Nuclear Track Detector

 

When an particle crosses a nuclear track detector it produces damages at the level of polymeric bonds within a cylindrical region extending to a few tens of nm around the particle trajectory, forming the so-called latent track (LT) .

The Restricted Energy Loss
The energy lost by the particle to form the latent track is the Restricted Energy Loss (REL). When the incoming particle has a velocity ßc < 10 -2 c the REL coincides with the total energy loss in the medium. For particles with ßc > 10-2c, the REL is a fraction of the electronic energy loss, leading to δ rays with energies lower than Emax, with Emax= 200 eV for CR39® and 350 eV for Lexan, respectively.

In the latter case, REL can be computed through the formula:

(1)


where K = 4π NAr2emec2 ( NA is the Avogadro number, reand me the classical radius and mass of the electron, respectively);
Z is the charge of the impinging ion; At, Zt and I are the atomic weight, the atomic number and the mean excitation
potential of the target, respectively; δ is the density effect termas shown below, where X=log10(η) and η = γβ:

(2)

Fig. 1: The breaking of the polimeric bonds by crossing chraged particle. The damaged region, called latent track (LT), extends to few tens of nm around the particle trajectory.

In Table 1.1 the parameter values for different materials are indicated with the plasma frequency ( ρ is the target density, and e is the electron charge in CGS units).

material I(eV) X0 X1 m d a
CR39® 70 0.2 2.0 3.0
CR39® DOP 70 0.2 2.0 2.0 " "
Lexan 100 0.2 0.3 0.3 " "
Al 166 0.1708 3.01 3.63 -4.25 "
Cu 3220 -0.0254 3.28 2.94 -4.42 "

Tab 1: parameters for the characterization of REL formula (1); the CR39® DOp contains 1% di D.O.P.


The shell correction term CS/Zt takes into account the possible charge screening to the incoming particle charge by the electrons of the atoms in the medium. This effect is significant when the velocity of the impinging ion is comparable or even smaller than the orbital velocity of the bounded electrons of the target.

 

The reduced etching rate p

Latent tracks can be made visible under an optical microscope by etching the exposed detector foils with appropriate chemical solutions. During the etching the material is removed along the LT at velocity vT and isotropically at velocity vB from the bulk of the material; if vT > vB etch pit cones are formed. In Figure 2 is sketched the evolution of the etch-pit cones versus the etching time for a normally incident relativistic particle.

Fig. 2: (a) the latent track for a nucleus with charge Z and velocity βc; (b) two etch pit cones are formed on both sides of the foil; (c) a prolonged etching can make the two cones connect.

 

In general, the cone base has an elliptical shape (circular for normally incident particles). From the measurements of the minor and major axes of the etch-pit cone base (here on called track) it is possible to determine the reduced etching rate p =vT /vBand the angle of incidence θ with respect to the detector surface:

 

(3)

 

(4)

 

 


with , and where a and b are the major and minor axes, respectively, of the tracks, and tetch his the etching time.

The bulk etching rate vB can be determined by measuring the detector foil thickness at different etching times. The charge of an incoming particle can be determined by the measured p of the corresponding tracks.

If the REL of a particle passing through a stack of foils is constant along its trajectory and if the same etching conditions are applied to all the sheets of one stack, the track etching rate vT is constant and identical cones are formed on all crossed detector surfaces.

Non relativistic particles represent a background to take into account. The etch-pit cones of such particles can be distinguished from cosmic ray nuclei's because low energetic particles are slowed down or even absorbed inside the detector, and their etch-pit cones have not the same size from foil to foil. For a slowing down particle the REL increases along its path, therefore the dimensions of the tracks will increase. The situation is sketched in Figure 3, with the particle stopping in the last foil (forming the so-called end of range ( EOR) etch-pit, whose termination is rounded and not conical).

Detection efficiency

Not all the particles which cross the CR39® and Lexan sheets are detected: it depends on the particle energy, charge and impinging angle.


The Z\β detection threshold

Fig. 3:  A low energy particle is stopped inside the stack. The figure shows the case of an incoming particle whose Z / ß is initially belovw the detection threshold (Z / ß )min of the detector. When the particle enters in the forst sheet, the etch-pit is not detected. By slowing down, Z / ß > (Z / ß )min , and the etch pit is formed. In the last sheet the particle stops, forming the so-called end of range (EOR) track.


A particle with velocity βc and charge Z is detected if Z / ß > (Z / ß )min (see Figure 3). For CR39® is (Z / ß )min ~ 5, while for Lexan is (Z / ß )min~ 50.


The limit angle
For a particle with charge Z and velocity ßc the etch-pit cone is produced only if the angle of incidence satisfies the relation vTcosζ ≤ vB (when referring to the complementary angle θ = π/2-ζ the relation is vTsinθ ≤ vB , as shown in Figure 4).

Fig. 4: The track formation for different impinging angles. Note:θ = π/2-ζ. (a) For zenith angle smaller than ζlim, i.e. when θ > θlim the etch-pit is formed; (b) (c) when the zenith angle is equal or above the limit angle, i.e.θ < θlim , no track is formed.

 

The maximum angle of incidence is given by

vT(Z)cosζlim = vB
(5)


The above condition reflects the following: when the solution etches the detector along a latent track up to a particular depth, at the same time, the detector is also etched isotropically up to the same depth (see Figure 4(b)). Thus, for ζ ≥ ζlim tracks are not detected anymore (see Figure 4(c)). Such ζlim is called the limit angle.

(6)

CR39® calibrations

The detector response as a function of the REL is determined by means of calibrations. The result of calibration depends strictly on the etching conditions. For the main part of this work, a chemical solution of 6.0 N NaOH at a temperature of (70.0±0.1) °C ( standard etching conditions) was used.

The calibrations of CR39® were performed using ions of different charge and energies. The results obtained using a relativistic beam of lead nuclei will be described in the following.

The experimental procedure
Stacks of CR39® foils were exposed to the 158 A GeV 207Pb82+ beam at the CERN-SpS. The beam was impinging normally on the stacks, then passed through some CR39® detector foils, interacted in the target (typically 10 mm thick Cu or Al plates) and then passed through CR39® foils which recorded the surviving original projectiles as well as their fragments (see Figure 5).
After the exposures, the stacks were etched in 6.0 N NaOH water solution at 70°C (standard conditions) for 27 h and also at 45°C for 286 hours ( slow-etching condition, in order to accurately extend the calibration to the heaviest nuclei with charge Z > 74, see next section "Determination of the reduced etch rate p").
The surface areas, eccentricities and the central brightness of the etch-pit cones were measured with the ELBEK® System in fully automated mode (see section \ref{s@elbek} for ELBEK specifics). Background reduction was obtained with quality cuts on the central brightness of the etch-pit cones and on the eccentricity values.

Fig.5: One stack used for calibration at CERN.

The measured areas of the etch-pit cones (tracks) increase with increasing the ion charges. Thus nuclear fragments may be detected as a change in the area of the tracks. The trajectory of each detected nucleus was reconstructed by tracking the etch cones successively through the stack. This multiple measurement can be exploited to achieve a charge resolution adequate to separate individual fragments. If area measurements of a nucleus on a single foil are distributed with mean µ1 and a variance σ12, the average µn of n successive values is distributed with variance σn2 = σ12/ n , assuming all sheet have variance σ12.

Small variations of the track areas from one surface to the other, due to a variety of effects, as for instance batch and etching parameter fluctuations, were corrected by normalizing the peak positions of each successive surface to those on the front surface of the first foil.

The results of the measurement of the track areas on two sheets (4 faces) of CR39® (4 measurements) exposed to the lead beam is shown in Figure 6. Each peak in the graph corresponds to a different charge value, as indicated for some of the peaks.

Fig.6: Etch-pit cone base areas of pb ions and their fragments in CR39®


The resolution becomes worse for higher charges: it is apparent that a good charge resolution is up to a charge value around Z=60; for Z > 74 the nuclear fragment peaks are mixed with the lead beam peak. The charge resolution is σZ= 0.3e for 7 ≤ Z ≤ 20 by using a single measurement, and 0.15e by using the average of four independent measurements.

 
 

Fig. 7: (a) For nuclear fragments with Z > 74, the track area measurements are not too sensitive to charge variations. In this case a high resolution is obtained for the measurement of the etch-pit cone lengths. (b) Etch-pit cone length distributions of pb tracks and fragments with Z>74 in CR39® (from a single measurement).





Determination of the reduced etch rate p

The beams used for calibrations were normally impinging to the detector sheets, the etch-pit cone bases were circles and the relation (3) transforms to

(7)



The bulk etching rate vB is determined by measuring the variation of the sheet thickness (s(t)) as:

(8)



For fragments with Z > 74 the size of the track area is not sensitive to charge variations (Figures 6 and 7(a)). In order to resolve the individual nuclear fragments with Z ≥ 74, the etch-pit cone lengths L were measured, instead of track areas. The sheet used to measure the cone lengths were etched at a temperature of 45 °C. At such temperature, vB is smaller than at 70°C and the etch-pit cones related to particles with Z > 74 after 286 hours were developed without perforating the sheet.
Equation (7) is still valid, and the following substitution is made:

(9)

where vT=vB+ L / tetc. Figure 7(b) shows the length distribution obtained by measuring the etch-pit cone heights on a single CR39® surface.

The calibration curves and detection limits


As shown in Figure 6 and Figure 7(b) every peak is related to an ion, starting from pb down to the minimum
detected nucleus. The REL for each ion was computed by means of Equation 1. The reduced etching rate p was computed by using the track areas or cone lengths. The CR39® calibration curve which relates p vs. REL, for the particular slow-etching condition is shown in Figure 8.

 

Fig.8: Two calibration curves for different etching condition in 6N NaOH: (a) slow-etching conditions (at 45°C for 283 hours corresponding to a vB=0.153 \uvmicron); (b) standard conditions (70°C for 40 hours ).

 

The detector response strongly depends on the bulk velocity vB, which varies with the etching conditions and may vary from foil to foil. In Figure 9, the reduced etching rate p is plotted versus charge numbers Z for three values of vB when is CR39® etched in standard conditions.

Fig 9: Calibration curves for three CR39® sheets etched with 6.0 N NaOH at (70.0 ± 0.1)°C. Small fluctuations of the etching conditions determine different values of vB.

The track etching rate vT depends on the chemical etching conditions. Using the calibration curves of Figure 9 and the relation (5), it is possible to determine the limit angle for all the impinging ions. In Figure 10 the limit angles obtained with the calibration curves for vB = (1.10÷ 1.15 ÷1.21)µm h-1, respectively, are plotted.

Fig 10: Limit angle for ions in CR39® for three values of the bulketching rate.

Makrofol calibration

Makrofol is a nuclear track detector similar to Lexan, but of more recent production. With the chemical solution NaOH, it was difficult to calibrate the nuclear track detector Lexan and Makrofol, since with this etchant the background was too high and the track contours were not well defined to allow an automatic measurement with the ELBEK® System.

For this reason a new etchant was used, the KOH. For the first time Lexan and Makrofol could be efficiently measured at ELBEK and the first calibrations could be performed \cite{b@koh}.

The search for the optimal etching conditions involved also the use of ethyl alcohol, mixed with KOH, since it can enhance the quality of the etched surface, lowering the background caused by plastic defects, as well as sharping the contrast of the tracks with respect to the sheet neighborhood. This was indeed what we found (Figura 11).

 
 

Fig 11: (a) Makrofol etched in 6N NaOH at 50\celsius for 95 hours; (b) Makrofol etched in 6N KOH with the addition of 20\% ethyl alcohol by volume for 8 hours. It is evident that with KOH the surface defects are drastically reduced and the sheets are more transparent.




Moreover, the use of ethyl alcohol speeds up chemical etching. For example, with a 50% percentage of ethyl alcohol, the
track etching rate vT was 13 times higher than with NaOH. However, a high concentration of ethyl alcohol makes the etched foils too transparent to be efficiently scanned at the optical microscope. In fact the data acquisition system is based on an auto-focus device, which drives the microscope focus and sets the best image definition for each of the analyzed portions of the sheet. Generally, when scanning the sheets' surface step by step, the microscope's focus is kept stable by the control-device which triggers the image depth to the sheet backgrounds of the scanned surface. If a sheet has not background, the focus is lost at every step. It was decided then to reduce the ethyl alcohol percentage to 20% both for Lexan and Makrofol.

The standard etching conditions for Lexan and Makrofol are then 6N KOH with ethyl alcohol (20% by volume) at 50°C for 8 hours.

Makrofol calibration curve
Figure 12 shows a distribution of measured track areas onto the surfaces of sheets of Makrofol which were exposed to 30 A GeV Pb calibration beams at SPS-CERN in September 2002. The data are reconstructed after a pattern recognition procedure which allowed the tracking of the particle trajectories through 3 foils of one stack. The measured threshold for Makrofol is 50. A similar value is expected for Lexan, whose calibration is currently on under completion.

Fig 12: The Makrofol calibration: the distribution of events with respect to the track areas. The measured minimum charge threshold for Makrofol is ~50.


Also for Makrofol, as well as for CR39® , the calibration results can indeed fluctuate significantly due to variation of the experimental conditions for the chemical etching environment. Stirring properly the etching solution is important to guarantee the isotropical diffusion of solution on to the surfaces of the sheets.

As already mentioned, the results shown in Figure 12 are preliminary. We intend to increase the statistics by measuring tracks on more sheets of the same stacks, as to reduce the uncertainties on track areas and, consequentially, to obtain higher chargeresolutions.

Also the response of CR39® etched in KOH + 3% of ethyl alcohol is currently under study. The reason of a new calibration of CR39® is given by the high grade of transparency and clearness of the sheets etched with such chemical solution.