Research of analog resonances in NSC KIPT
The review of the results received at research of isobar-analog resonances in NSC KIPT in 1967-2002 is carried out. The basic accent is made on the data received at studying of g-decay of analog resonances in nuclei of 1d2s-shell. The questions connected with М1 transitions between analog and antian...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1107152017-01-07T03:02:37Z Research of analog resonances in NSC KIPT Vodin, A.N. Nuclear reactions The review of the results received at research of isobar-analog resonances in NSC KIPT in 1967-2002 is carried out. The basic accent is made on the data received at studying of g-decay of analog resonances in nuclei of 1d2s-shell. The questions connected with М1 transitions between analog and antianalog states, core polarization states, Е1 and l-forbidden М1 transitions with DT = 1, compound-compound transitions and constants of isospin interaction are considered. Проведено огляд результатів, отриманих при дослідженні ізобар-аналогових резонансів у ННЦ ХФТІ за 1967-2002 роки. Основний акцент зроблений на дані, отримані при дослідженні g-розпаду аналогових резонансів у ядрах 1d2s-оболонки. Розглянуто питання, пов'язані з М1-переходами між аналоговим і антианалоговим станами, станами типу поляризації остова, Е1- і l-забороненими М1-переходами з DТ = 1, компаунд-компаунд переходами і константами ізоспин-ізоспинової взаємодії в ядрах. Проведен обзор результатов, полученных при исследовании изобар-аналоговых резонансов в ННЦ ХФТИ в 1967-2002 годах. Основной акцент сделан на данные, полученные при изучении g-распада аналоговых резонансов в ядрах 1d2s-оболочки. Рассмотрены вопросы, связанные с М1-переходами между аналоговым и антианалоговым состояниями, состояниями типа поляризации остова, Е1- и l-запрещенными М1-переходами с DТ = 1, компаунд-компаунд переходами и константами изоспин-изоспинового взаимодействия в ядрах. 2003 Article Research of analog resonances in NSC KIPT / A.N. Vodin // Вопросы атомной науки и техники. — 2003. — № 2. — С. 72-78. — Бібліогр.: 22 назв. — англ. 1562-6016 PACS: 24.30.G, 13.40.H, 21.60.E http://dspace.nbuv.gov.ua/handle/123456789/110715 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Nuclear reactions Nuclear reactions Vodin, A.N. Research of analog resonances in NSC KIPT Вопросы атомной науки и техники |
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The review of the results received at research of isobar-analog resonances in NSC KIPT in 1967-2002 is carried out. The basic accent is made on the data received at studying of g-decay of analog resonances in nuclei of 1d2s-shell. The questions connected with М1 transitions between analog and antianalog states, core polarization states, Е1 and l-forbidden М1 transitions with DT = 1, compound-compound transitions and constants of isospin interaction are considered. |
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Vodin, A.N. |
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Vodin, A.N. |
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Vodin, A.N. |
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Research of analog resonances in NSC KIPT |
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Research of analog resonances in NSC KIPT |
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Research of analog resonances in NSC KIPT |
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Research of analog resonances in NSC KIPT |
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Research of analog resonances in NSC KIPT |
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research of analog resonances in nsc kipt |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2003 |
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Nuclear reactions |
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http://dspace.nbuv.gov.ua/handle/123456789/110715 |
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Research of analog resonances in NSC KIPT / A.N. Vodin // Вопросы атомной науки и техники. — 2003. — № 2. — С. 72-78. — Бібліогр.: 22 назв. — англ. |
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Вопросы атомной науки и техники |
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AT vodinan researchofanalogresonancesinnsckipt |
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2025-07-08T01:01:34Z |
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RESEARCH OF ANALOG RESONANCES IN NSC KIPT
A. N. Vodin
NSC "Kharkov Institute of Physics and Technology" Kharkov, Ukraine
e-mail: vodin@kipt.kharkov.ua
The review of the results received at research of isobar-analog resonances in NSC KIPT in 1967-2002 is carried
out. The basic accent is made on the data received at studying of γ-decay of analog resonances in nuclei of 1d2s-
shell. The questions connected with М1 transitions between analog and antianalog states, core polarization states, Е1
and l-forbidden М1 transitions with ∆T = 1, compound-compound transitions and constants of isospin interaction are
considered.
PACS: 24.30.G, 13.40.H, 21.60.E
INTRODUCTION
Rapid development of the nuclear physics area con-
nected with isospin began after discovery by J. Ander-
son [1] in 1961 isobaric analog resonances (АR) in av-
erage and heavy nuclei. It became clear, that the isospin
concept could be used for description of nuclei of all the
periodic system. The even greater interest was caused
with revelation of analog states (AS) by J. Fox [2] as
resonances in compound nuclei.
Works on studying АR practically at once have been
started in KIPT (for the first time in the USSR). Pres-
ence of the precision electrostatic accelerator of protons
on 3 MeV has created necessary conditions for develop-
ment of works on research of АR in the (рγ) reaction.
The initial cycle of researches was stimulated by work
of V.Yu. Gonchar, E.V. Inopin and S.P. Tsytko [3] de-
voted to a question of applicability of generalized model
to light nuclei.
The problem has been put to investigate analog reso-
nances in nuclei of 1d2s-shell in the (рγ) reaction. By
development of the formulated problem the experimen-
tal technics has been created and methods of reception,
processing and analysis of experimental data are devel-
oped.
2. EXPERIMENTAL PROCEDURE
Researches were performed at the Nuclear Spec-
troscopy Laboratory of NSC “KIPT” with the proton
beam from the 3 MeV Van de Graaf accelerator which
provided high monochromaticity of a beam and possi-
bility of smooth adjustment of energy.
In experiments were used isotope (up to A = 40) tar-
gets by thickness ~ 2-5 keV at Ep = 2 MeV on tantalum.
On the basis of NaJ(Tl) and Ge(Li) detectors has
been created the complex of the equipment which al-
lows carrying out full studying properties of the γ-radia-
tion observed in the (pγ) reaction. For the created γ-
spectro-meters the basic characteristics have been mea-
sured (the energy resolution, efficiency), calibrations on
energy are carried out and recommendations concerning
a set of calibrating γ-lines from stable sources and from
nuclear reactions are given.
Methods of the analysis and processing of the exper-
imental data received from reaction of proton radiation
capture by light nuclei, resulted in Table 1 are devel-
oped.
Table 1. Light nuclei investigated in the (pγ) reaction
№ Target
Compound
nuclei E
p
, MeV E
*
, keV
1 20Ne 21Nа 1.0 - 3.0 3544 - 5030
2 22Ne 23Nа 1.0 - 3.0 9206 - 11650
3 24Mg 25Al 1.0 - 3.0 2485 - 4570
4 26Mg 27Al 1.5 - 3.0 8552 - 11143
5 27Al 28Si 2.3 - 3.2 13840 - 14661
6 28Si 29P 1.0 - 2.2 3102 - 4764
7 29Si 30P 1.0 - 3.0 5913 - 8461
8 30Si 31P 0.5 - 3.0 7780 - 10189
9 31P 32S 1.8 - 3.0 9207 - 11775
10 32S 33Cl 0.5 - 2.0 2850 - 4790
11 34S 35Cl 0.6 - 3.0 7065 - 9295
12 36S 37Cl 1.4 - 3.2 9184 - 11483
13 36Ar 37K 1.0 - 2.0 2750 - 4523
14 40Ar 41K 1.0 - 2.0 8832 - 9734
For the mentioned compound nuclei decay schemes
of resonant states have been offered, values of spins and
parities are determined, multipole mixing ratios and val-
ues of matrix elements of electromagnetic transitions
are established. Set of the received data allowed reveal-
ing the basic features of γ-decay of АR.
3. GAMMA-DECAY OF ANALOG STATES
IN LIGHT NUCLEI
3.1. IRREGULARITIES IN EXCITATION
FUNCTION OF THE (рγ) REACTION
Experimental studying of excitation function enables
to receive the important data on density of nuclei states.
Executed in KIPT researches of reactions of proton radi-
ation capture in the vicinity of nuclei of 1d2s-shell have
allowed to determine experimental values of density of
resonant states of 14 nuclei mentioned in Table 1.
72 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2003, № 2.
Series: Nuclear Physics Investigations (41), p. 72-78.
One of the possible processes influencing on
stochastic distribution of levels in resonant area, is oc-
currence of АR. The important assumption of properties
of resonant states in compound nuclei is the assumption
of their complex nature whereas АR usually have rather
simple structure. Besides number of АR is not enough
in comparison with full number of resonant states and
they cannot affect on statistical distribution of resonant
states significantly.
However strength of АR is much more above the av-
erage values of strengths of surrounding resonances. In-
vestigating distribution of density of levels depending
on energy of nuclear excitation the effect of reduction of
density of levels of nucleus with odd mass number A
close to АR is found out [4]. On the basis of existing
nuclear models at present it is impossible to carry out
detailed calculation of excitation function of (рγ) reac-
tions and by that to try to explain the reason of occur-
rence of irregularities in density of observable levels. It
is possible to assume only, that the observable effect is
connected to feature of configurations of AS and with
display shell properties of a nucleus.
3.2. FINE STRUCTURE OF AR
Results of many researches show that majority of
АR have fine structure which is distinctly displayed in
precision experiments on (pp), (pγ) and (3He,d) reac-
tions. Its existence grows out mixing of analog state
Т> = T0 + 1/2 with levels T< = T0 - 1/2 of compound nu-
cleus that is caused by presence in a nucleus of forces
not keeping isospin (Coulomb forces). It results to that
isospin parts of wave functions will include a compo-
nent of fine structure of AR both Т>, and T< component,
i.e. will not already be pure on isospin conditions. The
analysis of probabilities of γ-transitions from compo-
nents of fine structure of AR on low lying state T< en-
ables to establish value of isospin, giving the dominat-
ing contribution to wave function of initial state, con-
cerning γ-transition.
1760 1840
1500
3000
Ep , keV
Nγ
18
96
(5
/2+ )
18
94
(5
/2+ )18
80
(5
/2+ )
18
78
(7
/2- )
18
30
(5
/2+ )
18
15
(3
/2+ ,5
/2
)
18
08
(3
/2- )
17
70
(5
/2+ )
Fig. 1. Fine structure of d5/2 resonance in the 30Si(pγ)31P
reaction, θlab = 55°
Really, if isospin part of wave function of this reso-
nant state is defined, basically, by isospin Т> then rela-
tive intensities of γ-transitions to the given level from
the excited states corresponding to different components
of fine structure of AR, should be proportional to contri-
butions of Т> to wave functions of components, i.e. are
proportional to Γр values. At absence of linear correla-
tion between partial radiation widths of decay Γγi and
width of elastic scattering of protons Гр it is possible to
assume, that isospin parts of wave functions of resonant
states contain isospin T< as main component.
γ-Decay of components of fine structure of AR in
23Na, 27Al, 31P and 35, 37Cl nuclei is investigated [5-9]. As
an example, the excitation function of the 30Si(pγ)31P re-
action in the vicinity of d5/2 resonance is shown on
Fig. 1. Correlations between partial widths of decay of
fragmented АR are investigated, that has allowed re-
vealing for what channels the analog state is the com-
mon entrance state.
3.3. М1 TRANSITIONS АS → ААS
The special place in studying АR is occupied with γ-
transitions between AS and antianalog states (ААS).
Energy splitting of analogue-antianalogue is caused by
interaction of particle isospin t with core isospin Т0, and
has been explained phenomenologically by A. Lane [10]
by introduction in optical potential of an additional
term:
0
1 Tt ⋅
A
V (1)
At research of АR in reaction of proton radiation
capture 30 pairs of states like analogue-antianalogue are
identified. The most full information on structure of AS
and AAS is received at studying electromagnetic transi-
tions between them. One-partial evaluations of matrix
elements for magnetic dipole transitions AS → AAS ap-
peared good enough approximation [11]. Observed de-
viations between experimental values and one-partial
estimations have been explained by various authors with
the help of complication of wave functions of AS and
AAS.
3.4. THE MODIFIED NILSSON’S MODEL
It has been shown [12], that for the description of
probability of М1 transition between AS and AAS can
be used the generalized model in Nilsson scheme. Mod-
ification of the Nilsson’s model will consist in that at
calculation of probability of М1 transitions initial and fi-
nal states of system are considered as states with various
deformations. Then at transitions the state not only an
odd particle (as in Nilsson scheme), but also states of all
particles of a core changes. To these states there corre-
spond the determinants constructed from two various
sets of Nilsson one-partial wave functions.
In this connection the programs which have allowed
processing an experimental material have been devel-
oped and to carry out calculations of own functions and
own values of energy on Nilsson’s model for continuous
values of parameters of deformations. To expect energy
73
of levels without taking into account and in view of
mixing strips because of interaction of Coriolis forces,
and also to receive probabilities electric quadrupole
transitions in modified Nilsson’s model.
Thus, within the framework of this model the analy-
sis of matrix elements of electromagnetic transitions be-
tween the excited states in nuclei 23Na, 25, 27Al, 29, 31P and
35, 37Cl is carried out. It is shown, that dependence of de-
formations on mass number (from A ≈ 25 up to A ≈ 37)
for the ground and excited states of light nuclei is ob-
served.
From the analysis of Е2 transitions between low ly-
ing states of 23Na where Coriolis interaction is entered,
it is shown, that these transitions are more sensitive to
the contribution of a one-partial part of the wave func-
tion which are taking into account dependence on defor-
mation, than to Coriolis mixing.
3.5. М1 TRANSITIONS АS → CPS
However later in a number of precision experiments
it has been established, that in some nuclei М1 transi-
tions ) ,( π
>i
TJ → ) ,(
<
π TJ
f are considerably slowed
down in comparison with one-partial estimations. The
explanation of these facts needed introduction in model-
ing representations of a new degree of freedom of a nu-
cleus, states such as core polarization state (CPS).
The detailed calculations which have been carried
out within the framework of multiparticle shell model
with effective various residual interaction [11], have
shown, that the full probability of γ-decay of AS in odd
nuclei with 21 < A < 41 is allocated between М1 transi-
tions on AAS and CPS. This conclusion appeared suffi-
cient for interpretation of radiation widths of AS decay,
known by then in this vicinity of nuclei.
Isobaric collective 1+ states forming narrow group
are lower АR, have been found out for nuclei 31P and
37Cl [13, 9]. These states are sharply allocated with great
value of matrix elements of М1 transitions and settle
down on 4…5 MeV below АR. Originally they tried to
associate it with Gammov-Teller resonance (GTR),
however now it is clear, that it is necessary to compare
them with splitted CPS which agrees to quasiparticle es-
timation lies in this energy area.
It has been found out in the first experiments on the
(6Li,6He) reaction on 48Ca. From the new data on the
(pn) reaction it follows, that, apparently, it is necessary
to compare CPS with 1+ resonance laying below АR and
observable together with GTR in light and average nu-
clei. As collective 1+ states with such excitation energy
have В(GT) ≈ 1, and for GTR В(GT) ≈ N - Z it is natu-
ral, that they can compete with GTR on section of exci-
tation only in the field of light nuclei. As an example
distribution of experimental values of B(М1) for γ-tran-
sitions from АR on levels 31Р is shown on Fig. 2. We
can see that γ-decay of АR has selective character. Ex-
cept for ААS the group of states with Jπ = 1/2+, 3/2+ and
5/2+ which centre of gravity lies at Е* ≈ 4.41 MeV is
populated by direct γ-transitions. It corresponds to posi-
tion of CPS in 31Р, appreciated under the formula:
nP
A
V
TЕE ++=− 1
0CPSAS )2/1( , (2)
where Pn - pairing energy of a neutron.
0 4 8
0
4
8
1/2+
1/2+
3/2+
3/2+3/2+3/2+
5/2+
5/2+
5/2+
5/2+
5/2+
3/2+
1/2+
d 3/
2 -
A
A
S
d 3/
2-A
S
Elevel, МeV
B(
M
1)
, 1
02 µ2 N
Fig. 2. Distribution of B(М1) values for direct transi-
tions from analog d3/2 state on levels 31Р
3.6. ANALOG γ- AND β-TRANSITIONS
It is known, that in view of isobaric symmetry there
is a fundamental ratio between probability Λ(М1) of γ-
transition from АR and probability Λ(GT) for Gammov-
Teller β-transition in the same final state of a nucleus [14]:
)(11.01)1(
2
GT
isf
ilf
CM Λ+=Λ
τ
τ
, (3)
which is correct in the case if the analog resonance is
pure T> = T0+1/2-resonance. Then the Λ(М1) value is
determined only by a spin σ-part of the operator of
isovector М1 transition. The Λ(М1) value of γ-transition
is expressed as follows:
)1(
2
3
π4
)1(
2
MB
e
Mc
M
=Λ
. (4)
For the Λ(М1) value of β-decay we have:
ft
GT
4390
)( =Λ . (5)
This statement is checked for nuclei with A = 23, 31
and 37. In Table 2 values of Λ(М1) calculated under the
formula (4) on the basis of known data on values ft for
β-transitions to levels of final nuclei and experimental Λ
(М1) for corresponding γ-transitions from АR [9] are re-
sulted. For all considered γ-transitions significant excess
of the Λ(М1) value is observed in comparison with its
value appreciated under the formula (4). It testifies to
the essential contribution of an orbital l-part to probabil-
ity of the considered М1 transitions, caused by mixing
ААS and CPS in 23Na, 31P and 37Cl.
74
Table 2. Comparison of analog β- and γ-transitions in
nuclei with 20 < A < 40
Isobaric
nuclei
,**
fi EE →
MeV
J
π ftlg
Λ(M1), W. u.
“exp” “β“
23
Ne -
23
Na 7.89→ 0
→0.44
3/2
+
5/2
+
5.28
5.40
0.20
0.11
0.022
0.017
31
Si -
31
P 6.81→ 0
→1.27
1/2
+
3/2
+
5.52
5.6
0.28⋅10
-2
0.32⋅10
-3
0.082
37
S -
37
Cl 10.22→3.10
→3.74
→4.27
→4.40
7/2
-
5/2
-
7/2
-
5/2
-
4.38
6.15
5.98
6.54
3.7
7.8⋅10
-2
6.1⋅10
-2
11.5⋅10
-2
0.81
1.4⋅10
-2
2.0⋅10
-2
0.13⋅10
-2
Note: Both at β- and γ-transitions have other bran-
ches of decays (not represented in Table 2) which lead
on the excited states of 23Na, 31P and 37Cl
3.7. Е1 TRANSITIONS IN
SELF-CONJUGATED NUCLEI
Electromagnetic transitions in the self-conjugated
nuclei carry the information about isospin structure of
states in a nucleus. E1 transitions in the self-conjugated
nuclei between states with identical isospins, that is with
∆Т = 0, are forbidden. Е1 transitions with ∆Т = 0 ob-
servable on experiment it is possible to explain by exis-
tence of mixing of states with various isospins. The esti-
mation of intensity of mixing of states with isospins
Т = 0 and Т = 1 is possible to determine as the ratio of
average value of a square of a matrix element of the for-
bidden E1 transition to average value of a square of a
matrix element of the allowed E1 transition:
1
2
0
2
2
1
)1(
)1(
)0(
=∆
=∆
〉〈
〉〈
=α
T
T
E
E
M
M
(6)
Such estimation of a degree of mixing carries cleanly a
statistical character as at averaging probabilities of Е1
transitions dependence of a matrix element of γ-transi-
tion on other quantum numbers which are distinct from
isospin is ignored. So, for reception of the most reliable
values of mixing at calculation of average value of
probability of E1 transition it is necessary to use proba-
bly greater number of transitions. Usually average val-
ues of squares of the resulted matrix elements are calcu-
lated under the formula:
∑
=
=〉〈
n
i i
E
n
E
1
22
)1(lg
1
)1(lg MM (7)
where n - number of transitions on which averaging is
carried out. From value of intensity of mixing it is pos-
sible to receive value of a matrix element of Coulomb
interaction resulting to mixing, using expression:
10110 )0( ∆⋅α∝
cH (8)
where ∆10 - distance between levels having identical
spins and parities, but different isospins.
The received experimental data [15] have allowed
carrying out an estimation of intensity of mixing in nu-
clei of 1p- and 1d2s-shells (see Table 3). Such estima-
tion specifies dependence of mixing on isospin from
mass number. On the basis of a rule of selection on
isospin for Е1 transitions in the self-conjugated nuclei
the effect of decreasing of intensity of mixing on isospin
in the closed shells and subshells is established. It ex-
plains dependence of isovector Coulomb energy from
mass number.
Table 3. Average values of forbidden and allowed
on isospin Е1 transitions and intensities of mixing of
states with various isospins for the self-conjugated nu-
clei 18 ≤ A ≤ 40
Nucleus 0
2
)1( =∆〉〈 TEM 1
2
)1( =∆〉〈 TEM )0(
2
1α
18
F 1.24⋅10
-4
1.33⋅10
-3
0.090
20
Ne 5.3⋅10
-5
4.37⋅10
-3
0.011
24
Mg 9.52⋅10
-5
7.38⋅10
-4
0.129
26
Al 2.87⋅10
-4
1.11⋅10
-3
0.259
28
Si 7.46⋅10
-5
6.35⋅10
-4
0.117
30
P 1.96⋅10
-4
1.09⋅10
-3
0.179
32
S 1.79⋅10
-4
1.64⋅10
-3
0.109
36
Ar 1.55⋅10
-4
4.73⋅10
-4
0.327
40
Ca 1.95⋅10
-4
1.97⋅10
-3
0.099
3.8. Е1 TRANSITIONS WITH ∆Т = 1
IN ODD NUCLEI
Meanwhile in experiments of last years are found
out isovector γ-transitions which have not found the re-
flection in existing theoretical approaches. To them,
first of all, concern Е1 and the l-forbidden М1 transi-
tions such as T> → T<. Now in the modeling description
of Е1 radiation widths of decay of AS for near magic
nuclei with А > 40 achieve significant progress. In this
connection represents special interest studying and
statement of this question for nuclei of 1d2s-shell where
there is a hope for the adequate description of Е1 widths
of analog resonances within the framework of existing
theoretical representations.
75
The analysis of the collected experimental material
has allowed formulating some common conclusions [16].
1. Regular difference of experimental values of an
effective charge 1)(1)/(=e spexp2
exp ЕГЕГ γγ from unit is
observed. Here [17]
21
3
2exp
γ 12
)2(
9
16)1( β−γ
+
π=
fi
i
fi
M
j
SS
T
c
E
eEГ
(9)
Here β
fiM is the matrix element for first-forbidden Fer-
mi β-transition and within the single-particle approxi-
mation it is equal to
{ }ifiifffi rljYljM χχ=β
1)sp( , (10)
where iiff ljYlj 1 is the reduced matrix element.
It testifies to an essential role of the polarizing ef-
fects caused by virtual excitation of T> and T< compo-
nents of electric dipole giant resonance during E1 radia-
tion decay of AS.
2. The shell effects affecting on values of Гγ(Е1) in
process of approximation of number of neutrons in re-
searched nuclei to magic number N = 20 are revealed.
Values Гγ(Е1) are minimal in the vicinity of nuclei
A ≈ 37.
3. Appreciable correlation between values of Гγ(Е1)
and values of spectroscopic factors of AS is not found
out. At the same time absolute value Гγ(Е1) essentially
depends on an orbit occupied with an unpaired nucleon.
The most intensive appeared Е1 transitions which are
observed at decay of AS with Jπ = 3/2-.
4. It is established, that one-partial E1 transitions
with spin overturn ji = li ± ½ → jf = lf ± ½ appeared
more poorly the transitions keeping relative orientation
of spin and orbital moment ji = li ± ½ → jf = lf ½. This
selection rule is fairly for all area of odd nuclei with
20 < A < 40.
3.9. l-FORBIDDEN М1 TRANSITIONS
WITH ∆Т = 1 IN ODD NUCLEI
Other situation has developed for l-forbidden М1
transitions with ∆T = 1 in nuclei of 1d2s-shell. The reg-
ular calculations explaining the mechanism of removal
of l-interdiction, even in simple model have not been
executed and, probably, by virtue of a seeming theoreti-
cal inconsistency, to them have not given due attention.
It is possible, that mixing 1d and 2s configurations im-
poses some technical difficulties on calculations in
1d2s-shell. However more essential reason constraining
the further development of modeling representations for
this type of γ-transitions, is not so much difficulty of ba-
sic character as deficit of experimental data about l-for-
bidden М1 transitions with ∆T = 1 in this area of nuclei.
The analysis of the collected experimental material
[18] allows to formulate some general conclusions fol-
lowing from carried out studying of the given M1 transi-
tions in considered area of nuclei.
1. It is established, that l-forbidden М1 transitions
with change of isospin on unit are observed in all area
of odd nuclei A ≤ 70. Their intensity, in some cases, is
comparable under the order of size to intensity of one-
partial М1 transitions between analog and antianalog
states.
2. In distribution of factors of forbidenness
exp
calc
M )1(
)1(
MB
MBF = (11)
from mass number A it is traced two maxima, connected
with γ-transitions in nuclei with 20 < A < 40 ( MF ~ 800)
which are practically spherical, and in nucleus with
60 < A < 90 ( MF ~ 300). It evidently illustrates Fig. 3.
For the γ-transitions observed at decay of АR in nuclei
with A < 20 and 40 < A < 60 factors of an interdiction
MF are minimal (~ 10).
0 20 40 60 80
0
300
600
A
FM
Fig. 3. Behavior of the factor of forbidenness FM de-
pending on mass number A
3. It is not revealed appreciable correlation between
values MF and values of spectroscopic factors C2S of
АR. It allows to assume, that l-forbidden М1 transitions
T> → T< are carried out due to an impurity of other con-
figurations to an initial or final state of a radiating parti-
cle. That fact, that these transitions are observed in im-
mediate proximity from the filled shells, forces to draw
a conclusion that collective effects should not play an
essential role in removal of l-forbidenness. However
easing of l-forbidenness in the vicinity of nuclei A ~ 25
and 40 < A < 60 is connected by obvious image to a
growing role of collective effects, in the latter case, first
of all collective isobaric 1+ configurations of np type (a
condition such as CPS).
3.10. COMPAUND-COMPAUND TRANSITIONS
Doubtless interest represents researches of γ-transi-
tions between high excited compound states of nuclei
concerning from each other on ~ 1-2 MeV. Here both
initial and final states are complex on structure and
practically any component of wave function can give
76
the contribution in the probability of γ-transition be-
tween them.
In this connection there are some questions about the
nature of such γ-transitions. Whether they are deter-
mined by "tails" of giant multipole resonances (GMR)?
Or at energy of transitions, which is significant smaller
energy of maximum of GMR, the last already do not
play an essential role, and it allows to be shown to other
mechanisms of γ-transitions? What is hierarchy on mul-
tipolarities of γ-transitions? Whether show multyquasi-
particle components of wave functions of compound
state itself in these transitions? Or it is the transitions
determined any allocated component, for example AS
fragmented on compound stets?
All available material on partial γ-transitions be-
tween compound states of nucleus of 1d2s-shell is sys-
tematized and analyzed. On the basis of the received re-
sults the following conclusions [19] are formulated.
1. Soft ( `*
γE = *
cE -
*
/c
E ≈ 2 MeV) γ-transitions be-
tween high excited compound states are found out in all
area of nuclei of 1d2s-shell. Their greatest number falls
at nuclei, which have rather low on energy (< 3 MeV)
values Sp. Selective character in population by direct γ-
transi-tions of final compound states takes place.
2. γ-Transitions such as М1 appeared the most es-
sential here. It is possible, that in formation of their
widths can take place GMR. Value of radiating power
function )1(γ MS
/cc appeared equal 2∙10-8 MeV-3.
3. In the vicinity of nuclei Z = 20 and N = 20 abnor-
mal change of hierarchy of multipolarities of γ-transi-
tions is observed. γ-Transitions such as Е1 and Е2 ap-
peared here the basic. However this conclusion is pre-
liminary because of deficit of the data and demands the
further experimental confirmation.
3.11. CONSTANTS OF ISOSPIN INTERACTION
V1 AND /f 0
Experimental data on energy splitting of AS and
ААS in nuclei can serve as good check of realness of
those or other representations about АR. The available
data about such energies are compatible with expected
of the theory for some AS, but full check of all forecast-
ings is not carried out. In [20] the opportunity of the de-
scription of the data on energy position of AS and ААS
is in part appreciated by the example of odd nucleus
with A < 70 from positions of the ideas advanced in mi-
croscopic approaches and shell model of a nucleus. In
this connection independent check of value of a constant
/
0
f of isospin-isospin part of δ-functional universal am-
plitude of interaction of quasiparticles which is used in
calculations [21] for the description of AS in the nuclei
close to a strip of β-stability is carried out. The /
0
f val-
ues are determined from formula:
,
)1(1)1(1
1
Δε
/
0
/
0
/
0 AS
FААS fc
E
fc
f
E
−+
=
−+
+
= (12)
where ∆εF is the width of layer of excess neutrons.
Parameter V1 responsible for isospin part of one-par-
tial potential in a nucleus [22] is appreciated. Its value is
determined by the splitting energy of AS and AAS:
)( 210
1
ААSАS /T
A
V
E-EE +==∆ (13)
As a result of the carried out analysis of experimen-
tal data about energy splitting of AS and ААS in odd
nuclei with A < 70, it is possible to draw the following
conclusions:
1. It is revealed, that average value /
0f = 1,9 for reso-
nances with T> = 3/2 will be coordinated under the order
to value /
0f = 1,53 used in modeling calculation [21].
This fact is a little bit unexpected as in microscopic ap-
proach [21] for an estimation of energy of AS and ААS
is used approximation N – Z >> 1 which not absolutely
adequately represents a situation in considered area of
nuclei.
2. It is established, that in nuclei with 20 < N < 28
the maximal divergence (in 6 times) a theoretical esti-
mation /
0
f with its values received on the basis of ex-
perimental data about energy splitting isobar-analog
2p3/2, 1f7/2, and 1g9/2 resonances is observed. It evidently
illustrates Fig. 4.
8 12 16 20 24 28 32 36
0
4
8
T
>
=3/2
T
>
=5/2
T
>
=7/2
T
>
=9/2
f0
/ = 1,53
f0
/
N
Fig. 4. Experimental values /
0f from energy distance
between AS and AAS in nuclei with A < 70
3. Linear dependence of growth of values /
0f on
splitting energy of AS which is approximated by func-
tion 2/
0 )53,1(03,1 −∆= Ef is found out.
4. In the field of nuclei with N > 28 for AS with
T> = 5/2, 7/2 and 9/2 is observed an appreciable devia-
tion /
0
f from theoretical value aside the big sizes. How-
ever it is impossible to determine dependence of size
/
0
f on number of neutrons N as the data will insuffi-
ciently well be coordinated among them.
5. In considered area of nuclei the significant diver-
gence of experimental values of parameter V1 (Fig. 5)
with value V1 ~ 100 MeV, used in modeling calculations
[22] is observed. Meanwhile, it is necessary to note, that
average value of parameter V1 for 1f7/2 resonances is
77
equal to 105 MeV. However as a whole dependence of
parameter V1 on mass number A which is well described
by the empirical formula )61(220 3/2
1
−−= AV is observed.
20 30 40 50 60
0
90
180
V1=100 MeV
A
V 1,
М
eV
Fig. 5. Systematization of parameters V1 from ener-
gy splitting AS and AAS in nuclei with A < 70. Designa-
tions of experimental points as well as on Fig. 4
CONCLUSION
The further researches of γ-decays of АR are con-
nected to studying Е1 and l-forbidden М1, M2 and Е2
transitions that allows to receive the information on
structure of conditions of parent nuclei and degrees of
infringement isotopic symmetry of AS. It is reasonable
to expect, that there should be certain laws and that their
detection will help to systematize, at least, knowledge
on the given γ-transitions and by that to determine the
further prospects of researches of these questions in
wide area of nuclei. Obvious interest to these γ-tran-
sitions is caused by fundamentality of problem – finding
out a role of charging dependence of nuclear forces in
the mechanism of mixing of levels on isospin in nuclei.
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79
INTRODUCTION
CONCLUSION
REFERENCES
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