For some years Lanczos moments methods have been combined with large-scale shell-model calculations in evaluations of the spectral distributions of certain operators. This technique is of great value because the alternative, a state-by-state summation over final states, is generally not feasible. The most celebrated application is to the Gamow-Teller operator, which governs β decay and neutrino reactions in the allowed limit. The Lanczos procedure determines the nuclear response along a line $q=0$ in the $(\omega ,q)$ plane, where ω and q are the energy and three-momentum transferred to the nucleus, respectively. However, generalizing such treatments from the allowed limit to general electroweak response functions at arbitrary momentum transfers seems considerably more difficult: The response function must be determined over the entire $(\omega ,q)$ plane for an operator $O(q)$ that is not fixed, but depends explicitly on q. Such operators arise in any semileptonic process in which the momentum transfer is comparable with (or larger than) the inverse nuclear size. Here we show, for Slater determinants built on harmonic-oscillator basis functions, that the nuclear response for any multipole operator $O(q)$ can be determined efficiently over the full response plane by a generalization of the standard Lanczos moments method. We describe the piecewise moments method and thoroughly explore its convergence properties for the test case of electromagnetic responses in a full sd-shell calculation of ${}^{28}\mathrm{Si}$. We discuss possible extensions to a variety of electroweak processes, including charged- and neutral-current neutrino scattering.

Properties of symmetric and asymmetric nuclear matter have been investigated in the relativistic Dirac-Brueckner-Hartree-Fock approach based on projection techniques using the Bonn A potential. The momentum, density, and isospin dependence of the optical potentials and nucleon effective masses are studied. It turns out that the isovector optical potential depends sensitively on density and momentum, but is almost insensitive to the isospin asymmetry. Furthermore, the Dirac mass $m_D^{*}$ and the nonrelativistic mass $m_{\mathit{NR}}^{*}$ which parametrizes the energy dependence of the single particle spectrum, are both determined from relativistic Dirac-Brueckner-Hartree-Fock calculations. The nonrelativistic mass shows a characteristic peak structure at momenta slightly above the Fermi momentum $k_F$. The relativistic Dirac mass shows a proton-neutron mass splitting of $m_{D,n}^{*}<m_{D,p}^{*}$ in isospin asymmetric nuclear matter. However, the nonrelativistic mass has a reversed mass splitting $m_{\mathit{NR},n}^{*}>m_{\mathit{NR},p}^{*}$ which is in agreement with the results from nonrelativistic calculations.

The ${}^3\mathrm{He}$$(e,e^{\text{'}}p)d$ reaction is studied using an accurate three-nucleon bound state wave function, a model for the electromagnetic current operator including one- and two-body terms, and the Glauber approximation for the treatment of final state interactions. In contrast to earlier studies, the profile operator in the Glauber expansion is derived from a nucleon-nucleon scattering amplitude which retains its full spin and isospin dependence, and is consistent with phase-shift analyses of two-nucleon scattering data. The amplitude is boosted from the center-of-mass frame, where parametrizations for it are available, to the frame where rescattering occurs. Exact Monte Carlo methods are used to evaluate the relevant matrix elements of the electromagnetic current operator. The predicted cross section is found to be in quantitative agreement with the experimental data for values of the missing momentum $p_m$ in the range (0–700) MeV/c, but underestimates the data at $p_m\simeq 1$ GeV/c by about a factor of two. However, the longitudinal-transverse asymmetry, measured up to $p_m\simeq$ 600 MeV/c, is well reproduced by theory. A critical comparison is carried out between the results obtained in the present work and those of earlier studies.

Deformed states in ${}^{40}\mathrm{Ca}$ are investigated with a method of antisymmetrized molecular dynamics. Above the spherical ground state, rotational bands arise from a normal deformation and a superdeformation as well as an oblate deformation. The calculated energy spectra and $E2$ transition strengths in the superdeformed band reasonably agree to the experimental data of the superdeformed band starting from the $0_3^{+}$ state at 5.213 MeV. By the analysis of single-particle orbits, it is found that the superdeformed state has particle-hole nature of an $8p\text{−}8h$ configuration. One of new findings is parity asymmetric structure with ${}^{12}\mathrm{C}+{}^{28}\mathrm{Si}$-like clustering in the superdeformed band. We predict that ${}^{12}\mathrm{C}+{}^{28}\mathrm{Si}$ molecular bands may be built above the superdeformed band due to the excitation of intercluster motion. They are considered to be higher nodal states of the superdeformed state. We also suggest negative-parity bands caused by the parity asymmetric deformation.

Reaction-cross-section data for proton-nucleus scattering up to 1 GeV have been analyzed in a black-disk model. Simple phenomenological relations are derived, which make it possible to predict the energy dependence of proton-nucleus reaction cross sections. The relations require only the total cross sections in nucleon-nucleon scattering and the matter densities of the proton and the target nucleus.

The deformation and orientation dependence of the real part of the interaction potential is studied for two heavy deformed nuclei using the Hamiltonian energy density approach derived from the well-known Skyrme NN interaction with two parameter sets SIII and SkM${}^{*}$. We studied the real part of the heavy ion (HI) potential for ${}^{238}\mathrm{U}$+${}^{238}\mathrm{U}$ pair considering quadrupole and hexadecapole deformations in both nuclei and taking into consideration all the possible orientations, coplanar and noncoplanar, of the two interacting nuclei. We found strong orientation dependence for the physically significant region of the HI potential. The orientation dependence increases with adding the hexadecapole deformation. The azimuthal angle dependence is found to be strong for some orientations. This shows that taking the two system axes in one plane produces a large error in calculating the physical quantities.

We consider the analytical properties of the single-soliton solution in a Skyrmion-type Lagrangian that incorporates the scaling properties of quantum chromodynamics through the coupling of the chiral field to a scalar field interpreted as a bound state of gluons. The model was proposed in previous works to describe the Goldstone pions in a dense medium, being also useful for studying the properties of nuclear matter and the in-medium properties of mesons and nucleons. Guided by an asymptotic analysis of the Euler-Lagrange equations, we propose approximate analytical representations for the single-soliton solution in terms of rational approximants exponentially localized. Following the Padé method, we construct a sequence of approximants from the exact power-series solutions near the origin. We find that the convergence of the approximate representations to the numerical solutions is considerably improved by taking the expansion coefficients as free parameters and then minimizing the mass of the Skyrmion using our ansätze for the fields. We also perform an analysis of convergence by computation of physical quantities showing that the proposed analytical representations are very useful for further phenomenological calculations.

We use a simple configuration space chiral model to evaluate nucleon and $\Delta \sigma$-terms. Analytic expressions are consistent with chiral counting rules and give rise to expected nonanalytic terms in the chiral limit. We obtain the results 43 MeV $\le {\sigma }_N\le$ 49 MeV and 28 MeV $\le {\sigma }_{\Delta }\le$ 32 MeV, depending on the $\pi N\Delta$ and $\pi \Delta \Delta$ coupling constants used, which are compatible with values extracted from experiment and produced by other groups.

The isomeric cross section of ${}^{99}\mathrm{Rh}$ has been measured in the ${}^{12}\mathrm{C}+{}^{89}\mathrm{Y}$ reaction at sub-barrier energies using recoil catcher and $\gamma$-ray spectroscopy. The experimental results were compared with CASCADE calculations. The average angular momentum of the CN was obtained from the measured isomeric cross section ratios using GROGI2 and compared with the predictions of a one-dimensional barrier penetration model and a coupled-channel code. The average angular momenta were found to decrease with decreasing beam energy until the fusion barrier, below which it remained constant.

The phase transition around the critical point in the evolution from spherical to deformed γ-unstable shapes is investigated in odd nuclei within the interacting boson fermion model. We consider the particular case of an odd $j=3/2$ particle coupled to an even-even boson core that undergoes a transition from spherical U(5) to γ-unstable O(6) situation. The particular choice of the $j=3/2$ orbital preserves in the odd case the condition of γ-instability of the system. As a consequence, energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviors qualitatively similar to those of the even core. The results are also in qualitative agreement with the recently proposed E(5/4) model, although few differences are present, due to the different nature of the two schemes.

The ${}^3\mathrm{He}$($d,p$)${}^4\mathrm{He}$ reaction has been studied from $E_{c.m.}=600$ keV down to astrophysical energies by means of the “Trojan horse” method using the ${}^6\mathrm{Li}$(${}^3\mathrm{He}$,$p\alpha$)${}^4\mathrm{He}$ three-body reaction at $E_{\mathrm{lab}}=5$ and 6 MeV. Coincidence spectra were measured in kinematic conditions favoring the quasifree ${}^3\mathrm{He}+{}^2\mathrm{H}$ process. The bare astrophysical factor $S_b(E)$ for the ${}^3\mathrm{He}$($d,p$)${}^4\mathrm{He}$ reaction was extracted from the three-body cross section in the modified plane-wave Born approximation. Comparison with the $S_b$ extrapolation from the free two-body data is presented. The independent estimate of the screening potential as obtained with the present work seems to confirm the theoretical adiabatic limit.

Fission fragment anisotropies and fusion cross sections were measured for ${}^{13}\mathrm{C}+{}^{232}\mathrm{Th}$ in the energy range $0.9<E/V_B<1.2$. The experimental results were compared with ${}^{14}\mathrm{N}+{}^{232}\mathrm{Th}$ ($\alpha <{\alpha }_{\mathit{BG}}$) and ${}^{12}\mathrm{C}+{}^{232}\mathrm{Th}$ ($\alpha >{\alpha }_{\mathit{BG}}$). It is found that the observed anisotropies are much closer to that of the ${}^{12}\mathrm{C}+{}^{232}\mathrm{Th}$ system.

We calculate the muon capture rate on the deuteron to next-to-next-to-leading order in the pionless effective field theory. The result can be used to constrain the two-nucleon isovector axial coupling $L_{1,A}$ to $\pm 2$ fm${}^3$ if the muon capture rate is measured to the 2% level. From this, one can determine the neutrino-deuteron breakup reactions and the pp fusion cross section in the sun to the same level of accuracy.

The absolute cross section of the ${}^{13}\mathrm{C}$($\alpha ,n$)${}^{16}\mathrm{O}$ reaction has been measured at $E_{\alpha }=0.8$ to 8.0 MeV with an overall accuracy of 4%. The precision is needed to subtract reliably a background in the observation of geo-neutrinos, e.g. in the KamLAND detector.

The isoscalar giant monopole resonance (ISGMR) and isovector giant dipole resonance (IVGDR) in finite nuclei are studied within the framework of a relativistic transport approach. Small-amplitude oscillations are analyzed with the relativistic Vlasov equation, i.e., neglecting nucleon collision terms. The excitation energies of ISGMR and IVGDR are obtained for spherical nuclei with various sets of Lagrangian parameters. In the case of ${}^{208}\mathrm{Pb}$ we study in detail the dependence of the monopole response on the effective mass and symmetry energy at saturation $a_4$ given by the used covariant effective interaction. We show that a reduced $m^{*}$ and a larger $a_4$ can compensate for the effect on the ISGMR energy centroid of a much larger compressibility modulus $K_{\mathit{nm}}$. The role of the symmetry energy is confirmed by the observation of reduced corrections for the more symmetric ${}^{90}\mathrm{Zr}$. This result is important for overcoming the conflicting determination of nuclear compressibility between nonrelativistic and relativistic effective interactions. For symmetry-energy dynamical effects, we analyze the influence of the inclusion of an effective isovector-scalar channel, δ-meson field, with constant- and density-dependent couplings. We show that the δ-meson contribution, keeping fixed the equilibrium $a_4$ value, leads to a reduction in the centroid energy of the ISGMR and IVGDR for ${}^{208}\mathrm{Pb}$. The same mechanism can account for the apparent paradox of a decrease of the frequency of a IVGDR mode in heavy nuclei (of volume type) even in presence of a larger $a_4$. All that in fact reveals the sensitivity of the ISGMR and IVGDR collective motions for neutron-rich systems on the slope (or pressure) of the symmetry energy at saturation. Density-dependent vertices do not much affect our conclusions. Following as a guidance the dispersion relations in nuclear matter, we see two main reasons for that: The smoothness of the density dependences around saturation and the presence of compensation effects coming from rearrangement terms.

The level structure of ${}_{60}^{140}{\mathrm{Nd}}_{80}$ has been established up to spin 48 by in-beam γ-ray spectroscopy by use of the ${}^{96}\mathrm{Zr}$(${}^{48}\mathrm{Ca}$, $4n$) reaction. High-fold γ-ray coincidences were measured with the EUROBALL spectrometer. Twelve new rotational bands have been discovered at high spins. They are interpreted as being formed in a deep triaxial minimum at ${\varepsilon }_2\approx 0.25$ and $\gamma \approx {35}^{°}$. Possible configurations are assigned to the observed bands on the basis of configuration-dependent cranked Nilsson-Strutinsky calculations.

The E3 decays of the ${11}^{-}$ isomers in the isotopes ${}^{194}\mathrm{Pb}$ and ${}^{196}\mathrm{Pb}$ have been studied experimentally and evaluated in terms of configuration mixing due to the development of oblate deformation. New results include a remeasurement of the lifetime of the ${11}^{-}$ isomer in ${}^{194}\mathrm{Pb}$ and clarification of the intensities of its main decay branches including the known 496 keV E3 branch. Its intensity is an order of magnitude weaker than previously reported, leading to an E3 transition strength of 29(4) W.u. Limits are placed on possible E3 decays of the ${11}^{-}$ isomer in ${}^{196}\mathrm{Pb}$ to a previously assigned $8^{+}$ two-proton state. Neither the branch, nor the state is observed. An alternative 562 keV transition to a new state at 2630 keV is proposed, with an E3 strength of 26(2) W.u. The approximately constant E3 strength for the range of even-even isotopes ${}^{190-196}\mathrm{Pb}$ is consistent with an oblate deformation for the ${11}^{-}$ state of similar magnitude. This is supported by K-constrained potential-energy-surface calculations for the ${11}^{-}$ and $8^{+}$ configurations.

We apply a large-scale shell model to the study of proton-rich odd-mass nuclei with $N\approx Z$. Calculations predict unexpected structure in the ${}^{69}\mathrm{As}$ nucleus for which a detailed experiment was recently performed. In this odd-proton nucleus, one neutron competes with one proton for occupying the high-j intruder orbit $g_{9/2}$ in the $9/2_1^{+}$ state and almost solely occupies the $g_{9/2}$ orbit in other low-lying positive-parity states. The $T=0,J=9$ one-proton-one-neutron alignment takes place in the negative-parity states with medium-high spins. A unique coexistence of two lowest bands with positive and negative signs of spectroscopic quadrupole moments is predicted.