![Page 1: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/1.jpg)
INT Workshop Nov 2007 1
Band Structure of nuclei in Deformed Hartree-Fock and Angular Momentum Projection theory
C. R. PraharajC. R. PraharajInstitute of PhysicsInstitute of Physics
Bhubaneswar . IndiaBhubaneswar . India
![Page 2: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/2.jpg)
INT WorkshopNov 2007
C. R. Praharaj, IOP, Bhubaneswar 2
Outline of talk Motivation Formalism
HF calculation Angular momentum projection Band mixing
Results and Discussion Configurations and band structure
• Normal deformed bands• Large K bands• “Chiral” bands• Superdeformed bands
B(E2) & B(M1) Qs, Qt & µN
Conclusion
![Page 3: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/3.jpg)
INT WorkshopNov 2007
C. R. Praharaj, IOP, Bhubaneswar 3
Motivation
After coming of Heavy Ion accelerators and new generation of detector arrays:
Extend upto very high spins Many bands are known
Need theoretical frame work to correlate and understand these starting from a fundamental principle :-
Nucleon-nucleon interaction (Strong) Shell model (both closed and away from
that)
![Page 4: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/4.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 4
Some interesting phenomena in nuclear spectroscopy are
Regular and irregular spectra Known upto very high spins
Band crossings Inter-band transitions Signature effects
Large K bands. K selection violation Identical bands Staggering in B(E2) and B(M1)
![Page 5: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/5.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 5
Hartree-Fock (HF) method
![Page 6: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/6.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 6
![Page 7: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/7.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 7
![Page 8: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/8.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 8
![Page 9: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/9.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 9
![Page 10: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/10.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 10
RESIDUAL INTERACTIONS
![Page 11: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/11.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 11
See Ripka in Adv Nucl Phys vol 2
![Page 12: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/12.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 12
![Page 13: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/13.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 13
Superdeformed HF solutions in 84Zr
![Page 14: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/14.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 14
![Page 15: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/15.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 15
![Page 16: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/16.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 16
![Page 17: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/17.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 17
66Zn :
![Page 18: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/18.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 18
![Page 19: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/19.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 19
![Page 20: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/20.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 20
Angular momentum intensities in (a) K=0+ and RAL band (b,c).
![Page 21: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/21.jpg)
Bandcrossing andneutron RAL in 198Hg CRP and Khadkikar PRL 50,
1254 (1983)
![Page 22: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/22.jpg)
![Page 23: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/23.jpg)
![Page 24: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/24.jpg)
INT Worksshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 24
Model Space in Rare-earth Region Orbits for protons are 3s1/2, 2d3/2, 2d5/2, 1g7/2, 1h9/2, 1h11/2
and orbits for neutrons are 3p1/2, 3p3/2, 2f5/2, 2f7/2, 1h9/2, 1i13/2.
132Sn is considered as spherical inert core.
![Page 25: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/25.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 25
![Page 26: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/26.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 26
The nucleon orbits ( ) are approximately two fold degenerate.
HF orbits for 171Lu
![Page 27: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/27.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 27
Angular Momentum (J) Projection From the HF single particle orbits, HF
intrinsic and particle-hole intrinsic states are constructed by J projection.
Intrinsic state does not have a unique J quantum number.
By angular momentum projection from intrinsic states the spectra and other spectroscopic properties are obtained.
Angular momentum projection operator is
Where =
![Page 28: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/28.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 28
Band-mixing In general, two states and projected
from two intrinsic configurations are not orthogonal to each other even if and are orthogonal.
Thus, whenever necessary, we do band-mixing using the following equation to get better results.
Results for Lu, Re, Nd and K Isomeric bands are given below:
![Page 29: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/29.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 29
Regular and irregular bands
![Page 30: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/30.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 30
![Page 31: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/31.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 31
![Page 32: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/32.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 32
169Lu
![Page 33: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/33.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 33
169Lu
![Page 34: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/34.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 34
171Lu 173Lu
![Page 35: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/35.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 35
![Page 36: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/36.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 36
171Lu3qp bands
![Page 37: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/37.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 37
171Lu
![Page 38: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/38.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 38
![Page 39: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/39.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 39
![Page 40: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/40.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 40
![Page 41: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/41.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 41
![Page 42: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/42.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 42
![Page 43: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/43.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 43
![Page 44: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/44.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 44
HF orbits for 150Nd
![Page 45: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/45.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 45
![Page 46: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/46.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 46
Multi-quasi particle Large K bands
![Page 47: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/47.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 47
Oblate K Isomers in 146Ba. The ground band is Prolate. Not shown is a
band crossing due to i13/2 neutrons (prolate).
![Page 48: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/48.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 48
![Page 49: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/49.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 49
![Page 50: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/50.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 50
![Page 51: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/51.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 51
![Page 52: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/52.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 52
![Page 53: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/53.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 53
![Page 54: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/54.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 54
“Chiral” bands
The deformed HF orbits are calculated with a spherical closed shell core with Z=N=28
PHF studies of Chiral and Superdeformed bands See Ph.D. Thesis of Zashmir Naik
(Institute of Physics, Bhubaneswar) (unpublished)
![Page 55: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/55.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 55
![Page 56: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/56.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 56
![Page 57: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/57.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 57
![Page 58: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/58.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 58
![Page 59: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/59.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 59
![Page 60: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/60.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 60
Superdeformed bands
Superdeformed band structure of 104Pd is studied Model space and interaction are same as 122CS caseWe have performed calculation in two different ways
● 1st one is by occupying prolate deriving orbits and un-occupying oblate deriving orbits● 2nd one is by constraint HF calculation
![Page 61: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/61.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 61
105Ag
![Page 62: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/62.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 62
![Page 63: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/63.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 63
![Page 64: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/64.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 64
B(E2), B(M1) and B(M1)/B(E2)
![Page 65: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/65.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 65
![Page 66: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/66.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 66
![Page 67: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/67.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 67
![Page 68: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/68.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 68
![Page 69: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/69.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 69
![Page 70: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/70.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 70
Conclusions Deformed HF and J projection – a general manybody method No phenomenological assumptions. Reliable. Good predictive power Superdeformed bands. K isomers. Chiral bands. Bandcrossing. Signature effects. Need for effective interactions in large model spaces.
![Page 71: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/71.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 71
Band crossing due to intruder orbits are predicted
B(E2) and B(M1) values are predicted
Trends of the B(M1)/B(E2) ratios are predicted.
“Chiral” band structure are explained
Superdeformed bands are studied
Other spectroscopic properties (spectra, quadrupolemoments, magnetic moments, etc.,) are also quite well reproduced as compared to experimental results.
![Page 72: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/72.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 72
References For HFReferences For HF
![Page 73: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/73.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 73
References For J ProjectionReferences For J Projection
![Page 74: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/74.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 74
References For Expt.References For Expt.
![Page 75: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/75.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 75
QS and B(E2)
Effective charges proton :1.7e neutron: 0.7e
Core polarization are account by considering Effective charges.
![Page 76: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/76.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 76
µ and B(M1) Magnetic moment µ is given by
B(M1) value for γ-transition from initial state αJ1 to final state βJ2 is
g-factors (in µΝ)gsgl
½ × (-3.826)0Neutron½ × 5.5861proton
![Page 77: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/77.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 77
Superdeformed and Chiral Bands in Z = 50 region
![Page 78: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/78.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 78
![Page 79: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/79.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 79
![Page 80: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/80.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 80
Shape Coexistence in 52Cr
![Page 81: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/81.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 81
![Page 82: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/82.jpg)
07/31/07 C. R. Praharaj, IOP, Bhubaneswar 82
![Page 83: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/83.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 83
![Page 84: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/84.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 84
![Page 85: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/85.jpg)
INT Workshop Nov 2007
C. R. Praharaj, IOP, Bhubaneswar 85
Conclusions We are able to explain both regular and irregular
rotational bands.
The doublet structure and departure from regular rotational behavior of the low-K bands are explained.
We could relate staggering in spectrum with angular momentum carried by large-j nucleon.
Structure of one, three, five quasi-particles bands for odd A and zero, two, four quasi-particle bands for even A are explained.
![Page 86: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/86.jpg)
Def HF and J Projection formalism (J Phys G 14, 843 (1988)):
![Page 87: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/87.jpg)
![Page 88: Band Structure of nuclei in Deformed Hartree- Fock and ...INT Workshop Nov 2007 C. R. Praharaj, IOP, Bhubaneswar 85 Conclusions We are able to explain both regular and irregular rotational](https://reader036.vdocuments.us/reader036/viewer/2022062916/5ec9815b840bd01f0a0e2463/html5/thumbnails/88.jpg)
COLLABORATORS● Zashmir Naik (TIFR)● A.K. Rath (Sambalpur Univ) ● S.B. Khadkikar (PRL)● S.P. Pandya (PRL)● Experimentalists and Colleagues
from Universities and Institutions.