Question

(a) Calculate the differential cross section in the first Born approximation for a Coulomb potential $V(r) = Z_1 Z_2 e^2 / r$, where $Z_1 e$ and $Z_2 e$ are the charges of the projectile and target particles, respectively. (b) To have a quantitative idea about the cross section derived in (a), consider the scattering of an alpha particle (i.e., a helium nucleus with $Z_1 = 2$ and $A_1 = 4$) from a gold nucleus ($Z_2 = 79$ and $A_2 = 197$). (i) If the scattering angle of the alpha particle in the Lab frame is $ heta_1 = 60^circ$, find its scattering angle $ heta$ in the CM frame. (ii) If the incident energy of the alpha particle is 8 MeV, find a numerical estimate for the cross section derived in (a).

          (a) Calculate the differential cross section in the first Born approximation for a Coulomb potential $V(r) = Z_1 Z_2 e^2 / r$, where $Z_1 e$ and $Z_2 e$ are the charges of the projectile and target particles, respectively.
(b) To have a quantitative idea about the cross section derived in (a), consider the scattering of an alpha particle (i.e., a helium nucleus with $Z_1 = 2$ and $A_1 = 4$) from a gold nucleus ($Z_2 = 79$ and $A_2 = 197$). (i) If the scattering angle of the alpha particle in the Lab frame is $	heta_1 = 60^circ$, find its scattering angle $	heta$ in the CM frame. (ii) If the incident energy of the alpha particle is 8 MeV, find a numerical estimate for the cross section derived in (a).

(a) Calculate the differential cross section in the first Born approximation for a Coulomb potential V(r) = Z1 Z2 e^2 / r, where Z1 e and Z2 e are the charges of the projectile and target particles, respectively.
(b) To have a quantitative idea about the cross section derived in (a), consider the scattering of an alpha particle (i.e., a helium nucleus with Z1 = 2 and A1 = 4) from a gold nucleus (Z2 = 79 and A2 = 197). (i) If the scattering angle of the alpha particle in the Lab frame is heta1 = 60^circ, find its scattering angle heta in the CM frame. (ii) If the incident energy of the alpha particle is 8 MeV, find a numerical estimate for the cross section derived in (a).

Added by Charles A.

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