We have a spin-one-half projectile (mass m, Energy E = ℎ 2

2

ଶ

). This projectile scatters

a spin-one-target of infinite mass.

For this, the Hamiltonian is:

∫ = ଵଶ

−

In the above expression, µ > 0, σi represent the Pauli spin operators, where for i=1,

we have the spin operator for projectile and for i=2, we have spin operator for

target.

Evaluate ௗ

ௗΩ

(differential scattering cross section), in lowest order Born

approximation. The same should be calculated as a function of k and scattering

angle. Also, computation should be done averaging over initial; and summing over

final states of spin polarization.​

Order the sequence of ideas that lead to marie curies discovery of radioactive elements number the events in chronological order starting with the oldest

At 20∘c, the hole in an aluminum ring is 2.800 cm in diameter. you need to slip this ring over a steel shaft that has a room-temperature diameter of 2.804 cm . 1. to what common temperature should the ring and the shaft be heated so that the ring will just fit onto the shaft? coefficients of linear thermal expansion of steel and aluminum are 12×10−6 k−1 and23×10−6 k−1 respectively.

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b