PHENOMENON OF CAPTURE OF AN \(L_1\)-ELECTRON BY THE NUCLEUS

One of the known types of nuclear transformations is the phenomenon of \(K\)-capture, in which the nucleus interacts with a \(K\)-electron of the atom. According to the theory of \(\beta\)-decay, the probability of such a process is proportional to the square of the wave function of the \(K\)-electron in the region of the nucleus, \(\lambda_K \sim |\Psi_K(0)|^2\). In exactly the same way, the probability of capture by the nucleus of an \(L_1\)-electron is \(\lambda_{L_1} \sim |\Psi_{L_1}(0)|^2\), where \(\Psi_{L_1}(0)\) is, respectively, the wave function of the \(L_1\)-electron at the nucleus. A consequence of this is the difference in the half-life period (\(T'\)) of the neutral atom Be\(^7\) (a \(K\)-capturing isotope, \(T = 52.9\) days) and of the ionized atom of the same isotope Be\(^{++}\) (\(T\)), determined by the ratio of the wave functions of the \(K\)- and \(L_1\)-electrons

\[ \rho = \frac{T' - T}{T} \simeq \frac{|\Psi_{L_1}(0)|^2}{|\Psi_K(0)|^2}. \]

For Be\(^7\), theoretical calculations were carried out by the Slater method with allowance for screening of the nucleus,\(^{1,2}\) and more accurately with the use of Fock–Hartree wave functions.\(^{3}\) In the latter case, allowance was made for-offsetof

From Current Literature

exchange interaction between atomic electrons. The results of the calculations are given in the table:

In 1947 the first reports\(^{1,4}\) were published on experiments with \(\mathrm{Be}^7\). However, the experimental error almost covered the effect and did not permit definitive quantitative conclusions to be drawn. Later, more careful investigations were carried out\(^{5,6}\).

In the experiments of the French scientists\(^{5}\), from a lithium target irradiated with deuterons, two sources of equal activity were prepared: metallic beryllium and the compound \(\mathrm{BeF}_2\). In the experimental apparatus, consisting of two identical ionization chambers connected in a compensation circuit, the difference current was measured. Ionization in each of the chambers was produced by the \(\gamma\)-radiation following the nuclear transition of one of the two preparations. With time, in the apparatus, initially compensated, a current appeared which exceeded the instrumental fluctuations severalfold. For the difference current of the chambers \(|\Delta I|\) it is easy to obtain the relation

\[ \Delta I = I_0 \frac{\Delta T}{T}\, e^{-\lambda t}\cdot \lambda t . \]

The total current in a chamber \((I_0)\) was determined indirectly from the absorption of \(\gamma\)-radiation in brass plates. This method increases the error in connection with the inaccuracy of the absorption calculation, but it makes it possible to keep the geometry of the measurements unchanged throughout the entire experiment.

Finally, the following value of the effect was obtained in the work:

\[ \rho_{\mathrm{Be}-\mathrm{BeF}_2} = \frac{\Delta T}{T} = 0.01 \pm 0.003; \]

For comparison with theory the authors assume that in the Be atom only 50% of the \(L_1\)-electrons are in the \(s\)-state, and in \(\mathrm{BeF}_2\) 87% of all atoms should be regarded as ionized, i.e. the expected effect is

\[ \rho \approx 0.03 \times 0.87 \times 0.5 \approx 0.013. \]

In another work\(^{6}\) on the question under discussion, the difference in the half-life period of metallic beryllium and beryllium oxide was determined. The differential ionization chamber used in this work differs from the apparatus described above in the design of the ionization chambers and in the electrometric circuit. Methodically the works\(^{5}\) and \(^{6}\) are equivalent. The errors of this experiment are close to the observed effect

\[ \rho_{\mathrm{Be}-\mathrm{BeO}} = (3.0 \pm 1.8)\cdot 10^{-4}. \]

The authors show that in BeO one should expect 10% of the effect of a doubly ionized atom \(\mathrm{Be}^{++}\), and therefore state agreement of theory with experiment.

Thus the phenomenon of capture of an \(L_1\)-electron by the nucleus may be considered proved, the effect being close to that calculated by the Fock–Hartree method.

It is clear that capture by the nucleus of an \(L_1\)-electron is possible not only in the atom Be\(^7\), but also in atoms of other isotopes. Thus, for Ar\(^ {37}\) (\(K\)-capturing isotope) calculations by Slater’s method give for \(\rho\) the value \(\rho = 0.06\)^7, while the Fock–Hartree method gives the value \(\rho = 0.08\)^8.

Capture by the nucleus of the Ar\(^ {37}\) \(L_1\)-electron was observed with the aid of a proportional counter^9 containing an admixture of radioactive argon. The distribution of pulses by magnitude was investigated. The principal peak in the distribution corresponded to the energy of Auger electrons ejected by a Cl atom deprived of a \(K\)-electron. In addition, an additional peak was visible in the region of small energies (about 200 eV). The authors point out that the magnitude of this peak exceeds the possible number of electrons ejected by the atom together with the characteristic \(K_\alpha\) radiation. The result was explained by the phenomenon of capture by the nucleus of Ar\(^ {37}\) of an \(L_1\)-electron with subsequent illumination of the atom by emission of Auger electrons. Comparison of the two observed maxima gives for \(\rho\) the value 8–9%.

I. Estulin

CITED LITERATURE

1. R. Bouchez, R. Daudel, P. Daudel et R. Muxart, J. Phys. et Rad. 8, 336 (1947).
2. P. Benoist, C. R. 226, 243 (1948).
3. P. Benoist, C. R. 228, 309 (1949).
4. E. Segre, Phys. Rev. 71, 274 (1947).
5. R. Bouchez, R. Daudel, P. Daudel et Muxart, J. Phys. et Rad. 10, 201 (1949).
6. E. Segre and C. E. Wiegand, Phys. Rev. 75, 39 (1949).
7. R. E. Marshak, Phys. Rev. 61, 431 (1942).
8. P. Benoist, C. R. 228, 1848 (1949).
9. B. Pontecorvo, D. H. W. Kirkwood and G. C. Hanna, Phys. Rev. 75, 982 (1949).