Laboratoare Fizică II cu date prelucrate

1. Objectives

- study of the absorption of β particles by a material (aluminium);

- experimental determination of the end-point energy of β particles employing the absorption curve.

2. Theoretical Aspects

β-Disintegration represents the spontaneous emission of an electron or a positron by an unstable nucleus, or the electron capture by a nucleus. Consequently, an isobar nucleus is obtained, whose charge is different by one unit.

- β– decay occurs when a neutron inside a nucleus changes into a proton. The process is

n → p + e– + (1)

where is an antineutrino. The result is a change in the identity of the nuclide as follows

(2)

- β+ decay is similar but proceeds in the opposite direction

p → n + e+ + ν (3)

so the change in the nuclide is

(4)

- Electron capture is equivalent to β+ decay and can occur in nuclei that can undergo the β+ decay process. It looks that below

p + e– → n + ν (5)

A proton in the nucleus captures one of the orbital electrons and changes into a neutron and a neutrino. The net result is the same as equation (4).

Often the β-decay process leaves the residual nucleus in an excited state. This then decays to the ground state by γ-emission. This is generally an undesirable effect, as the γ rays interfere with the measurements we would like to make on the electrons. Some β– processes leave the residual nucleus in the ground state. These are called pure β– emitters.

The difference in the energy between E1 and E2 (see relation (2)) results from differences in the binding energy of the nucleus, and this energy is given up as kinetic energy when the antineutrino has zero energy

Eν = Emax – E (6)

If we denote by ΔE the difference between the initial and final energy of the nucleus and by Er the rebound energy, the energetic balance for the β– decay is

ΔE = E + Eν + Er

ΔE = Emax + Er  Emax (7)

This maximum energy is called the end-point energy.

The most important physical quantity in nuclear spectroscopy was considered, for a long time, the path range of a specific particle for various materials. By path range we understand the thickness of the material needed in order to completely stop the incident particle, perpendicular to the surface of the material. The path range for various particles is expressed in units of g/cm2,

R (g/cm2) = R (cm) × ρ (g/cm3)

where ρ is the density of the material. This unit is very common since the lost of energy by ionization is proportional to N Z. At least for light materials, the path range expressed in g/cm2 is, with an error of 10-20%, virtually identical. Indeed, the number of electrons from 1 cm3 of material is given by

(8) where N0 is Avogadro's number. Since in the case of light materials, Z/A  1/2, in a layer of this kind of material, with a thickness of 1 g/cm2, we find approximately N0 /2 electrons.

Determining the path range of the electron in a given material is a much bigger problem than in the case of heavy-particles, since the trajectory of the electron through the substance resembles a broken line due to the multiple scattering. Because of this, often it is used another characteristic of the penetrating power, similar to the maximum path range. This quantity, practically denoted path range, can be experimentally determined using the absorption curves for the electrons in the material, by extrapolating them to the point where all radiation has been blocked.