Quasi-genera of quadratic forms

Let f be a quadratic form in n variables (n > 1) with nonzero determinant d. A prime p is said to be exceptional with respect to f if every automorph of f with rational elements, determinant ±1 and denominator prime to 2d has a denominator which is a quadratic residue of p. (Throughout, slight modifications must be made if p = 2.) Except for certain binary forms, each exceptional prime induces a splitting of the genus into two quasi-genera. Building on previous results, necessary and sufficient conditions are given that a prime p be exceptional for n = 2 and n = 3 and necessary conditions for n > 3. It is proved that there are no exceptional primes for n > 4 and only possibly in special cases for n = 4. A connection is shown between representations of integers by certain ternary forms and the existence of quasi-genera. Possible connections with spinor genera are mentioned and a few unanswered questions are posed.     

207Pb(p,p') measurements at 135 and 61 MeV,the effective interaction and core polarization

Data at Einp = 61 and 135 MeV for neutron-hole transitions are used to study the proton-neutron part of the assumed NN force. Collective core-polarization strengths (A_L) from the present fits at 135 MeV are consistent with those extracted from the (e, e') reaction for two L = 2 transitions and one L = 4 transition. This is not the case at 61 MeV where the A_L values needed to fit the (p, p') data are much smaller for transitions to the $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole states. A fully microscopic DWBA fit is successful for the L = 3 transition to the doublet at 2.64 MeV of excitation at E_p = 61 MeV, but fails at 135 MeV; a fully microscopic DWIA calculation provides a reasonable fit to the data at 135 MeV.     

Adsorption of gold on low index planes of rhenium

On atomically rough areas of a thermally cleaned rhenium field emitter, adsorbed gold behaves like it does on tungsten. The average work function $\text{}\text{?}$gf increases at low average gold coverage $\text{}\text{?}$gq due to formation of gold-rhenium dipoles, and at high coverage a structural transformation in the gold layer leads to a $\text{}\text{?}$gq-independent work function. Broadly similar behaviour is found for gold on the low-index planes of tungsten, but on low-index rhenium planes gold behaves rather differently. When thermally cleaned at > 2200 K and annealed below 800 K, the work function, φ(clean), of (101&#x0304;1&#x0304;) takes one of two values 5.25 ± 0.04 eV, and 5.36 ± 0.04 eV, which are tentatively attributed to the two possible structures of this plane. Similar behaviour is expected and observed for (101&#x0304;0),but the values taken by φ(clean) are not well defined. Both forms of (101&#x0304;1&#x0304;) are thought to undergo reconstruction above 800 K forming a single structure with φ(clean) = 5.55 ± 0.03 eV. (112&#x0304;0) and (112&#x0304;2&#x0304;) each have only one possible structure, and in keeping with this, φ(clean) has a single well-defined value for each plane. The flatness of (101&#x0304;1&#x0304;) and (101&#x0304;0) leads to field reduction at their centres which produces an increase in their measured work functions by up to 10%. The initial increase in φ produced by gold condensed at 78 K and spread at low equilibration temperatures T_s on (112&#x0304;2&#x0304;), (101&#x0304;1&#x0304;) and (112&#x0304;0) is attributed to gold-rhenium dipoles, which, on the latter two planes approximate to the Topping model, giving dipoles characterised by μ₀(1011) = 0.1 × 10^?30 C-m with α = 10 ų and μ₀(112&#x0304;0) = 0.32 × 10^?30 C-m with α = 22 ų, where μ₀ is the zero-coverage dipole moment and α its polarizability. Failure of the Topping model on (112&#x0304;2&#x0304;) is attributed to its atomically rough structure. No dipole effect is seen on (101&#x0304;0). Energy spectroscopy of electrons field emitted at (202&#x0304;1&#x0304;) and (101&#x0304;1&#x0304;) demonstrates the non-free character of electrons in rhenium, while the small effect of adsorbed gold strengthens the belief that gold is bound through a greatly broadened 6s level centred 5.6 eV below the Fermi level and the dipolar nature of the bond supports this model. At higher values of T_s and $\text{}\text{?}$gq gold appears to form states which are well-characterised by a coverage-independent work function. (101&#x0304;0), (101&#x0304;1&#x0304;) and (112&#x0304;0) each form two such states, one in the range 2 < $\text{}\text{?}$gq < 4 (state 1), and the second at $\text{}\text{?}$gq > 4 (state 2). The atomic radii of gold and rhenium are thought to be sufficiently similar to allow the possibility that state 1 is a replication of the Re plane structure by gold. The high work function and thermal stability of state 2, taken together with the observed temperature dependence of the transformation of state 1 to state 2, encourages the belief that state 2 results from atomic rearrangement of state 1 into a close-packed Au(111) structure. State 2 also forms on (112&#x0304;2&#x0304;) and the absence of state 1 on this plane suggests some surface alloying at coverages below 4 $\text{}\text{?}$gq.     

Coherent amplification in fluorescent dye solutions. II. The inverse pre-resonance Raman spectrum of rhodamine 6G

Inverse pre-resonance Raman spectra of rhodamine 6G in solution in methanol have been recorded over the concentration range 10^?1 to 10^?4 mol ?^?1. The solute and solvent transitions are found to display perfectly normal lorentzian profiles over the whole of this concentration range. Intensities and depolarization ratios of the pre-resonance Raman features are recorded. It is shown that the spectra arise from monomeric rhodamine 6G molecules in the singlet electronic ground state and the relative merits of the CARS and inverse Raman methods for recording resonance Raman spectra are discussed.     

Analysis of the (ν1 + ν2) and (ν2 + ν3) combination bands of ozone

The fine structures of the (ν₁ + ν₂) and (ν₂ + ν₃) combination bands of ozone in the 5.7-μm region have been recorded and analyzed. The two vibrational states are coupled through Coriolis and second-order distortion terms. The interaction has been treated by the numerical diagonalization of the secular determinant for the two coupled states. With the centrifugal distortion parameters fixed to the ground state values, the following constants have been obtained: ν₁ + ν₂ = 1796.26₆, A₁₁₀ = 3.610₄, B₁₁₀ = 0.4414₅, $\text{C}{}^1{}_{110}\text{= 0.3902}{}_9$, ν₂ + ν₃ = 1726.52₆, A₀₁₁ = 3.553₇, B₀₁₁ = 0.4398₂, $\text{C}{}^1{}_{011}\text{= 0.3884}{}_4$, Y₁₃ = ?0.46₆, and X₁₃ = ?0.01₀ cm^?1. In addition, the following anharmonic constants have been obtained: x₁₂ = ?7.82₁ and x₂₃ = ?16.49₄ cm^?1. The value of the dipole moment ratio, $\text{R =}\text{〈011|μ}{}_{\mathrm{z}}\text{|0〉}\text{〈110|μ}{}_{\mathrm{x}}\text{|0〉}$, is 1.30 ± 0.10.     

Superconductivity of neutron irradiated Mo3Os

The effect of high energy neutron irradiation (E>1 MeV) on the superconducting transition temperature, T_c, of the A-15 compound Mo₃Os is reported. T_c was found to decrease with increasing neutron dose, but at a rate considerably less than observed in other A-15 compounds composed of non-transition metals. The results lend support to the idea that the effect of ordering on T_c is smaller for A-15 compounds composed only of transition metals than those composed of transition and non-transition metals.     

The laser-induced fluorescence spectrum of chromyl fluoride (chromium dioxidedifluoride) in a seeded molecular beam

We habe obtained part of the laser-induced fluorescence spectrum of chromyl fluoride in a free jet expansion at an instrumental resolution of better than 0.001 cm^?1. This spectrum (together with that of the dispersed fluorescence) allows the identification of the (0,0) band or the absorption spectrum and of several progressions in the lowest bending frequency.