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Namangan Institute of Engineering and Technology
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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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