Description of t band in 182 os with hfb gcm
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Description of t-band in 182 Os with HFB+GCM . Yukio Hashimoto Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan . Takatoshi Horibata Department of Software and Information Technology,

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Description of t-band in 182 Os with HFB+GCM

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Description of t band in 182 os with hfb gcm

Description of t-band in 182Os with HFB+GCM

Yukio Hashimoto

Graduate School of Pure and Applied Sciences,

University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

TakatoshiHoribata

Department of Software and Information Technology,

Aomori University, Aomori, Aomori 030-0943, Japan

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Description of t band in 182 os with hfb gcm

Contents

1. Introduction

2. Three-dimensional Cranking

3. Tilted states and GCM

4. Concluding remarks

2


Description of t band in 182 os with hfb gcm

1. Introduction: general rotation mode

3


Description of t band in 182 os with hfb gcm

ω

x

ω

x

ω

z

y

y

wobbling motion

tilted axis rotation

(high K t-band)

ω

x

x

z

z

y

y

4


Description of t band in 182 os with hfb gcm

wobbling band

Odegard et al.

Phys.Rev.Lett.86(2001), 5866

ω

5


Description of t band in 182 os with hfb gcm

t-band

g-band

ω

6

P.M.Walker et al., Phys. Lett. B309(1993), 17-22.


Description of t band in 182 os with hfb gcm

182Os

t-band

(even component )

g-band

7

P.M.Walker et al., Phys. Lett. B309(1993), 17-22.


Description of t band in 182 os with hfb gcm

theoretical frameworks

TAC

*S. Frauendorf, Nucl. Phys. A557, 259c(1993)

*S. Frauendorf, Nucl. Phys. A677, 115(2000).

*S. Frauendorf, Rev. Mod. Phys. 73, 463(2001).

HFB+RPA

*M. Matsuzaki, Nucl. Phys. A509, 269(1990).

*Y. R. Shimizu and M. Matsuzaki, Nucl. Phys. A588, 559(1996).

*M. Matsuzaki, Y. R. Shimizu and K. Matsuyanagi,

Phys. Rev. C65, 041303(R)(2002).

*M. Matsuzaki, Y. R. Shimizu and K. Matsuyanagi,

Phys. Rev. C69, 034325(2004)

HFB+GCM

*A. K. Kerman and N. Onishi, Nucl. Phys. A361, 179(1981).

*N. Onishi, Nucl. Phys. A456, 279(1986).

*T. Horibata and N. Onishi, Nucl. Phys. A596, 251(1996).

*T. Horibata, M. Oi, N. Onishi and A. Ansari,

Nucl. Phys. A646, 277(1999); A651, 435(1999).

*Y. Hashimoto and T. Horibata, Phys. Rev. C74, 017301(2006)

*Y. Hashimoto and T. Horibata, EPJ A42, 571(2009).

8


Description of t band in 182 os with hfb gcm

2. Three-dimensional cranked HFB

A.K.Kerman and N.Onishi, Nucl.Phys.A361(1981),179

9


Description of t band in 182 os with hfb gcm

Constraints for HFB calculation

ψ

x

x

z

y

y

10


Description of t band in 182 os with hfb gcm

Starting points of tilted wave functions

ω

11


Description of t band in 182 os with hfb gcm

18

Energy vs tilt angle

J = 18

ψ

x

ψ

z

TAR

y

y

12


Description of t band in 182 os with hfb gcm

j// ω

ω

13


Description of t band in 182 os with hfb gcm

TAR states and K=8 band

K ~ const.

30 * sin(15°) = 7.8

28 * sin(16°) = 7.7

26 * sin(17°) = 7.6

24 * sin(18°) = 7.6

TAR

22 * sin(20°) = 7.5

18 * sin(24°) = 7.3

tilt angle (degree)

14


Description of t band in 182 os with hfb gcm

TAR states ( K=8 band)

angular momentumJ

15


Description of t band in 182 os with hfb gcm

odd

t-band

even

g-band

3. Tilted states and GCM

P.M.Walker et al., Phys. Lett. B309, 17-22(1993).

16


Description of t band in 182 os with hfb gcm

s-branches

28

26

24

ψ

22

ψ

17


Description of t band in 182 os with hfb gcm

D, V smaller

ΔE larger

Energy splitting in tunneling effect

ーΨ

V

D

18


Description of t band in 182 os with hfb gcm

odd

t-band

even

V

g-band

P.M.Walker et al., Phys. Lett. B309(1993), 17-22.

19


Description of t band in 182 os with hfb gcm

Energy splitting in GCM

generator coordinatea :tilt angleψ

wave function

HFB solution ata

Cf. T.Horibata et al., Nucl.Phys.A646(1999), 277.

M.Oi et al., Phys. Lett. B418(1998), 1.

Phys. Lett. B525(2002), 255.

20


Description of t band in 182 os with hfb gcm

GCM amplitudes(J = 24,26,28)

(ΔE= 93 keV)

ΔE=252 keV

ΔE=130 keV

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Description of t band in 182 os with hfb gcm

4. Concluding Remarks

  1. We have microscopically calculated three-dimensional rotation.

  2. The TAR states are expected to be the members of

  a band with K = 8 (t-band).

 experimental results by Walker’s group.

  3. GCM calculations (refinement) are in progress.

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