The Feynman-Schwinger representation provides a convenient framework for the calculation of nonperturbative propagators. In this paper we first investigate an analytically solvable case, namely the scalar QED in 0+1 dimension. With this toy model we illustrate how the formalism works. The analytic result for the self-energy is compared with the perturbative result. Next, using a ${\chi }^2\phi$ interaction, we discuss the regularization of various divergences encountered in this formalism. The ultraviolet divergence, which is common in standard perturbative field theory applications, is removed by using a Pauli-Villars regularization. We show that the divergence associated with large values of Feynman-Schwinger parameter s is spurious and it can be avoided by using an imaginary Feynman parameter $\mathrm{is}.\mathrm{}$

The electromagnetic dipole response of ${}^{138}\mathrm{Ba}$ was measured up to 6.7 MeV excitation energy in a photon scattering experiment. Two Euroball Cluster detectors were used to detect the scattered photons under 94 and 132 degrees. The Cluster at 94 degrees served as a Compton polarimeter. The total observed dipole cross section is in good agreement with previous tagged photon data, but in the present experiment the transition strength and the electric character of most of the transitions has been determined on a state-by-state basis. The data show a concentration of $E1\mathrm{}$ strength around 6 MeV. For one of the strongest excitations $M1\mathrm{}$ character is suggested. The results of model calculations using the quasiparticle phonon model (QPM) agree with the observed electric dipole strength distribution.

At the Karlsruhe and Tübingen 3.75 MV Van de Graaff accelerators the thermonuclear ${}^{50}\mathrm{Ti}(n,\gamma {)}^{51}\mathrm{Ti}(5.8\mathrm{}\min )$ cross section was measured by the fast cyclic activation technique via the 320.852 and 928.65 keV $\gamma$-ray lines of the ${}^{51}\mathrm{Ti}$ decay. Metallic Ti samples of natural isotopic composition and samples of ${\mathrm{TiO}}_2$ enriched in ${}^{50}\mathrm{Ti}$ by 67.53% were irradiated between two gold foils which served as capture standards. The capture cross section was measured at the neutron energies of 25, 30, 52, and 145 keV, respectively. The direct capture cross section was determined to be $0.387\pm 0.011\mathrm{mb}$ at 30 keV. We found evidence for a bound state s-wave resonance with an estimated radiative width of 0.34 eV which destructively interferes with direct capture. The strength of a suggested s-wave resonance at 146.8 keV was determined. The present data served to calculate, in addition to the directly measured Maxwellian averaged capture cross sections at 25 and 52 keV, an improved stellar ${}^{50}\mathrm{Ti}(n,\gamma {)}^{51}\mathrm{Ti}$ rate in the thermonuclear energy region from 1 to 250 keV. The new stellar rate leads at low temperatures to much higher values than the previously recommended rate; e.g., at $kT=8\mathrm{}\mathrm{keV}$ the increase amounts to about 50%. The new reaction rate therefore reduces the abundance of ${}^{50}\mathrm{Ti}$ due to s processing in asymptotic giant branch stars.

We present an improved version of the dual parton model which contains a new realization of the diquark breaking mechanism of baryon stopping. We reproduce in this way the net baryon yield in nuclear collisions. The model, which also considers strings originating from diquark-antidiquark pairs in the nucleon sea, reproduces the observed yields of p and Λ and their antiparticles and underestimates cascades by less than 50%. However, Ω’s are underestimated by a factor of 5. Agreement with data is restored by final state interaction, with an averaged cross section as small as $\sigma =0.14\mathrm{}\mathrm{mb}.$ Hyperon yields increase significantly faster than antihyperons, in agreement with experiment.

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the quark condensate $〈\overline{q}q〉,$ the mixed quark gluon condensate $g_s〈\overline{q}{G}_{\mu \nu }{\sigma }^{\mu \nu }q〉,$ and the four-quark condensate $〈\overline{q}\Gamma q\overline{q}\Gamma q〉$ at the mean-field level in the framework of the global color symmetry model. The numerical calculation shows our results are compatible with the range obtained within other nonperturbative approaches. Moreover, we have calculated the lower dimensional nonlocal quark condensates in this paper.

The production of $\phi$ mesons in proton-proton collisions is investigated within a relativistic meson-exchange model of hadronic interactions. The experimental prerequisites for extracting the $\mathrm{NN}\phi$ coupling strength from this reaction are discussed. In the absence of a sufficient set of data, which would enable an accurate determination of the $\mathrm{NN}\phi$ coupling strength, we perform a combined analysis, based on some reasonable assumptions, of the existing data for both $\omega$- and $\phi$-meson production. We find that the recent data from the DISTO Collaboration on the angular distribution of the $\phi$ meson indicate that the $\mathrm{NN}\phi$ coupling constant is small. The analysis yields values for $g_{\mathrm{NN}\phi }$ that are compatible with the Okubo-Zweig-Iizuka rule.

We analyze the total cross section data for $p\overrightarrow{p}\mathrm{pp}\omega$ near threshold measured recently at SATURNE. Using an effective range approximation for the on-shell $\mathrm{pp}$ S-wave final-state interaction, we extract from these data the modulus $|\Omega |=0.53\mathrm{}$ ${\mathrm{fm}}^4$ of the threshold transition amplitude Ω. We present a calculation of various (tree-level) meson exchange diagrams contributing to Ω. It is essential that $\omega$ emission from the anomalous $\omega \rho \pi$ vertex interferes destructively with ω emission from the proton lines. The contribution of scalar $\sigma$-meson exchange to $\Omega$ turns out to be negligibly small. Without introducing off-shell meson-nucleon form factors the experimental value $|\Omega |=0.53\mathrm{}$ ${\mathrm{fm}}^4$ can be reproduced with an $\omega N$-coupling constant of $g_{\omega N}=\mathrm{10.7.}\mathrm{}$ The results of the present approach agree qualitatively with the Jülich model. We also perform a combined analysis of the reactions $p\overrightarrow{p}\mathrm{pp}{\pi }^0,$ $\mathrm{pn}{\pi }^{+},$ $\mathrm{pp}\eta ,$ $\mathrm{pp}\omega ,$ and $p\overrightarrow{n}\mathrm{pn}\eta$ near threshold.

We estimate the perturbative nuclear shadowing in the nuclear structure function $F_2^A{(x,Q}^2)$, mainly at the kinematic region of HERA using the Glauber-Mueller approach. The contributions of the quark and gluon sectors to the nuclear shadowing are estimated. We predict that the nuclear shadowing corrections are important and that saturation of the ratio $R_1{=F}_2^A{(x,Q}^2{)/AF}_2^N{(x,Q}^2)$ occurs at $Q^2>~1\hspace{0.5em}{\mathrm{GeV}}^2$ once the shadowing in the gluon sector is considered.

For the embedded Gaussian orthogonal ensemble of random matrices, the strength sums generated by a transition operator acting on an eigenstate vary with the excitation energy as the ratio of two Gaussians. This general result is compared to exact shell-model calculations of Gamow-Teller strength sums in nuclei. Good agreement is obtained in the chaotic domain of the spectrum, and strong deviations are observed as nuclear motion approaches a regular regime. Thus transition strength sums seem to be a new statistic sensitive to the chaoticity of the system.

The structure of neutron-rich nuclei in the $N\sim 20$ region is studied by the Monte Carlo shell model based on the quantum Monte Carlo diagonalization method. We present a comprehensive description of even-even isotopes of O, Ne, Mg, and Si. It is demonstrated that, for different nuclei, various particle-hole excitations from the $\mathrm{sd}$ to $\mathrm{pf}$ shell are mixed in different ways, producing distinct effects sometimes, for instance, in ${}^{28}\mathrm{Ne}.$ The monopole interaction is examined and modified, resulting in the shell gap changing from nucleus to nucleus. The drip line of O isotopes is then reproduced. The interplay between the $T=0\mathrm{}$ and $T=1\mathrm{}$ monopole interactions is discussed from the viewpoint of the potential energy surface and the effective single-particle energy. The extension of the neutron drip line of Ne isotopes is explained, and the boundary of the “island of inversion” is shown to be rather indistinct.

The ${}^{14}\mathrm{N}{(}^7\mathrm{Be}{,}^8\mathrm{B}{)}^{13}\mathrm{C}$ reaction was studied using an 85 MeV ${}^7\mathrm{Be}$ radioactive beam. The asymptotic normalization coefficients for the virtual transitions ${}^7\mathrm{Be}+p{\leftrightarrow }^8\mathrm{B}$ were determined from the measured cross section. These coefficients specify the amplitude of the tail of the ${}^8\mathrm{B}$ overlap function in the ${}^7\mathrm{Be}+p$ channel, and were used to calculate the astrophysical S factor for the direct capture reaction ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ at solar energies $S_{17}\mathrm{}\left(0\right).$ We find that $S_{17}\mathrm{}\left(0\right)=16.6\mathrm{}\pm 1.9$ eV b.

Recent theoretical investigations of the decay mechanism out of a superdeformed nuclear band have yielded qualitatively different results, depending on the relative values of the relevant decay widths. We present a simple two-level model for the dynamics of the tunneling between the superdeformed and normal-deformed bands, which treats decay and tunneling processes on an equal footing. The previous theoretical results are shown to correspond to coherent and incoherent limits of the full tunneling dynamics. Our model accounts for experimental data in both the $A\sim 150$ mass region, where the tunneling dynamics are coherent, and in the $A\sim 190$ mass region, where the tunneling dynamics are incoherent.

The spectrum of bremsstrahlung in alpha decay is calculated within the framework of quantum and classical electrodynamics. The formulas for the spectra of $E1\mathrm{}$ and $E2\mathrm{}$ radiation are obtained. The bremsstrahlung is evaluated for the Coulomb barrier and for the spherical symmetry rectangular potential barrier. Experimental results for the nuclei ${}^{210,214}\mathrm{Po}$ and ${}^{226}\mathrm{Ra}$ are analyzed. A concept of interference of the space regions in the emission amplitude is discussed.

Two-proton correlation functions have been measured in Si+Pb collisions at $14.6A\hspace{0.5em}\mathrm{GeV}/c$ and Au+Au collisions at 11.5A GeV/c by the E814/E877 Collaboration. Data are compared with predictions of the transport model RQMD and the source size is inferred from this comparison. Our analysis shows that, for both reactions, the characteristic size of the system at freeze-out exceeds the size of the projectile, suggesting that the fireball created in the collision has expanded. For Au+Au reactions, the observed centrality dependence of the two-proton correlation function implies that more central collisions lead to larger source sizes.

Information on the ${}^7\mathrm{Li}(p,\alpha {)}^4\mathrm{He}$ reaction cross section at energies relevant for astrophysics has been obtained by means of the indirect Trojan-horse method applied to the three-body ${}^2\mathrm{H}{(}^7\mathrm{Li},\alpha \alpha )n$ reaction. Measurements at ${}^7\mathrm{Li}$-beam energies of 19, 19.5, 20, and 21 MeV have been carried out. The results are reported in terms of the astrophysical $S\left(E\right)\mathrm{}$ factor. The value $S\left(0\right)\mathrm{}$ measured in the present experiment is compared with that extrapolated from a direct measurement.

High-spin positive-parity states in ${}^{72}\mathrm{Br}$ have been studied using the ${}^{16}\mathrm{O}{+}^{58}\mathrm{Ni}$ reaction. The $\pi g_{9/2}\nu g_{9/2}$ decoupled band in ${}^{72}\mathrm{Br}$ has been observed up to $\sim 10\hspace{0.5em}\mathrm{MeV}$ excitation energy and the expected odd-even staggering has been delineated. A larger signature splitting is observed for this band in ${}^{72}\mathrm{Br}$ than in the same collective structures in the heavier ${}^{74,76,78}\mathrm{Br}.$ No signature inversion at low spin is observed for this band in ${}^{72}\mathrm{Br},$ in contrast to the heavier isotopes, ${}^{74,76,78}\mathrm{Br},$ in which signature inversion is observed below $\sim 10ħ.$ The observations are in general agreement with theoretical models in this mass region which predict no signature inversion for nuclei with less than 39 protons and neutrons.

High spin states in neutron-rich odd-Z ${}^{143,145}\mathrm{Ba}$ nuclei have been investigated from the study of prompt γ rays in the spontaneous fission of ${}^{252}\mathrm{Cf}$ by using γ-γ- and γ-γ-γ- coincidence techniques. Alternating parity bands are identified for the first time in ${}^{145}\mathrm{Ba}$ and extended in ${}^{143}\mathrm{Ba}.$ A new side band, with equal, constant dynamic, and kinetic moments of inertia equal to the rigid body value, as found in superdeformed bands, is discovered in ${}^{145}\mathrm{Ba}.$ Enhanced $E1\mathrm{}$ transitions between the negative- and positive-parity bands in these nuclei give evidence for strong octupole deformation in ${}^{143}\mathrm{Ba}$ and in ${}^{145}\mathrm{Ba}.$ These collective bands show competition and coexistence between symmetric and asymmetric shapes in ${}^{145}\mathrm{Ba}.$ Evidence is found for crossing $M1\mathrm{}$ and $E1\mathrm{}$ transitions between the $s=+i$ and $s=-i$ doublets in ${}^{143}\mathrm{Ba}.$

Influence of the shape of thermalized source on various characteristics of the multifragmentation process, as well as its interplay with effects of the angular momentum and the collective expansion are studied for the first time and the most pertinent variables are proposed. The analysis is based on the extension of the statistical microcanonical multifragmentation model.

Excited states of the ${}^{133}\mathrm{Sm}$ nucleus have been populated to high spin via the ${}^{96}\mathrm{Ru}{(}^{40}\mathrm{Ca},2pn)$ reaction. Rotational structures have been observed and their characteristics studied by examination of their dynamic moments of inertia and alignment gains. These experimentally derived quantities have been compared with theoretical calculations from both standard cranked shell and self-consistent total Routhian surface calculations. The discovery of a new coupled band within the ${}^{133}\mathrm{Sm}$ nucleus has lead to the reassignment of the configuration of one of the previously identified bands. The new calculations predict strong polarization effects for different configurations, which result in quadrupole deformations that vary from ${\beta }_2\sim 0.28$ to $>~\mathrm{0.38.}$