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Chinese Physics C> 2015, Vol. 39> Issue(5) : 054105 DOI: 10.1088/1674-1137/39/5/054105

Wobbling geometry in a simple triaxial rotor

  • The spectroscopic properties and angular momentum geometry of the wobbling motion of a simple triaxial rotor are investigated within the triaxial rotor model. The obtained exact solutions of energy spectra and reduced quadrupole transition probabilities are compared to the approximate analytic solutions from the harmonic approximation formula and Holstein-Primakoff formula. It is found that the low lying wobbling bands can be well described by the analytic formulae. The evolution of the angular momentum geometry as well as the K-distribution with respect to the rotation and the wobbling phonon excitation are studied in detail. It is demonstrated that with the increase of the wobbling phonon number, the triaxial rotor changes its wobbling motions along the axis with the largest moment of inertia to the axis with the smallest moment of inertia. In this process, a specific evolutionary track that can be used to depict the motion of a triaxial rotating nucleus is proposed.

  • References

    [1] Bohr A, Mottelson B R. Nuclear Structure, Vol. II, Benjamin, New York, 1975[2] Frauendorf S, Meng J. Nucl. Phys. A, 1997, 617: 131[3] Frauendorf S. Rev. Mod. Phys., 2001, 73: 463[4] MENG J, ZHANG S Q. J. Phys. G: Nucl. Part. Phys., 2010, 37: 064025[5] degrd S W, Hagemann G B, Jensen D R, Bergstrm M, Herskind B, Sletten G, Trmnen S, Wilson J N, Tjm P O, Hamamoto I et al. Phys. Rev. Lett., 2001, 86: 5866[6] Jensen D R, Hagemann G B, Hamamoto I, degrd S W, Herskind B, Sletten G, Wilson J N, Spohr K, Hübel H, Bringel P et al. Phys. Rev. Lett., 2002, 89: 142503[7] Jensen D R, Hagemann G B, Hamamoto I, degrd S W, Bergstrom M, Herskind B, Sletten G, Tormanen S, Wilson J N, Tjom P O et al. Nucl. Phys. A, 2002, 703: 3[8] Schnwaer G, Hübel H, Hagemann G B, Bednarczyk P, Benzoni G, Bracco A, Bringel P, Chapman R, Curien D, Domscheit J et al. Phys. Lett. B, 2003, 552: 9[9] Amro H, MA W C, Hagemann G B, Diamond R M, Domscheit J, Fallon P, Gorgen A, Herskind B, Hubel H, Jensen D R et al. Phys. Lett. B, 2003, 553: 197[10] Hagemann G B. Eur. Phys. J. A, 2004, 20: 183[11] Bringel P, Hagemann G, Hübel H, Al-khatib A, Bednarczyk P, Bürger A, Curien D, Gangopadhyay G, Herskind B, Jensen D et al. Eur. Phys. J. A, 2005, 24: 167[12] Hartley D J, Janssens R V F, Riedinger L L, Riley M A, Aguilar A, Carpenter M P, Chiara C J, Chowdhury P, Darby I G, Garg U et al. Phys. Rev. C, 2009, 80: 041304[13] ZHU S J, LUO Y X, Hamilton J H, Ramayya A V, CHE X L, JIANG Z, Hwang J K, Wood J L, Stoyer M A, Donangelo R et al. Int. J. Mod. Phys. E, 2009, 18: 1717[14] Hamamoto I. Phys. Rev. C, 2002, 65: 044305[15] Hamamoto I, Mottelson B R. Phys. Rev. C, 2003, 68: 034312[16] Frauendorf S, Dnau F. Phys. Rev. C, 2014, 89: 014322[17] Shimizu Y R, Matsuzaki M. Nucl. Phys. A, 1995, 588: 559[18] Matsuzaki M, Shimizu Y R, Matsuyanagi K. Phys. Rev. C, 2002, 65: 041303[19] Matsuzaki M, Shimizu Y R, Matsuyanagi K. Eur. Phys. J. A, 2003, 20: 189[20] Matsuzaki M, Shimizu Y R, Matsuyanagi K. Phys. Rev. C, 2004, 69: 034325[21] Matsuzaki M, Ohtsubo S. Phys. Rev. C, 2004, 69: 064317[22] Shimizu Y R, Matsuzaki M, Matsuyanagi K. Phys. Rev. C, 2005, 72: 014306[23] Shimizu Y R, Shoji T, Matsuzaki M. Phys. Rev. C, 2008, 77: 024319[24] Shoji T, Shimizu Y R. Progr. Theor. Phys., 2009, 121: 319[25] Oi M, Ansari A, Horibata T, Onishi N. Phys. Lett. B, 2000, 480: 53[26] CHEN Q B, ZHANG S Q, ZHAO P W, MENG J. Phys. Rev. C, 2014, 90: 044306[27] Tanabe K, Sugawara-Tanabe K. Phys. Lett. B, 1971, 34: 575[28] Tanabe K, Sugawara-Tanabe K. Phys. Rev. C, 2006, 73: 034305[29] Tanabe K, Sugawara-Tanabe K. Phys. Rev. C, 2008, 77: 064318[30] Davydov A, Filippov G. Nuclear Physics, 1958, 8: 237[31] ZENG J Y. Quantume Mechanics, Vol. II. Beijing: Science Press, 2007 (in Chinese)[32] Holstein T, Primakoff H. Phys. Rev., 1940, 58: 1098[33] Oi M, Fletcher J. J. Phys. G, 2005, 31: S1753[34] Oi M. Phys. Lett. B, 2006, 634: 30[35] Sugawara-Tanabe K, Tanabe K, Yoshinaga N. Prog. Theor. Exp. Phys., 2014, 063D01[36] QI B, ZHANG S Q, MENG J, WANG S Y, Frauendorf S. Phys. Lett. B, 2009, 675: 175[37] QI B, ZHANG S Q, WANG S Y, YAO J M, MENG J. Phys. Rev. C, 2009, 79: 041302(R)[38] CHEN Q B, YAO J M, ZHANG S Q, QI B. Phys. Rev. C, 2010, 82: 067302[39] QI B, ZHANG S Q, WANG S Y, MENG J, Koike T. Phys. Rev. C, 2011, 83: 034303

  • References

    [1] Bohr A, Mottelson B R. Nuclear Structure, Vol. II, Benjamin, New York, 1975[2] Frauendorf S, Meng J. Nucl. Phys. A, 1997, 617: 131[3] Frauendorf S. Rev. Mod. Phys., 2001, 73: 463[4] MENG J, ZHANG S Q. J. Phys. G: Nucl. Part. Phys., 2010, 37: 064025[5] degrd S W, Hagemann G B, Jensen D R, Bergstrm M, Herskind B, Sletten G, Trmnen S, Wilson J N, Tjm P O, Hamamoto I et al. Phys. Rev. Lett., 2001, 86: 5866[6] Jensen D R, Hagemann G B, Hamamoto I, degrd S W, Herskind B, Sletten G, Wilson J N, Spohr K, Hübel H, Bringel P et al. Phys. Rev. Lett., 2002, 89: 142503[7] Jensen D R, Hagemann G B, Hamamoto I, degrd S W, Bergstrom M, Herskind B, Sletten G, Tormanen S, Wilson J N, Tjom P O et al. Nucl. Phys. A, 2002, 703: 3[8] Schnwaer G, Hübel H, Hagemann G B, Bednarczyk P, Benzoni G, Bracco A, Bringel P, Chapman R, Curien D, Domscheit J et al. Phys. Lett. B, 2003, 552: 9[9] Amro H, MA W C, Hagemann G B, Diamond R M, Domscheit J, Fallon P, Gorgen A, Herskind B, Hubel H, Jensen D R et al. Phys. Lett. B, 2003, 553: 197[10] Hagemann G B. Eur. Phys. J. A, 2004, 20: 183[11] Bringel P, Hagemann G, Hübel H, Al-khatib A, Bednarczyk P, Bürger A, Curien D, Gangopadhyay G, Herskind B, Jensen D et al. Eur. Phys. J. A, 2005, 24: 167[12] Hartley D J, Janssens R V F, Riedinger L L, Riley M A, Aguilar A, Carpenter M P, Chiara C J, Chowdhury P, Darby I G, Garg U et al. Phys. Rev. C, 2009, 80: 041304[13] ZHU S J, LUO Y X, Hamilton J H, Ramayya A V, CHE X L, JIANG Z, Hwang J K, Wood J L, Stoyer M A, Donangelo R et al. Int. J. Mod. Phys. E, 2009, 18: 1717[14] Hamamoto I. Phys. Rev. C, 2002, 65: 044305[15] Hamamoto I, Mottelson B R. Phys. Rev. C, 2003, 68: 034312[16] Frauendorf S, Dnau F. Phys. Rev. C, 2014, 89: 014322[17] Shimizu Y R, Matsuzaki M. Nucl. Phys. A, 1995, 588: 559[18] Matsuzaki M, Shimizu Y R, Matsuyanagi K. Phys. Rev. C, 2002, 65: 041303[19] Matsuzaki M, Shimizu Y R, Matsuyanagi K. Eur. Phys. J. A, 2003, 20: 189[20] Matsuzaki M, Shimizu Y R, Matsuyanagi K. Phys. Rev. C, 2004, 69: 034325[21] Matsuzaki M, Ohtsubo S. Phys. Rev. C, 2004, 69: 064317[22] Shimizu Y R, Matsuzaki M, Matsuyanagi K. Phys. Rev. C, 2005, 72: 014306[23] Shimizu Y R, Shoji T, Matsuzaki M. Phys. Rev. C, 2008, 77: 024319[24] Shoji T, Shimizu Y R. Progr. Theor. Phys., 2009, 121: 319[25] Oi M, Ansari A, Horibata T, Onishi N. Phys. Lett. B, 2000, 480: 53[26] CHEN Q B, ZHANG S Q, ZHAO P W, MENG J. Phys. Rev. C, 2014, 90: 044306[27] Tanabe K, Sugawara-Tanabe K. Phys. Lett. B, 1971, 34: 575[28] Tanabe K, Sugawara-Tanabe K. Phys. Rev. C, 2006, 73: 034305[29] Tanabe K, Sugawara-Tanabe K. Phys. Rev. C, 2008, 77: 064318[30] Davydov A, Filippov G. Nuclear Physics, 1958, 8: 237[31] ZENG J Y. Quantume Mechanics, Vol. II. Beijing: Science Press, 2007 (in Chinese)[32] Holstein T, Primakoff H. Phys. Rev., 1940, 58: 1098[33] Oi M, Fletcher J. J. Phys. G, 2005, 31: S1753[34] Oi M. Phys. Lett. B, 2006, 634: 30[35] Sugawara-Tanabe K, Tanabe K, Yoshinaga N. Prog. Theor. Exp. Phys., 2014, 063D01[36] QI B, ZHANG S Q, MENG J, WANG S Y, Frauendorf S. Phys. Lett. B, 2009, 675: 175[37] QI B, ZHANG S Q, WANG S Y, YAO J M, MENG J. Phys. Rev. C, 2009, 79: 041302(R)[38] CHEN Q B, YAO J M, ZHANG S Q, QI B. Phys. Rev. C, 2010, 82: 067302[39] QI B, ZHANG S Q, WANG S Y, MENG J, Koike T. Phys. Rev. C, 2011, 83: 034303

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2. Wang, Y.M., Chen, Q.B. Exploring wobbling motion in triaxial even-even nuclei[J]. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2024. doi: 10.1016/j.physletb.2024.139131
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4. Chen, Q.-B., Dai, H.-M., Li, Y.-Z. Study of wobbling motion within CDFT+PRM approach[J]. Chirality and Wobbling in Atomic Nuclei, 2023. doi: 10.1201/9781032691633-10
5. Jia, H., Wang, S.Y., Qi, B. et al. Possible wobbling motion in multiple chiral doublets[J]. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2022. doi: 10.1016/j.physletb.2022.137303
6. Chen, Q.B., Frauendorf, S. Study of wobbling modes by means of spin coherent state maps[J]. European Physical Journal A, 2022, 58(4): 75. doi: 10.1140/epja/s10050-022-00727-5
7. Broocks, C., Chen, Q.B., Kaiser, N. et al. g-Factor and static quadrupole moment of 135 Pr, 105 Pd, and 187 Au in wobbling motion[J]. European Physical Journal A, 2021, 57(5): 161. doi: 10.1140/epja/s10050-021-00482-z
8. Qi, B., Zhang, H., Wang, S.Y. et al. Influence of triaxial deformation on wobbling motion in even-even nuclei[J]. Journal of Physics G: Nuclear and Particle Physics, 2021, 48(5): 055102. doi: 10.1088/1361-6471/abcdf7
9. Poenaru, R., Raduta, A.A. Extensive study of the positive and negative parity wobbling states for an odd-mass triaxial nucleus i: Energy spectrum[J]. Romanian Journal of Physics, 2021, 66(7-8): 308.
10. Nandi, S., Mukherjee, G., Chen, Q.B. et al. First Observation of Multiple Transverse Wobbling Bands of Different Kinds in Au 183[J]. Physical Review Letters, 2020, 125(13): 132501. doi: 10.1103/PhysRevLett.125.132501
11. Chen, Q.B., Frauendorf, S., Kaiser, N. et al. g-factor and static quadrupole moment for the wobbling mode in 133La[J]. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2020. doi: 10.1016/j.physletb.2020.135596
12. Raduta, A.A., Poenaru, R., Raduta, C.M. Towards a new semi-classical interpretation of the wobbling motion in 163Lu[J]. Journal of Physics G: Nuclear and Particle Physics, 2020, 47(2): 025101. doi: 10.1088/1361-6471/ab5ae4
13. Chen, Q.B., Frauendorf, S., Petrache, C.M. Transverse wobbling in an even-even nucleus[J]. Physical Review C, 2019, 100(6): 061301. doi: 10.1103/PhysRevC.100.061301
14. Timár, J., Chen, Q.B., Kruzsicz, B. et al. Experimental Evidence for Transverse Wobbling in Pd 105[J]. Physical Review Letters, 2019, 122(6): 062501. doi: 10.1103/PhysRevLett.122.062501
15. Wu, X.H., Chen, Q.B., Zhao, P.W. et al. Two-dimensional collective Hamiltonian for chiral and wobbling modes. II. Electromagnetic transitions[J]. Physical Review C, 2018, 98(6): 064302. doi: 10.1103/PhysRevC.98.064302
16. Streck, E., Chen, Q.B., Kaiser, N. et al. Behavior of the collective rotor in wobbling motion[J]. Physical Review C, 2018, 98(4): 044314. doi: 10.1103/PhysRevC.98.044314
17. Budaca, R.. Semiclassical description of chiral geometry in triaxial nuclei[J]. Physical Review C, 2018, 98(1): 014303. doi: 10.1103/PhysRevC.98.014303
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22. Chen, Q.. Collective model of chiral and wobbling modes in nuclei[J]. Scientia Sinica: Physica, Mechanica et Astronomica, 2016, 46(1) doi: 10.1360/SSPMA2015-00359
23. Chen, Q.B.. Collective hamiltonian and its applications for chiral and wobbling modes[J]. Acta Physica Polonica B, Proceedings Supplement, 2015, 8(3): 545-550. doi: 10.5506/APhysPolBSupp.8.545
Get Citation
SHI Wen-Xian and CHEN Qi-Bo. Wobbling geometry in a simple triaxial rotor[J]. Chinese Physics C, 2015, 39(5): 054105. doi: 10.1088/1674-1137/39/5/054105
SHI Wen-Xian and CHEN Qi-Bo. Wobbling geometry in a simple triaxial rotor[J]. Chinese Physics C, 2015, 39(5): 054105.  doi: 10.1088/1674-1137/39/5/054105 shu
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Received: 2014-11-17
Revised: 1900-01-01
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Wobbling geometry in a simple triaxial rotor

    Corresponding author: CHEN Qi-Bo,
  • Received Date: 2014-11-17
  • Accepted Date: 1900-01-01
  • Available Online: 2015-05-05

Abstract: The spectroscopic properties and angular momentum geometry of the wobbling motion of a simple triaxial rotor are investigated within the triaxial rotor model. The obtained exact solutions of energy spectra and reduced quadrupole transition probabilities are compared to the approximate analytic solutions from the harmonic approximation formula and Holstein-Primakoff formula. It is found that the low lying wobbling bands can be well described by the analytic formulae. The evolution of the angular momentum geometry as well as the K-distribution with respect to the rotation and the wobbling phonon excitation are studied in detail. It is demonstrated that with the increase of the wobbling phonon number, the triaxial rotor changes its wobbling motions along the axis with the largest moment of inertia to the axis with the smallest moment of inertia. In this process, a specific evolutionary track that can be used to depict the motion of a triaxial rotating nucleus is proposed.

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