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GATE 2025 PH – Question 39

Nuclear and Particle Physics · nuclear force and two nucleon problem · 2 marks · Multiple choice

Two projectile protons P1 and P2 both with spin up (along the +z direction) are scattered from another fixed target proton T with spin up at rest in the xy plane, as shown in the figure. They scatter one at a time. The nuclear interaction potential between both the projectiles and the target proton is λL⃗ ⋅S , where L⃗ is the orbital angular momentum of the system with respect to the target, S is the spin angular momentum of the system and λ is a negative constant in appropriate units. Which one of the following is correct?

Two spin-up protons moving right above and below a fixed spin-up target.
  1. P1 will be scattered in the +y direction (upward) and P2 will be scattered in the −y direction (downward)
  2. P1 will be scattered in the +y direction (upward) and P2 will be scattered in the +y direction (upward)
  3. P1 will be scattered in the −y direction (downward) and P2 will be scattered in the +y direction (upward)
  4. P1 will be scattered in the −y direction (downward) and P2 will be scattered in the −y direction (downward)

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Correct answer: (D) P1 will be scattered in the −y direction (downward) and P2 will be scattered in the −y direction (downward)

Explanation

For rightward motion $L_z=-yp_x$. Thus $V=-\lambda yp_xS_z$ and $F_y=\lambda p_xS_z<0$, independent of the sign of the impact parameter. Both deflect downward.