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Energy estimation of photons in nuclear emulsions
Nuclear Instruments and Methods 178 (1980) 477-480 © North-Holland Publishing Company
ENERGY ESTIMATION OF PHOTONS IN NUCLEAR EMULSIONS S. SINGH, D.P. GOYAL, A. MOZUMDER and P.K. SENGUPTA Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India.
Received 20 May 1980
A comparison is made of the three methods by Stearns, Borsellino and Olsen used for estimating the photon energy from the opening angle of the e+e- pair. It is found that Olsen's method gives the most reliable estimate of photon energy.
mates of electron energies by confining multiple scattering measurements on 2 3 mm of flat tracks. This selection criterion, however, imposes a severe restriction on the amount of data on which measurements can be made. Therefore, several indirect methods [ 5 - 7 ] of energy estimation of the photon have been devised. These methods provide a simple relationship of the photon energy with the opening angle of the e+e pair, which could, in principle, apply for all electron energies. However, for a given opening angle of the pair, the different methods give widely different estimates of photon energies. In the present paper we compare the photon energies estimated by these methods with those calculated by measurements on some selected e*e - pairs. The selected pairs are those which have fairly flat, straight tracks over 2 - 3 mm, and therefore their energies could be measured by the multiple coulomb scattering method with a fair degree of reliance. We find that out of the three theoretical methods, the one due to Olsen [7] gives better energy estimates than the other two methods.
1. Introduction In nuclear emulsions, the materialization of photons in the vicinity of a nucleus provides their characteristic signatures in the form of a pair of electronpositron tracks. During this process, the photon transfers negligibly small momentum to the nucleus [1]. Therefore the energy of the photon can be assumed to be equal to the sum of the energies of the electron and the positron. The energy of an electron may be measured either by its range or by the size of the mean angle of the multiple coulomb scattering. Both these methods, however, have practical limitations. The rangeenergy method can be ordinarily applied in the range of electron energies of --~10 keV to --~2 MeV, for which range-energy tables are given in the literature [2]. For electron energies >2 MeV, we have generally to take recourse to the multiple scattering method. This method, again, has limitations, as even at ~-2 MeV the proportion of the electron energy that is lost by radiation becomes significant. In fact, at electron energies >~1 GeV, the radiation loss becomes dominant [3]. A characteristic difference between radiation loss and collision loss lies in the fact that the energy loss by radiation occurs in fewer and larger steps than the energy loss by collision. Thus whereas all electrons of a given energy traversing a given thickness lose practically the same energy by collision, they undergo considerable straggling in their energy loss by radiation. This fact can be utilized for the measurement of electron energies of some selected tracks. In the past, several workers [4] have determined reliable esti-
2. Description of the theoretical methods The main theoretical attempts at relating the photon energy with the opening angle of the e+e - pair have been made by Stearns [5], Borsellino [6] and Olsen [7]. According to Stearns [5], the root mean square angle between the trajectory of a secondary electron of energy E_ and that of the primary photon of energy E, is given by
( (.02 71/2 : 0d/E ) In(E/~,/) F z(L'_//5" ) 477
(l)
S. Singh et aL /Energy estimation of photons in nuclear emulsions
478
where/a is the rest energy of the electron and Fz is a function of the order of unity and depends primarily on the ratio, E_/E and the atomic number (Z) of the nucleus in the field of which the photon was materiatized. Stearns [5] has given curves for the estimation of Fz for different values of Z and E_/E. Borsellino [6] has shown that the most probable value cop of the pair opening angle co is given by cop = (4u/E) F'z(E_/E)
(2)
where F ) is again a function of the ratio, E_[E and the atomic number Z of the recoiling nucleus. F ) is of the order of unity for a wide range of values of the ratio, E_[12. Olsen [7] pointed out that the experimental distribution of the pair opening angle is considerably narrower than the theoretical distribution given by Borsellino [6]. The reason is that Borsellino's crosssection does not give the exact distribution of the opening angle for a fixed value of the energy between the pair electrons, but is rather the distribution of the invariant pair energy. Therefore, Olsen has calculated the high energy pair production cross-section as a function of opening angle and energy partition between the electron and the positron. He also considered the effect of multiple coulomb scattering on the opening angle and has given the following formulae for the estimation of the most probable value of the photon energy E from the projected opening angle. For not too large a value of L E (MeV) = 1.6L(1 + 2.5a2)/r,
(3)
where r is the pair separation at a distance L from the point of origin. Here, for nuclear emulsion a 2= 0.0022L. Both r and L are measured in microns and determine the projected opening angle coproj as coproj = r/L. For large values of L : E (MeV) = 2aL [1 + (In 2a 2 + 1.29)/4a2]/r.
(4)
For intermediate values of L, he has given an interpolation formula E (MeV) = 2L(0.62 + a2) 1/2 (1 + A)/r
(5)
where A = 0.017(1 + 19.4a 2 + 62.7a4)/ (1 + 4.27a 2 + 7.9a 4 + 6.12a 6) • In the present work, we have used eq. (3) forL ~< 100 #m, eq. (4) for L/> 300 lain andeq. (5) for the rest of the cases.
3. Experimental For the present work, a sample of 417 electron pairs was collected by the method of area - scanning under a total magnification of 45 X 15 in the NIKFI-R emulsion stack exposed to the beam of 5 GeV/c antiprotons. The scan was started at a distance of 3 mm from the leading edge of the emulstion; this was to ensure that the measurement of scattering and angles are not seriously affected by emulsion distortion near the edge. For each e÷e- pair, the projected opening angle was measured by the distance method: COproj= r/L. In order to minimize the effect of multiple coulomb scattering, L was kept as small as possible. The dip angle of each electron track was also measured to calculate the space opening angle of the pair. The overall efficiency for the detection of the electron pairs was estimated to be --~99%, by rescanning about one third of the total area scanned. Since the efficiency is quite high there is practically no geometrical loss of electron pairs. For scattering measurements only those pairs were selected in which the tracks of both the electron and the positron had projected lengths of 2 - 3 mm in the emulsion plate of their origin. This ensured at least 2 0 - 3 0 cells of 100 /am for each track. The number of such pairs was found to be 71. The elimination of noise and spurious scattering from the scattering observations is an important correction. To accomplish this, we have applied the Barkas formula [8] for calculating the value of p/3 from the scattering measurements. This method has already been verified [9] on the beam tracks at 5 GeV/c.
4. Results and discussion Figure 1 shows the ratio R of the theoretical and experimental (scattering measurements) estimates of photon energies as a function of the space opening angle of the pair. It is immediately clear from the figure that Olsen's formulae give the most accurate estimates of photon energy throughout the range of the measured values of opening angles. We have further checked the reliability of the Olsen's method in the following way. It is reasonable to assume [10] that the observed photons are primarily the decay products of n°'s produced in the primary particle interactions. Some average values
S. Singh et al. / Energy estimation of photons in nuclear emulsions
6-
° o
o
O/sen's
S t e a r n S' formula
formula
x
Borselhno's
formula
o
o
o
• o
479
o
o
o
o o ° o
o
Ox
o
o x
x
oe x
x x ×
-* "llrY'-~-
~L
o
g
o
x
x
oO
o o
,
XO I o
~"
o
•
o
•
I0
28
o •
o
1
x
o
x x
x I
I
~6
6z.
co (x 10-3 r a d i a n s )
Fig. 1. The variation of ratio R with the opening angle co of the e+e- pair (R denotes the ratio of energy estimated from 03 by different formulae (refs. [4 7]) to that estimated experimentally by scattering measurements). The solid line corresponds to the expected value of R.
pertaining to 1r°-spectrum can be thus calculated by using the following relations due to Kopytov [11 ] : (PL) = 2(qL)
(6)
(p}) = 3(q~-) - zmn ol z
(7)
where PL and PT respectively represent the longitudinal and transverse momenta o f n u, and qL and qT are the corresponding quantities for a photon. We calculated the above n ° parameters for a large sample of 1017 e+e - pairs whose photon spectrum was obtained from Olsen's method. The pairs were observed in an emulsion stack exposed to a 50 GeV/c n - beam [12]. We obtained the following results: ~oL) = (3.000 + 0.140) GeV/c
(8)
and (p~) = (0.153 -+ 0.013) (GeV/c) 2 .
GeV2/c 2 obtained in a Bubble chamber experiment of 18.5 GeV/c n - p and n*p interactions. This is so expected in view of the established [14] constancy of transverse momentum of secondaries in high energy n-N interactions for b e y o n d an energy of ~ 5 GeV. The above agreement of (PL) and (p~-) obtained b y using Olsen's method with those obtained from experimental measurements strengthens to a great extent the overall credibility of Olsen's method. We are grateful to Professor K.D. Tolstov of Dubna for lending us a part o f the 50 GeV/c 7r- emulsion stack. AM is grateful to the Council of Scientific and Industrial Research, India for the award of a Post Doctoral Fellowship. Thanks are due to Mrs. J. Bhowmik, Mrs. S. Goel and Mrs. M. Sen for their efficient scanning.
(9)
The above value of (PL) is in good agreement with the value of (PL) = 3.20 + 0.19 obtained for rr÷ mesons produced in 50 GeV/c n--emulsion interactions by Kumar et al. [13]. In the experiment o f Kumar et al., the momenta of the charged secondaries were obtained from the measurement of tracks' curvature, the emulsion stack being exposed under a pulsed magnetic field. The present value of ( p ~ ) = ( 0 . 1 5 3 - + 0.013) GeV2/c 2 is also in good agreement with the values (0.147 + 0.003) GeV2/c 2 and (0.149 -+ 0.003)
References [ 1 ] B. Rossi, in: High Energy Particles (Prentice Hall, Englewood Cliffs, NJ, 1952) p. 79. [2] W.H. Barkas, in: Nuclear Research Emulsions, vol. 1 (Academic, New York, 1963) p. 444. [3] W.H. Barkas, in: Nuclear Research Emulsions, vol. 1 (Academic, New York, 1963) p. 366. [4] C.F. Powell, P.H. Fowler and D.H. Perkins, in: The Study of Elementary particles by the Photographic method (Pergamon, London, 1959) p. 191.
480
S. Singh et al. / t~,'ner~tv estimation Qf photons h~ nuclear emulsions
[51 M. Stearns, Phys. Rev. 76 (1949) 836. 16] A. Borsellino, Phys. Rev. 89 (1953) 1023. [71 11. Olsen, Phys. Rev. 131 (1963) 406. [81W.It. Barkas, in: Nuclear Research Emulsions, Vol. 1 (Academic Press, New York, 1963) p. 313. [9[ B. Bhowmik and S. Singh, Phys. Rev. 9 (1974) 63. l l 0 ] ( ; . Donaldson, tt. Gordon, K.W. Lai, 1. Stumer, A. Barnes, J. Mallima, A. Tollestrup, R. Walker, O. l)ahl, R.A. Johnson, A. Ogawa, M. Pripstein and
S. Shannon, Phys. Rev. Lett. 36 (1976) 1110. [ 111 G.I. Kopylov, Nucl. Phys. B52 (1973) 126. [121 A. Mozumder, S. Singh and D.P. (;oyal, Nuovo Cim. Lett. 22 ~1978) 312. [131V. Kumar, Phi) thesis, University of Kurukshetra (1979) unpublished ; privalc communication (1979). [141 A. Mozumder, Pill) thesis, University of Delhi (1979) unpublished.
ENERGY ESTIMATION OF PHOTONS IN NUCLEAR EMULSIONS S. SINGH, D.P. GOYAL, A. MOZUMDER and P.K. SENGUPTA Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India.
Received 20 May 1980
A comparison is made of the three methods by Stearns, Borsellino and Olsen used for estimating the photon energy from the opening angle of the e+e- pair. It is found that Olsen's method gives the most reliable estimate of photon energy.
mates of electron energies by confining multiple scattering measurements on 2 3 mm of flat tracks. This selection criterion, however, imposes a severe restriction on the amount of data on which measurements can be made. Therefore, several indirect methods [ 5 - 7 ] of energy estimation of the photon have been devised. These methods provide a simple relationship of the photon energy with the opening angle of the e+e pair, which could, in principle, apply for all electron energies. However, for a given opening angle of the pair, the different methods give widely different estimates of photon energies. In the present paper we compare the photon energies estimated by these methods with those calculated by measurements on some selected e*e - pairs. The selected pairs are those which have fairly flat, straight tracks over 2 - 3 mm, and therefore their energies could be measured by the multiple coulomb scattering method with a fair degree of reliance. We find that out of the three theoretical methods, the one due to Olsen [7] gives better energy estimates than the other two methods.
1. Introduction In nuclear emulsions, the materialization of photons in the vicinity of a nucleus provides their characteristic signatures in the form of a pair of electronpositron tracks. During this process, the photon transfers negligibly small momentum to the nucleus [1]. Therefore the energy of the photon can be assumed to be equal to the sum of the energies of the electron and the positron. The energy of an electron may be measured either by its range or by the size of the mean angle of the multiple coulomb scattering. Both these methods, however, have practical limitations. The rangeenergy method can be ordinarily applied in the range of electron energies of --~10 keV to --~2 MeV, for which range-energy tables are given in the literature [2]. For electron energies >2 MeV, we have generally to take recourse to the multiple scattering method. This method, again, has limitations, as even at ~-2 MeV the proportion of the electron energy that is lost by radiation becomes significant. In fact, at electron energies >~1 GeV, the radiation loss becomes dominant [3]. A characteristic difference between radiation loss and collision loss lies in the fact that the energy loss by radiation occurs in fewer and larger steps than the energy loss by collision. Thus whereas all electrons of a given energy traversing a given thickness lose practically the same energy by collision, they undergo considerable straggling in their energy loss by radiation. This fact can be utilized for the measurement of electron energies of some selected tracks. In the past, several workers [4] have determined reliable esti-
2. Description of the theoretical methods The main theoretical attempts at relating the photon energy with the opening angle of the e+e - pair have been made by Stearns [5], Borsellino [6] and Olsen [7]. According to Stearns [5], the root mean square angle between the trajectory of a secondary electron of energy E_ and that of the primary photon of energy E, is given by
( (.02 71/2 : 0d/E ) In(E/~,/) F z(L'_//5" ) 477
(l)
S. Singh et aL /Energy estimation of photons in nuclear emulsions
478
where/a is the rest energy of the electron and Fz is a function of the order of unity and depends primarily on the ratio, E_/E and the atomic number (Z) of the nucleus in the field of which the photon was materiatized. Stearns [5] has given curves for the estimation of Fz for different values of Z and E_/E. Borsellino [6] has shown that the most probable value cop of the pair opening angle co is given by cop = (4u/E) F'z(E_/E)
(2)
where F ) is again a function of the ratio, E_[E and the atomic number Z of the recoiling nucleus. F ) is of the order of unity for a wide range of values of the ratio, E_[12. Olsen [7] pointed out that the experimental distribution of the pair opening angle is considerably narrower than the theoretical distribution given by Borsellino [6]. The reason is that Borsellino's crosssection does not give the exact distribution of the opening angle for a fixed value of the energy between the pair electrons, but is rather the distribution of the invariant pair energy. Therefore, Olsen has calculated the high energy pair production cross-section as a function of opening angle and energy partition between the electron and the positron. He also considered the effect of multiple coulomb scattering on the opening angle and has given the following formulae for the estimation of the most probable value of the photon energy E from the projected opening angle. For not too large a value of L E (MeV) = 1.6L(1 + 2.5a2)/r,
(3)
where r is the pair separation at a distance L from the point of origin. Here, for nuclear emulsion a 2= 0.0022L. Both r and L are measured in microns and determine the projected opening angle coproj as coproj = r/L. For large values of L : E (MeV) = 2aL [1 + (In 2a 2 + 1.29)/4a2]/r.
(4)
For intermediate values of L, he has given an interpolation formula E (MeV) = 2L(0.62 + a2) 1/2 (1 + A)/r
(5)
where A = 0.017(1 + 19.4a 2 + 62.7a4)/ (1 + 4.27a 2 + 7.9a 4 + 6.12a 6) • In the present work, we have used eq. (3) forL ~< 100 #m, eq. (4) for L/> 300 lain andeq. (5) for the rest of the cases.
3. Experimental For the present work, a sample of 417 electron pairs was collected by the method of area - scanning under a total magnification of 45 X 15 in the NIKFI-R emulsion stack exposed to the beam of 5 GeV/c antiprotons. The scan was started at a distance of 3 mm from the leading edge of the emulstion; this was to ensure that the measurement of scattering and angles are not seriously affected by emulsion distortion near the edge. For each e÷e- pair, the projected opening angle was measured by the distance method: COproj= r/L. In order to minimize the effect of multiple coulomb scattering, L was kept as small as possible. The dip angle of each electron track was also measured to calculate the space opening angle of the pair. The overall efficiency for the detection of the electron pairs was estimated to be --~99%, by rescanning about one third of the total area scanned. Since the efficiency is quite high there is practically no geometrical loss of electron pairs. For scattering measurements only those pairs were selected in which the tracks of both the electron and the positron had projected lengths of 2 - 3 mm in the emulsion plate of their origin. This ensured at least 2 0 - 3 0 cells of 100 /am for each track. The number of such pairs was found to be 71. The elimination of noise and spurious scattering from the scattering observations is an important correction. To accomplish this, we have applied the Barkas formula [8] for calculating the value of p/3 from the scattering measurements. This method has already been verified [9] on the beam tracks at 5 GeV/c.
4. Results and discussion Figure 1 shows the ratio R of the theoretical and experimental (scattering measurements) estimates of photon energies as a function of the space opening angle of the pair. It is immediately clear from the figure that Olsen's formulae give the most accurate estimates of photon energy throughout the range of the measured values of opening angles. We have further checked the reliability of the Olsen's method in the following way. It is reasonable to assume [10] that the observed photons are primarily the decay products of n°'s produced in the primary particle interactions. Some average values
S. Singh et al. / Energy estimation of photons in nuclear emulsions
6-
° o
o
O/sen's
S t e a r n S' formula
formula
x
Borselhno's
formula
o
o
o
• o
479
o
o
o
o o ° o
o
Ox
o
o x
x
oe x
x x ×
-* "llrY'-~-
~L
o
g
o
x
x
oO
o o
,
XO I o
~"
o
•
o
•
I0
28
o •
o
1
x
o
x x
x I
I
~6
6z.
co (x 10-3 r a d i a n s )
Fig. 1. The variation of ratio R with the opening angle co of the e+e- pair (R denotes the ratio of energy estimated from 03 by different formulae (refs. [4 7]) to that estimated experimentally by scattering measurements). The solid line corresponds to the expected value of R.
pertaining to 1r°-spectrum can be thus calculated by using the following relations due to Kopytov [11 ] : (PL) = 2(qL)
(6)
(p}) = 3(q~-) - zmn ol z
(7)
where PL and PT respectively represent the longitudinal and transverse momenta o f n u, and qL and qT are the corresponding quantities for a photon. We calculated the above n ° parameters for a large sample of 1017 e+e - pairs whose photon spectrum was obtained from Olsen's method. The pairs were observed in an emulsion stack exposed to a 50 GeV/c n - beam [12]. We obtained the following results: ~oL) = (3.000 + 0.140) GeV/c
(8)
and (p~) = (0.153 -+ 0.013) (GeV/c) 2 .
GeV2/c 2 obtained in a Bubble chamber experiment of 18.5 GeV/c n - p and n*p interactions. This is so expected in view of the established [14] constancy of transverse momentum of secondaries in high energy n-N interactions for b e y o n d an energy of ~ 5 GeV. The above agreement of (PL) and (p~-) obtained b y using Olsen's method with those obtained from experimental measurements strengthens to a great extent the overall credibility of Olsen's method. We are grateful to Professor K.D. Tolstov of Dubna for lending us a part o f the 50 GeV/c 7r- emulsion stack. AM is grateful to the Council of Scientific and Industrial Research, India for the award of a Post Doctoral Fellowship. Thanks are due to Mrs. J. Bhowmik, Mrs. S. Goel and Mrs. M. Sen for their efficient scanning.
(9)
The above value of (PL) is in good agreement with the value of (PL) = 3.20 + 0.19 obtained for rr÷ mesons produced in 50 GeV/c n--emulsion interactions by Kumar et al. [13]. In the experiment o f Kumar et al., the momenta of the charged secondaries were obtained from the measurement of tracks' curvature, the emulsion stack being exposed under a pulsed magnetic field. The present value of ( p ~ ) = ( 0 . 1 5 3 - + 0.013) GeV2/c 2 is also in good agreement with the values (0.147 + 0.003) GeV2/c 2 and (0.149 -+ 0.003)
References [ 1 ] B. Rossi, in: High Energy Particles (Prentice Hall, Englewood Cliffs, NJ, 1952) p. 79. [2] W.H. Barkas, in: Nuclear Research Emulsions, vol. 1 (Academic, New York, 1963) p. 444. [3] W.H. Barkas, in: Nuclear Research Emulsions, vol. 1 (Academic, New York, 1963) p. 366. [4] C.F. Powell, P.H. Fowler and D.H. Perkins, in: The Study of Elementary particles by the Photographic method (Pergamon, London, 1959) p. 191.
480
S. Singh et al. / t~,'ner~tv estimation Qf photons h~ nuclear emulsions
[51 M. Stearns, Phys. Rev. 76 (1949) 836. 16] A. Borsellino, Phys. Rev. 89 (1953) 1023. [71 11. Olsen, Phys. Rev. 131 (1963) 406. [81W.It. Barkas, in: Nuclear Research Emulsions, Vol. 1 (Academic Press, New York, 1963) p. 313. [9[ B. Bhowmik and S. Singh, Phys. Rev. 9 (1974) 63. l l 0 ] ( ; . Donaldson, tt. Gordon, K.W. Lai, 1. Stumer, A. Barnes, J. Mallima, A. Tollestrup, R. Walker, O. l)ahl, R.A. Johnson, A. Ogawa, M. Pripstein and
S. Shannon, Phys. Rev. Lett. 36 (1976) 1110. [ 111 G.I. Kopylov, Nucl. Phys. B52 (1973) 126. [121 A. Mozumder, S. Singh and D.P. (;oyal, Nuovo Cim. Lett. 22 ~1978) 312. [131V. Kumar, Phi) thesis, University of Kurukshetra (1979) unpublished ; privalc communication (1979). [141 A. Mozumder, Pill) thesis, University of Delhi (1979) unpublished.