RADIOACTIVE ISOTOPES OF HELIUM

K. Artemov and B. Dzhelepov

In nature there exist two stable isotopes of helium—He³ and He⁴. Their principal properties are given in Table I.

Table I

Properties of the stable isotopes of helium

He⁴ is the principal isotope. The abundance of He³ is very small—1.3·10⁻⁴% relative to He⁴.

The properties of He³ are discussed in the review by K. Tumanov⁴*).

The He² nucleus apparently cannot exist for any appreciable length of time. It is a system of two protons. Landau and Smorodinsky⁵ showed that the experimental data on proton–proton scattering directly imply the impossibility of stable states of the He² system (“biproton”). The He⁵ nucleus decays into He⁴ and a neutron. Only the He⁶ nucleus is an “ordinary” β-emitter.

) Uspekhi Fizicheskikh Nauk* has previously also published reviews devoted to the properties of the radioactive isotopes of hydrogen⁶, phosphorus⁷, iodine⁸, and nitrogen⁸ᵃ.

THE ISOTOPE He\(^5\) \((n;\ T \approx 10^{-20}\ \mathrm{sec}.)\)

The only mass number to which no stable or radioactive isotope in the usual sense of the word corresponds is the number five. Such a mass number could apparently belong only to isotopes of helium and lithium; however, such isotopes are known neither among the stable nor among the \(\beta\)-radioactive ones.

In 1934 Bleakney, Garvin, and others \(^{9}\) made an attempt to find He\(^5\) mass-spectrographically in ordinary helium. They found that He\(^5\), if it is present at all in ordinary helium, occurs in amounts less than \(1:10^6\).

Meshcheryakov, Reut, Grigor’ev, and Khrenina \(^{10}\) determined the upper limit of the relative abundance of He\(^5\) in helium, using a cyclotron as a mass spectrometer and thick-layer photographic plates as a particle detector. For helium from a gas well they obtained an upper limit equal to \(1:10^{14}\).

Thus, He\(^5\) apparently does not exist in the natural state. However, it can be produced as a result of certain reactions, for example:

\[ \mathrm{Li}^7 + \mathrm{H}^2 = \mathrm{He}^4 + \mathrm{He}^5; \]

\[ \mathrm{He}^4 + n = \mathrm{He}^5; \]

\[ \mathrm{He}^4 + \mathrm{H}^2 = \mathrm{He}^5 + \mathrm{H}^1. \]

These reactions have been investigated by many authors. We shall consider them in turn in this order.

THE REACTION \(\mathrm{Li}^7 + \mathrm{H}^2 = \mathrm{He}^5 + \mathrm{H}^4\)

In 1935 Oliphant, Kempton, and Rutherford \(^{11}\), measuring the energies of \(\alpha\)-particles produced when lithium was bombarded by deuterons with an energy of \(190\ \mathrm{keV}\), discovered a continuous spectrum of \(\alpha\)-particles extending up to \(8.29\ \mathrm{MeV}\) (range \(7.8\ \mathrm{cm}\)). The experimental scheme is given in Fig. 1. They attributed this spectrum to the reaction

\[ \mathrm{Li}^7 + \mathrm{H}^2 = \mathrm{He}^4 + \mathrm{He}^4 + n. \tag{1} \]

Indeed, if one starts from the presently accepted values of the masses \(^{47}\) of \(\mathrm{Li}^7\), \(\mathrm{H}^2\), \(\mathrm{He}^4\), and \(n\), then at a deuteron energy of \(190\ \mathrm{keV}\) one should expect, at an angle of \(90^\circ\) to the deuteron beam, the appearance of a continuous spectrum of \(\alpha\)-particles extending from 0 to \(8.46\ \mathrm{MeV}\) (range \(8.06\ \mathrm{cm}\)). Therefore the interpretation proposed by Oliphant, Kempton, and Rutherford appears quite correct.

In 1936, Kempton, Brown, and Maasdorp \(^{12}\) undertook a search for a homogeneous group of \(\alpha\)-particles which should arise if the reaction

\[ \mathrm{Li}^7+\mathrm{H}^2=\mathrm{He}^5+\mathrm{He}^4 . \tag{2} \]

takes place.

These authors did not find such a group and concluded that reaction (2), if it occurs at all at a deuteron energy of 190 kev, occurs at least 100 times more rarely than (1).

Williams, Shephard, and Haxby \(^{13,14}\) repeated these experiments in 1937 with apparatus which better differentiated \(\alpha\)-particles of different energy. The experiments were carried out according to the scheme of Fig. 1. The deuteron energy was 200 kev, and the \(\alpha\)-particles emitted at an angle of \(90^\circ\) to the deuteron beam were studied.

In Fig. 2 is shown the dependence of the readings of the differential ionization chamber on the thickness of the filter in the path of the \(\alpha\)-particles.

In the curve, a maximum \(A\) is clearly visible, corresponding to a monochromatic group of particles with a range of 7.1 cm; it lies against the background of the continuous spectrum of \(\alpha\)-particles from reaction (1).

Control experiments with separated isotopes \(\mathrm{Li}^6\) and \(\mathrm{Li}^7\) showed that peak \(A\) is undoubtedly connected with \(\mathrm{Li}^7\).

Fig. 1. Scheme of the experiments \(^{11-17}\).
\(d\)—deuteron beam; \(\mathrm{Li}\)—lithium target; \(T\)—tube in which the air pressure can be varied; \(K\)—\(\alpha\)-particle counter \(^{11,12}\), differential ionization chamber \(^{13,14}\), or thick photographic plate \(^{17}\).

The authors believe that peak \(A\) belongs to the \(\alpha\)-particles from reaction (2). In this case the \(\mathrm{He}^5\) peak should have lain at 4.35 cm, but no peak is observed at this position. If peak \(A\) belonged to \(\mathrm{He}^5\), then an \(\alpha\)-particle peak should have been observed at 11.9 cm, somewhat to the left of peak \(B\) (12.7 cm), which is produced by the \(\alpha\)-particles from the reaction

\[ \mathrm{Li}^6+\mathrm{H}^2=\mathrm{He}^4+\mathrm{He}^4 . \tag{3} \]

There is no such peak either.

The absence of peaks that could be attributed to \(\mathrm{He}^4\) and \(\mathrm{He}^5\) compels one to suppose that \(\mathrm{He}^5\) is so unstable that it decays before it has time to reach the ionization chamber.

If we assume that peak \(A\) belongs to the “ordinary” \(\alpha\)-particles of reaction (2), then the energy of these \(\alpha\)-particles is \(7.83\) MeV (range \(7.1\) cm). In this case \(\mathrm{He}^{5}\) must have an energy of \(6.33\) MeV and, consequently, the energy of reaction (2) is

\[ Q = 13.96\ \text{MeV}. \]

Taking the masses of \(\mathrm{Li}^{7}\), \(\mathrm{H}^{2}\), and \(\mathrm{He}^{4}\) to be, according to Mattauch and Flammersfeld \(^{47}\),

\[ \mathrm{Li}^{7} = 7.018203\ \text{m.u.} \]

\[ \mathrm{H}^{2} = 2.014721\ \text{m.u.} \]

\[ \mathrm{He}^{4} = 4.003887\ \text{m.u.}, \]

we obtain the mass of \(\mathrm{He}^{5}\):

\[ \mathrm{He}^{5} = 5.014042\ \text{m.u.} \]

As is easy to see, with such a mass \(\mathrm{He}^{5}\) must be unstable with respect to decay into an \(\alpha\)-particle and a neutron:

\[ \mathrm{He}^{5} = \mathrm{He}^{4} + \mathrm{n} + Q_{1}. \tag{4} \]

Taking the neutron mass to be \(1.008939\) m.u., we obtain:

\[ Q_{1} = 1.13\ \text{MeV}. \]

Fig. 2. Energy spectrum of \(\alpha\)-particles arising in the reaction \(\mathrm{Li}+\mathrm{d}\). Along the ordinate axis is plotted the ratio of the number of particles registered at a given absorber thickness to their number at the minimum absorber thickness. Curves \(I\) and \(II\) are the curves of Williams, Shepherd, and Haxby \(^{13,14}\) from two series of measurements. The numerals \(I\) and \(II\) at the right denote the zeros of the corresponding curves. \(C\) is the curve of Oliphant, Kempton, and Rutherford \(^{11}\).

THE LIFETIME OF \(\mathrm{He}^{5}\).

The question of the lifetime of the \(\mathrm{He}^{5}\) nucleus may be approached in the following way.

If the lifetime were comparable with the range time (\(\sim 10^{-8}\) sec.), a second maximum would be observed. By studying it, one could draw conclusions about the lifetime of \(\mathrm{He}^{5}\). The absence of such a peak indicates that \(\mathrm{He}^{5}\) has a lifetime \(T < 10^{-8}\) sec. If \(\mathrm{He}^{5}\) decays before it has had time to slow down, then the resulting \(\alpha\)-particles must give a continuous spectrum. If the mass of \(\mathrm{He}^{5}\) is taken to be \(5.0140\), then in experiments according to the scheme of Fig. 1 one should expect the appearance of a continuous spectrum of \(\alpha\)-particles extending from \(3.09\) MeV to \(7.34\) MeV (ranges from \(1.77\) cm to \(6.39\) cm). It is quite probable that the continuous

...spectrum observed in the experiments of Williams, Shepherd, and Haxby consisted of the α-particles of reaction (1) and the α-particles of the decay of He⁵.

Williams, Shepherd, and Haxby drew attention to the fact that peak \(A\) is somewhat broader than peak \(B\) (6 mm and 4 mm, respectively). From this they concluded that there was an additional uncertainty in the energy of the α-particles from reaction (2) of 70 keV and, applying the uncertainty principle in the form \(T\cdot \Delta E=h\), obtained for the mean lifetime of He⁵ the value

\[ T \simeq 6\cdot 10^{-20}\ \text{sec}. \]

From this this number entered a number of handbooks. However, if this additional width really exists and is not connected with the apparatus, the question arises: should it be attributed to the blurring of the level of the excited compound nucleus Be⁹* or to the blurring of the He⁵ level?

If the deuterons were strictly monochromatic, and the target infinitely thin, then all Be⁹ nuclei would be obtained with the same excitation energy. If, in this case, a broadening of the line were obtained, it would indicate the width of the He⁵ level, as absorbing part of the excitation energy of Be⁹.

In the experiments of Williams, Shepherd, and Haxby the conditions indicated above were not satisfied; therefore the conclusions become less definite.

Let us consider two cases.

1. Suppose that both reactions (2) and (3) proceed resonantly at any deuteron energy above 100 keV.

In this case the energy width of the deuteron beam would cause the same broadening of both α-particle lines. The additional width of the first line should then be attributed to He⁵.

1. Suppose that the levels of the compound nuclei Be⁹ and Be⁸ are broad, but finite. Then, if the energy width of the deuteron beam is less than the widths of both levels, the problem reduces to case 1. If, however, the deuteron width is greater than the width of the narrower of the Be⁹ and Be⁸ levels, then the deuterons would more strongly broaden the line associated with the broader level. If the width of the Be⁹ level were greater than the width of the Be⁸ level, then the corresponding line would broaden independently of He⁵.

Since, apparently, case 1 is more probable, the observed broadening of peak \(A\) may conditionally be attributed to the width of the He⁵ level. Then for the lifetime of He⁵ we obtain the value

\[ T \simeq \frac{h}{2\pi\Delta E}=10^{-20}\ \text{sec}. \]

The observations of Williams, Shepherd, and Haxby were basically confirmed in 1938 by Staub and Stephens\(^{15,16}\) according to the same scheme as in Fig. 1. On bombarding lithium with faster deuterons (up to 800 keV), they found a rather broad maximum,

corresponding to particles with a range of 7.6 cm. From the stated range there follow values somewhat different from the values obtained by Williams, Shephard, and Haxby, namely:

\[ Q = 14.20\ \text{Mev},\quad Q_1 = 0.89\ \text{Mev},\quad \mathrm{He}^5 = 5.013786\ \text{amu}. \]

Lattes, Fowler, and Cuer\(^{17}\) carried out experiments, replacing in the scheme of Fig. 1 the ionization chamber by an obliquely placed thick-layer photographic plate. The deuteron energy in their experiments was 900 kev. They obtained

\[ Q = 13.43\ \text{Mev},\quad Q_1 = 1.66\ \text{Mev},\quad \mathrm{He}^5 = 5.0146\ \text{amu}. \]

YIELD OF REACTION (2)

Apparently, the relative role of reaction (2) increases with increasing deuteron energy.

The yield of reaction (2), relative to the yield of reaction (1), is, at a deuteron energy of 200 kev, \( \dfrac{7}{1000}{}^{14}\), and at 800 kev is \( \dfrac{1}{5}{}^{16}\).

The latter number was also confirmed by Staub and Stephens\(^{16}\) from measurements of the relative number of neutrons arising in reaction (1) and in the decay of \(\mathrm{He}^5\). These measurements, however, do not possess great accuracy, since neutrons from \(\mathrm{He}^5\) are visible only as a small step in the continuous neutron spectrum.

REACTION \(\mathrm{He}^4 + \mathrm{n} = \mathrm{He}^5\)

If \(\mathrm{He}^5\) can exist for at least a short time, then resonance scattering in helium of neutrons of suitable energy should be observed.

Staub and Stephens\(^{18}\) in 1939 investigated the scattering of neutrons in helium and hydrogen.

They obtained the curve shown in Fig. 3.

Comparing the ratio

\[ \frac{\sigma_{\mathrm{scatt}}\ \text{in He}}{\sigma_{\mathrm{scatt}}\ \text{in H}}, \]

which they obtained experimentally, with this ratio calculated theoretically, the authors came to the conclusion that \(\mathrm{He}^5\) is formed in a \(p\)-state.

In 1940 a short note by Staub and Tatel\(^{19}\) appeared, in which they reported that the peak observed by the preceding authors consists of two components separated by 0.24 Mev.

In Goodman’s atlas\(^{20}\) unpublished data of Hall and Kunz are given. They are shown by crosses in Fig. 3; in the main they confirm the preceding works of Staub and Tatel.

However, the results of these works contradict the work of Bashkin, Petree, Mooring, and Peterson\(^{21}\), published in 1949. These

the authors measured the scattering cross section in helium of neutrons with energies from 40 keV to 6.4 MeV. The cross section rises smoothly from 0.8 barn at 40 keV to 6.7 barns at 1.1 MeV, then falls smoothly to 2.3 barns at 6.4 MeV. The accuracy of the measurements is ±0.1 barn. In the neutron energy interval from 0.95 to 1.32 MeV the scattering cross section was measured every 30 keV, but the two maxima of Staub and Tatel were not found.

Fig. 3. \(A\)—the ratio of the cross section for neutron scattering at \(180^\circ\) in helium \((\sigma_{\mathrm{He}})\) to the scattering cross section in hydrogen \((\sigma_{\mathrm{H}})\) as a function of neutron energy \(^{18}\); \(B\)—the neutron scattering cross section in helium \(^{20}\). The dashed curves are theoretical curves for angles \(180^\circ \pm 15^\circ\) and \(162^\circ \pm 8^\circ\), calculated on the assumption that the angular correlation between the directions of emission from the nucleus of the electron and the neutron is described by the expression

\[ 1-\frac{1}{3}\frac{v}{c}\cos\theta . \]

If the data of Bashkin et al. are used, then for the mass of \(\mathrm{He}^5\) one obtains the value

\[ \mathrm{He}^5 = 5.013772\ \text{m.e.}; \quad Q_1 = 0.88\ \text{MeV}. \]

REACTION \(\mathrm{He}^4 + \mathrm{H}^2 = \mathrm{He}^5 + \mathrm{H}^1\)

Joliot and Zlotowski \(^{22,23}\) bombarded paraffin containing deuterium with \(\alpha\)-particles from polonium and observed the appearance of a homogeneous group of particles, in their opinion protons, from the reaction

\[ \mathrm{He}^4 + \mathrm{H}^2 = \mathrm{He}^5 + \mathrm{H}^1 . \tag{5} \]

These experiments are apparently erroneous. Jensen \(^{24}\) showed that if this reaction occurs, then its yield is at least 30 times smaller than that of Joliot and Zlotowski.

From the experiments of Joliot and Zlotowski there followed the mass of \(\mathrm{He}^5\):

\[ \mathrm{He}^5 = 5.0106 \pm 0.0005 \ \text{m.e.} \]

With such a mass, \(\mathrm{He}^5\) would be stable with respect to the process of division into \(\mathrm{He}^4\) and \(n\), but, on the other hand, the well-known \(\mathrm{He}^6\) would have to decay into \(\mathrm{He}^5\) and \(n\). This also indicates the erroneousness of the experiments of Joliot and Zlotowski.

Fig. 4. Scheme of the formation and decay of \(\mathrm{He}^5\). The thick line corresponds to the ground state, or to the algebraic sum of the masses. The numbers standing next to the thick line indicate \(Q\) of the corresponding reaction. Higher states arising from the kinetic energy of the incident particle are indicated by a thin line; the light numbers standing next to them indicate the decay energy of the compound nucleus into \(\mathrm{He}^5\) and the corresponding particle (in the coordinate system of the center of mass). The light numbers next to the vertical arrows indicate the energies of the bombarding particles in the laboratory coordinate system. All energies are given in MeV. The numbers in circles on the arrows denoting transitions between states indicate references to the literature.

Guggenheimer, Heitler, and Powell^25 in 1947 investigated the scattering in helium of deuterons with an energy of 6.6 MeV. The reaction products were recorded by means of a thick-layer photographic plate. Along with the scattered deuterons, a homogeneous group of particles was found, which the authors attributed to protons produced in reaction (5).

According to their measurements, the energy of reaction (5) is

\[ Q=-2.9\ \text{MeV}. \]

From this follows the value of the mass for He\(^5\):

\[ \mathrm{He}^5=5.0137\ \text{a.m.u.} \]

MASS OF He\(^5\)

Table II gives the experimental data on the mass of He\(^5\).

Table II

Reaction energies, mass of He\(^5\), and decay energy of He\(^5\)

K. ARTEMOV AND B. DZHELEPOV

THE ISOTOPE He⁶ ($\beta^-$; $T = 0.823$ sec.)

HISTORY OF THE DISCOVERY AND ESTABLISHMENT OF $Z$ AND $A$

In 1936, Bjerge^26 discovered an activity with a half-life of about 1 sec., arising when beryllium was bombarded by fast neutrons from a source (Rn + Be).

In a subsequent paper Bjerge^27 reported that the radioactive substance is readily carried away by a stream of hydrogen washing over beryllium powder. He suggested that the substance he obtained was He⁶, formed by the reaction

\[ \mathrm{Be}^9 + \mathrm{n} = \mathrm{He}^6 + \alpha . \tag{6} \]

Polessitskii^28 showed that the gas obtained in the interaction of neutrons with beryllium is not adsorbed on a platinum catalyst and therefore is not an isotope of hydrogen. All reactions between Be and n give no other gaseous reaction products except He and H. Therefore, from the totality of the experiments listed it follows that the activity belongs to an isotope of helium. At the same time it becomes practically certain that reaction (6) occurs and He⁶ is obtained.

Subsequently He⁶ was obtained by the reactions

\[ \mathrm{Li}^6(\mathrm{n}, \mathrm{p})\mathrm{He}^6 \tag{7} \]

and

\[ \mathrm{Li}^7(\gamma, \mathrm{p})\mathrm{He}^6 . \tag{8} \]

HALF-LIFE

Table III gives the results of measurements of the half-life of He⁶ by various authors.

Table III

Half-life of He⁶ according to measurements by various authors

The latter value, obtained by Holmes, is the most accurate. It was obtained by the method used by Knol and Feldkamp[^30] as early as 1936.

The principle of the method is as follows (Fig. 5). A rim \(C\) rotates with a certain constant velocity. The substance being activated, deposited on the inner surface of the rim, is subjected to the action of neutrons from source \(A\). The activity formed is carried, as the rim rotates, to counter \(B\), which thereby gives a constant counting rate. The possibility of continuous counting over a long interval of time makes it possible to accumulate large statistics.

As shown by Hamia and Valen[^37], the equilibrium counting rate \(C\) is given by the equation

\[ C = k \frac{\omega}{\lambda} \left(1 - e^{-\frac{\lambda \alpha}{\omega}}\right) \times \left(1 - e^{-\frac{\lambda \beta}{\omega}}\right) \frac{e^{-\frac{\lambda \Phi}{\omega}}}{1 - e^{-\frac{2\pi\lambda}{\omega}}}, \tag{9} \]

Fig. 5. \(A\)—neutron source; \(B\)—counter; \(C\)—rotating rim with an inner surface coated with Be powder; \(Pb\)—lead shielding; \(\alpha\)—effective angular width of the source; \(\beta\)—effective angular width of the counter.

where \(\lambda\) is the decay constant of the radioactive substance, \(\omega\) is the angular velocity of the rim,

\[ \Phi = \pi - \frac{\alpha+\beta}{2}, \]

\(k\) is an instrumental constant, \(\alpha\) is the effective angular width of the source, and \(\beta\) is the effective angular width of the counter.

If \(\lambda\alpha \ll \omega\), \(\lambda\beta \ll \omega\), and \(\Phi \simeq \pi\), then (9) becomes

\[ C = C_0 \frac{x}{\operatorname{sh} x}, \tag{10} \]

where

\[ x = \frac{\lambda\pi}{\omega} = 0.347\,\frac{t}{T}, \]

\(t\) is the period of rotation of the rim, \(T\) is the half-life of the activity, and \(C_0\) is a constant.

Using these formulas, \(T\) can be determined from just two measurements with two different values of \(t\).

In Fig. 6 is shown the curve of the dependence of

\[ R = \frac{C}{C_0} \]

on \(\frac{t}{T}\). \(R\) differs little from unity at \(t = T\) and falls to 0.5 at

\(t = 6.3\,T\). In practice one takes the rotation period \(t\) sufficiently small (rapid rotation), so that \(R \approx 1\). Then the counting rate is not only maximal, but also almost independent of the rotation period.

Fig. 6. Change of the counting rate with the period of rotation of the rim; \(o\)—point of inflection.

Then \(R\) is measured at various rotation speeds; it is most advantageous to choose them so that \(\dfrac{t}{T}\) lies in the interval from 3 to 6. From each pair of values of \(R\) one obtains values of \(T\) for the half-life. From these data one can calculate the most probable value of \(T\).

LIMIT OF THE \(\beta\)-SPECTRUM

The results of measurements of the limit of the \(\beta\)-spectrum of \(\mathrm{He}^6\) by various authors are given in Table IV.

Table IV

Limit of the \(\beta\)-spectrum of \(\mathrm{He}^6\) according to measurements by various authors

RADIOACTIVE ISOTOPES OF HELIUM

The latter value is the most reliable. Perez-Mendez and Brown obtained \(\mathrm{He}^6\) by the reaction \(\mathrm{Be}^9(n,\alpha)\), bombarding a thin beryllium powder (grain size \(1\,\mu\)) with \(\mathrm{Be}+d\) neutrons. A stream of helium continuously swept over the Be powder and carried \(\mathrm{He}^6\) into a chamber attached to a magnetic spectrometer. Fig. 7 shows the Fermi plot for the \(\beta\)-spectrum of \(\mathrm{He}^6\) obtained by them. In the interval from 200 kev to the endpoint of the spectrum, located

Fig. 7. Fermi plot of the \(\beta\)-spectrum of \(\mathrm{He}^6\), uncorrected for the resolving power and absorption in the spectrometer window.

\[ f = F(E,Z)\,E\sqrt{E^2-1}; \]

\(N\) is the number of electrons per unit energy interval; \(\sqrt{N/f}\) is plotted in arbitrary units. The uncorrected endpoint of the \(\beta\)-spectrum of \(\mathrm{He}^6\) is

\[ E_{\mathrm{gr}} = 7.34\,m_0c^2 = 3.230 \pm 0.015\ \mathrm{Mev}. \]

The corrected endpoint is

\[ E_{\mathrm{gr}} = 7.30\,m_0c^2 = 3.215 \pm 0.015\ \mathrm{Mev}. \]

at 3.215 Mev, the points lie well on a straight line. This indicates that the \(\beta\)-spectrum follows the Fermi formula, and the decay apparently belongs to the allowed type.

Yuz, Hall, Eggler, and Goldfarb\(^{32}\) state in their paper devoted to \(\mathrm{Li}^8\) that the endpoint of the \(\beta\)-spectrum of \(\mathrm{He}^6\) is equal to 6 Mev; no further data are given in the paper.

It should be noted that such a value for the endpoint of the spectrum of \(\mathrm{He}^6\) seems improbable. In that case the mass of \(\mathrm{He}^6\) would be equal to 6.023396 a.m.u., and, consequently, it would be unstable with respect to disintegration into \(\mathrm{He}^5\) and \(n\) (sum of masses 6.022981) and even into \(\mathrm{He}^4 + 2n\) (sum of masses 6.021765).

γ-RADIATION OF He⁶

Knox[^40] attempted to detect the γ-radiation of He⁶ by measuring the absorption curve of He⁶ radiation. This curve is presented in Fig. 8.

The horizontal part of the curve indicates the magnitude of the background from bremsstrahlung γ-rays of the electrons of the β-spectrum. The experimental value of the background agrees with its calculated value.

Fig. 8. Absorption curve of He⁶ radiation. Electron range in g/cm² Al. The horizontal part of the curve is the background from bremsstrahlung radiation of the electrons of the β-spectrum.

From this Knox concludes that there are no γ-rays associated with the decay of He⁶, unless they have either very low energy (\(<100\) kev) or low intensity (\(<10\%\) of the transitions, if the γ-quantum energy is of the order of 1 Mev).

DECAY SCHEME OF He⁶

The product \(Tf\) for He⁶ is equal to 640. This is the smallest of the known values of \(Tf\). Apparently, the β-decay of He⁶ belongs to the allowed type; this, however, contradicts certain theoretical considerations[^43].

The data given above on β- and γ-radiation indicate that the principal fraction of He⁶ decays proceeds according to the scheme of Fig. 9.

The only indication of the existence of an excited level of Li⁶ in the interval 0–3.2 Mev is found in the work of Hashley[^44]. Hashley investigated γ-radiation arising when beryllium is bombarded with protons. The reaction Be⁹ \((p,\alpha)\) Li⁶ is exothermic and na

...is observed at small proton energies. However, at a proton energy of 2.52 MeV a sharp increase is observed in the yield of $\gamma$ rays with energy 3 MeV. These $\gamma$ rays may be attributed to the reaction $\mathrm{Be}^9(p,\alpha)\mathrm{Li}^{6*}$, but also to the competing reactions $\mathrm{Be}^9(p,n)\mathrm{B}^9$ and $\mathrm{Be}^9(p,\gamma)\mathrm{B}^{10}$. Therefore the question of the 3 MeV level in $\mathrm{Li}^6$ cannot be regarded as settled. $\beta$ decay to this level would be very difficult to detect. The decay of $\mathrm{He}^6$ to the ground state of $\mathrm{Li}^6$ is allowed; if the transition to the excited level is also allowed, then its probability must be smaller than for the transition to the ground state by a factor of $\dfrac{f_{\mathrm{exc}}}{f_{\mathrm{g.s.}}}$; if the transition to the excited level is forbidden, then its probability is still smaller. Calculation shows that $\dfrac{f_{\mathrm{exc}}}{f_{\mathrm{g.s.}}} \simeq 1/2000$; with the present state of $\beta$ spectroscopy it is practically impossible to detect so weak a soft component. It would be much easier to detect weak but hard $\gamma$ rays, which should follow the soft $\beta$ spectrum.

Fig. 9. Decay scheme of $\mathrm{He}^6$.

MASS OF $\mathrm{He}^6$

The mass of $\mathrm{He}^6$ can be determined in two ways.

1. From the upper limit of the $\beta$ spectrum of $\mathrm{He}^6$:

\[ \mathrm{He}^{6}_{2}=\mathrm{Li}^{6}_{3}+E_{\mathrm{gr}}. \]

Since $E_{\mathrm{gr}}=3.215\pm0.015$ MeV and $\mathrm{Li}^6=6.016952\pm0.00005$ a.m.u., it follows that

\[ \mathrm{He}^{6}=6.02041\pm0.00007\ \text{a.m.u.} \]

1. From the threshold of the reaction $\mathrm{Li}^{7}(\gamma,p)\mathrm{He}^{6}$:

\[ \mathrm{He}^{6}=\mathrm{Li}^{7}+h\nu_{\mathrm{thr}}-\mathrm{H}^{1} \]

(the momentum of the $\gamma$ quantum is neglected).

Taking $h\nu_{\mathrm{thr}}=9.8\pm0.5$ MeV, for the mass of $\mathrm{He}^6$ we obtain:

\[ \mathrm{He}^{6}=6.0206\pm0.0006\ \text{a.m.u.} \]

Within the limits of error the results of both methods agree. At present the most accurate value of the mass of $\mathrm{He}^6$ should be taken to be the value obtained from the upper limit of the $\beta$ spectrum:

\[ \mathrm{He}^{6}=6.02041\pm0.00007\ \text{a.m.u.} \]

CROSS SECTIONS AND THRESHOLDS OF REACTIONS (6), (7), (8)

Reaction \( \mathrm{Be}^{9}(n,\alpha)\mathrm{He}^{6} \).

Allen, Burcham, and Wilkinson\(^{29}\) in 1947 studied the cross section for attenuation of a beam of fast neutrons in \(\mathrm{Be}^{9}\) and the cross section of the reaction \(\mathrm{Be}^{9}(n,\alpha)\mathrm{He}^{6}\) as a function of neutron energy. They obtained the curves shown in Fig. 10.

It is evident that at a neutron energy of \(2.6\) MeV a resonance maximum of the cross section of reaction (5) is observed. The ratio of the cross section of the reaction

Fig. 10. \(A\)—cross section for attenuation of a neutron beam by beryllium \((\sigma_t)\); \(B\)—cross section of the reaction \(\mathrm{Be}(n,\alpha)\mathrm{He}^{6}(\sigma_\alpha)\).

\(\mathrm{Be}^{9}(n,\alpha)\mathrm{He}^{6}\) to the cross section for attenuation of a neutron beam in \(\mathrm{Be}^{9}\) at this energy is approximately equal to \(1/50\).

The experimental width of the maximum at \(2.6\) MeV of curve \(A\), Fig. 10, is about \(1\) MeV. Other maxima observed by the authors were five times narrower; this gives the authors grounds to regard the observed width as close to the true width of the level of the compound nucleus \(\mathrm{Be}^{10*}\). The corresponding lifetime of \(\mathrm{Be}^{10*}\), determined from the uncertainty relation, will be about \(10^{-21}\) sec, i.e., only slightly greater than the time of flight of the neutron through the Be nucleus.

The nucleus Be\(^{10*}\), formed upon the capture of neutrons with energy 2.6 MeV, turns out to be excited to 9.11 MeV; however, the \(\alpha\)-particles that can arise in the decay of Be\(^{10*}\) into He\(^6\) and He\(^4\) have an energy below the potential barrier. Therefore only \(^{1}/_{50}\) of the captures leads to the formation of He\(^6\); the remaining \(^{49}/_{50}\) apparently lead to the emission of neutrons and \(\gamma\)-rays.

Reaction Li\(^6\) (n, p) He\(^6\)

This reaction was observed by Knol and Feldkamp\(^{30,31}\) in 1936 and 1937. The activity arising upon bombardment of lithium with neutrons was erroneously attributed by the authors to Li\(^8\), produced in the reaction

\[ \mathrm{Li}^7(\mathrm{n},\gamma)\mathrm{Li}^8. \]

However, the yield of this reaction is in fact very small. According to measurements by Hughes, Hall, et al.\(^{32}\) in 1947, the cross section of this reaction for thermal neutrons is 0.033–0.049 barn. Under the experimental conditions of Knol and Feldkamp the activity of Li\(^8\) could not have been observed; therefore it is likely that they were dealing with He\(^6\).

Pool and Paul\(^{33}\) in 1946 detected He\(^6\), produced as a result of the reaction Li\(^6\) (n, p) He\(^6\), from its \(\beta\)-spectrum.

It follows from the mass table that the energy of the reaction Li\(^6\) (n, p) He\(^6\) is \(Q=-2.46\) MeV and, consequently, the threshold for the neutron energy is \(E_n=2.87\) MeV.

Reaction Li\(^7\) (\(\gamma\), p) He\(^6\)

This reaction was first observed by Becker, Hanson, et al.\(^{34}\) in 1947.

The threshold of the reaction was measured by these authors in 1947 and 1949.\(^{35}\) According to the latest data the reaction threshold is \(9.8 \pm 0.5\) MeV.

From the mass table it follows that the threshold should be 9.62 MeV.

APPLICATION OF He\(^6\) FOR TESTING THE NEUTRINO HYPOTHESIS AND THE BASIC CONCEPTS OF \(\beta\)-DECAY

The best way of testing the assumption that a neutrino is emitted in \(\beta\)-decay is to investigate an elementary act of \(\beta\)-decay. In this case it is necessary simultaneously to measure the momenta of the electron and of the recoil nucleus. If their vector sum is not equal to zero, then the equal and opposite momentum must be ascribed to the neutrino.

The recoil nuclei in \(\beta\)-decay have very low energy. In order that their energy not be changed as a result of slowing down in the material of the source, it is necessary to use either extremely

thin sources, or else to use radioactive gases. It is desirable to use light radioactive substances having a high end-point of the \(\beta\)-spectrum, since in this case the energy of the recoil nuclei will be greater.

Fig. 11. Scheme of the formation and decay of \(\mathrm{He}^6\).
See explanations to Fig. 4.

It is not difficult to see that \(\mathrm{He}^6\) is an exceptionally suitable substance from all these points of view; only the shortness of the half-life creates certain difficulties.

The elementary acts of \(\beta\)-decay of \(\mathrm{He}^6\) were investigated by Allen, Paneth, and Morrish\(^{42,45}\) in 1948–1949.

The authors set themselves the task of investigating the angular correlation between the directions of emission of the electron and the neutrino from the nucleus. The point is that, as Hamilton\(^{46}\) showed, this correlation depends on the type of interaction of the nucleons with the electron-neutrino field and, moreover,

to a much greater degree than the shape of the β-spectrum. Consequently, by studying the angular correlation, one can determine the form of the interaction and make a choice among the five variants of the theory of β-decay.

The idea of the experiment is as follows. The energy of the recoil nucleus, for given directions of flight of the nucleus and the electron, depends on the angle between the directions in which the electron and the neutrino leave the nucleus. From the conditions of the experiment the authors could calculate the distribution of recoil nuclei by energies, corresponding to different types of angular correlation between the electron and the neutrino. By comparing the observed distribution with the calculated one, one can try to establish the angular correlation.

Fig. 12. Schematic of the experiments of Allen, Paneth, and Morrish ^{42, 43}. \(A\)—a cylinder with \(\mathrm{He}^6\) at a pressure of \(10^{-5}\) mm Hg; \(B\)—a grid to which a retarding potential for ions is applied; \(ЭУ\)—an electron multiplier for registering ions; \(1, 2\)—diaphragms selecting an ion beam; \(3, 4\)—diaphragms specifying the direction of the electrons being registered; \(Cr\)—electron counter. The outputs of the electron multiplier and of the counter are connected in coincidence.

The experiments were carried out according to the scheme of Fig. 12. The β-particles were registered by the counter \(Cr\), and the recoil nuclei by the electron multiplier \(ЭУ\). In front of the multiplier there was a series of grids, which made it possible to create a retarding electric field and to analyze the energy of the recoil nuclei. The output of the electron multiplier and the counter were connected into a coincidence circuit.

The results of the experiments of Allen, Paneth, and Morrish are shown in Fig. 13. Curve \(A\) is the theoretical curve for the dependence of the number of coincidences on the retarding potential at an angle of \(180 \pm 15^\circ\) between the directions of flight of the electron and the recoil nucleus, calculated under the assumption that β-decay is not accompanied by emission of a neutrino. The horizontal part of the curve is due to coincidences occurring because of the decay of \(\mathrm{He}^6\) nuclei located between the grid system and the tube of the electron multiplier, i.e., in a region free from the retarding potential.

The data shown in Fig. 12 clearly show that the assumption of β-decay without a neutrino must be rejected: the experimental points in the upper part of the figure plainly do not lie on curve \(A\).

A considerable number of recoil nuclei flying at an angle of \(162 \pm 8^\circ\) with respect to the direction of flight of the electrons emitted by them also speaks decisively in favor of the existence of the neutrino.

Fig. 13. Results of the experiments of Allen, Paneth, and Morrish\(^{42,45}\). The unshaded circles give the number of coincidences of pulses from the counter and the electron multiplier per \(3.2 \cdot 10^4\) multiplier pulses, at an angle between the directions of the electrons and ions of \(180 \pm 15^\circ\).

The shaded circles give the number of coincidences per \(6.4 \cdot 10^4\) electron-multiplier pulses, at an angle between the directions of flight of the ions and electrons of \(162 \pm 8^\circ\).

Curve \(A\) is the theoretical curve for the dependence of the number of coincidences on the retarding potential at an angle of \(180 \pm 15^\circ\), calculated on the assumption that β-decay is not accompanied by the emission of a neutrino.

However, from these experiments it is difficult to draw a definite conclusion about the character of the angular correlation between the directions of emission from the nucleus of the electron and the neutrino. The authors believe that their experiments give some indication of a correlation of the form \(1 - \frac{1}{3}\frac{v}{c}\cos\theta\), which corresponds to the axial-vector variant of the theory of β-decay.

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