Collinear laser spectroscopy

In collinear laser spectroscopy , a laser beam is superimposed in parallel with a fast atom , molecule or ion beam . The rapid movement of the particles in the direction of the laser beam leads to a reduction in the Doppler line width due to the thermal movement of the particles. By increasing the kinetic energy of the particles, the Doppler line width can be reduced to such an extent that the natural line width of an atomic transition can be observed.

The width of the longitudinal (in the beam direction) energy distribution depending on the kinetic energy of a particle beam is described by the following formula:

${\displaystyle \delta E=\delta (1/2\,m\,c^{2}\,\beta ^{2})=m\,c^{2}\,\beta \cdot \delta \beta ={\text{const.}},}$

whereby . It follows for the width of the longitudinal velocity distribution: ${\displaystyle \beta =v/c}$

${\displaystyle \delta \beta ={\frac {\delta {v}}{c}}={\frac {\text{const.}}{m\,c^{2}}}\cdot {\frac {c}{v}}.}$

As you can see, the width of the velocity distribution shrinks with increasing velocity of the particle beam. At the same time, the frequency of the photon emitted by an excited, moving atom / ion shifts due to the Doppler effect . The frequency of the photon in the laboratory system is calculated according to the Doppler formula: ${\displaystyle \delta v}$

${\displaystyle \nu _{\text{Labor}}=\nu _{\text{Ruhe}}\times {\frac {1\pm \beta }{\sqrt {1+\beta }}}}$

where is the quotient of the particle speed and the speed of light used in the special theory of relativity . In the above formula, “+” is relevant for situations in which the particle moves towards the observer, “-” when it moves away from the observer. ${\displaystyle \beta }$ ${\displaystyle \beta =v/c}$

Special procedures

The use of collinear laser spectroscopy to study the properties of short-lived radioactive isotopes is of particular interest . These types of isotopes are generated using special processes in suitable systems, such as the ISOLDE facility at CERN , and then made available to the experimenters as an ion beam . The ions are accelerated by means of electromagnetic fields and thus have a kinetic energy that is far above the thermal energies. If one considers the above Doppler formula for ions that are accelerated in the electric field of a particle accelerator, the kinetic energy of the ion is given by:

${\displaystyle E_{\mathrm {tot} }=eU+mc^{2}={\frac {mc^{2}}{\sqrt {1-\beta ^{2}}}}}$

This results in the detected frequency in the laboratory depending on the accelerating voltage:

${\displaystyle \nu _{\text{Labor}}=\nu _{\text{Ruhe}}\times {\frac {mc^{2}+eU\pm {\sqrt {eU(2mc^{2}+eU)}}}{mc^{2}}}}$

In addition to “classic” detection methods, such as the observation of the fluorescent light that is emitted when the laser is in resonance with the transition in the electron shell, highly sensitive, non-optical detection methods can be used for radioactive isotopes .