RADIOACTIVE ISOTOPES OF PHOSPHORUS

B. G. Dzantiev and M. B. Neiman

Fifteen years ago, the discovery by I. Curie and F. Joliot of one of the radioactive isotopes of phosphorus marked the beginning of a new field of science—artificial radioactivity. Since then, many works have been published concerning the production, investigation, and application of artificially radioactive elements; a significant part of them has been devoted to radioactive phosphorus.

At present four radioactive isotopes of phosphorus are known: \(P^{29}\), \(P^{30}\), \(P^{32}\), \(P^{34}\).

The exceptional biological and chemical importance of phosphorus has made radiophosphorus one of the most widely used radioactive indicators in biology and chemistry \(^{1,2,3,4,144}\).

In physics, the isotope \(P^{32}\), which emits high-energy electrons in \(\beta\)-decay, has been used \(^{5,6}\) for an experimental verification of the Bethe–Heitler theory. What is important here is that, in the \(\beta\)-decay of \(P^{32}\), the transition occurs directly to the ground level and the \(\beta\)-particles are not accompanied by the emission of \(\gamma\)-quanta.

In the Metallurgical Laboratory \(^{7}\), the threshold reaction for producing radiophosphorus by the action of neutrons on sulfur,

\[ {}^{32}_{16}S(n,p){}^{32}_{15}P, \]

was used for comparing and determining the energy distribution of fast neutrons emitted by various neutron sources.

Recently, Sherrwin \(^{8}\), using \(P^{32}\), obtained yet another experimental confirmation of the existence of the neutrino, having found that in the \(\beta\)-decay of \(P^{32}\) the ratio between the momenta of the electrons and recoil nuclei is such that the law of conservation of momentum is not obeyed.

Along with the increasing use of radiophosphorus in applied problems of biology, chemistry, and physics, the study of the properties of the radioactive isotopes of phosphorus themselves, and of the methods and conditions for obtaining them, continues.

In the present article, for the individual radioactive isotopes of phosphorus we shall consider: a) the nuclear reactions leading to the formation of the given isotope, b) methods of separating radiophosphorus from various

targets; c) the dependence of the yield of radiophosphorus from the target on the energy of the bombarding particles; d) the thermal effects of the reactions and the masses of the isotopes; e) the half-life and f) the β-spectrum.

ISOTOPE P³²

The isotope P³² is the most interesting radioactive isotope of phosphorus from the standpoint of the possibility of its use as a radioactive tracer, and the largest number of studies has been devoted to it. It was first obtained from sulfur and from chlorine by Fermi and co-workers9, 10 in their first experiments on the production of artificially radioactive elements under the action of neutrons.

The mass numbers and concentrations of the stable isotopes of the elements Al, Si, P, S, Cl are such that the formation of P³² in reactions proceeding under the action of \(n\), \(p\), \(d\), \(\alpha\), \(\gamma\) and accompanied by the emission of one or two particles is practically possible in the following six cases:

\[ \begin{aligned} 1.\;&{}^{32}_{16}\mathrm{S}(n,p){}^{32}_{15}\mathrm{P}, \qquad &4.\;&{}^{31}_{15}\mathrm{P}(d,p){}^{32}_{15}\mathrm{P},\\ 2.\;&{}^{35}_{17}\mathrm{Cl}(n,\alpha){}^{32}_{15}\mathrm{P}, \qquad &5.\;&{}^{34}_{16}\mathrm{S}(d,\alpha){}^{32}_{15}\mathrm{P},\\ 3.\;&{}^{31}_{15}\mathrm{P}(n,\gamma){}^{32}_{15}\mathrm{P}, \qquad &6.\;&{}^{29}_{14}\mathrm{Si}(\alpha,p){}^{32}_{15}\mathrm{P}. \end{aligned} \]

All these reactions have in fact been realized. The formation of P³² in the fission of uranium under the action of neutrons does not occur.11 As is known, among the fission products there are no fragments with \(M < 70\).

It is interesting that recently P³² was obtained12 by bombarding spectroscopically pure copper with deuterons of energy 190 MeV in the 184-inch frequency-modulated cyclotron. From the copper subjected to bombardment \(\left({}^{63}_{29}\mathrm{Cu}+{}^{65}_{29}\mathrm{Cu}\right)\), a series of radioactive elements with atomic numbers from 30 to 15 was isolated. Phosphorus P³² is formed as the result of the greatest observed disruption of the copper nucleus, involving the loss (as compared with \({}^{65}_{29}\mathrm{Cu}\)) of 14 protons and 19 neutrons.

REACTION \({}^{32}_{6}\mathrm{S}+{}^{1}_{0}n={}^{32}_{15}\mathrm{P}+{}^{1}_{1}\mathrm{H}\)

As a target in this reaction one may use either sulfur or some sulfur-containing compound, for example, \(\mathrm{H_2SO_4}\), \(\mathrm{Na_2SO_4}\), \(\mathrm{CS_2}\). Elemental sulfur, because of the difficulties of separating from it the radioactive phosphorus formed under the action of neutrons, is used rather rarely13, 14, 15, 16 and chiefly in those cases where the only task is to obtain P³² without separating it from the target.17 An exception is the irradiation of sulfur in a uranium reactor, where 0.5 mC of radiophosphorus is formed per 1 g of S.14

Most often, carbon disulfide \(\mathrm{CS_2}\) is used as the target—a compound with a high concentration of sulfur atoms. High concen-

the concentration of sulfur in carbon disulfide ensures a sufficiently high yield of radiophosphorus, and the physical and chemical properties of this compound have made it possible to develop a number of fairly simple methods for more or less complete separation of P³² from the target. However, despite these advantages, a carbon disulfide target cannot be used in all cases. CS₂ is a very poisonous, volatile \((T_{\text{boil}} = 46^\circ\mathrm{C})\), and extremely fire-hazardous liquid, igniting even from objects heated to \(60^\circ\mathrm{C}\). Under conditions where the use of a carbon disulfide target is for some reason inconvenient, other sulfur-poorer compounds are used—H₂SO₄, Na₂SO₄.

P³² was first obtained by Fermi, Amaldi, and others⁹˒¹⁰ precisely by the reaction under consideration, S³²\((n,p)\)P³², sulfuric acid being used as the target. To H₂SO₄ irradiated with neutrons, after dilution with water, a carrier—sodium phosphoric acid salt—was added, and then the phosphorus was precipitated with ammonium molybdate. Activity with a half-life \(T = 14\) days accompanied the phosphorus into the precipitate and thus was identified as radiophosphorus formed from sulfur by the \((n,p)\) reaction. The formation of P³² under the action of neutrons on sulfur and sulfur-containing compounds was immediately confirmed by Ambrosen¹³, Alikhanov, Alikhanian, and Dzhelepov¹⁸˒¹⁹, and by a number of other authors¹⁴˒¹⁷.

When sulfur is irradiated with fast neutrons, along with the formation of P³² from the isotope S³², the formation of short-lived phosphorus P³⁴ and radiocreamium¹⁴ Si³¹ \((T = 2.8\) hours) from the stable sulfur isotope S³⁴ by the \((n,p)\) and \((n,\alpha)\) reactions is possible. However, this circumstance does not prevent the preparation of P³² in pure form, since, on the one hand, radiocreamium is readily separated chemically from radiophosphorus, and, on the other hand, the large difference in half-lives of P³² and the impurities, and in the concentrations of the initial stable sulfur isotopes \((\mathrm{S}^{32}—95.1\%,\ \mathrm{S}^{34}—4.2\%)^{20}\), ensure, in the main, the production of P³².

Separation of P³² from a carbon disulfide target

The data available in the published literature concerning methods for separating radiophosphorus from neutron-irradiated carbon disulfide may be divided into four groups: 1) separation of radiophosphorus by distillation of carbon disulfide; 2) separation by means of adsorption of P³² on various substances; 3) separation by means of an electric field; 4) chemical methods of separation.

1. The method of concentrating radiophosphorus by distillation of CS₂ is based on the high volatility of carbon disulfide²¹˒²²˒²⁸. At a thermostat temperature of \(50—60^\circ\mathrm{C}\), considerable amounts of CS₂ can be distilled off in a comparatively short time. In this method the point is not the separation of radiophosphorus from the target, but the separation of the entire target from the traces of phosphorus formed. The residue after evaporation

is subjected to chemical treatment in order to convert radiophosphorus into the required chemical state. Some authors \({}^{21}\), before distilling off the carbon disulfide, add traces of white phosphorus to it.

1. The adsorption method of concentrating radiophosphorus was proposed by Roginskii and co-workers \({}^{23}\). They drew attention to the fact that atoms of radioactive phosphorus are well adsorbed on a number of substances, especially at the moment of formation. According to these investigators, about \(30\%\) of the radiophosphorus is adsorbed on the walls of the glass vessel in which the irradiation of carbon disulfide with neutrons is carried out. Good adsorbents for radiophosphorus prove to be glass, manganese dioxide, ferric carbonate, copper foil, asbestos, and filter paper. Table I gives, according to the data of the above-mentioned authors, the adsorption capacities of various substances with respect to radiophosphorus, expressed in relative units.

Table I

Adsorption extraction of radiophosphorus from \(\mathrm{CS}_2\)

Adsorbent	\(A\)	Adsorbent	\(A\)
1. NiO, calcined	37	11. KCl	26
2. NiO, air-dry	76	12. Asbestos	72
3. \(\mathrm{MnO}_2\), air-dry	69	13. Glass, air-dry powder	25—52
4. \(\mathrm{SiO}_2\), air-dry	35—22	14. Zinc dust	16
5. MgO, calcined	57	15. Copper foil, cleaned	31
6. CuO, calcined	0	16. Filtration through the 1st paper filter	30
7. \(\mathrm{Al}_2\mathrm{O}_3\), air-dry	16—18	17. Same through the 2nd	20
8. \(\mathrm{FeCO}_3\), air-dry	73	18. Same through the 3rd	15
9. \(\mathrm{CuCO}_3\), air-dry	70
10. \(\mathrm{BaSO}_4\), air-dry	30

The operation of concentrating \(\mathrm{P}^{32}\) with the aid of an adsorbent consists in shaking the adsorbent powder with carbon disulfide for half a minute, followed by passing the liquid through fast-working filters. To transfer the radiophosphorus back into solution, exchange reactions in an ionogenic medium are used.

The advantages of the adsorption method are the speed and simplicity of the operations; however, here, of course, there is no question of quantitative separation of radiophosphorus.

It is possible that the considerable adsorption effects occurring on the walls of irradiation vessels are partly connected with the phenomenon, observed by a number of authors \({}^{24,25,26,27,28}\), of the precipitation of a weighable residue.

during irradiation of carbon disulfide with (Ra-Be) neutrons. According to Erbacher’s data,^25 the white phosphorus usually contained in carbon disulfide, under the action of $\gamma$-rays emitted by neutron sources, passes into a more stable modification—red phosphorus, insoluble in $\mathrm{CS}_2$. The latter precipitates, adsorbing on its surface up to 90% of the radiophosphorus. By boiling the precipitate with water, the radiophosphorus is almost completely transferred into solution. With prolonged irradiation, the carbon disulfide can be completely freed from white phosphorus.

According to Gowerts,^28 the formation of the precipitate is due to decomposition of carbon disulfide by $\gamma$-rays. According to this author, a black precipitate of the decomposition products of $\mathrm{CS}_2$ is formed even when very pure carbon disulfide is used, whereas a precipitate of red phosphorus is observed in this case only after very prolonged irradiations.

Whatever the nature of the precipitate formed in $\mathrm{CS}_2$, it can, of course, serve as an adsorbent for radiophosphorus and thus be responsible for the depletion of carbon disulfide in activity.

For rapid, nonquantitative separations of $\mathrm{P}^{32}$, besides the adsorption method, absorption of radiophosphorus in the aqueous layer is used. The irradiated carbon disulfide is shaken with a certain amount of water^24,25 or of phosphate solution.^29 After redistribution of the radiophosphorus in the carbon disulfide—water system, the aqueous layer is separated, a carrier is added, and $\mathrm{P}^{32}$ is precipitated.

3. Concentration of radiophosphorus by means of an electric field was proposed by Gowerts.^26,27,28 Copper electrodes are lowered into the vessel in which the irradiation of carbon disulfide takes place; between them a field is produced with a strength from 65 to 165 V/cm. The separation proceeds during irradiation with variation of the field strength over the course of irradiation. From the author’s data on the method it follows that the deposition of radiophosphorus on the electrodes immersed in carbon disulfide proceeds fairly completely. Evaporation and investigation of the residual activity in carbon disulfide that had previously been treated with an electric field show that the residual activity amounts to only 6–8% of the activity deposited on the electrodes. The chemical nature of the electrodes proves essential for complete separation of the radiophosphorus. When aluminum electrodes are used instead of copper ones, part of $\mathrm{P}^{32}$ remains in $\mathrm{CS}_2$. The mode of variation of the field strength with time is also important. The activity is collected chiefly on the anode; the ratio of the activities of the anode and cathode after completion of the process is 1.6–1.8.

Removal of radiophosphorus from the electrodes is achieved by placing them for 1 minute in dilute nitric acid. Boiling with water does not change the activity of the electrodes.

4. The chemical methods of concentrating radiophosphorus are based on operations transferring the product formed in the nuclear reaction

phosphorus into such a chemical state in which it can be separated from carbon disulfide and subsequently converted into a precipitate, i.e., concentrated in a small volume. In those cases when it is necessary to ensure completeness of separation, the technique of a stable carrier is used. Either all the irradiated carbon disulfide or the residue after its evaporation may be subjected to chemical treatment.

Usually attempts are made, by one method or another, to oxidize phosphorus to \(\mathrm{PO_4'''}\), then to separate it from the aqueous layer and precipitate it either with magnesia mixture or with ammonium molybdate. As oxidizing agents, either concentrated nitric acid or elemental bromine is used.

Brezhneva\({}^{29}\) treated irradiated carbon disulfide with concentrated \(\mathrm{HNO_3}\) and, upon subsequent precipitation, obtained preparations with an activity of up to 300,000 counts per minute. Mayer-Leibnitz\({}^{24}\) subjected to nitric-acid treatment a vessel in which carbon disulfide had been irradiated by a 100 mg (Rn-Be) source, and on whose walls a precipitate had formed under the action of \(\gamma\)-rays. The subsequent precipitation was carried out with the addition of inactive phosphate, and a preparation with an activity of 10,000 counts per minute was obtained.

Hall\({}^{30}\) specially investigated the question of the comparative effectiveness of nitric acid at different concentrations and of bromine as oxidants of radiophosphorus in the case of direct action on irradiated carbon disulfide without its preliminary distillation. Extraction of radiophosphorus with 6 \(N\) and 16 \(N\) acid does not give good results. Even after extraction with concentrated nitric acid, considerable quantities of radiophosphorus still remain in the carbon disulfide, which is detected upon subsequent treatment with bromine.

Hall\({}^{30}\) and Das Gupta with co-workers\({}^{31}\) recommend the following method for isolating radiophosphorus: liquid bromine is added dropwise to the neutron-irradiated carbon disulfide until its excess becomes visible from the color. The carrier is added either beforehand in the form of white phosphorus, or after oxidation in the form of phosphate. The resulting radiophosphoric acid, together with the inactive phosphate, is extracted with water.

Alikhanov, Alikhanyan, and Dzhelepov\({}^{19}\), for the purpose of concentrating \(P^{32}\), used the fact that phosphorus forms—immediately after the occurrence of the act of nuclear transformation—chemical compounds with specially added substances. These chemical compounds were subsequently extracted from the carbon disulfide and converted into a form convenient for precipitating radiophosphorus. The method consists in the following: several drops of bromine are added to carbon disulfide before irradiation; the radiophosphorus formed under the action of neutrons enters into combination with the bromine, distributed throughout the entire volume of the carbon disulfide, with the formation of \(\mathrm{PBr_3}\) and \(\mathrm{PBr_5}\). A portion of the radiophosphorus atoms may form in this case a compound not only with bromine, but also with atoms entering into the composition of carbon disulfide. For the decomposition of these

of carbon disulfide compounds after irradiation is treated with a small amount of nitric acid. Then to the irradiated CS₂ is added a carrier, obtained by carefully heating one drop of bromine and 0.2 g of phosphorus with a small amount of carbon disulfide until the color of the bromine disappears. Next, the active and inactive compounds of bromine with phosphorus are hydrolyzed by shaking the irradiated carbon disulfide with a small amount of water and pass into the aqueous layer in the form of H₃PO₄ and H₃PO₃. It turns out that in this process H₃PO₃ is mainly formed, and it is converted into H₃PO₄ by heating with an excess of bromine. The orthophosphoric acid thus obtained is precipitated by the action of ammonium molybdate.

Chemical methods of concentrating radiophosphorus give an especially high percentage of enrichment in those cases when they are applied not to the entire mass of the target, but to the residue obtained after evaporation of the carbon disulfide.

Dependence of the yield of P³² on neutron energy

The nuclear reaction S³²\((n,p)\)P³² is endothermic and does not proceed at just any neutron energy. It is induced only by neutrons possessing sufficiently high energy. The threshold of this reaction, as of any \((n,p)\) reaction leading to the formation of electron-active products, can be estimated without using the values of the masses of the initial and final nuclei, but proceeding only from well-known quantities: the masses of elementary particles and the maximum energy of the β-spectrum of P³².

Indeed, the heat effect of the reaction \(Q\) is equal to

\[ Q = M_{\mathrm{S}^{32}} + M_n - M_{\mathrm{P}^{32}} - M_p, \tag{1} \]

where the masses are expressed in energy units.

From this equality one can eliminate the masses of S³² and P³², since the phosphorus formed in the reaction from sulfur, upon β-decay, is converted again into sulfur, and the β-decay is not accompanied by γ-radiation,

\[ \mathrm{P}^{32} = \mathrm{S}^{32} + \beta^- + \nu . \tag{2} \]

Thus, proceeding from the law of conservation of mass–energy, the difference of the masses P³² and S³² can be written as the sum of the mass of the β-particle and the mass-equivalent energy carried away by the β-particle and the neutrino,

\[ M_{\mathrm{P}^{32}} - M_{\mathrm{S}^{32}} = M_\beta + E_\beta + E_\nu . \tag{3} \]

As is known, the sum \(E_\beta + E_\nu\) is constant and equal to the maximum energy of the β-spectrum \(E_\beta^{\max}\). From (1) and (3), substituting \(E_\beta + E_\nu = E_\beta^{\max}\), we have:

\[ Q = M_n - M_p - M_\beta - E_\beta^{\max}, \tag{4} \]

but

\[ M_p + M_\beta = M_H \]

and, consequently,

\[ Q=(M_n-M_H)-E_\beta^{\max}. \tag{5} \]

Substituting the numerical values\(^{2,32}\) \(M_n=1.00893,\ M_H=1.00812\) mass units and expressing \(\Delta M\) in MeV, we have:

\[ Q=0.75-E_\beta^{\max}. \tag{6} \]

For the case of interest to us, \(E_\beta^{\max}=1.70\ \text{MeV}\), and \(Q=-0.95\ \text{MeV}\).

Practically the same value for the thermal effect of the reaction \(S^{32}(n,p)P^{32}\) was obtained by Huber\(^{33,40}\) directly experimentally by irradiating \(SO_2\), enclosed in an ionization chamber, with monochromatic (D-D) neutrons with \(E_n=2.76\ \text{MeV}\).

Fig. 1. Oscillogram of the registration of the \(S^{32}(n,p)P^{32}\) and \(S^{32}(n,\alpha)Si^{29}\) reactions in an ionization chamber.

Figure 1 presents an oscillogram of pulses corresponding to the charges collected on the electrodes of the ionization chamber in each act of nuclear transformation accompanied by ionization of \(SO_2\) under the action of particles arising in the reaction. Two distinct groups of oscilloscope deflections are visible: large ones, corresponding to the reaction \(S^{32}(n,\alpha)Si^{29}\), accompanied by greater ionization of the gas filling the chamber, and smaller ones, corresponding to the reaction \(S^{32}(n,p)P^{32}\). In Fig. 2, the magnitudes of the oscilloscope deflections are plotted along the abscissa axis, and along the ordinate axis—the number of deflections of a given magnitude. Calibration of the oscilloscope deflections according to the magnitudes of the charges delivered to the electrodes of the ionization chamber, and the previously established ionization energy \(E_i\), equal to \(E_i=35\ \text{eV}\) for each ion pair, make it possible, from the magnitude of the pulse on the oscillogram, to determine the charge on the electrodes, and from the number of ion pairs,

Fig. 2. Distribution curve of oscilloscope deflections by energies during irradiation of sulfur with neutrons.

necessary for the creation of this charge, and from \(E_i\) determine the energy of the ionizing particles arising in the nuclear reaction. All the observed pulses fall into two groups. The first, with a maximum at \(q=8.37\cdot 10^{-15}\) coulombs, corresponds to the reaction \(S^{32}(n,p)P^{32}\); the second to the reaction \(S^{32}(n,\alpha)Si^{29}\). A charge of \(1\cdot 10^{-15}\) coulombs corresponds to an energy of the ionizing particles of \(0.219\) MeV. Thus the \((n,p)\)-maximum corresponds to an energy of the reaction products equal to \(1.83\) MeV. Taking into account \(E_n=2.76\) MeV, the heat effect of the reaction is obtained as \(Q=-0.93\).

The quantity \(E_{\mathrm{thr}}=|Q|\) is the lower limit for the energy of neutrons bombarding sulfur, beginning from which the reaction \(S^{32}(n,p)P^{32}\) is possible in principle. It is clear that in reality the energy threshold of the reaction lies somewhat higher, owing to the fact that, because of the presence of the Coulomb barrier, the proton emitted from the intermediate nucleus has an extremely small probability of leaving it with an energy close to zero. According to quantum-mechanical ideas, this probability increases rapidly with the proton energy. Thus real registration of the reaction and the practical production of radiophosphorus are possible only beginning from some neutron energy \(E_n>0.95\) MeV, at which the proton receives an energy \(E_p=E_n-|Q|\), sufficient to overcome the potential barrier with appreciable probability. It is clear that the real threshold is a quantity considerably less definite than \(E_{\mathrm{thr}}=|Q|\), and depends on the intensity of the source and the method of registering the reaction.

Until recently, data on the real threshold of the reaction \(S^{32}(n,p)P^{32}\) and on its excitation function, i.e. the dependence of the reaction cross section on neutron energy, were of a fragmentary character.

The first experiments on obtaining \(P^{32}\) by neutron bombardment of sulfur were carried out with \((\mathrm{Ra}\!-\!\mathrm{Be})\) and \((\mathrm{Rn}\!-\!\mathrm{Be})\) sources, whose spectra contain neutrons of very high energies. Later Bothe and Harteck \(^{34}\) showed that this reaction also proceeds on \((\mathrm{D}\!-\!\mathrm{D})\)-neutrons with neutron energy about \(E=2.5\) MeV. Amaki and Sugimoto \(^{35}\) investigated the relative yield of \(P^{32}\) when sulfur was irradiated with \((\mathrm{Li}\!-\!\mathrm{D})\)- and \((\mathrm{Be}\!-\!\mathrm{D})\)-neutrons at \(E_D=3\) MeV.

The reaction cross section \(\sigma\) is related to the yield \(N\) by the relation

\[ N=n(1-e^{-C\sigma x}), \tag{7} \]

which for small \(x\) becomes

\[ N=nC\sigma x, \tag{8} \]

where \(n\) is the number of neutrons that have passed through the target, \(C\) is the concentration of atoms participating in the reaction, and \(x\) is the thickness of the target.

The cross section \(\sigma\), generally speaking, depends on the neutron energy and has meaning as applied to monochromatic neutrons. For nonmonochromatic sources some equi-

valent cross sections. Thus, Ardenne\(^4\) gives for (Li–D)-neutrons the value \(\sigma = 0.9 \cdot 10^{-25}\ \text{cm}^2\). Dementii and Timoshuk\(^ {36}\) obtained for (Rn–Be)-neutrons \(\sigma = 1.38 \cdot 10^{-25}\ \text{cm}^2\). The latter value is underestimated, since in the calculation a certain total number of neutrons emitted by the source is taken into account, whereas in the initial part of the spectrum there are neutrons with energy \(E_n < E_{\text{thr}}\), which do not cause the reaction at all.

The absolute values of the cross section of the reaction \(\mathrm{S}^{32}(n,p)\mathrm{P}^{32}\) for monochromatic neutrons were recently published by Klemm and Hanson\(^ {37}\). Using (Li–p)- and (D–D)-neutrons at various \(E_p\) and \(E_D\), they determined the excitation function \(\sigma = f(E_n)\) for \(E_n\) in the interval 1.63–5.8 MeV. The monochromaticity of the neutrons was ensured, in the case of (Li–p)-neutrons, by using a thin target obtained by evaporating metallic lithium onto a tantalum backing, and, in the case of (D–D)-neutrons, by using gaseous deuterium as the target, enclosed in a cell closed with thin nickel foil (except for the points \(E_n = 2.5\) and \(E_n = 2.9\) MeV, obtained with a thick target of heavy ice).

Fig. 3. Schematic representation of the apparatus for determining the flux of neutrons passing through sulfur.

The neutron flux was determined during the irradiation of sulfur by means of the apparatus schematically shown in Fig. 3. The target, made in the form of two disks of fused elemental sulfur, was, during irradiation, enclosed in a cadmium shell and placed on the electrodes of an ionization chamber. On the high-voltage electrode, in addition to the sulfur disk, a metallic foil containing a known uranium deposit was placed under the protection of Cd. The number of neutrons that had passed through the ionization chamber—and at the same time through the sulfur target—was determined from the number of registered uranium fission events that occurred during the irradiation time, taking into account the known mass of uranium and \(\sigma_{\text{fiss.}}\).

The number of \(\mathrm{P}^{32}\) atoms formed in the target was determined by measuring the activity with a Geiger counter and extrapolating it to the moment of completion of irradiation. The activity was measured without chemical separation of radiophosphorus, by counting the \(\beta\)-particles emitted by sulfur cylinders placed on the counter, with wall thickness of 2.5 mm, made from the melted target. The effective counting coefficient

under such a geometry of the β-particle source, was determined in separate experiments. The inaccuracy in determining the counting coefficient, estimated by the authors of the work to be of the order of 15%, is the principal source of error in determining the absolute values of the cross sections.

Table II gives the values of the cross sections of the reaction \( \mathrm{S}^{32}(n,p)\mathrm{P}^{32} \) for various \(E_n\), with an indication of the degree of nonmonochromaticity of the neutrons at each point.

The numerical values of the cross sections were obtained from the experimental data by the formula:

\[ \sigma = I_0 / n\lambda\eta C = 2.69\cdot 10^{-17} I_0/n. \tag{9} \]

Here \(I_0\) is the initial activity of a thick sulfur sample, expressed in pulses per min. gram,

\(n\) is the flux of neutrons passing through \(1\ \mathrm{cm}^2\) of sulfur during the irradiation time,

\(\lambda\) is the decay constant of \(\mathrm{P}^{32}\), equal to \(3.35\cdot 10^{-5}\ \mathrm{min}^{-1}\),

\(\eta\) is the effective counting coefficient, taking into account the geometrical factor and the absorption of electrons in the sample and in the counter wall, \(=0.062\),

\(C\) is the number of \(\mathrm{S}^{32}\) atoms in \(1\ \mathrm{g}\) of sulfur, \(=1.79\cdot 10^{22}\).

The decay of radiophosphorus during the irradiation process is not taken into account, since the duration of irradiation is much smaller than the half-life.

The character of the change in the cross section of the reaction \( \mathrm{S}^{32}(n,p)\mathrm{P}^{32} \) with neutron energy is determined by the probability of penetration of the proton through the Coulomb barrier of the intermediate nucleus. In Fig. 4, the solid curve represents the experimentally determined excitation function, and the dotted curve the energy dependence of the probability of proton penetration through the Coulomb barrier. In the calculations the radius of the sulfur nucleus was taken\(^{38}\) to be

\[ r = 5.6\cdot 10^{-13}\ \mathrm{cm}. \]

The course of both curves coincides.

Table II

Dependence of the cross section of the reaction \( \mathrm{S}^{32}(n,p)\mathrm{P}^{32} \) on neutron energy

Neutron source	\(E_n\) in MeV	\(\Delta E_n\) in MeV	\(\sigma\cdot 10^{25}\ \mathrm{cm}^2\)
Li-p	1.63	\(\pm 0.05\)	0.0131
Li-p	1.83	\(\pm 0.05\)	0.0509
D-D	2.5	\(\pm 0.3\)	0.784
D-D	2.9	\(\pm 0.3\)	1.55
D-D	3.4	\(\pm 0.07\)	2.04
D-D	4.3	\(\pm 0.11\)	3.49
D-D	4.6	\(\pm 0.15\)	2.88
D-D	5.8	\(\pm 0.17\)	3.00

From Fig. 4 two further interesting conclusions can be drawn. Extrapolating the course of the excitation function, one can estimate the actual threshold of the reaction \( \mathrm{S}^{32}(n,p)\mathrm{P}^{32} \). Evidently, it lies near \(E_n = 1.5\ \mathrm{MeV}\).

With neutrons of lower energy, the production of radiophosphorus by this reaction is practically impossible.

The numerical values of the cross sections published in the above-mentioned work agree quite well with the “Taschek data” given in the review devoted to neutron cross sections by Goldsmith, Ibser, and Feld\(^{39}\) *), shown in Fig. 4 by crosses. These data were obtained in the interval \(E_n = 2\text{—}6\ \mathrm{MeV}\); the cross-section values lie somewhat higher than those discussed earlier. It is significant that in both cases, beginning with \(E_n = 4\text{—}4.5\ \mathrm{MeV}\), a slowing of the rapid rise of the curve is recorded; moreover, with further increase of \(E_n\) to \(5\text{—}6\ \mathrm{MeV}\) the cross section tends toward the limiting value \(\sigma = (3 \div 4)\cdot 10^{-25}\ \mathrm{cm}^2\). Indeed, since the height of the Coulomb barrier for a proton in sulfur is \(U = 4.1\ \mathrm{MeV}\), then at \(E_n > U + |Q| \simeq 5\ \mathrm{MeV}\) the probability of proton emission is \(g \simeq 1\), and there is no reason to expect an increase of the cross section with further growth of \(E_n\).

Fig. 4. Excitation function of the reaction \(S^{32}(n,p)P^{32}\): 1 — according to Klem and Hanson, 2 — according to Taschek, 3 — probability of proton penetration through the Coulomb barrier.

Also noteworthy is the circumstance that in both cases at \(E_n = 4.3\ \mathrm{MeV}\) an abnormally high value of the cross section was obtained, which does not fit the rather smooth excitation-function curves. This suggests the existence of a resonance at this value of \(E_n\). The fact that the remaining points fit the smooth curve rather well may be due to the comparatively small number of points taken over a considerable energy interval. In fact it is known\(^{40,41}\) that the interaction of neutrons with sulfur is accompanied by resonance effects.

Bleuer\(^{42}\) convincingly showed that in the range \(E_n = 2\text{—}3.7\ \mathrm{MeV}\) the excitation function of the reaction \(S^{32}(n,p)P^{32}\) has a number of resonance maxima. The reaction yield was measured not at several separate points of this energy interval, but with practically continuous variation of \(E_n\). The latter was achieved not by varying \(E_d\), but by the angular variation of the energy of (D–D) neutrons. Figure 5 shows the arrangement for irradiating the target and for measuring the activity obtained. The target, in the form of a ring of fused elemental sulfur, was placed near the source of (D–D) neutrons in such a way

*) The curve attributed by Goldsmith, Ibser, and Feld to Taschek represents unpublished data of Hanson and Klem.

in such a way that different points of the ring were subjected to the action of neutrons of different energy, monotonically decreasing from \(E_n=3.71\) MeV in the direct beam \((\vartheta=0)\) to \(E_n=1.88\) MeV \((\vartheta=180^\circ)\). The angular nonuniformity in the intensity of the neutron flux was taken into account by means of a certain eccentricity.

Fig. 5. Schematic representation of the arrangement for irradiating a sulfur target and measuring the activity during continuous variation of \(E_n\).

The measurement of the activity of \(P^{32}\) formed upon irradiation was carried out without separating it from the target. The activity was measured with a shielded Geiger counter with a slit 6 mm wide, which “probed” the ring at a number of closely spaced points corresponding to rotation of the ring of diameter 149 mm through an angle \(\Delta\varphi=4.5^\circ\). It turns out that, as \(\varphi\) changes, the activity changes not monotonically, but at certain \(\varphi\) passes through extrema (Fig. 6). The symmetrical arrangement of the extrema relative to the direction of the direct beam indicates that here what is manifested is not some side effect (for example, nonuniformity of the sulfur density along the circumference of the ring), but the resonant character of the change in the yield of radiophosphorus in the reaction \(S^{32}(n,p)P^{32}\).

Fig. 6. Angular variation of the activity of radiophosphorus under monotonic variation \(E_n=E_n(\varphi)\).

In Fig. 7 is presented the variation of the cross section of this reaction with neutron energy, obtained with allowance for the angular dependence of the intensity of the neutron beam. Here only the nature of the dependence is of interest; the numerical values of the cross sections given by the author are not of interest, since no absolute measurements were made either of the neutron flux or of the number of active atoms. The curve passes through maxima at \(E_n=2.39;\ 2.80;\ 3.10;\ 3.46;\ 3.65\text{--}3.7\) MeV, determined with an accuracy of \(\pm 0.05\) MeV. Hence it follows that the energy brought into the sulfur nucleus by neutrons with these values of \(E_n\), and equal to

\[ U=\varepsilon_n+\frac{32}{33}E_n, \]

(where \(e_n\) is the binding energy of the neutron in the nucleus \(S^{33}\)) coincides with the energy of one of the resonant energy levels of the intermediate nucleus \(S^{33}\). The first three values of the resonant \(E_n\) agree well with the old data of Wilhelmy\(^{40}\), who, in experiments with an ionization chamber filled with \(SO_2\) and \(SF_6\) and subjected to irradiation by nonmonochromatic \((\mathrm{Rn}\text{-}\mathrm{Be})\) neutrons, was the first to discover resonance effects in reactions occurring under the action of neutrons.

In the interaction of sulfur with neutrons, alongside the reaction \(S^{32}(n,p)P^{32}\), there occur a number of side processes leading either to scattering or to absorption of neutrons. Numerical values of the cross sections of these side processes and of the total cross section of sulfur for various \(E_n\) can be found in a number of papers\(^{41,44,45}\) and in the reviews of Kondrat’ev\(^{46}\), Goldsmith-Ibser-Feld\(^{39}\), and other authors\(^{47,48}\).

Fig. 7. Resonant character of the excitation function of the reaction \(S^{32}(n,p)P^{32}\).

\[ \text{REACTION } Cl^{35}_{17}+n^{1}_{0}=P^{32}_{15}+H^{4}_{2} \]

The production of \(P^{32}\) by the reaction \(Cl^{35}(n,\alpha)P^{32}\) was first carried out by Fermi, Amaldi, and others\(^{9,10}\), simultaneously with the reaction \(S^{32}(n,p)P^{32}\). Subsequently, Ambrosen\(^{13}\), with the aid of chemical operations and the study of half-life periods and \(\beta\)-spectra, established the identity of the phosphorus activities formed in both reactions.

In the interaction of neutrons with the two stable isotopes of chlorine—\(Cl^{35}\) (75.43%) and \(Cl^{37}\) (24.57%)—alongside radiophosphorus \(P^{32}\), a number of radioactive isotopes of sulfur, chlorine, and phosphorus are formed: \(S^{35}\) (\(T=87.1\) days, \(E_m=0.12\) MeV), \(S^{37}\) (\(T=5.04\) min., \(E_m=4.3\) MeV), \(Cl^{36}\) (\(T>10^3\) years, \(E_m=0.64\) MeV), \(Cl^{34}\) (\(T=33\) min., \(E_m=2.5\) MeV), \(Cl^{38}\) (\(T=37\) min., \(E_m\) up to 5 MeV), \(P^{34}\) (\(T=12.4\) sec., \(E_m=5.1\) MeV). Although the number of side radioactive products formed when neutrons act on chlorine is considerably greater than when neutrons interact with sulfur, in this case as well, owing to the considerable difference between the half-lives of \(P^{32}\) and the side products, the production of radiophosphorus in pure form does not present significant difficulties. The principal side product—the sulfur isotope \(S^{35}\), obtained from \(Cl^{35}\) by the \((n,p)\) reaction and possessing the closest period—is not registered when measuring the activity on

ordinary Geiger counter because of the low energy of the β-particles, which do not penetrate the walls of the counter.

While the production of $\mathrm{P}^{32}$ by the reaction $\mathrm{S}^{32}(n,p)\mathrm{P}^{32}$ has been investigated in detail in a large number of works, the reaction $\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}$ has been studied much less intensively. In some works$^{35,49}$ only the fact of the production of $\mathrm{P}^{32}$ by this reaction is established, on the basis of absorption measurements and determination of $T$ without chemical isolation of the radiophosphorus.

Isolation of $\mathrm{P}^{32}$ and targets

As targets in carrying out the reaction $\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}$, chlorine-containing substances are usually used: carbon tetrachloride$^{19,28}$, $\mathrm{NH}_4\mathrm{Cl}^{9,10}$, $\mathrm{NaCl}^{13}$, $\mathrm{KCl}^{35}$. Elemental chlorine is used only when this reaction is studied in an ionization chamber.

In isolating radiophosphorus from chlorine-containing inorganic salts$^{9,10}$ subjected to neutron irradiation, the latter are dissolved in dilute $\mathrm{HNO}_3$, and from the solution, upon addition of a carrier, the radiophosphorus is chemically transferred into a precipitate. The cationic parts of the corresponding salts must be chosen in such a way that, upon interaction with neutrons, activities with $T$ close to the half-life of $\mathrm{P}^{32}$ do not arise, since in this case the latter, upon adsorption on the precipitate, could contaminate the radiophosphorus.

In the case of a liquid target of carbon tetrachloride, for concentrating $\mathrm{P}^{32}$ in principle all those methods may be used which were described as applied to carbon disulfide. However, from the quantitative standpoint the results obtained in a number of cases are less satisfactory. Thus, according to Gowerts$^{28}$, when radiophosphorus is isolated from neutron-irradiated $\mathrm{CCl}_4$ with the aid of an electric field, only about 50% of the activity formed is deposited on the electrodes. Thus, in this method, as well as in other methods, the conditions of isolation that proved successful in the case of a carbon disulfide target cannot be mechanically transferred to $\mathrm{CCl}_4$. Alikhanov, Alikhanyan, and Dzhelepov$^{19}$ isolated radiophosphorus from $\mathrm{CCl}_4$, as well as from $\mathrm{CS}_2$, using specially formed intermediate chemical compounds, which subsequently underwent hydrolysis. However, in the case of $\mathrm{CCl}_4$, for formation of the intermediate compound in the target before irradiation, not bromine but several milliliters of $\mathrm{CCl}_4$ saturated with chlorine were added. The $\mathrm{P}^{*}\mathrm{Cl}_5$ formed in the course of irradiation, after addition to the $\mathrm{CCl}_4$ of a solution of inactive $\mathrm{PCl}_5$, was hydrolyzed by shaking with water. Phosphoric acid was extracted into the aqueous layer and precipitated with ammonium molybdate.

The chemical inertness of carbon tetrachloride makes it possible, for concentrating $\mathrm{P}^{32}$, also to use methods based on treatment of the target with oxidizing agents, which convert the radiophosphorus into a form convenient for separation from $\mathrm{CCl}_4$ and precipitation.

Dependence of the Yield of P³² on the Neutron Energy

The reaction Cl³⁵$(n,\alpha)$P³², in contrast to S³²$(n,p)$P³², is exothermic. The heat effect of the reaction can be roughly estimated from the masses of $n$, $\alpha$, Cl³⁵, P³², determining the mass of the radioactive isotope P³² from β-decay data. The $Q$ thus calculated, which depends to a considerable extent on the adopted$^{2,3,50}$ mass values of Cl³⁵ and S³², is on the average a quantity of the order of 1 MeV.

More definite information on the heat effect of the reaction Cl³⁵$(n,\alpha)$P³² was obtained by Hibbert, Roughton, and Rose$^{51}$ in experiments with an ionization chamber filled with chlorine and irradiated with monochromatic (D-D) neutrons with $E_n = 2.87$ MeV. The curve obtained by these authors in the coordinates: number of pulses $N$—energy of the ionizing particles produced in the reaction (Fig. 8), contains a number of maxima corresponding to groups of α-particles and protons, which are not always easy to assign to definite reactions. Essential, however, is the fact that no reactions are observed whose products would have an energy exceeding $E = 3.73 \pm 0.30$ MeV

\[ \left( E = \frac{q}{e}\cdot 23.5\ \mathrm{eV}, \right. \]

where $q$ is the charge formed on the electrodes of the ionization chamber, $e$ is the elementary charge, and 23.5 eV is the ionization energy in chlorine). The heat effect of this last reaction must be equal to $Q = E - E_n = 0.86 \pm 0.30$ MeV. Since from equality (6) it follows that the heat effect of the reaction Cl³⁵$(n,p)$S³⁵ is $Q = 0.63$ MeV, $Q = 0.86 \pm 0.30$ MeV must be assigned to the reaction Cl³⁵$(n,\alpha)$P³². Although in an ionization chamber in principle two more reactions can be detected—Cl³⁷$(n,p)$S³⁷ and Cl³⁷$(n,\alpha)$P³⁴—it is known$^{52,53}$ that they occur only under the action of high-energy neutrons and, evidently, are endothermic. Thus it may be considered established that the reaction Cl³⁵$(n,\alpha)$P³² is exothermic, with heat effect $Q = 0.86 \pm 0.30$ MeV.

Fig. 8. Limiting energy of ionizing particles produced in the reaction of chlorine with neutrons with $E_n = 2.87$ MeV.

A positive heat effect, however, does not mean that the production of radiophosphorus by the reaction Cl³⁵$(n,\alpha)$P³² is possible under the action of slow neutrons. The relatively high potential

the chlorine barrier for $\alpha$-particles, equal to $U=9.6\ \mathrm{MeV}$, makes the $(n,\alpha)$ reaction very unlikely under the action of slow neutrons. These considerations are confirmed by direct experiments$^{51}$. Two NaCl cylinders, one of which was shielded with cadmium, placed in a paraffin block symmetrically with respect to an (Ra–Be) source, after prolonged irradiation show the same activity with $T=14$ days. It follows from this that the reaction $\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}$ does not proceed to any noticeable degree on slow neutrons. It is interesting that the accompanying reaction $\mathrm{Cl}^{35}(n,p)\mathrm{S}^{35}$ with $Q=0.63\ \mathrm{MeV}$ proceeds on thermal neutrons, despite the presence of the Coulomb barrier, and is one of the few $(n,p)$ reactions that can occur in this way.

Just as the threshold endothermic reaction $\mathrm{S}^{32}(n,p)\mathrm{P}^{32}$ actually occurs not at $E_{\mathrm{thr}}=|Q|$, but at somewhat higher neutron energies, so the thresholdless exothermic reaction $\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}$, although in principle possible at $E_n=0$, occurs to a noticeable degree only beginning with some rather considerable values of $E_n$. In this sense the reaction $\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}$ represents an entire group of exothermic $(n,\alpha)$ reactions. It is known$^{41}$, for example, that in the case of nearby sulfur the reaction $\mathrm{S}^{32}(n,\alpha)\mathrm{Si}^{29}$, possessing a positive thermal effect $Q=1.16\ \mathrm{MeV}$, does not proceed in measurable amounts on slow neutrons.

Fig. 9. Energy distribution of particles formed in the reaction of chlorine with neutrons (according to Nemilov).

$N$ — number of revolutions per minute; $E$ — minimum energy of ionizing particles at which the mechanical relay is brought into action.

It is of interest to try to estimate the real threshold of the reaction $\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}$ or, in any case, to indicate the minimum value of $E_n$ for which the presence of the reaction was recorded. Nemilov$^{54}$, irradiating an ionization chamber filled with chlorine with neutrons from a nonmonochromatic (Rn–Be) source, found two monochromatic groups of ionizing particles with

\[ E=1.6\ \mathrm{MeV} \]

and $E=2.7\ \mathrm{MeV}$, the first group being more intense than the second (Fig. 9). If both groups in fact belong to one reaction $\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}$ and if the group of particles with $E=1.6\ \mathrm{MeV}$ does not owe its origin to the fact that the nucleus $\mathrm{P}^{32}$ after the reaction remains in an excited state with $E_{\mathrm{exc}}=1.1\ \mathrm{MeV}$, then, taking into account

\(Q = 0.86 \pm 0.30\) MeV, particles with \(E = 1.6\) MeV should correspond to neutrons with energy about \(E_n = 0.75 \pm 0.30\) MeV. Thus, under the assumptions made, the reaction \(\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}\) should occur under the action of neutrons with energies of the order of \(0.5\)–\(1\) MeV. Moreover, in this case it follows from Nemilov’s data that the reaction \(\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}\), like the reaction \(\mathrm{S}^{32}(n,p)\mathrm{P}^{32}\), is accompanied by resonance effects and the intermediate nucleus \(\mathrm{Cl}^{36}\) has resonance levels corresponding to neutron energies of about \(E_n = 0.75\) MeV and \(E_n = 1.85\) MeV.

Numerical values of cross sections for monochromatic neutrons for the reaction \(\mathrm{Cl}^{35}(n,\alpha)\mathrm{P}^{32}\) are unknown. In the case of nonmonochromatic neutrons Amaki and Sugimoto \(^{35}\) investigated the relative yields of radiophosphorus under the action on KCl of (Li-D)- and (Be-D)-neutrons, while Dementii and Timoshuk \(^{36}\) give for (Rn-Be)-neutrons the value \(\sigma = 2.2 \cdot 10^{-26}\ \text{cm}^2\) (calculated per the total number of neutrons emitted by the source, as determined by manganese).

REACTION \(\mathrm{P}^{31}_{15} + n^{1}_{0} = \mathrm{P}^{32}_{15} + \gamma\)

This reaction was first carried out by Preiswerk and Halban \(^{55}\) upon irradiation of phosphorus surrounded by paraffin with (Rn-Be)-neutrons. In this case, in addition to the previously known \(^{9,10}\) short periods belonging to \(\mathrm{Al}^{28}\) (\(T = 2.4\) min.) and \(\mathrm{Si}^{31}\) (\(T = 2.8\) hours)—products of \((n,\alpha)\)- and \((n,p)\)-reactions—an activity with \(T = 15\) days was found, which was attributed to the radiative neutron-capture reaction \(\mathrm{P}^{31}(n,\gamma)\mathrm{P}^{32}\). Since phosphorus has only one stable isotope, \(\mathrm{P}^{31}\), irradiation of it with slow neutrons alone gives radiophosphorus without any accompanying reactions.

Isolation of \(\mathrm{P}^{32}\) from the target

The target in this case may be elemental phosphorus, phosphoric acid, and inorganic \(^{56}\) and organic \(^{24,57}\) phosphates, both in the solid state and in solutions.

Since the initial isotope and the isotope formed are chemically identical, in choosing a target one must proceed from the requirement that it be possible, for concentrating radiophosphorus, to apply the Szilard–Chalmers method \(^{58}\). With an appropriate choice of the target substance, separation of the radioactive isotope of phosphorus from the stable one proves possible owing to a change in the valence and chemical behavior of \(\mathrm{P}^{32}\) as a result of recoil upon emission of a \(\gamma\)-quantum. The latter leads to the ejection of the phosphorus atom that has undergone radiative neutron capture from the molecule of the substance forming the target, and thus all radioactive phosphorus atoms turn out to be

in a different chemical state than the atoms of stable phosphorus, which is used for isotope separation.

Erbacher and Philipp^57 used as the target an organic derivative of phosphorus—triphenyl phosphate. The radiophosphorus formed as a result of the reaction is in the ionic form \(P^{+5}\) and is separated from the organic target by shaking with water or with activated carbon. According to the authors of the method, in both cases about 40% of the activity is extracted. The radiophosphorus adsorbed on the carbon is transferred into an aqueous solution by boiling the carbon with water, with about 70% of the activity contained in the carbon being desorbed. The completeness of the isolation of radiophosphorus according to Erbacher and Philipp depends substantially on the thoroughness with which the triphenyl phosphate and the water used for extraction have been purified from extraneous ionic impurities. Therefore they recommend a special method for purifying \((C_6H_5)_3PO_4\) and consider it necessary, before extraction, to subject the water to successive distillations over \(KMnO_4\), \(Ba(OH)_2\), \(H_2SO_4\), and to introduce the activated carbon into the flask with the irradiated triphenyl phosphate while passing nitrogen.

Yield of \(P^{32}\) in the reaction \(P^{31}(n,\gamma)P^{32}\)

Up to a certain limit the yield of radiophosphorus in the reaction \(P^{31}(n,\gamma)P^{32}\) can be increased by improving the conditions for slowing down the neutrons emitted by ordinary sources. For this purpose a target in the form of a benzene solution of triphenyl phosphate^24 may be used, but this does not eliminate the necessity of using water or paraffin.

The numerical values of the cross section of the reaction \(P^{31}(n,\gamma)P^{32}\) for thermal neutrons, according to data of various authors,4, 59, 60, 61, 62 lie mainly between \(\sigma = 0.15 \cdot 10^{-24}\ \text{cm}^2\) and \(\sigma = 0.3 \cdot 10^{-24}\ \text{cm}^2\). In measurements on a reactor^63 using an intense flux of thermal neutrons, \(\sigma = 0.23 \cdot 10^{-24}\ \text{cm}^2\) was obtained, with a probable error of \(\pm 20\%\).

REACTION \(P^{31}_{15} + H^2_1 = P^{32}_{15} + H^1_1\)

Newson^64,65, on irradiating phosphorus with deuterons of \(E_D = 3\) MeV, observed the appearance of an activity with \(T = 14.5\) days. By chemical methods it was shown that this activity was associated with phosphorus and, on the basis of magnetic and absorption measurements, was assigned to the known isotope \(P^{32}\), formed in this case by the reaction \(P^{31}(d,p)P^{32}\).

The accompanying reactions—\((d,n)\) and \((d,\alpha)\)—lead to stable isotopes \(S^{32}\) and \(Si^{29}\). Since the formation of \(P^{30}\) by the reaction \((d,H^3)\) was not detected,^65 it follows that the production of radiophosphorus \(P^{32}\) by the reaction \(P^{31}(d,p)P^{32}\) is not accompanied by the formation of side activities.

Separation of P³² from the Target

Since, in contrast to the preceding reactions, in the present case the formation of radiophosphorus takes place under the action of charged particles, the yield of P³² increases with increasing target thickness only up to a certain limit. Therefore the use of a large-volume target in this method of obtaining radiophosphorus is not rational, and consequently the question of concentrating P³² is less acute in this case. However, the question of the choice of target material here is nevertheless important, owing to the fact that the slowing down of deuterons, occurring in a relatively thin layer, leads to fairly considerable heating of the target. The elementary red phosphorus usually used as targets ^{6,66,67,68} and phosphorus pentoxide ^{69,70} are readily volatilized on heating and require cooling with liquid air or the use of special devices ^{141}. In addition, they are hygroscopic. Metal phosphides, in particular iron phosphide ^{71,142}, are more heat-resistant, but they are very hygroscopic and deliquesce in air. Phosphates are more stable, but most of them have a low percentage phosphorus content.

Hall and Williams ^{30,72} recommend using calcium metaphosphate, $\mathrm{Ca(PO_3)_2}$, as the target—a stable substance with a fairly high phosphorus content. Calcium metaphosphate can be obtained by igniting monocalcium phosphate, $\mathrm{Ca(H_2PO_4)_2}$. The resulting hard, brittle product is converted into powder, placed on platinum foil, and fused with an oxygen burner. To avoid losses of phosphorus, excessive heating of the metaphosphate should be avoided. The molten salt, on cooling, solidifies without crystallization and adheres well to the surface of the platinum. Since fused calcium metaphosphate is sparingly soluble, the target prepared in this way, after irradiation with deuterons, is fused with soda and then dissolved in $0.5\,N$ nitric acid. If it is necessary to obtain pure radiophosphoric acid, the calcium is removed by precipitating the phosphate with $\mathrm{Bi(NO_3)_2}$, followed by removal of the bismuth by passing hydrogen sulfide.

Yield of P³² in the Reaction

The yield of P³² from a thick target, i.e. under the condition that the target thickness exceeds the range of deuterons in the target material, is, for deuterons with $E_D = 8\,\mathrm{MeV}$ ^4, 1 atom of P³² per $2.8 \cdot 10^3$ deuterons; for deuterons with $E_D = 14\,\mathrm{MeV}$ ^{73}, $8.5$ rutherford/µA (1 rutherford $= 10^6$ β-decays per second), i.e. 1 atom of P³² per $1.5 \cdot 10^3$ deuterons. The reaction is exothermic, with a thermal effect of about 6 MeV.

REACTION \({}_{16}^{34}\mathrm{S}+{}_{1}^{2}\mathrm{H}={}_{15}^{32}\mathrm{P}+{}_{2}^{4}\mathrm{He}\)

As Segrè\(^{14}\) showed, the radioactive isotope \(\mathrm{P}^{32}\) is formed upon irradiation with deuterons not only of phosphorus, but also of sulfur. The initial isotope in this case is the low-abundance \(\mathrm{S}^{34}\) (4.2%), and the formation of radiophosphorus is due to the reaction \(\mathrm{S}^{34}(d,\alpha)\mathrm{P}^{32}\). This reaction is of no practical interest for obtaining radiophosphorus owing to its small yield. The latter is due both to the low abundance of the initial isotope and to the presence of a Coulomb barrier for both the deuteron and the \(\alpha\)-particle.

The secondary radioactive products formed upon irradiation of sulfur with deuterons are \(\mathrm{P}^{30}\), \(\mathrm{S}^{35}\), \(\mathrm{Cl}^{34}\).

REACTION \({}_{14}^{29}\mathrm{Si}+{}_{2}^{4}\mathrm{He}={}_{15}^{32}\mathrm{P}+{}_{1}^{1}\mathrm{H}\)

Fahlenbrach\(^{74,75}\) discovered yet another reaction leading to the formation of radiophosphorus \(\mathrm{P}^{32}\). With prolonged irradiation of silicon powder by \(\alpha\)-particles from a Th (B + C) source, a slight activity is obtained which, by its period \(T=14\) days and by the results of absorption measurements, is identical with \(\mathrm{P}^{32}\). This reaction was also carried out with \(\alpha\)-particles of \(E_{\alpha}=16\ \mathrm{MeV}\) in the irradiation of quartz in a cyclotron\(^{76}\). The initial product in this case is \(\mathrm{Si}^{29}\) (6.2%), and the formation of \(\mathrm{P}^{32}\) proceeds by the reaction \(\mathrm{Si}^{29}(\alpha,p)\mathrm{P}^{32}\). This reaction, like the preceding one, cannot serve as a practical source for obtaining radiophosphorus.

Along with \(\mathrm{P}^{32}\), irradiation of silicon with \(\alpha\)-particles produces the short-lived radioactive sulfur \(\mathrm{S}^{31}\).

HALF-LIFE OF \(\mathrm{P}^{32}\)

The half-life of \(\mathrm{P}^{32}\) has been determined many times, both in connection with studies of other characteristics of radiophosphorus\(^{10,13,14,21,37,55,75}\), and in works undertaken specifically\(^{17,77,78,79}\) to determine the exact value of \(T\). In connection with the ever-increasing use of radiophosphorus \(\mathrm{P}^{32}\) as an indicator in various fields of science, an exact determination of its half-life is of substantial importance.

The data of various authors lie within the limits \(T=14\text{–}18\) days. The accuracy of determining the half-life is determined by the intensity of the source and the duration of the measurement. The most accurate value is considered to be that obtained by Cassianout\(^{78}\), equal, in days, to \(T=14.295\pm2\%\). A number of authors\(^{19,21,37,77}\) indicate close values of the period, lying within \(T=14.3\text{–}14.5\) days. Values of the order of \(T=15\text{–}18\) days were all obtained\(^{13,17,55,77}\) with low-intensity sources and are considerably overestimated. Values \(T<14.3\) days in most cases were also obtained with sources of insignificant inten-

exceptions are the measurements of Mulder, Hoeksema, and Sizoo,^79 carried out with a highly active source. They were undertaken with the special purpose of determining the exact value of \(T\) and were performed on 10 samples with measurement durations from 2 to 6 months. The data, obtained by three different measurement methods and treated by the method of least squares, give on average \(T = 14.07 \pm 0.01\) days.

\(\beta\)-DECAY OF \(P^{32}\)

In the radioactive decay of \(P^{32}\), electrons are emitted with transition directly to the ground state of \(S^{32}\).

\[ P^{32} \longrightarrow S^{32} + \beta^{-}. \]

Thus the \(\beta\)-decay of radiophosphorus is not accompanied by the emission of \(\gamma\)-quanta.^10,13,66 This circumstance determines the simple form of the \(\beta\)-spectrum of \(P^{32}\).

A considerable number of works have been devoted to the study of the \(\beta\)-spectrum of \(P^{32}\), undertaken partly for the purpose of studying the properties of radiophosphorus, and partly for testing various theories of \(\beta\)-decay. Various techniques were used: absorption measurements with aluminum absorbers,^6,10,15,21,65,80 measurements in a Wilson chamber with a magnetic field,^13,66,68 measurements by means of a magnetic spectrometer.^18,19,67,70,71,81,82,83,84,85,146

The maximum energy of the \(\beta\)-spectrum, \(E_m\), determined by various methods, lies within the limits \(E_m = 1.6—2\) MeV. Most of the data lie near 1.71—1.72 MeV.

The results of absorption measurements in aluminum give, for the most part, the thickness of the absorbing layer \(R_m = 0.77—0.78\ \mathrm{g/cm^2}\) (2.85—2.9 mm), which, when converted by Fezer’s formula^86

\[ R_m = 0.543 E_m - 0.160 \tag{10} \]

corresponds to \(E_m = 1.71—1.72\) MeV. Lower values of \(E_m\), indicated by some authors, are often connected simply with the use of other variants of Fezer’s formula for converting experimental data.^21 Figure 10 presents a typical absorption curve for \(\beta\)-rays emitted by \(P^{32}\) in aluminum. Exponential absorption is established^6,15 at \(R > 0.4—\)

Fig. 10. Absorption of \(\beta\)-rays of \(P^{32}\) in aluminum.

0.5 g/cm² Al. Starting with these values of \(R\), the absorption coefficient is constant and equal to \(41\ \mathrm{cm}^{-1}\).

Measurements of the \(\beta\)-spectrum of \(\mathrm{P}^{32}\) in a Wilson chamber were carried out with preparations of low activity and give overestimated values of \(E_m\).

Numerous results of measurements with \(\beta\)-spectrometers, as in the case of absorption measurements, are grouped, as a rule, around the values \(E_m = 1.71\text{–}1.72\ \mathrm{MeV}\), with small deviations to one side or the other. The most recent data, belonging to Ziegban\(^{70,85}\), were obtained with a very thin and active source. The limit of the \(\beta\)-spectrum determined in these measurements is

\[ E_m = 1.712 \pm 0.008\ \mathrm{MeV}. \]

The \(\beta\)-spectrum obtained by Ziegban is shown in Fig. 11.

Fig. 11. \(\beta\)-spectrum of \(\mathrm{P}^{32}\).

Comparison of the experimentally obtained \(\beta\)-spectrum of \(\mathrm{P}^{32}\) with the theories of \(\beta\)-decay of Fermi and of Konopinski–Uhlenbeck, by means of F. Curie’s construction\(^{66}\), shows in all cases, except for the Wilson-chamber measurements, a divergence of the experimental data from the Konopinski–Uhlenbeck theory, which systematically gives overestimated values of \(E_m\). Fermi’s theory in all cases agrees satisfactorily with the experimental data in the region of high energies of the \(\beta\)-particles. The boundary at which the experimental points begin to diverge from the straight-line Fermi plot on passing to lower electron energies depends substantially on the thickness of the source and the character of the backing. As the thickness of the source is decreased, it moves farther and farther toward low energies.

Lawson\(^{71,82}\), using a specimen with density \(3\ \mathrm{mg/cm^2}\), obtained agreement with Fermi’s theory over a considerable region of the \(\beta\)-spectrum. Ziegban\(^{85}\) experimented with a very thin source consisting of a radiophosphorus salt weighing about \(0.1\ \mathrm{mg}\), deposited on foil of thickness \(\sim 0.1\) micron and diameter \(2\ \mathrm{cm}\), which was fastened on an ebonite ring. In this case, when scattering in the source and in the backing had been eliminated as far as possible, agreement with Fermi’s theory was obtained down to \(E = 0.1\ \mathrm{MeV}\).

Figure 12 presents a Fermi plot constructed from Ziegban’s experimental data in F. Curie coordinates. Along the abscissa is plotted the energy of the \(\beta\)-particles \(E\) in units of \(mc^2\). Along the ordinate is plotted the quantity \((N/f)^{1/2}\), where \(N\) is the number of \(\beta\)-particles in the given interval of momenta, \(f\) is a function of the nuclear charge \(Z\) and of the momentum of the \(\beta\)-particle \(\eta\), expressed in units \(mc\), \(f = f(Z,\eta)\).

For \(Z<29\) the function has the form

\[ f(Z,\eta)=\frac{\eta^2\,2\pi y}{1-e^{-2\pi y}}, \tag{11} \]

where

\[ y=\frac{Z(1+\eta^2)^{1/2}}{137\eta}. \tag{12} \]

According to the existing theories, the experimental data should lie on a straight line:

\[ a(N/f)^{1/k}=C-(E+1). \tag{13} \]

In Fermi’s theory \(k=2\), and in Konopinski–Uhlenbeck’s theory \(k=4\). Conversion from the experimentally determined quantity \(H\rho\) \([\text{oersted}\cdot\text{cm}]\) to \(E\) (MeV) and \(\eta(mc)\) is carried out for \(\beta\)-particles by means of the relations

Fig. 12. Fermi plot for the \(\beta\)-spectrum of \(P^{33}\).

\[ H\rho=\frac{1}{3}\cdot 10^4\,[E(E+1.02)]^{1/2}, \tag{14} \]

\[ \eta=H\rho/1700. \tag{15} \]

As is seen from Fig. 12, the experimental data lie on a straight line in the coordinates \((N/f)^{1/2}\) and \((E+1)\) for almost all values of the electron energy. It seems probable that, under limiting conditions, a straight line should be obtained over the entire extent of the spectrum.

Despite the fact that the \(\beta\)-decay of \(P^{33}\) is not accompanied by the emission of nuclear \(\gamma\)-quanta, in absorption measurements—even with radiophosphorus subjected to the most careful purification—after complete absorption of the \(\beta\)-particles, a slight penetrating radiat-

tion 5, 6, 15 (see Fig. 10). The latter is due to the braking of electrons in the source and absorber.

It is interesting that a number of investigators have observed in the radiation of radiophosphorus, alongside electrons, a certain number of positrons. The presence of the latter, as well as of $\gamma$-quanta, has recently been associated with secondary effects caused by the passage of electrons through matter. This phenomenon was first noted by Ambrosen$^{13}$, who, in investigating the $\beta$-spectrum of $P^{32}$ with the aid of a Wilson chamber, found, among 200 electron tracks, 4 positron tracks. In subsequent investigations$^{87,88,89,90,91}$ the ratio $\beta^+/\beta^-$ varies within the limits $10^{-2} — 10^{-3}$. The energy of the positrons is, as a rule, less than $E_m - 2mc^2 = 0.69$ MeV. ($E_m = 1.71$ is the maximum energy of the electrons of $P^{32}$, $2mc^2 = 1.02$ MeV is the energy equivalent to the rest mass of a pair of light particles.) In individual cases, however, it reaches 0.9 MeV.

The mass of the radioactive isotope $P^{32}$ can be calculated from experimental data either on $\beta$-decay or from the determination of the thermal effects of reactions leading to the formation of $P^{32}$. In both cases the accuracy of the calculation of the mass of radiophosphorus is determined not only by the reliability of the experimental data, but also by how accurately the masses of the elementary particles and of the stable isotopes $S^{32}$, $Cl^{35}$, $P^{31}$ are known. The latter are known with insufficient accuracy, and data concerning the masses of stable isotopes often undergo substantial changes. Therefore the known values of the mass of $P^{32}$, obtained from various data$^{3,50,92,93}$, range from 31.9827 to 31.98437. If one starts from the last known value of the mass of $S^{32}$—31.98089—and from the thermal effect of the reaction $S^{32}(n,p)P^{32}$, $Q=-0.93$ MeV, then the mass of $P^{32}$ is obtained as 31.98269 mass units.

ISOTOPE $P^{30}$

Radiophosphorus $P^{30}$ is one of the “oldest” artificially radioactive isotopes. For a number of years it has served as an object of study for a number of investigators.

$P^{30}$ is a positron-active isotope with a half-life $t' = 2.5$ minutes, which is obtained from Al, Si, P, S by the following reactions:

\[ \begin{array}{ll} 1.\ \mathrm{Al}^{27}_{13}(\alpha,n)\mathrm{P}^{30}_{15}, & 5.\ \mathrm{P}^{31}_{15}(n,2n)\mathrm{P}^{30}_{15},\\ 2.\ \mathrm{Si}^{30}_{14}(p,n)\mathrm{P}^{30}_{15}, & 6.\ \mathrm{P}^{13}_{15}(\gamma,n)\mathrm{P}^{30}_{15},\\ 3.\ \mathrm{Si}^{29}_{14}(d,n)\mathrm{P}^{30}_{15}, & 7.\ \mathrm{S}^{32}_{16}(d,\alpha)\mathrm{P}^{30}_{15},\\ 4.\ \mathrm{Si}^{28}_{14}(\mathrm{He}^{3}_{2},p)\mathrm{P}^{30}_{15}, & 8.\ \mathrm{S}^{32}_{16}(n,2np)\mathrm{P}^{30}_{15}. \end{array} \]

These reactions exhaust all the routes to the production of $P^{30}$ that have been realized up to the present time.

Radioactive Isotopes of Phosphorus

Reaction \( \mathrm{Al}^{27}_{13} + \mathrm{He}^{4}_{2} = \mathrm{P}^{30}_{15} + \mathrm{n}^{1}_{0} \)

Soon after it had been discovered that, when aluminum is irradiated with alpha particles, it emits neutrons \(^{94,95}\), I. Curie and

a

б                         в

Fig. 13. Wilson-chamber photographs of the radioactive decay of \( \mathrm{P}^{32} \). The first photographic registration of artificial radioactivity: a) the picture was taken during irradiation of an aluminum cylinder by \(\alpha\)-particles; б) the picture was taken five seconds after removal of the \(\alpha\)-particle source; в) the picture was taken 9 minutes after removal of the \(\alpha\)-particle source.

F. Joliot showed that, along with the emission of neutrons, the emission of positrons also takes place. The latter, in contrast to neu-

tron radiation, does not cease with the removal of the source of α-particles, but continues for some time, decreasing with a period of about 3 minutes[^96]. It was shown chemically that the carrier of the positron activity is phosphorus: when irradiated aluminum is dissolved in HCl, the activity volatilizes with hydrogen (PH₃), and when phosphorus is precipitated it is concentrated in the phosphorus precipitate[^97],[^98]. Thus the presence of the nuclear reaction \(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\) was established, which at the same time meant the discovery of the phenomenon of artificial radioactivity.

Figure 13 presents the first Wilson-chamber photographs of the β-decay of artificially radioactive phosphorus, made by L. Meitner[^99] immediately after the discovery of artificial radioactivity. Photograph a was taken during the irradiation of an aluminum cylinder with Po α-particles. Tracks are visible of protons due to the reaction \(\mathrm{Al}^{27}(\alpha,p)\mathrm{Si}^{30}\), of electrons (from the γ-rays of polonium), and of positrons. Photograph b was taken 5 seconds after removal of the α-particle source. In it only tracks of positrons are visible, indicating radioactive decay:

\[ \mathrm{P}^{30}_{15} \to \mathrm{Si}^{30}_{14} + \beta^{+}. \]

Photograph v was taken 9 minutes after removal of the polonium preparation, and even in it a positron track is still visible. These photographs at the time vividly demonstrated the fact of radioactive decay of an artificially produced isotope.

Dependence of the yield of \(\mathrm{P}^{30}\) on the energy of α-particles.

The yield of \(\mathrm{P}^{30}\) in the reaction \(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\) depends substantially on the energy of the α-particles \(E_\alpha\)[^100],[^101],[^102]. When \(E_\alpha\) is varied in the narrow interval 5.5–7 MeV, it increases by a factor of 15. Table III gives

Table III

Dependence of the yield of \(\mathrm{P}^{30}\) on \(E_\alpha\) in the reaction \(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\)

\(E_\alpha\), MeV . . . . . .	4.20	4.81	5.49	6.33	6.66	7.06	7.61	8.25
\(q(E_\alpha)\cdot 10^7\) . . . . .	0	0.02	0.13	0.7	1.1	2.0	4.7	6.4

the data of Ellis and Henderson, characterizing the dependence of the yield of \(\mathrm{P}^{30}\), in atoms per one α-particle, on the energy of the α-particles in MeV. These data were obtained with a thick target and therefore characterize the integral effect. The increase in yield with the growth of \(E_\alpha\) is associated both with a change in the reaction cross section and with an increase, as the range of the α-particles grows, in the number of target atoms interacting with the α-particles. According to other data[^103],[^104], the yield of the reaction reaches \(n/\alpha = 10^{-5}\).

It is of interest to determine the reaction threshold. The experimental estimate of this quantity depends on the intensity of the source;

RADIOACTIVE ISOTOPES OF PHOSPHORUS

of $\alpha$-particles and on the character of the registration of the reaction. According to data from various laboratories it lies in the range $E_\alpha = 3.2—4.5\ \text{MeV}$[^105][^106][^107][^108][^109].

It has been shown many times that, with a further monotonic increase of $E_\alpha$, the probability of the reaction grows in a stepwise manner. The process $\mathrm{Al}(\alpha,n)\mathrm{P}$ has a clearly expressed resonance character. This was first discovered by Fahlenbrach[^110], who, by varying with aluminum-foil screens the energy of $\alpha$-particles emitted by natural sources, found three maxima on the excitation curve. Subsequently, resonance maxima were observed by a number of authors[^106][^107][^108][^111] in experiments with both thin and thick targets. The positions of the resonance maxima found in different works agree well with one another. In a number of cases the obtaining of a clearly expressed phenomenon of resonance is hampered by the insufficient monochromaticity of the $\alpha$-particles. In these cases the resonance character of the reaction is revealed only upon differentiating the integral excitation curve.

Fünfer[^112], paying special attention to the production of monochromatic $\alpha$-particles, in experiments with a thick target found 13 clearly expressed resonance peaks on the excitation curve of the reaction $\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}$. In these experiments the course of the reaction was detected not by the positron activity of $\mathrm{P}^{30}$, but by the neutrons formed in the reaction. The latter were slowed down by paraffin and registered by proportional counters equipped with boron screens. The device for irradiating aluminum and determining the reaction yield is schematically shown in Fig. 14. At the center of a brass sphere, coated on the inside with a layer of aluminum $\delta = 50\ \mu$ and surrounded on the outside by lead, there is placed a polished platinum ball whose surface is activated by thorium emanation. The neutrons formed in the reaction, after leaving the aluminum, are slowed in the paraffin surrounding the apparatus to thermal velocities and are recorded by the counters. Variation of the energy of the $\alpha$-particles interacting with the aluminum is achieved by changing the pressure of $\mathrm{CO}_2$ inside the brass sphere. With such a method of varying $E_\alpha$ it proves possible to separate maxima lying very close together, investigating the reaction yield at intervals of
$\Delta E_\alpha = 70\ \text{keV}$.

Fig. 14. Device for registering the reaction $\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}$ by means of neutrons formed in the reaction.

In Fig. 15 is presented the excitation curve of the reaction $\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}$ obtained by Fünfer, possessing a clearly expressed fine structure. From it one can determine the position of the resonance levels of the intermediate nucleus $\mathrm{P}^{31}$.

It is of interest to determine whether the positions of the resonance maxima coincide in the case of excitation of the reaction \(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\) and of the only reaction accompanying it, \(\mathrm{Al}^{27}(\alpha,p)\mathrm{Si}^{30}\).

From the point of view of Bohr’s ideas, the probability of the reaction \(W\) may be represented as the product of three independent factors:

\[ W = W_E \cdot W_R \cdot W_T, \tag{16} \]

where \(W_E\) is the probability that the bombarding particle penetrates through the potential barrier of the nucleus,

\(W_R\) is the factor taking into account the probability of excitation of the intermediate nucleus,

\(W_T\) is the probability of decay of the intermediate nucleus in a definite manner. Whereas \(W_E\) is a monotonic function of the energy of the exciting particle, \(W_R\) passes through a maximum each time the excitation energy

\[ U = \varepsilon + (1-\eta)E \tag{17} \]

corresponds to one of the discrete energy states of the excited nucleus. Here \(\varepsilon\) is the binding energy of the particle, \(E\) is the kinetic energy of the particle,

\[ \eta = \frac{m}{M} \]

is the fraction of the kinetic energy of the particle of mass \(m\) which, according to the law of conservation of momentum, is transferred to the center of gravity of the intermediate nucleus of mass \(M\). The resonance energy levels of the nucleus have a finite width \(\Delta E\), which explains the finite width of the resonance maxima. From the uncertainty relation

\[ \Delta E \cdot \Delta t = \hbar \tag{18} \]

it follows that the longer the lifetime of the intermediate nucleus \(\tau = \Delta t\) (i.e., the lower the excitation energy), the narrower the energy levels and the more sharply the resonance character of the process should be manifested. The probability of excitation of the intermediate nucleus by a particle with energy \(E\) is determined by the number of nuclear levels near \(U = \varepsilon + E'\) and by their width. Thus, for light nuclei and at not too high energies, the factor \(W_R\) determines the resonance character of the variation of the reaction yield with excitation energy.

Fig. 15. Excitation curve of the reaction \(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\). Upper scale—pressure of \(\mathrm{CO}_3\) in the apparatus; lower scale—energy of the \(\alpha\)-particles acting on Al, expressed in cm of range in air.

RADIOACTIVE ISOTOPES OF PHOSPHORUS

Since \(W_R\) depends only on the properties of the intermediate nucleus, the character of the excitation curves and the positions of the yield maxima for the reactions \(\mathrm{Al}^{27}(\alpha,p)\mathrm{Si}^{30}\) and \(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\) must be identical. In both cases they are determined by the positions and widths of the resonance levels of one and the same intermediate nucleus \(\mathrm{P}^{31}\)

\[ \mathrm{Al}^{27}_{13}+\mathrm{He}^{4}_{2}\to \mathrm{P}^{31}_{15} \begin{matrix} \nearrow n+\mathrm{P}^{30}\\ \searrow p+\mathrm{Si}^{30} \end{matrix} \]

These considerations are indeed confirmed by experimental data. Table IV gives the values of the energies of \(\alpha\)-particles in MeV corresponding to the maxima on the excitation curves of the reaction \(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\), according to the data of Fonfer and Varing and Chang\(^{106}\), and of the reaction \(\mathrm{Al}^{27}(\alpha,p)\mathrm{Si}^{30}\), according to the data of Chadwick\(^{113}\) and Dunkanson\(^{114}\). It is seen that the positions of all the maxima found for the processes \((\alpha,n)\) and \((\alpha,p)\) agree well with one another.

Table IV

Positions of resonance maxima on the excitation curves of the reactions \(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\) and \(\mathrm{Al}^{27}(\alpha,p)\mathrm{Si}^{30}\)

Reaction
\(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\)	4.0	4.49	4.61	4.91	5.23	5.55	5.72	6.09
\(\mathrm{Al}^{27}(\alpha,p)\mathrm{Si}^{30}\)	4.0	4.49	—	4.86	5.25	—	5.75	—
\(\mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30}\)	6.26	6.39	6.61	7.0	7.17	7.33	7.50	—
\(\mathrm{Al}^{27}(\alpha,p)\mathrm{Si}^{30}\)	—	—	6.61	—	—	—	—	—

To conclude with this question, let us note that, in more detailed investigations using a thin target, it is found that the relation between the \((\alpha,n)\) and \((\alpha,p)\) resonance levels is somewhat more complicated. It turns out that each \((\alpha,p)\) resonance maximum corresponds to a “doublet” of two closely spaced \((\alpha,n)\) resonance levels\(^{109,115}\). (Fig. 16). One of them corresponds exactly to the position of the maximum on the excitation curve of the reaction \(\mathrm{Al}^{27}(\alpha,p)\mathrm{Si}^{30}\), while the other is shifted somewhat toward lower energies. An explanation of this phenomenon was proposed by Weizsäcker\(^{116}\), who proceeds from the fact that nuclei of the type \(\mathrm{P}^{31}_{15}\) have the structure \(k\alpha+2n+1p\), and assumes that the components of the doublet correspond to different mutual orientations of the spins of the three “excess” particles. The coincident \((\alpha,p)\)- and \((\alpha,n)\)-levels correspond to an antiparallel orientation of the neutron spins. The deeper-shifted \((\alpha,n)\)-level corresponds to a parallel orientation of the spins of all three particles. It is assumed here that, after the emission of the proton or neutron, the residual nucleus is found predominantly in the ground state.

Fig. 16. “Doublets” of \((\alpha,n)\)-resonances corresponding to each \((\alpha,p)\)-resonance.

Whereas the character of the variation in the yield of the reaction \( \mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30} \) with change in the energy of the \(\alpha\)-particle has been studied in considerable detail, the dependence of the absolute yield on \(E_\alpha\) is known much less definitely. Experiments with thick targets with insufficient monochromaticity of the \(\alpha\)-particles\(^{101,106,110}\) and relative measurements\(^{117}\) give only approximate results. At \(E_\alpha = 6.5\) MeV \(\sigma = (2 \div 3)\cdot 10^{-26}\ \mathrm{cm}^2\).

The heat effect of the reaction \( \mathrm{Al}^{27}(\alpha,n)\mathrm{P}^{30} \), according to Peck’s data,\(^{118}\) obtained by the photographic-plate method from the measurement of recoil-proton tracks, is \(Q = -2.93 \pm 0.17\) MeV. Hence the mass of the \(\mathrm{P}^{30}\) nucleus is \(29.98875 \pm 0.67\cdot 10^{-3}\) mass units. Bethe\(^{93}\) gives the value \(29.9873 \pm 1\cdot 10^{-4}\) mass units.

The other reactions for obtaining \(\mathrm{P}^{30}\) have been studied less thoroughly.

PRODUCTION OF \(\mathrm{P}^{30}\) FROM SILICON

Three stable isotopes of silicon are known: \(\mathrm{Si}^{28}\)—89.6%, \(\mathrm{Si}^{29}\)—6.2%, and \(\mathrm{Si}^{30}\)—4.2%. Each of them can be transformed into \(\mathrm{P}^{30}\) by bombardment with various particles.

Barkas\(^{119}\) obtained an activity with \(T = 2.5\) min upon bombardment of silicon with protons with \(E_p = 5.8\) MeV and ascribed it to the reaction

\[ {}^{30}_{14}\mathrm{Si} + {}^{1}_{1}\mathrm{H} = {}^{30}_{15}\mathrm{P} + {}^{1}_{0}n. \]

In subsequent investigations\(^{120,121}\) it was definitely established that the activity formed in the reaction belongs to \(\mathrm{P}^{30}\). It is interesting that, despite the low percentage content of the initial isotope in the target, the activity obtained proves to be appreciable.

The reaction

\[ {}^{29}_{14}\mathrm{Si} + {}^{2}_{1}\mathrm{H} = {}^{30}_{15}\mathrm{P} + {}^{1}_{0}n \]

was observed by Peck\(^{118}\) by the photographic-plate method from the tracks of recoil protons produced by the action of neutrons arising in the reaction. A thin film of the pure element was bombarded with deuterons of \(E_D = 3.72\) MeV. The heat effect of this reaction is estimated in such a way that the mass difference \(\mathrm{P}^{30} - \mathrm{Si}^{29}\) is \(1.00215 \pm 0.21\cdot 10^{-3}\) mass units.

Earlier, Newson\(^{65}\), by the usual method of observing positron activity with a Geiger counter, was unable to detect the presence of this reaction upon bombardment of silicon with deuterons.

Alvarez and Cornog\(^{122}\), irradiating silicon in a cyclotron with \({}^{3}_{2}\mathrm{He}\) ions of energy \(E = 24\) MeV, carried out the reaction

\[ {}^{28}_{14}\mathrm{Si} + {}^{3}_{2}\mathrm{He} = {}^{30}_{15}\mathrm{P} + {}^{1}_{1}\mathrm{H}. \]

PRODUCTION OF \(\mathrm{P}^{30}\) FROM THE STABLE ISOTOPE OF PHOSPHORUS

The formation of \(\mathrm{P}^{30}\) from stable phosphorus is possible in the case of removal of one neutron from the \(\mathrm{P}^{31}\) nucleus. This is accomplished in the reactions \((n,2n)\) and \((\gamma,n)\).

Pool, Cork, and Thornton^49 obtained \(P^{30}\) by bombarding phosphorus with (Li-D) neutrons with \(E_n > 20\) MeV. The formation of a three-minute positron activity is due to the reaction

\[ {}_{15}P^{31} + {}_{0}n^{1} = {}_{15}P^{30} + 2\,{}_{0}n^{1}. \]

Segrè^123 experimentally estimated the threshold of this reaction to be in the range \(5 < E_n < 7\) MeV.

The reaction

\[ {}_{15}P^{31} + \gamma = {}_{15}P^{30} + {}_{0}n^{1} \]

was carried out and investigated by Bothe and Gentner^124,125,126. The sources of \(\gamma\)-quanta in these experiments were \((p,\gamma)\)-reactions occurring when lithium and beryllium are bombarded with protons. In the first case, at \(E_p = 440\) KeV, \(\gamma\)-quanta with \(E_\gamma = 17\) MeV arise; in the second, three groups of \(\gamma\)-quanta are formed with an average value \(E_\gamma = 12.8\) MeV. The yield of the reaction changes insignificantly in this \(E_\gamma\) interval. The reaction \(P^{31}(\gamma,n)P^{30}\) was also carried out under the action of intense \(\gamma\)-quanta with \(E_\gamma = 50\) MeV and \(E_\gamma = 100\) MeV, obtained by means of the betatron and synchrotron^127,145.

The reaction threshold is \(E_\gamma = 12.4 \pm 0.2\) MeV^147.

It was not possible to carry out experimentally the reaction \(P^{31}(d,H^3)P^{30}\)^65.

PRODUCTION OF \(P^{30}\) FROM SULFUR

The initial isotope in this case is the principal isotope \(S^{32}\) (95.1%).

Segrè^14, upon short-term irradiation of sulfur in a cyclotron with deuterons of energy 4–6 MeV, obtained positron activity with \(T \simeq 3\) min. It was established chemically that it belongs to phosphorus. Thus, in this case the reaction is

\[ {}_{16}S^{32} + {}_{1}H^{2} = {}_{15}P^{30} + {}_{2}He^{4}. \]

Cork and Middleton^52, when bombarding sulfur with (Li-D) neutrons with \(E\) up to 24 MeV, discovered positron activity with \(T = 2.3\) min, which must be ascribed to phosphorus, as follows from chemical experiments. These same authors showed that when (Be-D) neutrons with \(E\) up to 13 MeV are used, radiophosphorus is not formed. Thus the process occurs only under the action of neutrons with energy close to the triple binding energy of the particle in the nucleus. Here, probably, there occurs a reaction with simultaneous emission of three particles:

\[ {}_{16}S^{32} + {}_{0}n^{1} = {}_{15}P^{30} + 2\,{}_{0}n^{1} + {}_{1}H^{1} \]

or

\[ {}_{16}S^{32} + {}_{0}n^{1} = {}_{16}S^{30} + 3\,{}_{0}n^{1}, \]

accompanied by positron decay: \({}_{16}S^{30} \to {}_{15}P^{30} + \beta^{+}\).

THE HALF-LIFE OF P³⁰

The first determinations of the half-life of P³⁰ gave a value of the order of \(T = 3\) min and even somewhat higher\(^{96,101,110,111}\).

Ridenour and Henderson\(^{103,128}\), measuring the activity of a strong source obtained by irradiating aluminum with \(\alpha\)-particles in a cyclotron, found a considerably lower value, \(T = 2.55 \pm 0.05\) min. Figure 17 gives the decay curve in semilogarithmic coordinates obtained by these authors. The result appears reliable, all the more so since subsequently the value \(T = 2.5\) min was confirmed in a number of laboratories\(^{119,121,122,127}\).

Fig. 17. Graph of the radioactive decay of P³⁰. The slope corresponds to \(T = 2.55 \pm 0.05\) min.

β-SPECTRUM OF P³⁰

The radioactive decay of P³⁰ consists in the emission of positrons with a transition directly to the ground state of Si³⁰:

\[ \mathrm{P}^{30} \longrightarrow \mathrm{Si}^{30} + \beta^{+}. \]

The \(\gamma\)-quanta observed in experiments with P³⁰ are due to annihilation of positrons\(^{100,102,129}\).

The results of measurements of \(E_m\) of the \(\beta\)-spectrum present an extremely motley picture, despite repeated attempts by various authors to obtain accurate data. The discrepancy between the values of \(E_m\) obtained by different methods in different laboratories reaches 200%.

The first measurements\(^{96,130,131}\), made with unenriched thick samples, give manifestly underestimated values of the order of 2 MeV. Alikhanov, Alikhanyan, and Dzhelepov\(^{18,19,102,132,133}\), using a coincidence arrangement constructed by them, were the first to obtain the complete curve of the \(\beta\)-spectrum of P³⁰ and to study it in detail. The value they found, \(E_m = 3.6\text{–}3.7\) MeV, substantially exceeds all previously obtained results. Subsequently, similar values of \(E_m\) were obtained by Manyan\(^{104}\) with the aid of a \(\beta\)-spectrometer \((E_m = 3.5 \pm 0.35\ \mathrm{MeV})\) and by Bleuler and Zünti\(^{134}\) \((E_m = 3.4 \pm 0.5\ \mathrm{MeV})\) by the absorption method.

Alongside the value \(E_m = 3.5\text{–}3.6\) MeV, the literature contains a number of data grouped around the value \(E_m = 3.0\) MeV\(^{98,101,111,121,129}\).

ISOTOPE P²⁹

Barkas¹³⁵ drew attention to the fact that, when using \(\mathrm{He}^{3}_{2}\) as the bombarding particle, another isotope of phosphorus can be obtained by the reaction

\[ \mathrm{Al}^{27}_{13}+\mathrm{He}^{3}_{2}=\mathrm{P}^{29}_{15}+n^{1}_{0}. \]

However, \(\mathrm{P}^{29}\) was first obtained by White, Creutz, Delsasso, and Wilson¹³⁶ in bombarding silicon with protons. Silicon crystals, pressed into a lead plate, were bombarded for 3 seconds with protons with \(E_p>8.6\) MeV. The active product obtained gave a complex decay curve. Alongside the known reaction \(\mathrm{Si}^{30}(p,n)\mathrm{P}^{30}\), the presence of a short-lived substance formed by the reaction was noted:

\[ \mathrm{Si}^{29}_{14}+\mathrm{H}^{1}_{1}=\mathrm{P}^{29}_{15}+n^{1}_{0}. \]

Measurements in a Wilson chamber established that \(\mathrm{P}^{29}\) is a positron-active isotope characterized by a half-life

\[ T=4.6\pm0.2 \]

seconds. The maximum energy of the \(\beta\)-spectrum is

\[ E_m=3.63\pm0.07\ \text{MeV}. \]

The half-life of \(\mathrm{P}^{29}\) was also measured by Japanese investigators¹³⁷, ¹³⁸.

The formation of very small quantities of \(\mathrm{P}^{29}\) may occur in the reaction

\[ \mathrm{P}^{31}_{15}+\gamma=\mathrm{P}^{29}_{15}+2n^{1}_{0} \]

when phosphorus is irradiated with \(\gamma\)-quanta with \(E_\gamma=80\) MeV¹²⁷.

Peck¹¹⁸, by recording the tracks of recoil protons on photographic plates, observed the reaction

\[ \mathrm{Si}^{28}_{14}+\mathrm{H}^{2}_{1}=\mathrm{P}^{29}_{15}+n^{1}_{0} \]

when silicon was irradiated with deuterons with \(E_D=3.72\) MeV.

The thermal effect of this reaction is

\[ Q=-0.80\pm0.10\ \text{MeV}. \]

Hence the mass of \(\mathrm{P}^{29}\) is \(28.99387\pm0.59\cdot10^{-3}\) mass units, which differs somewhat from the value \(28.9919\pm10\cdot10^{-4}\) mass units cited by Bethe⁹³.

ISOTOPE P³⁴

There exists still another short-lived radioactive isotope of phosphorus.

Cork and Millerton⁵², in irradiating sulfur with (Li-D) and (Be-D) neutrons, discovered an activity with \(T=12.7\) sec. Observations in a Wilson chamber established that, in \(\beta\)-decay, this active substance emits electrons. It seems probable that the activity is associated with \(\mathrm{P}^{34}\), formed by the reaction:

\[ \mathrm{S}^{34}_{16}+n^{1}_{0}=\mathrm{P}^{34}_{15}+\mathrm{H}^{1}_{1}. \]

Indeed, the stable sulfur isotopes \(S^{33}\) and \(S^{36}\) are very rare, while the \((n,p)\)-reaction with the principal isotope \(S^{32}\) leads to the well-known \(P^{32}\). The products of the \((n,2n)\)- and \((n,\alpha)\)-reactions are either stable or have known, different periods.

On the other hand, Huber, Lenard, and Waffler\(^{53}\), irradiating chlorine with (Ra-Be) neutrons, obtained an activity with \(T=14.7\pm1\) sec. It is not formed when (D-D) neutrons with \(\overline{E}_n=2.87\) MeV are used. Consequently, the reaction leading to its appearance requires neutrons of high energies for its excitation.

Since the reactions \((n,p)\), \((n,\alpha)\), \((n,2n)\) with the initial isotope \(Cl^{35}\) lead to known products, only one of the following reactions can be invoked to explain the origin of the observed activity: \(Cl^{37}(n,p)S^{37}\) or \(Cl^{37}(n,\alpha)P^{34}\).

The question of the identity of the activities obtained upon irradiation of sulfur and chlorine with fast neutrons was unequivocally resolved by Bleuler and Zünti\(^{139}\). Upon irradiating \(C_2Cl_6\), \(CCl_4\), \(CS_2\), \(S\) with (Li-D) neutrons, they obtained a short-lived activity with one and the same period \(T=12.40\pm0.12\) sec. It was shown chemically that it belongs to phosphorus. The same authors first obtained \(S^{37}\) and found that its \(T=5.04\) min. Thus it was definitely established that the isotope \(P^{34}\) exists and can be obtained by the reactions

\[ S^{34}+n=P^{34}+p \]

and

\[ Cl^{37}+n=P^{34}+\alpha . \]

\(P^{34}\) has a complex \(\beta\)-spectrum with endpoints \(E'_m=5.1\pm0.2\) MeV and \(E''_m=3.2\pm0.2\) MeV, with an intensity ratio of the groups \(3:1\). Consequently, the \(\beta\)-decay of \(P^{34}\) must be accompanied by \(\gamma\)-radiation with \(E_\gamma=1.9\) MeV.

The mass of \(P^{34}\), according to Bleuler and Zünti, is \(33.98257\pm30\cdot10^{-5}\) mass units, and according to the data cited by Bethe\(^{93}\), \(33.9826\pm40\cdot10^{-5}\) mass units.

The principal characteristics of the radioactive isotopes of phosphorus are given in Table V.

Table V

Principal characteristics of the radioactive isotopes of phosphorus

Isotope	Mass	Type of radiation	\(T\)	\(E_m\), in MeV	\(E_\gamma\), in MeV
\(P^{29}\) . . . . .	28.99387	\(\beta^+\)	4.6 sec.	3.63	—
\(P^{30}\) . . . . .	29.98875	\(\beta^+\)	2.55 min.	3.0–3.6	—
\(P^{32}\) . . . . .	31.98269	\(\beta^-\)	14.3 days	1.71	—
\(P^{34}\) . . . . .	33.98257	\(\beta^-\), \(\gamma\)	12.4 sec.	5.1; 3.2	1.9

For practical use as an indicator, radiophosphorus \(P^{32}\) is of particular interest. It has a sufficiently long half-life and emits \(\beta\)-particles of considerable energies. In a number of cases it may be significant that the \(\beta\)-decay of \(P^{32}\) is not accompanied by the emission of \(\gamma\)-rays. The most convenient and effective methods for obtaining \(P^{32}\) consist in bombarding sulfur- and chlorine-containing compounds with fast neutrons and in irradiating phosphorus and phosphorus-containing compounds with deuterons and slow neutrons.

CITED LITERATURE

1. M. B. Neiman, A. N. Nesmeyanov, Uspekhi khimii, 17, 401 (1948).
2. W. Riezler, Introduction to Nuclear Physics, pp. 239–253, IL, 1948.
3. E. Pollard, W. Davidson, Applied Nuclear Physics, pp. 211–215, Gostekhizdat, 1947.
4. Ardens, Physical Foundations of the Use of Radioactive and Stable Isotopes as Indicators, State Publishing House of Foreign Literature, Moscow, 1948.
5. E. Mc. Millan, Phys. Rev. 47, 801 (1935).
6. C. S. Wu, Phys. Rev. 59, 481 (1941).
7. B. Feld, R. Scalettar, L. Szilard, Phys. Rev. 71, 464 (1947).
8. C. Sherwin, Phys. Rev. 73, 216 (1948).
9. E. Fermi, E. Amaldi, O. D’Agostino, F. Rasetti, E. Segrè—Proc. Roy. Soc. A146, 483 (1934).
10. E. Amaldi, O. D’Agostino, E. Fermi, B. Pontecorvo, F. Rasetti, E. Segrè—Proc. Roy. Soc. A149, 522 (1935).
11. Fragments Formed in the Fission of Uranium Nuclei, UFN, 33, 77, 1947.
12. D. Miller, P. Thompson, B. Cunningham, Phys. Rev. 74, 347 (1948).
13. J. Ambrosen, Zeits. f. Physik, 91, 43 (1934).
14. R. Sagane, Phys. Rev. 50, 1141 (1936).
15. G. Sizoo, C. Eijkman, P. Groen, Physica 6, 1057 (1939).
16. M. Dols, B. Jansen, G. Sizoo, Proc. Kon. Akad. A’dam, 40, 547 (1937).
17. G. Sizoo, C. Koene, Physica 3, 1053 (1936).
18. A. I. Alikhanov, A. I. Alikhanyan, B. S. Dzhelepov, Nature 136, 257 (1935).
19. A. I. Alikhanov, A. I. Alikhanyan, B. S. Dzhelepov, Phys. Zeits. Sowjetun. 10, 78 (1936).
20. G. Seaborg, UFN 28, 285 (1946).
21. P. Capron, Physika 5, 882 (1938).
22. J. Govaerts, Nature 145, 624 (1940).
23. N. E. Brezhneva, S. Z. Roginskii, Uspekhi khimii 7, 1503 (1938).
24. H. Maier-Leibnitz, Zeits. angew. Chem. 51, 545 (1938).
25. O. Erbacher, Zeits. phys. Chem. B42, 173 (1939).
26. J. Govaerts, Nature 141, 871 (1938).
27. J. Govaerts, Nature 141, 1103 (1938).
28. J. Govaerts, J. Chim. Phys. 36, 130 (1939).
29. N. E. Brezhneva, Scientific-Research Works of the Chemical Institute and Laboratories of the Academy of Sciences of the USSR for 1940, p. 117, Publishing House of the Academy of Sciences of the USSR, 1941.
30. D. Hull, J. Am. Chem. Soc. 63, 1269 (1941).
31. N. Das Gupta, B. Purakajastha, S. Ghoshal, B. Sen, Science and Culture 11, 271 (1945).

1. G. Smith, Atomic Energy for Military Purposes, Goszheldorizdat, 1946.
2. P. Huber, Helv. Phys. Acta 14, 163 (1941).
3. E. Both, C. Hurst, Proc. Roy. Soc., A161, 248 (1937).
4. T. Amaki, A. Sugimoto, Phys. Rev. 58, 659 (1940).
5. B. S. Dementii, D. V. Timoshchuk, DAN 27, 926 (1940).
6. E. Klema, A. Hanson, Phys. Rev. 73, 106 (1948).
7. R. Sherr, Phys. Rev. 68, 240 (1945).
8. H. Goldsmith, H. Ibser, B. Feld, Rev. Mod. Phys. 19, 259 (1947).
9. E. Wilhelmy, Zeits. f. Physik 107, 769 (1937).
10. S. Stebler, P. Huber, Helv. Phys. Acta 21, 59 (1948).
11. E. Bleuer, Helv. Phys. Acta 20, 519 (1947).
12. A. Leipunskii, L. Rozenkevich, D. Timoshchuk, ZhETF 7, 33 (1937).
13. R. Fields, B. Russell, D. Sachs, A. Wattenberg, Phys. Rev. 71, 508 (1947).
14. L. Rainwater, W. Havens, J. Dunning, C. Wu, Phys. Rev. 73, 733 (1948).
15. V. N. Kondrat'ev, UFN 34, 169 (1948).
16. K. Diebner, W. Herrmann, E. Grassmann, Phys. Zeits 43, 440 (1942).
17. H. Volz, Zeits. f. Phys. 121, 201 (1943).
18. M. Pool, J. Cork, R. Thornton, Phys. Rev. 52, 239 (1937).
19. J. Mattauch, S. Flügge, Nuclear Physics Tables, Interscience Publishers, Inc., New York, 1946.
20. A. Gibert, P. Roggen, J. Rossel, Helv. Phys. Acta 17, 97 (1944).
21. J. Cork, W. Middleton, Phys. Rev. 58, 474 (1940).
22. O. Huber, O. Lenhard, H. Wäffler, Helv. Phys. Acta 15, 314 (1942).
23. Yu. A. Nemilov, ZhETF 9, 1029 (1939).
24. P. Preiswerk, H. Halban, Compt. Rand. 201, 722 (1935).
25. W. Libby, J. Am. Chem. Soc. 62, 1930 (1940).
26. O. Erbacher, K. Philipp, Zeits. f. phys. Chem. A179, 263 (1937).
27. L. Szilard, T. Chalmers, Nature 134, 462 (1934).
28. C. Lapointe, F. Rasetti, Phys. Rev. 58, 554 (1940).
29. F. Rasetti, Phys. Rev. 58, 869 (1940).
30. R. O’Neal, M. Goldhaber, Phys. Rev. 59, 102 (1941).
31. K. Sinma, H. Yamasaki, Phys. Rev. 59, 402 (1941).
32. L. Seren, H. Friedlander, S. Turkel, Phys. Rev. 72, 888 (1947).
33. N. Newson, Phys. Rev. 48, 482 (1935).
34. N. Newson, Phys. Rev. 51, 624 (1937).
35. F. Kurie, J. Richardson, H. Paxton, Phys. Rev. 49, 368 (1936).
36. E. Lyman, Phys. Rev. 51, 1 (1937).
37. H. Paxton, Phys. Rev. 51, 170 (1937).
38. E. Pollard, Phys. Rev. 57, 1086 (1940).
39. K. Siegbahn, Nature 153, 221 (1944).
40. J. Lawson, Phys. Rev. 56, 131 (1939).
41. D. Hull, J. Williams, Rev. Sci. Instrum. 11, 299 (1940).
42. E. Clarke, J. Irvine, Phys. Rev. 70, 893 (1946).
43. H. Fahlenbrach, Naturwiss. 23, 288 (1935).
44. N. Fahlenbrach, Zeits. f. Physik 96, 53 (1935).
45. L. King, W. Henderson, J. Risser, Phys. Rev. 55, 1118 (1939).
46. J. Cichocki, A. Sołtan, Acta Phys. Polon 7, 240 (1938).
47. N. B. Cacciapuoti, Nuovo cimento 15, 213 (1938).
48. D. Mulder, O. Hoeksema, C. Sizoo, Physica 7, 849 (1940).
49. B. Moore, Phys. Rev. 57, 355 (1940).
50. E. Liman, Phys. Rev. 50, 385 (1936).

Radioactive Isotopes of Phosphorus

1. J. Lawson, Phys. Rev. 55, 1136 (1939).
2. W. Libby, D. Lee, Phys. Rev. 55, 245 (1939).
3. C. Witcher, Phys. Rev. 60, 32 (1941).
4. K. Siegbahn, Phys. Rev. 70, 127 (1946).
5. N. Feather, Proc. Cambr. Phil. Soc. 34, 599 (1938).
6. H. Paxton, Phys. Rev. 49, 206 (1935).
7. P. Barendregt, J. Griffioen, G. Sizoo, Physica 7, 860 (1940).
8. L. Smith, G. Groetzinger, Phys. Rev. 70, 96 (1946).
9. T. Pi, C. Chao, Phys. Rev. 72, 639 (1947).
10. J. Barlow, F. Rogers, Phys. Rev. 74, 700 (1948).
11. M. Livingston, H. Bethe, Rev. Mod. Phys. 9, 373 (1937).
12. H. Bethe, Elementary Nuclear Theory, John Wiley & Sons, Inc., New York (1947).
13. I. Curie, F. Joliot, Compt. Rand. 196, 397 (1933).
14. P. Auger, G. Monod-Herzen, Compt. Rand. 196, 543 (1933).
15. I. Curie, F. Joliot, Compt. Rand. 198, 254 (1934).
16. I. Curie, F. Joliot, Compt. Rand. 198, 559 (1934).
17. I. Curie, F. Joliot, Nature 133, 201 (1934).
18. L. Meitner, Naturwiss. 22, 172 (1934).
19. C. Ellis, W. Henderson, Nature 133, 530 (1934).
20. C. Ellis, W. Henderson, Proc. Roy. Soc. A146, 206 (1934).
21. A. I. Alikhanov, A. I. Alikhanyan, B. S. Dzhelepov, Zeits. f. Physik 93, 350 (1935).
22. L. Ridenour, W. Henderson, Phys. Rev. 52, 889 (1937).
23. C. Maglian, Ann. phys. 15, 5 (1941).
24. P. Savel, J. Perrin, Compt. Rand. 198, 363 (1934).
25. J. Waring, W. Chang, Proc. Roy. Soc. A157, 652 (1936).
26. Yu-Yen-Sha, Zeits. f. Physik 107, 111 (1937).
27. E. Pollard, H. Schultz, G. Brubaker, Phys. Rev. 53, 351 (1938).
28. A. Szalay, Zeits. f. Physik 112, 29 (1939).
29. H. Fahlenbrach, Zeits. f. Physik 94, 607 (1935).
30. A. Meye, Zeits. f. Physik 105, 232 (1937).
31. E. Fünfer, Ann. der Physik 32, 313 (1938).
32. J. Chadwick, I. Constable, Proc. Roy. Soc. A135, 43 (1932).
33. W. Duncanson, H. Miller, Proc. Roy. Soc. A146, 396 (1934).
34. A. Szalay, Nature 141, 972 (1938).
35. C. Weizsäcker, Naturwiss. 31, 207 (1943).
36. C. Copeland, S. Lind, J. Phys. Chem. 42, 567 (1938).
37. R. Peck, Phys. Rev. 73, 947 (1948).
38. W. Barkas, Phys. Rev. 56, 287 (1939).
39. W. Barkas, E. Creutz, L. Delsasso, R. Sutton, M. White, Phys. Rev. 58, 194 (1940).
40. W. Barkas, E. Creutz, L. Delsasso, R. Sutton, M. White, Phys. Rev. 58, 383 (1940).
41. L. Alvarez, R. Cornog, Phys. Rev. 56, 613 (1939).
42. R. Sagane, Phys. Rev. 53, 492 (1938).
43. W. Bothe, W. Gentner, Naturwiss. 25, 90 (1937).
44. W. Bothe, W. Gentner, Zeits. f. Physik 106, 235 (1937).
45. W. Bothe, W. Gentner, Zeits. f. Physik 112, 45 (1939).
46. M. Perlman, G. Friedlander, Phys. Rev. 74, 442 (1948).
47. L. Ridenour, W. Henderson, M. Henderson, M. White, Phys. Rev. 51, 1013 (1937).
48. C. Ellis, W. Henderson, Proc. Roy. Soc. A152, 714 (1935).
49. L. Meitner, Naturwiss. 22, 388 (1934).
50. O. Frisch, Nature 133, 721 (1934).
51. A. I. Alikhanov, A. I. Alikhanyan, B. S. Dzhelepov, Nature 134, 251 (1934).

1. A. I. Alikhanov, A. I. Alikhanyan, B. S. Dzhelepov, Nature, 137, 314 (1935).
2. V. Bleuer, W. Zünti, Helv. Phys. Acta 19, 375 (1945).
3. W. Barka, Phys. Rev. 56, 1212 (1939).
4. W. White, E. Creutz, L. Delsasso, R. Wilson, Phys. Rev. 59, 63 (1941).
5. Members of Atom. Nucl. Res. Inst., J. Phys. Math. Soc. Japan 17, 544 (1943).
6. Members of Atom. Nucl. Res. Inst., Proc. Phys. Math. Soc. Japan 25, 616 (1943).
7. E. Bleuer, W. Zünti, Helv. Phys. Acta 19, 137 (1946).
8. P. Gugelot, P. Huber, P. Scherrer, Helv. Phys. Acta 14, 138 (1941).
9. F. Kurie, Rev. Sci. Instr. 10, 199 (1939).
10. R. Wilson, M. Kamen, Phys. Rev. 54, 1031 (1938).
11. Announcement from Headquarters, Manhattan Project, Science 103, 697 (1946).
12. M. Kamen, Radioactive Tracers in Biology, Academic Press Inc., Publishers, New-York, 1948.
13. G. Baldwin, G. Klaiber, Phys. Rev. 70, 259 (1946).
14. E. Scott, Phys. Rev. 74, 210 (1948).
15. J. McElhinney, A. Hanson, R. Duffield, Phys. Rev. 74, 1257 (1948).