Studies on the variation of the track etch rate along alpha particle trajectories in CR-39

At the beginning of the etching process a constant track etch rate can be assumed. In deeper detector layers, however, the etch rate varies drastically along the particle trajectories. Consequently, the indirect determination of the track etch rate by measuring the etch pit diameters on the detector surface does not yield correct results. Therefore, a method for the direct measurement of the track etch rate as a function of the depth within the detector was developed. Applying this method, the relationship between the track etch rate and the energy loss in CR-39/PATRAS could be derived.     

Measurement of the track etch rates along proton and alpha particle trajectories in CR-39 and calculation of the detection efficiency

Computation of the neutron response of CR-39 detectors needs to simulate the track formation by neutron induced charged particles taking into account the bulk etch rate and the track etch rate varying along the particle trajectories. The latter one was determined experimentally by track length measurement. The results allowed to derive the relationship between the track etch rate and the restricted energy loss of the charged particles. On this basis, the geometrical track parameters and track etch rates as well as the critical angle of particle incidence could be determined for protons and alpha particles in the energy range from 0.2 to 8.8 MeV. The energy dependence of the critical angle enabled to determine the detection efficiency for a charged particle of given energy and direction.     

Calibration of PM-355 nuclear track detectors; comparison of track diameter diagrams with track depth characteristics

The calibration diagrams, i.e. track diameters and track depths versus ion energy and etching time, as obtained for PM-355 track detector irradiated with He-ions are presented. The both detector characteristics are compared. The track etch rate is determined by two methods, as a function of the etch pit depth and the ion energy loss.     

(Q) corrections to particle multiplicity ratios in gluon and quark jets

The order (Q²) correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. Through (Q²) we find

, with r = <n>_{gluon jet}/<n>_{quark jet}. This ratio is independent of the opening angle chosen to define the jets.     

On the solidification front of a dilute binary alloy: Thermal diffusivity effects and breathing solutions

The asymptotic equation derived in [6],

, to describe the interfacial structure of the solidification front of a dilute binary alloy in the limit in which the solute rejection coefficient is close to unity, is demonstrated to be also valid to lowest order when the thermal diffusivities in the liquid and in the solid are unequal. At higher order nonequal thermal diffusivity effects contribute an integral term. A uniformly valid approximation for the interfacial structure is obtained. The integral term is shown to be capable of producing slowly travelling waves or breathing solutions along the interfacial front when the thermal diffusivity of the liquid is sufficiently larger than the thermal diffusivity of the solid. This slowly oscillatory behavior may signal the proximity of a chaotic region located within the region of linear instability. Latent heat of fusion effects are also discussed.     

Distance functions and statistics

This paper proves that the Riemannian distance function is maximal in the class of distance functions associated with the Riemannian metric tensor.

Secondly, it is proven that there exists a unique minimum of

on a complete Riemannian surface (M,g) with small curvature, small curvature change and injectivity radius +∞. Here p_iM and γ_v is the maximal geodesic with initial velocity v and 0<t₁<<t_m.     

Kinetic model for the relationship between mean diameter shortening and age reduction in glass samples

Fission tracks in glass samples are shortened when they experience thermal treatment. Consequently, the observable dimensions associated with track length also diminish. The dimension normally used to characterize track size is the mean diameter of the etched track at the surface, D. Another consequence of length shortening is the reduction of surface density, ρ, implying a reduction of the fission-track age. In this work, a kinetic model is developed to describe the relationship between fission-track mean diameter shortening and surface fission-track density reduction in glass samples, based on geometrical and etching hypotheses. The result is a two-parameter equation given by

(1)

in which h is the thickness of the layer removed during etching and n is a parameter related to the latent track geometry and etching reaction rate. The equation was compared with experimental data on Australite glass found in the literature and with fresh data on Macusanite glass presented in this work. The model fits the experimental curves quite well, showing that it describes the etching effects correctly (within its limitations). In addition, the model equation derived in this work can be very useful in age correction of partially annealed glass samples.     

Nonlinear and nonlocal dynamics of spatially extended systems: Stationary states, bifurcations and stability

Spatially extended systems with nonlocal dynamics (e.g. ferromagnetic resonance or current instability) of the type

with uε ⁿ will be studied near the soft-mode instability (wave number k_c ≠ 0) of a stationary and uniform state. An amplitude equation is derived within the framework of a multiple-scale perturbation theory. A particular example of this class of nonlocal dynamics is also treated numerically. As the main result we find that in contrast to the well-known supercritical bifurcation into a stable periodic state, the uniform state can bifurcate supercritically into a stationary state of an amplitude-modulated fast oscillation in space.     

Micro-track structure analysis for 100 MeV Si ions in CR-39 by using atomic force microscopy

To analyze the micro-track structure of heavy ions in a polymer material,parameters including bulk etch rate,track etch rate,etch rate ratio,and track core size were measured.The pieces of CR-39 were exposed to 100 MeV Si ions with normal incidence and were etched in 6.25N NaOH solution at 70 C.Bulk etch rate was read out by a profilemeter after several hours of etching.The other parameters were obtained by using an atomic force microscope(AFM)after a short time of etching.We have measured the second etch pits and minute etch pits to obtain the track growth curve and three dimension track structures to track the core size and etch rate measurements.The local dose of the track core was calculated by theδ-ray theory.In our study,we figure out that the bulk etch rate Vb=(1.58±0.022)μm/h,the track etch rate Vt=(2.90±0.529)μm/h,the etch rate ratio V=1.84±0.031,and the track core radii r≈4.65 nm.In the meantime,we find that the micro-track development violates the traditional track-growth model.For this reason,a scenario is carried out to provide an explanation.     

Calibration of different plastic track detectors using accelerated heavy ions

Measurements of the dependence of track etch rate on the energy-loss of different ions have been presented. In this method, ₁₈ ⁴⁰ Ar, ₁₀ ²² Ne, ₈ ¹⁶ O and ₆ ¹² C-ions of different energies are used as energetic heavy ions for track formation in the detectors. The bulk etch rate and track etch rate are measured for different temperatures and hence the activation energies are determined. The variation ofV =V _t /V _b along the trajectory of the track has been shown for different temperatures. The maximum etched track length is compared with the theoretical range as well as with the range reported earlier. The experimental results indicate the absence of a well-defined threshold in the plastics studied.     

A comparative study of track registration response of makrofol-(KG, KL & N) polycarbonate to Ar ions

In the present work a comparative study of track registration response of ⁴⁰Ar ions in different types of Makrofol polycarbonates viz. Makrofol-KG, KL & N have been done. The etched track parameters viz. bulk etch rate, track etch rate, etch rate ratio, cone angle and etching efficiency were calculated. The variation of etching rates with temperature were found to be exponential and follow the Arrhenius equation. The values of activation energy for bulk and track etching were also calculated. Maximum etchable track length/range were also obtained and compared with the theoretical values obtained from computer program RANGE. From the results it is found that the polycarbonates having same chemical composition manufactured by different chemical processes have slightly different behavior.     

Integral geometry on families of surfaces in the space

A complex {B_ξ} of submanifolds is called admissible in the sense of integral geometry if there are such densities μ_ξ on B_ξ, that the integral transformation

has a local inversion formula. We prove that compact smooth surfaces of an admissible complex in P³ has degree 3 and obtain complete classification of admissible complexes of quadrics. Several general theorems and conjectures about admissible complex of k-dimensional submanifolds are stated.     

From Planck to GUT via dimensional transmutation

Consider a gauge singlet superfield S coupled to a pair of adjoint fields in a SUSY-GUT. If the tree-level vacuum is flat in S, the vev S which defines the GUT scale will be determined via dimensional transmutation at a scale M where the soft-breaking (mass)² vanishes as a result of running from M_P = (8πG_N)^−1/2. Because of the large number of adjoint fields N_A coupled to S, one finds that M can be generically close to M_GUT = 2 × 10¹⁶GeV:

, where λ is a Yukawa 0.7. This work examines the symmetries and dynamical constraints required in a SUSY-GUT in order that the desired flatness in S is achieved, and that this flatness may survive in a supergravity framework.     

Observations on the geometries of etched fission and alpha-recoil tracks with reference to models of track revelation in minerals

The kinetic and atomistic theories of crystal growth and dissolution are used to interpret the shapes and orientations of fission-track, recoil-track and dislocation etch pits in tri-octahedral phlogopite and di-octahedral muscovite. An atomistic approach combined with symmetry considerations lead to the identification of the periodic bond chains that determine the etch pit morphologies and relative etch rates at a chemical level: O–Mg–O in phlogopite, O–Mg–O–Fe in biotite and O–Al–O in muscovite. Using first-order estimates of the bond strengths, it is possible to account for the relative track etch rates in these minerals. The reported, sometimes simultaneous, occurrence of triangular, polygonal and hexagonal etch pit contours in phlogopite, some of which violate the crystal symmetry, suggests that the cohesion of the phlogopite lattice is lost over a much larger radius than that of the track core around the trajectories of particles for which the energy loss exceeds a threshold value. This is interpreted as an indication of pronounced sublattice and anisotropic effects during track registration.     

Studies on the track formation mechanism of the heavy ions in CR-39

The bulk etch rate for two types of CR-39 detector was measured as a function of temperature and the activation energies of bulk etching was determined. Experimental values of track etch rate were derived directly from the function of the succesive measured track length vrs. etching time for ²⁰⁹Bi, ¹²⁹Xe and ²⁰Ne ions.

The maximum etchable length of 13 MeV/u ²⁰⁹Bi and 13.04 MeV/u ¹²⁹Xe ions have been measured at and below these energies. A comparison of the measured and calculated track length data is presented.     

Relative production of vector and pseudoscalar states for light- and heavy-flavour mesons

The relative fractions of vector, V, and pseudoscalar, P, primary mesons produced in and decays, and primary light-flavour mesons produced in fragmentation processes are explained by the hyperfine mass splitting. The difference in corresponding fractions arises from the difference in the constituent quark masses , m_s, m_c and m_b:

The production ratios for strange, charm and beauty mesons evaluated from the ρ/(3π) ratio, measured at LEP for primary produced ρ and π, agree with the results of LEP and lower energy e⁺e⁻ experiments.     

Differential operators on a Riemann surface with projective structure

Let X be a Riemann surface equipped with a projective structure and a theta characteristic on X, or in other words, is a holomorphic line bundle equipped with a holomorphic isomorphism with the holomorphic cotangent bundle Ω_X. The complement of the zero section in the total space of the line bundle has a natural holomorphic symplectic structure, and using , this symplectic structure has a canonical quantization. Using this quantization, holomorphic differential operators on X are constructed. The main result is the construction of a canonical isomorphism

, n≥0, provided i[−2(k−1),0].     

Longitudinal acceptance computation for A 50 MeV race track microtron

The algorithm for analysing of longitudinal motion and for calculating phase trajectory in race track microtron (RTM) with small injection energy and small energy gain per turn is described. A longitudinal acceptance is calculated.We are indebted to E. A. Perelshtein and N. Ju. Kazarinov and A. Ju. Molodozhencev for stimulating advices. We thank M. Slodika for work with program coding.     

Annealing of 54 132 Xe-ion tracks in Lexan and Makrofol plastic track detectors

Samples of Lexan and Makrofol-E polycarbonate plastic track detectors were exposed to 1·1 MeV/N ₅₄ ¹³² Xe-ions to investigate the thermal track fading properties of these plastics. The experimental results show that there is no effect of annealing on the bulk etch rate while the track etch rate decreases with annealing. The track diameter decreases with increase in annealing time and temperature. It is also observed that the track density is reduced as a result of annealing. The experiments reveal that the track lengths are, in general, decreased by the application of heat and that the oblique tracks are less stable than the vertical tracks. The decrease in diameter of ₅₄ ¹³² Xe-ion tracks in Makrofol-E due to heat treatment is faster than that of ₅₄ ¹³² Xe-ion tracks in Lexan.     

Annealing of heavy ion tracks in cellulose nitrate plastic track detectors

The effect of heat treatment on the latent tracks in cellulose nitrate plastic track detectors has been studied. The bulk etch rate increases with annealing temperature while the track diameters of different ions in cellulose nitrate decrease with increase in annealing time and temperature. Experimental results show that for heavier ions higher temperatures are needed for their complete erasure. The track length and track etch rate are decreased by the application of heat. Experiments reveal that annealing reduces track density. The vertical tracks are more stable than the oblique tracks and require higher temperature for their complete erasure.