Download presentation

Presentation is loading. Please wait.

1
**MP-41 Teil 2: Physik exotischer Kerne**

13.4. Einführung, Beschleuniger 20.4. Schwerionenreaktionen, Synthese superschwerer Kerne (SHE) 27.4. Kernspaltung und Produktion neutronenreicher Kerne 4.5. Fragmentation zur Erzeugung exotischer Kerne 11.5. Halo-Kerne, gebundener Betazerfall, 2-Protonenzerfall 18.5. Wechselwirkung mit Materie, Detektoren 25.5. Schalenmodell 1.6. Restwechselwirkung, Seniority 8.6. Tutorium-1 15.6. Tutorium-2 22.6. Vibrator, Rotator, Symmetrien 29.6. Schalenstruktur fernab der Stabilität 6.7. Tutorium-3 Klausur

2
**Shell structure Experimental evidence for magic numbers close to stability**

Maria Goeppert-Mayer J. Hans D. Jensen

3
**Experimental single-particle energies**

γ-spectrum single-particle energies 208Pb → 209Bi Elab = 5 MeV/u 1 h9/2 2 f7/2 1 i13/2 1609 keV 896 keV 0 keV

4
**Experimental single-particle energies**

γ-spectrum 208Pb → 207Pb Elab = 5 MeV/u single-hole energies 3 p3/2 898 keV 2 f5/2 570 keV 3 p1/2 0 keV

5
**Experimental single-particle energies**

particle states 209Bi 1 i13/2 1609 keV 209Pb 2 f7/2 896 keV 1 h9/2 0 keV energy of shell closure: 207Tl 207Pb hole states protons neutrons

6
**Level scheme of 210Pb 2846 keV 2202 keV 1558 keV 1423 keV 779 keV**

exp. single particle energies 1423 keV 779 keV 0.0 keV -1304 keV (pairing energy) residual interaction ! M. Rejmund Z.Phys. A359 (1997), 243

8
**The 100Sn/132Sn region, a brief background**

0.5 1.6 2.2 2.6 MeV d5/2 Single particle energies N=82 Z = 50 g7/2 d5/2 s1/2 d3/2 h11/2 Naïve single particle filling

9
**The 100Sn/132Sn region, isomeric states**

d3/2 h11/2 0.5 1.6 2.2 2.6 MeV d5/2 Single particle energies N=82

11
**Shell Model with residual interactions – mostly 2-particle systems**

Start with 2-particle system, that is a nucleus „doubly magic + 2“ Consider two identical valence nucleons with j1 and j2 Enormous simplifications of shell model calculations, reduction to 2-body matrix elements Energies of single magic nuclei Behaviour of g-factors g(41Ca)= g(43Ca)=g(45Ca)=g(47Ca) Parabolic systematics of intra-band B(E2) values and peaking near mid-shell Preponderance of prolate shapes at beginnings of shells and of oblate shapes near shell ends

12
**Shell Model with residual interactions – mostly 2-particle systems**

Start with 2-particle system, that is a nucleus „doubly magic + 2“ Consider two identical valence nucleons with j1 and j2 Two questions: What total angular momenta j1 + j2 = J can be formed? What are the energies of states with these J values?

13
**Coupling of two angular momenta**

j1+ j all values from: j1 – j2 to j1+ j2 (j1 = j2) Example: j1 = 3, j2 = 5: J = 2, 3, 4, 5, 6, 7, 8 BUT: For j1 = j2: J = 0, 2, 4, 6, … ( 2j – 1) (Why these?)

14
**Several methods: easiest is the “m-scheme”.**

How can we know which total J values are obtained for the coupling of two identical nucleons in the same orbit with total angular momentum j? Several methods: easiest is the “m-scheme”.

15
**Coupling of two angular momenta**

16
**Residual interaction - pairing**

Spectrum 210Pb: Assume pairing interaction in a single-j shell energy eigenvalue is none-zero for the ground state; all nucleons paired (ν=0) and spin J=0. The δ-interaction yields a simple geometrical expression for the coupling of two particles 2 4 6 8

17
**Pairing: δ-interaction**

wave function: interaction: with and A. de-Shalit & I. Talmi: Nuclear Shell Theory, p.200

18
**Pairing: δ-interaction**

wave function: interaction: with and A. de-Shalit & I. Talmi: Nuclear Shell Theory, p.200

19
**δ-interaction (semiclassical concept)**

q for and θ = 00 belongs to large J, θ = 1800 belongs to small J example h11/22: J=0 θ=1800, J=2 θ~1590, J=4 θ~1370, J=6 θ~1140, J=8 θ~870, J=10 θ~490

20
**Pairing: δ-interaction**

2 4 6 8 δ-interaction yields a simple geometrical explanation for Seniority-Isomers: DE ~ -Vo·Fr· tan (q/2) for T=1, even J energy intervals between states 0+, 2+, 4+, ...(2j-1)+ decrease with increasing spin.

21
**Generalized seniority scheme**

0.5 1.6 2.2 2.6 MeV d5/2 Single particle energies N=82 Z = 50 g7/2 The 100Sn / 132Sn region d5/2 s1/2 d3/2 h11/2 Naïve single particle filling

22
**Generalized seniority scheme**

0.5 1.6 2.2 2.6 MeV d5/2 Single particle energies N=82 The 100Sn / 132Sn region

23
**Generalized seniority scheme**

Seniority quantum number ν is equal to the number of unpaired particles in the jn configuration, where n is the number of valence nucleons. energy spacing between ν=2 and ground state (ν=0, J=0): independent of n energy spacing within ν=2 states: independent of n G. Racah et al., Phys. Rev. 61 (1942), 186 and Phys. Rev. 63 (1943), 367

24
**Generalized seniority scheme**

Seniority quantum number ν is equal to the number of unpaired particles in the jn configuration, where n is the number of valence nucleons. E2 transition rates: for large n ≈ Nparticles*Nholes Sn isotopes

25
**Generalized seniority scheme**

Seniority quantum number ν is equal to the number of unpaired particles in the jn configuration, where n is the number of valence nucleons. ≈ Nparticles*Nholes ≈ Nparticles*Nholes number of nucleons between shell closures

26
**Signatures near closed shells**

Excitation energy Sn isotopes N=82 isotones N=50 isotones

27
**Generalized seniority scheme**

Seniority quantum number ν is equal to the number of unpaired particles in the jn configuration, where n is the number of valence nucleons. E2 transition rates that do not change seniority (ν=2): Sn isotopes

Similar presentations

OK

Clustering in 12Be: Determination of the Enhanced monopole strength

Clustering in 12Be: Determination of the Enhanced monopole strength

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on hydrogen fuel cell vehicles Free download ppt on electricity for class 10 Download ppt on turbo generator design Corporate brochure ppt on architectural firm Ppt on acid-base titration equivalence point Ppt on sports day Ppt on standing order activation Ppt on properties of solid liquid and gases Ppt on mentoring and coaching Ppt on beer lambert law equation