THE INFLUENCE OF CHEMICAL STATE ON THE LIFETIME OF A RADIOACTIVE ATOM

Attempts to influence the lifetime of radioactive substances were undertaken for more than 30 years after the discovery of radioactivity. The influence of temperature, pressure, concentration, age, external fields, chemical state, and the external medium on the rate of decay was investigated. However, in none of these cases was it possible to establish reliably a change in the half-life.

Several years ago[^1][^2] it was pointed out that a change in the chemical state of an atom may lead to an appreciable change in the probability of a nuclear transition in the case when the necessary condition for such a transition is the presence of atomic electrons. Such nuclear transitions include the capture of an orbital electron and a nuclear isomeric transition accompanied by the emission of an internal-conversion electron.

Let us consider first the case of electron capture. The decay constant \(\lambda\) in this case is proportional, as is known from the theory of \(\beta\)-decay, to the density of the electron cloud at the site occupied by the nucleus, i.e. \(|\psi(0)|^2\). Thus, a change in the state of the atomic electrons should in principle lead to a change in the decay constant. If, for example, one could completely remove from an atom all its electrons, then such an atom would obviously be unable to decay by capture of an orbital electron. It is practically impossible to realize such a case. However, in light atoms, in which the outer valence electrons have an appreciable density \(|\psi(0)|^2\) in the nucleus, a change in the chemical state may lead to an appreciable change in \(|\psi(0)|^2\) and, consequently, to a change in the decay constant.

To test this possibility, the light isotope Be\(^7\) was used, whose half-life is 52.9 days. Each case of electron capture is accompanied by the emission of a \(\gamma\)-quantum with an energy of 455 keV.

A theoretical calculation shows[^3] that the decay constant of a neutral Be\(^7\) atom should exceed by 2.6% the decay constant of a doubly ionized atom. It is practically very difficult to experiment with Be in the ionized state for any prolonged period of time, and therefore the experiment investigated the change in \(\lambda\) arising when the chemical state of Be\(^7\) is changed.

In all the experiments described below, a differential method was used for measuring the difference in decay periods. The two samples being compared were placed in two identical ionization chambers connected in opposition to one another. From the change in the difference current with time, the relative change in the decay constant \(\Delta\lambda/\lambda\) is determined. For such measurements, the complete absence of other radioactive isotopes in the samples is of particular importance, since even the slightest impurities of these can easily distort the measurement results.

In one of the first experiments^4, the decay constants of metallic Be and BeO were compared. The measurements carried out gave the result

\[ \lambda(\mathrm{Be})-\lambda(\mathrm{BeO})=(1.5\pm0.9)\cdot10^{-4}\lambda(\mathrm{Be}), \]

i.e., a very small effect, which moreover exceeds the standard error by only a factor of 1.7. Therefore, the same authors carried out new measurements^5 with another pair of compounds, namely, with \(\mathrm{BeO}\) and \(\mathrm{BeF}_2\). In this case an unambiguous result was obtained:

\[ \lambda(\mathrm{BeO})-\lambda(\mathrm{BeF}_2)=(0.687\pm0.026)\cdot10^{-3}\lambda(\mathrm{BeO}). \]

Combining the results of both experiments, we obtain

\[ \lambda(\mathrm{Be})-\lambda(\mathrm{BeF}_2)=(0.837\pm0.09)\cdot10^{-3}\lambda(\mathrm{Be}), \]

i.e., an effect \(\Delta\lambda/\lambda\) of the order of \(0.1\%\). A direct measurement of

\[ \frac{\lambda(\mathrm{Be})-\lambda(\mathrm{BeF}_2)}{\lambda(\mathrm{Be})} \]

gave a considerably larger effect^6, namely, \(\Delta\lambda/\lambda=1\%\).

Bainbridge et al.^7 report that they repeated measurements with Be and \(\mathrm{BeF}_2\); the result they obtained \((0.07\%)\) agrees better with the result of Segre and collaborators^4. It is possible that the reason for such large discrepancies \((0.07\%\) and \(1\%)\) lies in differences in the methods of preparing the samples and, in particular, samples of metallic beryllium (see below).

Recently, positive results were also obtained in testing the possibility of an influence of the chemical state on the half-life of a nuclear isomer undergoing internal conversion^7. If the isomeric transition occurs as a result of internal conversion and emission of \(\gamma\)-rays, then, according to theory, the total decay constant corresponding to this transition is

\[ \lambda=\lambda_{\gamma}+\lambda_e=\lambda_{\gamma}(1+\alpha), \]

where \(\lambda_{\gamma}\) characterizes the process of emission of \(\gamma\)-rays, i.e., the probability of a radiative transition, and \(\alpha\) is the internal conversion coefficient (the ratio of the number of conversion electrons to the number of \(\gamma\)-quanta). The additivity of the decay constants means that internal conversion is a certain additional path of de-excitation of the nucleus, competing with the radiative transition^8. It should also be recalled that the presence of the electron shell has very little effect on the number of emitted \(\gamma\)-quanta. Thus, the electron shell increases the total transition probability of the excited nucleus, i.e., \(\lambda\), and consequently a change in the configuration of the atomic electrons by changing the chemical state of the atom may lead to a change in the value of \(\lambda\). Since the chemical state affects above all the electrons of the outer shells, one should expect the greatest effect in the case when precisely these electrons are emitted in internal conversion, i.e., when the energy of the isomeric transition is small.

The experiments were carried out with the isomer \(\mathrm{Tc}^{99*}\), whose transition energy is only \(2\ \mathrm{keV}\), which is sufficient only for the emission of \(M\)- or \(N\)-electrons. The half-life determined from this transition is approximately 6 hours. As a result of electron internal conversion, a \(\gamma\)-quantum with energy \(140\ \mathrm{keV}\) is emitted (the total excitation energy of the nucleus is \(142\ \mathrm{keV}\)). The decay product \(\mathrm{Tc}^{99}\) is a \(\beta\)-emitter and has a half-life of \(9.4\cdot10^5\) years.

The difference in the decay constants of metallic technetium \(\mathrm{Tc}^{99*}\), \(\mathrm{Tc}_2\mathrm{S}_7\), and \(\mathrm{KTcO}_4\) was measured. For the last two compounds, a very clear result was obtained:

\[ \lambda(\mathrm{KTcO}_4)-\lambda(\mathrm{Tc}_2\mathrm{S}_7)=(27\pm1)\cdot10^{-4}\cdot\lambda(\mathrm{Tc}_2\mathrm{S}_7). \]

Comparison of the decay constant of metallic Tc and either of the two indicated compounds proved to be a more difficult task, since the results depend substantially on the method of preparing the sample of pure metal. The authors explain these differences by the mutual diffusion of Tc and the backing metal (Ni or Pt) used in the reduction of technetium; apparently, the decay constant of Tc in its own crystalline lattice differs from the constant for atoms surrounded by atoms different from it. The experiments show that diffusion lowers \(\lambda\).

It is possible that, with a further increase in the accuracy of the method, measurement of the difference in the decay constants of isomers found in various chemical compounds may prove to be a useful means for studying the electronic structure of these compounds.

L. B.

References

1. R. Bouchez, P. Daudel, R. Daudel, R. Muxart, J. phys. et rad. 8, 336 (1947).
2. E. Segre, Phys. Rev. 71, 274 (1947).
3. P. Benoist, Comp. Rend. 228, 309 (1949).
4. E. Segre, C. Wiegand, Phys. Rev. 75, 39 (1949); 81, 284 (1951).
5. R. Leininger, E. Segre, C. Wiegand, Phys. Rev. 76, 897 (1949); 81, 280 (1951).
6. R. Bouchez, P. Daudel, R. Muxart, A. Rogozinski, J. phys. et rad. 10, 201 (1949).
7. K. T. Bainbridge, M. Goldhaber, E. Wilson, Phys. Rev. 90, 4, 430 (1953).
8. I. S. Shapiro, UFN, 40, 189 (1950).