A method is presented that allows the reconstruction of trajectories in particle spectrographs and the reconstructive correction of residual aberrations that otherwise limit the resolution. Using a computed or fitted high order transfer map that describes the uncorrected aberrations of the spectrograph, it is possible to calculate a map via an analytic recursion relation that allows the computation of the corrected data of interest such as reaction energy and scattering angle as well as the reconstructed trajectories in terms of position measurements in two planes near the focal plane. The technique is only limited by the accuracy of the position measurements, the incoherent spot sizes, and the accuracy of the transfer map. In practice the method can be expressed as an inversion of a nonlinear map and implemented in the differential algebraic framework. The method is applied to correct residual aberrations in the S800 spectrograph which is under construction at the National Superconducting Cyclotron Laboratory at Michigan State University and to two other high resolution spectrographs.

A fast timing βγγ(t) method has been used to measure level lifetimes in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Nd}$ as populated in the ${\mathrm{\beta }}^{\mathrm{-}}$ decay of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Pr}$. The following half-lives have been measured: ${\mathit{T}}_{1/2}$=330(14) and 53(10) ps for the 236.7 keV $4_1^{+}$ and the 484.0 keV $6_1^{+}$ members of the ground-state band, ${\mathit{T}}_{1/2}$=145(11), 12(7), and 64(56) ps for the 1542.0 keV $2^{\mathrm{-}}$, 1600.7 keV $3^{\mathrm{-}}$, and the 1683.2 keV $4^{\mathrm{-}}$ members of the ${\mathit{K}}^{\mathrm{\pi }}$=$2^{\mathrm{-}}$ band, and ${\mathit{T}}_{1/2}$=42(6) and 30(10) ps for the 1827.5 keV $3^{\mathrm{-}}$ and the 1893.3 keV $4^{\mathrm{-}}$ members of the ${\mathit{K}}^{\mathrm{\pi }}$=$3^{\mathrm{-}}$ band, respectively. The observed allowed M1 rates and large hindrance factors for the E1 transitions deexciting these bands is discussed in terms of K forbiddenness and the (suggested) dominant two-quasiparticle configurations. Systematics of the octupole vibrational bands in the rare-earth region is examined. The energy minima for the ${\mathit{K}}^{\mathrm{\pi }}$=$1^{\mathrm{-}}$ bands follow a narrow valley along N=94 associated with the two-quasineutron {ν5/$2^{+}$[642]-ν3/$2^{\mathrm{-}}$[521]} configuration, while minima for the ${\mathit{K}}^{\mathrm{\pi }}$=$2^{\mathrm{-}}$ bands follow narrow valleys at Z=66 and Z=74 associated with the two-quasiproton configurations {π7/$2^{\mathrm{-}}$[523]-π3/$2^{+}$[411]} and {π9/$2^{\mathrm{-}}$[514]-π5/$2^{+}$[402]}, respectively. In contrast, the lowering of the ${\mathit{K}}^{\mathrm{\pi }}$=$0^{\mathrm{-}}$ bands near ${}_{}{}^{146}{}_{}{}^{}\mathrm{Ba}$ is along both neutron and proton numbers, giving a flat minimum.

Three quasiparticle excitations for odd-even lead isotopes in the mass region 197≤A≤203 are calculated using a realistic two-body interaction. The analysis is performed in a correlated basis constructed by the tensor product of one times two quasiparticle states. Good agreement with available experimental data is found. The one phonon approximation of the weak coupling model is also analyzed.

The possible exotic cluster decay modes of some ‘‘stable’’ nuclei in the region 50<Z<82 are calculated using a preformed cluster model. The predicted half-life times for certain cluster decays of ${}_{56}{}^{120}{}_{}{}^{}\mathrm{Ba}_{64}^{}{}_{}{}^{}$ and ${}_{80}{}^{186}{}_{}{}^{}\mathrm{Hg}_{106}^{}{}_{}{}^{}$ nuclei, which lie in the neighborhood of the spherical magic shells Z=50 and 82 and the deformed magic shell N=108, are interesting cases of possible instabilities present in regions of ‘‘stable’’ nuclei. These are the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ decays of ${}_{}{}^{120}{}_{}{}^{}\mathrm{Ba}$ and the ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ decay of ${}_{}{}^{186}{}_{}{}^{}\mathrm{Hg}$, whose half-life times are predicted to be ∼${10}^{22}$, ${10}^{26}$, and ${10}^{28}$ s, respectively. The last case is an exciting new possibility of cluster radioactivity with a deformed daughter nucleus. Experimentally, however, both parent nuclei are short lived and their suggested cluster decays cannot be observed. In any case, the present study invokes further work to look for other similar instabilities in various regions of ‘‘stable’’ nuclei. It is possible that some of these decays are measurable and can be used to obtain the related new nuclear structure effects. The effects of reinforcement of shell gaps for nuclei with weak spherical closed shell at Z=64 and deformation starting to begin at N∼90 are also discussed.

A consistent set of Hartree-Fock-Bogolyubov calculations is carried out for the even Sr, Zr, and Mo isotopes in the neutron-deficient region near A=80 and the neutron-rich region near A=100. A common origin for the onset of deformation in both regions is found. Deformation is triggered by the strong neutron-proton interaction in orbitals with good spatial overlap.

We present a spectral method for computing one-loop vacuum polarization effects exactly in (1+1)-dimensional finite nuclei with hadronic degrees of freedom. The Dirac equation is solved exactly with periodic boundary conditions by diagonalizing the Dirac Hamiltonian matrix in a finite basis of free parity eigenstates, which in one spatial dimension amounts to a discrete Fourier decomposition of the exact fermion wave functions. We then carry out the renormalization in a manner consistent with the truncation of the finite basis which leads to well-behaved vacuum polarization densities for any basis size. To account for additional vacuum contributions arising from sea states outside our truncated basis, we employ the familiar derivative expansion (DE) in a form consistent with our finite basis. We emphasize the presence of a vector potential in these calculations, and show that, while a variety of methods which are adequate in the scalar-only case fail for the vector-scalar problem, our method treats both cases satisfactorily because consistency between the basis and the renormalization subtractions is scrupulously maintained. Finally, we examine the bulk properties of closed-shell nuclear solutions for a range of input parameters and make a careful comparison between our exact results and a variety of approximations. We find that the usual DE in general accurately approximates one-loop contributions.

Earlier results for two-component particle-hole state densities with good isospin have been rederived, removing a number of earlier approximations. The new results are shown to be consistent with the corresponding isospin-mixed state densities and are more suitable for light nuclei. Approximate results appropriate for reaction calculations are presented.

Recent experimental investigations of a sequence of samarium isotopes report an apparent quadratic deformation dependence of the total B(M1) strength of low-lying $1^{+}$ states. Considering these states as the fragmented distribution of a collective state, the angular analog to the giant dipole, it is demonstrated that such a deformation dependence arises quite naturally when short range correlations and surface effects are taken into account. The role of such additional parameters in determining the variation of the total transition strength is discussed and a comparison with the picture of pure contrarotation is made.

An approximate particle number projection at finite temperature using the Lipkin-Nogami method in the context of the static-path approximation is proposed. The numerical evaluation, performed in a simple degenerate 2Ω-level model, shows that the present approach can improve the standard unprojected static-path approximation and is superior to the usual prescription based on classical thermodynamics.

We derive an approximate boson-quasifermion mapping of a single-j shell-model algebra, applicable to the seniority classification scheme, as an expansion in the ratio of the seniority quantum number to the level degeneracy, with selective summation of higher order terms. The procedure used is an extension of the algebraic technique first applied to the purely bosonic part of the mapping by Bonatsos, Klein, and Li. Only the maps of the generators are needed to derive a Hamiltonian for the interacting boson fermion model (IBFM), and these can be obtained in Hermitian form without having to go through the intermediary of a mapping of the fermion operators. Application of the results is illustrated by a fresh discussion of the so-called exchange interaction of the IBFM. A consistent mapping of the single fermion in terms of bosons and quasifermions is also derived that includes a consideration of the unusual properties of the quasifermions.

For all even-A nuclei in the sd shell we evaluate the overlap between several low-lying states, obtained by diagonalizing the realistic Wildenthal interaction, and the eigenstates of the SU(4) Casimir operator. We find that the J=$0^{+}$ ground states of even-even nuclei near the middle of the shell have rather small overlaps (less than 0.5) with the lowest SU(4) Young tableaux, while the J=$0^{+}$ and $1^{+}$ lowest states of odd-odd nuclei have noticeably larger overlaps (0.6–0.7). We also find that the expansion in the SU(4) Young tableaux converges quite rapidly, and that the two or three lowest tableaux usually account for more than 90% of the nuclear wave function. We then extend the calculation to the fp shell and evaluate the overlaps between the J=$0^{+}$ ground states obtained by diagonalizing a realistic interaction and the SU(4) eigenstates for even-even nuclei with maximum isospin. For the fp shell the overlaps are even smaller than in the sd shell. Since we observe such sizable SU(4) symmetry breaking effects in the relatively simple sd and pf nuclei, we are rather pessimistic about the prospects of using conclusions based on SU(4) in heavier, more complex nuclei.

Differential cross sections for exciting the $2_1^{+}$ and $3_1^{\mathrm{-}}$ states of ${}_{}{}^{90,92,94,96}{}_{}{}^{}\mathrm{Zr}$ with 70-MeV ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ions have been measured. Calculations of the cross sections have been performed using a deformed optical model potential (DOMP) with OMP deduced from fits to the elastic data, as well as a folding model with an effective nucleon-nucleon interaction with a Yukawa form factor obtained from fits to the elastic data and transition densities obtained from open-shell random phase approximation (RPA) calculations. The DOMP fits to the data yield values of ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$ which are in good agreement with those predicted using the RPA. For the $2_1^{+}$ states, we find ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$ increases from less than N/Z to greater than N/Z in going from ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ to ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}$. However, for the $3_1^{\mathrm{-}}$ states ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$ remains less than N/Z for all cases, a result which is in disagreement with previous works. The folding model, with the RPA transition densities, provides good agreement with the $2_1^{+}$ measurements, but underpredicts the cross sections for the $3_1^{\mathrm{-}}$ states. A reanalysis of the earlier data from excitation of these states by (α,α’) reactions removes much of the apparent discrepancies between those measurements and other measurements, including the ones reported here. The localization of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ interaction is also discussed.

The (d${,}^2$He) reactions on light nuclei were studied at ${\mathit{E}}_{\mathit{d}}$=260 MeV with a large solid-angle, wide momentum-acceptance spectrometer. The data indicated the direct one-step nature of the reaction at this energy. Observed excitation-energy spectra for N=Z nuclei compared well with those from the (p,n) reactions at similar momentum transfer. The peaks corresponding to the $0^{+}$→$1^{+}$ transitions showed angle dependence characteristic of ΔL=0. The 0° (d${,}^2$He) cross sections were found to be proportional to the Gamow-Teller β-decay strengths.

The differential cross section for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(γ,${\mathit{p}}_0$${)}^{15}$N reaction has been investigated at photon energies ${\mathit{E}}_{\gamma }$ between 33 and 69 MeV using a bremsstrahlung beam; angular distributions at laboratory angles of 30°, 45°, 60°, 75°, 90°, and 120° were extracted from the tip region of the photoproton spectra when stepping the end point in 4 MeV intervals. The data are compared with calculations based on a self-consistent microscopic approach.

Inclusive measurements are presented for the differential cross sections and tensor analyzing powers ${(}^{\mathit{T}}$${\mathit{T}}_{20}$ and ${\mathit{T}}_{20}$) of ions produced by the fragmentation of a beam of polarized ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ incident on a ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ target at an energy of 195.5 MeV (8.5 MeV/nucleon). The data are discussed in terms of a simple ‘‘shape-effect’’ model, and compared to the predictions of the nuclear random-walk model which has been extended to the calculation of aligned, deformed projectiles. This model reproduces the principal features of the differential cross sections and the trends as a function of mass loss, but gives poorer agreement for the analyzing powers.

The cross sections for elastic scattering of 318 MeV ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ were measured. The data extend well beyond the rainbow angle into the region where the far-side scattering dominates, and thus define unique ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ phenomenological potentials. These complement earlier unique ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ potentials derived at an energy of 210 MeV. Double-folded real potentials also were generated using effective nucleon-nucleon interactions. The M3Y and Franey-Love 50 MeV nucleon-nucleon interactions gave similar potentials. A Woods-Saxon form was used for the imaginary potential. The experimental cross-section data were reasonably well reproduced without renormalization of the folded potentials.

The alpha-particle decay angular correlations for intermediate ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}_{}^{\mathrm{*}}{}_{}{}^{}$ excited states in the reaction ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$${(}^{12}$C${,}^{15}$${\mathrm{N}}^{\mathrm{*}}$→α${+}^{11}$B(g.s.))α are found to exhibit symmetry about 90° relative to the beam axis in the reaction plane, in the barycentric coordinates of the decay. The limiting case necessary to produce this symmetry also yields azimuthal symmetry. It is therefore sometimes unnecessary to measure out-of-plane correlations in order to integrate over all angles for the purpose of determining particle decay branching ratios. We use the observed symmetry to establish ${\mathrm{\Gamma }}_{\mathrm{\alpha }}$/Γ=0.60±0.04 for the 12.56 MeV excited state of ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ (absolute uncertainty is ∼15%).

Double charge exchange cross sections for 50 MeV pions to double isobaric analog states in ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, and ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ were measured. The results indicate that the effective double charge exchange operator at this energy has a strong short-range component. In addition, evidence is presented tending to implicate isospin mixing as the mechanism for excitation of the analog of the antianalog in ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$.

Using a hadronic transport model and its cascade limit for relativistic heavy ion collisions, we study properties of dynamical fluctuations from event to event by calculating the reduced scaled factorial moments as a function of the bin size in pseudorapidity. We found that the reduced scaled factorial moments of charged pions show an intermittent behavior due to the random cascading property of the reaction. The anomalous dimension increases with the increasing rank of the moment. Effects of mixing events of different impact parameters on the reduced scaled factorial moments have also been studied. Comparisons to available experimental data are made, and discrepancies between the model calculations and the experimental data are discussed.

Pion nucleon scattering up to 600 MeV laboratory kinetic energy is described by a manifestly covariant wave equation in which the pion is restricted to its mass shell. The kernel of the equation includes nucleon (N), Roper (${\mathit{N}}^{\mathrm{*}}$), delta (Δ), and ${\mathit{D}}_{13}$ poles, with their corresponding crossed pole terms approximated by contact interactions, and contact σ- and ρ-like exchange terms. The πNN vertex is treated as a mixture of ${\gamma }^5$ and ${\gamma }^{\mathrm{\mu }}$${\gamma }^5$ coupling, with a mixing parameter λ chosen so that the dressed nucleon pole will be unshifted by the interaction. Chiral symmetry is maintained at threshold. The resonance contributions are fully unitarized by the equation, with their widths determined by the dynamics included in the model. The Δ and ${\mathit{D}}_{13}$ are treated as pure spin 3/2 particles, with no spin 1/2 amplitude in the S channel. The complete development of this model, which gives a very good fit to all the data up to 600 MeV, is presented.