Levinson’s theorem for Dirac particles constrains the sum of the phase shifts at threshold by the total number of bound states of the Dirac equation. Recently, a stronger version of Levinson’s theorem has been proven in which the value of the positive- and negative-energy phase shifts are separately constrained by the number of bound states of an appropriate set of Schrödinger-like equations. In this work we elaborate on these ideas and show that the stronger form of Levinson’s theorem relates the individual phase shifts directly to the number of bound states of the Dirac equation having an even or odd number of nodes. We use a mean-field approximation to Walecka’s scalar-vector model to illustrate this stronger form of Levinson’s theorem. We show that the assignment of bound states to a particular phase shift should be done, not on the basis of the sign of the bound-state energy, but rather, in terms of the nodal structure (even/odd number of nodes) of the bound state.

Calculations of deuteron form factors in light-cone quantum mechanics are discussed. We focus on the criteria for choosing ‘‘good’’ matrix elements of the ‘‘good’’ components of the operator of electromagnetic current in the infinite-momentum frame and in the Breit frame. We develop techniques that can be easily generalized to other operators. The electromagnetic form factors A(${\mathit{q}}^2$) and B(${\mathit{q}}^2$), the axial form factor, and the tensor polarization of the deuteron are obtained and compared with previous calculations.

We propose a nucleon-nucleon potential for which the NN, NΔ, and ΔΔ channels are coupled by energy-independent, nonlocal interactions constructed from meson-exchange interactions. The same vertex couplings that were utilized in earlier studies based on the Bonn single-channel NN potential are adopted. We arrive at our interaction by applying an extension of the folded diagram expansion to coupled channels. The coupled-channel formalism facilitates studies of the interplay between nucleon and delta degrees of freedom and bound-state properties of nuclear matter and finite nuclei. It also establishes a framework that might simplify the treatment of nucleon-nucleon scattering to energies above pion-production threshold.

Ground state energies of the three-nucleon system interacting via standard S-projected potentials are studied using Born-Oppenheimer and hyperspherical adiabatic approximations. The extreme and the uncoupled hyperspherical adiabatic approximations, which are the lower and upper bounds for the exact ground state energy, are found to define a narrow band with the Born-Oppenheimer approximation lying close to it. While the hyperspherical adiabatic approximation conserves the basic symmetry requirements, the other does not. In spite of this, the Born-Oppenheimer approximation is found to be comparable to the other for potentials with a soft core repulsion.

The description of the three-nucleon system in terms of nucleon and Δ degrees of freedom is extended to allow for explicit pion production (absorption) from single dynamic Δ deexcitation (excitation) processes. This mechanism yields an energy dependent effective three-body Hamiltonian. The Faddeev equations for the trinucleon bound state are solved with a force model that has already been tested in the two-nucleon system above pion-production threshold. The binding energy and other bound-state properties are calculated. The contribution to the effective three-nucleon force arising from the pionic degrees of freedom is evaluated. The validity of previous coupled-channel calculations with explicit but stable Δ isobar components in the wave function is studied.

We study the NN phase shifts in a Hamiltonian obtained from quantization of the collective modes in the Skyrme model. We show that a combination of an adiabatic and a diabatic approximation gives a good NN force, with sufficient attraction to produce a bound deuteron. The description of the repulsive core appears to be the main cause for the remaining discrepancies between the Skyrme-model force and phonomenology. Finally we discuss the possibility of finding nonstrange dibaryon resonances in the ${\mathit{J}}^{\mathrm{\pi }}$=$3^{+}$, T=0 channel.

The transient field phenomenon has been ascribed to a polarization transfer between the electrons of the ionic projectiles and the surplus of majority spin electrons of the ferromagnetic host over the minority spin electrons. Earlier attempts to explain this crucial process failed to account for the order of magnitude of the experimentally observed transient field strengths. A recent model which proposes spin exchange scattering between bound projectile electrons and quasifree host electrons as the mechanism of polarization transfer arrives at the correct orders of magnitude but is in conflict with the weak velocity dependence of the experimental polarization, exhibiting a strongly decreasing behavior with increasing velocity. The new model presented here proposes spin exchange between the ionic shell and localized electrons of the ferromagnet as a more adequate approach to the problem. It is shown that calculations involving hydrogenlike ions explain the size of the experimentally observed polarization effects as well as their velocity dependence for various ion probes traversing thin iron foils.

Continuing the systematic investigation into the photoexcitation of isomers over wide mass and energy ranges, the production of ${}_{}{}^{77}{}_{}{}^{}\mathrm{Se}_{}^{\mathit{m}}{}_{}{}^{}$, ${}_{}{}^{79}{}_{}{}^{}\mathrm{Br}_{}^{\mathit{m}}{}_{}{}^{}$, and ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}_{}^{\mathit{m}}{}_{}{}^{}$ was studied with the bremsstrahlung facility at the superconducting Darmstadt linear accelerator. These isomers have half-lives on the order of seconds. Excitation functions were measured for the (γ,γ’) reactions populating the metastable states for energies of 2–7 MeV and the important intermediate states were identified. Nuclear structure calculations with the quasiparticle-phonon model for ${}_{}{}^{79}{}_{}{}^{}\mathrm{Br}$ and the particle- (hole-) core coupling approach for ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$ gave satisfactory descriptions for the strength and position of the dominant mediating levels. Admixtures of fragmented outershell single-particle strength shifted to low energies were identified as essential features of the wave functions of those states. Intermediate states in ${}_{}{}^{77}{}_{}{}^{}\mathrm{Se}$ displayed very large strengths compared to other isomers in the same mass region, providing further support for the correlation between integrated cross sections and ground state deformations recently discovered in the A=160–200 mass region. Such an enhancement would considerably improve the feasibility of a gamma-ray laser based on the sudden deexcitation of isomeric populations in deformed nuclei.

High spin states of doubly odd ${}_{}{}^{214}{}_{}{}^{}\mathrm{Fr}_{127}^{}{}_{}{}^{}$ have been investigated using in-beam γ-ray and conversion electron spectroscopy techniques through the ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$${(}^{11}$B, 3n) and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$${(}^{11}$B, 5n) fusion-evaporation reactions. Completely new spectrocopic information has been obtained. The yrast level structure is established up to spin (${19}^{+}$) and some information on γ transitions from higher-lying levels is also obtained. Two new isomers ${\mathit{T}}_{1/2}$=174(20) ns and ${\mathit{T}}_{1/2}$=11(2) ns were found. Configuration assignments for the low-lying levels are discussed. Information on residual proton-neutron interactions is extracted.

High angular momentum states in ${}_{}{}^{77}{}_{}{}^{}\mathrm{Br}$ were populated via the ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$${(}^{18}$O,α2n${)}^{77}$Br reaction at 65 MeV using the Florida State University (FSU) FN Tandem-LINAC accelerator. The Pitt-FSU array with 9 Compton-suppressed high purity Ge detectors was used to measure prompt γ-γ coincidences. Analysis of the coincidences led to an extension of the positive- and negative-parity bands to spins of (41/$2^{+}$) and (43/$2^{\mathrm{-}}$). Directional correlation of oriented nuclei ratios have been deduced where possible, and spin assignments made accordingly. A cranked-shell-model analysis shows that in the positive-parity band the ν${\mathit{g}}_{9/2}$ alignment occurs at the same frequency as in the neighboring isotopes, ${}_{}{}^{75,79}{}_{}{}^{}\mathrm{Br}$, but with a larger interaction strength. In the negative-parity bands the lower π${\mathit{g}}_{9/2}$ crossing also occurs at about the same frequency as in ${}_{}{}^{75}{}_{}{}^{}\mathrm{Br}$, but with a smaller interaction. The higher frequency ν${\mathit{g}}_{9/2}$ crossing is delayed in ${}_{}{}^{77}{}_{}{}^{}\mathrm{Br}$. Hartree-Fock-Bogolyubov cranking calculations predict considerable γ softness in ${}_{}{}^{77}{}_{}{}^{}\mathrm{Br}$, and particle-rotor model calculations support the interpretation of γ softness or variations in triaxiality within the bands.

The superdeformed band in ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pb}$ has been studied extensively using the reaction ${}_{}{}^{170}{}_{}{}^{}\mathrm{Er}$${(}^{30}$Si,4n) at beam energies of 142, 146, and 151 MeV. New transitions have been added at the top and bottom of the previously known band. Gamma-ray directionsl correlations were measured for most of the transitions in the band verifying the expected stretched E2 character. The collectivity of the band has been measured using the Doppler shift attenuation method yielding an intrinsic quadrupole moment ${\mathit{Q}}_0$ of 18.3±3.0 e b, in good agreement with theoretical predictions. The variations of the dynamic moment of inertia ${\mathit{scrI}}^{\mathrm{}\left(2\right)\mathrm{}}$ as a function of the rotational frequency ħω have been studied and compared with cranked shell model calculations. The dependence of ${\mathit{scrI}}^{\mathrm{}\left(2\right)\mathrm{}}$ on mass for superdeformed bands in the Pb isotopes is also investigated.

A cranking Bohr-Mottelson Hamiltonian is proposed and a formula for the rotational spectrum is derived, showing explicitly the coupling between rotational and vibrational motions. The formula is applied to the rotational bands of even-even nuclei in the rare-earth and actinide regions. The ground-state rotational band (below backbending) and the associated β and γ bands can be represented by a single formula. Nuclear structure information on the parameters is discussed.

The physical processes about x-ray emission, Auger electron emission, and nuclear excitation by electron transition (NEET) induced by deexcitations of the excited atomic states, e.g., the inner shell hole states, are studied self-consistently in the unified nonrelativistic quantum mechanics framework. The emphasis is on exploring the NEET process and its interference with the other two processes. The transition probabilities of these deexcitation channels are given in analytical forms. The numerical calculations for ${}_{76}{}^{189}{}_{}{}^{}\mathrm{Os}$, ${}_{79}{}^{197}{}_{}{}^{}\mathrm{Au}$, and ${}_{93}{}^{237}{}_{}{}^{}\mathrm{Np}$ have been done and compared with the available experimental results.

The photodisintegration of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ into n+ ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ or p+ ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ is calculated by employing the integrodifferential equation approach for the determination of the three- and four-body bound states involved, and by incorporating the final state interaction via an optical potential treatment. The results of this comparatively simple model reproduce the trends found within the integral equation approach, and are in a rather good agreement with the latest experimental data.

The structure of the reference vacuum state plays a very important role in a theoretical dynamic description of interacting particles. This structure is generated by the residual interaction acting between the valence particles and, in systems under extreme high temperature and consequently high pressure, cannot be treated in the framework of the perturbation theory. In this paper we elaborate a nonperturbative approximation to include the vacuum-polarization effects of superconductive type in the calculation of the many-body dynamics. In this proposed model, the wave functions of the system are characterized by the strong coupling of the valence particles with the intrinsic vacuum states. These are associated with (a) superconductive vacuum polarizations, and (b) superconductive virtual particles formed coupling the vacuum excitations to the non-normal parity states of the system. The coupling of the valence particles with the vacuum excitations (a) and (b), in this paper, is generated within the equations of motion methods which, in the limit of factorization methods defined to compute the matrix elements of the nuclear Hamiltonian in the resulting complex states, and with the use of energy-dependent linearization approximations, introduced to generate the superconductive collective modes, are of easy application in the low-energy domain of the interacting systems. The energy-dependent linearization approximations define collective modes which are loose and freely moving in this low-energy domain, while strongly interacting with increasing energy.

The effects of intruder states arising from general positive deformations on the excitation energies, the two-neutron transfer spectroscopic amplitudes for the reaction ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$(t,p${)}^{20}$O, and some electric quadrupole transition amplitudes between some low-lying positive parity states in ${}_{}{}^{20}{}_{}{}^{}\mathrm{O}$ are presented. The intruder states Hamiltonian matrices for infinite and zero deformations and the corresponding predictions obtained from them by mixing core-excited states and shell model states are also presented together with a general comparison of the results with experiments and with pure (sd${)}^4$ shell model results.

We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both complex and Grassmann variables. In addition to a known mapping for the full so(2N+1) algebra, we also uncover some other formal mappings, together with mappings relevant to collective subspaces.

In many physical problems one is faced with the calculation of matrix elements of the form 〈lm|f(θ)|l′m〉. We use matrix algebra to derive a powerful technique for the numerical evaluation of such integrals. We obtain two different integration formulas: one which may be used if f has no particular symmetry and a second which exploits reflection symmetry of this operator. Our final results are essentially generalizations of the Gauss quadrature formula especially suited to the evaluation of matrix elements of the above form. We demonstrate this with an application to the angular part of the barrier transmission coefficient for the α decay of a heavy nucleus. The derivation involves a unitary transformation to the eigenstates of the Legendre polynomials ${\mathrm{P}}_1$ or ${\mathrm{P}}_2$ in a truncated angular momentum space. The same transformation also relates the eigenchannels of the adiabatic treatment of the scattering of deformed nuclei to the corresponding physical channels.

A local model for the nuclear medium modifications to the photoproduction of η mesons through the ${\mathit{N}}^{\mathrm{*}}$(1535) resonance is applied to the study of the inclusive reaction in medium and heavy nuclei. The use of effective Lagrangians and many body quantum theory allows one to incorporate the nuclear decay channels of the ${\mathit{N}}^{\mathrm{*}}$ involving a pair of nucleons and Fermi sea effects. Also the ηN final state interaction is considered, taking into account the nuclear renormalization of the ηN scattering cross section, and assuming a classical propagation between collisions. The results show a depletion and broadening of the resonant shape. Total and differential cross sections for different nuclei are presented, and the cross section around resonance is found to behave like ${\mathit{A}}^{\mathrm{\alpha }}$ with α≃0.6.

Energy spectra of light charged particles have been measured in coincidence with fissionlike fragments using the 4π charged-particle detector AMPHORA. Preequilibrium, prescission, and postscission components of emitted protons, deuterons, and alphas have been extracted from the energy spectra using a multiple source fit procedure. Including previously measured exclusive neutrons, a complete data set for light particle emission from the system ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$${+}^{32}$S(26A MeV) is now available. Mass and excitation energy of an equilibrated composite system has been defined by application of the massive transfer model using multiplicities and apparent temperatures of the preequilibrium components. The results have been compared to statistical model computations. A fair overall agreement is observed for different parametrizations of the Fermi-gas level-density parameter with indications for a decrease of the level density parameter with increasing nuclear temperature. The correlations between slope parameter, prescission, and total particle multiplicity turned out to be a sensitive probe for the level density parameter. In the energy spectra of alpha particles a low-energy component has been observed with strong focusing into directions perpendicular to the fission axis.