The theory of the electromagnetic enhancement of nuclear beta decay, previously carried out in Coulomb gauge, is reformulated in electric-field gauge. Final results for the transition probability are identical in the two gauges, but significant differences appear in the two formulations. Whereas field interactions in Coulomb gauge arise from an intimate mixing of nuclear and decay-electron contributions, the entire effect is associated with the beta particle in electric-field gauge. This has the advantage that it is not necessary to assign field-interacting nuclear wave functions in electricfield gauge. The results are a demonstration that physical interpretations can be gauge dependent, even though measurable predictions are gauge invariant.

The ground-state quadrupole moments of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$, ${}_{}{}^{163}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{191}{}_{}{}^{}\mathrm{Ir}$, and ${}_{}{}^{193}{}_{}{}^{}\mathrm{Ir}$ were determined by measuring the quadrupole hyperfine-splitting energies of muonic $M$ x rays. The results are $Q=0.903\mathrm{}\left(10\right)\mathrm{}e$ b for ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$, $Q=2.412\mathrm{}\left(21\right)\mathrm{} e$ b for ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$, $Q=1.432\mathrm{}\left(8\right)\mathrm{} e$ b for ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$, $Q=2.648\mathrm{}\left(21\right)\mathrm{} e$ b for ${}_{}{}^{163}{}_{}{}^{}\mathrm{Dy}$, $Q=3,565\mathrm{}\left(29\right)\mathrm{} e$ b for ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$, $Q=3.365\mathrm{}\left(29\right)\mathrm{} e$ b for ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$, $Q=3.793\mathrm{}\left(33\right)\mathrm{} e$ b for ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$, $Q=0.816\mathrm{}\left(9\right)\mathrm{} e$ b for ${}_{}{}^{191}{}_{}{}^{}\mathrm{Ir}$, and $Q=0.751\mathrm{}\left(9\right)\mathrm{} e$ b for ${}_{}{}^{193}{}_{}{}^{}\mathrm{Ir}$. The present quadrupole moments, compared with values obtained from electronic-atom hyperfine measurements, show that the Sternheimer correction factors used in the rare-earth electronic-atom analysis are unreliable. Systematics of deformation parameters ${\beta }_2$ calculated from the present quadrupole moments for odd-$A$ nuclei, and from $B\left(E2\right)$ values of Coulomb excitation measurements for even-$A$ nuclei, also indicate that the largest deformation change so far known exists between ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$ and ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$. Except at the onset of nuclear deformation, the deformation parameters of the odd-$A$ nuclei are quite consistent with those of the even-$A$ neighbors.

Calculations within the framework of the neutron-proton interacting boson model with configuration mixing have been tested using data acquired from in-beam and beta decay experiments. The ($\mathrm{n},{\mathrm{n}}^{\prime }\gamma$) reaction on enriched targets of ${}_{}{}^{98}{}_{}{}^{}\mathrm{Mo}$ has been used to identify 28 levels of $J^{\pi }\lesssim 6$ up to 3212 keV in ${}_{}{}^{98}{}_{}{}^{}\mathrm{Mo}$ Levels with $3\lesssim J^{\pi }\lesssim 6$ have been studied by $\gamma$-ray spectroscopy of ${}_{}{}^{98}{}_{}{}^{}\mathrm{Nb}_{}^m{}_{}{}^{}$ produced by enriched targets of ${}_{}{}^{98}{}_{}{}^{}\mathrm{Mo}$ subjected to 14-MeV neutrons. When neutron-proton interacting-boson-model calculations that mix $N_{\pi }=1\mathrm{}$, $N_v=3\mathrm{}$ with cross subshell proton pair excitations of the type $N_{\pi }=3\mathrm{}$, $N_v=3\mathrm{}$ are performed, we can account for all the level properties of ${}_{}{}^{98}{}_{}{}^{}\mathrm{Mo}$ up to 2100 keV.

A detailed study of very neutron deficient nuclei with $Z\simeq 40$ (Sr,Zr) and $N\simeq 40$ has been carried out. Total potential energy surfaces taking into account both quadrupole and hexadecapole deformation have been calculated for the Zr ($Z=40\mathrm{}$) nuclei, starting from the Nilsson model. Also oddmass nuclei have subsequently been studied when coupling the odd particle to the deformed even-even core. After extensive band mixing calculations for the ${}_{38}{}^{79}{}_{}{}^{}\mathrm{Sr}_{41}^{}{}_{}{}^{}$ nucleus, comparison to the existing experimental data [energy spectra for positive and negative parity ${\frac{5}{2}}^{+}$ [422] and ${\frac{3}{2}}^{-}$ [301] bands; static moments $\mu$, $Q$; mixing ratios $\delta \left(\frac{E2\mathrm{}}{M1\mathrm{}}\right)$ and branching ratios] has been carried out. We have also concentrated on the excited state properties of even-even Sr nuclei within the framework of the interacting boson model. A critical analysis of the interacting boson model parameters, as obtained from calculations in nearby nuclei, i.e., ${}_{34}{}^{}{}_{}{}^{}\mathrm{Se}$, ${}_{36}{}^{}{}_{}{}^{}\mathrm{Kr}$ is carried out, especially for the behavior of $\kappa$, ${\chi }_{\pi }$ and ${\chi }_v$.

[NUCLEAR STRUCTURE Total potential energy surface calculations for even-even Zr nuclei ($36\le N\le 60$). Band-mixing calculations for the adjacent odd-mass nucleus (${}_{38}{}^{79}{}_{}{}^{}\mathrm{Sr}_{41}^{}{}_{}{}^{}$). Band-state properties: [$\mu ,Q,\delta \left(\frac{E2\mathrm{}}{M1\mathrm{}}\right)$, branching ratios]. Excited states in even-even Sr nuclei with $40\le N\le 48$ in the interacting-boson model (IBA-2). Discussion of IBA-2 parameters. Calculation of quadrupole moments $Q\left(2_1^{+}\right)$, nuclear radii and isomer shifts.]

The fragmentation of isovector quadrupole transition strengths among the two isospin components is discussed in the framework of a schematic model.

The variable moment of inertia model has been generalized so as to be applicable to transitional and vibrational nuclei by requiring that the extended models reduce at low angular momentum, $J$, to the polynomial dependence which agrees with the data. This dictates the introduction of at least three-parameter generalized phenomenological models. Two such models, the generalized variable moment of inertia model and the variable anharmonic vibrator model, are described and then tested against known yrast band data. Except for strongly deformed nuclei, these models substantially improve the agreement with the data.

The finite-temperature Hartree-Fock-Bogoliubov cranking equations are solved for the $i_{\frac{13}{2}}$ model. For any temperature below $k{T}_c=0.2\mathrm{}$ MeV, rotations induce a sharp first-order phase transition. When statistical fluctuations in the pair gap $\Delta$ are included, the phase transition is smoothed out for $\frac{1}{2}{T}_c<T<\mathrm{}{T}_c$. The rotation-aligned $i_{\frac{13}{2}}$ pair is unaffected by temperatures up to 0.5 MeV. The finite-temperature violation of the zero-temperature Hartree-Fock-Bogoliubov relation $R^2=R$ is given by the quasiparticle number fluctuation.

Monopole and quadrupole charge distributions of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$ and ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$ were investigated by muonic atom $K$ and $L$ x-ray measurements. The model-independent Barrett charge radii $R_k$ and the isotope shift $\Delta R_k$ were measured, and the value of $\Delta 〈r^2〉=0.606\mathrm{}\left(18\right)\mathrm{}$ ${\mathrm{fm}}^2$ was deduced. This isotope shift is the largest known of all nuclear pairs. The isomer shift of the first excited state of ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$ is found to be close to zero, in contrast to the large isomer shifts observed in its neighbors: ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$. The quadrupole moments of the first excited states were determined as $Q^{151}\left({\frac{7}{2}}^{+}\right)=1.28\mathrm{}\left(2\right)\mathrm{} e$ b and $Q^{153}\left({\frac{7}{2}}^{+}\right)=0.44\mathrm{}\left(2\right)\mathrm{} e$ b. The value for ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$ and its ground-state quadrupole moment of $Q^{151}\left({\frac{5}{2}}^{+}\right)=0.90\mathrm{}\left(1\right)\mathrm{} e$ b reported previously are several times larger than the respective single particle units. This fact shows that a fair amount of collectivity is involved in the ${\frac{5}{2}}^{+}$ ground state and in the ${\frac{7}{2}}^{+}$ first excited state of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$.

The strength distribution of the isoscalar giant quadrupole resonance for actinide nuclei, obtained from photon-, electron-, and hadron-induced reactions, is analyzed in terms of a cranking model for the fragmentation of the giant quadrupole resonance. The role played by the low-lying $E2$ strength for the correct delineation of the giant quadrupole resonance parameters is presented.

Combining independent yields directly measured or calculated from the charge distribution, the Kr, Rb, Sr, Sn, Sb, Te, Xe, Cs, and Ba isotopic distributions were investigated for the 12-30-MeV bremsstrahlung-induced photofission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$. At the same bremsstrahlung end point energies the Rb, Sn, Sb, Te, I, and Xe isotopic distributions were studied for the photofission of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. For both fissioning systems the tin distributions were significantly broader than all other distributions. From the elemental yields the proton odd-even effects were calculated as a function of $Z$. They turned out to be almost zero.

Among the many challenging problems concerning the structure of the $L-S$ closed shell ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, the question of the origin of the $M1\mathrm{}$ strength still predominates. We address this problem specifically, investigating within the context of the shell model the influence of $\Delta$ excitations, core polarization, and meson exchange on $M1\mathrm{}$ transition rates. Although these mechanisms are usually responsible for quenching $M1\mathrm{}$ transitions, we present quantitative results indicating for the first time the possibility that $M1\mathrm{}$ transitions could be enhanced due to the above mechanisms.

At 800 MeV/c momentum, with optical potentials defined from K-nucleon phase shifts, distortion effects in the K-nucleus wave function can be approximated by a simple form that may be useful in analyses of more complicated kaon induced nuclear reactions.

A microscopic multi-$j$ shell calculation is performed to describe the structure of the ground states of the even Sm isotopes within the pairing plus quadrupole model and in the collective pair approximation. Agreement with the experimental data is found for both quadrupole deformation $\beta$ and for the diffusivity of the Fermi surface. The variation with the mass number of the structure of the proton and neutron collective pairs is discussed in connection with the increased role of the quadrupole-quadrupole interaction and of the Pauli principle.

In the context of the consistent $Q$ formalism of the interacting boson approximation, which contains only one essential parameter, denoted $\chi$, it is possible to investigate the limits of allowable boson numbers $N$ for well deformed nuclei. This is done by examining the agreement with experiment of certain $E2$ branching ratios as a function of $N$. The results show that, in general, the best agreement is obtained for $N\approx N_{\mathrm{IBA}}$, where $N_{\mathrm{IBA}}$ is the usual interacting boson approximation value defined as the sum of half the number of valence protons and neutrons; moreover, significant discrepancies with experiment are obtained if $N<\left(\frac{3}{4}\right)N_{\mathrm{IBA}}$. The effect of additional terms in the interacting boson approximation Hamiltonian is also investigated.

A simple method based on direct reaction theory is proposed to describe the subbarrier fusion of two heavy ions. Application of this method is exemplified by explaining the difference between fusion in the ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ + ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ system and in the ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ + ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$ system.

It is shown that as a consequence of angular localization in heavy-ion reactions, approximations to the nuclear potential shape may change the rotational excitation probabilities in a nontrivial way.

In a recent work, Mermaz interprets fluctuations found in a phase shift analysis of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha ,\alpha )$ elastic scattering angular distributions below 50 MeV incident energy as a manifestation of an underlying intermediate structure resonance phenomenon. We show that a precise description of the data can be obtained in the framework of the optical model, without introducing any fluctuating component in the $S$ matrix beyond that due to interference effects between the internal- and barrier-reflected components of the optical model amplitude. The optical model likewise provides a natural description of the complicated and rapid energy dependence of the data, without any need for fluctuations of the potential parameters with energy.

We examine the penetrability (or fusion cross section) in the influence of a favorable $Q$ value transfer channel. We found that the formula for the cross section cannot be expressed as that given by Broglia et al. Our result does support their idea that the transfer channel gives rise to a large enhancement to the sub-Coulomb heavy ion fusion cross section.

The $\frac{7}{2}\mathrm{}\left[523\right]\mathrm{}$ and $\frac{7}{2}\mathrm{}\left[404\right]\mathrm{}$ bands are observed in ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tm}$ to $I=\frac{61}{2}$ and $\frac{43}{2}$, respectively, well beyond the $i_{\frac{13}{2}}$ neutron backbend. Before the backbend, the $\frac{7}{2}\mathrm{}\left[523\right]\mathrm{}$ band exhibits large signature splitting, the $\frac{7}{2}\mathrm{}\left[404\right]\mathrm{}$ none, which is interpreted as resulting from the very different driving influences of the $K=\frac{7}{2}$, $h_{\frac{11}{2}}$, and $g_{\frac{7}{2}}$ orbits, respectively, on the core triaxiality. The $i_{\frac{13}{2}}$ neutron alignment changes the signaure splitting in each band as a result of its dominant driving force to positive values of $\gamma$. Measured $\frac{B(M1;I\to I-1)}{B(E2;I\to I-2)}$ values increase dramatically after the backbend, and this is explained in terms of calculated increases in the $M1\mathrm{}$ transition rates and decreases in the $E2\mathrm{}$ rates.

Cross sections for evaporation residue formation following complete fusion of ${}_{}{}^{81}{}_{}{}^{}\mathrm{Br}$+${}_{}{}^{90,94}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Mo}$, and ${}_{}{}^{104}{}_{}{}^{}\mathrm{Ru}$ and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$+${}_{}{}^{90,94}{}_{}{}^{}\mathrm{Zr}$ have been measured over a broad range of energies from far below to well above the classical Coulomb barrier. We observe large changes of slope and magnitude among the excitation functions for these systems at all energies. There are pronounced structural variations at sub-barrier energies, less rapid than expected increases in evaporation residue formation at near-barrier energies and declining evaporation residue formation as the systems become heavier at still higher energies.