Bremsstrahlung Spectrum in α Decay

Using our previous approach to electromagnetic emission during tunneling, an explicit , essentially classical, formula describing the bremsstrahlung spectrum in α decay is derived. The role of tunneling motion in photon emission is discussed. The shape of the spectrum is a universal function of the ratio E γ /E 0 , where E γ is the photon energy and E 0 is a characteristic energy depending only on the nuclear charge and the energy of the α particle. During the α decay of a nucleus the α particle tunnels through the Coulomb barrier and is accelerated beyond the classical turning point to its final energy. Thus electromagnetic radiation should be emitted during the process. In spite of the fundamental nature of the γ emission duringα decay, the corresponding bremsstrahlung spectrum was neither measured, nor considered theoretically until recent years. Normally soft γ emission accompanying the Coulomb interaction of heavy particles is well described by classical electrodynamics. The case of α decay is somewhat special, since part of the 'trajectory' of the α particle lies within the underbarrier region and may be described classically only in some limited sense, as a motion in imaginary time. While the golden rule of quantum mechanics gives a straightforward recipe to calculate the emission probability, intuitively one would like to understand whether tunneling may be somehow incorporated in the general framework of classical electrodynamics and whether it makes any sense to say that photons are emitted during tunneling motion. In Ref. [1] the electromagnetic radiation by a charge tunneling through a potential barrier was considered under the conditions that the motion is quasiclassical, i.e. the barrier is smooth compared to the particle wave length, and that the energy of the emitted photons is small compared to the particle energy. It was shown that in this case the emission spectrum is described by the well known classical formula, involving the Fourier transform of the particle acceleration, with the only difference that the 1