Fusion suppression and sub-barrier breakup of weakly bound nuclei

The mechanism for the large suppression of complete fusion in the 9Be+208Pb reaction has been investigated through measurement of sub-barrier breakup of 9Be. Excluding breakup through the 8Be ground state, whose lifetime is too long, a prompt breakup component remains, having sufficient probability to explain the observed suppression of complete fusion. This appears to be associated with interactions at the nuclear surface. The fusion suppression is predicted to be almost proportional to the charge of the target nucleus, making it most significant in reactions with heavy nuclei.     

The finite size effects in fusion of deformed nuclei at incident energies near the barrier

By the end of the last century, the precision of heavy-ion-fusion cross-section measurement had been increased up to 1%. This allowed the measured cross sections to be converted into experimental fusion-barrier distributions. In the experimental analysis, the barrier distributions were analyzed using a Woods-Saxon shape for the nuclear part of the bare nucleus-nucleus potential. This potential was defined along the line joining the centers of the two nuclei (“centerline potential”), which, for deformed nuclei, contradicts the short-range character of the nucleon-nucleon (N N) nuclear interaction. We present the results of our theoretical study of the significant deviations of the simplified potential from a “realistic” nuclear potential. The finite-size effects on the potential for deformed nuclei were first investigated in an approximate geometrical way. Then a more rigorous approach, namely, a semimicroscopic double-folding model, was applied to calculate the nucleus-nucleus potential. The angle-dependent fusion barriers calculated with a simple delta-function-like exchange term of the N N M3Y interaction was found to be very similar to those calculated with a finite-range expression. This circumstance enables us to perform rather quick calculations of the fusion cross sections and the corresponding barrier distributions. Comparison of the results with the experimental data showed that the finite-size effects are substantial and cannot be ignored in a quantitative analysis of experimental fusion cross sections and barrier distributions. The text was submitted by the authors in English.     

Spectral-product methods for electronic structure calculations

Progress is reported in development, implementation, and application of a spectral method for ab initio studies of the electronic structure of matter. In this approach, antisymmetry restrictions are enforced subsequent to construction of the many-electron Hamiltonian matrix in a complete orthonormal spectral-product basis. Transformation to a permutation-symmetry representation obtained from the eigenstates of the aggregate electron antisymmetrizer is seen to enforce the requirements of the Pauli principle ex post facto, and to eliminate the unphysical (non-Pauli) states spanned by the product representation. Results identical with conventional use of prior antisymmetrization of configurational state functions are obtained in applications to many-electron atoms. The development provides certain advantages over conventional methods for polyatomic molecules, and, in particular, facilitates incorporation of fragment information in the form of Hermitian matrix representatives of atomic and diatomic operators which include the non-local effects of overall electron antisymmetry. An exact atomic-pair expression is obtained in this way for polyatomic Hamiltonian matrices which avoids the ambiguities of previously described semi-empirical fragment-based methods for electronic structure calculations. Illustrative applications to the well-known low-lying doublet states of the H₃ molecule in a minimal-basis-set demonstrate that the eigensurfaces of the antisymmetrizer can anticipate the structures of the more familiar energy surfaces, including the seams of intersection common in high-symmetry molecular geometries. The calculated H₃ energy surfaces are found to be in good agreement with corresponding valence-bond results which include all three-center terms, and are in general accord with accurate values obtained employing conventional high-level computational-chemistry procedures. By avoiding the repeated evaluations of the many-centered one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices in the antisymmetric basis states commonly employed in conventional calculations, and by performing the required atomic and atomic-pair calculations once and for all, the spectral-product approach may provide an alternative potentially efficient ab initio formalism suitable for computational studies of adiabatic potential energy surfaces more generally. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

A six-dimensional H(2)-H(2) potential energy surface for bound state spectroscopy

We present a six-dimensional potential energy surface for the (H(2))(2) dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer's center of mass. The surface is intended to describe accurately the bound and quasibound states of the dimers (H(2))(2), (D(2))(2), and H(2)-D(2) that correlate with H(2) or D(2) monomers in the rovibrational levels (v,j)=(0,0), (0,2), (1,0), and (1,2). We employ a close-coupled approach to compute the energies of these bound and quasibound dimer states using our potential energy surface, and compare the computed energies for infrared and Raman transitions involving these states with experimentally measured transition energies. We use four of the experimentally measured dimer transition energies to make two empirical adjustments to the ab initio potential energy surface; the adjusted surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm(-1). For 26 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. Finally, we use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.     

Structure of the Be(OH)4(2-) anion

Sr[Be(OH)(4)] has been synthesised and its structure determination contains the first definitive characterisation of the discrete Be(OH)(4)(2-) anion.     

Vibrational dependence of the H2-H2 C6 dispersion coefficients

We use the sum-over-states formalism to compute the imaginary-frequency dipole polarizabilities for H2, as a function of the H-H bond length, at the full configuration interaction level of theory using atom-centered d-aug-cc-pVQZ basis sets. From these polarizabilities, we obtain isotropic and anisotropic C6 dispersion coefficients for a pair of H2 molecules as functions of the two molecules' bond lengths.     

Angstrom-to-millimeter characterization of sedimentary rock microstructure

Backscatter SEM imaging and small-angle neutron scattering (SANS) data are combined within a statistical framework to quantify the microstructure of a porous solid in terms of a continuous pore-size distribution spanning over five orders of magnitude of length scale, from 10 A to 500 microm. The method is demonstrated on a sample of natural sandstone and the results are tested against mercury porosimetry (MP) and nuclear magnetic resonance (NMR) relaxation data. The rock microstructure is fractal (D=2.47) in the pore-size range 10 A-50 microm and Euclidean for larger length scales. The pore-size distribution is consistent with that determined by MP. The NMR data show a bimodal distribution of proton T(2) relaxation times, which is interpreted quantitatively using a model of relaxation in fractal pores. Pore-length scales derived from the NMR data are consistent with the geometrical parameters derived from both the SEM/SANS and MP data. The combined SANS/BSEM method furnishes new microstructural information that should facilitate the study of capillary phenomena in hydrocarbon reservoir rocks and other porous solids exhibiting broad pore-size distributions.     

Chaotic dynamics and vibrational mode coupling in small argon clusters

We have computed the local Kolmogorov entropy of molecular dynamics trajectory segments near the potential energy saddles of model Ar₃ and Ar₅ clusters. In the case of Ar₃ clusters bound with a Lennard-Jones potential, the local Kolmogorov entropy of the cluster is significantly smaller in the saddle region than in other areas of the potential surface. This behavior indicates an increase in the degree of nearly quasiperiodic motion near the Ar₃ saddle due to the partial decoupling of the cluster's vibrational modes there. Lennard-Jones Ar₅ clusters do not exhibit similar behavior, but Ar₅ clusters bound with a short-range Morse potential do. This suggests that the “regularizing” effect of saddle regions is strongly dependent on the shape of the energy surface near the saddle. From these observations, we can determine which features of the saddle are most important in this respect; the flatness of the saddle region seems to be one such feature.     

Atomic spectral methods for molecular electronic structure calculations

Theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to contain the totally antisymmetric irreducible representation of the symmetric group of aggregate electron coordinate permutations once and only once, but to also span other (non-Pauli) symmetric group representations known to contain unphysical discrete states and associated continua in which the physically significant Schrodinger eigenstates are generally embedded. These unphysical representations are avoided by isolating the physical block of the Hamiltonian matrix with a unitary transformation obtained from the metric matrix of the explicitly antisymmetrized spectral-product basis. A formal proof of convergence is given in the limit of spectral closure to wave functions and energy surfaces obtained employing conventional prior antisymmetrization, but determined without repeated calculations of Hamiltonian matrix elements as integrals over explicitly antisymmetric aggregate basis states. Computational implementations of the theory employ efficient recursive methods which avoid explicit construction the metric matrix and do not require storage of the full Hamiltonian matrix to isolate the antisymmetric subspace of the spectral-product representation. Calculations of the lowest-lying singlet and triplet electronic states of the covalent electron pair bond (H(2)) illustrate the various theorems devised and demonstrate the degree of convergence achieved to values obtained employing conventional prior antisymmetrization. Concluding remarks place the atomic spectral-product development in the context of currently employed approaches for ab initio construction of adiabatic electronic eigenfunctions and potential energy surfaces, provide comparisons with earlier related approaches, and indicate prospects for more general applications of the method.