7 Check that the Jacobian of the transformation between vector v 1 vector v 2

7 check that the jacobian of the transformation

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7. Check that the Jacobian of the transformation between ( vector v 1 , vector v 2 ) and ( vector v, vector V c ) is unity. You only need to consider any particular component, x , y , or z of these velocity vectors and show that the corresponding Jacobian is unity. 1
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8. Determine the production rate of 4 He in the PP2 chain assuming that all the interme- diate nuclear products have reached steady state. Express the result in terms of the reaction rate of the first reaction. 9. Determine the rate of energy generation per unit mass for the PP2 chain assuming that all the intermediate products have reached their equilibrium concentration. 10. Consider the first reaction of the CNO cycle discussed in class. Proceeding as we did for the proton-proton fusion determine the formula for the reaction rate of this process, up to an overall factor S ( E ) which we assume is a slowly varying function of E . Express the result as a power law in temperature in the vicinity of T = 1.5 × 10 7 K in order to understand the temperature dependence of this rate. 2
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  • Winter '18
  • S C Misra

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