PHL424: Nuclear surface vibration. Indian Institute of Technology Ropar

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Pearl Blake
5 years ago
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1 PL44: Nuclear surface vibration

2 Systeatics xcitation energy (kev) Ground state Configuration. Spin/parity π ; x kev

3 4 / nergy ratio: irrors systeatics xcitation energy (kev) 4 Ground state Configuration. Spin/parity π ; x kev

4 volution of nuclear structure as a function of nucleon nuber

5 Collective vibration * n general, ( ) ( ) R θ, φ R α Yµ θ, µ µ φ forbidden density change! forbidden CM oves! tie OK...

6 Collective vibration * n general, ( ) ( ) V C, µ R θ, φ R α Yµ θ, µ α µ haronic vibration µ φ : quadrupole vibration : octupole vibration

7 Collective vibration classical ailtonian µ µ µ µ α α C. ) ( ), ( / / corr shell A Z N a A Z a A a A a Z A A C S V ± δ inding energy of a nucleus: π 4 R A M ( ) ( ) ( ) ( ) ( ) 6 4 / π A r a e Z A a C S S a V 5.56 MeV a S 7.MeV a C.697 MeV a A.85 MeV a P. MeV constants:

8 Collective vibration classical ailtonian µ α µ µ C α µ πα µ C µ α µ πα µ, α µ i δ δ µ µ quantization [ ] µ x µ C x µ energy eigenvalue ω nµ µ ω ω / wave function ( ) x ψ n N n n x e erite polynoials

9 Second quantization ailton operator πα µ C µ α µ ω µ µ µ αα ħ ωω μμ μμ ππ αα ħ ωω μμ μμ rule for boson operators: µ µ µ µ δ δ µ µ

10 Second quantization ailton operator ω µ µ µ rule for boson operators: µ µ µ µ δ δ µ µ creation & annihilation operators increase or decrease the nuber of phonons in a wave function ground state -phonon state -phonon state > µ ~ > > µ µ > > (vacuu)

11 Second quantization ailton operator ω µ µ µ rule for boson operators: µ µ µ µ δ δ µ µ -phonon energy: < > ω < > < > < > ω < > < > < > ω < > < > < > ω < ( ) > < > ω ( ) ( )

12 Second quantization ailton operator ω µ µ µ rule for boson operators: µ µ µ µ δ δ µ µ -phonon energy: < > ~ ω < > < > < > ~ ω < ( ) > < ( ) > < > ~ ω < > < etc. > ~ ħ ωω noralization of wave function!!!

13 Second quantization ailton operator ω µ µ µ rule for boson operators: µ µ µ µ δ δ µ µ -phonon state: ΨM N ( M ) > noralization (approxiation): N < > N < ( ) > N < > N < ( ) ( )( ) > N

14 Second quantization ailton operator ω µ µ µ rule for boson operators: µ µ µ µ δ δ µ µ -phonon state: ΨM N ( M ) > noralization: ( M ) ( M ) < > N ( M ) ( M ) < [ δ δ ] > N ( M ) ( M ) [ δ ] δ δ δ N N δ { } ( M ) ( M ) δ ( M ) { } ( ) ( ) ( ) N M M δ N ( ) { } δ

15 Collective vibration NN ħωω NN 5 ħωω 5 ħωω 5 ħωω 5 ħωω 5

16 xaple of vibrational excitations - state? ħω ultiple phonon states, ideally degenerate n,, J π,, 4 ħω ħω n,, phonon (- ground state)

17 Second quantization ailton operator µ µ µ ω rule for boson operators: µ µ µ µ µ µ δ δ -phonon state: ( ) > Ψ M M N reduced transition probability: ( ) ( ) ( ) [ ] 4 ; M M f i R e Z ω π ( ) ( ), ; M f i M f f i ( ) ( ) * * 4,, p R R Z d Y r M α π τ φ θ ρ ( ) 4 ; π ω R e Z ~

18 Reduced transition probabilities -phonon state 4 π ω R Z Q vib ( ) ( ) ; i f i f i M ( ) ( ) ; ; n n n n ( ) ( ) ; ; n n n n -phonon state

19 Reduced transition probabilities,, 5 -phonon state n M ( ) n Q e vib -phonon state ( ), n Qvib e ( ), n Q vib e ( ), n Q e, n M 8 4, n M, n M vib -phonon state ( ) 4, n Q e, n M 9 6 n 9 4, M 7 vib ( ) 4, n Q e vib n 99 4, M 7 ( ), n Q e vib ( ) 4, n Q e, n M 6 vib ( ; ) M ( ) Q vib i f f i i Z R 4π ω ( ), n Q e, n M 5 n, M 7, n M, n 7 Q vib ( ), n Q e vib ( ) vib e ( ), n Q e, n M vib

Nuclear Physics (10 th lecture)

Nuclear Physics (10 th lecture) ~Theta Nuclear Physics ( th lecture) Content Nuclear Collective Model: Rainwater approx. (reinder) Consequences of nuclear deforation o Rotational states High spin states and back bending o Vibrational