The half-diagonal two-body density matrix ${\rho }_{2h}({\mathbf{r}}_1,{\mathbf{r}}_2,{\mathbf{r}}_{1^{\prime }})$ is a key quantity in theoretical descriptions of nucleon knockout reactions at intermediate energies, due to its central role in treatments of the propagation and final-state interactions of ejected nucleons in the nuclear medium. This quantity is calculated for a simple model of the ground state of infinite symmetrical nuclear matter, based on a Jastrow-correlated wave function and a Fermi hypernetted-chain analysis. The dependence of ${\rho }_{2h}$ on the variables $r_{{11}^{\prime }}=|{\mathbf{r}}_1-{\mathbf{r}}_{1^{\prime }}|,$ $r_{12}=|{\mathbf{r}}_1-{\mathbf{r}}_2|,$ and the angle $\theta$ between ${\mathbf{r}}_1-{\mathbf{r}}_{1^{\prime }}$ and ${\mathbf{r}}_1-{\mathbf{r}}_2$ is investigated in some detail. Significant departures from ideal Fermi gas behavior in certain domains reflect the importance of short-range correlations and their interplay with statistical correlations. The quality of approximations to ${\rho }_{2h}$ proposed by Gersch et al., Rinat, and Silver is assessed by comparison with the Fermi hypernetted-chain results.

Elastic, inelastic, and transfer angular distributions were measured for ${}^{12}\mathrm{C}{+}^{208}\mathrm{Pb}$ in the energy range from 58.9 to 84.9 MeV. While the fission fragment angular distributions were measured over the energy range from 58.9 to 79 MeV, the residue cross sections after $2n$ evaporation from the compound nucleus ${(}^{220}\mathrm{Ra})$ were measured by $\alpha$ counting at 58.9, 60.9, and 62.9 MeV. Combining the above data with the ones from the literature, the fusion cross sections have been obtained. Quasielastic excitation function at $170°$ was also measured to obtain the fusion barrier distribution. Optical model analysis of the elastic scattering data, using both phenomenological and microscopic models, brought out the pronounced energy dependence of the optical potential at near barrier energies. A simultaneous description of the elastic and all the nonelastic channels was obtained from the coupled reaction channel (CRC) calculations using a consistent set of parameters at all the energies. The effective nucleus-nucleus real potential, obtained from CRC calculations, explained the observed energy dependence of the real part of the optical potential. Thus, the real potential used in these calculations with such a large number of constraints can be considered as the bare nucleus-nucleus potential.

An implementation of the calculation for the two-step cross sections of the theory of Nishioka, Weidenmüller, and Yoshida is described. Cross sections that excite a $2p-2h$ state are expressed in a J scheme, and a Yukawa interaction is assumed for the particle-hole pair creation. The Green’s function, which connects the one-step matrix element to the two-step one, is represented in r space. An interference effect among the amplitudes for the different intermediate states is examined by means of a spectroscopic amplitude. A strong interference appears for a certain configuration, and this is interpreted by a boson approximation. Microscopically calculated two-step cross sections for ${}^{208}\mathrm{Pb}{(p,p}^{\prime })$ reactions are averaged together with the true level density, which is based on the random matrix theory, to give a two-step cross section to the continuum energy region.

A new method is suggested for calculating the charge and mass distributions of quasifission products. The quasifission is treated within a transport model describing the evolution of a dinuclear system in charge (mass) asymmetry and the decay of this system along the internuclear distance. The calculated yields of these products are in agreement with recent experimental data for the hot fusion reactions leading to superheavy nuclei. The quasifission distributions in cold Pb-based fusion reactions are predicted.

We investigate the breakup of the one-neutron halo nuclei ${}^{11}\mathrm{Be}$ and ${}^{19}\mathrm{C}$ within a dynamical model of the continuum excitation of the projectile. The time evolution of the projectile in coordinate space is described by solving the three-dimensional time dependent Schrödinger equation, treating the projectile-target (both Coulomb and nuclear) interaction as a time dependent external perturbation. The pure Coulomb breakup dominates the relative energy spectra of the fragments in the peak region, while the nuclear breakup is important at higher relative energies. The coherent sum of the two contributions provides a good overall description of the experimental spectra. Cross sections of the first order perturbation theory are derived as a limit of our dynamical model. The dynamical effects are found to be of the order of $10\%–15\%$ for beam energies in the range of 60–80 MeV/nucleon. A comparison of our results with those of a post-form distorted wave Born approximation shows that the magnitudes of the higher order effects are dependent on the theoretical model.

A systematic study is performed of fully integrated particle multiplicities in central Au-Au and Pb-Pb collisions at beam momenta of $1.7A\hspace{0.5em}\mathrm{GeV}/c,\hspace{0.5em}11.6A\hspace{0.5em}\mathrm{GeV}/c$ (Au-Au), and $158A\hspace{0.5em}\mathrm{GeV}/c$ (Pb-Pb) by using a statistical-thermal model. The close similarity of the colliding systems makes it possible to study heavy ion collisions under definite initial conditions over a range of center-of-mass energies covering more than 1 order of magnitude. In order to further study the behavior of strangeness production, an updated study of Si-Au collisions at $14.6A\hspace{0.5em}\mathrm{GeV}$ is also presented. The data analysis has been performed with two completely independent numerical algorithms giving closely consistent results. We conclude that a thermal model description of particle multiplicities, with additional strangeness suppression, is possible for each energy. The degree of chemical equilibrium of strange particles and the relative production of strange quarks with respect to u and d quarks are higher than in $e^{+}{e}^{-},$ $pp,$ and $p\overline{p}$ collisions at comparable and even at lower energies. The behavior of strangeness production as a function of center-of-mass energy and colliding system is presented and discussed. The average energy per hadron in the comoving frame is close to 1 GeV per hadron despite the fact that the energy increases more than tenfold.

Charge-changing and fragment production cross sections have been obtained for interactions of a 600 MeV/nucleon neon beam in H, C, Al, Cu, Sn, Ta, and Pb targets. The H target results were obtained using a polyethylene target and subtracting the cross sections obtained with the carbon target. At 600 MeV/nucleon, the angular distributions of the fragments are strongly forward peaked, and consequently the spectra seen in the detectors with the largest angular acceptance—corresponding to a forward cone with half angle 7°—show obvious fragment peaks only for charges 5 through 9. No clear peaks are seen below charge 5 in the large-acceptance detectors, but spectra from detectors subtending smaller angular acceptances show peaks for all fragment species, and additional identifiable peaks from events with between two and four fragments in coincidence. Production cross sections for all fragment species are reported here and, where possible, compared to earlier measurements and to the predictions of three model calculations (Nucfrg2, Qmsfrg, and an empirical parametrization that is tuned for higher-mass beams). The cross sections for fragments of charge 5 and below have not been previously reported. Also, the charge-changing cross sections are compared to earlier measurements and to Nucfrg2 and the Bradt-Peters model.

Skyrme-Hartree-Fock-BCS calculations show that the nuclear mass data constrain the value of the isovector effective mass $M_v^{*}$ in the vicinity of the Fermi surface to lie in the range of $0.90M\pm 0.20M,$ M being the real nucleon mass. These rather large error bars imply uncertainties of up to 4 MeV in the mass extrapolations out to the neutron-drip line, but the corresponding uncertainties in the extrapolated neutron-separation energies $S_n,$ beta-decay energies $Q_{\beta },$ and nuclear level densities are too small to be significant for the r process of nucleosynthesis.

Li, Liou, Timmermans, and Gibson conclude in their paper [Phys. Rev. C 58, R1880 (1998)] that the effect of noncoplanarity in proton-proton bremsstrahlung is significant. To overcome the problems with kinematic singularities in the cross section, they recommend the use of the Harvard noncoplanar coordinate system in the analysis of data. We show that this coordinate system introduces other experimental problems. Alternatively, we propose to present data as the square of the invariant matrix elements, along with cross sections.

We respond to the Comment by Huisman and Kalantar-Nayestanaki [Phys. Rev. C 64, 029801 (2001)]. In particular, we point out that the proposal to present noncoplanar proton-proton bremsstrahlung data as squared matrix elements involves unresolved theoretical problems.

We investigate higher order effects in electromagnetic excitation of neutron halo nuclei using a zero-range model for the neutron-core interaction. In the sudden (or Glauber) approximation all orders in the target-core electromagnetic interaction are taken into account. Small deviations from the sudden approximation are readily calculated. We obtain very simple analytical results and scaling laws for the next-to-leading order effects, which have a simple physical interpretation. For intermediate energy electromagnetic dissociation, higher order effects are generally small. We apply our model to Coulomb dissociation of ${}^{19}\mathrm{C}$ at $67A\mathrm{MeV}$ and of ${}^{11}\mathrm{Be}$ at 72A MeV. The analytical results are compared to numerical results from the integration of the time-dependent Schrödinger equation. Good agreement is obtained. We conclude that higher order electromagnetic effects are well under control.

The $(n,\gamma )$ cross sections of the stable europium isotopes ${}^{151}\mathrm{Eu}$ and ${}^{153}\mathrm{Eu}$ have been measured by irradiating oxide samples in a quasistellar neutron spectrum. From the induced activities, the stellar cross sections of ${}^{151}\mathrm{Eu}$ and ${}^{153}\mathrm{Eu}$ at a thermal energy of $kT=30\mathrm{}\hspace{0.5em}\mathrm{keV}$ were found to be $〈\sigma v〉{/v}_T=3821\mathrm{}\pm 152\hspace{0.5em}\mathrm{mb}$ and $2733\pm 110\hspace{0.5em}\mathrm{mb},$ respectively. These results allowed us to resolve severe discrepancies among previous data. Similar activation measurements were also performed on ${}^{152,154}\mathrm{Sm}$ and ${}^{164,170}\mathrm{Er}.$ Among these results, the stellar cross section of the s-only isotope ${}^{164}\mathrm{Er}$ $〈\sigma v〉{/v}_T=1084\mathrm{}\pm 51\hspace{0.5em}\mathrm{mb}$ at $kT=30\mathrm{}\hspace{0.5em}\mathrm{keV}$ is particularly important. Statistical model calculations were performed with emphasis on the effect of excited states as well as on the unstable isotopes ${}^{151}\mathrm{Sm},$ ${}^{152}\mathrm{Eu},$ and ${}^{154}\mathrm{Eu}.$ The combined set of cross sections was used for an updated analysis of the branchings at $A=151,$ 152, 154, and 163. The temperature and density estimates derived via the classical approach are discussed and compared to stellar models for helium shell burning in low mass stars.

Intermediate-energy nucleon-nucleus interactions were investigated in order to achieve a more comprehensive understanding of spallation reactions. Inclusive ${}^{12}\mathrm{C}{(p,p}^{\prime })$ spectra at 300 MeV were measured in a wide energy range and compared with two theoretical calculations: the quantum molecular dynamics model and the intranuclear cascade model. The calculations are in good agreement with the experimental results in the quasifree region. In the lower energy domain, however, the calculations underestimated the experimental results by a factor of about 2. The cause of the discrepancy was discussed in terms of a collective excitation process.

Using a multiphase transport model (AMPT), which includes both initial partonic and final hadronic interactions, we study the rapidity distributions of charged particles such as protons, antiprotons, pions, and kaons in heavy ion collisions at RHIC. The theoretical results for the total charged particle multiplicity at midrapidity are consistent with those measured by the PHOBOS Collaboration in central Au+Au collisions at $\sqrt{s}=56\mathrm{}$ and $130A\hspace{0.5em}\mathrm{GeV}.$ We find that these hadronic observables are much more sensitive to the hadronic interactions than to the partonic interactions.

Three different cluster expansions for the evaluation of correlated one-body properties of $s-p$ and $s-d$ shell nuclei are compared. Harmonic oscillator wave functions and Jastrow-type correlations are used, while analytical expressions are obtained for the charge form factor, density distribution, and momentum distribution by truncating the expansions and using a standard Jastrow correlation function f. The harmonic oscillator parameter b and the correlation parameter $\beta$ have been determined by a least-squares fit to the experimental charge form factors in each case. The information entropy of nuclei in position space ${(S}_r)$ and momentum space ${(S}_k)$ according to the three methods are also calculated. It is found that the larger the entropy sum, ${S=S}_r{+S}_k$ (the net information content of the system), the smaller the values of ${\chi }^2.$ This indicates that maximal S is a criterion of the quality of a given nuclear model, according to the maximum entropy principle. Only two exceptions to this rule, out of many cases examined, were found. Finally an analytic expression for the so-called “healing” or “wound” integrals is derived with the function f considered, for any state of the relative two-nucleon motion, and their values in certain cases are computed and compared.

The decay of the $3s$ isomer of ${}^{100}\mathrm{Nb}$ has been investigated by $\gamma$ spectroscopy of online mass separated ${}^{100}\mathrm{Nb}.$ Several new transitions in the daughter nucleus ${}^{100}\mathrm{Mo}$ have been observed. This results in a more consistent decay pattern leading to a firm $5^{+}$ assignment to the ${}^{100}\mathrm{Nb}$ isomer. A QRPA based calculation reproduces the decay features best if the $\pi g_{9/2}-\pi p_{1/2}$ gap is enlarged, confirming the importance of the subshell gap at $Z=40\mathrm{}$ previously introduced to account for low-lying $0^{+}$ states in other $N=58\mathrm{}$ isotones.

Angular distributions of inelastic-scattering cross sections were measured for deuterons of 13.2 and 16.0 MeV, exciting the $2_1^{+}$ and $3_1^{-}$ states of ${}^{94}\mathrm{Mo}$ and ${}^{98}\mathrm{Mo}.$ The analysis of the Coulomb-nuclear interference patterns displayed by these angular distributions was favored by the quality of the data obtained with the S. Paulo Pelletron-Enge-Spectrograph facility. The distorted-wave Born approximation–deformed-optical-model analysis with global parameters yielded values for the ratio $C_L={\delta }_L^C/{\delta }_L^N$ and for ${\delta }_L^N$ (where ${\delta }_L^C$ and ${\delta }_L^N$ are, respectively, the charge and isoscalar deformation lengths), which inform the reader about the isospin character of the excitations. A reduced isoscalar transition probability, $B\left(\mathrm{ISL}\right),$ was defined, in analogy to $B\left(\mathrm{EL}\right),$ the ratio $B\left(\mathrm{EL}\right)/B\left(\mathrm{ISL}\right)\mathrm{}$ being proportional to the square of $C_L.$ The latter quantity is, however, experimentally better determined. The results obtained for $C_2,$ $C_3,$ ${\delta }_2^N,$ and ${\delta }_3^N$ at the two incident energies, 13.2 and 16.0 MeV, are consistent for each ${}^{94}\mathrm{Mo}$ and ${}^{98}\mathrm{Mo}.$ The values of $C_L$ reveal a slight predominance of the protons in the quadrupolar transitions, in both ${}^{94}\mathrm{Mo}$ and ${}^{98}\mathrm{Mo}.$ The $2_1^{+}$ and the $3_1^{-}$ states are more collective in ${}^{98}\mathrm{Mo}$ than in ${}^{94}\mathrm{Mo},$ both with respect to the protons (charge) and with respect to protons and neutrons (mass).

Parity nonconservation (PNC) has been studied in neutron p-wave resonances of ${}^{117}\mathrm{Sn}.$ The longitudinal asymmetries were measured for 29 p-wave resonances in the neutron energy range 0.8 eV to 1100 eV. Statistically significant PNC effects were observed for four resonances. A statistical analysis determined the rms weak mixing matrix element and the weak spreading width. A weak spreading width of ${\Gamma }_w{=(0.28\mathrm{}}_{-0.15}^{+0.56\mathrm{}})\times {10}^{-7}\hspace{0.5em}\mathrm{eV}$ was obtained for ${}^{117}\mathrm{Sn}.$

Based on an axially symmetric rotor plus quasiparticles model, the study of the signature inversion (SI) in odd-odd nuclei in the mass region $A=160\mathrm{}$ is extended to include the region $A=80.\mathrm{}$ In spite of many differences between the two mass regions, the calculation results show that the possible SI mechanism, which has been confirmed by the calculation of odd-odd nuclei in the $A=160\mathrm{}$ region (i.e., the competition between the $n-p$ interaction and the Coriolis force in low-$K$ space) is also appropriate for odd-odd nuclei in the $A=80\mathrm{}$ region. This seems to indicate that there may be a universal mechanism of SI in odd-odd nuclei for different mass regions.

The transverse momenta ${(p}_x{,p}_y)$ of projectile fragments produced by $1.0A\hspace{0.5em}\mathrm{GeV}{\hspace{0.5em}}^{197}\mathrm{Au}$ nuclei incident on Au and C targets have been measured. The medium and heavy fragments have $p_x$ and $p_y$ distributions, which are wider than predicted by models. For the Au target the widths of the distributions are significantly larger than those for C, particularly for the heavy fragments. The C distributions show a different gross structure, which may be due to the target-projectile size difference.