Properties of Excited States in the ^{160}Dy Nucleus

Abstract

Positive-parity levels and 16 rotational bands are theoretically analyzed on the basis of phenomenological models of the atomic nucleus with the use of new experimental data on excited states in the ^{160}Dy nucleus recently gained in the investigation of the decay ^{160}Er → ^{160m,g}Ho → ^{160}Dy.

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arXiv:nucl-th/0408028v1 11 Aug 2004
PROPERTIES OF EXCITED STATES
IN THE160Dy NUCLEUS
J. Adam1,2, V. P. Garistov3,M. Honusek2,
J. Dobes2, J. Zvolski2, J. Mrazek2, A.A. Solnyshkin1
1Joint Institute for Nuclear Research, Dubna, Russia.
2Institute of Nuclear Physics, Czech Academy of Sciences, Rez.
3Institute for Nuclear Reseach and Nuclear Energy,BAS, Sofia, Bulgaria
February 8, 2008
Abstract
Positive-parity levels and 16 rotational bands are theoretically ana-
lyzed on the basis of phenomenological models of the atomic nucleus with
the use of new experimental data on excited states in the160Dy nucleus
recently gained in the investigation of the decay160Er −→160m,gHo →
160Dy.
INTRODUCTION
The160Dy nucleus is classified with deformed nuclei (β = 0.23) and has
quite a complicated scheme of excited states. By now it has been well studied
experimentally in nuclear reactions, Coulomb excitation, and β decays of160Tb
and160m,gHo [1]. Our recent investigation of the decay160Er →160m,gHo →
160Dy [2] has made it possible to expand considerably the scheme of excited
160Dy states and to correlate the reaction and β decay data. Over a hundred
new levels are added to the previously known excited states in the160m,gHo
→160Dy decay scheme. The complete list of these levels is given in Table
1 together with their quantum characteristics. In this paper positive-parity
level energies calculated by us are compared with the experimental data and
the experimentally known positive-parity and negative-parity bands (sometimes
with new levels added by us) in the160Dy nucleus are theoretically analyzed on
the basis of existing nuclear models.
1 POSITIVE PARITY LEVELS
Properties of deformed nuclei can be described within the symmetrical rotator
model [3] and the interacting boson model IBM-1 [4] in the SU(3) limit. Some
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differences in the descriptions are due to the symmetry of the Hamiltonian and
the finite number of bosons which only have the angular momentum L = 0 and
L = 2. In the IBM-1 we used a simple Hamiltonian
H = −kQQ − k′LL + k′′PP. (1)
In the SU(3) limit k′′= 0, the energies of the β and γ bands are degenerate
and become identical, the energies of the ground-state band are designated as
(λ,0), those of the β and γ bands as (λ−4,2), and these energies are calculated
as a function of the spin I by the formula
E(I) = (0.75k − k′)I(I + 1) − kC(λ,µ), (2)
where C(λ,µ) are the eigenvalues of the Casimir operator
C(λ,µ) = λ2+ µ2+ λµ + 3(λ + µ), (3)
here λ is the number of valence nucleons (for160Dy we have λ = 28). Using
equations (2) and (3) and the experimental energies of the first (86.8keV) and
second (966.2keV) 2+levels in the160Dy nucleus, we calculate the coefficients
k and k′by the formulae
k =E(2+
2) − E(2+
6(λ − 1)
1)
(4)
k′= 0,75k −E(2+
1)
6
(5)
and get k = 5.43keV, k′= 10.39keV. Since the energies of the β and γ vibra-
tional states in the rotational bands in160Dy are actually not identical, we in-
clude a pairing term in (1) for their calculation, find the parameter k′′= 14.6keV
by the least squares method, and calculate most of the energy spectrum of160Dy
positive-parity levels presented in Table 2 in comparison with the experimental
data. Analysis of Table 2 shows that the approach used allows a satisfactory
description of only the lowest excited positive-parity states in the160Dy nu-
cleus. The discrepancy between the calculated and experimental level energies
considerably increases with increasing excitation energy. Therefore, we confined
ourselves to calculation of energies of levels with spins Iπ
states with higher i are experimentally known (for instance, for levels with Iπ
= 2+i may be even larger 16, see Table 1). In general, the difference between
the experimental and theoretical energies of the states included in Table 2 vary
from a few keV to a few hundred keV. The average deviation of theory from
experiment is <| Ee − Ec |>= 209.6keV, which can hardly be regarded as
satisfactory. Obviously, this value will increase if we take into consideration
higher-lying excited states with i > 5. It should be stressed, however, that the
model IBM-1 makes it possible to calculate energies of all head states of rota-
tional bands which have to be described by individual free parameters in other
models.
iwith i ≤ 5, though
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2 DESCRIPTION OF ROTATIONAL BANDS
We used four widely known, well-working model approaches to describe the
experimental energy spectra of excited states of rotational bands in the160Dy
nucleus. First of all, it is the geometrical Bohr - Mottelson model [3], where
intraband state energies as a function of the spin I and the quantum number
K are calculated by formula
EI= E0+
?
n=1
An[I(I + 1)]n+ (−1)I+K(I + K)!
(I K)!
?
m=0
Bm[I(I+!)]m, (6)
where Anand Bmare the model parameters.
Another approach is the Q - phonon model [5], where positions of the
rotational-band levels are calculated by expression
EI= E0+b1
2I +b2
8I(I − 2) +b3
48I(I − 2)(I − 4), (7)
with the parameters b1, b2and b3.
The third approach is calculation by three-parameter formula following from
the model of the variable moment of inertia with dynamical asymmetry [6]
EI= E0+ a1I + a2I2+ a3I3+ b0(−1)i, (8)
where the parameters a1, a2and a3are governed by the moment of inertia of
the ground state of the nucleus and by its ”softness” and asymmetry parameters
and where b0(−1)iis the sign-changing term allowing calculation of bands with
any value of the quantum number K (i = (I + 1)/2 at ∆I = 2 and odd I;
i = (I + 2)/2 at ∆I = 2 and even I; i = I + 1 at ∆I = 1).
Finally, the fourth approach is calculation by formula proposed in [7]
EI= E0+ A1I(I + 1)A2[I(I + 1)]2+ A1/2
?
I(I + 1) + B0(−1)i, (9)
where in addition to the normal terms of the Borh - Mottelson formula, there
appears a term with the parameter A1/2taking into account the Coriolis in-
teraction and a sign-changing term with the parameter B0similar to the sign-
changing term in (8).
3RESULTS AND DISCUSSION
According to the data collected in [1], there are about 15 known bands of dif-
ferent nature in160Dy, which where established in various types of nuclear
reactions and in the β decay. Some of these bands are traced to rather high
energies and spins. For example, in [8] the study of the reaction in the beam of
7Li ions revealed excitation of levels up to the energy of 7231keV with the spin
Iπ= 28+in the Kπ= 0+ground-state band, up to 6642keV
in the Kπ= 2+S band, up to 4875keV with Iπ= 20+in the S band, and up
with Iπ= 25+
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to 6967keV with Iπ= 26−and 4937keV with Iπ= 19−in the Kπ= 2−and
Kπ= 1−octupole bands respectively. In our calculations we confined ourselves
to the intraband states with energies not higher than the160m,gHo →160Dy β
decay energy of 3300keV. In Tables 3.1-3.16 we present the energies of excited
states in all experimentally established rotational bands of the160Dy nucleus
calculated by (6), (7), (8), and (9) in comparison with the experimental data.
The last two rows of each table show the average deviations of the calculated
energies from the experimental values < |Ee − Ec| > for each formula and the
values of the parameters at which the best agreement between theory and ex-
periment was achieved. The second columns of the tables show the values of
the inertia parameters
2Θcalculated by the formulae
?2
?2
2Θ=
Eγ
4I − 2
for E(I) → E(I − 2) transitions,(10)
?2
2Θ=Eγ
2I
for E(I) → E(I − 1) transitions. (11)
Notesa,b,cin Tables 3.1-3.16 are explained under Table 3.16. After the calcu-
lation of the average deviations < |Ee−Ec| > all calculated state energies were
rounded off to the first decimal digit. It should be particularly mentioned that
when calculating rotational bands for which the number of the experimentally
known levels was not enough, we artificially extended the band by adding states
with approximately expected energies and obviously large errors. Then we re-
peated the fitting procedure using the energies of the missing band levels found
in the first fitting. Though reducing to zero average deviations of theory from
experiment for the known states in some cases, this procedure predicts to an
extent positions of possibly existing but not yet experimentally found intraband
levels.
3.1Kπ= 0+ground-state band
Levels of this band are known from the experiment [8] up to Iπ= 28+. We
confine our consideration to states with Iπ? 16+(see Table 3.1), which were
studied before the investigation [8] in many types of nuclear reactions, Coulomb
excitation, and β decay [1]. The lowest states with Iπ= 2+,4+and 6+manifest
themselves practically in all above-mentioned processes while the levels with
higher spins 8+,10+,12+,14+and 16+show up only in some of them and not
in the β decay (see [1] for details), where excitations of these states are unlikely
or absolutely impossible because of their high spins and energies. Recently [2]
the state with the energy of 966.8keV and Iπ= 8+was nevertheless found
during the investigation of the160Er →160m,gHo →160Dy decay. This state is
de-excited to the level at 581.1keV with Iπ= 6+by an intraband γ transition
of energy 385.7keV which showed itself in the spectrum of γγ coincidences with
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the 297.5keV
populated from higher states by a few low-intensity γ transitions whose total
intensity is totally counterbalanced by the intensity of the 385.7keV transition.
As is evident from Table 3.1, our calculations for this band by all four formulae
show approximately the same good agreement with the experiment. In all cases
the average deviation of the experimental energies from the theoretical ones
< |Ee − Ec| > does not exceed 7keV . To get comparable agreement of the
calculations by (8) and (9) with the calculations by (6) and (7), we had to
increase the number of the parameters from three to four. The inertia parameter
?2
2Θtends to decrease smoothly from 14.46 to 9.30keV as the energies and spins
of the band levels increase from 86.8(2+) to 3091.7(16+)keV .
γ line de-exciting the 581.1keV state. The 966.8keV level is
3.2Kπ= 2+γ vibrational band
The first three states of this band (see Table 3.2) with Iπ= 2+,3+and 4+
are quite well known both from the reactions and Coulomb excitation and from
the β decays of the160Ho and160Tb nuclei [1]. The Iπ= 5+level unambigu-
ously manifests itself in the160Ho and160Tb β decays and in reactions with
α particles. The Iπ= 6+state is observed in the160Ho β decay, in reactions
with α particles, and in the Coulomb excitation. The next six levels with Iπ
= 7+,8+,9+,10+,11+and 12+were earlier observed only in reactions with α
particles; three of them with Iπ= 7+,8+and 9+have been recently confirmed
in [2], where the decay160Er →160m,gHo →160Dy was studied. These states
were introduced in the160m,gHo →160Dy decay scheme on the basis of the
γγ coincidences and energy and intensity balances. The last two states with
Iπ= 13+and 14+in Table 2 were first established in the reaction with7Li in
[8], where existence of all other members of the band was confirmed and the
more accurate value 2708.0keV was found for the energy of the Iπ= 12+level,
earlier known [1] to be a level at 2698.0keV . As is evident from Table 3.2, our
calculations reproduce the energies of the levels from this band in the best way
in all cases. The average deviation from experiment < |Ee −Ec| > is no larger
than 7keV for calculations by (7), (8) and (9), and 2.67keV for the calculations
by traditional Bohr - Mottelson formula (6). In calculations by (6) this agree-
ment was achieved by including a sign-changing term with the coefficient B0,
which depends not only on the spin I, as in (8) and (9), but also on the quantum
number K. The parameter
2Θ, as in the case of the ground-state band, gen-
erally tends to decrease slightly with increasing energy and spin of intraband
states. Yet, for the neighboring levels with even and odd spins a systematic
difference in values of
2Θis observed, which increases with increasing energy.
The values of?2
2Θfor odd-spin members of the band are larger than for even-spin
ones.
?2
?2
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3.3Kπ= 2−octupole vibrational band
The first head level (Table 3.3) of this band with Iπ= 2−and the third one with
Iπ= 4−are known from the β decay of the160Ho and160Tb nuclei and from
reactions with α particles and deuterons [1]. The best studied state from this
band is the second level with Iπ= 3−, which is easy to observe in both β decays,
at the Coulomb excitation, and in almost all reactions mentioned in [1]. The
level with Iπ= 5−shows itself in reactions with α particles and deuterons, at
the Coulomb excitation, and in the β decay of the160Ho nucleus. Higher-lying
states with higher spins, beginning with Iπ= 6−and up to Iπ= 14−, except
Iπ= 13−, were observed only in reactions with α particles. It is only recently
that excitation of160Dy states with Iπ= 6−,7−,8−and 9−in the β decay
has been observed during the investigation of the160Er →160m,gHo →160Dy
decay [2]. The missing level with Iπ= 13−showed up in the reaction with7Li
[8]. Level energies calculated for this band are in slightly poorer agreement with
the experimental values than for the bands considered above. In all cases the
average deviation < |Ee − Ec| > is as a large as a few tens of keV (see Table
3.3). The inertia parameter
2Θshows considerable difference in value for states
with even and odd spins typical of octupole bands.
?2
3.4Kπ= 0+S band
This band deserves particular attention because of unusually small spins of its
experimentally observed low-lying levels. The state with Iπ= 4+(see Table
3.4) was established in the β decay of the160Ho nucleus and in the reaction
with3He nuclei, the level with Iπ= 6+is known from the β decay of the
160Ho nucleus and reactions with α particles, the state Iπ= 8+is found in the
reactions with α particles and3He, and the state with Iπ= 10+is found only
in reactions with α particles [1]. All these states are assigned to the same band
and are interpreted [1] as members of the band of the states aligned in such a
way that the rotational moment and the moment of two aligned neutrons i13/2
are not parallel, as is typical of many known S bands in other nuclei. Recently
the band was extended to Iπ= 20+in [8]. We included in Table 3.4 only two
states with Iπ= 12+and 14+out of all those observed in [8]. In [1] a Kπ= 0+
band based on the Iπ= 0+state with the energy 1443.7keV is reported. This
band comprises two more levels with Iπ= 2+and 4+and energies 1518.8 and
1703.2 keV respectively. The Iπ= 2+level is known from the160Ho decay
and the (t,p) reaction. It is reliably confirmed in [2] as the Iπ= 2+level with
the energy 1518.4keV while the statement that there exists the Iπ= 4+level
is based on 30-year-old data on the β decay of160Ho and may be erroneous.
The existence of the 1443.7keV head state is not confirmed in [2] either. The
1357.0keV γ transition associated with this state on the basis of earlier data is
unambiguously placed elsewhere in the160m,gHo →160Dy decay scheme on the
basis of γγ coincidences in [2]. The E0 transition to the ground state, which
was earlier the main evidence for existence of the excited 0+level at 1443.7keV,
was not observed at all despite our specific search for lines corresponding to
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this transition in the spectrum of internal conversion electrons from the160Ho
β decay [2]. On the contrary, we found a state at 1456.7keV de-excited by two
γ transitions. First to the Iπ= 2+level of the ground band and second to Iπ=
2+level of γ vibrational band. This state (1456.7keV) been populated by a few
γ transitions from higher-lying levels with Iπ= 1−, except the 2896.3keV level
with Iπ= 2+. Earlier the state at this energy (1457keV) was observed in (t,p)
reactions in [9], where the authors assigned the characteristics Iπ= 0+to this
level and assumed that it and the 2+state at 1513keV observed by them, which
probably corresponded to the 1518.4keV level (see Table 3.4), may be assigned
to the S band. Though it seems somewhat strange that there is no noticeable
E0 transition (our estimation is X = B(E0)/B(E2) < 2.2 × 10−3) from the
1456.7keV level to the ground state, the results of our latest investigations [2]
are not in conflict with the assignment of the spin-parity Iπ= 0+to this level.
Thus, if one accepts the interpretation [9], to which we are also inclined, the
S band appears to be as shown in Table 3.4, while the data given in [1] on
the Kπ= 0+band built upon the 1443.7keV level that proved not to exist,
including the fact that one of its member (Iπ= 4+level at 1703.2keV) is
absent, seem to be incorrect. However, it may as well be hypothesized that the
band in question is not an S band but a normal band built upon the 0+state at
1456.7keV that is similar to other Iπ= 0+bands established in the160Dy and
other nuclei. Whichever interpretation is true, this band is rotational and we
calculated the energies of its levels by the same rotational formulae (6), (7), (8),
and (9) which we used for other bands considered in this paper. The results of
the calculations are given in Table 3.4. They are in rather good agreement with
the experimental data. In all cases the average deviation < |Ee − Ec| > varies
between 15 and 20keV. However, it should be noted that equivalent agreement
between experiment and calculations was obtained with only one parameter
used in calculations by (6) in contrast to three-parameter calculations by (7),
(8), and (9). The values of the inertia parameters
Iπ= 2+,4+,6+, and 8+show some irregularity, which is probably due to
different influence of the neighboring bands on the above-mentioned states. As
the energy and spin increase and the influence becomes weaker or the same for
all states, the parameters take on approximately identical values around 7 keV
(see Table 3.4).
?2
2Θfor the lowest states with
3.5First Kπ= 1+band
In [1] this band is treated as a band upon the two-particle state at 1804.7keV
with Iπ= 1+and the (n5/2[523] − n3/2[521]) configuration, which also com-
prises two more levels at 1869.5keV with Iπ= 2+and at 1960.4keV with
Iπ= 3+. It is stated that all three levels were found in the160Ho β decay
and the 1869.5keV level also showed itself in (d,d′) and (t,p) reactions as a
state at 1875keV. In our latest studies of the β decay160Er →160m,gHo →
160Dy [2] we managed to confirm only the first two states with Iπ= 1+and 2+.
The previously drawn conclusion that there exists a third level at 1960.4keV
Iπ= 3+is likely to be wrong. This state was introduced on the basis of two γ
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transitions with energies 994.4 and 1873.1keV from this level to the 2+levels of
the γ band and the ground-state band respectively. According to our data [2],
the 994.4keV γ transition is unambiguously placed elsewhere in the160m,gHo
→160Dy decay scheme and there is no 1873.1keV
if this band exists, only its first two levels with Iπ= 1+and 2+are reliably
established. To extend the band, we tried to select possible candidates with
the necessary quantum characteristics Iπ= 3+,4+,5+and 6+(see Table 3.5)
from the spectrum of the experimentally known (see Table 1) excited states.
The level at 1903.2keV was earlier known from the160Ho β decay and the
(d,d′) reaction, the state at 2049.4keV was observed in the (t,p) reaction as
a level of energy 2046keV, the level at 2113.7keV was first observed in [2] in
the160Er →160m,gHo →160Dy β decay, and the state at 2187.0keV showed
itself in the (d,d′) and (3He,α) reactions as a level of energy 2190 and 2188keV
respectively. The common feature of all these states, including the first two,
is existence of γ transitions de-exciting them to the levels of the ground-state
band. Reproduction of this band by means of the rotational formulae results in
rather good agreement, < |Ee−Ec| > ˜ 4keV (see Table 3.5), but requires a lot
of parameters. This is evident from the calculations by (7), where the average
deviation for the formula with fewer parameters is much worse than 21.33keV.
It is noteworthy that there is a sharp difference in
bers of this band, which is not typical of positive-parity bands.
γ transition at all. Thus,
?2
2Θvalues between the mem-
3.6 Second Kπ= 1+band
This band was reported in [11] to be a rotational band built upon the 2085.3keV
level with Iπ= 1+, a doublet state for the 1694keV level with Iπ= 4+
known as a two-quasiparticle state with parallel spins of two unpaired nucle-
ons (n5/2[642] + n3/2[521]). Apart from the head level, this band comprised
three more levels with Iπ= 2+,3+and 4+at 2138.8, 2210.2 and 2286.4keV re-
spectively. In [1] the energies 2084.96 and 2138.14keV are given for two positive-
parity states known from the160Ho β decay, but their spins were not uniquely
established and their belonging to a band was not mentioned. To the next two
states at 2210.2 and 2286.4keV there might correspond the levels at 2214 and
2296keV observed in the (t,p) reaction, whose quantum characteristics are not
fully known. The latter levels also shows up in the (d,tγ) reaction as a state
of energy 2294keV. The states of close energies 2200.8 and 2309.9keV were
observed in our latest studies of the160Er →160m,gHo →160Dy β decay [2],
where existence of the levels at 2084.8 and 2138.2keV was also confirmed. All
these four states are de-excited in a similar way and fit well into the Kπ= 1+
band under consideration, though their spins are not conclusively established.
This is demonstrated both by the values of the inertia parameters
lated by us for each member of the band, which fall within a reasonable range
from 10.5 to 13.5keV, and by our calculations by rotational formulae (6), (7),
(8) and (9) with the average deviation of the experimental band level energies
from the theoretical values < |Ee − Ec| > not exceeding 4keV even in the
worst case (see Table 3.6). However, there arises a question. Which of the two
?2
2Θcalcu-
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Kπ= 1+bands considered above (see Tables 3.5 and 3.6) corresponds to the
(n5/2[523] − n3/2[521]) configuration? Based on our theoretical analysis we
believe that preference should be given to the earlier interpretation [11], where
this configuration is assigned to the band built upon the 1+state at 2084.8keV.
3.7Kπ= 1−octupole vibrational band
The first four states of this band (see Table 3.7) with Iπ= 1−,2−,3−and 4−are
quite reliably established both from the β decay and from many reactions [1].
The level with Iπ= 5−showed itself in the160Ho β decay and in the scattering
of deuterons from160Dy nuclei. The states with higher spins Iπ= 6−,8−and
10−were previously known only from the reactions with α particles; excitation of
two of them with Iπ= 6−and 8−was first observed in our recent investigations
[2]. Until 2002 year two missing levels with intermediate spins Iπ= 7−and
9−could not be observed in experiments. Only recently [8] they have first
been identified together with the Iπ= 11−,12−and 13−states in the reaction
with7Li. Our calculations describe the energies of all members of the band
given in Table 3.7 quite satisfactorily, especially the calculations by (8) and (9),
where the average deviations of theory from experiment are about 5keV while
in calculations by (6) and (7) these deviations are worse, 18.1 and 22.6keV
respectively. The increase in the number of parameters to five and more in
(6) does not essentially improve the agreement. The values of the parameter
?2
2Θsharply change as one goes from odd to even spins of band levels, which is
typical of octupole bands.
3.8 Second Kπ= 1−band
The levels at 2701.1 and 2720.6keV with Iπ= 1−and 3−(see Table 3.8) were
earlier known from the160Ho β decay [1] and were tentatively interpreted in
[12] as two-phonon β quadrupole - octupole states. In our latest studies of
the β decay160Er →160m,gHo →160Dy [2] we observed these levels and also
states with the excitation energies 2718.9, 2755.0 and 2757.1keV and respective
quantum characteristics Iπ= 2−,(4−) and (4,5). All these states, including
the levels at 2701.1 and 2720.6keV, are populated only directly from the160Ho
decay and have channels of de-excitation to the levels of the ground-state band.
Therefore, we assume that they may belong to the same band based on the
2701.1keV level with possible characteristics IπK = 1−1. Calculation by all
four formulae describe the energies in the this band equally well. The average
deviation of the experimental energies from the theoretical values < |Ee−Ec| >
varies from 1.22 to 4.86 keV (see Table 3.8). Note that the values of the inertia
parameters?2
bands in160Dy, abruptly change as one goes from even to odd spins, which is
typical of negative-parity bands.
2Θ, though slightly underestimated in comparison with?2
2Θfor other
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3.9Kπ= 0+band on the Iπ
i= 0+
2state
As follows from [1], the Iπ= 0+ground level of this band show itself in the
160Ho β decay and the (p,t) reaction, the second state with Iπ= 2+is es-
tablished in a few types of reactions, Coulomb excitation, and160Ho β decay,
and the level with Iπ= 4+is excited only in the160Ho β decay. There is not
doubt about existence of this band, all its members are confirmed in our latest
experiment [2]. The data on the known level energies are well reproduced by
our calculations, except the calculation by (7). These calculations may help to
search for so far unknown but probably existing states with Iπ= 6+and 8+
in future investigations. The values of the inertia parameters
tolerable range (see Table 3.9).
?2
2Θfall within a
3.10Kπ= 0+band on the Iπ
i= 0+
4state
This band is absent in [1] and we are the first to introduce it. During the
investigation of the160Ho β decay [10] a state at 1757.2keV was observed and
assigned the quantum characteristics Iπ= (2+,3,4+) as the most probable in
view of the gained data on its de-excitation. Later this level was confirmed
in the investigations of the (t,p) reactions [9], where, in addition, a state at
1709keV with Iπ= 0+was observed for the first time. Both states distinctly
showed themselves in our recent investigations of the160Er →160m,gHo →
160Dy decay [2], where their energy values were refined and their quantum
characteristics were uniquely determined. The Iπ= 0+level at 1708.2keV is
populated by γ transitions from four higher states, three with Iπ= 1−and one
with Iπ= 2+. The intensity of these transitions is totally counterbalanced by
the sole E2 transition of 1621.36keV to the Iπ= 2+of the ground band. Quite
unexpected, as with the 1456.7keV 0+head level of the S band (see 3.4), is the
absence of the E0 transition from the 0+level at 1708.2keV to the160Dy ground
state (our estimation for this transition is X = B(E0)/B(E2) < 3.5 × 10−2)
while for two other 0+states at 1280.0 and 1952.3keV known form the160Ho
β decay X = 0.31 and 0.14 respectively. We regard the state at 1756.9keV
(the value refined by us, see Table 3.10) as the second level of the band on
the 1708.2keV 0+level. It is linked to 16 excited levels with known quantum
characteristics via its populating and de-exciting γ transitions for most of which
multipolarities are established [2]. This allowed ambiguity to be removed and
the unique spin-parity Iπ= 2+to be established for the 1756.9keV state. As
should be expected, in all cases the calculations exactly reproduce energies of
the first two experimentally known Iπ= 0+and 2+levels with the minimum
number of parameters. In a sense these calculations predict the energy range
for the search for subsequent states with higher spins Iπ= 4+,6+and 8+that
might exist in this band (see Table 3.10). The parameter?2
which does not significantly differ from the expected value.
2Θis equal to 8.11keV,
10

Page 11

3.11Kπ= 0+band on the Iπ
i= 0+
5state
Two states with Iπ= 0+and 2+given in Table 3.11 are known from the160Ho
β decay [10] and are treated as the members of the same band [1]. In our latest
experiments [2] it was possible to confirm only the fact that those states existed
and to refine their energy values. As is evident from the table, all calculations
describe these states in the best way and predict possible energies of the states
with higher spins which are not yet found experimentally. As in the case of the
previous band, the parameter
2Θhas a reasonable value, which is 10.07keV for
this band.
?2
3.12Kπ= 0−(octupole?) band
This band is treated in [1] as a possible octupole band with Kπ= 0−and
comprises two experimentally known levels (see Table 3.12). The first level
with Iπ= 1−was observed in the160Ho β decay and the (γ,γ′) reaction, the
other level with Iπ= 3−was observed in the (d,d′) reaction and at Coulomb
excitation [1]. Later [2] we observed the Iπ= 3−level in the160Ho β decay
as well. The above states are well reproduced by our calculations, which also
yield possible energies of excited states with Iπ= 5−,7−and 9−lying higher
in energy and belonging to the band in question (see Table 3.12). The value of
the inertia parameter
2Θis 15.38keV and is not in conflict with the required
value.
?2
3.13Kπ= 4−(n5/2[642] + n3/2[521]) band
By now four states have been identified in this band (see Table 3.13). The head
states with Iπ= 4−is known from the160Ho β decay and (3He,α) and (d,t)
reactions, the next two levels with Iπ= 5−and 6−showed up in the same
processes and in reactions with α particles, the state with Iπ= 7−showed itself
only in reaction with α particles [1].
Note that in our latest investigations of the160Er →160m,gHo →160Dy
decay [2] we failed to identify the Iπ= 6−level at 1954.3keV. The 665.7keV
γ transition, which according to [1] de-excites this state to the Iπ= 5+level
at 1288.7keV and is the main argument in favor of its existence, should have
manifested itself in the spectra of γγ coincidences with rather intensive γ lines of
1004.9 and 707.6keV. However, we did not observe anything of the kind. More-
over, our data dictate two other places for this γ transition in the160m,gHo →
160Dy decay scheme and its multipolarity composition is predominantly M1,E2,
which is in conflict with its placement between the levels of 1954.3and 1288.7keV
with different parities [2]. As is evident from Table 3.13, the calculations with
the same number of parameters in all cases equally well (< |Ee−Ec| > ˜ 2keV )
describe the energies of four experimentally known states with Iπ= 4−,5−,6−
and 7−, and the extension of the band predicts energies of possibly existing
states with Iπ= 8−and 9−. The inertia parameters for this band are close
in value to those for other bands in160Dy. However, there is no sharp change
11

Page 12

in the
negative-parity bands.
?2
2Θvalues as one goes from even to odd spins as is the case in other
3.14Kπ= 4+(n5/2[523] + n3/2[521]) band
Until our latest investigations [2] the band upon the two-particle state with
IπK = 4+4 and the energy 1694.4keV was known to comprise two next levels
with Iπ= 5+and 6+( see Table 3.14), all of which, including the head level,
were earlier reliably established from the reactions with α particles and the
160Ho β decay [1]. The fourth member of this band at 2074.2keV with Iπ
= 7+was earlier observed in two processes as a level at 2075keV. In one of
them, the reaction with α particles, it was assigned to the band in question
and in the other, the (3He,α) reaction, it was interpreted as the head level of
the Kπ= 3−band. It turned out that in160Dy there are actually two states
at closely spaced energies 2074.2 and 2077.4keV but with different quantum
characteristics Iπ= 7+and Iπ= 3−, which were unambiguously established in
our recent investigation [2]. It is evident from Table 3.14 that all four formulae
describe the level energies for this band in the best way and also predict energies
of three possibly existing states with higher spins Iπ= 8+,9+and 10+. For
the already known levels with Iπ= 4+,5+,6+and 7+the average deviation of
theory from experiment is no larger than 0.2keV in all cases. The parameter
?2
2Θpractically does not change from level to level and has a reasonable value.
3.15 Second Iπ= 4+band upon Iπ= 4+
Only the head state with Iπ= 4+was known in this band (see Table 3.15). It
was established in the160Ho β decay and the (d,t) reaction [1]. Another state
at 2194.4keV with Iπ= 5+was firstly found by us in the recent investigation
of the160Er →160m,gHo →160Dy decay [2]. According to the γγ coincidence
data, this state, like the 2096.9keV Iπ= 4+head state, is mainly de-excited
to the levels of the Kπ= 2+γ band, which allows these states to be regarded
as the members of the same band. As might be expected, the calculations
accurately describe the energies of the first two known states of the band and
point to possible positions of the next three levels. The parameter
keV , which is only slightly different from the values for the Kπ= 4+band upon
the state at 1694.4keV.
?2
2Θis 9.76
3.16Kπ= 3−(octupole - vibrational) band
As was pointed out above, in our work [2] we observed a state at 2077.4keV
with Iπ= 3−, which seems to correspond to the 2075keV state observed in
the (3He,α) reaction and interpreted as the head level of the Kπ= 3−band
[1]. We take this interpretation as the basis and add to this band two more
levels at 2143.7keV with Iπ= 4−and 2372.4keV with Iπ= 6−(see Table
3.16), whose energies and quantum characteristics were first established by us
during the investigation of160Er →160m,gHo →160Dy β decay [2]. The latter
12

Page 13

level is also known from the (3He,α) reaction, but only its energy 2372keV was
found from this reaction. All three states have a common feature: they are de-
excited by γ transitions of noticeably intensity to the levels of the γ vibrational
band [2], which allowed us to regard the states as members of the same band.
As is evident from Table 3.16, our calculations reproduce the energies of the
experimentally known Iπ= 3−,4−and 6−states of this band quite well and
predict possible positions of the intermediate level with Iπ= 5−and higher-
lying states with Iπ= 7−,8−and 9−in the160Dy excitation energy spectrum.
Two values of the parameter
2Θfor the even-spin states are closely spaced and
do not contradict the expected values.
?2
4 CONCLUSIONS
Most of the experimentally observed energy values of160Dy collective states lev-
els with positive parity are compared with theoretically calculated values using
interacting bosons model (IBM). The mean differences between experimental
and calculated values are about 210keV.
As a result of the detail analysis of 16 rotational bans they were supple-
mented with 17 new levels. Also, within this analysis the existence of 1443.7keV
0+level was not confirmed, while into160Dy decay scheme was integrated a
band with a head level Kπ= 0+with the energy 1708.2keV . Large amount
of explicit β decay states we could not include into any rotatational band (see
Table 1).
The internal states energy values, calculated with phenomenological equa-
tions (6), (7), (8), (9) produce a good agreement with the corresponding exper-
imental values.
All the models used in our investigation of the levels energies and their
quantum characteristics in very rich and complicate spectrum of160Dy nucleus
provide a relatively good agreement with experiment. However, in the region of
high spins and energies the disagreement between calculations and experimental
data increases. So it is somehow straightforwardto apply for our further analysis
of this experimental data the recently developed Interacting Vector Boson Model
(IVBM) [13]. This work now is in progress.
The investigation was supported by the RFBR.
References
[1] Reich C.W. Nucl. Data Sheets. 1996. V. 78. P. 547.
[2] Adam J., Vaganov Yu.A., Vagner V., Volnykh V.P., Zvolska V., Zvolski J.,
Ibraheem Y.S, Islamov T.A., Kalinnikov V.G., Kracik B., Lebedev N.A.,
Novgorodov A.F., Solnyshkin A.A., Stegailov V.I., Sereeter Zh., Fisher M.,
Caloun P. BRAS, Phys. 2002, V. 66, N. 10, P. 1384.
13

Page 14

[3] Bohr A., Mottelson B.R. Nucl.Structure. Benjamin. N.Y. 1975. V. 2.
[4] Arima A., Iachello F. Ann. Phys. N.Y. 1976. V. 99. P. 253 and 1978. V.
111. P. 201.
[5] Jolos R.V. Yadernaya Fizika. 2001. V. 64. N. 3. P. 520.
[6] Begzhanov R.B., Bilenkii V.M., Dubro V.G. ” Structure of deformed nu-
clei.” M.: Energoatomizdat. 1983. (in Russian)
[7] Peker L.K., Pearlstein S., Rasmussen J.O., Hamilton J.H. Phys. Rev. Lett.
1983. V. 50. P. 1749.
[8] Jungclaus A., Binder B., Dietrich A., Hartlein T., Bauer H., Gund Ch.,
Pansegrau D., Schwalm D., Egido J.L., Sun Y., Bazzacco D., de Angelis
G., Farnea E., Gadea A., Lunardi S., Napoli D.R., Rossi-Alvarez C., Ur C.,
Hagemann G.B. Phys. Rev. C. 2002. V. 66. P. 014312.
[9] Burke G.D., Lovhoiden G., Thorsteinsen T.F. Nucl. Phys. 1988. V. A483.
P. 221.
[10] Aleksandrov A.A., Butsev V.S., Vylov T., Grigoriev E.P., Gromov K.Y.,
Kalinnikov V.G., Lebedev N.A. BAS USSR, Phys.1974.V.38. N.10. P. 2103.
[11] Grigoriev E.P., Gromov K.Y., Zhelev Z.T., Islamov T.A., Kalinnikov V.G.,
Nazarov U.K., Sabirov S.S. BAS USSR, Phys.1970. V. 33. N. 4. P. 585.
[12] Grigoriev E.P., Dadamukhamedov T.R. BAS USSR, Phys.1987. V. 51. N.
11. P. 1950.
[13] H. Ganev, V. P. Garistov, A. Georgieva, Phys. Rev. C. 2004. V. 69. P.
0143XX.
14

Page 15

Table 1. 160Dy levels excited in the β β β β decay 160Er →
Elev.(∆Elev.)
[keV]
0.00 0+0
86.788(5) 2+0
283.821(8) 4+0
581.07(2) 6+0
966.17(1) 2+2
966.8(1) 8+0
1049.12(1) 3+2
1155.83(1) 4+2
1264.77(1) 2–2
1279.95(4) 0+0
1285.62(2) 1–1
1286.71(2) 3–2
1288.67(2) 5+2
1349.81(3) 2+0
1358.67(2) 2–1
1386.46(2) 4–2
1398.98(2) 3–1
1408.49(3) 5–2
1438.57(3) 6+2
1456.7(1) 0+S
1489.49(3) 1–0
1518.42(2) 2+S
1522.4(1) 4+0
1535.14(2) 4–1
1586.69(4) 5–1
1586.69(4) 5–1
1594.38(11) 6–2
1603.77(8) 4+
1606.9(1) 6+
1607.9(1) 4+S
1614.1(1) 7–2
1617.3(1) 7+2
1643.3(1) 3–0
1650.87(4) 5–5
1652.1(1) (4,5,6)
1653.7(1) (2,3)
1655.1(1) (3,4+)
1694.36(2) 4+4
1708.2(1) 0+0
1720.4(1) 6+S
1756.88(4) 2+0
1784.7(1) 4–4
1787.9(1) 6–1
1801.2(1) 8+2
1802.24(2) 5+4
1804.70(2) 1+1
1860.14(11) 5–4
1869.54(3) 2+1
1882.7(1) 8–2
1901.2(1) 9–2
1903.19(3) 3+1
1929.19(2) 6+4
1952.33(4) 0+0
2009.5(1) (1,2)
2012.72(8) 2+0
2022.0(1) 9+2

→→
→ 160m,gHo →
IπK
→→
→ 160Dy
Elev.(∆Elev.)
[keV]
2605.8(1)
2610.0(1)
2630.3(1)
2630.76(2)
2634.7(1)
2645.9(1)
2647.2(1)
2661.50(2)
2665.8(1)
2674.72(3)
2681.9(1)
2696.5(1)
2697. 75(10)
2701.09(2)
2704.25(3)
2717.25(3)
2718.91(7)
2720.6(1)
2727.2(1)
2729.82(4)
2734.72(3)
2755.0(1)
2756.3(1)
2757.1(1)
2760.5(1)
2760.5(1)
2763.0(1)
2767.7(1)
2772.1(1)
2777.6(1)
2822.2(1)
2833.8(1)
2851.70(4)
2853.6(1)
2858.1(1)
2861.05(10)
2877.10(4)
2879.4(1)
2885.6(1)
2896.32(10)
2904.3(1)
2931.7(1)
2941.7(1)
2958.5(1)
2969.0(1)
2969.9(1)
2977.5(1)
2994.7(1)
3004.4(1)
3024.5(1)
3033.7(1)
3060.5(1)
3061.93(5)
3081.4(1)
3098.9(1)

IπK
Elev.(∆Elev.)
[keV]
2049.4(1)
2068.09(4)
2074.2(1)
2077.36(4)
2084.83(3)
2088.8(1)
2090.9(1)
2096.87(2)
2112.8(1)
2113.7(1)
2126.43(7)
2130.6(1)
2138.22(4)
2140.2(1)
2141.7(1)
2143.7(1)
2144.5(1)
2149.9(1)
2155.3(1)
2165.4(1)
2187.0(1)
2191.0(1)
2194.43(3)
2200.8(1)
2208.4(1)
2208.4(1)
2208.8(1)
2230.5(1)
2245.0(1)
2255.7(1)
2267.0(1)
2271.27(4)
2279.0(1)
2297.5(1)
2309.9(1)
2323.2(1)
2325.3(1)
2327.7(1)
2354.6(1)
2367.5(1)
2372.4(1)
2374.5(1)
2383.8(1)
2386.9(1)
2393.5(1)
2396.9(1)
2450.22(5)
2469.73(15)
2474.9(1)
2503.8(1)
2553.6(1)
2556.8(1)
2560.0(1)
2572.4(1)
2574.4(1)
2602.67(5)
IπK
(3,4)
1–
7+4
3–3
(1,2)+
(2–)
(2,3)–
4+4
8–1
(4,5)
3–
3–
(2)+
(3)
(3)
(4–)
(2–)
(1,2)
(4–)
(2,3,4)
(5,6)
(3–)
5+4
(3,4)
4+
4+
(2–)
(2)
3+
(1,2+)
3–
2–
(3–)
(2)+
(3,4)
(1,2)+
(1,2)+
(2+)
2+
3+
6–
(4–)
6–
(3)+
(2,3)
(1,2)
(1–)
(3)–
(3)
2+
(3–)
5–
(3,4)+
(4)
(1,2,3)–
(1,2)–
(2,3,4)+
(2+)
(1,2)+
1–
(1,2,3)+
3–
(3,4)–
2–
(3,4)+
1–
5+
(2,3)–
2+
1–
2–
2+
2–
3–
(4)
2–
1–
(4–)
(2–)
(4,5)
(1,2)
(1,2)
(4,5)
1–
(3,4,5,6)
(4)+
1+
(2,3,4)
1–
5–
3–
1+
1–
(2)
(2,3)–
2+
(2,3,4)
(4–)
(4,5,6)
3–
(1,2)
(4,5)
(4,5)
(2,3,4)
(1,2)
(1,2)
(4,5)–
(3,4,5,6)
(1,2+)
(4,5,6)
6+