Namangan Institute of Engineering and Technology
nammti.uz
10.25.2023
Pg.251
3. Прохорова М.П., Ваганова О.И. Участие преподавателей вуза в разработке открытых
онлайн-курсов // Отечественная и зарубежная педагогика. 2019. Т. 1. № 5 (62). С. 90-103.
4. Кутепов М.М. Дидактические возможности
интерактивных электронных
образовательных ресурсов // Baltic Humanitarian Journal. 2020. Т. 9. № 3(32). - С. 128-130.
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).
