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

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Takatoshi Horibata 　　 Department of Software and Information Technology, Aomori University, Aomori, Aomori 030-0943, Japan

Contents

1. Introduction 2. Three-dimensional Cranking 3. Tilted states and GCM 4. Concluding remarks

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1. Introduction: general rotation mode

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ω

ω ω

x

y

z

y

x

x x

y y

zz

wobbling motiontilted axis rotation (high K t-band)

ω

4

Odegard et al.Phys.Rev.Lett.86(2001), 5866

wobbling band

ω

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

g-bandt-band

ω

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P.M.Walker et al., Phys. Lett. B309(1993), 17-22. 7

182Os

g-band

t-band(even component )

theoretical frameworksTAC 　　　 *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).

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2. Three-dimensional cranked HFBA.K.Kerman and N.Onishi, Nucl.Phys.A361(1981),179

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Constraints for HFB calculation

x

y

z

x

y

ψ

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Starting points of tilted wave functions

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ω

Energy vs tilt angle18

TARyz

x

y

ψ

ψ

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J = 18

j // ω

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ω

24 * sin(18°) = 7.622 * sin(20°) = 7.5

18 * sin(24°) = 7.3

26 * sin(17°) = 7.6

28 * sin(16°) = 7.7

TAR

30 * sin(15°) = 7.8

TAR states and K=8 bandK ～ const.

tilt angle (degree)14

angular momentum 　 J

TAR states ( K=8 band)

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t-band

g-band

even

odd

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

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3. Tilted states and GCM

s-branches

ψ

ψ

17

22

24

26

28

Energy splitting in tunneling effect

D

V

D, V smaller ΔE larger18

ー Ψ

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

t-band

g-band

even

odd

V

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　 Energy splitting in GCM

HFB solution at awave function

generator coordinate 　 a : tilt angle ψ

∫

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

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M.Oi et al., Phys. Lett. B418(1998), 1. 　 Phys. Lett. B525(2002), 255.

GCM amplitudes 　 (J = ２４ , ２６ , ２８ )

ΔE=130 keV

ΔE=252 keV

（ ΔE= 93 keV ）

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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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