Loading in 5 sec....

Description of weakly bound nuclei with PTG/HFB and Gamow/HFB approachesPowerPoint Presentation

Description of weakly bound nuclei with PTG/HFB and Gamow/HFB approaches

- 86 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Description of weakly bound nuclei with PTG/HFB and Gamow/HFB approaches' - cheryl

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Description of weakly bound nuclei with PTG/HFB and Gamow/HFB approaches

Nicolas Michel(ESNT/SPhN/CEA)

Kenichi Matsuyanagi (Kyoto University)

Mario Stoitsov (ORNL – University of Tennessee)

Plan Gamow/HFB approaches

- Scientific motivation: drip-line nuclei
- Gamow states, Berggren completeness relation, Gamow Shell Model
- Gamow quasi-particle states and HFB densities
- Applications: Nickel chain (spherical)
- Pöschl-Teller-Ginocchio (PTG) basis for loosely bound systems
- Resonant structure with PTG basis
- Applications: Nickel chain (spherical)
Zirconium and Magnesium (deformed)

- Conclusion and perspectives

Scientific motivation Gamow/HFB approaches

Gamow states Gamow/HFB approaches

- Georg Gamow : a decay
G.A. Gamow, Zs f. Phys. 51 (1928) 204; 52 (1928) 510

- Definition :

Complex scaling method Gamow/HFB approaches

- Radial integral calculation : complex scaling
- Analytic continuation : integral independent of R and θ

Completeness relations with Gamow states Gamow/HFB approaches

- Berggren completeness relation (l,j) :
T. Berggren, Nucl. Phys. A 109, (1967) 205

- Continuum discretization :
- N-body discretized completeness relation (all l,j) :

Application : He, Li and O chains Gamow/HFB approaches

- He, Li chains : valence particles above 4Hecore : H = WS (5He) + SGI
0p3/2, 0p1/2 (resonant), p3/2 and p1/2 scattering continuums

SGI : Surface Gaussian Interaction :

- Dependence on number of nucleons for T=0
- Spherical Gamow Hartree-Fock basis from H = WS + SGI

N. Michel et al., Gamow/HFB approaches

Phys. Rev C, 67 054311 (2003)

Rev. Mex. Fis., 50 S2 74 (2004)

Helium anomaly

reproduced

Bound from unbound basis

Halo density Gamow/HFB approaches

N. Michel et al., Phys. Rev. C Gamow/HFB approaches70, 064313 (2004)

Satisfactory

results

(schematic model)

S-components

missing

E (MeV)

Gamow HFB space Gamow/HFB approaches

Densities with Gamow HFB Gamow/HFB approaches

- HFB equations:
- Complex particle and pairing densities:
- HF associated bound and narrow resonant states in discrete sum

Quasi-particle pole states Gamow/HFB approaches

- Bound, resonant states:
S matrix poles => outgoing wave function behavior

Quasi-particle scattering states Gamow/HFB approaches

- Scattering states:
u(r):incoming and outgoing components

v(r):outgoing wave function behavior

Gamow Gamow/HFB approachesquasi-particle states norm

- Normalization:
S-matrix poles:complex scaling

Scattering states: Dirac delta normalization

Continuum discretization:

Gamow Hartree-Fock diagonalization method Gamow/HFB approaches

- Two-basis method
Basisgenerated by ph part of HFB hamiltonian:

B. Gall et al., Z. Phys. A348 183 (1994)

- HFB matrix structure:
- Diagonalization of HFB matrix in Gamow HF basis

Description of Nickel calculations Gamow/HFB approaches

- Considered nuclei:84Ni, 86Ni, 88Ni, 90Ni
- Interaction and space:
Skyrme interaction: Sly4, Ecut = 60 MeV, l: 0 →10

Rcut = 20 fm, kmax = 4 fm-1, Nscat (l,j) = 100 for GHF basis.

- Interest:Resonant structure directly put in HFB basis

PTG basis for HFB calculations Gamow/HFB approaches

- Gamow HF(B) basis:
Advantages:good asymptotics, smoothly varying continuums

Inconvenients: complex arithmetic, long calculations

- Weakly bound systems:realcontinuous bases sufficient
- Real Gamow HF basis:problematic due to resonant structure in continuum
- PTG basis:resonances replaced by bound states
No resonant state in (l,j) partial wave: Hankel/Coulomb functions

Smooth continuums for all partial waves

Weakly bound systems asymptotics well described

HF/PTG potentials Gamow/HFB approaches

Accepted in Phys. Rev. C

---- : PTG p Gamow/HFB approaches

---- : PTG n

: Box p

: Box n

.… : HO

r (fm)

r (fm)

Accepted in Phys. Rev. C

Conclusion and perspectives Gamow/HFB approaches

- Gamow Shell Model:
Hybrid method: Gamow Hartree-Fock basis necessary

He, Li chains with schematic Hamiltonians

Next step : realistic interactions, effective interactions with continuum

- HFB expansions with Gamow and PTG bases
Precise tool to study dripline heavy nuclei

PTG basis near-optimal for weakly bound systems

Nickel chain, 40Mg and 110Zn : spherical and deformed ground states

- Conclusions and perspectives
Weakly bound nuclei : fast and stable method with PTG basis

Future QRPAcalculations withquasi-particle basis from HFB/PTG

Gamow-HFB: problems remain for unbound nuclei

Download Presentation

Connecting to Server..