Quadratic Shift Research Articles

Quadratic hfs Pressure Shifts of Muonium in Argon and Krypton

The very precise, low-pressure measurements of the hfs interval $\ensuremath{\Delta}\ensuremath{\nu}(p)$ of muonium in Ar and Kr described in the preceding Letter are combined with the high-pressure measurements from Yale to determine the magnitude of quadratic pressure shifts. Fitting by the form $\ensuremath{\Delta}\ensuremath{\nu}=\ensuremath{\Delta}\ensuremath{\nu}(0)[1+ap+b{p}^{2}]$, we find $b(\mathrm{Ar})=7.1(2.3)$ and $b(\mathrm{Kr})=8.7(3.1)$ (in units of ${10}^{\ensuremath{-}15}$ ${\mathrm{Torr}}^{\ensuremath{-}2}$). Older evidence for these quadratic shifts from similar fits involving earlier Chicago data is reviewed.

Stark effect of the F+centre in CaO

An upper limit has been found experimentally for the magnitude of the Stark effect for the broad band at 340 nm of the f+ centre in CaO and a small quadratic red shift has been measured for the accompanying zero-phonon line at 355.7 nm. An explanation of the zero-phonon line red shift is given which requires near degeneracy for the 2s and 2p states of the F+ centre.

Ground-State Wave Function of Shallow Donors in Uniaxially Stressed Silicon: Piezohyperfine Constants Determined by Electron-Nuclear Double Resonance

Stress-induced changes in the ENDOR spectra of a shallow donor electron interacting with various ${\mathrm{Si}}^{29}$ nuclei neighboring the donor have been experimentally and theoretically investigated. For each of the three measured donors - As, P, and Sb - the compressional, uniaxial stress was applied along the [001] axis and its magnitude corresponded to strains up to ${10}^{\ensuremath{-}3}$. To describe the observed linear and quadratic shifts and splittings of the lines in an ENDOR shell, we have defined a set of piezohyperfine constants. One piezohyperfine constant was measured for each $〈111〉$-axis-class shell; three independent piezohyperfine constants were measured for each shell of the other shell symmetry classes. Piezohyperfine constants are reported for more than 15 measured lattice shells about each donor. Analysis of the results shows that the constants for any one shell can be attributed primarily to changes in the Fermi contact hyperfine constants at the various lattice sites within that shell. Consequently, the stress-induced changes are directly related to wave-function density changes at specific points in the lattice. Calculations of these wave-function density changes have been performed using a model based on the valley-repopulation effect and on an effect due to the redistribution of the radial envelope function (RREF effect). The calculations and experimental results are qualitatively in good agreement. The quanitative theoretical accuracy is not sufficient to match all the experimental shells to the actual lattice shells, but a new match of shell $Q$ and the (1,1,5) shell has been determined and other matchings are suggested. The theoretical and experimental results provide information on two intrinsic lattice parameters: the deformation-potential constant ${\ensuremath{\Xi}}_{u}$, and the location of the conduction-band minimum ${k}_{0}$. Difficulties with assigning a value to ${\ensuremath{\Xi}}_{u}$ because of the RREF effect are discussed. A revised "spin-resonance" value for ${\ensuremath{\Xi}}_{u}$ was found to be 10 \ifmmode\pm\else\textpm\fi{} 1 eV. Applying the above model to the previously matched shells [A and (0,0,4), $B$ and (4,4,0), $K$ and (0,0,8)], one finds an average ${k}_{0}=(0.86\ifmmode\pm\else\textpm\fi{}0.02){k}_{max}$.

Experimental Verification of the Relativistic Doppler Effect

An experiment has been performed to measure the quadratic Doppler shift, ∼(1−υ2/c2)−12, predicted by the special theory of relativity. A moving beam of radiating hydrogen atoms with velocities ranging up to 2.8 × 108 cm/sec has been viewed from the incoming and outgoing directions simultaneously. Averaging wavelength measurements of a particular spectral line for the two observations gives a measurement of the quadratic shift. The number (12) in the theoretically predicted exponent can be compared to the experimental results. The latter gives the value of this exponent to be 0.498 ± 0.025. The predominant factor leading to the experimental uncertainty is the width of the spectral lines involved in the measurement.

LOSS OF PHOSPHOLIPID IN THE SKIN OF TUMOR-BEARING RATS

There occurs a unique, statistically significant fall in the level of phospholipid in the skin of albino rats bearing large Walker carcinosarcomata 256. The shift is similar to that produced by application of methylcholanthrene. It is preceded by loss of skin weight and increases in levels of skin water, cholesterol, and cholestrol esters. It is accompanied by loss of skin neutral fat and cholesterol esters. The quadratic shift in cholesterol esters occurs in hair before it occurs in skin, and is accompanied by a loss of hair weight and a slight but significant rise in levels of hair neutral fat. Declining levels of skin phospholipid may be part of the mechanism of production of the sallow appearance of the skin in late malignancy.

LOSS OF PHOSPHOLIPID IN THE SKIN OF TUMOR-BEARING RATS

There occurs a unique, statistically significant fall in the level of phospholipid in the skin of albino rats bearing large Walker carcinosarcomata 256. The shift is similar to that produced by application of methylcholanthrene. It is preceded by loss of skin weight and increases in levels of skin water, cholesterol, and cholestrol esters. It is accompanied by loss of skin neutral fat and cholesterol esters. The quadratic shift in cholesterol esters occurs in hair before it occurs in skin, and is accompanied by a loss of hair weight and a slight but significant rise in levels of hair neutral fat. Declining levels of skin phospholipid may be part of the mechanism of production of the sallow appearance of the skin in late malignancy.

Effect of a Two-Dimensional Pressure on the Curie Point of Barium Titanate

By hydraulic means, a single crystal of barium titanate in the shape of a flat circular disk was subjected to a pressure exerted on its edges and not on its faces. A very slight pressure removed all domains that were not normal to the disk. The stress system then consisted of equal pressures on the two $a$ axes, and no pressure on the $c$ axis. The transition temperature increased with the square of the two-dimensional pressure, while, according to Merz, a hydrostatic pressure produces a linear drop. Using Devonshire's expansion for the free energy and the appropriate Legendre transformation, the free energy, depending on polarization and pressure, was obtained for both two-dimensional and hydrostatic stress systems. This yielded a purely linear-pressure dependence, and it was, therefore, necessary to supplement Devonshire's expansion with higher terms in order to obtain a quadratic effect.Although it was too difficult to evaluate the effect of pressure on the transition temperature itself when higher terms were included, it was easy to determine the effect on the Curie-Weiss temperature ${T}_{0}$. This is the temperature at which the inverse susceptibility of the cubic phase extrapolates to zero, and its pressure dependence will be the subject of a future paper. For both two-dimensional and hydrostatic pressures, the linear part of the shift of the Curie-Weiss temperature was found to depend only on the lower terms in the free energy, and provide two independent relations for determining the two $g$ coefficients. The quadratic shift of the Curie-Weiss temperature depends on the higher terms with which Devonshire's expansion was supplemented, and a reasonable interpretation of these higher terms gave an upward direction to the quadratic shift of the Curie-Weiss temperature.

The quadratic Zeeman-effect in the principal series of caesium, rubidium and potassium

The quadratic shift due to the atomic diamagnetism has been observed in the principal series of caesium, rubidium and potassium in absorption by means of the Amsterdam cyclotron magnet and a grating mounting. The theoretical formula for the quadratic Zeeman-effect is shown to account reasonably well for the observed displacements. In caesium weak components are found corresponding to electron transitions involving Δm s = ± 1, which are to be expected in the intermediate stages between anomalous Zeeman-effect and complete Paschen-Back effect.