The formalism for the nucleon-pair approximation of the shell model (NPSM) is greatly simplified by applying the Wick theorem for the coupled cluster in a more sagacious way. Using a new coupling scheme of the basis, the new formalism not only unifies the analytic expressions of the Hamiltonian matrix elements for even and odd nuclei (odd-even or odd-odd), but more importantly reduces the computing time drastically, which is crucial for the NPSM calculations of odd nuclei to be realizable.

In a transport model that combines initial state interactions of the photon with final state interactions of the produced particles we present a calculation of inclusive photoproduction of mesons in nuclei in the energy range from 1 to 7 GeV. We give predictions for the photoproduction cross sections of pions, etas, kaons, antikaons, and ${\pi }^{+}{\pi }^{-}$ invariant mass spectra in ${}^{12}\mathrm{C}$ and ${}^{208}\mathrm{Pb}.$ The effects of nuclear shadowing and final state interaction of the produced particles are discussed in detail.

The expansion coefficients $x_k$ generated by expanding the thermodynamic potential in powers of the fugacity are the same as the cluster functions used in calculating the canonical partition function. Using the well-known results for the expansion of the thermodynamic potential symmetrization effects can be included exactly in calculating with the canonical distribution. Contributions from bound states and particle-particle interactions can be included in a systematic manner.

We calculated the differential and total cross sections of the reaction $\pi \overrightarrow{d}\eta \mathrm{NN}$ near threshold taking into account all the single- and double-scattering graphs within a relativistic formalism. The net effect of the second order diagrams is very small since there is a strong cancellation between the pion-exchange diagram and the sum of the η exchange with the nucleon-nucleon final state interaction diagrams. Our theoretical results are compared with recent experimental data for the differential yield, corresponding to the counting rate for the detection of the two photons into which the produced η decays. The quality of the agreement between theory and existing data between 35 and 100 MeV above threshold does not indicate, at those energies, effects of a possible $\eta \mathrm{NN}$ quasibound state.

The Holstein-Primakoff mapping for pairs of bosons is extended in order to accommodate single boson mapping. The proposed extension allows a variety of applications and especially puts the formalism at finite temperature on firm ground. The new mapping is applied to the $O(N+1\mathrm{})\mathrm{}$ anharmonic oscillator with global symmetry broken down to $O\left(N\right).$ It is explicitly demonstrated that N-Goldstone modes appear. This result generalizes the Holstein-Primakoff mapping for interacting bosons as developed by Aouissat, Schuck, and Wambach [Nucl. Phys. A618, 402 (1997)].

We report quantum Monte Carlo calculations of ground and low-lying excited states for $A=8\mathrm{}$ nuclei using a realistic Hamiltonian containing the Argonne $v_{18}$ two-nucleon and Urbana IX three-nucleon potentials. The calculations begin with correlated eight-body wave functions that have a filled $\alpha$-like core and four p-shell nucleons $\mathrm{LS}$ coupled to the appropriate ${(J}^{\pi };T)$ quantum numbers for the state of interest. After optimization, these variational wave functions are used as input to a Green’s function Monte Carlo calculation made with a new constrained path algorithm. We find that the Hamiltonian produces a ${}^8\mathrm{Be}$ ground state that is within 2 MeV of the experimental resonance, but the other eight-body energies are progressively worse as the neutron-proton asymmetry increases. The ${}^8\mathrm{Li}$ ground state is stable against breakup into subclusters, but the ${}^8\mathrm{He}$ ground state is not. The excited state spectra are in fair agreement with experiment, with both the single-particle behavior of ${}^8\mathrm{He}$ and ${}^8\mathrm{Li}$ and the collective rotational behavior of ${}^8\mathrm{Be}$ being reproduced. We also examine energy differences in the $T=1,2\mathrm{}$ isomultiplets and isospin-mixing matrix elements in the excited states of ${}^8\mathrm{Be}.$ Finally, we present densities, momentum distributions, and studies of the intrinsic shapes of these nuclei, with ${}^8\mathrm{Be}$ exhibiting a definite $2\alpha$ cluster structure.

Low-lying collective states in nuclei are investigated in the framework of the interacting boson model using an ensemble of random many-body interactions. It is shown that whenever the number of bosons is sufficiently large compared to the rank of the interactions, the spectral properties are characterized by a dominance of $L^P{=0\mathrm{}}^{+}$ ground states and the occurrence of both vibrational and rotational band structures. This indicates that these features represent a general and robust property of the collective model space.

A dynamical model based on effective Lagrangians is proposed to describe the bremsstrahlung reaction $\pi \overrightarrow{N}\pi N\gamma$ at low energies. The Δ(1232) degrees of freedom are incorporated in a way consistent with both electromagnetic gauge invariance and invariance under contact transformations. The model also includes the initial- and final-state rescattering of hadrons via a T matrix with off-shell effects. The $\pi N\gamma$ differential cross sections are calculated using three different T-matrix models and the results are compared with the soft photon approximation, and with experimental data. The aim of this analysis is to test the off-shell behavior of the different T matrices under consideration.

The recently proposed irreducible tensor formalism for hadron scattering and reactions is extended to pion production in $\mathrm{NN}$ collisions and a form akin to that of Wolfenstein for elastic $\mathrm{NN}$ scattering is derived together with exact partial wave expansions for the amplitudes. Explicit formulas are derived for spin observables relevant to differential as well as total cross section measurements employing a polarized beam on a polarized target which are currently of experimental interest.

Using the Landau theory of phase transitions we investigate the shape evolution of strontium and zirconium isotopes as a function of temperature and spin. The expansion of the free energy up to sixth power in β is used in these calculations. The spin dependence is introduced by additional constants which are obtained by fitting with the temperature-dependent moment of inertia. Thermal fluctuations are included in the usual way. Orientation fluctuations have been ignored in these calculations. We show that in the presence of thermal fluctuations, the average shapes differ from the most probable shapes.

Fusion cross sections were measured for the systems ${}^{16}\mathrm{O}$ and ${}^{28}\mathrm{Si}{+}^{120}\mathrm{Sn}$ in order to understand the role of specific channels involved in sub-barrier fusion. Fusion cross sections were measured by direct detection of the evaporation residues. Extracted fusion barrier distributions were analyzed using the exact coupled-channel code CCFULL as well as the simplified code CCMOD. These calculations show that the observed fusion barrier distribution for the Si+Sn system is reproduced only if the rotational excitation in ${}^{28}\mathrm{Si}$ is taken into account.

In view of the recent experiments on neutrino oscillations performed by the LSND and KARMEN Collaborations as well as future experiments, we present new theoretical results of the flux-averaged ${}^{12}\mathrm{C}({\nu }_e{,e}^{-}{)}^{12}\mathrm{N}$ and ${}^{12}\mathrm{C}({\nu }_{\mu },{\mu }^{-}{)}^{12}\mathrm{N}$ cross sections. The approaches used are charge-exchange random-phase approximation (RPA), charge-exchange RPA among quasiparticles (QRPA), and the shell model. With a large-scale shell-model calculation the exclusive cross sections are in nice agreement with the experimental values for both reactions. The inclusive cross section for ${\nu }_{\mu }$ coming from the decay-in-flight of ${\pi }^{+}$ is $15.2\times {10}^{-40}\hspace{0.5em}{\mathrm{cm}}^2$ (when Hartree-Fock wave functions are used), to be compared to the experimental value of $12.4\pm 0.3\pm 1.8\times {10}^{-40}\hspace{0.5em}{\mathrm{cm}}^2,$ while the one due to ${\nu }_e$ coming from the decay-at-rest of ${\mu }^{+}$ is $16.4\times {10}^{-42}\hspace{0.5em}{\mathrm{cm}}^2$ which agrees within experimental error bars with the measured values. The shell-model prediction for the decay-in-flight neutrino cross section is reduced compared to the RPA one, namely $19.2\times {10}^{-40}\hspace{0.5em}{\mathrm{cm}}^2.$ This is mainly due to the different kind of correlations taken into account in the calculation of the spin modes (in particular, because of the quenching in the $1^{+}$ channel) and partially due to the shell-model configuration basis which is not large enough, as we show using arguments based on sum rules. Results for exclusive and inclusive muon capture rates and $\beta$ decay are given and are close to the experimental findings.

It is shown how to construct a basis in which two arbitrary complex antisymmetric matrices C and $C^{\prime }$ acquire simultaneously canonical forms. The present construction is not restricted by any conditions on the properties of the $C^{+}{C}^{\prime }$ matrix. Canonical bases pertaining to the generator-coordinate-method treatment of many-fermion systems are discussed.

A phenomenological analysis of diffractive dissociation of nuclei in proton-nucleus and meson-nucleus collisions is presented. The theoretical approach employed here is able to take into account at once data of the HELIOS and EHS/NA22 Collaborations that exhibit quite different atomic mass dependences. Possible extensions of this approach to hard diffraction in nuclear processes are also discussed.

Configuration-constrained nuclear shape calculations are used to show that reinforcing neutron and proton orbital structures create exceptional conditions for the formation of multiquasiparticle isomers in neutron-rich hafnium isotopes, with axially symmetric, prolate shapes. Highly excited, long-lived states are predicted. However, at angular momenta close to 40$ħ,$ orbital alignment effects for collective oblate rotation lead to a deep potential minimum that competes energetically with the prolate multiquasiparticle states.

Evaporation residue cross sections for ${}^{28}\mathrm{Si}{+}^{198}\mathrm{Pt}$ and ${}^{76}\mathrm{Ge}{+}^{150}\mathrm{Nd},$ both of which form a compound nucleus ${}^{226}\mathrm{U},$ were measured in the vicinity of the Coulomb barrier. The measurement gives direct evidence that the system really fuses together to form a fully equilibrated compound nucleus. For the ${}^{28}\mathrm{Si}{+}^{198}\mathrm{Pt}$ reaction, we have measured the fission fragments to determine the fusion cross section by taking advantage of the highly fissile character of ${}^{226}\mathrm{U}.$ The evaporation residue cross section and the fusion cross section for ${}^{28}\mathrm{Si}{+}^{198}\mathrm{Pt}$ allowed us to investigate the deexcitation process (exit channel) of the compound nucleus ${}^{226}\mathrm{U},$ and the parameters entering in a statistical model calculation could be determined. By estimating the deexcitation of the compound nucleus ${}^{226}\mathrm{U}$ with the statistical model, the effect of the deformed nucleus ${}^{150}\mathrm{Nd}$ on the fusion reaction ${}^{76}\mathrm{Ge}{+}^{150}\mathrm{Nd}$ was extracted. The experimental data indicated that there is more than 13 MeV extra-extra-push energy for the system to fuse together when the projectile ${}^{76}\mathrm{Ge}$ collides at the tip of the deformed ${}^{150}\mathrm{Nd}$ nucleus. On the contrary, for the side collision which is more compact in configuration than the tip collision, no fusion hindrance is suggested.

A systematic study of predictions of the interacting boson approximation (IBA)-2 model leads to the identification of two parameter invariants such that calculations with the same values of the invariants yield results that are identical in certain cases and show close similarities under a wider set of conditions. The invariants validate a much-used form of the IBA-2 Hamiltonian and provide a systematic method to simplify IBA-2 calculations by choosing a truncated Hamiltonian with the same invariant values as more general Hamiltonians.

Fusion-evaporation cross sections have been measured for ${}^{36}\mathrm{S}{+}^{90,96}\mathrm{Zr}$ to high accuracy near the Coulomb barrier. The sub-barrier cross sections for ${}^{36}\mathrm{S}{+}^{96}\mathrm{Zr}$ are much larger compared to ${}^{36}\mathrm{S}{+}^{90}\mathrm{Zr}.$ The extracted fusion barrier distributions have different shapes, with essentially one peak for ${}^{36}\mathrm{S}{+}^{90}\mathrm{Zr},$ and a wider and more complex structure for ${}^{36}\mathrm{S}{+}^{96}\mathrm{Zr}.$ Coupled-channels calculations explain the larger sub-barrier enhancement for ${}^{36}\mathrm{S}{+}^{96}\mathrm{Zr}$ as due mainly to the strong octupole vibration in ${}^{96}\mathrm{Zr}.$ However, the calculations do not reproduce well the barrier distribution for this system. The comparison with ${}^{40}\mathrm{Ca}{+}^{90,96}\mathrm{Zr}$ suggests that couplings to nucleon transfer channels may play a role in the large enhancement of sub-barrier fusion for ${}^{40}\mathrm{Ca}{+}^{96}\mathrm{Zr}.$

Tilted-axis cranking calculations have been performed for multiquasiparticle states in well-deformed $A\approx 180$ nuclei. In the limit of zero pairing, not only are the calculated moments of inertia substantially smaller than for rigid rotation, but also they are close to the experimental values. The moments of inertia are found to be insensitive to dynamic pair correlations.

Existing cross-section data for $1p$-shell knockout in the reaction ${}^{12}\mathrm{C}{(e,e}^{\prime }{p)}^{11}\mathrm{B}$ —as obtained under different kinematic conditions—are shown to be mutually consistent, apart from a recent measurement performed in Mainz. New data have been collected at the Amsterdam Pulse Stretcher that confirm the normalization of the older measurements. An analysis of the world’s ${}^{12}\mathrm{C}{(e,e}^{\prime }{p)}^{11}\mathrm{B}$ data has yielded precise values of the spectroscopic factor for $1p$-shell and $1s$-shell knockout from ${}^{12}\mathrm{C}.$ These values have been used to evaluate the transparency of the ${}^{12}\mathrm{C}$ nucleus for $1p$-shell and $1s$-shell protons separately on the basis of recent high-energy ${}^{12}\mathrm{C}{(e,e}^{\prime }{p)}^{11}\mathrm{B}$ data taken at a four-momentum transfer squared $Q^2$ of 1.1 $(\mathrm{GeV}{/c)}^2.$ As the resulting average value of the nuclear transparency, $0.81\pm 0.04,$ is considerably higher than the value obtained from previous analyses and theoretical estimates, the high $Q^2$ data were used instead for an independent determination of the spectroscopic strength for $1p+1s$ knockout. Combining these results with the low $Q^2$ data the spectroscopic factors appear to be momentum-transfer dependent. Possible explanations of these surprising results in terms of reaction-mechanism effects or a possible breakdown of the quasiparticle concept at high $Q^2$ are discussed as well.