A pure neutron-rich ${}^{26}\mathrm{Ne}$ beam was obtained at the ISOLDE facility using isobaric selectivity. This was achieved by a combination of a plasma ion source with a cooled transfer line and subsequent mass separation. The high quality of the beam and good statistics allowed us to obtain new experimental information on the ${}^{26}\mathrm{Ne}$ $\beta$-decay properties and resolve a contradiction between earlier experimental data and prediction of shell-model calculations.

The ground states and excited states of the Lipkin model Hamiltonian are calculated using a new theoretical approach that has been derived from an extended time-dependent Hartree-Fock theory known as the time-dependent density-matrix (TDDM) theory. TDDM theory enables us to calculate correlated ground states, and its small amplitude limit (STDDM), which is a version of extended RPA theories based on a correlated ground state, can be used to calculate excited states. It is found that this TDDM plus STDDM approach gives much better results for both the ground states and the excited states than the Hartree-Fock ground state plus RPA approach.

The three-body model of ${}^{14}\mathrm{C}+n+n$ is applied to study the $E2$ transition in ${}^{16}\mathrm{C}$. The $n\text{‐}{}^{14}\mathrm{C}$ potential is chosen to reproduce the single-particle energies of ${}^{15}\mathrm{C}$. The wave functions of ${}^{16}\mathrm{C}$ are obtained as a combination of correlated Gaussians by including the Pauli requirement. It is found that the hindered $E2$ transition can be accounted for by a polarization charge of about $0.10e$ while the $E2$ transition in ${}^{15}\mathrm{C}$ requires a little larger charge of $0.16e$. The soundness of this result is contrasted to the $E2$ transitions in $({}^{17}\mathrm{O},{}^{18}\mathrm{O})$ and $({}^{17}\mathrm{F},{}^{18}\mathrm{Ne})$ nuclei. The longitudinal momentum distribution of ${}^{15}\mathrm{C}$ fragments from ${}^{16}\mathrm{C}$ breakup can be well reproduced.

A parametrization of SU(3) shell-model spectroscopic factors for light nuclei is proposed. It is shown that spectroscopic factors, as calculated from first principles, can be reproduced nearly perfectly, including taking full account of the Pauli principle, without recurring to sophisticated microscopic procedures. The results show that microscopic spectroscopic factors follow a surprisingly simple pattern.

Two high-spin regularly spaced rotational bands with large dynamical moments of inertia have been identified in ${}^{175}\mathrm{Hf}$ with the Gammasphere spectrometer. These new bands are very similar to the previously identified triaxial superdeformed bands in the hafnium nuclei. However, the new bands in ${}^{175}\mathrm{Hf}$ have been linked into the known level scheme and thereby provide the first firm spin assignments for these structures in this region. In order to understand the new bands, theoretical calculations have been performed based on the ULTIMATE CRANKER code. The new bands in ${}^{175}\mathrm{Hf}$ are deduced to be built upon highly deformed structures. No experimental evidence for triaxiality was established and this work suggests that the structure of the so-called “triaxial” superdeformed bands in the $\mathrm{Hf}$ nuclei may be quite different from those identified in the lighter mass $\mathrm{Lu}$ nuclei. Since the two highly deformed bands in ${}^{175}\mathrm{Hf}$ are associated with different deformations, this work also identifies the role of the intruder orbits in polarizing the nuclear shape.

Variational wave functions based on a Margenau-Brink cluster model with short-range and state-dependent correlations and angular momentum projection are obtained for some nuclei with $12⩽A⩽16$. The calculations have been carried out starting from the nucleon-nucleon interaction by using the variational Monte Carlo method. The configuration used consists of three alpha clusters located at the apexes of an equilateral triangle and an additional cluster, not necessarily of alpha type, forming a tetrahedron. This cluster is located at the top of its height. Short-range and state dependent correlations are included by means of a central Jastrow factor and a linear operatorial correlation factor, respectively. Angular momentum projection is performed by using the Peierls-Yoccoz operators. Optimal structures are obtained for all the nuclei studied. Some aspects of our methodology have been tested by comparing with previous calculations carried out without short-range correlations. The binding energy, the root mean square radius, and the one- and two-body densities are reported. The effects of correlations on both the energy and nucleon distributions are analyzed systematically.

Static and dynamic quadrupole moments of C and Ne isotopes are investigated by using the deformed Skyrme Hartree-Fock model and also shell model wave functions with isospin-dependent core polarization charges. We point out that the deformations of C and Ne isotopes have a strong isotope dependence as a manifestation of spontaneous symmetry breaking effect in nuclear physics. The effect of spontaneous symmetry breaking is a general phenomenon known in many fields of physics. It is shown at the same time that the quadrupole moments $Q$ and the magnetic moments $\mu$ of the odd C and odd Ne isotopes depend clearly on assigned configurations, and their experimental data will be useful to determine the deformations of the ground states of nuclei near the neutron drip line. Electric quadrupole $\left(E2\right)$ transitions in even C and Ne isotopes are also studied using the polarization charges obtained by the particle vibration coupling model with shell model wave functions. Although the observed isotope dependence of the $E2$ transition strength is reproduced properly in both C and Ne isotopes, the calculated strength overestimates an extremely small observed value in ${}^{16}\mathrm{C}$.

A study of the interaction of the loosely bound nuclei ${}^{6,7}\mathrm{Li}$ at 9 and $19\mathrm{MeV}∕\text{nucleon}$ with light targets has been undertaken. With the determination of unambiguous optical potentials in mind, elastic data for four projectile-target combinations and one neutron transfer reaction ${}^{13}\mathrm{C}({}^7\mathrm{Li},{}^8\mathrm{Li}){}^{12}\mathrm{C}$ have been measured over a large angular range. The kinematical regime encompasses a region where the mean field (optical potential) has a marked variation with mass and energy, but turns out to be sufficiently surface transparent to allow strong refractive effects to be manifested in elastic scattering data at intermediate angles. The identified exotic feature, a “plateau” in the angular distributions at intermediate angles, is fully confirmed in four reaction channels and is interpreted as a prerainbow oscillation resulting from the interference of the barrier and internal barrier far-side scattering subamplitudes.

Three previously unknown high-energy $\gamma$-ray transitions between 4.2 and 5.4 MeV were identified in the $T_z=-1∕2$ nucleus ${}^{51}\mathrm{Fe}$ following the fusion-evaporation reaction ${}^{32}\mathrm{S}{({}^{28}\mathrm{Si},2\alpha 1n)}^{51}\mathrm{Fe}$. These transitions represent decays of core excited states. The $\gamma$ rays were detected in the Ge detector array Gammasphere combined with the neutron detector system Neutron Shell and the charged-particle array Microball. The three transitions are related to the mirror transitions in the $T_z=+1∕2$ nucleus ${}^{51}\mathrm{Mn}$, and the resulting mirror-energy difference diagram is discussed with predictions from large-scale shell-model calculations.

The possibility of observing the neutrinoless double $\beta$ decay and thus proving the Majorana nature of neutrinos as well as providing a sensitive measure of its mass is a major challenge of today’s neutrino physics. As an attractive alternative, we propose to study the inverse process—the radiative neutrinoless double-electron capture $\left(0\nu 2\mathrm{EC}\right)$. The associated monoenergetic photon provides a convenient experimental signature. Other advantages include the favorable ratio of the $0\nu 2\mathrm{EC}$ to the competing $2\nu 2\mathrm{EC}$ capture rates and, very importantly, the existence of a coincidence trigger to suppress the random background. These advantages partly offset the expected longer lifetimes. Rates for the $0\gamma 2\mathrm{EC}$ process are calculated. High $Z$ atoms are strongly favored. A resonance enhancement of the capture rates is expected to occur at an energy release comparable to the $2P\text{−}1S$ atomic level difference. The resonance conditions are likely to be met for decays to excited states in final nuclei. Candidates for such studies are considered. The experimental feasibility is estimated and found encouraging.

We investigate the energy loss of quark and gluon jets in quark-gluon plasma produced in the central $\mathrm{Au}+\mathrm{Au}$ collisions at RHIC energy. We use the physical characteristics of initial and mixed phases found in the effective quasiparticle model (Yu. A. Tarasov, hep-ph/0307300). We also take into account the possibility of hot glue production at the first stage. We calculate the suppression of ${\pi }^0$ spectrum, which is caused by the energy loss of gluon and quark jets. We compare this suppression with data reported by PHENIX. We find that the suppression is described correctly by the quasiparticle model with decrease of thermal gluon mass and effective coupling in the region of phase transition (at $T\to T_c$ from above). Thus it is possible to investigate the structure of phase transition with the help of hard processes. We also show, that the energy loss at SPS energy is too small to be observable. This is caused, in fact, by too low initial temperature of the plasma phase at this energy.

We study the generalized sum rules and polarizabilities of the nucleon in the framework of the hypercentral constituent quark model (CQM). We include in the calculation all the well-known $3*$ and $4*$ resonances and consider all the generalized sum rules for which there are data available. To test the model dependence of the calculation, we compare our results to the results obtained in the harmonic oscillator CQM. We furthermore confront our results to the model-independent sum rules values and to the predictions of the phenomenological MAID model. The CQM calculations provide a good description of most of the presented generalized sum rules in the intermediate $Q^2$ region (above $\sim 0.2{\mathrm{GeV}}^2$) while they encounter difficulties in describing these observables at low $Q^2$, where the effects of the pion cloud, not included in the present calculation, are expected to be important.

We explore the effects of a microscopic nuclear three-body force on the threshold baryon density for kaon condensation in chemical equilibrium neutron star matter and on the composition of the kaon condensed phase in the framework of the Brueckner-Hartree-Fock approach. Our results show that the nuclear three-body force affects strongly the high-density behavior of nuclear symmetry energy and consequently reduces considerably the critical density for kaon condensation provided that the proton strangeness content is not very large. The dependence of the threshold density on the symmetry energy becomes weaker as the proton strangeness content increases. The kaon condensed phase of neutron star matter turns out to be proton rich instead of neutron rich. The three-body force has an important influence on the composition of the kaon condensed phase. Inclusion of the three-body force contribution in the nuclear symmetry energy results in a significant reduction of the proton and kaon fractions in the kaon condensed phase which is more proton-rich in the case of no three-body force. Our results are compared to other theoretical predictions by adopting different models for the nuclear symmetry energy. The possible implications of our results for the neutron star structure are also briefly discussed.

The impact of nuclear deformation and effective mass $m^{*}∕m$ on the momentum distributions (MD) of occupied proton states in ${}^{238}\mathrm{U}$ is investigated in the self-consistent Skyrme-Hartree-Fock (SHF) scheme with parameterizations SkT6, $\mathrm{Sk}{\mathrm{M}}^{*}$, SLy6, and SkI3 as well as with the phenomenological Woods-Saxon (WS) shell model. The deformation effect turns out to be significant in the low-momentum domain of $K^{\pi }=1∕2^{\pm }$ states (mainly of those lying near the Fermi surface) and negligible for other states. The most remarkable result is that all Skyrme parameterizations (with essentially different $m^{*}∕m$) and the WS potential give very similar MD. This means that the value of effective mass, although crucial for single-nucleon spectra, is not important for the spatial shape of the wave functions and thus for the MD. For the description of MD at $0⩽k⩽300\mathrm{MeV}∕c$, one may use any single-particle scheme fitted properly to the global ground state properties.

The ground and low-lying states of neutron-rich exotic Te and Sn isotopes are studied in terms of the nuclear shell model by the same Hamiltonian used for the spherical-deformed shape phase transition of Ba isotopes, without any adjustment. An anomalously small value is obtained for $B\left(E2;0_1^{+}\to 2_1^{+}\right)$ in ${}^{136}\mathrm{Te}$, consistent with a recent experiment. The levels of ${}^{136}\mathrm{Te}$ up to yrast ${12}^{+}$ are shown to be in agreement with observed ones. It is pointed out that ${}^{136}\mathrm{Te}$ can be an exceptionally suitable case for studying mixed-symmetry $1^{+}$, $2^{+}$, and $3^{+}$ states, and predictions are made for energies and $M1$ and $E2$ properties. Systematic trends of structure of heavier and more exotic Sn and Te isotopes beyond ${}^{136}\mathrm{Te}$ are studied by the Monte Carlo shell model, presenting an unusual and very slow evolution of collectivity/deformation.

We present a detailed theoretical investigation of hadron attenuation in deep inelastic scattering off complex nuclei in the kinematic regime of the HERMES experiment. The analysis is carried out in the framework of a probabilistic coupled-channel transport model based on the Boltzmann-Uehling-Uhlenbeck equation, which allows for a treatment of the final-state interactions beyond simple absorption mechanisms. Furthermore, our event-by-event simulations account for the kinematic cuts of the experiments as well as the geometrical acceptance of the detectors. We calculate the multiplicity ratios of charged hadrons for various nuclear targets relative to deuterium as a function of the photon energy $\nu$, the hadron energy fraction $z_h=E_h∕\nu$, and the transverse momentum $p_T$. We also confront our model results on double-hadron attenuation with recent experimental data. Separately, we compare the attenuation of identified hadrons (${\pi }^{\pm }$, ${\pi }^0$, $K^{\pm }$, $p$, and $\overline{p}$) on ${}^{20}\mathrm{Ne}$ and ${}^{84}\mathrm{Kr}$ targets with the data from the HERMES Collaboration and make predictions for a ${}^{131}\mathrm{Xe}$ target. At the end we turn towards hadron attenuation on ${}^{63}\mathrm{Cu}$ nuclei at EMC energies. Our studies demonstrate that (pre-)hadronic final-state interactions play a dominant role in the kinematic regime of the HERMES experiment while our present approach overestimates the attenuation at EMC energies.

We present calculations for the energies and widths of the lowest $1∕2^{+}$, $1∕2^{-}$, and $5∕2^{+}$ levels of ${}^9\mathrm{B}$, taking into account the information known for the mirror levels in ${}^9\mathrm{Be}$. Comparison is made with the experimental data.

Inelastic scattering of ${}^{11}\mathrm{Li}$ on proton targets at energy of $68\mathrm{MeV}∕\text{nucleon}$ has been studied in the microscopic four-body distorted-wave model. The ground state and three-body continuum excitations of ${}^{11}\mathrm{Li}$ were calculated in the ${}^9\mathrm{Li}+n+n$ cluster model using the method of hyperspherical harmonics. The theory describes the experimental data well and clarifies contributions from the three-body monopole resonance in ${}^{11}\mathrm{Li}$ and from its soft dipole excitation. Various aspects of the ${}^{11}\mathrm{Li}$ excitations and their nature are discussed in terms of correlation plots.

We analyze the Lipkin model in the strong coupling limit using effective operator techniques. We present both analytical and numerical results for low energy effective Hamiltonians. We investigate the reliability of various approximations used to simplify the nuclear many body problem, such as the cluster approximation. We demonstrate, in explicit examples, certain limits to the validity of the cluster approximation but caution that these limits may be particular to this model where the interactions are of unlimited range.

Under the assumption that isospin $T$ is a good quantum number, isobaric analog states and various analogous transitions are expected in isobars with mass number $A$. The strengths of $T_z=\pm 3∕2\to \pm 1∕2$ analogous Gamow-Teller (GT) transitions and analogous $M1$ transitions within the $A=41$ isobar quartet are compared in detail. The $T_z=+3∕2\to +1∕2$ GT transitions from the $J^{\pi }={3∕2}^{+}$ ground state of ${}^{41}\mathrm{K}$ leading to excited $J^{\pi }={1∕2}^{+}$, ${3∕2}^{+}$, and ${5∕2}^{+}$ states in ${}^{41}\mathrm{Ca}$ were measured using the $({}^3\mathrm{He},t)$ charge-exchange reaction. With a high energy resolution of $35\mathrm{keV}$, many fragmented states were observed, and the GT strength distribution was determined up to $10\mathrm{MeV}$ excitation energy $\left(E_x\right)$. The main part of the strength was concentrated in the $E_x=4–6\mathrm{MeV}$ region. A shell-model calculation could reproduce the concentration, but not so well details of the strength distribution. The obtained distribution was further compared with two results of ${}^{41}\mathrm{Ti}$ $\beta$ decay studying the analogous $T_z=-3∕2\to -1∕2$ GT strengths. They reported contradicting distributions. One-to-one correspondences of analogous transitions and analog states were assigned up to $E_x=6\mathrm{MeV}$ in the comparison with one of these ${}^{41}\mathrm{Ti}$ $\beta$-decay results. Combining the spectroscopic information of the analog states in ${}^{41}\mathrm{Ca}$ and ${}^{41}\mathrm{Sc}$, the most probable $J^{\pi }$ values were deduced for each pair of analog states. It was found that ${5∕2}^{+}$ states carry the main part of the observed GT strength, while much less GT strength was carried by ${1∕2}^{+}$ and ${3∕2}^{+}$ states. The gross features of the GT strength distributions for each $J$ were similar for the isospin analogous $T_z=\pm 3∕2\to \pm 1∕2$ transitions, but the details were somewhat different. From the difference of the distributions, isospin-asymmetry matrix elements of $\approx 8\mathrm{keV}$ were deduced. The Coulomb displacement energy, which is sensitive to the configuration of states, showed a sudden increase of about $50\mathrm{keV}$ at the excitation energy of $3.8\mathrm{MeV}$. The strengths of several $M1$ transitions to the IAS in ${}^{41}\mathrm{Ca}$ were compared with the strengths of analogous GT transitions. It was found that ratios of the $M1$ and GT transition strengths were similar, suggesting that the contributions of the $\ell \tau$ term in $M1$ transitions are small.