The ${}^{173}$Yb${(}^{24}$Mg,$5n)$ reaction at $E$${(}^{24}$Mg) = 134.5 MeV with a gold-backed target was used to populate high-angular momentum states in ${}^{192}$Pb. Resulting $\gamma$ rays were detected with Gammasphere located at the 88-Inch Cyclotron. A discrete transition of energy $E_{\gamma }$ = 2057.7(6) keV has been identified in the depopulation the yrast superdeformed (SD) band in ${}^{192}$Pb. This transition has been tentatively placed in the level scheme based on coincidence relationships. Thus, the excitation energy of the SD level populated by the 262-keV in-band transition is tentatively assigned $E_x$ = 4.572(1) MeV. Confidence limits are discussed. Other transitions in coincidence with the SD band and general features of the band and its decay are also presented. In particular, we confirm that the ${\mathcal{J}}^{\mathrm{}\left(2\right)\mathrm{}}$ of the SD band decreases by $\approx 13\%$ at the lowest frequency. Also, by comparing the masses of the SD ground states in ${}^{192,194}$Pb to liquid drop model expectations and to each other we have been able to confirm enhanced stability for $N=112\mathrm{}$ at superdeformation.

A nuclear resonance fluorescence (NRF) study was performed on the heavy deformed nucleus ${}^{175}$Lu. We observe the beginning of a rotational band built on the coupling of the unpaired proton to the $K^{\pi }{=0\mathrm{}}^{-}$ octupole vibration in the neighboring nucleus ${}^{174}$Yb. The dipole strength distribution is also discussed in terms of the scissors mode.

In a recent experiment performed with the EUROGAM II γ-ray spectrometer three superdeformed (SD) bands have been established in ${}^{153}\mathrm{Ho}.$ The properties of these bands are discussed in terms of single-particle proton excitations and are compared with respect to the SD magic nucleus ${}^{152}\mathrm{Dy}.$ These results represent the first observation of SD structures in a holmium nucleus and provide further information on the proton orbitals lying above the $Z=66\mathrm{}$ shell gap.

The reaction ${}^{58}$Ni${(}^{28}$Si,$2n\gamma )$ at 90 MeV incident energy has been used to populate the $N=Z$ nucleus ${}^{84}$Mo. The GASP array was used together with the ISIS Silicon ball, which allowed a subtraction of the charged particle channels in the γ-γ coincidences. The only known transition $2_1^{+}\to 0_1^{+}$ of 443.8 keV in ${}^{84}$Mo has been found in coincidence with a γ ray of 673.5±0.4 keV which was assigned as the second ${(4\mathrm{}}_1^{+}\to 2_1^{+})$ yrast transition. The behavior of the resulting yrast line indicates that ${}^{84}$Mo is a transitional nucleus. The correlation between the excitation energies of the 2${}_1^{+}$ and 4${}_1^{+}$ levels of the $N=Z$ nuclei reveals a systematic deviation from the average behavior defined by all collective even-even nuclei.

The nucleus ${}^{168}\mathrm{Y}\mathrm{b},$ and its near neighbors, have been studied at the very highest angular momenta using the full Gammasphere array. The experiment was performed in order to search for evidence for the existence of hyperdeformed states, which have predicted nuclear axis ratios of $\approx$3:1. After exhaustive searching for both discrete and continuum γ rays associated with a hyperdeformed shape, using a wide variety of different analysis techniques, no evidence for the existence of hyperdeformation has been found. This search of unprecedented sensitivity has been carried out with the full Gammasphere, and was performed on arguably the best candidate nucleus. A maximum achievable observational limit of $\approx 0.02\%$ of the ${}^{168}\mathrm{Yb}$ channel has been calculated for this particular experiment, using Monte Carlo simulations of the response of Gammasphere.

The scaling properties of the exact wave functions in the two-level pairing model are studied and a well-defined limit, when the number of pairs goes to infinity, is found. An approximate method for obtaining the scaled wave functions is discussed. Well-known methods for relating finite-difference equations with differential ones are used, together with a semiclassical expansion. The approximate results obtained agree well with the exact ones. A comparison with the time-dependent Hartree-Fock approach is also done.

We calculate breathing-mode energies in the scaling model for several parameter sets that are under discussion in nuclear relativistic mean-field theory. The relativistic Hartree approximation is used together with a schematic approach for the surface incompressibility. Empirical data can only be reproduced reasonably with parameter sets that lead to a nuclear matter compressibility modulus not higher than 230 MeV.

The nuclear superdeformed rotational bands in the $A\sim 190$ region were systematically analyzed by using the Harris two-parameter formula and the ab expression. Similar to the situation in normally deformed nuclei, there exists obvious and systematic deviation of the Harris formula from the experiment. In contrast, the prediction of the $\mathrm{ab}$ formula is very close to the experiment, and may be conveniently used for the description of both normally deformed and superdeformed bands.

A study of low-lying magnetic and electric dipole excitations is carried out in ${}^{166,168}\mathrm{Er},$ ${}^{172,174}\mathrm{Yb},$ and ${}^{178}\mathrm{Hf}$ within the quasiparticle-phonon nuclear model with the wave functions consisting of one- and two-phonon terms. It is shown that computed $M1\mathrm{}$ strength below 4 MeV in these nuclei is much stronger fragmented than in Gd and Dy isotopes in agreement with the relevant experimental observation. The scissors state is strongly fragmented and the overlapping between the scissors state and any $1^{+}$ state is less than 0.1. The fragmentation of the one-phonon $1^{+}$ states, as a rule, is stronger than the fragmentation of the one-phonon states with $K^{\pi }{=0\mathrm{}}^{-}$ and $1^{-}.$ The resulting $M1\mathrm{}$ and $E1\mathrm{}$ spectra are compared with available experimental data. The calculated $M1\mathrm{}$ and $E1\mathrm{}$ strengths summed in the energy range 2–4 MeV are in agreement with the relevant experimental data.

We use a 4ħΩ shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the ${}^{10}{\mathrm{C}\to }^{10}\mathrm{B}$ superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence of $T=1\mathrm{}$ partial waves. Our results suggest the isospin-mixing correction ${\delta }_C\approx 0.1\%,$ which is compatible with previous calculations. The correction obtained in those calculations, performed in a 0ħΩ space, was dominated by deviation from unity of the radial overlap between the converted proton and the corresponding neutron. In the present calculation this effect is accommodated by the large model space. The obtained ${\delta }_C$ correction is about a factor of 4 too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.

The ground state energy of a six-neutron drop is computed with variational and Green’s function Monte Carlo methods using the Argonne $v_{18}$ two-nucleon and the Urbana three-nucleon potentials. Combined with earlier results from investigations of the drops ${}^{8}n$ and ${}^{7}n,$ this energy gives a $1p$-shell pairing energy of $(1.8\mathrm{}\pm 0.4)\mathrm{MeV}.$ The generalized Skyrme effective interaction discussed in the earlier work is applied to these nuclei by calculating, for the open-shell drops ${}^{7}n$ and ${}^{6}n,$ the matrix elements of the Skyrme $t$ matrix directly for the states involved. The pairing energy obtained is 1.50 MeV, in reasonable agreement with the accurate calculations.

Elementary demonstrations of the three-body Efimov effect are provided for several models involving a light particle and two heavy ones, and differing by the nature of the two-body (local or nonlocal) potentials which bind at zero energy the light particle to each of the heavy ones. The proofs rely on Born-Oppenheimer approximations, which are actually projections of the Hamiltonian into suitable subspaces, and they use the correct reduced mass. A numerical estimate of the long-range potential responsible for the accumulation of Efimov bound states is obtained through Padé approximants.

The details of a recent experimental study of the ${}^2\mathrm{H}(p\to ,\gamma {)}^3$He and the ${}^1\mathrm{H}(d\to ,\gamma {)}^3$He reactions for beam energies below 80 keV are discussed. In this study, both polarized and unpolarized incident beams were used to measure the cross section $\sigma (\theta ,E)$, the astrophysical $S$ factor $S(\theta ,E)$, the vector analyzing power $A_y(\theta ,E)$, and the tensor analyzing power $T_{20}\left(\theta \right)$. In addition, the $\gamma$-ray linear polarization $P_{\gamma }\left(\theta \right)$ was measured for an unpolarized incident beam. The experimental details of these measurements are discussed and the data are analyzed to obtain the amplitudes and phases of the contributing transition-matrix elements. The results of our measurements are compared with recent ab initio three-body theoretical calculations. This comparison reveals the large sensitivity of the polarization observables, especially the vector analyzing power ${(A}_y)$, to the presence of meson-exchange current effects and indicates the need for further study. The tensor analyzing power data $\left[T_{20}\right(\theta )$] are used to extract a value of the asymptotic $D$- to $S$-state ratio, $\eta$, for ${}^3$He.

Evaporation residue excitation functions of the reaction ${}^{19}$F + ${}^{93}$Nb $\to$ ${}^{112}$Sn${}^{*}$, in the bombarding energy range between 54 and 95 MeV, have been measured using the recoil catcher technique. Energy spectra, angular distributions, and correlations between angular anisotropy and ejectile energy of evaporated protons and alpha particles have been measured for the above system at 73 and 95 MeV bombarding energies. The experimental data are compared with the predictions of the statistical model code PACE2 making use of two different level density formalisms. The level density parameters derived from the proton and alpha spectra are presented. The angular-anisotropy ejectile-energy correlations of the alpha particles show a peak in the variation of the anisotropy with the ejectile energy in the subevaporation barrier range. The sensitivity of the angular-anisotropy ejectile-energy correlations to the statistical model parameters is discussed.

The fivefold differential cross section of the reaction ${}^{26}\mathrm{Mg}{(e,e}^{\prime }c)$ was measured for transferred momenta of 0.35 and $0.54{\mathrm{fm}}^{\mathrm{-}1}$ and emitted particle angles from $-10°$ to 270° with respect to the transferred-momentum direction. Angular correlation functions for the emitted ${\alpha }_0$ were obtained from the data. A model-independent analysis allowed us to obtain the $E0,$ $E1,$ and $E2\mathrm{}$ multipole components of the ${}^{26}\mathrm{Mg}{(e,e}^{\prime }{\alpha }_0{)}^{22}\mathrm{Ne}$ cross section, between 14 and 26 MeV of excitation energy. The $E1\mathrm{}$ component shows a bump around 16.5 MeV, associated with the $T_{<}$ isospin component of the giant dipole resonance. The evaluated strengths associated with the ${\alpha }_0$ decay channel, presented in percentage of the respective energy-weighted sum rules are 0.45(7)% for $E1,$ 1.4(3)% for $E2,$ and 0.2(1)% for $E0.\mathrm{}$

Asymmetries $A_y$ for ${\pi }^{+}$ and ${\pi }^{-}$ elastic scattering from polarized ${}^3$He were measured at incident energies passing through the $\pi$ nucleon $P_{33},$ or $\Delta$(1232), resonance. The data were taken at the Clinton P. Anderson Meson Physics Facility using the high-energy pion channel $P^3$ and a large acceptance spectrometer to detect the scattered pions. The polarized ${}^3$He target, originally developed at TRIUMF, was modified for these experiments by the addition of diode lasers. Completely unexpected negative asymmetries were observed at and below the resonance in ${\pi }^{+}$ scattering near $50°$–60$°$, which cannot be reproduced by multiple scattering theory and Faddeev wave functions. A hybrid model, which adds a $\Delta$-neutron spin-spin interaction term to the conventional calculations, provides a good description of the ${\pi }^{+}$ data. For ${\pi }^{-}$ scattering this term predicts a negligible effect on $A_y$ and the data do not show the anomalous $A_y$ seen with ${\pi }^{+}$.

A canonical ensemble model is used to describe a caloric curve of the nuclear liquid-gas phase transition. Allowing a discontinuity in the freeze-out density from one spinodal density to another for a given initial temperature, the nuclear liquid-gas phase transition can be described as first order. Averaging over various freeze-out densities of all possible initial temperatures for a given total reaction energy, the first order characteristics of the liquid-gas phase transition is smeared out to a smooth transition. Two experiments, one at low energy and one at high energy, show different caloric behaviors and are discussed.

Competition among particle evaporation, temperature gradient, and flow is investigated in a phenomenological manner, based on a simultaneous analysis of quantum statistical correlations and momentum distributions for a nonrelativistic, spherically symmetric, three-dimensionally expanding, finite source. The parameters of the model emission function are constrained by fits to neutron and proton momentum distributions and correlation functions in intermediate-energy heavy-ion collisions. The temperature gradient is related to the momentum dependence of the radius parameters of the two-particle correlation function, as well as to the momentum-dependent temperature parameter of the single particle spectrum, while a long duration of particle evaporation is found to be responsible for the low relative momentum behavior of the two-particle correlations.

We consider deuteron formation in hot and dense nuclear matter close to equilibrium and evaluate the lifetime of the deuteron fluctuations within the linear response theory. To this end we derive a generalized linear Boltzmann equation where the collision integral is related to equilibrium correlation functions. In this framework we then utilize finite temperature Green functions to evaluate the collision integrals. The elementary reaction cross section is evaluated within the Faddeev approach that is suitably modified to reflect the properties of the surrounding hot and dense matter.

It is suggested that, contrary to previous proposals, the properties of the ${\frac{3}{2}}^{+}$ levels of ${}^5\mathrm{He}$ and ${}^5\mathrm{Li}$ may be understood as easily from the conventional $R$-matrix parameters as from the complex-energy poles of the $S$ matrix.