title: Namangan Institute of Engineering and Technology
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  Namangan Institute of Engineering and Technology Pdf ko'rish
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  Bog'liq ТўпламNamangan Institute of Engineering and Technology
  nammti.uz
  10.25.2023
  Pg.252
  In the free triaxiality approximation the rotational energy operator has the form expands into
  a power series (γ -γ
  0
  ), γ
  0
  - the parameter of transverse deformations of the nucleus surface is in the
  ground state. This approach, in contrast to the work [17,18] allows you to take into account the full
  range of changes in γ variable (0
  0
  < γ
  0
  <60
  0
  ).
  In the case of zero approximation in the expansion of the rotational energy operator in the
  framework of the free triaxiality model [8], we obtained the following expressions for the energy
  spectrum
  2
  4
  1
  2
  2
  0
  1
  2
  4
  4
  n n I
  I
  E
  = n
  n
  , (2)
  where n
  β
  and n
  γ
  - quantum numbers of β
  2
  - and γ- vibrations, respectively; ε
  Iτ
  - eigenvalues of
  the triaxial rotator; the index τ enumerates the wave functions related to the same IM; μ
  β
  and μ
  γ
  -
  "nonadiabacity" dimensionless parameters with respect to β
  2
  - and γ- vibrations, respectively;
  corrections the second ε
  1
  and third ε
  2
  terms in the expansion of the rotational energy operator.
  Note that the expression (2) depends on the parameters ћω, γ
  0
  , μ
  β
  , μ
  γ
  .
  The comparison of theoretical and experimental values [10] is carried out for nuclei lanthanide
  and actinides of ratio R
  4/2
  =E(4
  1
  )/E(2
  1
  ), R(0
  β
  )=E(0
  β
  )/E(2
  1
  ) and R(2
  γ
  )=E(2
  γ
  )/E(2
  1
  ) respectively. As well
  as, the values of the parameters: ћω, μ
  β
  , μ
  γ
  , γ
  0
  and RMS (in keV). Note that the triaxial parameter γ
  0
  takes a value 9
  0
  ÷14.4
  0
  for lanthanide, 7.8
  0
  ÷10.6
  0
  for actinide. The quadrupole deformation
  parameter μ
  β
  =0.22÷0.39. Note at 2.74/2
  <10/3, the collective behavior of the energy spectrum of
  the levels will be rotational. And at 24/2
  <2.4 it will be vibrational. In our case R
  4/2
  =2.93÷3.31, i.e.
  the energy spectrum of the levels is rotational.
  The behavior energy levels of (2) ground state band and γ -band is completed for values of the
  parameters γ
  0
  =10
  0
  , μ
  γ
  =2 and μ
  β
  =0.3 Note that here we observe bandcrossing at values I=7. This
  means that at large spins the behavior of the moment of inertia of nucleus will be anomalous
  [11,12].
  The experimental values excited states for the γ -band of even-even nuclei are studied.
  Following some even-even nuclei has high spin states in γ -band:
  156
  Dy (I
  max
  =13 and γ
  0
  =13.9
  0
  ),
  156
  Gd
  (I
  max
  =13 and γ
  0
  =10.4
  0
  ),
  164
  Er (I
  max
  =13 and γ
  0
  =13
  0
  ),
  232
  Th (I
  max
  =12 and γ
  0
  =9.2
  0
  ) and
  238
  U (I
  max
  =26 and
  γ
  0
  =7.9
  0
  ). Simultaneously, the explanation of the excited states of the ground-state-band and γ -band
  of the above-mentioned nuclei at high spins (I>7) is inappropriate.
  The sequence of the energy levels of the ground and γ -bands for different values of the
  triaxiality parameter γ
  0
  were analyzed. It can be seen from this table that for small values of the
  triaxiality parameter of the energies of the levels of the ground and γ bands are very different. In
  this case these bands have no interactions.
  As the values of the triaxiality parameter γ
  0
  increase, the energies of the levels of the ground
  and γ -bands take on close values at I=12 and γ
  0
  =5
  0
  . And for large values of the triaxiality parameter
  γ
  0
  , the energies of the levels of the ground and γ -bands take close values, already at I=4 and γ
  0
  =30
  0
  .
  Since with increasing energy of the excitation or angular momentum, the value of the moment of
  inertia of the nucleus increases. This is due to the decrease in the pairing forces with increasing
  energy. This happens when energy levels with the same spins from different ones are close or there
  is an intersection of the bands. Thus the increase in the value of the moment of inertia of the nucleus
  is the result of the manifestation of interaction or crossing of the bands.
  Note that here we observe bandcrossing at values I=7. This means that at large spins the
  behavior of the moment of inertia of nucleus will be anomalous [11,12]. Experimental data provide
  convincing evidence that reverse bending is a manifestation of the intersection of the ground state
  band with another rotational band that has a large moment of inertia. "Coriolis antipairing" and
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