Interference Minima Research Articles

Observation of a narrow minimum and of inelastic shadow effects in deuteron-deuteron elastic scattering at √ s = 53 GeV

We report on experimental results on deuteron-deuteron elastic scattering at a centre-of-mass energy of √ s = 53 GeV. The data were obtained using the Split Field Magnet detector at the CERN intersecting Storage Rings. The t-dependence of the elastic cross section is measured up to − = 1.5 GeV 2. We observed a narrow interference minimum in the differential cross section at − = 0.18 GeV 2. The inclusion of inelastic intermeduate states in the multiple scattering Glauber theory is essential in the description of the data over the entire t-range where discrepancies of up to 25% are observed with the basic theory.

Proton-proton scattering from 0.35 to 1.0 MeV

Differential cross sections for the scattering of protons by protons have been measured at energies from 0.35 to 1.0 MeV over an angular range from 24° to 110° in the c.m. system with an absolute accuracy of 0.2 %. Special care was taken at energies around the interference minimum where, due to the extremely small values of the cross section, the accuracy has been 0.8 % at θ c.m. = 90°. The resulting value for the minimum energy is E IM = 382.48 ± 0.10 keV. The high accuracy could be achieved mainly by using a new double compensated calorimeter for the current integration.

Third-order nonlinear susceptibility ratio by CARS of mixtures: CS2 in C6H6

A precise value of the third-order nonresonant susceptibility ratio of carbon disulphide to benzene is determined from coherent anti-Stokes Raman scattering (CARS) experiments in mixtures of the two liquids. The value is derived from the variation of the frequency separation between the Raman resonance and the interference minimum as a function of the relative concentration of the liquids. The method offers special advantages in many situations of interest.

Observation of Striking Shape Differences between21+Angular Distributions for Heavy-Ion-Induced Two-Neutron Stripping and Pickup Reactions in Transitional Samarium Nuclei

The reactions /sup 148/Sm(/sup 18/O,/sup 16/O)/sup 150/Sm, /sup 150/Sm(/sup 16/O,/sup 18/O)/sup 148/Sm, have been performed as part of a heavy-ion study of the transitional samarium region. The angular distributions for the ground-state transitions have a typical bell shape. While the 2/sub 1//sup +/ angular distribution is bell shaped in the stripping reaction, it is flat with an interference minimum in both pickup reactions. The striking difference between 2/sub 1//sup +/ angular distributions is not explained satisfactorily by current theories.

Diffraction efficiency of continuously etched gratings in As 2S 3 films

The diffraction efficiency of gratings in chalcogenide glass thin films during the chemical etching process is described. The experiment is performed by a simultaneous etching and detection technique, and two absolute maxima with intermittent interference maxima and minima are observed. Theoretical analysis including interference effect is presented, and excellent agreement with experimental curve is obtained. Application of this technique to lithographic process for etching control is briefly discussed.

Coulomb-nuclear interference and nuclear reorientation in the scattering of 16, 18O by 58Ni and 64Ni

The inelastic scattering of 16O and 18O projectiles by 58Ni and 64Ni has been studied to investigate the interference between Coulomb and nuclear excitation. The interference minimum for the excitation of the first 2 + state in 18O is found to be shifted towards forward angles when compared to the excitation of the 2 + state in the Ni target nuclei. This shift could not be reproduced by first order DWBA calculations, but reasonable agreement was obtained in a coupled channel analysis allowing for reorientation effects. The coupled channel results depended sensitively on the values of the static quadrupole moments of the excited 2 + states.

Image speckle patterns of weak diffusers

The use of weak phase-retarding diffusers in coherent imaging systems is analyzed. It is shown that ringing caused by diffraction from dust or blemishes can be significantly reduced by a diffuser that scatters light slightly beyond the first interference minimum of the diffraction pattern, provided that the specular transmission of the diffuser is small. Weak phase diffusers, whose phase standard deviations are a small part of a wavelength, accomplish this is an optimal manner. The characteristics of the speckle patterns that consititute their spatially filtered images are found to depend not only on the size of the aperture of the imaging system, but on the Wiener spectrum of the phase and the statistical law that the phase obeys. It is shown that random diffusers with normally distributed phase can easily be constructed that produce image speckle patterns whose Wiener spectra consist primarily of high spatial frequencies, if the size of the aperture of the imaging system is greater than a specified minimum. Speckle patterns are also found to exist near the image of a phase diffuser even when the aperture of the imaging system is large, and their Wiener spectra are functions of their distances from the image of the diffuser.

Intercollisional Interference in the S Lines of H2–He Mixtures

Further experimental results on the pressure induced spectrum of normal H2–He in the region of the S(1) branch of the fundamental band are presented. These results show a well-defined minimum at the transition frequency of the free molecule. The S line is found to be the sum of two components. One of these is of essentially the same nature as the Q branch and should therefore show a pronounced intercollisional interference minimum. The second component shows the usual quadrupolar line shape without a minimum. Finally, a value for the strength parameter characterizing the short range component of the induced dipole moment is determined.

H2(p, 2p)nCross Sections for ConstantNNRelative Energies

Measurements and various $s$-wave model calculations of $p+d$ breakup cross sections were made along constant-relative-energy loci as suggested by Jain, Rogers, and Saylor. The measurements utilized special gas scattering apparatus to accurately measure cross sections in the vicinity of destructive interference minima. The data agreed with the most realistic of the models used except at the position of the interference minimum where a discrepancy of a factor of 3 was found.

Inelastic nuclear-coulomb interference and direct-two-step interference in heavy-ion induced two-nucleon transfer reactions on rare-earth nuclei

The almost pure two-step population of the 2 + ground-state rotational band member of 184W in the two-neutron transfer reaction 186W( 12C, 14C) 184W, resulting in an angular distribution characterized by a dramatic nuclear-Coulomb interference minimum in the vicinity of the grazing angle, is compared with the corresponding angular distribution for the two-proton transfer reaction 186W( 12C, 10Be) 188Os, where the interference minimum is shown to arise primarily from direct-two-step (nuclear-dominated) interference.

Amplitude and phase fluctuations of the signals from the radio station GBR (f=16 kHz) in the neighborhood of the interference minimum

Amplitude and phase fluctuations of the signals from the radio station GBR (f=16 kHz) in the neighborhood of the interference minimum

Interference between Coulomb and nuclear excitation in the inelastic scattering ofNe22fromSr88

We have measured the excitation function at ${\ensuremath{\theta}}_{\mathrm{lab}}=175\ifmmode^\circ\else\textdegree\fi{}$ for the excitation of the first ${2}^{+}$ state in $^{88}\mathrm{Sr}^{*}$ by inelastic scattering of $^{22}\mathrm{Ne}$. At the same time we obtained similar data for the excitation of the first ${2}^{+}$ state of the beam particle itself. The measurements span the energy range 49-65 MeV containing the region of the Coulomb-nuclear interference. In terms of Rutherford trajectories, the $^{22}\mathrm{Ne}^{*}$ interference minimum is located at a separation \ensuremath{\sim} 0.2 fm greater than for $^{88}\mathrm{Sr}^{*}$. An optical potential was obtained by a fit to elastic scattering data consisting of an excitation function at ${\ensuremath{\theta}}_{\mathrm{lab}}=175\ifmmode^\circ\else\textdegree\fi{}$ and an angular distribution at 65.4 MeV lab. A collective model distorted-wave Born-approximation calculation with this potential can account for the $^{88}\mathrm{Sr}^{*}$ data but fails to describe the shape of the $^{22}\mathrm{Ne}^{*}$ excitation function.NUCLEAR REACTIONS $^{88}\mathrm{Sr}$($^{22}\mathrm{Ne}$, $^{22}\mathrm{Ne}$), $E=49\ensuremath{-}65$ MeV; measured $d\ensuremath{\sigma}(E)$ at ${\ensuremath{\theta}}_{1}=175\ifmmode^\circ\else\textdegree\fi{}$ for g.s., first ${2}^{+}$ state in $^{88}\mathrm{Sr}$ and $^{22}\mathrm{Ne}$, $d\ensuremath{\sigma}(\ensuremath{\theta})$ at 65.4 MeV for g.s.; deduced optical model potential, deformation parameters. Enriched target.

Theory of Intercollisional Interference Effects. IV. Does a Zero Minimum in Induced Absorption Imply the Proportionality of the Induced Dipole Moment to the Force?

We show that, within the limits of the theory of intercollisional interference effects developed for collision-induced absorption by a Lorentz gas in paper I of this series, an intercollisional interference minimum which goes precisely to zero implies that the induced dipole moment is exactly proportional to the intermolecular force.

Model independent analysis of the structure in pp scattering

An empirical study of the structure at t≈−1.1 in dσ dt (pp → pp), in terms of two exponential amplitudes plus interference, gives the following results. The steeper exponential shows standard Regge shrinkage, corresponding to a trajectory α ≈1+0.3 t. The other exponential slope stays constant; the overall energy dependence of this amplitude is approximately s −1 for 10–30 GeV, leveling off possibly to a constant at ISR. The relative phase is about 2.1 rad at the lower momenta, becoming 2.5 at ISR. These results suggest a simple physical picture, in which a relatively unstructured shrinking Regge amplitude interferes with an even-signature non-Regge background. This interpretation predicts that the interference minimum in dσ dt is deepest at an intermediate momentum near 175 GeV where measurements will soon be made at NAL.

New Approach to the Analysis of Nucleon-Deuteron Breakup Data

We propose calculations and measurements of $N+d$ breakup cross sections as a function of a new set of kinematic variables. When carried out as a function of these variables, separable-potential calculations predict cross sections which exhibit a very deep destructive interference minimum over a wide range of bombarding energies. We proposed a procedure for isolating the effect of the crucial ${M}_{d2}$ amplitude on the cross section.

Theory of Intercollisional Interference Effects. II. Induced Absorption in a Real Gas

The kinetic theory of intercollisional interference effects in induced infrared spectra developed in the first publication of this series for a Lorentz gas is extended to a real gas.A principal conclusion is that intercollisional interference in absorption is always destructive in the systems considered. Though the theory is mathematically less tractable for the real gas than for the Lorentz gas, a useful upper bound to the intercollisional interference dip minimum is obtained. This upper bound is evaluated for the exponential model developed previously, for all values of the mass ratio m1/m2. The intercollisional interference minimum itself is calculated for this model with m1 = m2. Finally, a simplification of the expression for the line-shape function is discussed.

Experimental studies of sea-surface effects on low-angle radars

This paper presents results of measurements made during the years 1953?56 on the effects of sea-surface reflections on low-angle radars at Xband frequencies. The work was done in three parts and comprised a study of the polarisation properties of sea clutter as a function of sea state, wind direction and incidence angle, a study of the position and depth of interference minima close to the sea surface and a study of the reflecting properties of the sea over a wide range of incidence angles, in so far as these affect the properties of a possible image target. The sea-clutter measurements yielded a well marked polarisation pattern, but the effect of incidence angle did not conform to the conventional linear theory. The interference minima were located close to the positions predicted by the 4/3-earth theory when the aircraft flew at heights of 400ft or more. At lower altitudes, however, the range of the horizon and of the farthest minima considerably exceeded the theoretical values. The peak voltage-reflection coefficients over a range of angles between 1° and 40° relative to glancing incidence very seldom exceeded 0.3 for vertical polarisation and 0.6 for horizontal polarisation. Brewster-angle behaviour was clearly visible for all sea states, and the horizontally polarised reflection was always dominant. In all the results, features were observed for which no theoretical explanations are apparent.

Analysis ofp−pData Near the Interference Minimum

In the first part of this paper $p\ensuremath{-}p$ elastic scattering data at 90\ifmmode^\circ\else\textdegree\fi{}c.m. near the Coulomb-nuclear interference minimum are analyzed. The energy of the minimum of the 90\ifmmode^\circ\else\textdegree\fi{} cross section is found to be at 0.38243 \ifmmode\pm\else\textpm\fi{}0.00020 MeV. The nuclear $s$-wave phase shift, defined with respect to wave functions which solve the Coulomb plus vacuum polarization potential problem, is found to be ${{\ensuremath{\delta}}_{0}}^{E}=0.25501\ifmmode\pm\else\textpm\fi{}0.00020$, at the precise energy 0.38243 MeV. In the second part of the paper the phase shift just obtained is used, in conjunction with four very accurate phase shifts from 1.4 to 3.0 MeV, to determine the parameters of the $s$-wave effective-range expansion. If this expansion is cut off after three terms (quadratic fit) then the scattering length is found to be $a=\ensuremath{-}7.815\ifmmode\pm\else\textpm\fi{}0.008$ F; the effective range ${r}_{0}=2.795\ifmmode\pm\else\textpm\fi{}0.025$ F; and the shape-dependent parameter $P=0.028\ifmmode\pm\else\textpm\fi{}0.014$. However, it is argued that the first three coefficients in the actual power-series expansion of the effective-range function are not known this well, and in particular, $P$ may be very different from the actual coefficient occurring in the ${k}^{4}$ term.

Absolute Velocity Gauge for Nuclear Particle Beams

An instrument for determining the energies of accelerator particle beams in the 0–9 MeV range has been built in the form of a coaxial cylindrical cavity. It has been used to establish data points in the vicinity of the Coulomb-nuclear interference minimum in p-p scattering at 382.43 keV, with an accuracy of better than one part in 104 in energy. This is an order-of-magnitude higher precision than has been achieved previously with this technique. The collimated particle beam passes through 0.46-mm gaps separated by the 125-cm length of a hollow inner cylinder made of Invar. The beam is intensity modulated at 72 Mc, and the cavity is tuned to the modulation frequency. As the beam energy is adjusted until the particle transit time is an odd half-multiple of the cavity period, and the shunt capacitors at opposite ends are adjusted for equal and opposite electromagnetic signals across the two gaps, a sharp null occurs in the signal picked up by an antenna in the cavity. The Q was 4000. The 19F(p,αγ)16O resonance was relocated at 340.45±0.04 keV, with an order-of-magnitude increase in precision.

Possible proton-alpha scattering experiments at 40 MeV

Recently, qualitatively different phase-shift analyses of the 40 MeV proton-alpha elastic scattering and polarization data have appeared in the literature. The question arises whether further experimental data can decide in favour of one or the other of these analyses. Two classes of experiments, measurement of the triple scattering parameters R and A and measurement of the polarization P in the region of the Coulomb interference scattering cross-section minimum, have been examined to see if these provide additional information to resolve the ambiguity. We conclude that a measurement of the polarization near the Coulomb interference minimum would serve to establish on a purely experimental basis the complete scattering amplitude in the forward direction. This information would remove the ambiguity in the phase-shift analysis of these data. No further information could be gained from triple scattering experiments unless these experiments were of very high precision.