K. Kadner

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.

Intercomparative study of the detection characteristics of the CR-39 SSNTD for light ions : Present status of the Besancon-Dresden approaches

For the last few years, the Besancon and Dresden teams have been working in a parallel way on light ion (protons and alphas) registration characteristics for the CR-39 SSNTD. Even if the two groups use different approaches, the main part of both investigations concerns the study of the track etch rate (VT) and the consequences of the obtained results, which have provided us with greater understanding of detection limits. After recalling the methods used to determine the VT from both teams, will show how fundamental datal related to the registration properties of the CR-39 detector can be extracted. Indeed, the knowledge of an analytical relation for the VT enables the relationship between this velocity and the primary deposited energy to the examined with respect to the same spatial variable (the instantaneous depth of penetration (x) of the incoming particle). According to experimental uncertainties, the Bragg peak of the primary ionization coincides within a very close range with the maximum of the VT. Moreover, if increasing the etching parameters (C, T) increases the maximum VT value, these changes do not affect its position with respect to the instantaneous depth of penetration. Taking into account the reduced etch rate, the Dresden team found that both protons and alphas exhibit the same behavior when this rate is plotted versus the primary energy deposition rate. As a consequence, the corresponding reduced etch rate is always identical no matter what type of particle deposits a given amount of energy (e.g. proton or alpha). The Besancon team has corroborated the results obtained by the Dresden group for alphas and have extended the study to various etching conditions. From these results, the sensitivity of the CR-39 SSNTD is obtained in terms of critical LET and leads to a very low energy threshold for alpha particles. We will see throughout this paper that the lower threshold does not seem to depend on the etching parameters.

Dependence of the etch rate ratio on the energy loss of light ions in CR-39

Abstract Mathematical simulation of the etch pit evolution requires the knowledge of the relationship between the etch rate ratio and the restricted energy loss of charged particles. Whereas a unique correlation of both quantities independent of the kind of particle and its initial energy was found for protons, deuterons and alpha particles the results of the depth-dependent track etch rates for 7 Li , 11 B and 12 C ions indicated a different behaviour for heavier ions. A detailed analysis of the etch rate ratio in dependence on the restricted energy loss confirmed the existence of specific relationships for ions of different kind and initial energy. The spread of the corresponding curves is explained by the gradual increase of the track etch rate over a certain distance from the detector surface. The speed of this increase is the higher the lower the restricted energy loss is.

Variations of the track etch rates along the alpha particle trajectories in two types of CR-39

The simulation of track formation processes in nuclear etched track detectors requires a quantitative formulation of registration criteria on the basis of the ratio of track etch to bulk etch rate. Whereas the bulk etch rate is measurable with sufficient accuracy by means of relatively simple techniques the track etch rate has been determined up to now indirectly by measuring the track diameters on the detector surface and assuming a constant etch rate along the particle trajectories. In deeper detector layers this assumption is, however, not valid because the energy loss strongly increases at the end of the particles range. The aim of the studies described was the direct experimental determination of the track etch rate as a function of the depth within the detector as well as the derivation of the relationship between the etch rate and the actual particle energy within the detector.

Variation of the track etch rate along the trajectories of light ions in CR-39

Abstract The track etch rate has been found to be described by a generalised function of the restricted energy loss in good approximation along the trajectories of protons, deuterons and alpha particles. Extending the studies to tracks of 7 Li , 11 B and 12 C ions, curves for the track etch rates as a function of the depth within the detector were obtained the shape of which is like that of the Bragg curve in principle. In detail, however, systematic deviations from a unique correlation of the track etch rate with the restricted energy loss are observed which are more distinct the heavier the ion and the lower its initial energy. This effect is explained by a gradual increase of the track etch rate to the value expected at a given restricted energy loss. At the beginning of the etching process the track etch rate is, therefore, lower than the value observed for larger depths when the same restricted energy loss is presumed.

Inter-comparison of geometrical track parameters and depth dependent track etch rates measured for Li-7 ions in two types of CR-39

Abstract The depth dependent track etch rates of two types of CR-39, TASTRAK and BARYOTRAK, for Li-7 ions with incident energies of 4.82, 6.75 and 10.77 MeV have been evaluated from track length measurements. The pit lengths versus the etching time obtained by three different laboratories have the same trend, but did not agree completely. The differences can be attributed to an error margin of less than one decimal point in the etching temperature. Significant deviations were also present for the assessed track etch rates. Most of the deviation was attributed to the derivation step of the growth curves. A sufficient amount of data and reasonably smooth growth curves were required near the Bragg peak in order to make a precise estimation.

A new approach to characterising the etch rate ratio in CR-39 using a function of two variables

Abstract The formation of etched tracks in solid-state nuclear track detectors is usually described assuming an unequivocal correlation of the etch rate ratio with the energy loss of charged particles. For protons, deuterons and alpha particles this assumption could be verified within the scatter of the experimental data. Experimental studies with 7 Li , 11 B and 12 C ions yielded, however, systematic deviations from the expected results. Analysing the complete experimental data set for CR-39, a dependence of the etch rate ratio was found not only on the particles energy loss, but also on the depth within the detector where this energy loss occurs. Arranging the etch rate ratio as a function of both these variables all experimental results appear without inconsistencies. The etch rate ratio represented by a two-dimensional matrix can be used, then, for characterising the etch kinetics along the trajectories of charged particles of different kinds and initial energy.

Studies of experimentally determined etch-rate ratios in CR-39 for ions of different kinds and energies☆

The ratio of track etch rate to bulk etch rate is correlated with the energy transfer of a penetrating ion. For quantifying this correlation the etch-rate ratio, V, in dependence on the restricted energy loss, REL, for ions of different kinds and energies was studied. The track etch rate was taken as depth-dependent function derived from track length measurements. A unique V(REL) relationship was found for all cases where the reduction of the track etch rate at the beginning of the etching process is of little influence. Etch-rate ratios determined after the common method of track diameter evaluation have been found to be systematically too low with the exception of the region near the detector surface.

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.

Response of electrochemically etched CR-39 detectors to protons

The neutron response of electrochemically etched (ECE) CR-39 detectors is determined by the energy and angular dependence of the response to neutron-induced charged particles. This response has been measured for the example of protons with various initial energies and angles of incidence. Besides, some studies were made for modeling the mechanism of ECE of the proton trajectories with the aim of deriving the critical angle of incidence.