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Nuclear de-excitation

Nuclear de-excitation. nucleus. Outline of approach…. ??. Source of radiation. ??. Propagation of radiation field. Detection of radiation. Propagation of radiation field. Electromagnetic radiation ( quantized ); v = c.

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Nuclear de-excitation

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  1. Nuclear de-excitation

  2. nucleus Outline of approach… ?? Source of radiation ?? Propagation of radiation field Detection of radiation

  3. Propagation of radiation field • Electromagneticradiation (quantized); v = c • Power radiated P(,) depends on the nature of the source (e.g., electric dipole, magnetic dipole, electric quadrupole, magnetic quadrupole, …) (May be simultaneously more than one; one will dominate.) • Source uniquely describes P(,) and, conversely,P(,) allows the determination of the source of the radiation. • P(,) comes from E-M radiation theory (Maxwell)

  4. Angular distribution of intensity of radiation field: Legendre polynomials(from Maxwell’s Eq) dipole field quadrupole field Properties of radiation field • Multipole order of the radiation field: 2L • L = 1 (dipole field); L = 2 (quadrupole); L = 3… • “EL”  electric multipole of order L • “ML”  magnetic multipole of order L

  5. oscillation amplitude radiation frequency Properties of radiation field • The parity of the radiation field: • (EL) = (-1)L • (ML) = (-1)L+1 • Parity of E or M multipoles of same order is opposite. • The total (integrated) radiated power in the classical radiation field: (10.8)  (10.5) if L=1

  6. The total (integrated) radiated power in the classical radiation field: nuclear matrix element oscillation amplitude Transition operator Transition between initial and final nuclear states In quantum mechanics…

  7. In quantum mechanics…These properties remain unchanged - • Multipole order of the radiation field: 2L • Angular distribution of intensity of radiation field • The parity of the radiation field: • (EL) = (-1)L • (ML) = (-1)L+1 • Parity of E or M multipoles of same order is opposite. In QM what is more meaningful is the decay rate - or the probability per unit time of de-excitation =  …

  8. radiated power: watts = joules/sec Energy per quantum (photon) of frequency  () …from the nuclear source In quantum mechanics…These properties remain unchanged - Therefore - the number of photons emitted per unit time is -- The form of the operators mfi is quite “classical” - it represents the nature of the time-dependent charge distribution in the nucleus to produce this radiation field.

  9. E-M matrix element Then, we can compute -- In quantum mechanics…The transition matrix elements- We need to know three quantities… The initial state nuclear wave function The final state nuclear wave function The transition operator

  10. Due to intrinsic magnetic moment Due to spatial coordinates In quantum mechanics…The transition matrix elements- If we know these three quantities, we can compute --

  11. ?? ?? source term The and are the sum of A integrals and involve the Pauli spin martices… In quantum mechanics…The transition matrix elements- As an example, the electric and magnetic matrix elements due to spatial coordinates can be written -- Note: each is a sum of Z integrals!

  12. Assume: ~constant for 0  r  R In quantum mechanics…The transition matrix elements- To get an estimate, try something “simple” -- Consider only a single proton transition: In general: average over initial states m’and sum over final states m”.

  13. In quantum mechanics…The transition matrix elements- Results for single proton transitions:

  14. For E-M interactions: Conserve Consider a transition: Example: Transition selection rulesAngular momentum & parity conservation

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