Single Bubble SonoLuminescence of Particles model
  The Single Bubble SonoLuminescence is a phenomenon where the vapor bubble trapped in a liquid collapse by emitting of a light. It is very known that the temperature inside the bubble depends on the radius, during the collapse, the temperature can reach thousands of Kelvins and that the light would be emitted by radiation of the ionized gas inside the bubble. So, studies show that in certain cases neither an imploding shock nor a plasma has been observed and the temperature is not high enough to explain the spectrum observed. The Single Bubble SonoLuminescence remains a subject of study. For this study we consider the bubble as a box where the free particles (particularly electrons) stemming from the molecules dissociation, are are trapped and confined within the bubble. The confinement allows the particles to acquire some energy during the collapse which they lose in the form of light and also to be considered to bind to the bubble as an electron is bound to the nucleus in an atom. So, with regard to the bubble the energy of the particles can be considered to quantify, and with the quantum theory, by putting some hypotheses, their energy is determined well. The energy is physically acceptable that if the bubble is spherical. This necessary condition of a spherical bubble of the model is observed experimentally in the collapse phase but not in the afterbounce phase of the bubble, explain why the bubble emits of light in the collapse but not in the phase of the afterbounces where she can be smaller, and constitute a validation of the Single Bubble SonoLuminescence of particles model. For the application of the Single Bubble SonoLuminescence of particles model we consider a electron free particle of mass . We note that the interval of time between and energy (who can be considered as the duration when the bubble emits some light) is of the order of picoseconds, the same order that the shortest pulses observed experimentally. 
Mahamadou Adama Maiga, M Adama, Adama Maiga M
physics.flu-dyn cond-mat.other physics.class-ph quant-ph