The level structure of ${}^{214}\mathrm{At}$ has been studied using the alpha decay of the ground state and high spin isomer of ${}^{218}\mathrm{Fr}$ and coincident gamma rays. This study was also aided by observing the alpha decay of the ground state and high spin isomer of ${}^{214}\mathrm{At}$ into known levels in ${}^{210}\mathrm{Bi}.$ Four additional levels and minor changes in level energies are observed. Of greater importance is the tentative assignment of a large number of spins and parities. This in turn allows the tentative identification of 9 of the 10 members of the $\pi {(h}_{9/2}{)}^3\nu {(g}_{9/2}{)}^3$ configuration which is also calculated theoretically. A survey of the experimental systematics of the $\pi {(h}_{9/2}{)}^m\nu {(g}_{9/2}{)}^n$ configuration in the odd-odd nuclei from ${}^{210}\mathrm{Bi}$ to ${}^{218}\mathrm{Fr}$ shows quite clearly the compression of the level structures and the increased mixing between the configurations with the addition of nucleons. This is also mirrored in the theoretical calculations.

The decay structure of the particle-unstable nucleus ${}^{10}\mathrm{Li}$ was studied using the method of sequential neutron decay spectroscopy (SNDS) at 0°. The decay energies of ${}^{10}\mathrm{Li}$ can be derived from the relative velocity spectrum of the ${}^9\mathrm{Li}$ daughter and the neutron measured in coincidence. Evidence for low-lying s-wave strength was observed with a scattering length of $<-20\mathrm{fm},$ corresponding to a peak energy of $<50\mathrm{}\mathrm{keV}.$

Isoscalar spin-transfer excitations have been measured in ${}^{90}\mathrm{Zr}$ and ${}^{208}\mathrm{Pb}$ by inelastic scattering of vector and tensor polarized 400 MeV deuterons in an excitation energy range from 2.5 to 43 MeV and 2.3 to 23 MeV, respectively. For ${}^{90}\mathrm{Zr},$ spin excitations were found between 7.5 and 10.7 MeV and in a large structure in the continuum (18 to 28 MeV). For ${}^{208}\mathrm{Pb},$ spin excitations were found at 3.55 and 5.85 MeV, between 6.5 and 11 MeV, and spread over the continuum. Elastic scattering cross sections and vector and tensor analyzing powers were measured between 3.4 and $24°$ for Zr and Pb, and optical potential parameters were derived. The experimental results are compared to DWIA/RPA calculations. The transition densities used are generated using the continuum random phase approximation.

The yrast spectra, quadrupole moments, quadrupole deformation parameter ${\beta }_2,B\left(E2\mathrm{}\right)\mathrm{}$ transition probabilities and occupation probabilities for each angular momentum state are calculated for ${}^{108–114}\mathrm{Pd}$ isotopes by carrying out cranked Hartree-Bogoliubov (CHB) calculations. These calculations have been performed by employing pairing-plus-quadrupole-quadrupole and also octupole-octupole interaction operating in a reasonably large valence space outside ${}^{76}\mathrm{Sr}$ core. The calculations show a marked improvement in agreement with experiments when the octupole-octupole interaction term is included in the Hamiltonian.

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both $m_{\pi }$ and $1/a$ (where a is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the ${}^1{S}_0\hspace{0.5em}\mathrm{and}{\hspace{0.5em}}^3{S}_1$ channels. Analogous theorems are developed for the energy dependence $\epsilon$ parameter which describes ${}^3{S}_1{-}^3{D}_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_{\pi }$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_{\pi }$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.

Quantum-number projection is applied to generate exact eigenstates of angular momentum or of particle numbers from the self-consistent solution of the angular-momentum- and particle-number-constrained Hartree-Fock-Bogoliubov (CHFB) equation. Calculations are based on the symmetry-conserving microscopic Hamiltonian and the large single-particle space spanned by spherical Nilsson bases covering about 1.5 major shells for both protons and neutrons in the case of the yrast bands for ${}^{158,164,168}\mathrm{Er}$ and almost three major shells in the case of the superdeformed bands as well as g and s bands for ${}^{132}\mathrm{Ce}.$ The residual interaction is given by the monopole- and quadrupole-pairing interactions plus the quadrupole-quadrupole interaction. Symmetry properties of the Hamiltonian are fully taken into account through both stages of solving the CHFB equation and projections to reduce computational time substantially. A great mixture of angular momentum components requires the projection while particle-number projections become less important at high spins, especially along superdeformed bands with vanishingly small static gaps. It is shown that the angular momentum projection is effective to reproduce $K=0\mathrm{}$ superdeformed levels appearing in the yrast band together with the g and s bands.

Based on the relativistic continuum Hartree-Bogoliubov theory, the pseudospin approximation in exotic nuclei is investigated in Zr and Sn isotopes from the proton drip line to the neutron drip line. The quality of the pseudospin approximation is shown to be connected to the competition between the pseudocentrifugal barrier and the pseudospin orbital potential (PSOP). The PSOP depends on the derivative of the difference between the scalar and vector potentials $dV/dr.\mathrm{}$ If $dV/dr=0,$ the pseudospin symmetry is exact. The pseudospin symmetry is found to be a good approximation for normal nuclei and to become much better for exotic nuclei with a highly diffuse potential, which have $dV/dr\sim 0.$ The energy splitting of the pseudospin partners is smaller for orbitals near the Fermi surface (even in the continuum) than the deeply bound orbitals. The lower components of the Dirac wave functions for the pseudospin partners are very similar and almost equal in magnitude.

The spreading of transition strength is studied in the doorway picture by taking the coupling to the continuum explicitly into account. The internal (configurational) coupling mixes the doorway state with the background states and is responsible for all the states actually having a decay width. Therefore, external mixing of the states via the continuum is induced. If it is large, resonance trapping appears and the states will be demixed. Thus the residual interaction is effectively reduced. As a consequence, the spreading of transition strength can be small also at high excitation energy. The relation to the golden rule is discussed.

The ground-state properties of Hg isotopes are investigated by the deformed skyrme-Hartree-Fock (DSHF) model with new force parameters SKI4 [P. G. Reinhard and H. Flocard, Nucl. Phys. A584, 467 (1995)]. Calculations show that the deformed Skyrme-Hartree-Fock model with the above force parameters provides a good description of the binding energies, radii, and deformation parameters of Hg isotopes. Six kinds of configurations, which include a spherical shape, prolate one, oblate one, and three sets of triaxial shapes, are considered in our calculations, and this almost exhausts all possibilities of deformations for nuclei. A detailed discussion of the numerical results is given in this paper.

The static path plus random phase approximation (SPA+RPA) to the partition function is formulated exactly in a canonical ensemble, for the case of a density decomposition of an arbitrary two-body Hamiltonian. The canonical mean field plus RPA approach is also discussed. Numerical results are shown for a quadrupole interaction, where excellent agreement with the exact canonical results for a light nucleus is obtained. An effective canonical mean field plus RPA approach is in this case also developed, which avoids the sharp phase transition of the ordinary mean field and provides a reliable estimate of full SPA+RPA results.

The breakdown of the isospin symmetry, at the level of the quasiparticle mean field approximation, and its partial restoration by effective interactions, at the quasiparticle random phase approximation (QRPA) level of approximation, are studied. The method used to define effective symmetry breaking two-body interactions has been applied previously to particle-number and rotational symmetry violations. The connection between the present approach and the proton-neutron QRPA method with renormalized two-particle interactions is discussed. The formalism is applied to calculate nuclear matrix elements for Fermi double beta decay transitions.

Motivated by the sensitivity of collective $M1\mathrm{}$ excitations to the hexadecapole-hexadecapole interaction, we explore the influence of this and other features of sdgIBM on the ground-state band properties of deformed rare-earth nuclei. We adopt microscopically motivated choices of the Hamiltonian parameters and work within the angular-momentum-projected intrinsic state formalism, deriving analytic expressions for observables in which the dependence on wave functions and parameters of the model is explicit. We find that energies of ground-state band excitations are insensitive to the hexadecapole-hexadecapole interaction. On the other hand, its contribution to the deformation energy term in the nuclear binding energy is substantial. Our results indicate that angular momentum projection is important even for well-deformed nuclei and that at least two g bosons should be utilized in the corresponding sdgIBM calculations.

A new Nijmegen soft-core OBE potential model is presented for the low-energy $\mathrm{YN}$ interactions. Besides the results for the fit to the scattering data, which largely defines the model, we also present some applications to hypernuclear systems using the G-matrix method. The potentials are generated by the exchange of nonets of pseudoscalar, vector, and scalar mesons. As is standard in the Nijmegen soft-core models, we also include the $J=0\mathrm{}$ contributions from the tensor $f_2{,f}_2^{\prime }{,a}_2,$ and pomeron Regge trajectories, and use Gaussian form factors to guarantee that the potentials have a soft behavior near the origin. An important innovation with respect to the original soft-core potential is the assignment of the cutoff masses for the baryon-baryon-meson (BBM) vertices in accordance with broken $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_F,$ which serves to connect the $\mathrm{NN}$ and the $\mathrm{YN}$ channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the ${}^3{P}_0$ model with a Gell-Mann–Okubo hypercharge breaking for the BBM coupling. Charge-symmetry breaking in the $\Lambda p$ and $\Lambda n$ channels is included as well. We present six hyperon-nucleon potentials which describe the available $\mathrm{YN}$ cross section data equally well, but which exhibit some differences on a more detailed level. The differences are constructed such that the models encompass a range of scattering lengths in the $\Sigma N$ and $\Lambda N$ channels. In all cases, we obtained ${\chi }^2{/N}_{\mathrm{data}}\approx 0.55$ for 35 $\mathrm{YN}$ data. In particular, we were able to fit the precise experimental datum $r_R=0.468\mathrm{}\pm 0.010$ for the inelastic capture ratio at rest. For the scalar-meson mixing angle we obtained values ${\theta }_S=37\mathrm{}°–40°,$ which points to almost ideal mixing angles for the scalar $q\overline{q}$ states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of $\Lambda$ hypernuclei.

A new result of investigations of the hyperfine structure (hfs) anomaly in Be isotopes is presented. The hfs constant for ${}^{11}\mathrm{Be}$ is obtained by using the core plus neutron type wave function$\hspace{1em}|{2s}_{1/2}〉+|{1d}_{5/2}\times 2^{+};{\frac{1}{2}}^{+}〉.$ A large hfs anomaly of ${}^{11}\mathrm{Be}$ is found, which is mainly due to the large radius of the halo single-particle state.

The statistical properties of quasiparticle spectra in deformed heavy nuclei are studied. It has been found that at the ground state and at minima of the potential, Poisson-like spacing distributions are observed both in the quasiparticle spectra and in the single-particle ones. However, at the saddle point configuration in an even system, the original Wigner-like single-particle spacing distribution changes to a mixture of Wigner- and Poisson-like quasiparticle distributions, whereas for an odd system the pairing hardly changes the Wigner-like distribution. Therefore, from this study we have observed the tendency of the pairing effect to act to make the system more stable.

We measured the ${}^{12}\mathrm{C}{(e,e}^{\prime }p)$ cross section as a function of missing energy in parallel kinematics for $(q,\omega )=(970\mathrm{}\hspace{0.5em}\mathrm{MeV}/c,\hspace{0.5em}330\hspace{0.5em}\mathrm{MeV})$ and $(990\mathrm{}\hspace{0.5em}\mathrm{MeV}/c,\hspace{0.5em}475\hspace{0.5em}\mathrm{MeV}).\mathrm{}$ At $\omega =475\mathrm{}\hspace{0.5em}\mathrm{MeV},$ at the maximum of the quasielastic peak, there is a large continuum ${(E}_m>50\mathrm{}\hspace{0.5em}\mathrm{MeV})$ cross section extending out to the deepest missing energy measured, amounting to almost 50% of the measured cross section. The ratio of data to distorted-wave impulse approximation (DWIA) calculation is 0.4 for both p and s shells. At $\omega =330\mathrm{}\hspace{0.5em}\mathrm{MeV},$ well below the maximum of the quasielastic peak, the continuum cross section is much smaller and the ratio of data to DWIA calculation is 0.85 for the p shell and 1.0 for the s shell. We infer that one or more mechanisms that increase with $\omega$ transform some of the single-nucleon knockouts into a multinucleon knockout, decreasing the valence knockout cross section and increasing the continuum cross section.

Neutron production, in coincidence with fragments emitted in the ${}^{40}\mathrm{C}\mathrm{a}+\mathrm{H}$ reaction at $E_{\mathrm{lab}}=357A$ and $565A\hspace{0.5em}\mathrm{MeV},$ has been measured using a 3-module version of the multifunctional neutron spectrometer MUFFINS. The mean neutron multiplicities for neutrons detected in the angular range covered by MUFFINS $\left(0\mathrm{}°-3.2°\right)$ have been estimated from the comparison between the neutron cross sections, in coincidence with the fragments, and the elemental cross sections. We have found evidence for a preequilibrium emission of prompt neutrons in superposition to a “slower” deexcitation of the equilibrated remnant by emission of nucleons and fragments, as already seen in inclusive rapidity distributions. The energy dependence of the inclusive neutron production cross sections, measured in a previous work, is here interpreted as due to the stronger neutron focusing in the forward direction at the higher energy. Comparison with a BNV+phase space coalescence model is discussed.

The ground-state cross sections and angular distributions of ${}^9\mathrm{Be}(\gamma ,p),{}^9\mathrm{Be}(\gamma ,t),{}^9\mathrm{Be}\left(\gamma {,}^3\mathrm{He}\right),$ and ${}^9\mathrm{Be}(\gamma ,d)$ are reported, together with the cross section for the ${}^9\mathrm{Be}(\gamma ,d)$ reaction to the first excited state. Qualitative discussions of these cross sections are made on the basis of a simple model which assumes free clusters in ${}^9\mathrm{Be}.$ This is similar to the two-cluster model used for ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ for which theoretical calculations have been made. Predictions on the basis of this model indicate the importance of clustering in the photodisintegration of ${}^9\mathrm{Be},{}^6\mathrm{Li},$ and ${}^7\mathrm{Li}.$ The observed angular distributions are consistent with contributions due to $E1\mathrm{}$ and $E2\mathrm{}$ transitions.

The present work provides new results for the half-life of cluster radioactivity and cold fission processes from neutron-deficient nuclei of atomic number near proton shell closure. Results are also reported for the half-life of possible decays leading to the neutron-deficient, doubly magic island near ${}^{100}\mathrm{Sn}.$ The model reproduces the well-established experimental systematics of Geiger-Nuttall diagrams for alpha decay, as well as predicting similar diagrams for heavy cluster emission and cold fission processes.

Weakly populated multinucleon transfer reactions have been studied in ${}^{64}\mathrm{Ni}{+}^{238}\mathrm{U}$ at $E_{\mathrm{lab}}=390\mathrm{}\hspace{0.5em}\mathrm{MeV}$ with a time-of-flight magnetic spectrometer. Angular and Q-value distributions for multinucleon transfer channels have been measured up to the pickup of six neutrons and the stripping of six protons. Differential and total cross sections have been extracted and compared with calculations based on the GRAZING model for grazing reactions. The evolution of the system from a quasielastic to a more complex regime and the present limitations to a detailed understanding of these processes are discussed. The results confirm that a clear experimental distinction can be made between the collisions in the grazing (quasielastic and deep-inelastic) regime and in a more complex one (quasifission).