DISINTEGRATION OF LIGHT AND HEAVY PHOTOEMULSION NUCLEI BY γ-QUANTA WITH ENERGIES UP TO 2 GeV

V. V. MAMEEV, V. A. FILIMONOV, D. A. GALSTYAN*

(Presented by the scientific-technical seminar of the High-Energy Laboratory of the Research Institute of Nuclear Physics)

Nuclear photoemulsion is a mixture of various elements, which may be divided into two groups sharply differing from one another—heavy (Ag and Br) and light (C, N, O, H). In studying the interaction of high-energy particles with photoemulsion nuclei, in order to separate events on light and heavy nuclei, certain criteria for event selection are usually introduced, or else calculations are carried out for an “average” nucleus without separating interactions on light and heavy nuclei.

In some cases use is made of the fact that the Coulomb barrier of heavy nuclei is higher than that for light nuclei. The Coulomb barrier of unexcited heavy nuclei for α-particles is 12–14 MeV. This energy corresponds to an α-particle range in an emulsion of the BR-2 type of about 80 μm. The probability of the appearance of a particle with a range less than 50 μm will be small if it is assumed that the particle has passed through the Coulomb barrier of a heavy nucleus. However, experiment shows that more than half of the stars ($N_h \ge 3$) produced when emulsions are irradiated with γ-quanta have tracks shorter than 50 μm, and according to the assumption stated above they should be attributed to the disintegration of light nuclei.

The study of star formation in normal and diluted photoemulsions makes it possible statistically to separate interactions with light and heavy nuclei. In diluted photoemulsion the amount of gelatin is increased and, consequently, the relative number of light nuclei is increased.

Irradiation of layers of relativistic photoemulsions of type BR-2 (400 μm) and diluted type BR-2×4 (250 μm) with fourfold dilution was carried out analogously to works [1, 5] in direct beams of bremsstrahlung radiation with maximum energies of 300, 600, and 900 MeV at the “Sirius” electron synchrotron of the Research Institute of Nuclear Physics, and 2000 MeV at the synchrotron of the Yerevan Physical Institute. The emulsion layers were placed perpendicular to the axis of the γ-beam in order to reduce the influence of the electron-positron pair background. Development of the photoemulsions was carried out at the Laboratory of High Energies of JINR according to standard technology. The thickness of the layers

* Yerevan Physical Institute.

was measured before development. All events with a number of tracks \(\ge 2\) were recorded. Details of the irradiation and scanning are given in [1].

The elemental composition of the BR-2 emulsion was taken from the data of [2]. The composition of the diluted BR-2 \(\times 4\) emulsion was determined from the composition of the BR-2 emulsion and the known ratio of the amount of gelatin in photoemulsions. Data on the elemental composition of the photoemulsions are given in the table.

Table

Hydrogen is excluded from the number of light elements, since the probability that a multiprong star is formed on it is small.

The cross section for star formation per equivalent quantum per emulsion nucleus was determined by the formula

\[ \sigma_Q=\frac{N-N_\phi}{Qnt\eta}. \]

where \(N\) is the number of recorded events;

\(N_\phi\) is the number of background events;

\(Q\) is the number of equivalent quanta, \(Q=W/E_{\gamma m}\);

\(W\) is the total energy of the \(\gamma\)-beam;

\(E_{\gamma m}\) is the maximum energy of the \(\gamma\)-quanta;

\(n\) is the number of nuclei in \(1\ \text{cm}^3\);

\(t\) is the thickness of the emulsion layer;

\(\eta\) is the scanning efficiency.

The cross sections for star formation on light and heavy elements are, respectively, equal to

\[ \sigma_H= \frac{(1+k_n)\sigma_n-(1+k_r)\sigma_r}{k_n-k_r}, \]

\[ \sigma_L= \frac{k_r(1+k_n)\sigma_n-k_n(1+k_r)\sigma_r}{k_n-k_r}, \]

where

\[ k_r=\frac{n_{Hr}}{n_{Lr}},\quad k_n=\frac{n_{Hn}}{n_{Ln}} \]

is the ratio of the number of heavy and light nuclei in the diluted and normal photoemulsions;

\(\sigma_r\) and \(\sigma_n\) are the cross sections for star formation in the diluted and normal photoemulsions;

Cross section per equivalent quantum, \(10^{-27}\ \mathrm{cm}^2\)

Number of tracks

\(300\ \mathrm{MeV}\), \(\times 1.5\)
\(600\ \mathrm{MeV}\)
\(900\ \mathrm{MeV}\)
\(2000\ \mathrm{MeV}\)

\(\sigma_H\)
\(\sigma_L\)

Fig. 1. Dependence of the cross sections for photoproduction of stars on light and heavy nuclei on \(N_h\) at various \(E_\gamma\).

\(k_n\) and \(k_r\) — for emulsions of type BR-2 and BR-2×4 are, respectively, equal to 0.744 and 0.194 (hydrogen among the light nuclei is excluded).

Figure 1 gives the calculated cross sections \(\sigma_h\) and \(\sigma_L\) for events with different numbers of tracks. The cross sections on light nuclei are much smaller than on heavy ones, and practically all events with a number of produced charged particles \(\geq 7\) are due to the interaction of \(\gamma\)-quanta with heavy nuclei. Low-prong stars are the product of the disintegration of both light and heavy nuclei. Complete breakup of the \(O^{16}\) nucleus (the heaviest of the light nuclei; \(S^{32}\) may be disregarded, since sulfur constitutes only 0.1% of the light nuclei) corresponds to the formation of 8 gray or black tracks. In light nuclei the cascade usually develops weakly, and most of the tracks are produced by evaporation particles from the residual nucleus. In the evaporation of particles from a nucleus excited to an energy close to the total binding energy of the nucleus, the ratio of the numbers of doubly charged particles to singly charged particles approaches 0.3 and, consequently, the maximum number of tracks is \(\approx 6\), which agrees with the experimental data.

Fig. 2. Ratio of cross sections on light and heavy nuclei as a function of \(N_h\) at \(E_{\gamma m}=2\) GeV.

Figure 2 shows the ratio \(\sigma_L/\sigma_h\). This quantity decreases sharply as the number of tracks in the star increases. The mean atomic weight of a heavy emulsion nucleus is \(A_h = 93.9\), and for a light one, \(A_L = 13.7\). For events with a number of tracks \(\geq 2\), the ratio of cross sections per nucleon for light and heavy elements,

\[ \frac{\sigma_L}{\sigma_h}\frac{A_h}{A_L}, \]

is shown in Fig. 3. Within the errors this quantity is equal to 1 in the range \(E_{\gamma m}\) from 0.3 to 2 GeV. This fact agrees with the model according to which the cross section for the interaction of \(\gamma\)-quanta with a nucleus is proportional to the mass number of the target nucleus.

Of the stars with \(N_h \geq 2\), more than 80% belong to heavy nuclei, and the separation of events on light and heavy nuclei by the shortest range of the charged particles is very crude. Short-range particles

Fig. 3. Dependence of the quantity \(\dfrac{\sigma_L A_H}{\sigma_H A_L}\) on \(E_{\gamma m}\).

can be formed both at the cascade stage of the interaction and at the evaporation stage. The evaporation mechanism of emission of low-energy protons is discussed in the work of Le Couteur [3]. As a result of the predominant evaporation of neutrons (especially at the end of the evaporation process), the product nucleus will have a certain neutron deficit, and the separation energy of the least-bound proton will be less than the binding energy of a neutron in the upper level. If such a nucleus retains an excitation energy whose value lies between the two values of the neutron and proton binding energies, then proton emission will occur by tunneling, since the radiative width at these excitation energies is still small compared with the particle width. The energy of the decay protons lies between 0 and 4 MeV. Emission of \(\alpha\)-particles as a result of such a mechanism is unlikely owing to the large Coulomb barrier.

Calculations of the cascade stage of the interaction of hadrons of various energies with heavy nuclei, carried out by the Monte Carlo method, also show that there is a significant probability of the appearance of low-energy particles [4].

The authors thank the administration of the Yerevan Physics Institute for providing the opportunity to irradiate the photoemulsions at the YerPhI synchrotron; the staffs of the YerPhI and “Sirius” synchrotrons of the YaFÉA Scientific Research Institute; and the scanning group of the YaFÉA Scientific Research Institute.

REFERENCES

1. V. M. Bobrina, V. V. Mameev, V. A. Filimonov. Izvestiya vuzov, “Fizika,” No. 10, 126 (1968).

2. K. S. Bogomolov, L. P. Vakhtanov. JINR Preprint R13-3163, Dubna (1967).

3. K. J. Le Couteur. Proc. Phys. Soc., 63, No. 363A, 259 (1950).

4. I. Dostrovsky, P. Rabinovich, B. Bivins. Phys. Rev., 111, 1659 (1958).

5. C. E. Roos, V. Z. Peterson. Phys. Rev., 124, 1610 (1961).