Nucleus and quantum mechanics

The Nucleus as a test Lab for Quantum Mechanics

We will consider four domains where the atomic nuclear model proposed by Rutherford is crucial to understanding physical phenomena. These are the domains of atomic, molecular, condensed matter, and nuclear phenomena.

Atomic, molecular and condensed matter:
In 1913 Neils Bohr introduced the "old" quantum theory to explain the spectrum of the hydrogen atom. This theory requires the use of a model of the atom which is Rutherford's atomic nuclear model. The introduction of quantum mechanics by Schroedinger and others subsequent to Bohr's model refined quantum mechanics, but still requires the nuclear model of the atom. Once the basic structure of the atom is understood, i.e., a small very dense positive core surrounded by a cloud of electrons, it is possible to extend quantum mechanics to the molecular and condensed matter domain.

The nuclear atom tells us ... conflict with classical dynamics

Quantum mechanics tells us that a system can exist in the lowest state of excitation call the ground state.
Atomic electrons can make the transition from state 2 to state 1 giving off a photon of energy e1-e2. In the ground state, #1, the atom can not emit any more energy even though classically we expect the electron to experience an acceleration due to its attraction to the nucleus. The nuclear atomic model plus the rules of quantum mechanics force us to abandon the classical expectation that every accelerated charge must emit energy.

Alpha particle decay
It was known that the nuclear force holding the alpha particle inside the nucleus was of short range, of radius R in the diagram ~10^-12 cm for a heavy nucleus decay. Outside this radius, r > R, the alpha particle feels the repulsive electrical force from the positively charged nucleus ( Coulomb repulsion). The energy E of the alpha particle measured outside the nucleus is less than Vmax. The region in red, R<r<Rc is classically forbidden, and hence we would expect that the alpha particle would be stuck forever within the nucleus. Quantum mechanics allows the kinetic energy to be negative in the forbidden region through a process called quantum tunneling.

Tunneling in sub-coulomb barrier nuclear reactions.
Cockcroft and Walton showed (1932) that protons could be captured by nuclei even for bombarding energies below Vmax, that is, E < Vmax. This is the inverse of alpha decay. Classically we do not expect that protons could penetrate the forbidden region between R and Rc. This would like rolling a ball up a hill but never getting to the top (Vmax). We would, indeed, be surprised to find the ball in the hole in this case. Gamow's predictions of quantum tunneling were verified by both alpha particle decay and the sub-barrier capture reactions studied by Cockcroft and Walton.

The nuclear atom tells us ...	conflict with classical dynamics
	Quantum mechanics tells us that a system can exist in the lowest state of excitation call the ground state. Atomic electrons can make the transition from state 2 to state 1 giving off a photon of energy e1-e2. In the ground state, #1, the atom can not emit any more energy even though classically we expect the electron to experience an acceleration due to its attraction to the nucleus. The nuclear atomic model plus the rules of quantum mechanics force us to abandon the classical expectation that every accelerated charge must emit energy.
	Alpha particle decay It was known that the nuclear force holding the alpha particle inside the nucleus was of short range, of radius R in the diagram ~10^-12 cm for a heavy nucleus decay. Outside this radius, r > R, the alpha particle feels the repulsive electrical force from the positively charged nucleus ( Coulomb repulsion). The energy E of the alpha particle measured outside the nucleus is less than Vmax. The region in red, R<r<Rc is classically forbidden, and hence we would expect that the alpha particle would be stuck forever within the nucleus. Quantum mechanics allows the kinetic energy to be negative in the forbidden region through a process called quantum tunneling.
	Tunneling in sub-coulomb barrier nuclear reactions. Cockcroft and Walton showed (1932) that protons could be captured by nuclei even for bombarding energies below Vmax, that is, E < Vmax. This is the inverse of alpha decay. Classically we do not expect that protons could penetrate the forbidden region between R and Rc. This would like rolling a ball up a hill but never getting to the top (Vmax). We would, indeed, be surprised to find the ball in the hole in this case. Gamow's predictions of quantum tunneling were verified by both alpha particle decay and the sub-barrier capture reactions studied by Cockcroft and Walton.