Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands in ^{158}Er at Ultrahigh Spin

doi:https://doi.org/10.1103/PhysRevLett.108.092501

Title: Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands in ^{158}Er at Ultrahigh Spin

Abstract

Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in ^{158}Er at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes - as done in previous cranking calculations - two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation gamma. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation of the two triaxial minima at a very similar quadrupole shape obtained in the principal axis cranking approach. Several TSD configurations have been predicted, including a highly deformed band expected to cross lesser elongated TSD bands at the highest spins. Its transitional quadrupole moment Q_{t} ~ 10.5 eb is close to the measured value of ~11 eb; hence, it is a candidate for the structure observed in experiment.

Authors:

Shi, Yue ^[1]; Dobaczewski, J. ^[2]; Frauendorf, S. ^[3]; Nazarewicz, Witold ^[4]; Pei, J. C. ^[5]; Xu, F. R. ^[1]; Nikolov, N. ^[6]

Peking University
Warsaw University
University of Notre Dame, IN
ORNL
University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL)
University of Tennessee, Knoxville (UTK)

Publication Date:: 2012-01-01

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1050324

DOE Contract Number:: DE-AC05-00OR22725

Resource Type:: Journal Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 108; Journal Issue: 9; Journal ID: ISSN 0031-9007

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFIGURATION; DATA; DEFORMATION; QUADRUPOLE MOMENTS; QUADRUPOLES; SHAPE; SPIN

Citation Formats


                    Shi, Yue, Dobaczewski, J., Frauendorf, S., Nazarewicz, Witold, Pei, J. C., Xu, F. R., and Nikolov, N. Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands in ^{158}Er at Ultrahigh Spin.  United States: N. p., 2012. 
        Web.  doi:10.1103/PhysRevLett.108.092501.

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                    Shi, Yue, Dobaczewski, J., Frauendorf, S., Nazarewicz, Witold, Pei, J. C., Xu, F. R., & Nikolov, N. Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands in ^{158}Er at Ultrahigh Spin.  United States.  https://doi.org/10.1103/PhysRevLett.108.092501

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                    Shi, Yue, Dobaczewski, J., Frauendorf, S., Nazarewicz, Witold, Pei, J. C., Xu, F. R., and Nikolov, N. Sun .  
        "Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands in ^{158}Er at Ultrahigh Spin".  United States.  https://doi.org/10.1103/PhysRevLett.108.092501.

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@article{osti_1050324,

  title        = {Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands in ^{158}Er at Ultrahigh Spin},

  author       = {Shi, Yue and Dobaczewski, J. and Frauendorf, S. and Nazarewicz, Witold and Pei, J. C. and Xu, F. R. and Nikolov, N.},

  abstractNote = {Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in ^{158}Er at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes - as done in previous cranking calculations - two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation gamma. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation of the two triaxial minima at a very similar quadrupole shape obtained in the principal axis cranking approach. Several TSD configurations have been predicted, including a highly deformed band expected to cross lesser elongated TSD bands at the highest spins. Its transitional quadrupole moment Q_{t} ~ 10.5 eb is close to the measured value of ~11 eb; hence, it is a candidate for the structure observed in experiment.},

  doi          = {10.1103/PhysRevLett.108.092501},

  url          = {https://www.osti.gov/biblio/1050324},
  journal      = {Physical Review Letters},

  issn         = {0031-9007},

  number       = 9,

  volume       = 108,

  place        = {United States},

  year         = {2012},

  month        = {1}

}

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Works referenced in this record:

Spontaneous symmetry breaking in rotating nuclei
journal, June 2001

Frauendorf, Stefan
Reviews of Modern Physics, Vol. 73, Issue 2
https://doi.org/10.1103/RevModPhys.73.463

Evidence for the Wobbling Mode in Nuclei
journal, June 2001

Ødegård, S. W.; Hagemann, G. B.; Jensen, D. R.
Physical Review Letters, Vol. 86, Issue 26
https://doi.org/10.1103/PhysRevLett.86.5866

Evidence for Second-Phonon Nuclear Wobbling
journal, September 2002

Jensen, D. R.; Hagemann, G. B.; Hamamoto, I.
Physical Review Letters, Vol. 89, Issue 14
https://doi.org/10.1103/PhysRevLett.89.142503

Tilted rotation of triaxial nuclei
journal, May 1997

Frauendorf, S.
Nuclear Physics A, Vol. 617, Issue 2
https://doi.org/10.1016/S0375-9474(97)00004-3

Triaxial shapes of rotating nuclei with neutron numbers 88, 89, 90
journal, June 1983

Frauendorf, S.; May, F. R.
Physics Letters B, Vol. 125, Issue 4
https://doi.org/10.1016/0370-2693(83)91277-7

Additivity of effective quadrupole moments and angular momentum alignments in $A ~ 130$ nuclei
journal, September 2007

Matev, M.; Afanasjev, A. V.; Dobaczewski, J.
Physical Review C, Vol. 76, Issue 3
https://doi.org/10.1103/PhysRevC.76.034304

Wobbling motion in atomic nuclei with positive- $γ$ shapes
journal, March 2002

Matsuzaki, Masayuki; Shimizu, Yoshifumi R.; Matsuyanagi, Kenichi
Physical Review C, Vol. 65, Issue 4
https://doi.org/10.1103/PhysRevC.65.041303

Shape coexistence effects of super- and hyperdeformed configurations in rotating nuclei with 58 ≤ Z ≤ 74
journal, March 1992

Werner, T. R.; Dudek, J.
Atomic Data and Nuclear Data Tables, Vol. 50, Issue 2
https://doi.org/10.1016/0092-640X(92)90036-H

Return of Collective Rotation in ${}^{157}{Er}$ and ${}^{158}{Er}$ at Ultrahigh Spin
journal, January 2007

Paul, E. S.; Twin, P. J.; Evans, A. O.
Physical Review Letters, Vol. 98, Issue 1
https://doi.org/10.1103/PhysRevLett.98.012501

Evidence for particle–hole excitations in the triaxial strongly-deformed well of 163Tm
journal, April 2007

Pattabiraman, N. S.; Gu, Y.; Frauendorf, S.
Physics Letters B, Vol. 647, Issue 4
https://doi.org/10.1016/j.physletb.2007.01.057

New shape minimum in ${}^{160}{Yb}$ : Evidence for a triaxial, strongly deformed band
journal, February 2008

Aguilar, A.; Campbell, D. B.; Chandler, K.
Physical Review C, Vol. 77, Issue 2
https://doi.org/10.1103/PhysRevC.77.021302

Triaxial strongly deformed bands in ${}^{160, 161}{Tm}$
journal, July 2008

Teal, C.; Lagergren, K.; Aguilar, A.
Physical Review C, Vol. 78, Issue 1
https://doi.org/10.1103/PhysRevC.78.017305

Ultrahigh-spin spectroscopy of ${}^{159, 160}{Er}$ : Observation of triaxial strongly deformed structures
journal, December 2009

Ollier, J.; Simpson, J.; Wang, X.
Physical Review C, Vol. 80, Issue 6
https://doi.org/10.1103/PhysRevC.80.064322

Structure changes in ${}^{160}{Er}$ from low to ultrahigh spin
journal, April 2011

Ollier, J.; Simpson, J.; Riley, M. A.
Physical Review C, Vol. 83, Issue 4
https://doi.org/10.1103/PhysRevC.83.044309

Quadrupole moments of collective structures up to spin <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo>∼</mml:mo><mml:mn>65</mml:mn><mml:mi>ℏ</mml:mi></mml:math> in 157Er and 158Er: A challenge for understanding triaxiality in nuclei
journal, August 2011

Wang, X.; Riley, M. A.; Simpson, J.
Physics Letters B, Vol. 702, Issue 2-3
https://doi.org/10.1016/j.physletb.2011.07.007

Shape evolution in the transitional gadolinium, dysprosium, erbium, and ytterbium nuclei
journal, January 1985

Dudek, J.; Nazarewicz, W.
Physical Review C, Vol. 31, Issue 1
https://doi.org/10.1103/PhysRevC.31.298

Rotational bands and particle-hole excitations at very high spin
journal, March 1985

Bengtsson, Tord; Ragnarsson, Ingemar
Nuclear Physics A, Vol. 436, Issue 1
https://doi.org/10.1016/0375-9474(85)90541-X

Termination of rotational bands: disappearance of quantum many-body collectivity
journal, December 1999

Afanasjev, A. V.; Fossan, D. B.; Lane, G. J.
Physics Reports, Vol. 322, Issue 1-2
https://doi.org/10.1016/S0370-1573(99)00035-6

Tilted cranking
journal, May 1993

Frauendorf, S.
Nuclear Physics A, Vol. 557
https://doi.org/10.1016/0375-9474(93)90546-A

Description of multi-quasiparticle bands by the tilted axis cranking model
journal, September 2000

Frauendorf, S.
Nuclear Physics A, Vol. 677, Issue 1-4
https://doi.org/10.1016/S0375-9474(00)00308-0

Nuclear rotations studied by the time-dependent variational method
journal, May 1981

Kerman, A. K.; Naoki, Onishi
Nuclear Physics A, Vol. 361, Issue 1
https://doi.org/10.1016/0375-9474(81)90475-9

Critical Frequency in Nuclear Chiral Rotation
journal, July 2004

Olbratowski, P.; Dobaczewski, J.; Dudek, J.
Physical Review Letters, Vol. 93, Issue 5
https://doi.org/10.1103/PhysRevLett.93.052501

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.
journal, January 2012

Schunck, N.; Dobaczewski, J.; McDonnell, J.
Computer Physics Communications, Vol. 183, Issue 1
https://doi.org/10.1016/j.cpc.2011.08.013

Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force
journal, September 1982

Bartel, J.; Quentin, P.; Brack, M.
Nuclear Physics A, Vol. 386, Issue 1
https://doi.org/10.1016/0375-9474(82)90403-1

A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities
journal, May 1998

Chabanat, E.; Bonche, P.; Haensel, P.
Nuclear Physics A, Vol. 635, Issue 1-2
https://doi.org/10.1016/S0375-9474(98)00180-8

Gamow-Teller strength and the spin-isospin coupling constants of the Skyrme energy functional
journal, May 2002

Bender, M.; Dobaczewski, J.; Engel, J.
Physical Review C, Vol. 65, Issue 5
https://doi.org/10.1103/PhysRevC.65.054322

Probing the nuclear energy functional at band termination
journal, February 2005

Zduńczuk, Honorata; Satuła, Wojciech; Wyss, Ramon A.
Physical Review C, Vol. 71, Issue 2
https://doi.org/10.1103/PhysRevC.71.024305

Solution of the Skyrme–Hartree–Fock equations in the Cartesian deformed harmonic-oscillator basis. (III) HFODD (v1.75r): a new version of the program
journal, September 2000

Dobaczewski, J.; Dudek, J.
Computer Physics Communications, Vol. 131, Issue 1-2
https://doi.org/10.1016/S0010-4655(00)00121-1

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Title: Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands in ^{158}Er at Ultrahigh Spin

Abstract

Citation Formats

Spontaneous symmetry breaking in rotating nuclei journal, June 2001

Evidence for the Wobbling Mode in Nuclei journal, June 2001

Evidence for Second-Phonon Nuclear Wobbling journal, September 2002

Tilted rotation of triaxial nuclei journal, May 1997

Triaxial shapes of rotating nuclei with neutron numbers 88, 89, 90 journal, June 1983

Additivity of effective quadrupole moments and angular momentum alignments in A ~ 130 nuclei journal, September 2007

Wobbling motion in atomic nuclei with positive- γ shapes journal, March 2002

Shape coexistence effects of super- and hyperdeformed configurations in rotating nuclei with 58 ≤ Z ≤ 74 journal, March 1992

Return of Collective Rotation in Er 157 and Er 158 at Ultrahigh Spin journal, January 2007

Evidence for particle–hole excitations in the triaxial strongly-deformed well of 163Tm journal, April 2007

New shape minimum in Yb 160 : Evidence for a triaxial, strongly deformed band journal, February 2008

Triaxial strongly deformed bands in Tm 160 , 161 journal, July 2008

Ultrahigh-spin spectroscopy of Er 159 , 160 : Observation of triaxial strongly deformed structures journal, December 2009

Structure changes in Er 160 from low to ultrahigh spin journal, April 2011

Shape evolution in the transitional gadolinium, dysprosium, erbium, and ytterbium nuclei journal, January 1985

Rotational bands and particle-hole excitations at very high spin journal, March 1985

Termination of rotational bands: disappearance of quantum many-body collectivity journal, December 1999

Tilted cranking journal, May 1993

Description of multi-quasiparticle bands by the tilted axis cranking model journal, September 2000

Nuclear rotations studied by the time-dependent variational method journal, May 1981

Critical Frequency in Nuclear Chiral Rotation journal, July 2004

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. journal, January 2012

Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force journal, September 1982

A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities journal, May 1998

Gamow-Teller strength and the spin-isospin coupling constants of the Skyrme energy functional journal, May 2002

Probing the nuclear energy functional at band termination journal, February 2005

Solution of the Skyrme–Hartree–Fock equations in the Cartesian deformed harmonic-oscillator basis. (III) HFODD (v1.75r): a new version of the program journal, September 2000

Spontaneous symmetry breaking in rotating nuclei
journal, June 2001

Evidence for the Wobbling Mode in Nuclei
journal, June 2001

Evidence for Second-Phonon Nuclear Wobbling
journal, September 2002

Tilted rotation of triaxial nuclei
journal, May 1997

Triaxial shapes of rotating nuclei with neutron numbers 88, 89, 90
journal, June 1983

Additivity of effective quadrupole moments and angular momentum alignments in $A ~ 130$ nuclei
journal, September 2007

Wobbling motion in atomic nuclei with positive- $γ$ shapes
journal, March 2002

Shape coexistence effects of super- and hyperdeformed configurations in rotating nuclei with 58 ≤ Z ≤ 74
journal, March 1992

Return of Collective Rotation in ${}^{157}{Er}$ and ${}^{158}{Er}$ at Ultrahigh Spin
journal, January 2007

Evidence for particle–hole excitations in the triaxial strongly-deformed well of 163Tm
journal, April 2007

New shape minimum in ${}^{160}{Yb}$ : Evidence for a triaxial, strongly deformed band
journal, February 2008

Triaxial strongly deformed bands in ${}^{160, 161}{Tm}$
journal, July 2008

Ultrahigh-spin spectroscopy of ${}^{159, 160}{Er}$ : Observation of triaxial strongly deformed structures
journal, December 2009

Structure changes in ${}^{160}{Er}$ from low to ultrahigh spin
journal, April 2011

Shape evolution in the transitional gadolinium, dysprosium, erbium, and ytterbium nuclei
journal, January 1985

Rotational bands and particle-hole excitations at very high spin
journal, March 1985

Termination of rotational bands: disappearance of quantum many-body collectivity
journal, December 1999

Tilted cranking
journal, May 1993

Description of multi-quasiparticle bands by the tilted axis cranking model
journal, September 2000

Nuclear rotations studied by the time-dependent variational method
journal, May 1981

Critical Frequency in Nuclear Chiral Rotation
journal, July 2004

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.
journal, January 2012

Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force
journal, September 1982

A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities
journal, May 1998

Gamow-Teller strength and the spin-isospin coupling constants of the Skyrme energy functional
journal, May 2002

Probing the nuclear energy functional at band termination
journal, February 2005

Solution of the Skyrme–Hartree–Fock equations in the Cartesian deformed harmonic-oscillator basis. (III) HFODD (v1.75r): a new version of the program
journal, September 2000