2.) Consider a universe with only two neutrino flavor eigenstates, ve and v, and two mass...

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2.) Consider a universe with only two neutrino flavor eigenstates, ve and v, and two mass eigen- states, v and v2, with m = 0.0362 eV and m = 0.0425 eV. The mixing between these states occurs as described in the textbook. An accelerator produces a beam of No neutrinos that are pure ve at an energy of 27.7 MeV. The number of ve is measured at various locations along the beam and is observed to reach a minimum value of 0.863No. a.) (10 points) What are all of the possible values of the mixing angle 0 in the range - < 0 ? There are eight possible values, one of which is between 1.3 and 1.4 rad. b.) (5 points) Given the mixing angles found in part (a), what are the possible values for the probability that a ve would be observed to have mass m? c.) (7 points) What is the location of the first minimum in the number of ve? The answer is between 50 and 100 km. d.) (3 points) What first location (other than the source itself) where the number of ve is at its maximum value? e.) (5 points) If 1 million ve are initially produced, what would be the number of ve measured 317 km from the source? Hints: You will need to be careful when inverting trigonometric functions and the square function. You may want to consult the document "Inverse Trigonometric Functions" posted on CourseSite. If you are having trouble with the numerical calculations, try putting everything into mks units. 1 eV/c = 1.78266192.10-36 kg. 2.) Consider a universe with only two neutrino flavor eigenstates, ve and v, and two mass eigen- states, v and v2, with m = 0.0362 eV and m = 0.0425 eV. The mixing between these states occurs as described in the textbook. An accelerator produces a beam of No neutrinos that are pure ve at an energy of 27.7 MeV. The number of ve is measured at various locations along the beam and is observed to reach a minimum value of 0.863No. a.) (10 points) What are all of the possible values of the mixing angle 0 in the range - < 0 ? There are eight possible values, one of which is between 1.3 and 1.4 rad. b.) (5 points) Given the mixing angles found in part (a), what are the possible values for the probability that a ve would be observed to have mass m? c.) (7 points) What is the location of the first minimum in the number of ve? The answer is between 50 and 100 km. d.) (3 points) What first location (other than the source itself) where the number of ve is at its maximum value? e.) (5 points) If 1 million ve are initially produced, what would be the number of ve measured 317 km from the source? Hints: You will need to be careful when inverting trigonometric functions and the square function. You may want to consult the document "Inverse Trigonometric Functions" posted on CourseSite. If you are having trouble with the numerical calculations, try putting everything into mks units. 1 eV/c = 1.78266192.10-36 kg.