Track theory and nuclear photographic emulsions for Dark Matter searches

Radiation Measurements 50 (2013) 7e15

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Track theory and nuclear photographic emulsions for Dark Matter searches V.A. Ditlov* Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya str. 25, 117259 Moscow, Russia

h i g h l i g h t s < Specific features of Dark Matter Search in nuclear photographic emulsions. < Track theory for WIMP search in nuclear emulsions. < Primary efficiency for single WIMP registration. < Properties of primary WIMP registration efficiency. < Primary registration efficiency of WIMP flow.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 December 2011 Received in revised form 13 November 2012 Accepted 16 November 2012

This work is devoted to the analysis of possibilities of nuclear emulsions for Dark Matter search, particles of which can produce slow recoil-nuclei. Tracks of such recoil-nuclei in developed nuclear emulsion consist from several emulsion grains. The analysis was carried out with Monte-Carlo calculations made on the basis of the Track Theory and the various factors influencing Dark Matter particles registration efficiency were investigated. Problems, which should be solved for optimal utilization of nuclear emulsions in Dark Matter search, were formulated."Body Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Dark Matter Track theory Nuclear emulsion Registration efficiency

1. Introduction One of important nowadays problems for understanding of Space physics is the search of a Dark Matter (DM). There are several cosmological and theoretical facts in favor of DM existence (Sadouler, 1996). It is known that Universe contains only 4.6% of baryon matter, 72.6% is Dark energy and 22.8% of Universe is invisible DM (Bernabei, 1995). There are developed several hypotheses about its nature (Bernabei, 1995) and all this defines a great actuality of search and registration of DM particles (Ryabov et al., 2008). Particles of DM are expected to be very weakly interacting massive particles or shortly WIMPs (Sadouler, 1996; Yakushev, 2009). The only way to detect WIMPs in nuclear emulsion is to observe recoil nuclei after collisions of WIMPs with nuclei of matter. Already several decades the scientists have been

* Alikhanov Institute of Theoretical and Experimental Physics, Russia. Tel.: þ7 (0) 95 7145207. E-mail address: [email protected]. 1350-4487/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.radmeas.2012.11.016

planning and performing several experiments for DM searches, for example, experiments based on one or two phase detectors for measuring electroluminescence from matter after recoil nuclei moving (Akimov, 2001; Akimov et al., 2002; Ditlov et al., 2002a,b). Recently some experimental works, devoted to preparation for WIMPs search with help of nuclear photographic emulsion, were published (Tatsuhiro et al., 2008). Nuclear emulsions have a set of advantages against other detectors: high gravity of sensitive microscopic AgBr crystals r ¼ 6.47 g/cm3; wide diapason of atomic numbers of elements in nuclear emulsion structure; possibilities to exposure large amount of nuclear photographic emulsion and to use automatic methods of developed photographic layers scanning for events analyses. Besides, it is reasonable to expect that interactions with matter of WIMPs and of neutrinos will be more distinguishable in photo emulsion than in other detectors, such as Xenon camera for example. Physicists have almost centenary experience of photographic materials use and Track Theory is already well developed (Bogomolov, 1958; Katz, 1970; Ditlov, 2001). The aim of this work is to use possibility of Track Theory for numerical analysis of photoemulsion possibilities in DM Search experiments.

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V.A. Ditlov / Radiation Measurements 50 (2013) 7e15

1.1. Specific features of Dark Matter Search in nuclear photographic emulsions

The atoms of Silver and Bromine give a main yield production of recoil-nuclei (Fig. 2), which was calculated for nuclear emulsion type-R2 with chemical structure from Rodicheva data (1958).

Here are listed several features of DM Search in nuclear emulsions: 1. The cross section of interaction of WIMPs is equal (Yakushev, 2009):

sWIMP w1042 O1044 cm2 ;

(1)

2. The mass of DM Particle is still unknown and it is expected to be a very heavy inside the interval:

MWIMP ¼ 10O1000 GeV=c2 ;

(2)

3. WIMPs have some Maxwellian-like distribution over their velocities (Kamionkowski, 1998; Green, 2010):


 2 1 3=2 2 vv2 f ðvÞdv ¼ 4p v e 0 dv; pv0

(3)

6. As the recoil nuclei have energies Erec of several tenths of keV, their residual ranges R(Erec) are comparable with emulsion microcrystal sizes and distances between MC (see Table 1). So, it is necessary calculate R(Erec) with energy losses dE/ds in gelatin and in MC separately. It was done with code SRIM2011. 7. Energy losses of silver recoil nuclei knocked by WIMPs in nuclear emulsion are in the region of Bragg peak, where the component of energy losses in elastic nucleusenucleus collisions is greater than the component of energy losses in nucleus-atomic electron collisions (Fig. 3). 8. Passing through any matter nuclei suffer range straggling, which is increasing with decreasing energy. For some of them prolonged straggling sstr is of their residual ranges order (see Table 1). 9. Atomic electrons being released by slow recoil nuclei have very low energies and they are not capable to create own visible tracks in the emulsions. Column 10 of Table 1 presents maximal energies of such electrons in nuclear emulsion which were calculated by formula:

where vo is the velocity, at which the distribution has a maximum.

vo w220  20 km=s; and velocity diapason v ¼ 10O1000 km=s

umax ðbÞ ¼ (4)

2b

2

1b

2

m0 c2

1 2
2m0 m0 gþ 1þ MWIMP MWIMP

(6)

Here mo is mass of electron. 4. WIMPs have low kinetic energy EWIMP, which can be easily calculated and the next family of lines V(MWIMP) for set of constant EWIMP of WIMPs is presented in Fig. 1. EWIMP, depending on its mass, can be expected from fractions of electron volts up to energies close to energies of nuclear bound. Near to a maximum of the velocity distribution the energies of WIMPs lay in an interval 2.8 O 517 keV. 5. According to work (Bernabei, 1995) WIMP cross-section sN of interaction with any nucleus Z can be expressed through a reduced-to-proton cross section sp by the next formula:

sN ¼

m2 ðN; WÞ sp ; A2 red m2red ðp; WÞ

1.2. Track theory for WIMP search in nuclear emulsions Because of absence of delectrons, any track, produced by recoil-nucleus after WIMP collision, should have a kind of chain consisting from several developed grains and its measurement should be fulfilled in regime of “grain counting” (Katz, 1970). For such tracks it is suitable a part of Track Theory developed by Bogomolov (1958). For number of developed grains along path of track this theory gives:

0 (5)

here N is the number of nucleons and A is the mass number of atomic nucleus, mred(N,W) is reduced mass of system WIMP and nucleus with N nucleons, mred(p,W) e is reduced mass of system WIMP e proton.

  dE ds

1

sða0 Þ B C _ $  ,C B stypeR2 dE C 3 VAgBr B B ds 0;typeR2 C $B1e ndev ¼100$ $ C ½grains=100mm; C 4 a B B C @ A

(7)

Fig. 1. Family of lines V(MWIMP) for set of constant of WIMPs kinetic energies.

Fig. 2. Relative probabilities of WIMP interactions with different nuclei of emulsion type-R2.

V.A. Ditlov / Radiation Measurements 50 (2013) 7e15

9

Table 1 Ranges and straggling of recoil nuclei in gelatin and in AgBr microcrystals of nuclear emulsion type-R2 for WIMP with M ¼ 104.8 GeV/c2, V ¼ 222.3 km/s and EWIMP ¼ 28.77 keV. 1

2

3

4

5

6

7

8

9

10

n

Recoil nuclei

Atomic fraction nZ %

Erecoil [keV]

Vrecoil [km/c]

gelatin [nm]

[nm]

AgBr[nm]

AgBr[nm]

umax, electr[eV]

1 2 3 4 5 6 7 8

1H 1 12 C 6 14 N 7 16 O 8 32 S 16 80 Br 35 108 Ag 47 127 I 53

37.59 17.76 4.78 13.62 0.05 13.10 13.06 0.03

1.018 10.06 11.36 12.57 19.90 27.96 28.76 28.67

440.6 401.6 395.2 389.1 345.8 259.6 226.6 208.6

25.21 41.62 39.92 38.68 34.15 32.17 29.66 29.45

16.08 15.26 14.02 39.57 9.56 6.96 5.80 5.49

10.86 21.31 20.87 20.07 17. 92 14.37 12.60 12.13

16.98 24.50 22.74 21.85 14.94 9.11 7.20 6.54

2.202 1.831 1.774 1.719 1.357 0.7655 0.5833 0.4941

VAgBr is total volume of MC occupied in unit of emulsion volume; s(a0) e fragment of particle path inside the surface sensitive lay with thickness b of emulsion spherical MC with radius a:


b b2 sðaÞ ¼ 4b$ 1  þ a 3$a2

(8)

stype-R2 is the same value for emulsion type-R2 with a ¼ 0.14 mm; (dE/ds)stopping power of particle into MC and (dE/ds)0,typeR2 is characteristic stopping power (Ditlov, 2001) for emulsion type-R2.

1.3. Calculation method Slow recoil nuclei ranges, energy losses in gelatin and AgBr crystals can be separately calculated with method Monte-Carlo. All listed particularities of WIMP registration were taken into account. Next events and values were simulated: 1. Collision of WIMP with one of nuclei Z of emulsion atomic structure. This simulation was made with formulas (5), which was used for construction of a probability of WIMP interaction with element Zk:

nZ;k sN;k PZ;k ¼ P nZ;j sN;j

(9)

j

This probability depends on amount of atoms nZ,k with given atomic number Zk in unit of emulsion volume and on value of interaction cross-section sN,k of WIMP with nucleus of atom Zk. If WIMP met Ag or Br, it means that the interaction was in MC. The interactions with other nuclei reveal interactions in gelatin (see. Fig. 4).

Fig. 3. Stopping power of recoil nuclei of Ag calculated by SRIM2011 in gelatin and in AgBr crystals.

2. Erec lays in an interval 0OEmax , where Emax was defined from energy and momentum conservation laws as:

Erec;max ¼

4MWIMP mrecl ðMWIMP þ mrec Þ2

EWIMP

(10)

It was supposed, that for isotropic scattering (Bernabei et al., 1996; Schnee, 2011) the energy of recoil nucleuses can get with equal probability any meaning from this interval. 3. Point (x,r) of the recoil-nucleus start in MC was simulated, if a collision was inside it. Here r  is impact parameter, distance between the MC axis and trace of WIMP (see Fig. 4). 4. Size a of MC was simulated every time, when WIMP interaction occurred inside MC or when recoil-nucleus entered into MC. There was used mean radius , dispersion < s2a >and Gaussian distribution over MC diameter a: ðaÞÞ2 2

 df ðaÞ 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie da 2p < s2a >

(11)

5. A distance L, at which recoil-nucleus can meet first or sequent MC after its start or after its exit from crossed MC respectively (see Fig. 4). 6. Impact parameter r for recoil-nucleus, while it meets MC with simulated size.

Fig. 4. Scheme of WIMP interactions in gelatin and in AgBr crystal.

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V.A. Ditlov / Radiation Measurements 50 (2013) 7e15

8. The code “Em_DM”, having calculated energy DE left by recoilnucleus into crossed MC, simulated the capability to be developed for this MC using (7).

Table 2 Assortment of emulsions with different AgBr crystals. Emulsion type

[nm] 150 140

3 4

G-5 Type eR2 (NIKFI-R2) Kodak XNB2 Ilford K

100e150 100

5 6 7

L4 Type-M2 Ilford L4

80 70 70

3 3.6

8

Gevaert NUC-715

75

9.9

9 10 11 12

Perfilov PR-2 Ilford L4 Perfilov PR Gevaert NUC-307

60 50 40 35

9.8

13 14 15

Gevaert NUC-307 Kodak NTE NIT VAgBr: Vgel ¼ 3:7

22.5 20 20  4.5

1 2

Fog 1/103 mm3 3 3.3

6

References

1.4. Primary WIMP registration efficiency

Perfilov et al., 1964 Bogomolov et al., 1956 Young and Kopriwa 1964 Ilford nuclear emulsions. 2005 Perfilov et al., 1964 Ditlov et al., 2002a,b Young and Kopriwa et al., 1964 Young and Kopriwa et al., 1964 Perfilov et al., 1964 Hulser and Rajewsky, 1966 Perfilov et al., 1964 Young and Kopriwa et al., 1964 Hulser and Rajewsky, 1966 Hulser and Rajewsky, 1966 Tatsuhiro et al., 2008

ε ¼

Ntracks NWIMPs

ðRÞÞ2 2s2str

(12)

(13)

Similar it is possible to use primary partial registration efficiency (PPRE) for events, which give tracks with n developed grains:

εn ¼

Nn NWIMPs

(14)

There is the next connection between these definitions of WIMP registration efficiencies:

ε ¼ ε1 þ ε2 þ .

7. R(Erec) were simulated every time when moving recoil nucleus changed gelatin for AgBr matter, or in opposite, when it changed MC for gelatin. For simulation it was used mean residual range , prolonged straggling dispersion from code SRIM2011 and Gaussian distribution:

 df ðRÞ 1 ¼ pffiffiffiffiffiffiffi e dR 2psstr

Primary registration efficiency (PRE) can be defined as ratio of recoil nuclei number Ntracks to total amount of interacted WIMPs NWIMPs in absence of any background:

(15)

1.5. Calculated PRE for registration single WIMPs of different masses with velocity near maximum of their Maxwellian distribution It is useful to consider here emulsions with different MC sizes either, so in Table 2 a set of nuclear emulsions is presented. The results of PRE calculations are presented in Fig. 5 for WIMPs with VWIMP ¼ 215 km/s. For accumulation enough statistics the simulation of WIMP interactions was reproduced million times. It is equivalent to real experiment with w300000 kg$days:

Fig. 5. Calculated primary WIMP registration efficiencies for one-grains (a), two-grains (b), three-grains (c) and four-grains (d) tracks.

V.A. Ditlov / Radiation Measurements 50 (2013) 7e15

It was supposed that all emulsions have AgBr and gelatin volumes in the same proportion w52:48. Indeed, each spherical MC can be posed into minimal cube with side 2a0. The maximal density can be achieved when such cubes touch each other. Only for emulsion TIN with AgBr microcrystal radius a ¼ 20 nm the proportion VAgBr : Vgelatine ¼ 3 : 7 was kept (Tatsuhiro et al., 2008). Another assumption was done, that all emulsions were sensitized by the same method as in emulsion type-R2, so that Formula (7) was applicable for each of them. One-grain tracks. Fig. 5a contains ε1 of one-grain tracks for listed in Table 2 emulsions plus five simulated nuclear emulsions with MC radiuses 1,2, 5,10 and 15 nm. Maximums of ε1 are between 70 and 80%. So, if WIMPs would be alone reason for the grains development, the emulsions with large MC were good detectors for WIMP registration. But there are many other reasons for grain development. First of them is own emulsion fog, which, for instance for emulsion type-R2, consists of three developed grains per 1000 mm3 or 7.5  1011 grains/kg. It is a very large value for registration such rare events, as WIMP interactions. Indeed, knowing total mass r Universew1022 g/cm2 of DM in unit of Space volume (Bernabei, 1995), WIMP cross section of interaction sWIMP,j with jth nucleus and their velocity vWIMP, it possible to write rate counting for any detector with gravity r:

Vcount ¼

rUniverse $vWIMP $Snat;j sWIMP;j r$MWIMP

(16)

For MWIMP ¼ 10 O 1000 GeV/c2 the counting rate lays in a interval nWiMP ¼ 0.0297 O 2.97 1/(kg$days). Thus, for WIMP

11

one-grain track registration in emulsion type-R2 the fog should be reduced more than in 1012 times. As the one-grain tracks can not be used, their “high efficiency registration” from advantage turns to their disadvantage: nuclear emulsions with big grains take away about 80% of WIMP interactions. From this point of view according to Fig. 5a emulsions with a  10 nm are much better. Two-grains tracks. In Fig. 5b ε2 efficiencies are shown for twograins tracks. WIMPs can produce two-grains tracks in all considered nuclear emulsions! Emulsion with ao ¼ 1 nm should have maximal efficiency ε2 ¼ 33% at mass MWIMP ¼ 68 GeV/c2. When ao ¼ 2 nm efficiency ε2 has value 39% at MWIMP ¼ 147 GeV/c2. For registration two-grains tracks there is a problem of fog separation too: Two fog grains being occasionally developed in neighbor points can be identified as two-grains track. Knowing number of fog grains nfog and amount ncrystal of MC in the same volume, the probability that one fog grain will be developed in given point is:

Pfog ¼

nfog ncrystals

(17)

Number of false 2-grains tracks given by fog is expected as: 2 n2grtracks zncrystals Pfog ¼ nfog Pfog

(18) 7

For emulsion type-R2 this value is 5.32  10 1/(kg$day) and it still significantly exceeds the number of possible WIMP interactions. For emulsions with ¼20 nm it is already 1.5  105 1/(kg$days)

Fig. 6. Emulsion AgBr microcrystals and properties of primary efficiency. a) Dependence of the efficiency on WIMP mass for two concentrations of emulsion with microcrystal radius. b) Dependence of efficiency on WIMP mass for different dispersions of microcrystal distribution over microcrystal radius c) dependence of efficiency on WIMP mass for different dispersions of microcrystal distribution over microcrystal radius.

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V.A. Ditlov / Radiation Measurements 50 (2013) 7e15

and this fog should be reduced more than 105e107 times for WIMP registration with two-grains tracks in this emulsion. As it is seen from Fig. 5b and Fig. 5c, all existing emulsions have very low efficiency of registration of three-grains tracks, only simulated emulsions with grains 1e5 nm keep three- and four-grains track registration efficiency ε3,4  10%. For these MC sizes 3-grains and 4-grains track of Fig. 5d fog gives 7.6  106 O 4.9  1010 1/kg and it is possible already to speak about fog rejections, which belong to interval 2.5  105 O 1.6  109 for 1 kg$days. 1.6. Properties of registration efficiency Ratio volumes VAgBr:Vgelatin of silver bromide VAgBr and gelatin Vgelatin occupied in emulsion has weak influence on one-grain track

efficiency ε1, but it changes in several times two- and three-grains track efficiencies, though the ratio VAgBr:Vgelatin was not changed so much. The greater emulsion dilution is, the less track registration efficiency. It can be seen in Fig. 6a). Increasing of microcrystal dispersion leads to reducing of ε, as it follows from Fig. 6b and Fig. 6c. When characteristic stopping power (dE/ds)0 is growing up, both sensitivity and track registration efficiency of nuclear emulsion are going down (see Fig. 7). It would be very useful, if these values of εel for electrons or other radiations are running down faster, than for recoil nuclei. It is possible to postulate εel either as the production: εel ¼ 100%$P þ ðEÞ (Ditlov, 1999). Then we can consider a dependence of ratio r ¼ εel =εtr as a function of (dE/ds)0. Such dependences for two

Fig. 7. Characteristic energy losses and properties of primary efficiency. Dependence of the efficiency on WIMP mass for set of different characteristic energy losses in emulsion with microcrystal radius for one-grains tracks (a) and for two-grains registration (b) ratios of electron and WIMP two-grains track registration efficiencies as functions of characteristic energy losses (c) roles of nucleonenucleon and nucleon-electron collisions for one-grain track (d) and for two-grains track registration efficiency (e).

V.A. Ditlov / Radiation Measurements 50 (2013) 7e15

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Thus, this dependence of their ratio on (dE/ds)0 is disappearing. At the same time εtr continues to fall down without improving electron rejection and at this moment desensibilization should be stopped at εtr ¼ 0.8%. In probability (Ditlov, 2001) the frequency of effective ionization acts was written as:

x ¼

Fig. 8. Two-grains registration efficiency.

energies of electrons are presented in Fig. 7c). It is seen, that for low characteristic energy losses the ratio of efficiencies is quickly decreasing with characteristic energy losses increasing, but beginning after (dE/ds)0 ¼ 100 keV/mm it becomes almost constant. It is understandable according to the (7) written for low x:


VAgBr

ndev ¼ 100$x ¼ 100$ $
s_ type-R2 dE ds

dE ds 



0;type-R2

(19) þ

When frequencies x are small, probability of response P is back proportional to (dE/ds)0 both for recoil nuclei and for electrons.

(20)

Physicists of 1940e1950 years worked on creation photographic emulsion, sensitive to relativistic electrons with so small (dE/ds)0, as far as it was possible. With this purpose the technique of creation of the sensitive centers in MC, which can easily turn into the grain development centers after ionization by relativistic electrons, was built up. But in region of Bragg peak nucleusenucleus interactions of recoil nuclei (dE/ds)nucl gives much larger yields into grain development, than their nucleus-atomic electrons interactions (dE/ds)electr, as it is seen from the Fig. 7 for one-grain tracks (d) and for two-grains tracks (c) of emulsion with ¼20 nm. Moving through AgBr lattice recoil nuclei produce defects in it, which work as new development centers. This phenomenon should be described by own characteristic stopping power (dE/ds)0,nucl and x must be rewritten as:

x ¼ ½grains=100 mm

ðdE=dsÞnucl þ ðdE=dsÞelectr ðdE=dsÞ0

ðdE=dsÞnucl ðdE=dsÞelectr þ ðdE=dsÞ0;nucl ðdE=dsÞ0;electr

(21)

The value (dE/ds)0,nucl should weakly depend on emulsion sensibilization or possibly doesn’t depend on it at all. It should be defined by properties of AgBr lattice. Thus there is no use to form the second member of expression (21) in the WIMP search. Increasing (dE/ds)0,electr and as a result reducing the emulsion sensitivity to electrons it possible not only to improve rejection of

Fig. 9. One-grain (a), two-grains (b), three-grains (c) and four-grains (d) track registration efficiencies for WIMP flow.

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V.A. Ditlov / Radiation Measurements 50 (2013) 7e15

Fig. 10. Exclusion regions for one- (a), two- (b.) and three-grains (c) track registration efficiencies for set of nuclear emulsions with different radii of AgBr microcrystals.

electrons, but simultaneously to reduce the fog of emulsion e at the absence of sensitivity centers the fog should disappear. 1.7. Registration efficiency of flow with different WIMP velocities The amount nWIMP of DM particles in unit of volume can be found from their total mass MWIMPin unit volume of solar system known from cosmological researches, dividing it by prospective meaning of unknown mass Mi,WIMP of individual particle:

ni;WIMP ¼

Msum ; MWIMP;i

(22)

(Here index i numerates chosen meanings of mass MWIMP, i). Either numerating WIMP velocities by index j and using Maxwellian distribution over their velocities f(vj) it is possible to write a PPREof WIMPs in flow: i;max X     εflow MWIMP;i ; vj ¼ ni;WIMP ,ε MWIMP;i ; vj ,ni = ni;WIMP i¼1

(23) These values for two-grains tracks are presented in Fig. 8 in kind of two-dimensional diagram. Its maximum lays near a point with VWIMPw300 km/s and MWIMPw1000 GeV/c2. For flow of DM Particles with velocities from 10 up to 1000 km/s it can be written as:

  εflow MWIMP;i ¼

1000ZGeV=c2

10 GeV=c2

  εflow MWIMP;i ; v f ðvÞdv

(24)

General behavior of WIMP registration efficiency in Fig. 9 is left the same as in Fig. 5 for 1-. 2-. 3- and 4-grains tracks. Only amount of nuclear emulsions with contributions in 3- and 4- grains efficiencies is increased. 2. Exclusion regions for WIMP interactions As the efficiencies are expressed in percentage, the exclusion region should be described by ratio 100/ε(MWIMP). This ratio shows in how many times the WIMP interaction cross-section should be increased in order to register the same amount of WIMPs, as well as at 100% efficiency:

sexcl ðMWIMP Þ ¼ 100

sp εðMWIMP Þ

:

(25)

This dependence is shown in Fig. 10 for registration of one-grain tracks (a) and of two-grains tracks (b). For three-grains tracks registration exclusion regions dependence on mass of WIMP are shown in Fig. 10c. 3. Conclusions Here only the primary WIMP registration efficiencies were studied. In real experiments for WIMP search there will be a set of factors that inevitably reduce efficiencies. Usually experimenters at first measure the final efficiency of set-up for any particle registration and then, step by step, they consider different factors, which reduced the registration efficiency, and finally reconstruct the registration efficiency called here as primary registration efficiency (Lebedenko et al., 2009).

V.A. Ditlov / Radiation Measurements 50 (2013) 7e15

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Table 3 Problems and possible solutions. Problems

Probable solutions

1. Fog of emulsion 2. Own radiation background of nuclear 3. Background radiation of environment

-

a. Electron rejection b. Rejection of fast non recoil nuclei 4. There is efficiency of counting of developed tracks which is falling down with grain size reducing; For example for a ¼ 20 nm efficiency of optical measurements are about 80% (Tatsuhiro et al., 2008).

It can be reduced by using emulsion with low sensitivity, without centers of sensitivity It should be a special study in each concrete emulsion. Here should be used experience of emulsion neutrino experiments. It can be reduced by using emulsion with low sensitivity, without centers of sensitivity. Here can be recoil nucleus identification with help of track theory. Track counting may be fulfilled not only by optical microscope, but electronic microscope. There are also possible chemical methods of grain increasing (Gromova et al., 1984), physical development and gelatin swelling in developed emulsions.

Track Theory allows to find at first PRE of nuclear emulsions and then to appreciate factors, which reduce the efficiency for concrete conditions. From this work it follows, that nuclear emulsions has good chance to be used for WIMP search, but it is necessary to overcome still some way for its realization. A list of problems to be solved and possible methods for their solutions are given in Table 3. Acknowledgments The author thanks Dr. Dmitri Yurievich Akimov for the useful discussion of problems considered in this work. References Akimov, D.U., Batayev, V.F., Borovlev, S.P., Danilov, M.V., Ditlov, V.A., et al., 2002. Liquid Xenon for wimp searches measurement with a two phase prototype. In: Spooner, Neil J.C. (Ed.), The Identification of Dark Matter. York. UK. 2e6 September 2002. Vitaly Kudryavtsev, Singapore-London-Hong Kong, pp. 371e376. Akimov, D.Yu, 2001. Experimental methods for particle dark matter detection (review). Instruments Esperimental Tech. 44 (5), 617e676. Bernabei, R., 1995. Researches on Dark matter. Rivista del Nuovo Cimento 18 (5), 1e63. Bernabei, R., Belli, P., Ladoni, V., et al., 1996. Improved limits on WIMP-19F elastic scattering and first limit on the 2EC2n 40Ca decay by using a low radioactive CaF2(Eu) scintillator. Phys. Lett. B 389, 757. Bogomolov, C.S., Dobroserdova, E.P., Jarkov, V.N., 1956. Journ. Nauch. Prikl. Got. Kino. 1 (2), 84. Bogomolov, K.S., 1958. La theorie fluctuatoire de l’action photographique des particules nucleares faiblement ionisantes. In: Ergebnisse der Int. Konferenz f. Wiss. Photographe. Hellwich, Koln, pp. S.352e360. Ditlov, V.A., Akimov, D.U., Danilov, M.V., et al., 2002a. In: Spooner, Neil J.C. (Ed.), Three-dimensional Reconstruction of Event Space Coordinates in Xenon Chamber. The Identification of Dark Matter. York. UK. 2e6 September 2002. Vitaly Kudryavtsev, Singapore-London-Hong Kong, pp. 383e389. Ditlov, V.A., 2001. The evolution of track theory throughout the history of the international solid state detector conferences. Radiat. Meas. 34, 19e26.

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