Beta-spectrometer, an instrument for measuring the energy distribution (the spectrum) of the electrons and positrons emitted in β-decay, and also of conversion electrons and of the electrons produced when gamma, X-ray and other radiations interact with matter. The main characteristics of a beta-spectrometer are its resolving power and its transmission. The resolving power characterises the smallest difference in electron energy that a beta-spectrometer is able to register.
Fig. 1. The spectrum of the conversion electrons of 170Tm: p — the momentum in G·cm, N is the number of electrons.
When the energy or the momentum of the electrons is varied, a distribution containing maxima is obtained (Fig. 1). The ratio of the width of a maximum at half its height to the energy Ε or the momentum p of the electrons (ΔΕ/Ε or Δp/p) is called the resolving power of the beta-spectrometer. The transmission of a beta-spectrometer is the ratio of the number of electrons that reach the detector to the total number of electrons of the given energy emitted by the source. The product of the transmission of a beta-spectrometer and the area of the source is called the luminosity and is expressed in cm2. The greater the luminosity, the more sensitive the beta-spectrometer.
A distinction is drawn between beta-spectrometers that measure the energy of electrons from their effect on matter and beta-spectrometers that separate electrons of different energies in space in electric and magnetic fields. Instruments of the first type include ionisation chambers, scintillation counters and semiconductor detectors. Their action amounts to converting the energy of the electrons in matter into electrical pulses. The advantage of beta-spectrometers of this type is that practically the whole spectrum can be recorded at once with multichannel pulse-height analysers; their serious drawback is a low resolving power ΔΕ/Ε, especially for slow electrons. In ionisation chambers and scintillation counters ΔΕ/Ε is usually ≈ 10% , and in semiconductor detectors ≈ 5—20% .
Beta-spectrometers with spatial separation of the electrons have, as a rule, a much higher resolving power; their field of application is considerably wider, despite the difficulty of making them. An electric (E) or a magnetic (H) field separates electrons of different energies and focuses the monoenergetic electrons that leave the source within a certain solid angle. The field strength must be held constant to an accuracy of ΔH/H=10-6. The spatial separation of the electrons takes place in a vacuum chamber (pressure 10-4—10-9 mm Hg). The Earth's magnetic field is screened or compensated to within 10-4 Oe.
The first magnetic beta-spectrometer was the one constructed in 1912 by the Polish physicist J. Danysz. In it the electrons move in a uniform magnetic field in a plane along a circle whose radius r is proportional to the momentum of the electrons p and inversely proportional to the magnetic induction B. In a magnetic beta-spectrometer it is convenient to measure the momentum in units of Bρ (G•cm). In a beta-spectrometer with a uniform transverse magnetic field the electrons are focused at the largest angles of emission from the source in the plane perpendicular to B. An image of the source is formed when the radius vector of the electron has turned through 180° (a beta-spectrometer with semicircular focusing); in the plane parallel to B the electrons move along a spiral (Fig. 2). The electrons leaving the source are focused in the plane parallel to B and perpendicular to the direction in which they leave the source. Despite their low transmission, such beta-spectrometers are often used because they are simple and because they allow energy to be measured absolutely. Photographic plates usually serve as the detector (see Nuclear photographic emulsion).
Fig. 2. Diagram of the electron trajectories in a magnetic β-spectrometer with a uniform magnetic field (with semicircular focusing). Electrons that leave the source in the direction perpendicular to B as a flat diverging beam of angular width φ are focused, after turning through 180°, on a photographic plate lying in the plane parallel to B. There is no focusing in the angle ψ (in the plane parallel to B).
In 1946 the Swedish scientists N. Svartholm and K. Siegbahn created a magnetic beta-spectrometer with double focusing, in which the magnetic field is perpendicular to the electron trajectories but is not uniform, falling off with the radius ρ as 1/ρ. In it the focusing is of the first order in the angle φ and of the second order in the angle ψ (Fig. 2). The angle between the radius vectors of the source and of its image is π√2 (such an instrument is also called a π√2 beta-spectrometer). In the focal plane Δp/p≈0.1%, and this is retained when the energy of the electrons is reduced to a few eV. The magnetic field in a π√2 beta-spectrometer is produced either by current-carrying coils or by iron electromagnets with profiled poles. In 1960 an iron-free β-spectrometer was built in Canada with ρ=1 m and Δp/p=0.01% at a transmission of 0.06% (R. L. Graham, J. T. Ewan, J. S. Geiger). The resolving power of the best iron π√2 β-spectrometers also reaches 0.03%, but it deteriorates badly on passing to slow electrons. Photographic plates, Geiger counters, semiconductor detectors and electron multipliers are used to detect the electrons.
In Vladimirsky's toroidal beta-spectrometer the magnetic field is produced by a current-carrying toroidal coil. The source and the detector are placed on the axis of the coil. The electrons enter the field and leave it through the gaps between the turns, whose shape ensures that the electrons are focused over a wide range of angles of emission. The transmission of such beta-spectrometers can exceed 20%. To analyse the spectrum of slow electrons, electrostatic beta-spectrometers are used with an analyser in the form of a spherical capacitor. The source and the detector lie outside the electric field E, which is perpendicular to the trajectories of the particles. For non-relativistic electrons double focusing is achieved. Electrostatic beta-spectrometers have a good resolving power (up to 0.05%) at a transmission of 0.1%. The slow electrons at the output of electrostatic beta-spectrometers are usually registered by a system of electron multipliers.
In 1946 the Swedish scientists N. Svartholm and K. Siegbahn created a magnetic beta-spectrometer with double focusing, in which the magnetic field is perpendicular to the electron trajectories but is not uniform, falling off with the radius ρ as 1/ρ. In it the focusing is of the first order in the angle φ and of the second order in the angle ψ (Fig. 2). The angle between the radius vectors of the source and of its image is π√2 (such an instrument is also called a π√2 beta-spectrometer). In the focal plane Δp/p≈0.1%, and this is retained when the energy of the electrons is reduced to a few eV. The magnetic field in a π√2 beta-spectrometer is produced either by current-carrying coils or by iron electromagnets with profiled poles. In 1960 an iron-free β-spectrometer was built in Canada with ρ=1 m and Δp/p=0.01% at a transmission of 0.06% (R. L. Graham, J. T. Ewan, J. S. Geiger). The resolving power of the best iron π√2 β-spectrometers also reaches 0.03%, but it deteriorates badly on passing to slow electrons. Photographic plates, Geiger counters, semiconductor detectors and electron multipliers are used to detect the electrons.
In 1946 the Swedish scientists N. Svartholm and K. Siegbahn created a magnetic beta-spectrometer with double focusing, in which the magnetic field is perpendicular to the electron trajectories but is not uniform, falling off with the radius ρ as 1/ρ. In it the focusing is of the first order in the angle φ and of the second order in the angle ψ (Fig. 2). The angle between the radius vectors of the source and of its image is π√2 (such an instrument is also called a π√2 beta-spectrometer). In the focal plane Δp/p≈0.1%, and this is retained when the energy of the electrons is reduced to a few eV. The magnetic field in a π√2 beta-spectrometer is produced either by current-carrying coils or by iron electromagnets with profiled poles. In 1960 an iron-free β-spectrometer was built in Canada with ρ=1 m and Δp/p=0.01% at a transmission of 0.06% (R. L. Graham, J. T. Ewan, J. S. Geiger). The resolving power of the best iron π√2 β-spectrometers also reaches 0.03%, but it deteriorates badly on passing to slow electrons. Photographic plates, Geiger counters, semiconductor detectors and electron multipliers are used to detect the electrons.