# Quantum Theory of the Atomic Nucleus G. Gamow, currently in Göttingen. With 5 illustrations. (Received on August 2, 1928.) The author attempts to study the processes of α-radiation based on wave mechanics and to theoretically obtain the experimentally established relationship between the decay constant and the energy of α-particles. Section 1. It has been often suggested that non-Coulombic forces play a significant role in the atomic nucleus. Many hypotheses can be made about the nature of these forces. They could be attractions between the magnetic moments of individual nuclear components or forces due to electric and magnetic polarization. These forces decrease rapidly with increasing distance from the nucleus and only dominate near the nucleus over the Coulombic force. From experiments on α-ray scattering, we conclude that for heavy elements, the attractive forces are not yet noticeable up to a distance of about 10⁻¹² cm. Thus, we can assume the potential energy curve shown in Figure 1. Here, p'' is the distance up to which Coulombic attraction is experimentally proven. From p' (unknown and possibly much smaller than p'') deviations begin, and at r₀ the U-curve has a maximum. For r' < r₀, attractive forces are already present, and the particle would orbit the nucleus like a satellite. However, this motion is not stable because the particle's energy is positive, and eventually, the α-particle will escape (α-radiation). This presents a fundamental problem. To escape, the α-particle must overcome a potential barrier of height U₀ (Figure 1), with its energy not less than U₀. However, experimentally, the energy of α-particles is much smaller. For example, in the study of α-ray scattering from uranium, the Coulomb law applies up to a distance of 3.2×10⁻¹² cm. On the other hand, the energy of α-particles emitted by uranium corresponds to a distance of 6.3×10⁻¹² cm (r₂ in Figure 1). For an α-particle to escape from the nucleus, it would have to pass through the region between r₁ and r₂, where its kinetic energy would be negative, which is impossible classically. To overcome this difficulty, Rutherford assumed that α-particles are neutral in the nucleus because they contain two electrons. Only after a certain distance from the nucleus does the particle lose these electrons, which fall back into the nucleus, and it escapes under Coulombic repulsion. However, this assumption seems unnatural and unlikely to correspond to experimental facts. Section 2. From the perspective of wave mechanics, the above difficulty disappears. In wave mechanics, there is always a non-zero probability of transition from one region to another of equal energy, separated by an arbitrarily high but finite potential barrier.# Quantum Theory of the Atomic Nucleus G. Gamow, currently in Göttingen. With 5 illustrations. (Received on August 2, 1928.) The author attempts to study the processes of α-radiation based on wave mechanics and to theoretically obtain the experimentally established relationship between the decay constant and the energy of α-particles. Section 1. It has been often suggested that non-Coulombic forces play a significant role in the atomic nucleus. Many hypotheses can be made about the nature of these forces. They could be attractions between the magnetic moments of individual nuclear components or forces due to electric and magnetic polarization. These forces decrease rapidly with increasing distance from the nucleus and only dominate near the nucleus over the Coulombic force. From experiments on α-ray scattering, we conclude that for heavy elements, the attractive forces are not yet noticeable up to a distance of about 10⁻¹² cm. Thus, we can assume the potential energy curve shown in Figure 1. Here, p'' is the distance up to which Coulombic attraction is experimentally proven. From p' (unknown and possibly much smaller than p'') deviations begin, and at r₀ the U-curve has a maximum. For r' < r₀, attractive forces are already present, and the particle would orbit the nucleus like a satellite. However, this motion is not stable because the particle's energy is positive, and eventually, the α-particle will escape (α-radiation). This presents a fundamental problem. To escape, the α-particle must overcome a potential barrier of height U₀ (Figure 1), with its energy not less than U₀. However, experimentally, the energy of α-particles is much smaller. For example, in the study of α-ray scattering from uranium, the Coulomb law applies up to a distance of 3.2×10⁻¹² cm. On the other hand, the energy of α-particles emitted by uranium corresponds to a distance of 6.3×10⁻¹² cm (r₂ in Figure 1). For an α-particle to escape from the nucleus, it would have to pass through the region between r₁ and r₂, where its kinetic energy would be negative, which is impossible classically. To overcome this difficulty, Rutherford assumed that α-particles are neutral in the nucleus because they contain two electrons. Only after a certain distance from the nucleus does the particle lose these electrons, which fall back into the nucleus, and it escapes under Coulombic repulsion. However, this assumption seems unnatural and unlikely to correspond to experimental facts. Section 2. From the perspective of wave mechanics, the above difficulty disappears. In wave mechanics, there is always a non-zero probability of transition from one region to another of equal energy, separated by an arbitrarily high but finite potential barrier.