Decay sequence of the hot ${}^{31}\mathrm{P}$ nucleus has been investigated through exclusive light charged particle measurements using the reaction ${}^{19}\mathrm{F}(96\mathrm{}\hspace{0.5em}\mathrm{MeV}{)+}^{12}\mathrm{C}.$ Information on the sequential decay chain has been extracted through comparison of the experimental data with the predictions of the statistical model. It is observed from the present analysis that exclusive light charged particle data may be used as a powerful tool to probe the decay sequence of hot light compound systems.

The experimental data on the ${}^{16}\mathrm{O}{+}^{12}\mathrm{C}$ and ${}^{18}\mathrm{O}{+}^{12}\mathrm{C}$ elastic scatterings and their optical model analysis are presented. Detailed and complete elastic angular distributions have been measured at the Strasbourg Vivitron accelerator at several energies covering the energy range between 5 and 10 MeV per nucleon. The elastic scattering angular distributions show the usual diffraction pattern and also, at larger angles, refractive effects in the form of nuclear rainbow and associated Airy structures. The optical model analysis unambiguously shows the evolution of the refractive scattering pattern. The observed structure, namely the Airy minima, can be consistently described by a nucleus-nucleus potential with a deep real part and a weakly absorptive imaginary part. The difference in absorption in the two systems is explained by an increased imaginary (mostly surface) part of the potential in the ${}^{18}\mathrm{O}{+}^{12}\mathrm{C}$ system. The relation between the obtained potentials and those reported for the symmetrical ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}{+}^{12}\mathrm{C}$ systems is drawn.

We develop a fully relativistic distorted wave impulse approximation (DWIA) model for photonuclear reactions using the relativistic mean field theory for the bound state, and the Pauli reduction of the scattering state, which is calculated from a relativistic optical potential. Results for the ${}^{12}\mathrm{C}(\gamma ,p)$ and ${}^{16}\mathrm{O}(\gamma ,p)$ differential cross sections and photon asymmetries are displayed in a photon energy range between 60 and 257 MeV, and compared with nonrelativistic DWIA calculations. The effects of the spinor distortion and of the effective momentum approximation for the scattering state are discussed. The sensitivity of the model to different prescriptions for the one-body current operator is investigated. The off-shell ambiguities are large in $(\gamma ,p)$ calculations, and even larger in $(\gamma ,n)$ knockout.

The spectral function of ${}^4\mathrm{He}$ is extracted from a plane-wave approximation to the ${(e,e}^{\prime }p)$ reaction using a fully relativistic formalism. We take advantage of both an algebraic “trick” and a general relativistic formalism for quasifree processes developed earlier to arrive at transparent, analytical expressions for all quasifree ${(e,e}^{\prime }p)$ observables. An observable is identified for the clean and model-independent extraction of the spectral function. Our simple relativistic plane-wave calculations provide baseline predictions for the recently measured, but not yet fully analyzed, momentum distribution of ${}^4\mathrm{He}$ by the A1 Collaboration from Mainz. Yet in spite of its simplicity, our approach predicts momentum distributions for ${}^4\mathrm{He}$ that rival some of the best nonrelativistic calculations to date. Finally, we highlight some of the challenges and opportunities that remain, both theoretically and experimentally, in the extraction of quasifree observables.

The $\pi N$ s-wave scattering lengths have been inferred from a joint analysis of the pionic hydrogen and the pionic deuterium x-ray data using a nonrelativistic approach in which the $\pi N$ interaction is simulated by a short-ranged potential. This potential is assumed to be isospin invariant and its range, the same for isospin $I=3/2\mathrm{}$ and $I=1/2,$ is regarded as a free parameter. The proposed model admits an exact solution of the pionic hydrogen bound state problem, i.e., the $\pi N$ scattering lengths can be expressed analytically in terms of the range parameter and the shift $\left(\epsilon \right)$ and width $\left(\Gamma \right)$ of the $1s$ level of the pionic hydrogen. We demonstrate that for small shifts and short ranges from the exact expression, one retrieves the standard range independent Deser-Trueman formula. The $\pi d$ scattering length has been calculated exactly by solving the Faddeev equations and also by using a static approximation. It has been shown that the same very accurate static formula for $\pi d$ scattering length can be derived (i) from a set of boundary conditions; (ii) by a reduction of Faddeev equations; and (iii) through a summation of Feynman diagrams. By imposing the requirement that the $\pi d$ scattering length, resulting from the Faddeev-type calculation, be in agreement with pionic deuterium data, we obtain bounds on the $\pi N$ scattering lengths. The dominant source of uncertainty in the deduced values of the $\pi N$ scattering lengths are the experimental errors in the pionic hydrogen data.

Charged current reactions of ${\nu }_e$ on ${}^{12}\mathrm{C}$ have been studied using a ${\mu }^{+}$ decay-at-rest ${\nu }_e$ beam at the Los Alamos Neutron Science Center. The cross section for the exclusive reaction ${}^{12}\mathrm{C}({\nu }_e{,e}^{-}{)}^{12}{\mathrm{N}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ was measured to be $(8.9\mathrm{}\pm 0.3\pm 0.9)\times {10}^{-42}$ ${\mathrm{cm}}^2.$ The observed energy dependence of the cross section and angular distribution of the outgoing electron agree well with theoretical expectations. Measurements are also presented for inclusive transitions to ${}^{12}\mathrm{N}$ excited states, ${}^{12}\mathrm{C}({\nu }_e{,e}^{-}{)}^{12}{\mathrm{N}}^{*}$ and compared with theoretical expectations. The measured cross section, $(4.3\mathrm{}\pm 0.4\pm 0.6)\times {10}^{-42}$ ${\mathrm{}\mathrm{cm}}^2,$ is somewhat lower than previous measurements and than a continuum random phase approximation calculation. It is in better agreement with a recent shell model calculation.

The $(p,\gamma )$ cross sections of three stable Sr isotopes have been measured in the astrophysically relevant energy range. These reactions are important for the p process in stellar nucleosynthesis and, in addition, the reaction cross sections in the mass region up to 100 are also of importance concerning the $\mathrm{rp}$ process associated with explosive hydrogen and helium burning. It is speculated that this $\mathrm{rp}$ process could be responsible for a certain amount of p nuclei in this mass region. The $(p,\gamma )$ cross sections of ${}^{84,86,87}\mathrm{Sr}$ isotopes were determined using an activation technique. The measurements were carried out at the 5 MV Van de Graaff accelerator of the ATOMKI, Debrecen. The resulting cross sections are compared with the predictions of statistical model calculations. The predictions are in good agreement with the experimental results for ${}^{84}\mathrm{Sr}(p,\gamma {)}^{85}\mathrm{Y}$ whereas the other two reactions exhibit differences that increase with mass number. The corresponding astrophysical reaction rates have also been computed.

We present measurements of the ${}^{12}\mathrm{C}(p,{\gamma }_0{)}^{13}\mathrm{N}{/}^{13}\mathrm{C}(p,{\gamma }_0{)}^{14}\mathrm{N}$ S factor ratio at $E_p=160\mathrm{}\hspace{0.5em}\mathrm{keV}.$ The overall result of $0.33\pm 0.03$ is in good agreement with the value of this ratio obtained from previous experimental values of the S factors for the ${}^{12}\mathrm{C}(p,{\gamma }_0{)}^{13}\mathrm{N}$ and the ${}^{13}\mathrm{C}(p,{\gamma }_0{)}^{14}\mathrm{N}$ reactions. A value for the total S factor ratio of $S{[}^{12}\mathrm{C}(p,{\gamma }_{\mathrm{total}})]/S{[}^{13}\mathrm{C}(p,{\gamma }_{\mathrm{total}}\left)\right]=0.24\mathrm{}\pm 0.03$ is computed by correcting the ${}^{13}\mathrm{C}(p,{\gamma }_0)$ S factor for transitions to the other intermediate states. The direct + resonance model calculation of this ratio and the impact on the CNO cycle are also explored.

The elastic scattering cross section of ${}^{92}\mathrm{Mo}(\alpha ,\alpha {)}^{92}\mathrm{Mo}$ has been measured at energies of $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\approx 13,$ 16, and 19 MeV in a wide angular range. The real and imaginary parts of the optical potential for the system ${}^{92}\mathrm{Mo}-\alpha$ have been derived at energies around and below the Coulomb barrier. The result fits into the systematic behavior of $\alpha$-nucleus folding potentials. The astrophysically relevant ${}^{96}\mathrm{Ru}(\gamma ,\alpha {)}^{92}\mathrm{Mo}$ reaction rates at $T_9=2.0\mathrm{}$ and $T_9=3.0\mathrm{}$ could be determined to an accuracy of about 16% and are compared to previously published theoretical rates.

A new relation between the neutron skin of a heavy nucleus and the radius of a neutron star is proposed: the larger the neutron skin of the nucleus the larger the radius of the star. Relativistic models that reproduce a variety of ground-state observables cannot determine uniquely the neutron skin of a heavy nucleus. Thus, a large range of neutron skins is generated by supplementing the models with nonlinear couplings between isoscalar and isovector mesons. We illustrate how the correlation between the neutron skin and the radius of the star can be used to place important constraints on the equation of state and how it may help elucidate the existence of a phase transition in the interior of the neutron star.

Transfer reactions constitute a stringent test for nuclear supersymmetry, a theory that simultaneously describes neighboring nuclei with bosonic and fermionic character. We construct and analytically evaluate one-nucleon transfer matrix elements between supersymmetric partners with the $\mathrm{U}\mathrm{}(6/4)\mathrm{}$ case as an example, and stress the need for a careful treatment of bosonic and fermionic operators in the construction of mixed tensor operators.

We study the isospin-singlet neutron-proton pairing in bulk nuclear matter as a function of density and isospin asymmetry within the BCS formalism. In the high-density, weak-coupling regime the neutron-proton paired state is strongly suppressed by a minor neutron excess. As the system is diluted, the BCS state with large, overlapping Cooper pairs evolves smoothly into a Bose-Einstein condensate of tightly bound neutron-proton pairs (deuterons). In the resulting low-density system a neutron excess is ineffective in quenching the pair correlations because of the large spatial separation of the deuterons and neutrons. As a result, the Bose-Einstein condensation of deuterons is weakly affected by an additional gas of free neutrons even at very large asymmetries.

The isospin, density, and energy dependence of the nucleon mean free path in isospin-asymmetric nuclear matter is obtained through geometrical considerations of isospin dependent Pauli blocking and Fermi motion. The nuclear medium isospin effects on nucleon mean free path are studied systematically. It is found that the isospin-dependent nuclear medium effects are important for mean free path of a nucleon in isospin-asymmetric nuclear matter. Meanwhile, the importance of isospin-dependent Pauli blocking in isospin-asymmetric nuclear matter is also discussed.

Using several theoretical models, we have obtained estimates for the spreading widths ${\Gamma }^{\downarrow }$ for the decay out of a superdeformed (SD) band. We pay particular attention to the statistical model by Gu and Weidenmüller. Our results for ${}^{194}\mathrm{Hg}$ and ${}^{194}\mathrm{Pb}$ are compared to other theoretical predictions and to experimental upperbounds for ${\Gamma }^{\downarrow }.$ We find that the models of Gu and Weidenmüller and of Vigezzi et al. yield a consistent description of the data. We relate ${\Gamma }^{\downarrow }$ to the strength $v$ of the interaction that couples the normally deformed levels to the SD level at which the decay out of the SD band occurs. Using an exponential spin dependence of $v,$ we are able to reproduce the intraband intensities in the SD bands in ${}^{194}\mathrm{Hg}$ and ${}^{194}\mathrm{Pb}.$

Rotational band structures in ${}^{162,164}\mathrm{Dy}$ were studied by projectile inelastic excitation on a ${}^{118}\mathrm{Sn}$ target at near-barrier energies. States with spin up to ${24}^{+}{(22\mathrm{}}^{+})$ of the ground-state band and ${18}^{+}{(18\mathrm{}}^{+})$ of the $\gamma$-vibrational band in ${}^{162}\mathrm{Dy}{(}^{164}\mathrm{Dy})$ were populated in these reactions. States with spin spanning from $8^{+}$ to ${20}^{+}$ of the rotationally aligned S band in ${}^{162}\mathrm{Dy}$ were populated by way of its band-crossing point with the $\gamma$-vibrational band at spin ${12}^{+},$ where strong mixing occurred due to an accidental degeneracy. This S band eventually crosses the ground-state band at spin ${18}^{+}$ and becomes the yrast at spin ${20}^{+}.$ From the peripheral-collision $\gamma$-ray yield data, sets of electromagnetic matrix elements for both the intraband and interband transitions were determined by using the Coulomb excitation code, GOSIA. The measured intraband $E2\mathrm{}$ matrix elements were used to derive a quadrupole deformation of the S band that is $\approx 20\%$ larger than those of the nearby low-lying collective bands. This represents the first measurement made for the quadrupole deformation of the S band for states well below the crossing point with the ground-state band. The two-phonon $\gamma$-vibration harmonic strength in ${}^{162}\mathrm{Dy}$ is highly fragmented, 36% of the strength is located in two $K^{\pi }{=4\mathrm{}}^{+}$ bands at excitation energies 1535.9 and 2181.0 keV, respectively. Significant octupole collectivity was observed coupling the ground-state band to the $K^{\pi }{=2\mathrm{}}^{-}$ band in ${}^{162}\mathrm{Dy}.$

Results from the study of the β decay of ${}^{40}\mathrm{P},$ produced in the fragmentation of a ${}^{48}\mathrm{Ca}$ beam, are presented. The ${}^{40}\mathrm{P}$ half-life and delayed-neutron emission probability have been measured to be $153\pm 8\hspace{0.5em}\mathrm{ms}$ and $15.8\pm 2.1\%,$ respectively. On the basis of γ-ray singles and $\gamma \gamma$ coincidence data, $21\gamma$ rays have been assigned to the decay. Three γ rays are assigned to excited states in ${}^{39}\mathrm{S}$ populated in the delayed-neutron branch while a total of $15\gamma$ rays were placed in a level scheme for ${}^{40}\mathrm{S}$ with nine excited states up to 5 MeV. The structure of low-energy states in ${}^{40}\mathrm{S}$ has been fit using the geometrical collective model that indicates the structure to be consistent with that of an anharmonic oscillator with a soft potential.

A method is proposed to improve the treatment of the ground-state correlations in a finite Fermi system compared with the standard random phase approximation (RPA) or earlier suggested renormalized RPA. The correlations lead to nonzero quasiparticle occupancies in the ground state. The method employs modified quasiparticles obtained by a canonical transformation of usual quasiparticles explicitly involving the quasiparticle occupation numbers. A set of equations is derived, which allows one to determine these occupation numbers along with the RPA modes. The formalism is illustrated with the Lipkin-Meshkov-Glick model, and a model for superconducting pairing at a finite temperature. With the new approach, the ground-state correlations are significantly reduced, the energy of the first excited state becomes closer to the exact solution around the region where the RPA collapses, and the superconducting gap monotonously decreases instead of the sharp phase transition. We discuss the effective equivalence of the interaction effects and variation of temperature for the ground-state correlations.

Precise excitation functions for the fusion of ${}^{12}\mathrm{C},$ ${}^{16}\mathrm{O},$ ${}^{28}\mathrm{Si},$ and ${}^{35}\mathrm{Cl}$ on ${}^{92}\mathrm{Zr}$ were measured for bombarding energies spanning the Coulomb barrier regions. Experimental fusion barrier distributions were derived from these data and compared with the results of realistic coupled-channels calculations, which included couplings to all orders and treated excitation energies correctly. To gain reasonable agreement for the heavier projectiles it was necessary to include double-phonon excitations of the first $2^{+}$ and $3^{-}$ vibrational states in ${}^{92}\mathrm{Zr}.$ The diffuseness parameter required to fit the high-energy cross sections increases with increasing charge of the projectile and, as found in earlier work, is higher than that required to fit elastic-scattering data. It is suggested that a potential which falls more rapidly at large distance than the Woods-Saxon form might help explain the anomaly.

A microscopic quantum-mechanical approach to breakup reactions into the low-energy continuum of Borromean two-neutron halo nuclei is developed, taking simultaneously into account Coulomb and nuclear dissociation. The importance of including both elastic and inelastic fragmentation is demonstrated for ${}^6\mathrm{He}$ breakup on C and Pb targets at intermediate energies, for kinematically complete experiments. Recent GSI experimental data are analyzed quantitatively and the results reveal a rich and complex interplay of reaction mechanisms and low-lying halo excitations.

Hot rotating compound nuclei are modeled as ellipsoidally shaped liquid drops. A formalism for the determination of their equilibrium shape distribution is presented. Commonly used metrics associated with the volume element in deformation space are derived with a discussion of their underlying assumptions. Example calculations of shape distributions are presented. These distributions are not characterized by any one type of shape in particular; the full range of deformations from oblate to prolate are populated including spherical and triaxial deformations. However the tail of the distributions extending towards highly deformed prolate configurations is more pronounced especially at the higher angular momenta. The shape of the Coulomb-barrier distributions for the evaporation of charged particles from the nuclear surface, averaged over the equilibrium distribution of shapes, is calculated and its relevance for the understanding of the yield of low-energy $\alpha$ particles observed in evaporation spectra is discussed.