A complete discrete set of spherical single-particle wave functions for studies of weakly bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator wave functions. Unlike the harmonic oscillator states, the new wave functions decay exponentially at large distances. Using the new basis, characteristics of weakly bound orbitals are analyzed and the ground state properties of some spherical doubly magic nuclei are studied. The basis of the transformed harmonic oscillator is a significant improvement over the harmonic oscillator basis, especially in studies of exotic nuclei where the coupling to the particle continuum is important.

A new method is developed to combine the large-basis shell-model and Hartree-Fock methods. The Hartree-Fock method is used to obtain the absolute uncorrelated binding energies, a starting set of single-particle energies, and the single-particle radial wave functions. The shell model Hamiltonian is modified to remove the monopole terms and these are replaced by Hartree-Fock single-particle energies. The shell model is then used to calculate the ground-state correlation energy and the excited state spectrum. Applications are made to the nuclei ${}^{47–60}\mathrm{Ca}.$ A detailed comparison is made for ${}^{48}\mathrm{Ca}$ including the electron scattering data for ${}^{48}\mathrm{Ca}.$

The spectral statistics of calcium isotopes are studied with realistic shell-model calculations. For these nuclei, there are significant deviations from the predictions of the random-matrix theory. In particular, we observe an order-chaos transition when the excitation energy is increased and a clear quantum signature of the breaking of integrability when the single-particle energy spacings are decreased.

A successful, simultaneous reproduction of density and momentum distributions in ${}^4\mathrm{He}$ is presented in a method accounting for nucleon correlations using only two functions $(1s$ and $1d)$ and totally three parameters, while in the best fit of equal quality known to us there are 12 parameters. Further, a physical interpretation of the $1d$ state involved is given as coming from an internal rotation of nucleons. Such an interpretation provides a hint that the neutron skin and neutron halo in exotic nuclei could have a rotational origin.

In the fraamework of a relativistic Dirac-Brueckner analysis the pion contribution to the ground state energy of nuclear matter is studied using pseudovector coupling. Evidence is presented that the role of the tensor force in the saturation mechanism is substantially reduced compared to its dominant role in a usual nonrelativistic treatment. The reduction of the pion contribution in nuclear matter is due to many-body effects present in a relativistic treatment. In particular, we show that the damping of the one-pion-exchange potential is actually due to the decrease of $M^{*}/M$ with increasing density.

We investigate the structure of the potential energy surfaces of the superheavy nuclei ${}_{158}^{258}{\mathrm{Fm}}_{100},$ ${}_{156}^{264}{\mathrm{Hs}}_{108},$ ${}_{166}^{278}112,$ ${}_{184}^{298}114,$ and ${}_{172}^{292}120$ within the framework of self-consistent nuclear models, i.e., the Skyrme-Hartree-Fock approach and the relativistic mean-field model. We compare results obtained with one representative parametrization of each model which is successful in describing superheavy nuclei. We find systematic changes as compared to the potential energy surfaces of heavy nuclei in the uranium region: there is no sufficiently stable fission isomer any more, the importance of triaxial configurations to lower the first barrier fades away, and asymmetric fission paths compete down to rather small deformation. Comparing the two models, it turns out that the relativistic mean-field model gives generally smaller fission barriers.

A $k-i$ basis shell model with an accessible heritage truncation scheme for the coefficients of fractional parentage (CFP) is proposed. A relation to particle-hole symmetry is also derived. By exploiting the derived particle-hole symmetry and the heritage truncation scheme, the required computation and storage is reduced. By using this approach, all the CFP with $k<~2,$ $i<~\frac{7}{2},$ and the heritage quantum number $u<~\min (N,{\Omega }_{\mathrm{ki}}-N+2)$ are computed, where N is the particle number, ${\Omega }_{\mathrm{ki}}$ is the pair degeneracy of a $k-i$ shell, and $u<~\min (N,{\Omega }_{\mathrm{ki}}-N+2)$ means taking the smaller of the two quantities in parentheses. This provides the means to implement shell model calculations for heavy nuclei.

The $T=0\mathrm{}$ energy spectrum and the electromagnetic transitions of the ${}^{32}\mathrm{S}$ nucleus are described in terms of the semimicroscopic algebraic cluster model. ${}^{28}\mathrm{Si}+\alpha$ and ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ configurations are considered for the low-lying bands and molecular resonances, respectively. The cluster configurations, including their Hamiltonians, are treated in a unified framework. The densities of high-lying core-plus-alpha-particle states are predicted in those energy windows, where good-resolution experiments have been carried out.

The nuclear collective response at finite temperature is investigated for the first time in the quantum framework of the small amplitude limit of the extended time-dependent Hartree-Fock approach, including a non-Markovian collision term. It is shown that the collision width satisfies a secular equation. By employing a Skyrme force, the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitations in ${}^{40}\mathrm{Ca}$ are calculated and important quantum features are pointed out. The collisional damping due to decay into incoherent two-particle–two-hole states is small at low temperatures but increases rapidly at higher temperatures.

As a test for the time scale of neutron emission, two-neutron intensity interferometry was applied to the reaction ${}^{40}{\mathrm{A}\mathrm{r}+}^{165}\mathrm{Ho}$ at $E/A=25\mathrm{}\mathrm{MeV}.$ After appropriate corrections for neutron scattering, the correlation function showed a lifetime that was about a factor of two shorter than the lifetime predicted for the statistical decay of an equilibrated nucleus. Preequilibrium emission may explain some of this difference.

Relative population of states in ${}^{11}\mathrm{B}$ following the ${}^{12}\mathrm{C}(\gamma ,p)$ reaction has been measured with high resolution using the deexcitation γ-ray technique. The states near 7 MeV in ${}^{11}\mathrm{B}$ are clearly resolved and the measured population clarifies earlier conflicting data. Comparison of the results with new calculations indicates the importance of both one-nucleon and multinucleon processes.

Excitation functions for the production of the 2.74, 6.13, 6.92, and 7.12 MeV $\gamma$ rays by inelastic proton scattering on ${}^{16}\mathrm{O}$ have been measured in steps of 200–500 keV for proton energies $E_p=8.4\mathrm{}–20\hspace{0.5em}\mathrm{MeV}.$ For the 4.44 MeV $\gamma$ rays of ${}^{12}\mathrm{C}$ produced by inelastic proton scattering on ${}^{12}\mathrm{C}$ data have been obtained for proton energies $E_p=8.4\mathrm{}–14\hspace{0.5em}\mathrm{MeV}$ and at $E_p=17.25,18.25,$ and 19.75 MeV. Eight high efficiency Ge detectors with anti-Compton shielding for the $\gamma$-ray detection were used to obtain the laboratory $\gamma$-angular distributions. The results of Legendre polynom fits to these distributions are discussed and presented in suitable form for use in $\gamma$-ray astronomy.

The elastic breakup of the deuteron has been measured in a kinematical condition of ${\theta }_p={\theta }_n=0\mathrm{}°$ at $E_d=140\mathrm{}\mathrm{MeV}$ and 270 MeV on seven targets ranging from $Z=6\mathrm{}$ to 82. A double-peaked structure with its minimum at $E_p\simeq E_n$ is observed for all the measured triple-differential cross sections, which indicates a large contribution from Coulomb breakup. While a symmetric shape is expected for an $E1\mathrm{}$ transition, the observed proton-energy distribution is asymmetric, showing considerable dependence on both the target and the incident energy. These data and previous data at 56 MeV have been analyzed using the post-form of the distorted-wave Born approximation (DWBA) theory. Although the calculations account reasonably well for the asymmetric shape, by including the nuclear potential, they consistently overestimate the magnitudes of the cross sections over the whole measured region. Limitations of the post-form DWBA are discussed.

The study of the ${}^{208}\mathrm{Pb}(\overrightarrow{d}{,t)}^{207}\mathrm{Pb}$ reaction at $E_d=200\mathrm{}\mathrm{MeV}$ has been extended up to typically $E_x=40\mathrm{}\mathrm{MeV}$ in ${}^{207}\mathrm{Pb}$ using a polarized beam with both vector and tensor components. Two-step pickup reactions involving low multipolarity collective transitions have been evaluated for the first time via systematic coupled channel calculations, allowing a new approach of the background determination. The $(\overrightarrow{d},t)$ observables corresponding to the overlapping ${1h}_{11/2},$ ${1g}_{7/2},$ and ${1g}_{9/2}$ inner hole responses have been analyzed up to $E_x=25\mathrm{}\mathrm{MeV}$ via a least squares fit procedure. Necessary input values were deduced for hole states of interest from finite range distorted wave (DWBA) calculations. The optical parameters and the range function were those successfully used in a previous survey of valence state observables. The highest $j$ transitions are enhanced in the reaction and analyzing powers exhibit strongly characteristic features for $j_{-}=l-1/2$ versus $j_{+}=l+1/2\mathrm{}$ states. We have calculated for the first time the separation energy dependence of $\mathrm{nlj}$ transition observables, taking into account the form factor modifications induced by the hole coupling with surface vibrations. The calculations have been performed in the framework of the quasiparticle-phonon model (QPM). This analysis (QPMFF) predicts a large variation of differential cross sections with excitation energy of the hole fragments, while angular distribution shapes remain quite stable. The strength distributions resulting of the QPMFF analysis and of a standard analysis using DWBA observables calculated at the centroid energies are systematically compared. As a general rule, the QPMFF analysis increases the strength concentration toward lower excitation energy. The corresponding ${1h}_{11/2},$ ${1g}_{7/2},$ and the tentative ${1g}_{9/2}$ strength distributions are compared and discussed with the available theoretical calculations. In particular, the narrower spreading widths deduced via the QPMFF analysis are quite well predicted by the calculation of spectral functions in a modified mean field. The ${1i}_{13/2}$ and ${1h}_{9/2}$ valence strength distributions are revisited along this new approach and found to be in fair agreement with the fragmentation predicted by the QPM, which is not the case of inner hole strength distributions.

The neutron elastic and inelastic scattering double-differential cross sections of ${}^6\mathrm{Li}$ were measured at incident neutron energies of 11.5, 14.1, and 18.0 MeV. A phenomenological neutron optical model potential of ${}^6\mathrm{Li}$ was constructed to describe the total and elastic scattering cross sections from 5 MeV to several tens MeV, based on the present data together with information from other works. This potential was found to describe the inelastic scattering to the first excited state ${(E}_x=2.186\mathrm{}\hspace{0.5em}\mathrm{MeV})$ well via the distorted-wave Born approximation (DWBA) calculation with the macroscopic vibrational model. The continuum neutron energy spectra and angular distributions were then analyzed by the theory of final-state interaction extended to the DWBA form, with an assumption that the $d-\alpha$ interaction is dominant in the three-body final state consisting of $n,\hspace{0.5em}d,$ and α particles. Such a calculation was found to be successful in explaining the major part of the low-excitation neutron spectra and angular distribution down to the Q-value region of $-9\hspace{0.5em}\mathrm{M}\mathrm{e}\mathrm{V},$ except for the Q-value range where the $n-\alpha$ quasifree scattering will give a non-negligible contribution at forward angles.

Differential cross section and analyzing power measurements have been made for 200 MeV inelastic proton scattering from ${}^{58}\mathrm{Ni}.$ Using the code LEA, neutron transition densities have been obtained for four $2^{+},$ one $3^{-},$ and five $4^{+}$ low lying states. Charge transition densities obtained from electron scattering were used in order to minimize the nuclear structure uncertainty, along with a recent 200 MeV empirical effective interaction. Two types of calculations have been used in comparison to the data, one in which the neutron transition densities are obtained by scaling the charge transition densities by $N/Z,$ the other in which the neutron transition densities are allowed to vary to obtain a best fit to the data. Multipole matrix elements are obtained and compared to collective model analyses using both intermediate energy protons and pion scattering results. The radial shapes of the neutron transition densities for the lowest lying $2^{+}$ and $3^{-}$ states are compared to those calculated using the energy density method.

The eigenchannel approximation is applied to the calculation of fusion cross section for the case when the intrinsic nuclear excitations are treated as simple-harmonic vibrations. The resulting expression has been expressed as an average over a smooth distribution of fusion barriers. The mean-barrier parameters are obtained from the optical model, and the nuclear oscillation parameters from the liquid-drop model or expressed in terms of electromagnetic transition strengths, so that the obtained barrier distribution does not, in principle, involve any free parameter. The target excitation energies are subsequently taken into account by replacing the incident energy in the expression for the transmission coefficient by the mean value of the initial and final kinetic energies in each channel. As a result, the barrier distribution becomes more extended towards larger barriers and shows strong oscillatory behavior. These oscillations are strongly reduced when the barrier distributions are represented as the derivative of the fusion cross section. Corrections for angular momentum transfer are discussed in terms of the concept of tangential friction. The calculated distributions of fusion barriers are in reasonable agreement with the empirical distributions corresponding to the interaction of ${}^{16}\mathrm{O}$ with vibrational target nuclei, but fail in the case of rotational nuclei where the present formalism is hardly justified. The distributions are shown to be useful in resolving the parameter ambiguity of the optical potential.

In the framework of a two-dimensional Vlasov model, we study the time evolution of the “coarse-grained” generalized entropy (GE) in a nuclear system which undergoes a multifragmentation (MF) phase transition. We investigate the GE both for the gas and the fragments (surface and bulk part, respectively). We find that the formation of the surface causes the growth of the GE during the process of fragmentation. This quantity then characterizes the MF and confirms the crucial role of deterministic chaos in filling the new available phase space: at variance with the exact time evolution, no entropy change is found when the linear response is applied. Numerical simulations were used also to extract information about final temperatures of the fragments. From a fitting of the momentum distribution with a Fermi-Dirac function we extract the temperature of the fragments at the end of the process. We calculate also the gas temperature by averaging over the available phase space. The latter is a few times larger than the former, indicating a gas not in equilibrium. Though the model is very schematic, this fact seems to be very general and could explain the discrepancy found in experimental data when using the slope of light particles spectra instead of the double ratio of isotope yields method in order to extract the nuclear caloric curve.

Nonlocal coordinate space optical potentials for the scattering of 65 MeV protons from nuclei ranging in mass from ${}^6\mathrm{Li}$ to ${}^{238}\mathrm{U}$ have been defined by folding a complex, medium-dependent effective interaction with the density matrix elements of each target. The effective interaction is based upon solutions of the Lippmann-Schwinger and Brueckner-Bethe-Goldstone equations having the Paris potential as input. The nuclear structure information required in our folding model is the one-body density matrix elements for the target and the single- nucleon bound state wave functions that they weight. For light mass nuclei, very large basis shell model calculations have been made to obtain the one-body density matrix elements. For medium and heavy mass nuclei, a very simple shell model prescription has been used. The bound-state single-particle wave functions that complete the nuclear density matrices are either Woods-Saxon or harmonic oscillator functions. The former are employed in most cases when large basis structure is available. For light nuclei $(A<~16)$ Woods-Saxon potential parameters and harmonic oscillator lengths are determined from fits to electron scattering form factors. For all other nuclei, we use harmonic oscillator functions with the oscillator lengths set from an $A^{1/6}$ mass law. Using this microscopic model, optical potentials result from which differential cross sections, analyzing powers, and spin rotations are found. In general the calculated results compare very well with data when the effective interactions are determined from a mapping of nucleon-nucleon g matrices. This is not the case when effective interactions built from a mapping of (free) t matrices are used.

The electromagnetic interactions of a relativistic two-body bound state are formulated in three dimensions using an equal-time (ET) formalism. This involves a systematic reduction of four-dimensional dynamics to a three-dimensional form by integrating out the time components of relative momenta. A conserved electromagnetic current is developed for the ET formalism. It is shown that consistent truncations of the electromagnetic current and the $\mathrm{NN}$ interaction kernel may be made, order by order, in the coupling constants, such that appropriate Ward-Takahashi identities are satisfied. A meson-exchange model of the $\mathrm{NN}$ interaction is used to calculate deuteron vertex functions. Calculations of electromagnetic form factors for elastic scattering of electrons by deuterium are performed using an impulse-approximation current. Negative-energy components of the deuteron’s vertex function and retardation effects in the meson-exchange interaction are found to have only minor effects on the deuteron form factors.