isobaric analog of the ground state of these targets. Widths obtained are, respectively, 116 ± 35, 175 ± 25, 192 ± 25, 235 ± 35, 257 ± 35, and 273 ± 30 keV assuming a Breit-Wigner line shape for the analog resonance. These results support the disagreement of previous $p,n$ measurements with $p,n\overline{p}$ measurements for the widths of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. Results are shown to be sensitive to choice of resonance line shape and provide a possible explanation for discrepancies between $p,n$ and $p,n\overline{p}$ measurements. The need for a more precise theoretical understanding of the structure of unbound analog resonances is indicated.

NUCLEAR REACTIONS ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{}{}^{206,207,208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}\mathrm{}(p,n)\mathrm{}$ $E=25.8\mathrm{}$ MeV measured widths of isobaric analog states.

Contrary to a claim by Rafelski and Klein, one cannot use nonrelativistic elastic heavy ion collisions to probe the large $q^2$ behavior of the photon propagator.

Absorption effects in $d+\alpha$ scattering are taken into account by a simple modification in the resonating-group formulation. It is shown that this modification results in the elimination of spurious resonances and leads to a satisfactory agreement with measured values for differential scattering and total reaction cross sections.

NUCLEAR SCATTERING $\alpha \mathrm{}(d,d)\mathrm{}$, $E=0\mathrm{}-22$ MeV; calculated phase shifts and and $\sigma \left(\theta \right)$. Resonating-group method with absorption.

The branching ratio of the $0^{+}$ state of ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ at 3788 keV for decay by $e^{+}{e}^{-}$ pair emission to the $0^{+}$ ground state is measured to be (2.7 ± 0.4) × ${10}^{-3\mathrm{}}$. Combining this branching ratio with the previously measured lifetime of the state leads to an $E0\mathrm{}$ matrix element of (0.054 ± 0.009) single particle units.

NUCLEAR STRUCTURE ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$; measured branching ratio $E0\mathrm{}$ decay 3788-keV level; deduced $E0\mathrm{}$ matrix element.

We used the Oak Ridge National Laboratory low-background $\gamma$-ray spectrometer in an attempt to measure the decay of ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}$. Less than 0.13 disintegration ${\min }^{-1\mathrm{}}$ was observed from a sample enriched in ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}$; this corresponds to a $t_{\frac{1}{2}}\ge 3.56\times {10}^{17}$ yr and a $log\mathrm{ft}$ value of ≥21.6.

RADIOACTIVITY ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}$ (from nature); measured $I_{\gamma }$ from ${}_{}{}^{96}{}_{}{}^{}\mathrm{Nb}$; set limit on specific activity and $t_{\frac{1}{2}}$.

Application of the multiconfiguration Hartree-Fock method to the exactly solvable Lipkin model is critically examined.