ph135c_hw9

# ph135c_hw9 - π → μ ν μ Such an experiment would...

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Physics 135c H. W. Assignment 9 1.) 2.) In class we derived two-component neutrino oscillations. Perform a more “rigorous” derivation by using a phase diFerence between the two components of (¯ h = c = 1): φ = ( E 2 - E 1 ) t - ( p 2 - p 1 ) x rather than simply φ = ( E 2 - E 1 ) t as we did in class. Show that this leads to the same oscillation probability P ( ν e ν μ ) = sin 2 (2 θ ) sin 2 ( πx/L osc ) with L osc = 4 π ¯ h < E ν > Δ m 2 c 3 and < E ν > = ( E 1 + E 2 ) / 2, as long as we require x = < v > t , where < v > is the average neutrino velocity. 3.) As shown in Prob. 2, 2-component oscillations travel with two diFerent momenta. Imagine an experiment measuring the momentum of muons from
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Unformatted text preview: π + → μ + + ν μ . Such an experiment would reveal two momentum peaks corresponding to the two neutrino masses. Show that you cannot observe these two peaks and neutrino oscillations (e.g. by measuring the momenta vs. x- the distance from the source) due to the uncertainty principle (what else?!). 4.) The sun has an average surface magnetic ±eld on the order of 1 gauss. Use this data to estimate the magnetic ±eld of a 1 solar mass neutron star. State your assumptions. Compare with typical neutron star magnetic ±elds of 10 12 gauss....
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## This note was uploaded on 12/04/2011 for the course PHY 7070 taught by Professor Smith during the Spring '11 term at University of Wisconsin.

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