Method of grain counting for identification of nuclear tracks in diluted photographic emulsion

Radialion

Pergamon

Measuremenrs,

13504487(94)00O!I7-2 . I

METHOD OF GRAIN COUNTING IDENTIFICATION OF NUCLEAR TRACKS PHOTOGRAPHIC EMULSION

Vol. 24, No. 2, pp. 145-151, 1995 Elk&r Science Ltd Printed in Great Britain I350-4487/95 $9.50 + 0.00

FOR IN DILUTED

V. A. DITLOV AND V. BRADNOVA* Scientific Institute of Photo-Chemical Industry, Leningradski Prospekt 47, Moscow, Russia; and *Joint Institute of Nuclear Research, Dubna, Russia (Received 28 April 1993; revised 26 September 1994; in final form 27 September 1994)

Abstract-In the present paper we consider the experiment on heavy nuclei identification by the method of grain counting in photographic emulsions exposed on board a spacecraft as early as 1974. Since we carried out the experiment, the theory of nuclear track detection has undergone a considerable evolution, and in the present paper based on this experiment we trace how the theory’s evolution influences its interpretation. The proposed consideration of the experiment is the third one. It has been done based on a new theoretical approach [Ditlov V. A. (1980) Theory of special calculation of primary action of 6-electrons in track detectors with account of multiple scattering. In Solid Stare Nuclear Track Detectors, Vol. 2. Pergamon Press, Oxford]. The first one was made in 1975 [Bogomolov C. S. (1975) Scientific Reports Proceedings. GosniichimJotoproekt 20, pp. 22-34.1, the second one in 1976 [Bogomolov C. S. and Ditlov V. A. (1977) The determination of nuclear charges by the method of grain counting heavy particles tracks. Rad. Effecrs 2, 105-l 151.At the end of the paper the results of counting are proposed and discussed for further experiments on heavy and superheavy nuclei identification.

1. INTRODUCTION

For the last few decades the class of solid state nuclear track detectors (SSNTD) has been considerably widened and nuclear photographic emulsions are now of less importance than, for example, ten years ago. However, there are a number of problems the solutions of which require photographic materials. Such problems include the search for superheavy elements (SHE) in cosmic rays. To solve this problem, Bogomolov (1975) proposed the method for grain counting over track cross-section for heavy relativistic nuclei in diluted photographic emulsion. 2. METHODOLOGY

OF

THE

EXPERIMENT

(Rogomolov, 1975)

By means of a microscope we count the number of developed grains in two rectangular parallelepipeds, ‘bars’, located parallel to the track axis at the same distance from it (see Figs 1 and 3). To study the possibility for the application of this procedure for nuclei identification, an experiment using extra-atmospheric exposures has been carried out (see Bogomolov, 1975). To select the optimum photographic materials and their dilutions, laboratory samples of layers (types RK, RK x 4, RK x 6, RK x 8, RK x 32, R2, R2 x 4,. . ,R2 x 32, and then the same series with original emulsions, types M

and LD) were prepared. (Numerals mean the degree of emulsion dilution.) All photographic layers have the same area size: 9 x 12 cm2, but different thickness: R and M series layers, 400 pm; and RK and LD series, 200 pm. The characteristics for the original emulsions are given in Table 1. Thirty layers of the above types were irradiated on board a Soyuz space ship. The results of scanning the developed layers on a microscope led to the following conclusions: 1. ultra-fine grain nuclear emulsions (M,LD) are not very suitable for the given purpose, as fine developed grains are semi-transparent and their counting is labored; 2. coarse grain emulsions, especially those strongly exposed, have a large inner light diffusion making observation difficult; 3. non-diluted emulsions show a very strong diffusion in this particular experiment (overirradiation); 4. dilutions, types x 16 and x 32, are too high; 5. dilutions, type R2 x 8, are considered optimum photolayers for studying multicharged relativistic particles by the method of grain counting in areas parallel to the nucleus path. Four tracks of particles were detected in the layer of emulsion R2 x 8; those belonging to an iron group being the most likely. More dense tracks were not observed, and less dense layers were not suitable for carrying out the given experimental procedure. 145

V. A. DITLOV and V. BRADNOVA

146

Fig. I. Geometry of the method for grain counting in emulsions, type R2 x 8. Grain counting was done in squares located at a distance of 2.85 nm from the nucleus trajectory.

Based on the supposed tracks of iron nuclei, an optimum procedure for grain counting was chosen from the point of view of information capacity. It is characterized by the geometry shown in Fig. I. A square eyepiece grid was set so that the particle track axis was at an equal distance from the horizontal sides of the squares. The grains in the squares where the track passed were not counted. All grains located in adjacent squares on both sides of the central ones were counted. The grid cell size was 5.7 x 5.7 pm’. The observation depth was selected as 5.0 pm which corresponds to 5.7 pm thickness of an undeveloped layer, accounting for development shrinkage thickness. Grain counting in squares more remote from the nucleus track was not done because of the prevalence of background there. The results of grain counting in four selected tracks are given in Table 2. The numbers of grains N in measured track segments (C N) are normalized to the ‘bar’ length, 100 pm. The validity for track interpretation in the above method is determined by the level of the evolution for a theoretical description of the track forming process parameters to be measured along with other factors. 3. THEORETICAL INTERPRETATION OF THE RESULTS FOR GRAIN COUNTING The following approximate approach was used in the first interpretation (Bogomolov, 1975). For distances from the heavy particle track axis of less than one tenth of the range R(w) of a a-electron with initial energy W, it was supposed that the 6-electron was moving along the straight line and the number of microcrystals N having obtained the ability to develop at the initial rectilinear section of its path with length p, is given by the expression: N = N,@(s),

s=R(w)-p.

(1)

Table 1. Characteristics of original non-diluted emulsions

Type of emulsion

Mean diameters of I.tm

Density of tracks for relativistic electron Grains/100 pm

0.44 0.28 0.14 0.10

40 45 32 no tracks

RK R2 M LD

Here N, is the number of microcrystals per path unit, G(s) is the probability that a microcrystal may develop after the passing of an electron with residual range s through it, which for a one-hit model is written as follows: Q(r) = 1 - emccs),

where w, is the frequency of effective ionization acts made by an electron in relativistic ionization minimum, AE(s) the effective energy losses of electrons in a microcrystal and BE, the effective electron energy losses in relativistic minimum. For distances larger than 0.1 of the B-electron range, an approximate calculation for multiple scattering, as a result of which their paths are accidental curves, was made in Bogomolov (1975). For this purpose the function of photographic effect distribution over the electron range projection upon its initial movement direction found from the experiment was used. The second interpretation of this experiment was made in 1976 (Bogomolov and Ditlov, 1977). Here, the probability for emulsion grain development at some point r was supposed to be equal to the integral over the b-electron spectrum of the probability for

Table 2. Results for grain counting in tracks for nuclei of the iron group

Tracks

I 2 3 4

Horizontal projection of measured segment L, (pm)

Vertical projection of measured segment L, (pm)

Length nm

Whole grain number in segment

Grain number per IOOpm of bask

456 1311 211 570

193 350 315 350

496 1360 376 667

385 714 168 508

17.6 52.5 44.2 75.8

IDENTIFICATION

OF NUCLEAR

TRACKS

147

Table 3.

the development of a grain after passing a separate S-electron with residual range s through it:

Interpretation of nuclei tracks

Tracks

x

Z

B

Z

B

Z

B

17.6 52.5 44.2 75.8

26 26 26 26

0.70 0.86 0.93 0.70

26 26 25 26

0.78 0.96 0.96 0.79

26 22 20 26

0.84 0.86 0.84 0.85

1

2nf(r, u, s) du.

(3)

s0

Here fir, v, s) is the distribution function for an electron flow along the spatial coordinate r, residual range s and over the directions of electron movement v; dn/dw describes the energetic spectrum of emitted 6-electrons; and a, is the radius of an undeveloped emulsion microcrystal. The inner double integral was found by the Spencer method (Spencer, 1955; Jensen et al., 1976; Jacobson and Rosander, 1973). However, the solution of only a flat task when 100 keV electrons are emitted perpendicular to the source plane was used; e(s) is the function described by formula (2). The results of the second interpretation are presented in columns 5 and 6 of Table 3. In spite of some simplification of the task, such as neglecting the emission angle dependence on the initial a-electron energy, this theoretical interpretation of the experimental results included new principal statements. Firstly the spatial distribution of dissipated energy for a d-electron flow (Katz and Kobetich, 1968; Jacobson and Rosander, 1973; Jensen et al., 1976) was not used for the calculation of spatial local response distributions in a track of multicharged nuclei, and the probability for emulsion grain development at some point r was supposed to be equal to the integral over the 8-electron spectrum of the probability for the development of a microcrystal by a grain when a h-electron passes through it. As shown in Ditlov (1980), this supposition is valid for small densities of a B-electron flow. In the case of type R2 nuclear emulsion the space distribution of local responses is described by the expression: p: (r) = 1 _e-
Number of grains per IOOpm

Cl”?,

(4)

where:

2 3 4

1975

1976

1991

Let us check its feasibility in relation to the experiment to be done. For the considered emulsion, type R2 x 8, the calculated values of atomic number, atomic weight and ionization potential, averaged over the emulsion volume, are as follows: z=5.521;

A = 11.082; fl=

131.35eV.

(7)

For the calculated value of emulsion weight density we obtain p = 1.94 g/cm’. For a constant multiplier in the Bete-Bloch expression (Brandt and Peter, 1948) it is possible to find: PL = 2nnri m,c2(Z*)* = 0.014857(Z*)2 keV/pm,

(8)

dE/dx = PLf(/?)/fi’.

(9)

By means of (8) and (9) we find out that the distance from the track axis to the nearest bar edge equal to 2.85 pm can be overcome in the experiment using d-electrons with energy more than 15 keV. To evaluate the complete number of electrons which are able to pass through a microcrystal surface, ~a;;, located on the above bar edge, the following equation can be written:

(Z*)2 zo.34 x 10-5-. P?

(10)

Assuming that P: (~11) - 1, this value coincides with the power low exponent in the probability for the one-hit response model (Ditlov, 1980): naPT(pIl)=(l

-e-Q,%00.34x

(z*Y

lo-‘---.

(l,)

0’ x

“f(r,v, s) dv.

I0

(5)

We adapted the Spencer method for the reconstruction of spatial distributions of quantities (c’(s) e-;“)), which allows us to find spatial local response distributions P:(r). So, we can see now that equation (3) is the private case of (4) rewritten for the small density of the 6 -electron flow, when: (1 -e-Q,c
(6)

Thus, for nuclei of the iron group with Z - 26 we obtain: (1

-e-~),,_:,_o.23;iX210-‘. (12)

From this evaluation of nuclei of the iron group it follows that condition (6) is fulfilled only for relativistic velocities, and for p < 0.1, its value is already comparable to: (1 - e-‘)* 2 0.23.

V. A. DITLOV and V. BRADNOVA

148

If we consider more multicharged nuclei, for example the transuranic element with Z = 114, then we obtain from (9):

(13)

B For the transuranic nucleus the value is greater than 0.23 at /? < 0.44. Generally speaking, from (11) it is possible to find the equation for a straight line at which (1 - e-c)a = 0.1 and which divides the expansion applicability areas of formulas (3) and (4): /? N 0.005832*.

0.5

In Fig. 2 this dependence is shown by a straight for the distance from the track axis p = 2.85 pm. relative increase of expansion (3) on the straight itself is already u 5%. At the point (Z, p) over straight line the inequality takes place:

line The line this

(1 -e-<),
(15)

Hence, in this area the use of approximation (3) is acceptable and vice versa at the points (Z, p) lying under the straight line, and tolerance (14) is considerable and exceeding 5%. If we neglect the dependence of conditional probability P +( p 11) on the velocity of the registered nucleus, j?, then from (11) for parameter pairs (N,,, N,,,) of two different tracks (Z,, N,) of two different tracks (Z,,, &) and (Z,,,, 8,) one can write:

(16) This relation is often used (Bogolomov, 1975) not only in grain counting but also during the measurement of optical densities D in track cross-sections (Jensen et al., 1976). In this case, optical densities D, should be used instead of N,,,. The applicability area of formula (16) coincides with that of (3) but here /?, and /I$,,should be rather close here in order to

100

50

(14)

120

Z*

Fig. 2. Family of straight lines at which the following relation holds: (1 - e-‘) u 0.1 for different distances from the track axis. o-Four tracks identificated in diluted emulsion R2 x 8.

fulfil the condition of PC (p 11) independence on velocity fi. As was found in the paper of Bogomolov and Ditlov (1977) for Z = 26 and /J = 1 in emulsion type R2 x 8, the calculated Nz6 is equal to 48.3 for the grain sum in two bars (Fig. 1). The parameters of registered nuclei (see Table 3, columns 5 and 6) were obtained using (16). In Fig. 2 their values are marked by dots. As seen from the figure, these points are located much higher than straight line (14) for five percent errors. Equation (16) for them is accurate and the integration of probabilities over the spectrum of d-electrons is right (Bogomolov, 1975). Possible interpretation mistakes are unavoidable owing to the simplified procedure for solving the tasks for the theory of multiple scattering: when integrating over an energetic spectrum of 8-electrons in expressions for radial response distributions, the Spencer ratios, found for the task with a flat electron source at E,, = 300 keV emitted at a right angle to its surface,

X

*..-

d .--.r.

Fig. 3. Scheme for integration according to formula (17)over the ‘bar’ cross-section in the method of grain counting.

IDENTIFICATION

OF NUCLEAR

TRACKS

149

were used. Our approach (Ditlov, 1980) allows a more accurate interpretation to be given. 10,000

6000 4000

4. ESTIMATION OF THE DEPENDENCE OF THE NUMBER OF DEVELOPED GRAINS IN TWO BARS ON THEIR DISTANCES TO THE TRACK AXIS According to Fig. 3, the complete number of developed grains in two bars located equidistant from the track axis is described by the integral: d,? N(p) = 4n,L dx s I,

For emulsions, series type R2, the response probability described by the one-hit model is given by expression (4). Figure 4 gives the estimated relationships (5), calculated by a computer, for four crosssections of the iron nucleus track. Integral (17) was calculated by the formula of Simpson parabolas. Figure 5 presents the estimated dependences ln[N(p)] for eight cross-sections of the iron nucleus track with /I = 0.177, 0.264, 0.325, 0.374, 0.415, 0.51, 0.69 and 0.87. All points (2, /?) of these cross-sections lie above the straight line for five percent errors of Fig. 2, and so with equal p and different 2 the relation between numbers N takes place at the same distance from the track axis p:

(18) With the help of this expression, it is easy to go from relationships N(p) for the iron nucleus (Fig. 4)

t In
6 7

12345

-3

8 9

Inpw

-10 ??i

!04984urn

Fig. 4. Calculated sections

&0.32 Es53.6

E=lSO

l3=0.5

Rx1961

R=10965

relationships (I - e-?),, for four crossof the iron nucleus track in emulsion R2 x 8.

2000 1000

5% 2 z

100

11

1

0

5

I

I

I

I

IO

15

20

25

\ 30

Cell number Fig. 5. Estimated dependences In[N(P)] for eight crosssections of the iron nucleus track in emulsion R2 x 8.

to analogous ones for other nuclei above the straight line of five percent errors (Fig. 2). Relationships N(p) (Fig. 5) are estimated for a large interval of values of the coordinate p; however the method for grain counting has some limitations considerably narrowing the working range. So, if the number of developed grains in the measured bars is N > 100, then it becomes difficult to distinguish grains from each other. If, vice versa, N is small and comparable to the background contribution N l0g, then the difficulty of fog extraction appears. Limitations when N is large are determined by the limitations of a device or eyesight, and a limitation from the bottom is connected with the properties of an emulsion layer. So, in accordance with TC-6. for an undiluted emulsion of the type R2 there are three fog grains per 10cm3 of the volume, that is within a two bar 3 x 3 x 200 pm3 volume with n, = 49.9 pm-’ for which Ntog= 19.5. Hence, the working range for the method of counting in this emulsion is 40-100 grains. The recalculation of the fog of emulsion. type R2, to the fog of diluted emulsion, type R2 x 8, for which no = 8.24 pm-l gives Nrog- 4 grains determining a wider working range for the method of counting (20 + 100). In Fig. 5 this range is shown by two horizontal dashed lines. As seen from the figure, the iron nucleus with /? = 0.177 does not make a contribution to the second cell of the eyepiece grid located at a distance of 11.4pm from the track axis. We obtain N - Nf_ for this cell with relativistic nucleus velocities b > 0.86 close to the nearest border of the working range. This very case was observed for all four detected tracks of iron group nuclei. In Fig. 6 the family of curves for relationship N(p) at the point

V. A. DITLOV and V. BRADNOVA

150

discrepancy in the values of Z and a smaller one in 8. Besides, the new interpretation shows that the values for pairs (Z, I?) in the first interpretation are impossible as they lie apart from the curves for possible values (see Fig. 7).

pd.4 pm

zs30

2=20

Z=lO

5. GRAIN COUNTING AND PROGNOSIS FOR THE EXPERIMENT OF SHE SEARCH The increase of atomic number for the working range of registered nuclei for values of p will be shifted to large values and widened. Fig. 8 presents the calculated results of the relationship N(p) for SHE (Z = 114) for velocities and energies given in Table 4. The working range seen in Fig. 8, is about 200 cells for this nucleus and changed from 22.8 pm to 140gm. Hence, the method for grain counting

Fig. 6. Family of curves N( 8). calculated at p = 5.4 pm for nuclei with Z changing from 10 to 30.

p = 5.4 pm is given for a set of nuclei with Z, changing from 10 to 30, for the first cell with

p = 3 pm. Relativistic nuclei with Z < 10 give N smaller than the low border of the working interval and with Z 2 30, N is already near the top. If one of the parameters Z or fi is known for the nucleus to be studied, then from Fig. 6 another parameter /? or Z, respectively, can easily be found for the measured number of grains N,,,. But if both parameters are unknown, then the measured value of N5,, makes it only possible to plot a curve for the dependence of possible values of the nucleus Z, on possible values of velocity /I. In Fig. 7 four such dependences are presented for the measured values of N(p) (see Table 3, column 2). These curves are easily obtained by recalculating the estimated results in Figs 5 and 6. From the general character of the above dependences it is possible to draw conclusions resulting in a decrease in the range of possible values of Z and /I. Firstly, in the second cell of the eyepiece grid, all four tracks have a small number of grains at the level of the background. According to Fig. 5 this can be observed, either with /3 < 0.177 or with ,fI > 0.8. Iron nuclei with jI =0.177 have a range R = 282 pm in an emulsion of the type R2 x 8 while the tracks in the emulsion were much larger in length, exceeding the layer sizes. Hence, the observed tracks are formed by relativistic nuclei, and the version with /I < 0.177 is taken away. But in this case (see Fig. 7), the upper limit is Z = 30 for tracks 2 and 4, Z = 26 for 2, and Z = 23 for 3. If tracks I and 4 are related to the iron nucleus, then from Fig. 7 it is possible to obtain 8, = 0.845 and p4 = 0.855, respectively. At a velocity close to these values for tracks 2 and 3, Zz = 22, /I2 = 0.86 and Z, = 20, /I3 = 0.845. Thus, the new interpretation based on a more accurate consideration of the task differs from the first one (Bogomolov, 1975) by the fact that it gives a larger

40

30

z 20

10

I

I

I

I

I

I

I

I

I

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 B

Fig. 7. Correlations of atomic numbers Z and velocities /I on the plane (Z, 8) possible for the measured set of numbers N(p): I. N,, = 77.6; 2. N,,, = 52.6; 3. N,,, = 44.2; and 4. N,,, = 75.8. o-The first interpretation of Bogomolov (1975). x-The second interpretation of Bogomolov and Ditlov (1977). The figures are the serial numbers of tracks of the same experiment.

IDENTIFICATION

OF NUCLEAR

TRACKS

151

Table 4. T MeV/n

P 0.1454 0.1454 0.59743 0.68073 0.738561 0.781062 0.813508 0.838976 0.859402 0.876074

230 340 450 560 670 780 890 1000

IO

as related to SHE is more informative than for the iron group nuclei and makes it possible to determine, simultaneously, both 2 and fl from the radial distribution of a separate track cross-section. Relationships N(p) are shown in Fig. 8 on a natural scale for the working ranges 10 < N(p) 6 100 and 22.8 pm

Rpm 199.877 2731.35 6941.29 12426.20 18862.6 26026.0 33756.6 41927.9 50453.6 59255. I

d T/d R keV/p m 19106.2 9550.39 6673.64 5458.88 4798.57 4388.74 3919.06 3919.87 3779.06 3674.41

energy: E = 120, 230 and 340 MeV/n. The vertical lines show different values of N(p) for Z = 114 and Z = 110 which can reach a value of 5 within a distance range of 35-55 pm. At large distances p, SHE with Z = 110 and Z = 144 become practically indistinguishable. The resolution of the grain counting method for these nuclei decreases with increasing velocity.

6. CONCLUSIONS A more accurate consideration of four relativistic tracks for iron group nuclei shows that the discrepancy in velocities for four registered nuclei appears to be lower than in the previous evaluations. At the same time a high discrepancy in Z is obtained. The method of grain counting has good possibilities for searching for a heavy component of the cosmic irradiation spectrum. The preferable areas for measurement with regard to the track axis are determined for heavy relativistic nuclei including SHE.

REFERENCES

60 z

2=114

z

2~298

Bogomolov

40

30

20

10

136.8

79.8

Scientific

Reports

Proceedings.

I I-34. C. S. and Ditlov V. A. (I 977) The determination

50

0 22.8

C. S. (1975)

Gosniichimfotoproekf

153.9

p Pm

Fig. 8. The dependence of N( p) for 10 cross-sections tracks SHE with Z = 114 and E = 1 GeV/n.

of the

20,

Bogomolov of nuclear charges by the method of grain counting heavy particles tracks. Rad. ,!$I 2, IOS- 115. Brandt H. L. and Peter B. (1948) Investigation of the primary cosmic radiation with nuclear photographic emulsion. Whys. Rev. 74, 1828-1837. Ditlov V. A. (1980) Theory of Special Calculation of Primary Action of 6-electrons in Track Detectors with Account of Multiple Scattering. In Solid State Nuclear Track Detectors. Pergamon Press, Oxford. Jacobson L. and Rosander R. (1973) The energy does concept applied to heavy ion tracks of fast heavy ions tracks in nuclear emulsion. Cosmic Ray Physics Report, LUR-CR-73-13, 23. Sweden. Jensen M., Larsson L. and Matiesen 0. (1976) Experimental and theoretical absorbance profiles of tracks of fast heavy ions in nuclear emulsion. Physica Scripla 13, 65.-74.

Katz R. and Kobetich E. J. (1968) Formation of etchable tracks in dielectrics. Phys. Rev. 170, 401405. Spencer L. V. (1955) Theory of electron penetration. Php. Rev. 98, 1597.