We discuss a comparison between the Hartree-Fock-Bogoliubov approximation and functional integral results obtained with Monte Carlo methods. We considered the $\mathrm{pairing}+\mathrm{quadrupole}$ model for ${}^{166}\mathrm{Er}.$

The nuclear structure of ${}^{24}\mathrm{Mg}$ with ${}^{12}\mathrm{C}+3\mathrm{}\alpha$ and $3\alpha +3\mathrm{}\alpha$ configurations, existing at an extremely highly-excited energy domain is studied by the microscopic coupled-channels (MCC) calculation based on the double-folding interactions using 3α-RGM wave functions of ${}^{12}\mathrm{C}$ and a realistic nucleon-nucleon interaction called DDM3Y. The dinuclear ${}^{12}\mathrm{C}{+}^{12}\mathrm{C}$ configuration of ${}^{24}\mathrm{Mg},$ corresponding to the so-called “higher-energy molecular resonances,” is also investigated by the same MCC framework. The MCC calculation predicts the existence of three kinds of the molecular bands having $3\alpha +3\mathrm{}\alpha ,$ ${}^{12}\mathrm{C}+3\mathrm{}\alpha ,$ and ${}^{12}\mathrm{C}{+}^{12}\mathrm{C}$ structures around the excitation energy of about 40 MeV with respect to the ground state of ${}^{24}\mathrm{Mg}.$ The channel coupling among the 3α states in each ${}^{12}\mathrm{C}$ plays very important roles for the formation of the ${}^{12}\mathrm{C}+3\mathrm{}\alpha$ and $3\alpha +3\mathrm{}\alpha$ molecular bands. It is found that the populations of the ${}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}{+}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}},$ ${}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}{+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+}),$ and ${}^{12}\mathrm{C}{(0\mathrm{}}_2^{+}{)+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+})$ channels are very small in the individual molecular bands with ${}^{12}\mathrm{C}{+}^{12}\mathrm{C},$ ${}^{12}\mathrm{C}+3\mathrm{}\alpha ,$ and $3\alpha +3\mathrm{}\alpha$ configurations, respectively. The reaction mechanism for the inelastic scattering leading to the ${}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}{+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+})$ and ${}^{12}\mathrm{C}{(0\mathrm{}}_2^{+}{)+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+})$ excitation channels is also investigated in relation to the obtained three kinds of the molecular bands. The result suggests that the inelastic scattering to the ${}^{12}\mathrm{C}{(0\mathrm{}}_2^{+}{)+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+})$ ${[}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}{+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+}\left)\right]$ channel can be interpreted in terms of weak transitions from the ${}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}{+}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ component of the ${}^{12}\mathrm{C}{+}^{12}\mathrm{C}$ molecular bands to the ${}^{12}\mathrm{C}{(0\mathrm{}}_2^{+}{)+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+})$ ${[}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}{+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+}\left)\right]$ component of the multicluster $3\alpha +3\mathrm{}\alpha$ ${(}^{12}\mathrm{C}+3\mathrm{}\alpha )$ molecular bands. All the results are discussed in connection with the band crossing model which was proposed in describing the higher-energy molecular resonance with dinuclear configuration as well as the resonances observed in the ${}^{12}\mathrm{C}{(0\mathrm{}}_2^{+}{)+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+})$ and ${}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}{+}^{12}\mathrm{C}{(0\mathrm{}}_2^{+})$ exit channels.

Theoretical approach for studies on particle-particle angular correlations in nuclear reactions induced by light and semiheavy ions with an incident energy up to 10 MeV/nucleon is developed. The generalized methods for calculations of the angular correlation functions and the spin tensors of the density matrix for the reaction products based on the distorted-wave model with finite interaction range and the compound nucleus model are presented for reactions involving high-lying excited states. The differential cross sections and $d-\alpha$ correlation functions in the ${}^{12}\mathrm{C}{(}^{14}\mathrm{N}{,d)}^{24}{\mathrm{Mg}}^{*}(\alpha {)}^{20}\mathrm{Ne}$ reaction induced by ${}^{14}\mathrm{N}$ ions at $E_{\mathrm{lab}}=29\mathrm{}–45\mathrm{MeV}$ are analyzed both in the framework of the model of direct ${}^{12}\mathrm{C}$ transfer and the statistical compound nucleus model. The reduced width amplitudes for the higher-excited states in ${}^{24}\mathrm{Mg}$ with ${}^{12}\mathrm{C}{\otimes }^{12}\mathrm{C}$ quasimolecular structure are extracted. The importance of relative motion of ${}^{12}\mathrm{C}{+}^{12}{\mathrm{C}}^{*}$ nuclei is demonstrated.

New experimental data for the ${}^{12}\mathrm{C}{+}^{12}\mathrm{C}$ reaction have been measured in the center-of-mass energy range $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=40\mathrm{}–59\mathrm{}\mathrm{MeV}.$ Excitation functions for a number of single and mutual ${}^{12}\mathrm{C}$ inelastic channels have been measured which include the $0_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{+},$ $2_1^{+},$ $0_2^{+},$ $3_1^{-},$ and $4_1^{+}$ ${}^{12}\mathrm{C}$ states. All of the reactions display largely unstructured excitation functions over this energy range. The absence of further resonances in this energy region for the ${}^{12}\mathrm{C}{(}^{12}\mathrm{C}{,}^{12}\mathrm{C}\left[3_1^{-}\right]{)}^{12}\mathrm{C}\left[3_1^{-}\right]$ reaction confirms theoretical predictions of the termination of the band of resonances found at lower center-of-mass energies in this channel.

We have calculated the cross section for the process $n\overrightarrow{p}\eta d$ in the region near threshold, within the framework of a three-body model. We studied the dependence of the cross section to the production mechanism and to the initial- and final-state interactions. We found that the magnitude of the cross section is highly dependent on the reaction mechanism. However, its shape is essentially determined by the $\eta d$ final-state interaction alone. This strong signature in turn directly provides information about the $\eta N$ scattering length. For a variety of reaction mechanisms it is verified that the $n\overrightarrow{p}\eta d$ experimental data can only be explained if the $\eta N$ scattering length has a small real part, as it happens, for instance, in the $\eta N$ interaction model proposed recently by the Jülich group.

The Coulomb breakup of neutron halo nuclei is considered within the framework of the postform distorted-wave Born approximation (DWBA). The quality of commonly used additional approximations to the DWBA theory is investigated by comparing the approximate with the exact DWBA calculations. The exact DWBA amplitude is expressed in momentum space as a three-dimensional integral and evaluated numerically. Calculations are presented for the Coulomb breakup of deuteron and ${}^{11}\mathrm{Be}$ at very forward angles at the beam energy of $\sim 70\hspace{0.5em}\mathrm{MeV}/\mathrm{nucleon}.$ The factorization approximation to the DWBA amplitude is studied and found to be suspected.

The nucleon is modeled, using light front dynamics, as a relativistic system of three bound constituent quarks surrounded by a cloud of pions. The pionic cloud is important for understanding low-momentum transfer physics, especially the neutron charge radius, but the quarks are dominant at high values of $Q^2.$ The model achieves a very good description of existing data for the four electromagnetic elastic form factors.

The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full $0ħ\omega$ shell-model spaces we calculate the Hartree-Fock $\mathrm{}\left(\mathrm{HF}\right)\mathrm{}+\mathrm{RPA}$ binding energy, and compare it to exact diagonalization. We find that often, but not always, the $\mathrm{HF}+\mathrm{RPA}$ gives a good approximation to the “exact” ground state energy. In those cases where the RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wave function. This weakens the reliability of the RPA for computing binding energies.

We propose a simple approach to predict the angular momentum I ground state $(I$ g.s.) probabilities of many-body systems that does not require the diagonalization of Hamiltonians with random interactions. This method is found to be applicable to all cases that have been discussed: even and odd fermion systems (both in single-$j$ and many-$j$ shells), and boson (both $\mathrm{sd}$ and $sdg)$ systems. A simple relation for the highest angular momentum g.s. probability is found. Furthermore, it is suggested for the first time that the 0 g.s. dominance in boson systems and in even-fermion systems is given by two-body interactions with specific features.

We perform calculations for $M1\mathrm{}$ transitions and allowed Gamow-Teller (GT) transitions in the even-even titanium isotopes—${}^{44}\mathrm{Ti},$ ${}^{46}\mathrm{Ti},$ and ${}^{48}\mathrm{Ti}.$ We start with the FPD6 interaction. To study the effect of the $T=0\mathrm{}$ two-body matrix elements on the $M1\mathrm{}$ and GT rates we introduce a second interaction in which all the $T=0\mathrm{}$ two-body matrix elements are set equal to zero (A) and a third in which all the $T=0\mathrm{}$ two-body matrix elements (B) are set to a constant. For these two interactions the $T=1\mathrm{}$ matrix elements are the same as for FPD6. We are thus able to study the effects of the fluctuating $T=0\mathrm{}$ matrix elements on $M1\mathrm{}$ and GT rates with interactions A and B, and comparing them with the results of using the full FPD6 interaction (C). We find that transition rates are much more sensitive to the details of the $T=0\mathrm{}$ interaction than are the spectra of low-lying states of even-even nuclei.

A finite rank separable approximation for particle-hole random phase approximation (RPA) calculations with Skyrme interactions is extended to take into account the pairing. As an illustration of the method energies and transition probabilities for the quadrupole and octupole excitations in some O, Ar, Sn, and Pb isotopes are calculated. The values obtained within our approach are very close to those that were calculated within quasiparticle RPA (QRPA) with the full Skyrme interaction. They are in reasonable agreement with experimental data.

Differences in the density dependence of the symmetry energy predicted by nonrelativistic and relativistic models are suggested, at least in part, as the culprit for the discrepancy in the values of the compression modulus of symmetric nuclear matter extracted from the energy of the giant monopole resonance in ${}^{208}\mathrm{Pb}.$ “Best-fit” relativistic models, with stiffer symmetry energies than Skyrme interactions, consistently predict higher compression moduli than nonrelativistic approaches. Relativistic models with compression moduli in the physically acceptable range of $K=200\mathrm{}–300\mathrm{MeV}\mathrm{}$ are used to compute the distribution of isoscalar monopole strength in ${}^{208}\mathrm{Pb}.$ When the symmetry energy is artificially softened in one of these models, in an attempt to simulate the symmetry energy of Skyrme interactions, a lower value for the compression modulus is indeed obtained. It is concluded that the proposed measurement of the neutron skin in ${}^{208}\mathrm{Pb},$ aimed at constraining the density dependence of the symmetry energy and recently correlated to the structure of neutron stars, will also become instrumental in the determination of the compression modulus of nuclear matter.

The antiproton annihilation experiments help to extract so-called peripheral factors representing the ratio of neutron to proton densities at the annihilation site that is about 2.5 fm away from the half-density radius of the nucleus. The relativistic mean field (RMF) approach is used to calculate the peripheral factors. The RMF equations (with frozen gap) and relativistic Hartree-Bogoliubov (RHB) equations (with finite range Gogny interaction-D1S for pairing) are solved employing the basis expansion method. The RHB equations are also solved in the coordinate space using a large box (30 fm); with an effective zero range density dependent interaction (consistent with Gogny D1S interaction) for pairing. The results are analyzed to ascertain quantitatively the effect of using these different techniques for solving the RMF/RHB equations. The calculated peripheral factors obtained by solving RHB equations in the coordinate space are relatively closer to the corresponding experimental values.

We have measured the α-particle and proton spectra at different laboratory angles from the fusion reactions ${}^{16}\mathrm{O}{+}^{63}\mathrm{Cu}$ at 109 MeV and ${}^{34}\mathrm{S}{+}^{45}\mathrm{Sc}$ at 140 MeV. The energies are selected so that both of these systems lead to the compound nucleus ${}^{79}{\mathrm{Rb}}^{*}$ with the same value of the angular momentum. The spectra from the asymmetric ${}^{16}\mathrm{O}{+}^{63}\mathrm{Cu}$ reaction are in agreement with the predictions of the statistical model using rotating liquid drop model values of the moment of inertia and transmission coefficients for the spherical nuclei in the inverse absorption channel. The spectra in the case of symmetric ${}^{34}\mathrm{S}{+}^{45}\mathrm{Sc}$ reaction are not consistent with the predictions of the statistical model and thus to explain the experimental spectra the dynamical model analysis was done. The comparison of the decay times with the formation times implies that the light charged particles with higher angular momentum are preferentially emitted prior to the full relaxation of the compound nucleus in the case of symmetric entrance channel.

Exclusive measurements of the cross section and analyzing power for the ${}^{208}\mathrm{Pb}(\overrightarrow{p}{,2p)}^{207}\mathrm{Tl}$ proton knockout reaction at 202 MeV are presented for three quasifree angle pairs. Energy-sharing cross section distributions are found to be in excellent agreement with distorted wave impulse approximation (DWIA) calculations, yielding spectroscopic factors that are in reasonable agreement with ${(e,e}^{\prime }p)$ studies and theoretical expectations. The measured analyzing powers are, however, in significant disagreement with results of standard DWIA calculations that utilize the free nucleon-nucleon interaction. Analyzing power calculations are furthermore found to be insensitive to variations in the distorting potentials, different descriptions of the bound state, different energy prescriptions of the two-body interaction, and nonlocality effects. Agreement between theory and experiment is shown to improve only when the density dependence of the nucleon-nucleon interaction is incorporated within the DWIA.

We present the centrality dependence of proton and deuteron rapidity distributions in Ru+Ru collisions at $400A\mathrm{MeV}.$ Data are compared with isospin quantum molecular dynamics (IQMD) calculations under various assumptions on the nucleon-nucleon cross section in the medium. The rapidity spectra of both particles can be reproduced by IQMD with a free nucleon-nucleon cross section for the most central collisions. The ratio of baryon rapidity distributions in isospin asymmetric collision systems shows incomplete mixing and partial transparency of the projectile and target nuclei at this beam energy.

The yrast decay sequence of ${}^{41}\mathrm{Cl},$ populated in deep inelastic processes produced by the interaction of 234 MeV ${}^{37}\mathrm{Cl}$ ions with a ${}^{160}\mathrm{Gd}$ target, has been studied using the highly sensitive EUROBALL IV $\gamma$-ray detector array. Yrast states are established for the first time at energies of 130 and 891 keV.

Claims in a recent paper by Wu et al. [Phys. Rev. C 64, 014307 (2001)] for the $\gamma \gamma$ character of $K^{\pi }{=4\mathrm{}}^{+}$ bands are based on a flawed argument. A paper they do not cite has explained this weakness in detail, and concluded a dominant g boson or hexadecapole structure is required to explain other data inconsistent with the $\gamma \gamma$ description.

The claim that the two-phonon $\gamma$-vibrational configuration constitutes a major component for the $I_K^{\pi }{=4\mathrm{}}_4^{+}$ states in osmium nuclei is based on solid experimental evidence, such as the systematics of the excitation energies, the absolute $E2\mathrm{}$ strengths, the branching ratios, and the static quadrupole moments. Nevertheless, a non-negligible two-quasiparticle or hexadecapole component must exist in order to explain the observed $E4\mathrm{}$ strength and the cross sections for the nucleon-transfer reactions.