Giant multipole resonances
The review of the experimental discovery of and further research into giant multipole resonances performed at the Kharkov Institute of Physics and Technology is outlined. These results are compared with theoretical and experimental ones obtained in other laboratories.
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irk-123456789-1107182017-01-07T03:02:26Z Giant multipole resonances Khvastunov, V.M. Nuclear reactions The review of the experimental discovery of and further research into giant multipole resonances performed at the Kharkov Institute of Physics and Technology is outlined. These results are compared with theoretical and experimental ones obtained in other laboratories. Дано огляд експериментального виявлення і подальшого дослідження гігантських мультипольних резонансів, виконаних у Харківському фізико-технічному інституті. Дано порівняння з експериментальними і теоретичними результатами, отриманими в інших лабораторіях. Дан обзор экспериментального обнаружения и дальнейшего исследования гигантских мультипольных резонансов, выполненных в Харьковском физико-техническом институте. Дано сравнение с экспериментальными и теоретическими результатами, полученными в других лабораториях. 2003 Article Giant multipole resonances / V.M. Khvastunov // Вопросы атомной науки и техники. — 2003. — № 2. — С. 50-55. — Бібліогр.: 48 назв. — англ. 1562-6016 PACS: 24.30.Ca http://dspace.nbuv.gov.ua/handle/123456789/110718 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Nuclear reactions Nuclear reactions Khvastunov, V.M. Giant multipole resonances Вопросы атомной науки и техники |
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The review of the experimental discovery of and further research into giant multipole resonances performed at the Kharkov Institute of Physics and Technology is outlined. These results are compared with theoretical and experimental ones obtained in other laboratories. |
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Article |
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Khvastunov, V.M. |
| author_facet |
Khvastunov, V.M. |
| author_sort |
Khvastunov, V.M. |
| title |
Giant multipole resonances |
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Giant multipole resonances |
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Giant multipole resonances |
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Giant multipole resonances |
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Giant multipole resonances |
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giant multipole resonances |
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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/123456789/110718 |
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Giant multipole resonances / V.M. Khvastunov // Вопросы атомной науки и техники. — 2003. — № 2. — С. 50-55. — Бібліогр.: 48 назв. — англ. |
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Вопросы атомной науки и техники |
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AT khvastunovvm giantmultipoleresonances |
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2025-07-08T01:01:49Z |
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2025-07-08T01:01:49Z |
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1837038579623133184 |
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GIANT MULTIPOLE RESONANCES
V.M. Khvastunov
National Science Center "Kharkov Institute of Physics and Technology", Kharkov, Ukraine
e-mail: khvastunov@kipt.kharkov.ua
The review of the experimental discovery of and further research into giant multipole resonances performed at
the Kharkov Institute of Physics and Technology is outlined. These results are compared with theoretical and
experimental ones obtained in other laboratories.
PACS: 24.30.Ca
1. INTRODUCTION
A giant resonance (GR) was predicted theoretically
by A.B. Migdal in 1945 [1] on the ground of
calculations according to sum rules. In two years GR
was observed in experiment by Baldwin and Klaiber
[2]. Then there followed a large number of papers in
which GR was studied in experiment with photon beams
of bremsstrahlung of electrons.
The experiments revealed the GR excitation in all
nuclei. It was established that the GR excitation in
photonuclear reactions possesses a electric dipole (E1)
pattern.
After some time the giant dipole resonance (GDR)
was studied with monochromatic photon beams,
electron scattering as well as with hadron scattering
(protons, 3Не and α-particles).
Models based on collective motion of nuclei as well
the shell model were proposed for explaining the
;experimental data on GDR [3].
The dynamic collective model (DCM) [4] predicts,
apart from the electric dipole (Е1) resonance, the
electric quadrupole (Е2) and monopole (Е0) resonances,
the ratio of excitation energies for these resonances
having the following form: Е(Е1):Е(Е2):Е(Е0)=
1:1,6:2,16.
The first experimental evidence of the giant
quadruple resonance was obtained from the experiments
on photoabsorption by 159Тb [5] and 165Ho [6] nuclei.
These data have shown that above the electric Е1
resonance the Е2 resonance is observed, whose cross
section amounts to less than 7% of the dipole absorption
cross section and it is well described within the DCM
framework [7].
2. DISCOVERY OF GIANT MULTIPOLE
RESONANCES
2.1. Electron scattering
2.1.1. Experiments in Kharkov
In 1968-1969 in Kharkov at the experimental
installation [8], located at the exit of the LUE-300 KIPT
AN UkrSSR electron linac there was performed the
research into the GR electroexcitation in 28Si [9], 60Ni
[10], 12C [11] nuclei. The experiments were made with
electron energies 150, 200, 225 МeV and scattering
angles of 200 to 800. It was observed that with the
increase of the momentum transfer q to the nucleus the
relative contributions of the levels, shaping the GR, are
redistributed in a way to enrich the low energy part of
the spectrum. Figure 1 presents four spectra of inelastic
electron scattering by the 28Si nuclei for various q [9].
Fig. 1. Inelastic electron spectra in 28Si measured
for different momentum transfers q. Radioactive tails
from elastic and inelastic peaks are subtracted; ε is the
excitation energy. Vertical lines represent the particle-
hole model calculations of the longitudinal formfactor.
The length of the lines is given in relative units
As is seen from Fig. 1, the cross section in the range
of excitation energies 16-19 МeV increases with respect
50 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2003, № 2.
Series: Nuclear Physics Investigations (41), p. 50-55.
to that for higher excitation energies with q increasing.
This work pointed out that the enrichment at low
energies can be explained assuming the electric
quadrupole (Е2) pattern of excitation in this part of the
spectrum. The studies performed with the 60Ni [10] and
12C [11] nuclei also have shown that apart from the GR
at lower energies there occurs the excitation of the
levels with the quadrupole excitation pattern.
Before these experiments started there were no
experimental or theoretical data pointing to the
existence of such transitions in this energy range,
therefore it was necessary to perform additional
experiments in this energy range of nuclei excitation.
In two years such work started almost
simultaneously in several laboratories. The experiments
were performed with the beams of electrons, protons,
3Не-particles and α-particles.
2.1.2. Experiments in other laboratories
With the help of the inelastic electron scattering
performed in Darmstadt (FRG) [12-14] in 1971-1973
with the initial energies 50 and 65 МeV at large angles
(930, 1290, 1650) on natural targets out of Ce, La, Pr,
there were found the magnetic dipole (М1) and electric
quadrupole or monopole (Е2 or Е0) GR with the
excitation energies below the Е1 resonance.
In 1972-1973 in the Tohoku University (Japan) there
were performed the experiments on inelastic electron
scattering with the energies from 125 до 300 МeV on
the 90Zr, 208Pb nuclei [15,16]. These experiments have
shown the presence of the Е2 (Е0) GR with the
excitation energies below the Е1 resonance, and with
the 208Pb nucleus there were found with the excitation
energies 19 and 22 МeV the Е2 (or Е0), Е3 giant
resonances, located above the Е1 resonance. The
resonance at the 22 МeV was interpreted as the
isovector electric Е2 (or Е0) resonance.
It is known [3], that the energy position of the
electric GR is well described by the formula: 80А-
1/3 МeV. In the paper [17] in 1974 there were proposed
the phenomenological formulas for the description of
the energy position of some other electric multipole
resonances: 53 А-1/3 МeV (Е0, isoscalar); 63 А-1/3 МeV
(Е2, isoscalar); 105 А-1/3 МeV (Е3); 130 А-1/3 МeV (Е2,
isovector); 195 А-1/3 МeV (Е0, isovector).
2.2. Scattering of hadrons
Experiments on inelastic scattering of protons have
shown the Е2 GR excitation for the energies below the
Е1 resonance. In paper [18] in 1973 there was
performed the study of inelastic scattering of protons
with the energy 66 МeV on the 27Al, Cu, In, Pb nuclei.
Proton spectra maxima were found to be systematically
shifted to the lower energies compared with the location
of the Е1 resonance. The angular dependence of the
excitation cross section with the energy below 11 МeV
agrees the best with one calculated for the Е2 transition
with the ∆Т=0, i.e., for a isoscalar quadrupole transition.
Studies with the inelastic scattering of 3He particles
with the energy 41 МeV [19], performed in USA in
1973 on the 24Mg, 26Mg, 50Cr, 60Ni, 90Zr nuclei did not
furnish the encouraging results. The process cross
section turned out to be 3 orders of magnitude less than
the proton cross section for similar q. This was
associated with a strong absorption of 3He particles
inside the nucleus. The successful performance of the
experiment was also impeded by specific problems
associated with a large background and low sensitivity
of the equipment [19]. However the analysis [20] of the
results on inelastic scattering of 3He particles with the
energy of 75 МeV and the alpha-particles with the
energy of 90 МeV on the 208Pb, 197Au, 181Ta nuclei made
later has shown that these two methods can also be
successfully applied for studying the excitation in nuclei
of giant multipole resonance (GMR).
Here we have mentioned only a very small part of
the works in which the GMR was studied before 1975.
The GMR studies during this period are more fully
outlined by us in the review [21].
2.3. Conclusions
Our assumptions on the quadrupole (E2) character of
level excitation for the energies below GDR for the
28Si[9], 60Ni [10], 12C[11] nuclei are supported by the
data obtained with different methods on other nuclei in
other laboratories. The data in the range of excitation
energies agree with the classification for the isoscalar
E2 resonance.
3. STUDY OF GIANT MULTIPOLE
RESONANCES
For studying GMR we have processed the data on
electron scattering on nickel isotopes [22] and
performed measurements on the 64Zn, 65Cu and 124Sn
nuclei.
3.1. Isospin splitting of GDR in nickel isotopes
Isospin conservation for electromagnetic transitions
in a nucleus leads to that the GDR in the nuclei with the
isospin of the ground state Т0≠0 (N>Z) is split into two
components with Т<=Т0 and Т>=Т0+1 [23]. The value of
the energy splitting amounts to several МeV, that
permits to observe the isospin splitting (IS) of the GDR
in experiment.
A number of studies [24-26], performed for the 58Ni
and 60Ni nuclei with the help of partial photonuclear
reactions and inverse to them have shown that the IS
GDR is observed in these nuclei.
To study the isospin influence on the GDR
electroexcitation in the nuclei with different Т0 in the
ground state we have analyzed the spectra of electrons
scattered inelastically on three nickel isotopes: 58Ni, 60Ni
and 64Ni [10], which were registered with equal value of
the momentum transfer to the nucleus q=130 МeV/с.
All section of the spectrum of scattered electrons was
decomposed into three Gaussian peaks. The peaks
located near the energy ω=13 МeV in all three isotopes
are associated with the excitation of the isoscalar Е2
resonance [27], and the peaks above the energy of
16 МeV were considered by us as associated with the
excitation of GDR isospin components. Comparison
between our results and the data on the (γ,n)-reaction
[26] and the joint analysis of data for the (γ,n)-reaction
[25] and the process of radiation capture of protons,
51
performed in paper [24], shows a good agreement. The
theoretical studies of the isospin effect for the GDR
excitation show that this effect will lead to the energy
splitting of the GDR, and the relation between isospin
components will depend on the isospin value T0 [25].
Fig. 2. Ratio of the squares of form-factors
F2
T0+1/F2
T0 against Т0. Circles are for our experimental
data, solid curve is for the calсulations according to the
formulas of papers [22,28]
The calculations of ratios of isospin components
with Tо and (T0 + 1) show, they change fast with the
change of the isospin Tо. Such calculations were
performed up to date only for photonuclear reactions,
what corresponds to the so-called photon point (q≈
20 МeV/с), and our data correspond to q=130 МeV/с.
To calculate the ratios for such q we have obtained the
theoretical xpressions for the form-factors [22,28]. The
ratios of the GDR form-factors F2
T0+1(q) and F2
T0(q) for
q=130 МeV/с, differing in an isospin are presented in
Fig. 2 with a solid line. One sees from the figure that
our results are in good agreement with the theoretical
predictions [22,28].
Thus our data on electron scattering support the
conclusions on the presence of the GDR isospin
splitting in 58Ni and 60Ni, obtained from studying the
photonuclear reactions in papers [24-26], and they show
that the same splitting is also observed for 64Ni.
The subsequent measurements on 58,60Ni were
performed in USA [29] and on 58Ni in Germany [30]. In
these papers the results of our studies were discussed.
New data obtained in more than 10 years after our
measurements, have revealed a more complicated
structure in the distribution of the forces of multipole
resonances. Thus in the resonance at the energy of
13 МeV that we have defined as the Е2 resonance the
E1 transitions make a contribution. This contribution
amounts to about 2% [29] or more [30] from the total
contribution calculated with the energy weighted sum
rules (EWSR). And at the E1 resonance we had
determined at the energy of 16 МeV there is observed
the contribution of the Е2 transitions. Thus, it was
shown that a mixing of resonance of different
multipolarity is observed at the same excitation energy.
3.2. Giant resonances of high multipolarity
For the continuation of studies there was improved
in two times the monochromaticity of the electron beam
at the target [31] and the multi-channel detector with a
higher energy resolution was built [32]. A new
technique of processing spectra was also developed. It
consisted of the radiation deciphering, subtraction of the
quasielastic scattering and of the method of separating
the spectrum obtained into narrow bands of 0.5…
1 МeV in width. This technique permitted a more
accurate separation of different multipoles for one
excitation energy determined by the band width. For
every band we have obtained the form-factors and the
calculated curves in the form of the sum of several
multipole form-factors were fitted to them.
With the improved experimental technique and a
new technique for data processing the studies of the 64Zn
and 124Sn nuclei were performed [33-35]. Earlier there
were no such studies on these nuclei.
The fitting of calculated curves permitted to separate
the excitations with different multipolarities and obtain
the dependence of the reduced transition probabilities
B(EL) on the excitation energy Ex. In Fig. 3 the
dependence B(EL) of the E1-E5 transitions on the
excitation energy Ex for the б4Zn nucleus. Similar
dependences of the reduced probabilities of E1-E7
transitions were obtained for the 124Sn nucleus.
Fig. 3. 64Zn. B(EL) against excitation energy. To
the left is the Helm model, to the right is the High
Energy Approximation
The theoretical calculations of the magnitudes
B(EL) of excitations for the 64Zn nucleus are not
available up to now. For the 124Sn nucleus the
calculations are made only for the Е1 excitation within
the framework of the theory of finite Fermi-
systems [33].
52
The presence of resonances above the threshold of
particle emission permitted to split the separated
excitations into some sections. The magnitudes B(EL)
for the Е1, Е2, Е3 and Е4 excitations was presented as a
combination of two or three Gaussians fitted according
to the mean square method to experimental points. Such
fitting make possible the high accuracy determination of
the energy locations Ех, half-widths Гх, reduced
transition probabilities В(ЕL) and the exhausting the
EWSR for GMR.
The obtained locations of the E1-E3 resonances
coincide well with the results of calculations according
to ДКМ, to the chaotic phase approximation technique,
to the method of finite Fermi-systems and with the
calculations based on the sum rules [33].
The location of the observed peaks in the Е1
resonances in 64Zn and 124Sn match well the predictions
of the isospin splitting of the isovector Е1 resonance.
The distribution of Е2 forces reveals the resonances
at the energies 15.0±0.2, 25.1±0.7, 30.4±0.8 МeV in the
64Zn nucleus and 11.7±0.5, 19.8±0.7, 24.9±0.2 МeV in
the 124Sn nucleus. The resonances at 15.0 and 11.7 МeV
are isoscalar Е2 resonances. The paper [36] has shown
that for the nuclei with N≠Z, apart from the isovector
Е1 resonance, the isovector E2 resonance must also split
according to the isospin The calculations performed
according to paper [36] furnish the values of IS Е2
resonance 2.6 and 5.8 МeV in 64Zn and 124Sn,
respectively. The comparison of the experimental values
with calculated ones shows a good agreement for 124Sn
and a somewhat worse one for 64Zn. The data obtained
are the first observation of IS E2 resonance [37]. A later
theoretical paper [38] also permits to conclude that we
have discovered the IS of the isovector E2 resonance.
In the 124Sn nucleus there is observed the resonance
at 16.5±1.0 МeV. We have determined it as a isoscalar
electric monopole (Е0) resonance that occupies (54±
25)% of the monopole EWSR. Our discovery [33] of the
isoscalar monopole (Е0) resonance in 124Sn at 16.5±1.0
МeV is the first experimental evidence of the existence
of the Е0 resonance in nuclei. The energy position,
width and exhaustion value for EWSR obtained for the
resonance are in good agreement with the data obtained
later with other techniques [39].
The first experimental proof of the existence of a
giant hexadecapole resonance (HDR) was obtained by
us in the paper [33]. This resonance was predicted
theoretically earlier in several papers (See [40] and
references therein). We discovered the GHR in the 64Zn
nucleus at the energies of 12.9±0.5 and 25.4±0.8 МeV.
Presently we may treat these two resonances as the
isoscalar and isovector hexadecapole resonances due to
the 2ω transitions. These resonances exhaust only a
very small part of EWSR, but the main part, which must
be due to the 4ω transitions, is not sufficiently defined
up to now. Theoretical calculations show [41], that the
Е4 force must be strongly scattered in the excitation
spectrum and therefore it will be very difficult to
observe it in the experiment.
The further development of the experimental
technique was the creation of the system for energy
compression of the electron beam [42] that permitted to
get the energy resolution of 0.3%. Under these
conditions the studies on electron scattering with the
energies of 150 and 225 МeV on the 65Cu nucleus were
performed [43]. Obtained dependencies of the reduced
transition probabilities B(EL) against the excitation
energy are shown in Fig. 4.
Fig. 4. В(ЕL) against the excitation energy ω in the
65Си nucleus. Solid curves are the Gaussian lines fitted
to data. The scale for the low energy sections of
Е2(Е0)- and E3-transitions, connected with a line is
changed in the noted number of times
The data (Fig. 4) for the Е1-transitions are well des-
cribed by two Gaussian peaks with the distance between
them ∆Е=4.66±0.49 МeV and the ratio of intensities Вт
</Вт>=6.3±1.9. Such a behavior of the Е1-transitions
can be treated as associated with the IS on the ground of
a not bad agreement of the data with the calculated
values: ∆Е=3.81 МeV and Вт</Вт> = 5.0 [38].
The electric monopole force (E0) can also be present
in the distribution of the electric quadrupole force (Е2),
as the form-factors for the transitions of both types
behave similarly as a function of q. Apart from the
known low lying states, the distribution is approximated
with three peaks. The first resonance (the most intensive
one) in undoubtedly the 2ω branch Т=0, of the Е2-
resonance. Two other resonances can be interpreted
differently. They can present the E2 resonance splitted
with respect to the spin Т=1. However, such an
interpretation has substantial shortcomings. First,
though the experimental value ∆Е =7.4±0.3 МeV is
comparable with the calculated one ∆Е=6.37 МeV,
however Вт</Вт>=1.3±0. is in complete disagreement
with the calculated value 4.7 [38]. Second, under this
assumption the resonance exhausts more than 100%
53
Т=1, Е2 EWSR. It is more probable that the resonance
at ω =23.31 МeV is the Т=0, Е0-resonance. The
classification for the energy of this resonance obtained
mainly from the study of the inelastic scattering of α-
particles, gives the energy 18…19 МeV [39].
Distribution of the force ЕЗ has a structural low
energy branch and a resonance-like structure at ω
=18.34 МeV. These structures are associated,
correspondingly, with the 1ω branches of the Т=0
(T=1), EЗ-resonance. The additional force is higher than
25 МeV, and perhaps it is associated with the 3ω
branch of the T=0, EЗ-resonance, the energy of which
from the existing classification must be ~27 МeV [40].
Electric hexadecapole (E4) force has three regions of
accumulation. The first two regions may present the 2ђ
ω and 4ђω branches of T=0, and the last one may be the
2ђω branch T=1, E4-resonance.
From the results obtained on the 65Cu nucleus, we
note the following general rules. First, the dipole and
quadrupole (monopole) transitions exhaust almost all
their force predicted by EWSR, and the octupole and
hexadecapole ones are only a part of this force. Perhaps
our assumption that all cross section of inelastic electron
scattering in the region of the maximum of the quasi-
elastic scattering peak is associated only with this
process is sufficiently conditional. Second, a rather
distinct link is observed between the energy locations of
E1-и E3-, as well as also between E2- and E4-
resonances, i.e., the predictions of the schematic model
turn out to be sufficiently valid [35].
The studies of isotopes with the identical Z permit to
obtain additional data on the effect of neutrons on the
GMR excitation. Presently we are processing the
experimental data on scattering of 226 MeV electrons
on the 54Fe and 56Fe nuclei in the energy excitation range
up to 40 МeV. We have already processed the discrete
levels up to the excitation energy of 8 MeV for the
momentum transfers q=0.6…1.7 Fm-1 [44]. A non-
conventional technique was applied for processing. We
have obtained the data on В(ЕL) and multipolarity of
transitions for 12 states of the 54Fe nucleus and 10 states
of the 56Fe nucleus. The five states of the 54Fe nucleus
and three levels in the 56Fe nucleus were identified in
the (е, е′) reaction for the first time [44]. The
information about two of them are absent in the modern
compilation of the data on discrete levels [45]. The
processing of data in the excitation range of the GMR
for these nuclei commenced
The studies of nuclear fission, using linearly
polarized photons performed at the KIPT, is a new
direction in the research within the GR excitation
energy range [46-48]. In these experiments the uranium
isotopes were first used for measurements. As a result,
the Σ-asymmetry of the 232Th, 233,235,236,238U nuclei was
measured and for even-even nuclei a dependence of the
Σ-asymmetry against the mass number of nuclei А was
obtained. The value of the Σ-asymmetry experiences
considerable change with a not large change of А. The
existence of the dependence of the Σ-asymmetry not
only on Z, but also on N points out to the fact that either
other multipoles (for example, E2 or M1) make a
contribution to its value apart from the E1 resonance, or
such changes are very sensitive to the relative height of
the hills of the fission barrier, and this is observed in our
experiment for the nuclei with identical Z.
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55
56
PACS: 24.30.Ca
Fig. 2. Ratio of the squares of form-factors F2T0+1/F2T0 against Т0. Circles are for our experimental data, solid curve is for the calсulations according to the formulas of papers [22,28]
REFERENCES
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