tailieunhanh - The Quantum Mechanics Solver 4

The Quantum Mechanics Solver 4 uniquely illustrates the application of quantum mechanical concepts to various fields of modern physics. It aims at encouraging the reader to apply quantum mechanics to research problems in fields such as molecular physics, condensed matter physics or laser physics. Advanced undergraduates and graduate students will find a rich and challenging source of material for further exploration. This book consists of a series of problems concerning present-day experimental or theoretical questions on quantum mechanics | Oscillations of Three Species Atmospheric Neutrinos 21 later time t. Write the probability I . - t to observe a neutrino of flavor p at time t. . We define the oscillation lengths at an energy E pc by 4nhp L Arnj c2 Am2 m2 mJ . iJ b J Notice that there are only two independent oscillation lengths since Am212 Am23 0. For neutrinos of energy E 4 GeV calculate the oscillation lengths L12 and L23. We will choose for Am22 the result given in and we will choose IAm231 c4 x 10 _3 eV2 a value which will be justified later on. . The neutrino counters have an accuracy of the order of 10 and the energy is E 4 GeV. Above which distances 12 and 22 of the production point of the neutrinos can one hope to detect oscillations coming from the superpositions 1 2 and 2 3 . The Super-Kamiokande experiment performed in 1998 consists in detecting atmospheric neutrinos. Such neutrinos are produced in the collision of high energy cosmic rays with nuclei in the atmosphere at high altitudes. In a series of reactions n mesons are produced abundantly and they decay through the chain n p v followed by p e ve ip and an analogous chain for n mesons. The neutrino fluxes are detected in an underground detector by the reactions and . To simplify things we assume that all muons decay before reaching the surface of the Earth. Deduce that in the absence of neutrino oscillations the expected ratio between electron and muon neutrinos R _ N v NV N Ve N Ve would be equal to 2. . The corrections to the ratio R e due to the fact that part of the muons reach the ground can be calculated accurately. Once this correction is made one finds by comparing the measured and calculated values for R e R jmeasured _. o_O5 . R e calculated In order to explain this relative decrease of the number of vM s one can think of oscillations of the types v ve and v vT. The Super-Kamiokande experiment consists in varying the time of flight of the neutrinos by measuring .