Reports of the Academy of Sciences of the USSR

1. Volume 160, No. 6

PHYSICS

Academician of the Academy of Sciences of the Ukrainian SSR A. P. Komar, E. D. Makhnovskii

LOW-ENERGY CHARGED PARTICLES IN THE PHOTODISINTEGRATION OF THE Be\(^9\) NUCLEUS

The energy spectra and yields of charged particles produced upon irradiation of Be\(^9\) with bremsstrahlung with \(E_{\gamma \max} = 35\) MeV were investigated. A beryllium target \(4.7\) mg/cm\(^2\) thick was irradiated in a vacuum chamber with photographic plates, located in a uniform magnetic field \((H = 13\,500\) oersted), approximately perpendicular to the direction of particle emission \((^1)\). The particle ranges \(R\) and the orientations of their tracks in the emulsion were measured. The latter made it possible to determine the radii of curvature \(\rho\) of the trajectories in the magnetic field and, by comparison with calculated dependences \(\rho(R)\) for a given \(H\), to identify the particles. The scatter of the \(\rho\) measurements was taken into account by constructing the corresponding “error corridors.” The irradiation doses were measured with a quantometer \((^2)\). In the proton region the total background for the two photographic plates examined was \(38\%\), and in the \(\alpha\)-particle region \(23\%\). All measured background particles had ranges \(\leq 50\,\mu\).

In Fig. 1 the calculated dependences \(\rho(R)\) are shown by solid curves. The points represent the results of measurements after subtraction of the background. The triton region practically coincides with the region for \(\alpha\)-particles; therefore it is not shown in the figure.

Figure 2 presents the energy distribution of 252 protons. The maximum of the energy distribution is not at \(1.5 \div 2.5\) MeV, as obtained in \((^3)\), but at \(E_p \simeq 4\) MeV. The intense maximum in the low-energy region of the proton spectrum obtained in \((^3)\), where particle discrimination was not carried out, is most probably due to a large contribution from \(\alpha\)-particles.

Figure 3 shows the excitation function of the reaction Be\(^9(\gamma,p)\)Li\(^8\), calculated under the assumption that all identified protons are due to this reaction, that the angular distribution of the photoprotons is isotropic, and that the recoil nucleus Li\(^8\) is in all reaction cases formed in the ground state. Judging from the position of the maximum of the curve (at \(E_\gamma \simeq 22\) MeV), its half-width, and the magnitude of the integral cross section measured from \(E_\gamma = 18\) MeV to \(E_\gamma = 26\) MeV, the excitation function constructed by us agrees well with the excitation functions of the \((\gamma,p)\)-reaction measured in \((^{4,5})\) from the characteristic \(\beta^-\)-activity of the recoil nucleus Li\(^8\). In accordance with Fig. 3,

\[ \int_{18}^{26} \sigma_{\gamma p}(E_\gamma)\,dE_\gamma = (12 \pm 1.8)\ \text{mb}\cdot\text{MeV}. \]

The bremsstrahlung-spectrum-weighted cross section of the \((\gamma,p)\)-reaction on Be\(^9\),

\[ \int \frac{\sigma_{\gamma p}(E_\gamma)}{E_\gamma}\,dE_\gamma, \]

according to calculations, should be \(1.06\) mb \((^6)\). It was shown in \((^5)\) that the integral cross section of the \((\gamma,p)\)-reaction increases with increasing \(\gamma\)-quantum energy up to \(E_\gamma \simeq 57\) MeV. If the excitation function obtained by us is smoothly continued from \(E_\gamma = 18\) MeV to the threshold \((Q = 16.9\) MeV) and from \(E_\gamma = 31\) MeV to \(E_\gamma = 35\) MeV, then

\[ \int_{16.9}^{35} \frac{\sigma_{\gamma p}(E_\gamma)}{E_\gamma}\,dE_\gamma \simeq 0.73\ \text{mb}. \]

In accordance with the data of \((^5)\),

\[ \int_{35}^{57} \frac{\sigma_{\gamma p}(E_\gamma)}{E_\gamma}\,dE_\gamma \simeq 0.32\ \text{mb}. \]

Altogether,

\[ \int_{16.9}^{57} \frac{\sigma_{\gamma p}(E_\gamma)}{E_\gamma}\,dE_\gamma \simeq 1.05\ \text{mb}, \]

which

Fig. 1. Distributions of photoparticles from $\mathrm{Be}^9$ by radii of curvature of the trajectories in a magnetic field and by ranges in the emulsion: a — for a photographic plate with $\varphi_0 = 35^\circ$, b — for a photographic plate with $\varphi_0 = 65^\circ$ ($\varphi_0$ is the angle between the line connecting the centers of the target and the photographic plate and the direction of the $\gamma$-quantum beam). 1 — particle zone; 2 — deuteron zone; 3 — proton zone.

is in good agreement with the theoretical value of this quantity given above (1.06 mb).

The angular distribution of photoprotons with \(E_p \geqslant 2.6\) MeV has the form of a function increasing with increasing \(\theta\) from 40 to \(90^\circ\). This is not in contradiction with the form of the angular distributions of nucleons in direct photoemission for \(1p \to 1d\) and \(1p \to 2s\) transitions \((^7)\).

Fig. 2. Energy distribution of photoprotons from \(\mathrm{Be}^9\)

From the analysis of the data it also follows that, for \(E_\gamma < 35\) MeV, the reactions \(\mathrm{Be}^9(\gamma,p)\mathrm{Li}^{8*}(n)\mathrm{Li}^7\) and \(\mathrm{Be}^9(\gamma,p)\mathrm{Be}^{8*}(p)\mathrm{Li}^7\) are improbable. It is difficult to suppose that these reactions occur with the emission of protons only with energies of 1 MeV, which were not recorded in the present work.

A rather high value was established for the ratio of the deuteron yield to the proton yield. For particles with energies \(3.7 \div 14.2\) MeV, \(Y_d/Y_p = 0.20 \pm 0.10\). On the whole, about 90 of the particles recorded in the experiment should have been identified as deuterons. The cross section of photoreactions accompanied by deuteron emission amounts to \(6 \div 7\%\) of the total absorption cross section of \(\gamma\)-quanta with energies from 16.7 to 35 MeV. From a comparison of our data with the data of work \((^6)\) it may be concluded that not less than half of the particles assigned by us to deuterons are apparently due not to many-particle decays of the beryllium nucleus, but to the reaction \(\mathrm{Be}^9(\gamma,d)\mathrm{Li}^7\).

Fig. 3. Excitation function of the reaction \(\mathrm{Be}^9(\gamma,p)\mathrm{Li}^8\)

The energy spectra of \(\alpha\)-particles are shown in Fig. 4. The spectra were constructed taking into account the contribution of only deuterons in the region for \(\alpha\)-particles. In the photodisintegration of \(\mathrm{Be}^9\), \(\alpha\)-particles may arise in \((\gamma,n)\) and \((\gamma,\alpha)\)-reactions. From a comparison of the integral cross sections calculated in accordance with \((^{8,9})\), it follows that the form of the obtained energy spectrum of \(\alpha\)-particles is determined mainly by the reaction
\(\mathrm{Be}^9(\gamma,n)\mathrm{Be}^{8*} \to 2\alpha\). Cases of the \((\gamma,n)\)-reaction in which \(\mathrm{Be}^8\) is formed in the ground or in the first excited state were not recorded by us. As follows from the figure, at \(E_\alpha\) near 6 and 10 MeV there are two broad peaks. According to the kinematics of the \((\gamma,n)\)-process, the position of any group of \(\alpha\)-particles in the experimental spectrum at a given energy of the “primary” neutrons is characterized by the dependence

\[ \overline{E}_\alpha = E_\alpha^0 + E_n/16 . \tag{1} \]

Here, \(E_\alpha^0 = (E_{\mathrm{Be}^{8}}^* + 0.094)/2\) is the kinetic energy of an \(\alpha\)-particle in the center-of-mass system of the \(\mathrm{Be}^8\) nucleus having excitation energy \(E_{\mathrm{Be}^{8}}^*\); \(E_n = \frac{8}{9}(E_\gamma - Q)\) is the energy of the “primary” neutron emitted from \(\mathrm{Be}^9\); \(Q = 1.66 + E_{\mathrm{Be}^{8}}^*\).

Taking into account the data of work \((^6)\), the addition \(E_n/16\) in (1) has a value \(\lesssim 0.5\) MeV; consequently, the positions of the different groups of \(\alpha\)-particles are determined mainly by the value \(E_\alpha^0\). In Fig. 4 the arrows at energies 5.7; 8.1; 8.4; 8.8; 10.0 and 11.3 MeV indicate the values of \(E_\alpha^0\) corresponding to the decay of \(\mathrm{Be}^8\) in known excited states at 11.4; 16.08; 16.7; 17.6; 19.9 and 22.6 MeV \((^{10,11})\). It is seen that the broad maximum in the region \(E_\alpha\) about

6 MeV can be identified with the decay of \(\mathrm{Be}^8\) only in the excited state at 11.4 MeV. The second group of \(\alpha\)-particles, with an average energy of about 10 MeV, is explained by the formation and subsequent decay of \(\mathrm{Be}^8\) in states with \(E^*_{\mathrm{Be}^8}\) from 16.08 to 22.6 MeV.

Taking into account the results of the present work and the data given in \((^{5,8,12,13})\), the absorption cross section of \(\gamma\)-quanta by the \(\mathrm{Be}^9\) nucleus, weighted over the bremsstrahlung spectrum, is

\[ \sigma_{-1}=\int_{1.7}^{150}\frac{\sigma(E_\gamma)}{E_\gamma}\,dE_\gamma \simeq (6\pm 1)\ \text{mb}. \]

In the shell model with a harmonic-oscillator potential, \(\sigma_{-1}=0.36\,A^{4/3}\) mb \((^{13})\). For \(\mathrm{Be}^9\) one obtains \(\sigma_{-1}=6.7\) mb, which agrees with the experimental value given above. \(\sigma_{-1}\) is related to the mean-square radius of the charge distribution in the nucleus \((^{14-16})\):

\[ \sigma_{-1}=\frac{4\pi^2}{3}\frac{e^2}{\hbar c}\frac{NZ}{A-1}(1-\Lambda)(\overline{R_c^2}-\overline{R_p^2}). \tag{2} \]

\(\Lambda=0.84(1+22A)^{-1}\), \(\overline{R_p^2}\) is the mean square radius of the proton charge distribution. If \(\sigma_{-1}=6\) mb is adopted, then for \(\mathrm{Be}^9\) we obtain \(\overline{R_c}\simeq 2.0\cdot 10^{-13}\) cm. This agrees with the value \(\overline{R_c}=(2.2\pm0.2)\cdot 10^{-13}\) cm obtained by Hofstadter \((^{17})\).

According to our data and those cited in \((^{5,8,12,18})\), for \(\mathrm{Be}^9\) the quantity

\[ \sigma_{-2}=\int_{1.7}^{150}\frac{\sigma(E_\gamma)}{E_\gamma^2}\,dE_j \simeq \]

\[ \simeq 395\ \mu\text{b}\cdot\text{MeV}^{-1}. \]

Migdal showed that \(\sigma_{-2}\) is proportional to the polarizability of the nucleus under the action of an electromagnetic field \((^{19})\). In accordance with the results of his calculations, \(\sigma_{-2}=2.25\,A^{5/3}\ \mu\text{b}\cdot\text{MeV}^{-1}\) \((^{18})\). For \(\mathrm{Be}^9\) this dependence gives 87 \(\mu\text{b}\cdot\text{MeV}\), which is 4.5 times smaller than the experimental value.

Fig. 4. Energy spectrum of \(\alpha\)-particles arising in the photodisintegration of \(\mathrm{Be}^9\) (histogram). The smooth curve shows the spectrum obtained by viewing the photographic plate at \(\varphi_0=35^\circ\).

Physicotechnical Institute named after A. F. Ioffe
Academy of Sciences of the USSR

Received
9 VII 1964

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