IONIZATION OF THE $K$-SHELL OF RECOIL ATOMS IN THE $\alpha$-DECAY OF POLONIUM

Nuclear transitions are, to one degree or another, associated with a “disturbance” of the electron shells of the atoms within which these transitions occur. The following causes of the “disturbance” of electron shells in nuclear transitions may be indicated:

1. Direct interaction of nuclear radiation with shell electrons.
2. Recoil experienced by the nucleus in nuclear transformations or collisions.
3. Change in the nuclear charge occurring in the case when the nucleus emits a charged particle.

Depending on how large the disturbance is and on what causes have produced it, it may have either the character of an adiabatic change in the state of the shell, ending, roughly speaking, in a slow (in comparison with electronic periods) change in the form of the charge distribution, or the character of a nonadiabatic “shake-up”—a sudden rearrangement of the shell, accompanied by excitation or ionization of the daughter atom (recoil atom).

The probability of ionization of recoil atoms in alpha and beta decay has been the subject of calculations by a number of authors1–3. The calculation shows that the probability of ionization of the outer electron shells of recoil atoms, both in $\alpha$-decay and in $\beta$-decay, is of the order of unity. This means that all (or almost all) recoil atoms arise as ions. Such a conclusion agrees with experimental facts concerning the behavior of recoil atoms in $\alpha$-decay4 and $\beta$-decay5 in electric and magnetic fields. Unfortunately, up to now there has been no information concerning the detailed picture of ionization of the outer shells of recoil atoms, i.e., information on the probability that a recoil atom arising as a result of $\alpha$- or $\beta$-decay has this or that initial charge. Such information is especially necessary for experiments on the study of recoil atoms in $\beta$-transformations6 or for experiments on the study of the interaction of recoil atoms with matter7.

As regards the ionization of the inner electron shells of recoil atoms in $\alpha$- or $\beta$-transformations, until recently there had been no convincing experimental evidence for this phenomenon, although theoretical calculations1,2 had been made comparatively long ago. This is explained, on the one hand, by the small probability of such processes and, on the other hand, by the

on the other hand, the necessity of using perfected experimental methodology and technique for their detection. In this connection, the papers that appeared in 1951–1952⁸, ⁹, ¹⁴–¹⁶ are of interest; their results, with one or another degree of accuracy, make it possible to assert the experimental proof of the ionization of the inner electron shells of recoil atoms arising in $\alpha$-decay.

Since ionization of the inner shell of recoil atoms is accompanied by the emission of characteristic X-rays or of the corresponding conversion (Auger) electrons, its detection in principle reduces to detecting and identifying this radiation, i.e. to proving that the radiation under consideration actually exists and that it is atomic in origin. As for the mechanism of excitation of the X-radiation accompanying a nuclear transition, information about it can be obtained by an additional study of the relative intensities of the atomic and nuclear transitions.

The authors of the papers under review studied the $\alpha$-decay of Po$^{210}$. The decay scheme of Po$^{210}$ had been studied fairly well¹⁰. The question reduced to studying the relative intensity of the 800-kev gamma radiation emitted in the decay of polonium¹¹, and the intensity of the “soft” radiation with mean energy $\sim 80$ kev existing, according to the decay scheme of Po$^{210}$ found by Fierz and his co-workers¹². Fierz identified the latter as nuclear, occurring in a cascade with the harder 800-kev radiation. In so doing, he considered that, when the Po$^{210}$ nucleus emits a short-range $\alpha$-particle, a transition to an excited level of the Pb$^{206}$ nucleus with excitation energy $\sim 880$ kev takes place. According to Fierz’s scheme, the transition to the ground state consists in the consecutive emission of quanta of energy $\sim 80$ kev and 800 kev*). This conclusion was based on the fact that the intensities of the “soft” (80 kev) and “hard” (800 kev) radiations are comparable, and on the results of experiments on the critical absorption of the soft radiation in various materials.

Fierz’s conclusion could not be considered final. Since the mean energy of the characteristic $K$-radiation of lead (the daughter atom in the decay of Po$^{210}$) is $\sim 75$ kev, it was natural also to suppose that the soft radiation observed in the decay of Po$^{210}$ is X-radiation belonging to lead. A program of investigations devoted to clarifying the nature of the soft radiation and the mechanism of its excitation had necessarily to include the following sections:

1. Measurement of the absolute intensity of the polonium source (by counting $\alpha$-particles); control of the purity, thickness, and uniformity of the distribution of the active polonium deposit in the source;

2. Measurement of the relative intensity of the “hard” $\gamma$-quanta in the decay of polonium

\[ \left(\frac{N_{800}}{N_\alpha}\right); \]

1. Determination of the absolute value of the energy of the “soft” radiation emitted in the decay of Po$^{210}$;

2. Measurement of the relative intensity of the “soft” radiation: relative to the intensity of the $\alpha$-particles

\[ \left(\frac{N_{80}}{N_\alpha}\right) \]

and relative to the intensity of the “hard” $\gamma$-radiation

\[ \left(\frac{N_{80}}{N_{800}}\right); \]

*) A decay scheme in which the sequence of emission of the $\gamma$-quanta is different was excluded, since in the latter case the transition from the level 80 kev to the ground state either would have to be accompanied by a very large change in angular momentum, or the intensity of the 80-kev radiation would have to be comparable with the intensity of the $\alpha$-particles of the main group.

1. Measurement of coincidences between the “hard” and “soft” radiation of Po \(^{210}\).

2. Measurement of the relative intensity of electrons arising in the conversion of the “hard” or “soft” radiations \(\left(\dfrac{N_e}{N_\alpha}\right)\).

The carrying out of this program, which constitutes the content of the reviewed works \(^{8,9}\), should give an unambiguous answer to the question of the energy levels of the Pb \(^{206}\) nucleus produced in the decay of Po \(^{210}\), and of the mechanism of origin of the “soft” radiation accompanying this nuclear transition. In addition, the quantitative results of the indicated measurements should serve as a check on theoretical calculations \(^{1}\) concerning the probabilities of ionization of the inner shells of recoil atoms in \(\alpha\)-decay.

The relative intensity of the “hard” \(\gamma\)-radiation, determined in one of the reviewed papers \(^{8}\), proved to be equal to

\[ \frac{N_{800}}{N_\alpha}=(1.8\pm0.14)\times10^{-5} \]

quanta per \(\alpha\)-particle. The measurements were carried out with a thin-walled aluminum counter. The result was compared with a measurement of the number of \(\gamma\)-quanta from the Co \(^{60}\) source line, calibrated at \(1.2\) Mev, used with the same “geometry” as the Po \(^{210}\) source. Naturally, the dependence of the counter efficiency on the radiation energy was taken into account.

In another paper \(^{9}\), the quantity \(\dfrac{N_{800}}{N_\alpha}\) was calculated from the experimentally determined relative intensities

\[ \frac{N_{80}}{N_{800}} \quad \text{and} \quad \frac{N_{80}}{N_\alpha}, \]

and was found to be

\[ (1.5\pm0.4)\cdot10^{-5}. \]

As can be seen, the agreement, within the upper limit, is quite satisfactory.

Determination of the absolute value of the energy of the soft radiation of polonium is of great importance for elucidating its nature. Fiser \(^{12}\) found the energy of the soft radiation to be \((84\pm4)\) kev. In paper \(^{9}\) the energy of the soft radiation was found to be \((76\pm4)\) kev. This value agrees much better with the mean energy of the characteristic \(K\)-radiation of lead. In the latter paper \(^{9}\) the integral distribution of the magnitudes of pulses produced in a scintillation counter (NaI·Tl crystal) by the “soft” radiation of Po \(^{210}\), on the one hand, and by the characteristic \(K\)-radiation of lead, on the other, were compared. An additional check was also carried out: differential curves were recorded for the distribution of pulse magnitudes produced under identical conditions by the “soft” radiation of Po \(^{210}\) and by the x-ray \(K\)-radiation of lead. Both these checks convincingly showed the similarity of the “soft” radiation of polonium and the characteristic x-ray \(K\)-radiation of lead. However, they are still insufficient for finally identifying the “soft” radiation as atomic radiation of lead. It is necessary to show that there is no nuclear radiation of the same energy and that the “soft” radiation in the decay of Po \(^{210}\) is not x-ray radiation of any element adjacent to lead.

The first problem is accomplished by studying the count of coincidences of the “hard” and “soft” rays emitted in the decay of polonium. Experiments of this kind were carried out in both reviewed papers and showed that the coincidence count is small. This gives grounds for concluding \(^{9}\) that the “soft” radiation in the decay of polonium, at least \(90\%\) of it, is atomic radiation with energy 76 kev; if a cascade process of emission of \(\gamma\)-rays \(^{12}\) takes place, then the lifetime of the intermediate state must be greater than \(12\cdot10^{-6}\) sec. (the resolving time of the coincidence scheme used in paper \(^{9}\)).

The second problem can best be solved by using a proportional counter. The technique of studying soft radiation (with energies up to $\sim 100$ keV) with proportional counters filled with heavy noble gases (krypton, xenon) with an admixture of carbon dioxide or methane has become widespread in recent years1. Since low-energy radiation is absorbed in the gas of such counters predominantly through the photoelectric effect, the magnitude of the proportional pulse is proportional to the energy of the absorbed beam. The efficiency of proportional counters for “soft” radiation is high (reaching, with a suitable choice of filling gas, 100%). The authors[^8], using an energy-calibrated proportional counter placed in a strong magnetic field ($\sim 7000$ gauss)*, studied the distribution of the pulse magnitudes produced in the counter by “soft” radiation from polonium. The energy resolution was quite sufficient to allow clear separation of the “peaks” corresponding to the $K_{\alpha}$ and $K_{\beta}$ lines of the X-radiation of lead.

Since the accuracy of the energy calibration of the proportional counter was not sufficiently high, a series of additional experiments was carried out on the critical absorption of the “soft” radiation in tungsten, iridium, platinum, gold, and osmium. These experiments showed that the soft X-radiation accompanying the $\alpha$-decay of $\mathrm{Po}^{210}$ belongs to lead, and not to atoms of neighboring elements.

The next task of the investigation was to elucidate the mechanism by which the lead $K$-radiation arises in the decay of polonium. X-rays of lead can arise either as a result of internal conversion of the “hard” (800-keV) radiation of polonium, or because of ionization of the inner shells of the recoil atom occurring as a consequence of $\alpha$-decay. Both processes may also occur simultaneously. The presence of the first mechanism, ionization of the $K$ shell of the recoil atom in the decay of $\mathrm{Po}^{210}$, was proved in the work by detecting internal-conversion electrons. The energy of the electrons was not measured, but their relative intensity was measured:

\[ \frac{N_e}{N_{\alpha}} = (1.2 \pm 0.5)\cdot 10^{-6}\ \text{electrons per } \alpha\text{-decay}. \]

This quantity was determined by comparing the electron absorption curves from a calibrated $\mathrm{Po}^{210}$ source and from a standard $\mathrm{Ra}(D+E)$ source in aluminum. On the other hand, in the same work[^8], using measurements with a proportional counter of the differential distribution curves of the “soft” radiation by energy, the relative intensity of the “soft” radiation was determined:

\[ \frac{N_{80}}{N_{\alpha}} = (1.5 \pm 0.5)\cdot 10^{-6}. \]

If one assumes that all the electrons detected in the experiment are electrons produced in the internal conversion of the 800-keV $\gamma$-radiation, then from comparison of $\frac{N_e}{N_{\alpha}}$ and $\frac{N_{80}}{N_{\alpha}}$ it follows that the principal mechanism of ionization of the $K$ shell of recoil atoms in the decay of $\mathrm{Po}^{210}$ is internal conversion of the 800-keV radiation. From these same measurements the internal-conversion coefficient was determined to be $\alpha = 0.067 \pm 0.017$.

* The magnetic field reduces to a minimum the “leakage” of photoelectrons produced in the gas of the counter to the outside and thereby increases the efficiency of the counter. Owing to this, the efficiency of the counter can be calculated directly from the “geometry” and the known absorption coefficients of the filling gas.

FROM CURRENT LITERATURE

The authors of another paper\(^9\) also measured the relative intensities of the “soft” and “hard” radiations in the decay of Po\(^{210}\). For this purpose they used differential curves of the pulse-height distributions obtained in a scintillation counter (NaI·Tl crystal) for the “soft” and “hard” radiations and for the \(\alpha\)-particles produced in the decay of Po. The efficiency of the counter for each of the radiations mentioned was determined on the basis of theoretical calculations of the differential cross sections for the processes occurring in the crystal upon absorption of the radiation (Compton effect, photoeffect, secondary processes), taking into account the “geometry” of the setup.

As a result of these measurements and calculations it was established that:

\[ \frac{N_{76}}{N_{800}}=(0.134 \pm 0.025), \quad \frac{N_{76}}{N_{\alpha}}=(2.00 \pm 0.38)\cdot 10^{-6}, \]

\[ \frac{N_{800}}{N_{\alpha}}=(1.5 \pm 0.4)\cdot 10^{-5}. \]

Introducing, further, an 11% correction for the conversion of the soft X-radiation (Auger effect), the authors\(^9\) finally established, for the relative ionization intensity of the \(K\)-shell of recoil atoms (lead), the value

\[ \frac{N_k}{N_{\alpha}}=(2.2 \pm 0.42)\cdot 10^{-6}, \]

which is approximately 30% higher than the result of earlier measurements\(^8\) and, correspondingly,

\[ \frac{N_k}{N_{800}}=0.15 \pm 0.028. \]

If the ionization of the \(K\)-shell of recoil atoms occurred only because of internal conversion of the 800-keV \(\gamma\)-radiation, then the conversion coefficient of this radiation would be, according to measurements and calculations\(^9\), \(\sim 15\%\).

Independent measurements\(^ {14}\) have shown that the ratio of the conversion coefficients of 800-keV radiation on the \(K\)- and \(L\)-shells is equal to 3.7, and that the total conversion coefficient is less than 5%. Even if, as the value of the total conversion coefficient of the 800-keV radiation, one uses the quantity \(\alpha = 0.067 \pm 0.017\), determined in paper\(^8\), then the conversion coefficient on the \(K\)-shell, \(\alpha_k = 0.053 \pm 0.013\), is still too small to explain completely the ionization probability of the \(K\)-shell by internal conversion alone. Obviously, as the authors\(^9\) concluded, only \(1/3\), or in the best case \(1/2\), of the total number of ionizations of the \(K\)-shell of recoil atoms in the decay of Po\(^{210}\) can be explained by this mechanism. The other, larger part of the ionization of the \(K\)-shell can be explained only by the direct influence of the \(\alpha\)-decay on the state of the electron shell of the recoil atom. The probability of such a process, referred to one \(\alpha\)-decay, is readily calculated if one uses the quantities \(\frac{N_k}{N_{800}}\), \(\frac{N_k}{N_{\alpha}}\), and \(\alpha_k\). It was found to be equal to \((1.4 \pm 0.35)\cdot 10^{-6}\) ionizations per decay.

Migdal\(^1\), considering the influence of \(\alpha\)-decay on the state of the electron shell of the recoil atom, calculated the probability of ionization of inner shells using the methods of perturbation theory. In this treatment the change in the nuclear charge was regarded as a small perturbation, and it was assumed that the \(\alpha\)-particles outside the nucleus move uniformly. A nonrelativistic hydrogen-like function was used to describe the atom.

The probability of ionization of the \(K\)-shell of recoil atoms, calculated in these approximations, proved to be equal to

\[ 2.2\left(\frac{137v_{\alpha}}{Z^2 c}\right)^2, \]

which for the decay of Po\(^{210}\) gives

\(2.6\cdot 10^{-6}\) ionizations per single \(\alpha\)-decay. (\(v_\alpha\) is the velocity of the \(\alpha\)-particle, \(Z\) is the atomic number of the daughter atom.) Despite the fact that the theory gives an overestimated value for the probability of ionization of the \(K\)-shell in \(\alpha\)-decay, the agreement between the conclusions of the theory and the experimental results should be regarded as satisfactory.

Somewhat later, papers \(^{15,16}\) appeared devoted to the study of soft radiation in the decay of \(\mathrm{Po}^{210}\). The authors of paper \(^{15}\), using a scintillation coincidence spectrometer, obtained results that agree with those of paper \(^{9}\).

In paper \(^{16}\) it was shown that the soft radiation observed as early as 1930 in the decay of polonium (with energy \(\sim 10\ \mathrm{keV}\)) is the X-radiation of lead. The study of this radiation was carried out by the method of critical absorption with the use of a proportional counter. Ionization of the \(L\)-shell can be explained only by the direct influence of \(\alpha\)-decay on the state of the electron shell, i.e., by the mechanism considered in Migdal’s paper \(^{1}\). The intensity of the soft \(L\)-radiation observed in paper \(^{16}\), however, proved to be higher than that predicted by the theory.

The papers reviewed are of interest in two respects: as proof of the ionization of the inner shells of recoil atoms as a consequence of \(\alpha\)-decay, and as an interesting example of the application of various methods of atomic and nuclear spectroscopy for detecting and identifying weak radiation against the background of other radiations.

A. R.

CITED LITERATURE

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