The productions of thorium and uranium are key ingredients in $r$-process nucleo-cosmochronology. With the combination of improved nuclear and stellar data, we have made a detailed investigation of the $r$-process abundance pattern in the very metal-poor halo stars based on the classical $r$-process approach. It is found that the results are almost independent of specified simulations to observed abundances. The influence from nuclear mass uncertainties on a Th/U chronometer can approach 2 Gyr. Moreover, the ages of the metal-poor stars HE $1523-0901$, CS $31082-001$, and BD $+{17}^{°}3248$ are determined as $11.8\pm 3.7$, $13.5\pm 2.9$, and $10.9\pm 2.9$ Gyr, respectively. The results can serve as an independent check for age estimates of the Universe.

The computation of radiative energy loss in a finite-size QCD medium with dynamical constituents is a key ingredient for obtaining reliable predictions for jet quenching in ultrarelativistic heavy-ion collisions. We here present a theoretical formalism for the calculation of the first order in opacity radiative energy loss of a quark jet traveling through a finite-size dynamical QCD medium. We show that, while each individual contribution to the energy loss is infrared divergent, the divergence is naturally regulated once all diagrams are taken into account. Finite-size effects are shown to induce a nonlinear path-length dependence of the energy loss, recovering both the incoherent Gunion-Bertsch limit, as well as destructive Landau-Pomeanchuk-Migdal limit. Finally, our results suggest a remarkably simple general mapping between energy-loss expressions for static and dynamical QCD media.

Three-nucleon scattering equations with irreducible three-nucleon force are solved in momentum-space. The Coulomb interaction between the two protons is included using the method of screening and renormalization. The need for the renormalization of the scattering amplitudes is demonstrated numerically. The Coulomb and Urbana IX three-nucleon force effects on the observables of elastic proton-deuteron scattering and breakup are studied.

We construct a simple two-phase equation of state intended to resemble that of compressed baryon-rich matter and then introduce a gradient term in the compressional energy density to take account of finite-range effects in nonuniform configurations. With this model we study the interface between the two coexisting phases and obtain estimates for the associated interface tension. Subsequently, we incorporate the finite-range equation of state into ideal or viscous fluid dynamics and derive the collective dispersion relation for the mechanically unstable modes of bulk matter in the spinodal region of the thermodynamic phase diagram. Combining these results with time scales extracted from existing dynamical transport simulations, we discuss the prospects for spinodal phase separation to occur in nuclear collisions. We argue that these can be optimized by a careful tuning of the collision energy to maximize the time spent by the bulk of the system inside the mechanically unstable spinodal region of the phase diagram. Our specific numerical estimates suggest cautious optimism that this phenomenon may in fact occur, though a full dynamical simulation is needed for a detailed assessment.

Developments and applications are presented of an algebraic version of Bohr's collective model. Illustrative examples show that fully converged calculations can be performed quickly and easily for a large range of Hamiltonians. As a result, the Bohr model becomes an effective tool in the analysis of experimental data. The examples are chosen both to confirm the reliability of the algebraic collective model and to show the diversity of results that can be obtained by its use. The focus of the paper is to facilitate identification of the limitations of the Bohr model with a view to developing more realistic, computationally tractable models.

The three-dimensional wave function for a sharply cut-off Coulomb potential is analytically derived. The asymptotic form of the related scattering amplitude reveals a failure of the standard renormalization factor which is believed to be generally valid for any type of screening.

By measuring the ${}^{31}\mathrm{P}({}^3\mathrm{He},t){}^{31}\mathrm{S}$, ${}^{31}\mathrm{P}({}^3\mathrm{He},t){}^{31}\mathrm{S}{}^{*}(p){}^{30}\mathrm{P}$, and ${}^{32}\mathrm{S}(d,t){}^{31}\mathrm{S}$ reactions, the level scheme of ${}^{31}\mathrm{S}$ has been refined and extended up to $E_x=9.5$ MeV. A total of 17 new levels, and 5 tentative new levels, have been measured. In addition, 5 tentatively known levels have been confirmed. The uncertainties in the excitation energies of many known ${}^{31}\mathrm{S}$ levels have been reduced substantially. Spin constraints have been made for 8 proton-unbound levels by measuring 18 triton-proton angular correlations from the ${}^{31}\mathrm{P}({}^3\mathrm{He},t){}^{31}\mathrm{S}{}^{*}(p){}^{30}\mathrm{P}$ reaction. Finite proton-decay branching ratios (including discrimination between decays to the ground state and first two excited states of ${}^{30}\mathrm{P}$) have been measured for 38 levels, and upper limits have been set for 3 additional levels. The lowest isospin $T=3/2$ level has been observed, and candidates for the second and third $T=3/2$ levels have been identified. The new experimental information on ${}^{30}\mathrm{P}+p$ resonance parameters has been used together with data from previous measurements to calculate the thermonuclear, resonant ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate over three orders of magnitude in temperature: $0.01<T<10$ GK. Good agreement is found with estimates based on Hauser-Feshbach statistical models over the range $0.08<T<10$ GK, but differences are found with rates previously estimated using the experimental information at hand.

The problem of how to compute accurately and efficiently the sign of the overlap between two general Hartree-Fock-Bogoliubov (HFB) wave functions is addressed. The results obtained can easily be extrapolated to the evaluation of the sign of the trace of a density operator exponential of one body operators.

We derive the space-time distribution of energy and momentum deposited by a fast parton traversing a weakly coupled quark-gluon plasma by treating the fast parton as the source of an external color field perturbing the medium. We then use our result as a source term for the linearized hydrodynamical equations of the medium. We show that the solution contains a sonic Mach cone and a dissipative wake if the parton moves at a supersonic speed.

We discuss the least-squares and linear-regression methods, which are relevant for a reliable determination of good nuclear-mass-model parameter sets and their errors. In this perspective, we define exact and inaccurate models and point out differences in using the standard error analyses for them. As an illustration, we use simple analytic models for nuclear binding energies and study the validity and errors of models’ parameters and uncertainties of its mass predictions. In particular, we show explicitly the influence of mass-number-dependent weights on uncertainties of liquid-drop global parameters.

The structure of high-spin and nonyrast states of the transfermium nucleus ${}^{250}\mathrm{Fm}$ has been studied in detail. The isomeric nature of a two-quasiparticle excitation has been exploited in order to obtain spectroscopic data of exceptional quality. The data allow the configuration of an isomer first discovered over 30 years ago to be deduced, and provide an unambiguous determination of the location of neutron single-particle states in a very heavy nucleus. A comparison to the known two-quasiparticle structure of ${}^{254,252}\mathrm{No}$ confirms the existence of the deformed shell gaps at $N=152$ and $Z=100$.

On the basis of the kinetic equation with self-consistent relativistic mean fields acting on baryons and antibaryons, we study dynamical response of the nucleus to an antiproton implanted in its interior. By solving numerically the time-dependent Vlasov equation, we show that the compressed state is formed on a rather short time scale of about 4–10 fm/c. This justifies the assumption, that the antiproton annihilation may happen in the compressed nuclear environment. The evolution of the nucleus after antiproton annihilation is described by the same kinetic equation including collision terms. We show, that nucleon kinetic energy spectra and the total invariant mass distributions of produced mesons are quite sensitive observables to the antiproton annihilation in the compressed nucleus.

We argue that the ratio of cross sections of quasielastic electron scattering for heavy and light nuclei at x>1 and ${\mathit{Q}}^2$>1 (GeV/c${)}^2$ should exhibit simple scaling relations which are ultimately expressed through the ratio of the light-cone nucleon distributions in nuclei. We extract these cross section ratios from existing data in a practically model independent way. The results are found to be in reasonable agreement with our x-scaling relations for the region of 2>x≥1.4 where the contribution of two-nucleon short-range correlations are expected to dominate. The ratios exhibit scaling in the light-cone fraction, α, of the struck nucleon for the range 2>x≥0.9. The α scaling is in agreement with the expectations of the light-cone quantum mechanics of nuclei, providing further evidence for the dominance of short-range correlations in nuclei at k>0.3 GeV/c. An extension of this analysis to the interpretation of color transparency experiments is discussed.

A unified shell-model description of nuclear deformation valid throughout the periodic table is presented. Microscopic calculations for the Zr and Mo isotopes are carried out in the frameworks of the shell model and the Hartree-Fock-Bogoliubov method, respectively, to study the shape transition in these nuclei. It is shown that deformation is produced by the isoscalar component of the neutron-proton ($n-p$) interaction in this region, as in the lighter ($2s$,$1d$)-shell region. Deformation sets in when the $T=0\mathrm{}$ $n-p$ interaction dominates over the sphericity-favoring pairing interaction between $T=1\mathrm{}$ pairs of nucleons. When shell effects are important, as for the light and medium-weight regions mentioned above, the simultaneous occupation of neutrons and protons of spin-orbit "partner" orbitals plays a crucial role in determining the onset of deformation. However, their effect is probably less important in the rare-earth and transuranic regions due to the rapid accumulation of single-particle orbitals.

NUCLEAR STRUCTURE Microscopic description of nuclear deformation; shell-model calculations of ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{98}{}_{}{}^{}\mathrm{Zr}$, and ${}_{}{}^{100}{}_{}{}^{}\mathrm{Zr}$; HFB calculations of ${}_{}{}^{98}{}_{}{}^{}\mathrm{Mo}$-${}_{}{}^{110}{}_{}{}^{}\mathrm{Mo}$; discussion of light and heavy deformed nuclei; relation to interacting boson approximation.

The energy spectra of protons and light nuclei produced by the interaction of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ projectiles with Al and U targets have been investigated at incident energies ranging from 0.25 to 2.1 GeV per nucleon. Single fragment inclusive spectra have been obtained at angles between 25° and 150°, in the energy range from 30 to 150 MeV/nucleon. The multiplicity of intermediate and high energy charged particles was determined in coincidence with the measured fragments. In a separate study, fragment spectra were obtained in the evaporation energy range from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ bombardment of uranium. We observe structureless, exponentially decaying spectra throughout the range of studied fragment masses. There is evidence for two major classes of fragments; one with emission at intermediate temperature from a system moving slowly in the lab frame, and the other with high temperature emission from a system propagating at a velocity intermediate between target and projectile. The high energy proton spectra are fairly well reproduced by a nuclear fireball model based on simple geometrical, kinematical, and statistical assumptions. Light cluster emission is also discussed in the framework of statistical models.

NUCLEAR REACTIONS $\mathrm{U}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},X)$, $E=250\mathrm{}$ MeV/nucl.; $U({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},X)$, $U(\alpha ,X)$ $E=400\mathrm{}$ MeV/nucl.; $\mathrm{U}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},X)$, $\mathrm{Al}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},X)$, $E=2.1\mathrm{}$ GeV/nucl.; measured $\sigma (E,\theta )$, $X=p,d,t,{}_{}{}^3{}_{}{}^{}\mathrm{He},{}_{}{}^4{}_{}{}^{}\mathrm{He}$. $\mathrm{U}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},X)$, $U(\alpha ,X)$, $E=400\mathrm{}$ MeV/nucl.; $U({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},X)$, $E=2.1\mathrm{}$ GeV/nucl.; measured $\sigma (E,\theta )$, Li to O. $\mathrm{U}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},X)$, $U({}_{}{}^{12}{}_{}{}^{}\mathrm{C},X)$, $E=2.1\mathrm{}$ GeV/nucl.; measured $\sigma (E,90°)$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ to B. Nuclear fireballs, coalescence, thermodynamics of light nuclei production.