A study of the ^9 Be nucleus

The reaction ⁷Li(³He, p)⁹Be has been used to measure excitations and intrinsic widths of levels in ⁹Be below the ⁷Li + d threshold. Previously unreported levels have been found at excitations of (13.78 ± .03) MeV and (16.671 ± .008) MeV with widths of (590 ± 60) keV and (41 ± 4) keV respectively. Two overlapping levels have been found at (11.81 ± .02) MeV and (11.29 ± .03) MeV with widths of (400 ± 30) keV and (620 ± 70) keV respectively. Branching ratios from ⁹Be levels populated in this reaction to the ground and first excited states of ⁸Be have been measured by observing the associated protons in coincidence with the decay neutrons. Branching ratios were found to be:

Excitation in ⁹Be .... Branching Ratio.......... Final Nucleus.........

(MeV) .......................... (percent) .....................................

.. 2.43 ........................... 7.5 ± 1.5 .............. ⁸Be(g.s.)

.. 3.03 ........................... 87 ± 13......................................

.. 4.65 ........................... 13 ± 4.......................................

.. 6.76 .............................. ≤ 2 ......................................

.. 11.29 ...............................≤ 2 ......................................

.. 11.81 ...............................≤ 3 ......................................

.. 6.76 ........................... .41 ≤ B.R. ≤ .69 ....... ⁸Be(2⁺)

.. 11.29 ........................... 14 ± 4 .......................................

.. 11.81 ........................... 12 ± 4 .......................................

Corresponding reduced widths for neutron emission are calculated and a comparison of the results with the expectations of current nuclear models is made. In particular the measured branching ratio to ⁸Be(g.s.) from ⁹Be(2.43 MeV) corresponds to an f-wave reduced with θ²_f = 2.1 x 10^-2, in units of ħ²/mR², with R = 4.35 fm. A comparison of this value with that predicted by a Nilsson model calculation, in which ⁹Be is taken to be a deformed nucleus, is discussed. The measured value for θ²_f is found to be consistent with that expected on the basis of measured E2-transition rates between rotational levels in ⁹Be.

Formation of jets by implusive acceleration of a curved free surface

The sudden axial acceleration of a column of liquid bounded at one end by a concave free surface has been found, experimentally, to produce a jet which issues from the free surface with a speed several times that imparted to the column.

Theoretical approximations to such flows, valid for small time, are formulated subject to the assumption that the fluid is inviscid and incompressible. In a special two-dimensional case, it is found that, for vanishingly small time, the velocity at the point on the free surface from which the jet emanates is π/2 times the velocity imparted to the column. The solutions to several problems in two and three dimensions assuming that the initial curvature of the free surface is small, lead to values for this ratio dependent upon the curvature—the initial velocity in the case of axial symmetry exceeding that of the analogous two-dimensional problem by approximately 25%.

Experiments conducted upon the phenomenon give values systematically in excess of those predicted by the theory, although theory and experiment are in qualitative agreement with respect to the displacement of the free surface. It is suggested that the discrepancy is attributable to effects of finite curvature having been imperfectly accounted for in the axially-symmetric analysis.

Photographic materials on pp. 115, 120, and 121 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

Part I. Approximate Hartree-Fock wavefunctions one-electron properties and electronic structure of the water molecule. Part II. Perturbation-variational calculation of the nuclear spin-spin isotope coupling constant in HD

Part I

Several approximate Hartree-Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann-Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p-orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.

Part II

The perturbation-variational theory of R. M. Pitzer for nuclear spin-spin coupling constants is applied to the HD molecule. The zero-order molecular orbital is described in terms of a single 1s Slater-type basis function centered on each nucleus. The first-order molecular orbital is expressed in terms of these two functions plus one singular basis function each of the types e^-r/r and e^-r ln r centered on one of the nuclei. The new kinds of molecular integrals were evaluated to high accuracy using numerical and analytical means. The value of the HD spin-spin coupling constant calculated with this near-minimal set of basis functions is J_HD = +96.6 cps. This represents an improvement over the previous calculated value of +120 cps obtained without using the logarithmic basis function but is still considerably off in magnitude compared with the experimental measurement of J_HD = +43 0 ± 0.5 cps.

Lurking in ULIRGs: Molecular Gas in local Merging Galaxies

Mergers and interacting galaxies are pivotal to the evolution of galaxies in the universe. They are the sites of prodigious star formation and key to understanding the starburst processes: the physical and chemical properties and the dynamics of the molecular gas. ULIRGs or Ultraluminous Infrared Galaxies are a result of many of these mergers. They host extreme starbursts, AGNs, and mergers. They are the perfect laboratory to probe the connection between starbursts, black hole accretion and mergers and to further our understanding of star formation and merging.

NGC 6240 and Arp 220 can be considered the founding members of this very active class of objects. They are in different stages of merging and hence are excellent case studies to further our understanding about the merging process. We have imaged the dense star-forming regions of these galaxies at sub-arcsec resolution with CARMA C and B Configurations (2" and 0.5 - 0.8"). Multi-band imaging allows excitation analysis of HCN, HCO⁺, HNC, and CS along with CO transitions to constrain the properties of the gas. Our dataset is unique in that we have observed these lines at similar resolutions and high sensitivity which can be used to derive line ratios of faint high excitation lines.

Arp 220 has not had confirmed X-ray AGN detections for either nuclei. However, our observations indicate HCN/HNC ratios consistent with the chemistry of X-ray Dominated Regions (XDRs) -- a likely symptom of AGN. We calculated the molecular Hydrogen densities using each of the molecular species and conclude that assuming abundances of HNC and HCO⁺ similar to those in galactic sources are incorrect in the case of ULIRGs. The physical conditions in the dense molecular gas in ULIRGs alter these abundances. The derived H2 volume densities are ~ 5 x 10⁴ cm^-3 in both Arp 220 nuclei and ~ 10⁴ cm^-3 in NGC 6240.

Tsunamis - a model of their generation and propagation

A general solution is presented for water waves generated by an arbitrary movement of the bed (in space and time) in a two-dimensional fluid domain with a uniform depth. The integral solution which is developed is based on a linearized approximation to the complete (nonlinear) set of governing equations. The general solution is evaluated for the specific case of a uniform upthrust or downthrow of a block section of the bed; two time-displacement histories of the bed movement are considered.

An integral solution (based on a linear theory) is also developed for a three-dimensional fluid domain of uniform depth for a class of bed movements which are axially symmetric. The integral solution is evaluated for the specific case of a block upthrust or downthrow of a section of the bed, circular in planform, with a time-displacement history identical to one of the motions used in the two-dimensional model.

Since the linear solutions are developed from a linearized approximation of the complete nonlinear description of wave behavior, the applicability of these solutions is investigated. Two types of non-linear effects are found which limit the applicability of the linear theory: (1) large nonlinear effects which occur in the region of generation during the bed movement, and (2) the gradual growth of nonlinear effects during wave propagation.

A model of wave behavior, which includes, in an approximate manner, both linear and nonlinear effects is presented for computing wave profiles after the linear theory has become invalid due to the growth of nonlinearities during wave propagation.

An experimental program has been conducted to confirm both the linear model for the two-dimensional fluid domain and the strategy suggested for determining wave profiles during propagation after the linear theory becomes invalid. The effect of a more general time-displacement history of the moving bed than those employed in the theoretical models is also investigated experimentally.

The linear theory is found to accurately approximate the wave behavior in the region of generation whenever the total displacement of the bed is much less than the water depth. Curves are developed and confirmed by the experiments which predict gross features of the lead wave propagating from the region of generation once the values of certain nondimensional parameters (which characterize the generation process) are known. For example, the maximum amplitude of the lead wave propagating from the region of generation has been found to never exceed approximately one-half of the total bed displacement. The gross features of the tsunami resulting from the Alaskan earthquake of 27 March 1964 can be estimated from the results of this study.