21.Nuclear reaction induced by heavy protons.

An example of a nuclear reaction , carried out by the bombardment of accelerated protons is the reaction :

 7Li +1H → 4He +4 He.

For charged particles that can cause nuclear reactions are alpha particles , protons, the nuclei of deuterium - deuterons and nuclei of heavier elements. Electrons and positrons are also charged particles , but they do not possess the ability to interact with other particles using nuclear forces , nuclear reactions and therefore they do not cause. To a charged particle can penetrate into the nucleus, it must overcome the electrostatic repulsion forces , since all charged particles have positive electrical charges , as well as atomic nuclei .

. In practice, widely used reaction 9Be (α, n) 12C , which can be accomplished by mixing the powder with a powder beryllium any alpha- emitting nuclides , such as radium and polonium and drive the mixture in a sealed cover. So prepared neutron sources that continuously emit neutrons .

Protons can only call endoenergetic reaction with high thresholds . Since the threshold energy of the reaction 3H (p , n) 3He is 1.02 MeV, and the reaction 7Li (p, n) 7Be - 1,88 MeV , so for their implementation requires more complex and expensive accelerators . Capable of accelerating protons to an energy of at least 1.5 - 2 MeV. Energy neutrons in such reactions as a first approximation En = Ep - Epor . Therefore , changing the energy of the accelerated protons neutrons can be obtained with small and, moreover, infinitely adjustable energies , which is very valuable in conducting some experiments.

30.The Rutherford cross section

The stationary Schrödinger equation for a Coulomb potential is 

(1)

with E being the cm energy and positive (scattering case). Substituting the energy with the wave number and the Sommerfeld parameter 

(2)

with in mass units andin MeV for the latter and, it can be shown that there is a general solution to (1)of the form

(3)

with obeying the Laplace equation

(4)

The function are then solutions to the Laplace equation and therefore sums of the linearly independent standard solutionsand(hypergeometric confluent functions, see Messiah) which in turn can be interpreted as the incoming and the scattered wave, respectively. With the asymptotic solution forandthe asymptotic scattered (outgoing) wavefunction can be written as

	(5)
	(6)

as the Coulomb amplitude. It is 

(7)

the Coulomb phase angle.

This can be compared to the general scattering solution

(8)

While the term never disappears in(5) approaching infinity in,becomes very large against it (or more thoroughly, the current density becomes the same with or without this term), the result is

(1.21)

Therefore is 

(1.22)

the same as the ``classical" Rutherford cross section. For calculations of real experiments in the laboratory frame both the scattering angle, the energy and the solid angle have to be converted to the laboratory frame.