Table 1 
Multipole mixture coefficients

Table 1
Multipole mixture coefficients
δ( 2
1)
E
M
for
158
Gd
I
i
K
i
I
f
K
f
E
,
МeV
)
2
(
E
B
efm
2
)
1
(
M
B
μ
N
exp.
[6]
.
theor
.
adiab
20
2
2gr
1,1804
-3,226
0,0434
-0,70(7)
-0,73
-
40
2
4gr
1,1454
-5,953
-0,0571
+1,0(2)
1,0
-
20
3
2gr
1,4379
5,841
0,0447
-1,5(4)
1,58
-
40
3
4gr
1,4058
6,539
0,0563
+6(2) or (-0,76(11))
+1,6(5) [2]
1,36
-
22
1
2gr
1,1076
-16,540
-0,0116
+80 ≤ δ ≤ -25
-9,0(15) [2]
13,17
-
32
1
2gr
1,1859
-17,070
-0,010
+30 (+32,-14)
16,88
-
32
1
4gr
1,0040
13,300
0,0091
-23(+19,-7)
12,24
-
42
1
4gr
1,0970
-14,370
-0,0525
+6,4(+14,-10)
or (-0,73(4))
2,49
-
21
2
2gr
1,8846
1,943
-0,1706
-0,08(12) or
+2,9(+18,-9)
-0,18
-0,39
Namangan Institute of Engineering and Technology
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10.25.2023
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31
2
2gr
2,0099
4,956
0,1161
+0,45(20) or
+7(+70,-4)
0,72
0,77
41
2
4gr
1,8337
-0,195
-0,1742
+0,25(13) or+1,8(6)
0,02
-0,20
11
2
22
1
0,7431
4,390
0,0018
+0,17(15)
15,11
-
31
2
22
1
0,9024
-1,965
-0,0013
+1,5(7)
11,4
-
References
1. P. N.Usmanov, I.N.Mikhailov // Phys. Part. Nucl. 28,4 (1997)
2. P. N.Usmanov, А.А. Okhunov, U.S. Salikhbayev, А.I.Vdovin // Part. Nucl., Lett., 7(3) (2010)
3. C.W.Reich, Nucl. Data Sheets 113, 2575 (2012)
4. R.G. Helmer, Nucl. Data Sheets 77, 481 (1996)
5. C.W. Reich, Nucl.Data Sheets 105, 555 (2005)
6. L. I. Govor, A.M. Demidov, I. V. Mikhailov // Phys. At. Nucl. 64(7) (2001)
STUDY OF ELECTROMAGNETIC PROPERTIES OF EXCITED STATES ISOTOPES
156,158,160
Gd
P.N.Usmanov, E.K.Yusupov
Namangan Institute of Engineering and Technology
Е-mail:
yusupov.elmurod@gmail.com
Abstract—The theoretical analysis of electric characteristics of the positive parity states in
isotopes
158,160
Gd has been carried out in the phenomenological model taking into account the
Coriolis mixing of low-lying states in rotational bands. The energy spectrum of the levels of positive
parity, the wave functions of states, and the reduced probabilities of E2 transitions have been
calculated.
Keywords: nuclei; energy; states; rotational bands; phenomenological model
Within the framework of the phenomenological model [1, 2], which takes into account the
Coriolis mixing of low-lying states of rotational bands, the structure of excited states and
nonadiabatic effects manifested in the probabilities of magnetic transitions were studied. The
energy, structure of wave functions, and electromagnetic characteristics of excited states are
calculated. The calculated values of energy, probabilities of E2-,
1
M
-transitions, magnetic
moments of
μ ( )
gr
I
states of the main rotational band and multipole mixture coefficients of
δ( 2 / 1)
E
M
out of
1
2
2
3
β (0 ) ,β (0 ) , γ(2 )
and
π
+
ν
1
K
bands are compared with the
available experimental data [3-7], which give satisfactory agreement. The calculated and
experimental [5,6,7] energy values for
156
Gd
are presented in the figure and the coefficients of
the mixture of multipoles
δ( 2 / 1)
E
M
from the states of
+
ν
0
-,
γ
-
and
π
1
K
bands for
160
Gd
are given in the table.
It is shown that the effect of mixing of low-lying bands plays an important role and is
significantly manifested in the probabilities of electromagnetic transitions even at low spins. The
calculation results showed that for a more adequate description of the experimental characteristics,
it is necessary to use some additional method to determine the sign of the parameters included in
the multipole operators of the E2- and -
1
M
-transitions.
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