title: Foydalanilgan adabiyotlar
text: Foydalanilgan adabiyotlar
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  o’qitishda interfaol usullardan foydalanish uslublari. O’zMU xabarlari вестник нууз acta nuuz мирзо
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  metodi Mutafakkir illmiy jurnali 2-son ISSN:2181-3310 №1 2- may Toshkent 2022 y 159-164 betla.
  Namangan Institute of Engineering and Technology
  nammti.uz
  10.25.2023
  Pg.251
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  TRIAXIALITY IN QUADRUPOLE DEFORMED HEAVY EVEN-EVEN NUCLEI
  M.S.Nadirbekov, O.A.Bozarov, S.N.Kudiratov
  Institute of Nuclear Physics
  Introduction. Most of the atomic nuclei are deformed in their ground states and possess
  axially symmetric prolate or oblate shapes [1]. It is known that the prolate shapes essentially
  dominate over the oblate ones [2]. However, various theoretical studies suggest for some nuclear
  regions the possible deformations of each nuclide have been examined. The possible appearance of
  triaxial deformations has been suggested [3,4].
  Quadrupole shapes are described by the parameters β
  2
  and γ for the axial deformation and
  the deviation from axiality. In Ref. [5] the free triaxiality model was proposed, where deformation
  parameters β
  2
  and γ taking into account are dynamic. In Ref. [4], a comparative analysis of some
  non-adiabatic models was carried out, and it was determined that the free triaxiality model
  reproduces the experiment better than other models.
  In Ref. [6], the free triaxiality model was developed taking into account the high-order terms
  of the rotational energy operator series.
  In Ref.[7] taking into account the high-order terms of the rotational energy operator on
  variable γ leads to improve considerably the agreement of the results with experimental data. And
  in Ref. [8] intra-/inter-band reduced E2-transitions probabilities in excited collective states of even-
  even lanthanide and actinide nuclei was studied.
  In Ref. [9] one-parameter Davydov-Filippov model [4] has been used to study the intra-/inter-
  bands ratios B(E2)-transition in ground-state and γ -bands for the triaxially deformed nuclei. But in
  this work low-spin states are restricted and variables β
  2
  and γ are statistic.
  Thus, in the works cited above, deformed triaxial nuclei were studied, but the full range of
  variation of the deformation parameter γ (0<γ<30) was not taken into account. Present work we
  will solve this problem.
  Free triaxiality model
  In Ref. [4] we consider the possibility of describing the energy levels of the ground-state-band,
  γ -rotational, and γ - and β-rotational-vibrational bands by the Hamilton operator [8] containing five
  dynamic variables
  2
  2
  β
  2
  (
  , )
  rot
  H = T
  T
  T
  V
  , (1)
  here T
  β
  - operator kinetic energy of β-vibrations, T
  γ
  - operator kinetic energy of γ -vibrations,
  T
  rot
  - operator rotational energy, V(β
  2
  ,γ) - potential energy of β
  2
  - and γ -vibrations.
  It is known that simple special solutions of the Bohr Hamiltonian, which come from the exact
  separation of variables in the corresponding Schredinger equation [14], can be obtained when the
  potential V(β
  2
  ,γ) is represented as V(β
  2
  ,γ)=V(β
  2
  )+V(γ
  0
  ).
  The solution of the Schredinger equation for this form of potential was obtained for the value
  of the γ -variable γ
  0
  =0
  0
  and γ
  0
  =30
  0
  in the rotational energy operator. Here we use Davidson potential
  for V(β
  2
  ) and V(γ).
  |