A recently proposed hybrid variational procedure for nuclear structure calculations is improved and reformulated in a way that allows for going beyond the mean-field approximation. The numerical feasibility of the resulting approach is tested by applying it in the s-d shell. Selected examples demonstrate that the procedure works equally well for odd-mass and even-mass nuclei, giving solutions that rapidly converge to the exact ones.

Inequalities have been established by Bertlmann and Martin which link the rms radius and the kinetic energy of the 1s orbit to the lowest dipole transition energy. The derivation is based on the Thomas-Reiche-Kuhn sum rule, which requires a local Hamiltonian. In the present work, we extend these inequalities to Hamiltonian where the nonlocality can be expressed via spatial dependent effective mass. We discuss the case of hypernuclei, which provides a suitable example to verify the Bertlmann-Martin inequalities.

Angular-distribution data have been obtained for the inelastic scattering reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${(}^{12}$C${,}^{12}$C[$0_2^{+}$]${)}^{12}$C($0_2^{+}$) at center-of-mass energies between ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=29.5 and 35.5 MeV, in the region of a large structure previously observed in the excitation function for this reaction. The angular-distribution data suggest dominant l values near 14–16, but also show strong evidence for the contribution of several constructively interfering angular momenta at the peak of the excitation function structure.

Vector and tensor analyzing powers (${\mathit{iT}}_{11}$,${\mathit{T}}_{20}$,${\mathit{T}}_{21}$, and ${\mathit{T}}_{22}$) for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${(}^6$Li→${,}^6$Li${)}^{12}$C elastic scattering and inelastic scattering leading to the $2^{+}$ (4.44 MeV) and $3^{\mathrm{-}}$ (9.64 MeV) states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are presented over the c.m. angular range 15–138° for a ${}_{}{}^6{}_{}{}^{}\to$ bombarding energy of 30 MeV. These are the first complete set of $3^{\mathrm{-}}$ analyzing powers for ${}_{}{}^6{}_{}{}^{}\to$ scattering. The results of a coupled channels analysis that uses an optical potential with a double-folded real part show the necessity to include projectile excitation, an explicit spin-orbit potential, and reorientation terms in the potential in order to achieve a reasonable overall description of the analyzing-power data. The deformation lengths are set by normalizing the calculations to previously measured ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ($3^{+}$,$2^{+}$) inelastic-scattering cross sections. The explicit spin-orbit potential is the major contributor to the vector analyzing power ${\mathit{iT}}_{11}$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ($2^{+}$) inelastic scattering, while the reorientation of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground state contributes strongly to the analyzing power ${\mathit{T}}_{21}$ for elastic scattering. The calculations fail to account for the relatively large magnitude of the experimental tensor analyzing powers for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ($3^{\mathrm{-}}$) inelastic scattering.

At energies in the range 400–500 MeV, pion-induced double charge exchange cross sections leading to the double analog state appear to behave differently for even and odd isospin.

The multiparticle decay in collisions induced by 44 MeV/nucleon ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ and ${}_{}{}^{132}{}_{}{}^{}\mathrm{Xe}$ projectiles on several targets is studied using MEDEA 4π detection system. The impact parameter dependence of the charged particle multiplicity is determined. The dependence is strong in peripheral and midcentral collisions and becomes weaker in central collisions. The prediction of a molecular dynamics simulation is in agreement with the experiment.

Differential cross sections, vector and tensor analyzing powers of the (d→,t) reaction on ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been measured at 200 MeV bombarding energy. Deuteron elastic scattering measurements have been performed on ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ at the same energy. These data have been analyzed together with previous ones on ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ to get best fit optical parameters describing deuteron elastic scattering. The (d→,t) experimental survey bears on 28 transitions populating well known valence levels, including previous data in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{27}{}_{}{}^{}\mathrm{Si}$. The vector and tensor analyzing powers exhibit striking similarities for transitions measured in different nuclei. The angular distributions are found to strongly depend on the number of nodes in the neutron form factor and on the coupling of spin and angular momentum ${\mathit{j}}_{\mathrm{-}}$=l-1/2 versus ${\mathit{j}}_{+}$=l+1/2. The j effect is especially pronounced, for both analyzing powers for n=1 transitions. The slopes of the differential cross sections in different nuclei depend mainly on the number of nodes. Exact finite range calculations including S and D components have been performed, using two sets of deuteron parameters together with a deep triton potential. Both analyses reproduce rather well the differential cross sections and currently adopted spectroscopic factors. The conventional analyses with deuteron parameters fitting elastic scattering data reproduce rather well analyzing powers of n>1 transitions (with l=0,1,2), but disagree with the data for n=1 transitions (except for ${\mathit{j}}_{+}$${\mathit{A}}_{\mathit{y}\mathit{y}}$ values). Good or qualitative agreement is achieved for all transitions with the second deuteron potential, characterized by larger spin orbit terms and an additional imaginary tensor term. This allows using the reaction as a spectroscopic tool.

The spontaneous agitation of collective modes in unstable nuclear matter is addressed with an extended Boltzmann-Langevin (BL) theory that incorporates a memory time in the stochastic force. The growth of the modes is then governed by effective diffusion coefficients which are renormalized by time-dependent factors, relative to the standard treatment. These correction factors deviate significantly from unity in the most unstable domain of the density-temperature phase plane, indicating the importance of including a memory time in numerical BL simulations of nuclear dynamics.

Phenomenological relativistic optical models for scattering of nucleons from a spin-0 nucleus mainly use two different approaches. In the first, one essentially uses the Schrödinger equation incorporating appropriate relativistic kinematical terms. In the second approach, which is superior especially in reproducing spin observables, one starts with the Dirac equation and obtains an equivalent Schrödinger equation which forms a convenient basis for the calculation of experimental observables. Adopting a mathematical procedure developed earlier within the framework of potential scattering, we calculate the regionwise contribution to the reaction cross section for spin-1/2–spin-0 systems using both these types of relativistic optical models. The relative importance of different regions of intermediate energy optical potential in generating the total reaction cross section is examined using the method of regionwise absorption and it is found that reaction process is surface dominant. These findings are further elaborated by depicting the general features of S matrix and scattering amplitudes as a function of angular momentum.

The power-law relation between higher order and second order scaled factorial moments has been investigated for secondary particles produced in interactions of 800 GeV protons with emulsion nuclei in one-dimensional (pseudorapidity and azimuthal angle) and two-dimensional (pseudorapidity and azimuthal angle) spaces for three multiplicity intervals. The moment power law is found to be independent of multiplicity cuts and phase space dimension. A universal scaling exponent is determined which indicates that there is no second-order phase transition in the interactions. The ratios of higher-order anomalous fractal dimensions with respect to the second-order anomalous fractal dimension are well represented by the Lévy-stable distribution and give clear evidence of a self-similar cascading mechanism in the interactions.

A unified approach, involving the two-center picture of the nucleus, is proposed for the description of the behavior of nuclei at high angular momentum. This picture involves nine parameters, fixed by solving the system of nine nonlinear equations, obtained from equilibrium constraints. This shape enables us to calculate the potential energy surfaces. For the calculations of shell effects we adopt the Strutinsky formalism. The shell effects play the dominant role in deciding the fission path and the phenomenon of superdeformation in ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$. The calculated moment of inertia of the isomeric state is close to the observation and hence it supports the theoretical description of its shape.

Experimental cross sections for the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(γ,${\mathrm{\pi }}^0$) at low energy have been used to deduce the isovector-multipole combination [2${\mathit{M}}_{1+}$(v)+${\mathit{M}}_{1\mathrm{-}}$(v)]/qk for the nucleon near ${\mathrm{\pi }}^0$ threshold. The effects of pion-wave distortion (distorted-wave impulse approximation) and Fermi motion in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are addressed in detail. By incorporating additional constraints on certain combinations of the p-wave multipoles as deduced from the Mainz ${}_{}{}^1{}_{}{}^{}\mathrm{H}$(γ,${\mathrm{\pi }}^0$) data, near-threshold values are obtained for the reduced proton p-wave (γ,${\mathrm{\pi }}^0$) multipoles ${\mathit{M}}_{1+}$/qk,${\mathit{M}}_{1\mathrm{-}}$/qk, and ${\mathit{E}}_{1+}$/qk which are in excellent agreement with the VPI multipoles as given by the said code but disagree with the findings of other authors. Combined with a conservative theoretical estimate of the isoscalar amplitude ${\mathit{M}}_{1\mathrm{-}}$(s), these results permit a decomposition of ${\mathit{M}}_{1\mathrm{-}}$(p) into isoscalar and isovector components in the near-threshold region.

The validity of the local density approximation as applied to the construction of the nucleon-nucleus optical potential is studied. A Wentzel-Kramers-Brillouin (WKB) local equivalent potential to the second-order term of the Kerman, McManus, and Thaler (KMT) multiple scattering expansion of the nucleon nucleus optical potential is derived. Assuming that the nucleon-nucleon transition amplitude is on the energy shell, we compare the microscopic KMT optical potential with the approximate potential deduced from the nuclear matter limit by use of the local density approximation. Calculations are presented for the nucleon${\mathrm{-}}^{16}$O system at 135 and 200 MeV incident energies. It is shown that the use of the local density prescription leads to surface peaking of the optical potential. This effect is absent from the second-order term of the optical potential derived microscopically from the KMT approach.

Effects of nucleon-nucleon correlations on exclusive (e,e’p) reactions on closed-shell nuclei leading to single-hole states are studied using ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(e, e’p${)}^{15}$N (6.32 MeV, 3/$2^{\mathrm{-}}$) as an example. The quasihole wave function, calculated from the overlap of translationally invariant many-body variational wave functions containing realistic spatial, spin, and isospin correlations, seems to describe the initial state of the struck proton accurately inside the nucleus; however, it is too large at the surface. The effect of short-range correlations on the final state is found to be largely cancelled by the increase in the transparency for the struck proton. It is estimated that the values of the spectroscopic factors obtained wth the distorted wave impulse approximation may increase by a few percent due to correlation effects in the final state.

Previous calculations of coherent jet production in pion nucleus scattering use a plane wave approximation that violates the orthogonality of the initial and final state wave functions. We argue that such plane wave approximations give the correct A and transverse momentum dependence, but overestimate the magnitude of the cross section.

Various features of the charge yield in heavy ion collisions are studied. Considered here are the nuclear emulsion data of ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$, ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ in the energy range of 1 GeV/A. Mean charge yields and multiplicity distribution of these data indicate that the nuclear fragmentation at this energy is a multiprocess phenomena. Power moments of the charge distribution exhibit some degree of scale invariance. While small nuclei (Kr and Xe) show a nuclear size dependence, large nuclei (Au and U) exhibit some scale independent behavior in their charge distribution. The spacing distribution may indicate a possible existence of a chaotic behavior in nuclear fragmentation.

The energy dependence of the algebraic potential for heavy-ion elastic scattering near to the Coulomb barrier is investigated. The inclusion of an additional term in the complex algebraic potential to take into account the reflection due to the imaginary well is proposed. With this new term 12 elastic scattering angular distributions of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$${+}^{63}$Cu system ranging from E=39 to 64 MeV in the laboratory system were analyzed. The real and imaginary strengths of the algebraic potential exhibit a dependence with energy similar to the dispersive behavior associated with the threshold anomaly.

The Vincent-Phatak procedure for solving the momentum-space Schrödinger equation with combined Coulomb-plus—short-range potentials is extended to angular momentum states coupled by an optical potential—as occurs in spin 1/2×1/2 scattering. A generalization of the Blatt-Biedenharn phase shift parametrization is derived and applied to 500 MeV polarized-proton scattering from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The requisite high-precision partial-wave expansions and integrations are described.

Inclusive double differential multiplicities ${\mathit{d}}^2$N/dy d${\mathit{p}}_{\mathit{t}}$ and related quantities have been measured for protons and deuterons produced in 14.6A GeV/c Si+Al and Si+Pb collisions using the E814 forward spectrometer at the AGS at BNL. Collision ‘‘centrality’’ is determined by measuring ${\mathit{N}}_{\mathit{c}}$, the total charged particle multiplicity in the pseudorapidity range 0.85<η<3.8. For both systems Si + Al and Si + Pb, an increase in the proton rapidity distribution dN/dy at midrapidity and a corresponding decrease at higher rapidities are observed with increasing ${\mathit{N}}_{\mathit{c}}$. For Si+Pb, Boltzmann slope parameters ${\mathit{T}}_{\mathit{B}}$ increase significantly in the most central collisions. The measured distributions exhibit a centrality dependence even when σ/${\mathrm{\sigma }}_{\mathrm{geo}}$≲10%, where full overlap between the Si and Pb nuclei occurs in a simple geometric picture. The proton rapidity distribution dN/dy is presented for the symmetric system Si+Al over the entire rapididty interval. The total number of protons, which is the integral of this quantity over rapidity, varies with ${\mathit{N}}_{\mathit{c}}$. Results are compared with various model calculations, mostly using the hadronic cascade codes ARC and RQMD. No significant nuclear transparency is observed, indicating that large baryon and energy densities are produced in these collisions.

The Bose-Einstein correlations of photons emitted from a longitudinally expanding system of excited matter produced in ultrarelativistic heavy ion collisions are studied. Two effects found in recent calculations—that the correlation function in longitudinal direction exhibits oscillations, and that it takes values below unity—are demonstrated to be numerical artefacts and/or the results of inappropriate approximations. Thus, the general quantum statistical bounds for the two particle correlation function of a chaotic source with Gaussian fluctuations are confirmed. Two different expressions for the two-photon inclusive distribution are considered. Depending on which of the two expressions is used in the calculation, the width of the correlation function may vary by as much as 30%.