application of the adiabatic self-consistent collective coordinate (ascc) method to

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Application of the Adiabatic Self- Application of the Adiabatic Self- Consistent Collective Coordinate Consistent Collective Coordinate (ASCC) Method to (ASCC) Method to Shape Coexistence/ Mixing Shape Coexistence/ Mixing Phenomena Phenomena Nobuo Hinohara (Kyoy o) Takashi Nakatsukasa (RIKEN) Masayuki Matsuo (Niig ata) Kenichi Matsuyanagi (Kyoto)

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Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to Shape Coexistence/ Mixing Phenomena. Nobuo Hinohara (Kyoyo) Takashi Nakatsukasa (RIKEN) Masayuki Matsuo (Niigata) Kenichi Matsuyanagi (Kyoto). - PowerPoint PPT Presentation

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Page 1: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Application of the Adiabatic Self-Consistent Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to Collective Coordinate (ASCC) Method to

Shape Coexistence/ Mixing PhenomenaShape Coexistence/ Mixing Phenomena

Application of the Adiabatic Self-Consistent Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to Collective Coordinate (ASCC) Method to

Shape Coexistence/ Mixing PhenomenaShape Coexistence/ Mixing Phenomena

Nobuo Hinohara (Kyoyo)Takashi Nakatsukasa (RIKEN)Masayuki Matsuo (Niigata)Kenichi Matsuyanagi (Kyoto)

Page 2: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

2008.1.17 学位論文公聴会

日野原 伸生

Microscopic Description of Microscopic Description of Nuclear Large-Amplitude Collective Nuclear Large-Amplitude Collective

Motion Motion by Means of by Means of

the Adiabatic Self-Consistentthe Adiabatic Self-ConsistentCollective Coordinate MethodCollective Coordinate Method

Hinohara Nobuo

Sunny Field

Life lively grows

doctoral dissertation defense

The major part of this thesis will appear in Prog. Theor. Phys. Jan. 2008 within a few days

Page 3: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Shape coexistence in N~Z~40 regionShape coexistence in N~Z~40 region

50

28

20

343438

42

36

40

neutron single particle energy

oblate-prolate shape coexistence oblate ground state shape coexistence/mixing

Z,N = 34,36 (oblate magic numbers)Z,N = 38 (prolate magic number)

Bouchez et al. Phys.Rev.Lett.90(2003) 082502.Fischer et al. Phys.Rev.C67 (2003) 064318.

Skyrme-HFB: Yamagami et al. Nucl.Phys.A693 (2001) 579.

68Se 72Kr

Page 4: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Prolate

Oblate

Spherical

Many-Body Tunneling between Different Vacua

Why localization is possible for such a low barrier ?!Basic question

Page 5: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

I am going to report the first application of the microscopic theory of large amplitude collective motion, based on the time-dependent mean-field (TDHFB) theory,  to real nuclear structure phenomena in nuclei with superfluidity.

Coexistence/mixing of oblate and prolate shapes  is a typical phenomenon of large amplitude collective motion.

Main points

Page 6: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

In contrast to the GCM, collective coordinate and momentum are microscopically derived; i.e., self-consistently extracted from huge-dimensional TDHFB phase space.

In Se and Kr, the collective paths,connecting the oblate and prolate minima, run in the triaxially deformed region.

7268

Main points

Page 7: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Collective paths obtained by means of the ASCC method

Comparison with theaxially symmetric path

Collective coordinate

Page 8: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

The collective Hamiltonian, derived microscopically, is quantized and excitation spectra, E2 transitions and quadrupole moments are evaluated for the first time.

The result indicates that the oblate and prolate shapes are strongly mixed at I=0, but the mixing rapidly decreases with increasing angular momentum.

Main points

Calculated spectra

Page 9: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

After a long history (more than 30 years) ,a way for wide applications of large-amplitude theory is now open.

SCC and quasiparticle SCC

ATDHF and ATDHFB

ASCC

Villars, Kerman-Koonin, Brink,Rowe-Bassermann, Baranger-Veneroni, Goeke-Reinhard, Bulgac-Klein-Walet, Giannoni-Quentin, Dobaczewski-Skalskiand many colleagues, reviewed in G. Do Dang, A. Klein and N.R. Walet, Phys. Rep. 335 (2000), 93.

Marumori-Maskawa-Sakata-Kuriyama, Yamamura, Matsuo, Shimizu-Takada,and many colleagues,reviewed in Prog. Theor. Phys. Supplement141 (2001).

Page 10: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Time dependent mean-field

time-dependent variational principle

collective momentum p

collecive coordinate q

Adiabatic expansion (ATDHFB)

Find an optimum direction at every point of q

Page 11: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to
Page 12: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

ASCC Basic EquationsASCC Basic EquationsMoving-frame HFB equation

moving-frame Hamiltonian

Local harmonic equations (moving-frame QRPA equations)

Canonical variable conditions

(from 1st-order in p)

(from 2nd-order in p)

(from 0-th order in p)

Terms not included in QRPA

Not included in HFB

Collective Hamiltonian

Page 13: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Basic Scheme of the ASCC Basic Scheme of the ASCC method (1)method (1)

1st Step: Solve ASCC equations and find collective path.

collective potentialcollective mass

Moving-frame HFB eq. Moving-frame QRPA  eq.

Double iteration for each q

Thouless-Valatin Moment of Inertia formoving-frame Hamiltonian

Page 14: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

An important remark

The ASCC method was proposed in

    M. Matsuo, T. Nakatsukasa and K. Matsuyanagi ,      Prog. Theor. Phys. 103 (2000) 959.

Quite recently, it was found that its basic equations areinvariant against gauge transformations associated withpairing correlations.

Gauge invariant ASCC method.

Choosing an appropriate gauge fixing condition, numerical instabilities encountered previously

are now completely removed. N. Hinohara et al., Prog. Theor. Phys. 117 (2007) 451

Page 15: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Collective path in Collective path in 6868SeSeCollective potential Collective mass

Moving-frame QRPA frequency

G2=0: Kobayasi et al., PTP113(2005), 129.

γ

β

Moment of Inertia

Triaxial deformation connects two local minima Enhancement of the collective mass and MoI by the quadrupole pairing

collective path

due to the time-odd pair field

Prog.Theor.Phys.115(2006)567.

P0+P2+QQ interaction

Page 16: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Collective potential Collective mass

Moving-frame QRPA frequency

G2=0: Kobayasi et al., PTP113(2005), 129.

oblateprolate

γ

β

β

β

β

γ

γγ

Collective path in Collective path in 7272KrKr

Moment of Inertia

Dynamical symmetry breaking of the path Triaxial degrees of freedom: important Enhancement of the collective mass and MoI by the quadrupole pairing

q=0

P0+P2+QQ interaction

Page 17: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Collective wave function

Basic Scheme of the ASCC Method (2)Basic Scheme of the ASCC Method (2)

2nd Step: Requantize the collective Hamiltonian.

vibrational wave functions

Collective Schrodinger eq.rotational wave functions

Page 18: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Excitation spectra of Excitation spectra of 6868SeSe

two rotational bands 02

+ state quadrupole pairing lowers ex.energy

( ) …B(E2) e2 fm4

effective charge: epol = 0.904

EXP: Fischer et al., Phys.Rev.C67 (2003) 064318.

Page 19: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Collective wave functions in Collective wave functions in 6868SeSe

I = 0: oblate and prolate shapes are strongly mixed via triaxial degree of freedom ground band: mixing of different K components 、 excited band: K=0 dominant oblate-prolate mixing: strong in 0+ states, decreases as angular momentum increases

G2 = 0G2 = G2

self

localizatio

n

Page 20: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Excitation Spectra of Excitation Spectra of 7272KrKr

( ) …B(E2) e2 fm4

effective charge is adjusted to this value

EXP : Fischer et al., Phys.Rev.C67 (2003) 064318, Bouchez, et al., Phys.Rev.Lett.90 (2003) 082502. Gade, et al., Phys.Rev.Lett.95 (2005) 022502, 96 (2006) 189901

two rotational bands small inter-band B(E2): shape mixing rather weak

Page 21: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Collective wave functions in Collective wave functions in 7272KrKrG2 = 0

G2 = G2self

oblate prolate

01+ state: well localized around oblate shape

02+ state: weak oblate-prolate shape mixing

other states: well defined shape character

oblate prolate

Page 22: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Spectroscopic quadrupole momentsSpectroscopic quadrupole moments

positive positive

negativenegative

ground bandexcited band ground band excited bandangular momentum angular momentum

Page 23: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

Probabilities of the Oblate and Prolate Components

ground band excited band

prolate

prolate

prolate

prolate

oblate

oblate

oblate

oblate

as a function ofangular momentum

as a function ofangular momentum

(different definitions)

Page 24: Application of the Adiabatic Self-Consistent Collective Coordinate (ASCC) Method to

For the first time, excitation spectra and E2 properties were evaluated quantizing the collective Hamiltonian derived by the ASCC method

The result indicates interesting properties of the oblate-prolate shape mixing dynamics, like

decline of mixing with increasing angular momentum.

Summary

Calculated spectra

Wide applications can be envisaged in the coming years