The isospin generalized BCS equations and the Hartree-Fock-Bogoliubov equation are solved for the ground states of even $N=Z$ nuclei with mass number $A=76\mathrm{}-96.$ The calculations include isospin $T=1\mathrm{}$ ($pp,$ $nn,$ and $\mathrm{np}$) pair correlations as well as isospin $T=0\mathrm{}$ $\mathrm{}\left(\mathrm{np}\right)\mathrm{}$ pair correlations. There is a transition from $T=1\mathrm{}$ pairing at the beginning of this isotope sequence to $T=0\mathrm{}$ pairing at the end of the sequence, with the possibility of a mixed phase containing both $T=0\mathrm{}$ and $T=1\mathrm{}$ pairing near the middle of the sequence.

The scattering length for the η-meson collision with deuteron is calculated on the basis of rigorous few-body equations (AGS) for various $\eta N$ input. The results obtained strongly support the existence of a resonance or quasibound state close to the $\eta d$ threshold.

Cross sections for the $\mathrm{}(p,t)\mathrm{}$ reaction to ground states of even-even nuclei from Zr to Hg are interpreted in a simple approach. They are shown to be sensitive both to the degree of shell filling (which is related to the number of $L=0\mathrm{}$ pairs in the ground state) and to the difference in the number of these pairs between target and final nuclei (that is, to the overlap of the initial and final systems). The cross sections separate according to the two broad classes of nuclei—vibrational and rotational. The analysis is carried out in both a model-independent way and within the framework of the interacting boson approximation.

We found the hidden symmetry of the pseudospin approximation which is inherent in the Dirac equation both for the spherical potential and for the deformed potential with axially symmetric shape. For both cases, we found two kinds of conditions, i.e., an exact condition and an approximate condition for the pseudospin symmetry. The former condition is not always satisfied in real nuclei, but the latter condition is realistic and applicable to real nuclei.

The first measurement of the cross section of the quasifree $p\overrightarrow{n}\mathrm{pn}\eta$ reaction has been carried out at the CELSIUS storage ring using a deuterium internal cluster jet target. The energy dependence of the cross section is extracted using a fixed incident proton energy of $T_p=1350\mathrm{}\hspace{0.5em}\mathrm{MeV}$ and exploiting the Fermi momentum of the struck neutron. The data cover a range of center-of-mass excess energies from 16 to 109 MeV. The shape of the excitation function is broadly similar to that of the $p\overrightarrow{p}\mathrm{pp}\eta$ reaction, though with a cross section about a factor of 6.5 larger.

$\gamma$-ray spectroscopy of the high-spin states of the neutron-deficient nucleus ${}^{187}\mathrm{Pb}$ has been conducted with the ${}^{155}\mathrm{Gd}{(}^{36}\mathrm{Ar},4n)$ reaction. A cascade of three transitions was deduced from $\gamma -\gamma$ coincidence data gated by detection of recoiling evaporation residues in a gas-filled recoil separator. In an earlier, separate experiment, two of these $\gamma$ rays were positively identified with ${}^{187}\mathrm{Pb}$ by recoil-$\gamma$ coincidence measurements with a high-resolution, recoil mass spectrometer. From comparison with similar sequences in heavier odd-$A$ lead isotopes, the cascade in ${}^{187}\mathrm{Pb}$ is associated with the sequence of three $E2\mathrm{}$ transitions from the yrast ${\frac{25}{2}}^{+}$ level to a low-lying ${\frac{13}{2}}^{+}$ isomer. The variation of excitation energy with mass number of the levels concerned suggests that their structure can be associated with weak coupling of an odd $i_{13/2}$ neutron to states in the spherical well. However, the possibility that they are influenced by mixing with states in the prolate-deformed well cannot be discounted.

The $\beta$ decay of ${}^{40}\mathrm{Ti}$ and ${}^{41}\mathrm{Ti}$ was studied by measuring the $\beta$-delayed proton and $\gamma$ emission. The half-lives for ${}^{40}\mathrm{Ti}$ and ${}^{41}\mathrm{Ti}$ were determined to be 54(2) and 82(3) ms, respectively. The experimental $\beta$-decay strengths are compared with shell-model calculations and results from other measurements. The integrated Gamow-Teller strengths for ${}^{40}\mathrm{Ti}$ and ${}^{41}\mathrm{Ti}$ were found to be quenched, compared to the calculations, by factors of 0.79(3) and 0.93(3), respectively. Based on the experimental ${}^{40}\mathrm{Ti}\hspace{0.5em}\beta$-decay strength, the neutrino absorption cross section and induced neutrino event rates for ${}^{40}\mathrm{Ar}$ were determined to be $14.3\left(3\right)\mathrm{}\times {10}^{-43}\hspace{0.5em}{\mathrm{cm}}^2$ and $9.4\pm 0.2\left(\mathrm{stat}{)}_{-1.6}^{+1.3\mathrm{}}\right(\mathrm{syst})$ SNU, respectively.

The ${}^{102}\mathrm{Ru}{\mathrm{}(d,p)\mathrm{}}^{103}\mathrm{Ru}$ reaction was studied at the Pelletron-Enge-spectrograph facility up to 3.5 MeV with the nuclear emulsion technique. In all 73 levels were populated and for 64 of them angular distributions are presented. Through the usual distorted wave Born approximation analysis, transferred l values and the corresponding spectroscopic factors could be attributed with certainty to 31 and doubtfully to $\sim 20$ more excitations, several of them new. Most of the one-particle strength is concentrated in the yrast levels, below 0.3 MeV. Only the $l=2\mathrm{}$ strength is appreciably fragmented. Even within the extended excitation energy range and with the low detection limit of the present experiment, about half of the expected $\mathrm{}(d,p)\mathrm{}$ strength remains undetected in ${}^{103}\mathrm{Ru},$ in contrast to ${}^{101}\mathrm{Ru}.$

High-spin states in ${}^{108}\mathrm{Sb}$ were populated using the ${}^{54}\mathrm{Fe}{(}^{58}\mathrm{Ni},3pn)$ reaction at a beam energy of 243 MeV and the subsequent γ decay was studied using the Gammasphere array. A new sequence of magnetic dipole transitions has been observed in addition to a previously known $M1\mathrm{}$ band in ${}^{108}\mathrm{Sb}.$ These bands may be interpreted, within the tilted axis cranking model as magnetic rotational bands with $\pi [g_{7/2}^2\otimes {(g}_{9/2}{)}^{-1}]$ $\otimes \nu \left[h_{11/2}\right]$ and $\pi [h_{11/2}{g}_{7/2}\otimes {(g}_{9/2}{)}^{-1}]\otimes \nu \left[{(g}_{7/2}{d}_{5/2}\right)]$ configurations.

In-beam γ rays have been observed in the neutron-deficient isotopes ${}^{170,171,172}\mathrm{Pt}$ using the recoil-decay tagging technique. The yrast transition sequence proposed for ${}^{172}\mathrm{Pt}$ indicates that the $0^{+}$ bandhead of the deformed intruder band is situated about 900 keV above the weakly deformed ground state, i.e., its excitation energy has risen by about 300 keV compared to ${}^{174}\mathrm{Pt}.$ The measured energy of the $2^{+}\to 0^{+}$ transition in ${}^{170}\mathrm{Pt}$ supports an even larger increase in the excitation energy of the intruder configuration with the departure from the middle of the 82–126 major neutron shell. Furthermore, a band with transition energies almost identical to those found in ${}^{172}\mathrm{Pt}$ has been assigned to ${}^{171}\mathrm{Pt}$ and was interpreted as corresponding to a rotationally aligned $i_{13/2}$ neutron orbital coupled to the core excitations.

The ${}^{13}\mathrm{C}{(}^{14}\mathrm{N}{,}^{13}\mathrm{C}{)}^{14}\mathrm{N}$ proton exchange reaction has been measured at an incident energy of 162 MeV. Angular distributions were obtained for proton transfer to the ground and low-lying excited states in ${}^{14}\mathrm{N}.$ Elastic scattering of ${}^{14}\mathrm{N}$ on ${}^{13}\mathrm{C}$ also was measured out to the rainbow angle region in order to find reliable optical model potentials. Asymptotic normalization coefficients for the system ${}^{13}\mathrm{C}+\overrightarrow{p}{}^{14}\mathrm{N}$ have been found for the ground state and the excited states at 2.313, 3.948, 5.106, and 5.834 MeV in ${}^{14}\mathrm{N}.$ These asymptotic normalization coefficients will be used in a determination of the S factor for ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ at solar energies from a measurement of the proton transfer reaction ${}^{14}\mathrm{N}{(}^7\mathrm{Be}{,}^8\mathrm{B}{)}^{13}\mathrm{C}.$

The reactions ${}^{152}\mathrm{Sm}{(}^7\mathrm{Li},4n)$ at 45 MeV and ${}^{124}\mathrm{Sn}{(}^{36}\mathrm{S},p4n)$ at 165 MeV were used to study high-spin states of the $N=90\mathrm{}$ nucleus ${}^{155}\mathrm{Tb}.$ Previously known bands have been greatly extended in spin $\left(I\approx 45ħ\right)$ and a new decoupled sequence was identified. Several band crossings or quasiparticle alignments have been observed in each of the structures, and as a result a configuration assignment has been given to the new band. $B\left(M1\mathrm{}\right)/B\left(E2\mathrm{}\right)\mathrm{}$ transition strength ratios have been extracted from the data and comparisons were made with theoretical predictions. A comprehensive analysis of the signature splitting in the energy levels and $B\left(M1\mathrm{}\right)/B\left(E2\mathrm{}\right)\mathrm{}$ ratios for the $\pi h_{11/2}$ bands of the $A\approx 160$ region has been performed. Possible interpretations for the observed trends in the signature splitting of these structures are discussed.

The quasiparticle random phase approximation (QRPA) and its renormalized version (RQRPA) are used to investigate the particle number fluctuations and the number of particle pairs with $J=0,$ $T=1\mathrm{}$ and $J=1,$ $T=0\mathrm{}$ in the ground state of ${}^{76}\mathrm{Ge}$ as a function of the residual proton-neutron interaction. The study is performed in realistic model spaces including many single particle orbitals. While the RQRPA remains stable after the QRPA collapse the sudden increase in particle number fluctuations exhibits its limitations. The analysis of the number of pairs shows that the isoscalar-isovector phase transition found in exact calculations is causing the QRPA collapse and is missed in the RQRPA formalism.

Neutron deficient collision products with $Z=30\mathrm{}$ to 40 at high excitations are investigated. The proton drip line is significantly altered due to temperature and rotation. The effects of thermal and rotational excitations on proton separation energy are investigated. The level density parameter and the nuclear level density of the isotopes of these f p shell nuclei are also calculated.

We report on the first microscopic study of the properties of two-phonon giant resonances in deformed nuclei. The cross sections of the excitation of the giant dipole and the double giant dipole resonances in relativistic heavy ion collisions are calculated. We predict that the double giant dipole resonance has a one-bump structure with a centroid 0.8 MeV higher than twice the energy for the single giant dipole resonance in the reaction under consideration. The width of the double resonance equals 1.33 of that for the single resonance.

We evaluate the thermal properties of ${}^{40}\mathrm{Ca}$ and ${}^{90}\mathrm{Zr}$ with two different effective Hamiltonians in a mean-field approach. Observed differences in the results are traced to the dependence of thermal properties on the shell gap near the Fermi surface which varies with the choice of Hamiltonian.

A new mechanism for the backbending phenomenon in ${}^{48}\mathrm{Cr}$ is discussed based on a careful analysis of the yrast band, where no level crossing of the single-particle orbits is expected. A newly developed numerical code for solving the self-consistent cranked Hartree-Fock-Bogoliubov (HFB) equation with a maximum overlap criterion is applied to ${}^{48}\mathrm{Cr},$ and various continuous cranked HFB solutions forming many rotational bands are obtained. By using the first derivative of the cranked HFB wave function with respect to the total angular momentum, and by comparing the Thouless-Valatin and the Inglis moments of inertia, it is pointed out that a fully self-consistent mean-field treatment, which properly takes into account the two-body residual interaction, is crucial in explaining cases of backbending phenomena that are not associated with a single-particle level crossing.

We obtain a correlation between the incompressibility $K_{\mathrm{v}}$ and the anharmonicity $K^{\prime }$ of nuclear saturation curves for current Lagrangians and Skyrme-Gogny effective forces—all practically equivalent for the description of binding energies and radii of nuclei. We illustrate explicitly why a change in $K_{\mathrm{v}}$ can be compensated by modifying $K^{\prime }$ and/or the surface thickness t of large nuclei. A realistic value of $t=2.3\mathrm{}\hspace{0.5em}\mathrm{fm}$ fixes $K_{\mathrm{v}}$ to a value of about $(210\mathrm{}\pm 30)\hspace{0.5em}\mathrm{MeV},$ consistent with recent breathing-mode analyses. We refer to previous nonrelativistic Thomas-Fermi approaches that came to the same conclusion.

The isothermal and isentropic incompressibility of asymmetrical nuclear matter are investigated in the framework of the lowest order constrained variational method. Various phenomenological nucleon-nucleon interactions, namely, the Reid, the $\Delta$-Reid, and the new Argonne potentials are used. It is found that the temperature as well as the asymmetry parameter reduce the incompressibility of asymmetrical nuclear matter. The pressure is calculated along isentropic paths. It is shown that the equation state is much harder than the one usually assumed in the hydrodynamical simulations of supernova collapse. Various discussions are made in connection with the problem of supernova explosions and other many-body model calculations.

The interplay between fermionic and bosonic degrees of freedom, in the context of many-body systems and with reference to applications in nuclear and elementary particle physics, is revisited. Starting from the formulation due to Geyer, Hahne, and co-workers, bifermion operators which obey bosonic transformation rules are introduced. Fermion-boson coupling terms are included in the original Hamiltonian. Exact solutions to this Hamiltonian are compared to approximate ones. The occurrence of fermion and boson condensates is discussed.