Triaxiality and Cubic Terms From Casimir Invariants

Yıl 2020, Cilt: 2 Sayı: 1, 40 - 47, 29.12.2020

Ramesh Kumar Şadiye Çakmak

Öz

Etkileşen Bozon Modeli (IBM) Hamiltoniyen'in O(6) simetrisini kıran kübik terimler, U(6) ve alt gruplarının Casimir değişmezlerinden oluşturulmuştur. Bu yazıda, yukarıdaki Casimir değişmezlerinden oluşturulabilen kübik terimleri ele alıyor ve bu tür terimlerin kalıcı üç eksenli deformasyona yol açıp açamayacağını araştırılmıştır. Kübik terimlerin klasik sınırı elde edilmiştir ve hiçbirinin kalıcı üç eksenli deformasyona yol açmasını beklemediği gösterilmiştir.

Anahtar Kelimeler

Casimir invariants, Interacting Boson Model (IBM), Triaxial deformation

TRIAXIALITY AND CUBIC TERMS FROM CASIMIR INVARIANTS

Öz

Cubic terms breaking O(6) symmetry of the Interacting Boson Model (IBM) Hamiltonian are constructed out of the Casimir invariants of U (6) and its subgroups. In this paper, we consider cubic terms which can be constructed out of the above Casimir invariants and investigate whether such terms can give rise to permanent triaxial deformation. The classical limit of these cubic terms is obtained, and it is shown that none of them expect one can give rise to permanent triaxial deformation.
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Anahtar Kelimeler

Casimir invariants, Triaxial deformation, Interacting Boson Model (IBM)

Kaynakça

• Referans1 Casten RF, Brentano P von. An extensive region of O(6)-like nuclei near A = 130. Phys. Lett. B 1985; 152: 22-28.
• Referans2 Arima A, Iachello F. Interacting Boson Model of Collective States I. The Vibrational Limit. Ann.Phys. (NY) 1976; 99 : 253-317.
• Referans3 Arima A, Iachello F. Interacting boson model of collective nuclear states II. The rotational limit. Ann.Phys. (NY) 1978; 111 : 201-238.
• Referans4 Arima A, Iachello F. Interacting boson model of collective nuclear states IV. The O(6) limit. Ann.Phys. (NY) 1979; 123 : 468-492.
• Referans5 Iachello F, Arima A. The interacting Boson Model Cambridge. United Kingdom, UK: Cambridge University Press, 1987.
• Referans6 Wilets L, Jean M. Surface Oscillations in Even-Even Nuclei. Phys. Rev. 1956; 102 : 788-796.
• Referans7 Casten RF, Brentano P Von, Heyde K, Isacker P Van and Jolie J. The interplay of γ-softness and triaxiality in O(6)-like nuclei. Nucl. Phys. A 1985; 439: 289-298.
• Referans8 Isacker P Van, Chen JQ. Classical limit of the interacting boson Hamiltonian. Phys. Rev. C 1981; 24: 684-689.
• Referans9 Heyde K, Isacker P Van, Waroquier M and Moreau J. Triaxial shapes in the interacting boson model. Phys. Rev. C 1984; 29: 1420-1427.
• Referans10 Vander Berghe G, Meyer H E de and Isacker P Van. Symmetry-conserving higher-order interaction terms in the interacting boson model. Phys. Rev. C 1985; 32: 1049-1056.
• Referans11 Vanthournout J, Jeugt J Van, Meyer H de and Vanden Berghe G. On the spectrum of a third‐order SO(3) scalar in the enveloping algebra of SO(6). J. Math. Phys. 1988; 29: 802-805.
• Referans12 Vanthournout J, Jeugt J Van, Meyer H de and Vanden Berghe G. Symmetry-preserving higher-order terms in the O (6) limit of the interacting boson model. Phys. Rev. C 1988; 38: 414-418.