Track Theory and Radiation Effects.

Ditlov V.A.

Alikhanov Institute of Theoretical and Experimental Physics. 117124, Moscow, B. Cheremushkinskaya 25, Russia

Assumption of R. Katz

«No» «Yes»

ZLatent nuclear track in solids

ZDeveloped track in nuclear emulsion

Z Latent track visulisation by etching

Here – is the mean number of hits per one target. The realization of the case for the first three values is shown in Fig. 3, where we left only the inactivated cells.

Blau M., Altenburger K., 1922. Uber einige Wirkungen von Strahlen II. Z. Physik, 12, p. 315

ei

Pi

i

!(3)

Many-hit model

1

1 !

11

i

E

sEw

or

r

ei

nsncut

ds

sdEsE

)(1)(

Bogomolov K. S Fluctuation Theory of photographic action of weakly charged particles.

r

r E

sEw

Z37

),(),(

D

sDs

1

1

),(),(!

11),(

i

si esi

sP

Unified Track Theory R.Katz

R.Katz considered tracks in two regimes: grains counting and regime of spatial distributions

N

q l

l

i

q

j

e

ji

k

eek

el

qrP

ji

0

1

1 1 1

11

, !!

!

11)(

,

1

0

d n dQ f s ds k l

n

j i

j i

( ) ( , , ) ; ;

( )

,

,

k k s

n

e d n dQ s e f s ds

( ) ( , , ) ( , , )( , , )

( ) 0

Theory of Track formation with account of multiple scattering of -electrons.

P r ee

11

1

( )

P r e ee

21

1 1

( )

;),,()(0)(

e

n

NdQsrfnrdd

Considering a chain of random events in frame of many-hit model general expression for probability of local response was deduced for sensitivity microregion of arbitrary form with account function from the theory of.multiple electron scattering. Number hits l maybe composed by different hits from one or more electrons.

),,( srf

),,( sf

So, we have the next four registration parametrs of the approach:

These registration parameters can be found theoreticaly as in the Fluctuation theory of K. Bogomolv or they can be found from calibration experiments, as it was done for application of R.Katz Unified Track Theory.

These paratemeters serve as a bridge between real radiation effects and probability of local response of our Track Theory, which these radiation effects capable to evoke.

This is a very principal moment, Track Theory doesn’t describe radiation effects and didn’t assignt for it. There exists a inumerous number of radiation effects. Some of them participate in given local response formation and for given detector others have no relation with it. On the other side, knowning mechanism of radiation effects evoking the given local response, it is possible to use these knowledges for registration parameters calculation by theoretical way.

0

)()(

ds

dE

sRELs wcut

cutds

dEa ,,,

0

In the upper expressions frequency of effective

Local responses can have absolutely different natures:

•Thermal spike mechanism2. Mechanisms of shock waves and radial Coulomb explosions.3. Arising amorphous regions in crystalls and crystallic microstructures in amorphous materials.4. Set other kinds of phase transitions5. Produces a long and narrow disordered zone along its trajectory.6. Different kinds of throwing material out from track axis and appearing hollow volumes inside along track axis.7. Arising point deffects at track axis and around it.8. Rough or thin Molecular changes in some limited regions of polimer detectors (and sometimes in non polimer detectors) There are can be many other mechanisms of local response formation… Sometimes there can be competion between different mechanisms, but sometimes they can produce joint action for local response formation.

All these mechanisms have or can have their own mathematical descriptions and all they are, in fact, radiation effects. Track theory can use these radiation effects. If there are built up a method for description any effect participating in local response forming, this method can be used in Track Theory. But Track Theory is not designed for radiation effect description!

In spite this, it is impossible to built up any theory describing all radiation effects.

But is it possible at least one step in this direction? Yes it is! It is possible, because all kinds of radiation effects have commen origin – interaction of moving ion with the matter of the detectors and this interactions has discret nature. These interactions are limited in space expansion and in time duration and it is possible to appreciate them!

Besides -electrons, there exist either other possibilities to delieve energy in point, distant from track axis, and to produce there a local reponse. I suppose, for example, that phonons quite capable for it and equations for probabilities of local response formation are availbles for it, only it is necessary to use differential function of phonon (not of d-electrons!) distributions. Similar, the same equation are suitable for description of positron flows. In this case track theory should buitifully work as for different detectors as for different kind transportation energy from track axis to other points of its body.

xPx

dx

dE

cx

min

With this aim we can use uncertainty relations of Geisenberg:

tEc

dx

dEt

min

It can be easely deduced:

There is a no sens to speak about less interval of space and time, defined by these functions.

Lower limits of x and t, defined by Geisenberg relations.

0,1

1

10

100

1000

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

x [

nm]

an

d

t 10

17

[c]

x

t

d - diameter of emulsion grains

Comparison of minimal x and t for protonwith two other characteristic space values L and l

in nuclear emulsion type-R .

0,0000001

0,000001

0,00001

0,0001

0,001

0,01

0,1

1

10

100

1000

10000

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

v/c

Siz

es

[n

m]

x

L of Komarov

l

Amount of characterisic spatial intervals for proton per 100 nm and and nuber of time interval uncertainty intervals t. per one second

0,01

0,1

1

10

100

1000

10000

100000

1000000

10000000

100000000

1000000000

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Frique

ncies

1/l

1/x Geisenberg

1 / t Geisenberg1/x Komarov

Amount of characterisic spatial intervals per 100 nm and and nuber of time interval uncertainty intervals t. per one second

0,01

0,1

1

10

100

1000

10000

100000

1000000

10000000

100000000

1000000000

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Friq

uenc

ies

1/l

1/x Geisenberg

1/ t 1016 Geisenberg1/x Komarov

Comparison of behavior of different characterstic parameters

0

0,2

0,4

0,6

0,8

1

0,05 0,15 0,25 0,35 0,45 0,55 0,65 0,75 0,85 0,95

v/c

fun

cti

on

s

x1/x Geisenberg

t1/t

P+()

l 1/l

(dE/ds)/(dE/ds)1

x1/x Komarov

Lower limits of x and t, defined by Geisenberg relationsfor nuclear emulsion Type-R2.

0

5

10

15

20

25

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

x

[nm

]

an

d

t 10

17 [

c]

x

t

Lower limits of x and t, defined by Geisenberg relationsin detector CR-39.

0

5

10

15

20

25

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

x

[nm

]

an

d

t 10

17 [

c]

x

t

Thus, it turned out that for different radiation effects and for different detectors there exists not common phenomenon – discretness of interaction acts, but common relation – inequality of Geisenberg, which allows appreciate minimal spatial intervals, inside which local response is birthing.

Conclusions:

1. In formation of local responses can participate competiting or cooperating different radiation effects.

2. Delivery of energy for formation of spatial distributions of local responses can be realised by any flows different from flow of –electrons.

3. There exist minimal extensions in space and time for interaction of charged particles and ions with material of detector. They defined limit possibilities for different ions and detectors in scientific research and in technological application, such as, for example, nanotechnology.

4. There exist maximal frequancies of the discussed interactions in space and in time.

5. For quick appraciations the uncertainty relations of Geisenberg can be rewriten as:

B

c

Zx

min

cBZt

1min

In a supposition that:

BZ

ds

dE2

2

Thank you for your attention!

0

3

2

4~1

22

1

tq

ao

For example, processes initiated by radiation can formate size of local response, as it takes place in Wilson camera. For which using data about pressures and surface tension of liquid drop it is possible to find its radius of the drop.

Similar, in the model of thermal spike another phase transition is considered for nuclear core diameter calculation.

In general case simultaneous several radiation effects can be joint in a cooperation for local response formation. That is why, for example, it is reasonable to consideration some composition of radiation effects as it is tested in works ….

dEds/dEds(1)

ds1/ds d

s1_KOM/ds_Kom P_em

debr1/debre sq

r(Ce4)/sqr1 dt1/dt

0.05 1 1 1 1 1 1 1

0,1 0,3879 0,4404 0,2509 1 0,4981 0,4997 0,8808

0,15 0,2075 0,263 0,1116 0,9956 0,33 0,3312 0,7891

0,2 0,1306 0,1807 0,06279 0,967 0,2453 0,2463 0,723

0,25 0,09054 0,1346 0,04019 0,906 0,1939 0,1947 0,6729

0,3 0,06684 0,1055 0,02792 0,8255 0,1592 0,1599 0,6334

0,35 0,05162 0,08586 0,02051 0,7403 0,134 0,1346 0,6012

0,4 0,04123 0,07177 0,0157 0,6594 0,1147 0,1152 0,5745

0,45 0,0338 0,06126 0,01241 0,5864 0,09938 0,09978 0,5517

0,5 0,0283 0,05318 0,01005 0,5225 0,08674 0,08708 0,5322

0,55 0,02411 0,0468 0,008307 0,4673 0,07605 0,07635 0,5153

0,6 0,02085 0,04166 0,00698 0,4199 0,06679 0,06704 0,5005

0,65 0,01826 0,03745 0,005948 0,3793 0,05857 0,05878 0,4876

0,7 0,01617 0,03396 0,005128 0,3446 0,05112 0,05129 0,4763

0,75 0,01448 0,03103 0,004467 0,3149 0,04419 0,04434 0,4665

0,8 0,01309 0,02857 0,003926 0,2896 0,03759 0,03771 0,4582

0,85 0,01197 0,0265 0,003478 0,2685 0,03107 0,03116 0,4517

0,9 0,01109 0,02478 0,003102 0,2514 0,02429 0,02435 0,4474

0,95 0,01051 0,02347 0,002784 0,24 0,0165 0,01653 0,4476