Bulg. J. Phys. 41 (2014) 10–23

New Low-Lying Excited 0+ States in 160DyNucleus

J. Adam1, D.D. Bogachenko2, O.K. Egorov2, V.P. Garistov1,3,A.I. Georgieva3, T.A. Islamov1, V.V. Kolesnikov2, V.I. Silaev2,A.A. Solnyshkin1

1Joint Institute for Nuclear Research, Dubna, Russia2Institute of Theoretical and Experimental Physics, Moscow, Russia3Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy ofSciences, Sofia, Bulgaria

Received 31 August 2014

Abstract. We report our results of the experimental search for new low-lyingexcited 0+ states in the 160Dy nucleus. The energy interval in which they shouldbe observed was theoretically predicted by the parabolic energy distribution of0+ states in the space of the monopole bosons, that are built from fermion pairs,as well as in the framework of the interacting vector bosons model (IVBM).

In the experiment, a new more sensitive technique is used for measuring emul-sion spectrograms of internal conversion electrons (ICE) using the AutomatedScanning Microscope MAS−1. In the region of the theoretically predicted en-ergies, new E0 transitions and excited 0+-states are observed in the spectrum ofthe 160Dy nucleus.

PACS codes: 21.10.Re, 21.60.Fw, 23.20.Lv, 23.20.Nx

1 Introduction

Low-lying excited 0+ states in atomic nuclei are still one of the main points ofinterest in nuclear structure studies. The observed abundance of new experimen-tal data on 0+ states [1–7] triggered the interest in the theoretical description oftheir complex structure. This has resulted in the development of various newapproaches for the interpretation of the 0+ excitations, such as microscopic de-scription of unharmonic effects [8–11], mixing of quadrupole and pairing oscil-lation modes [12], double beta decay in processes of internal electron conver-sion, etc.

The correct description of the energies and the electromagnetic decays of excitedstates is a serious test for the nuclear structure models, such as the shell model,

10 1310–0157 c© 2014 Heron Press Ltd.

New Low-Lying Excited 0+ States in 160Dy Nucleus

cluster models, quasiparticle-phonon model and various algebraic fermion orboson models. Most of these models describe one or another aspect of the natureof the excited 0+ states, depending on their respective model assumptions. Butthe observed existence of so many low lying 0+ excitations in some nuclei [1–7], obviously requires not only to describe the structure of the observed states,but to make as well some reliable model predictions, which could help in theobservation of these states. The experimental techniques for the detection ofthe transitions between them, which leads to their correct location in the nuclearspectra is rather sensitive and complicated, hence an advanced indication fortheir positions is of great help in their experimental search.

In this paper we report the discovery of two new low lying and very close inenergy 0+ states in 160Dy nucleus, which is based on the theoretical predictionsof a simple model for the the energy distribution of the excited 0+ states in thespectrum of each even-even nucleus, introduced by V.P. Garistov [13]. This dis-tribution is represented by a second order polynomial in respect to an integer andpositive definite parameter. It is showing persistently good accordance with theexperimental data in most of the heavy even-even nuclei with more than threeexcited 0+ states observed. It attracted the attention of theoreticians, who workon applications of group-theoretical methods in the investigation of excited nu-clear states [14–16] and gave a new impetus to experimental search for thesestates. The later was the motivation for this investigation, leading to the obser-vation of new excited 0+ states based on their theoretical prediction. Our aimis as well, to provoke further theoretical and experimental investigation of theseimportant basic excited collective states.

2 Theoretical Prediction of the New Excited 0+ States

In [13] a phenomenological Hamiltonian

H = αR+R− + βR0R0 +βΩ

2R0, (1)

built by boson creation and annihilation operators representing fermion pairsfrom the same j− sub shell and coupled to a zero total momentum was pro-posed. The operators R+, R− and R0 in (1) obey the commutation rules[R0, R±] = ±R± and [R+, R−] = 2R0, α and β are the model parametersand Ω = (2j + 1)/2. When the Hamiltonian H (1) is rewritten in terms ofideal monopole bosons, defined by [b†, b] = 1; [b, b] = [b†, b†] = 0, using theHolsteinPrimakoff transformation [17, 18]

R+ = b+(2Ω− b+b)1/2;R− = (2Ω− b+b)1/2b;R0 = b+b− Ω (2)

it (1) takes the formH = ab+b− bb+bb+b (3)

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and generates the spectrum of the monopole excitations in the form of a parabola

E(n) = an− bn2, (4)

where n is the number of monopole bosons for the state, a and b are the modelparameters. The normalized n-boson excited state |n〉 is defined as

|n〉 =(b+)n|0〉(n!)1/2

; b|0〉 = 0.

In analogy to the model Hamiltonian (3), we can also consider the Hamiltonianof the symplectic Interacting Vector Boson Model (IVBM) [16], based on theboson implementation of sp(12, R) algebra constructed by two types of vectorbosons that differ by the projection of the “pseudospin” introduced in the IVBMin analogy with the F−spin in the proton–neutron version of the InteractingBoson Model-2 [19, 20]. The model is described at length in [16].

It is easy to verify that in one of the dynamical symmetry chains, namelysp(12, R) ⊃ sp(4, R) ⊗ so(3) governing the behavior of the collective stateswith a fixed angular momentum in the IVBM [14] the energy distribution of thecorresponding basis states is also obtained as second order polynomial of thenumber of vector bosons N :

E(N) = AN +BN2 + C, (5)

whereA,B andC are combinations of the parameters of the IVBM Hamiltonianin the considered chain. For the excited states with Jπ = 0+ the parameter Cis zero. By means of the vector bosons all the other positive (N− even) andnegative parity (N−odd) states with J = 0, 1, 2, 3 . . . can be constructed. In thiswork we are aiming at the prediction of the 0+ excited band head configurations,hence we use the simplified expression (4) for the description of the energiesand structure of 0+ states in the even-even nuclei. We obtain the values of theparameters in (4) by comparing the values χ2 of their fits to the experiment forall possible distributions of the energies in respect to n and take the best oneas a solution. Figure 1 shows the distributions of the experimentally known 0+

energies in 180W [4], 178Hf [1], 158Gd [3], and 162Dy [4] nuclei in respect to themonopole boson number n (4). On the left panel of Figure 2 the experimentaldata recently obtained by D. Bucurescu [6] for 166Er nucleus is compared toour theoretical predictions. The values of the parameters a, b from (4) and the

rms deviation ∆ = 1k

√Σki=1(Eiexp − Eith)2, where k is the number of points,

are given for each nucleus on the figures.

Almost all available experimental data for even-even deformed nuclei are repro-duced with a good accuracy. Thus, according to the proposed model, which issimple to use but gives persistently good results for a large number of deformednuclei, each 0+ state can be characterized by an additional intrinsic degree of

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New Low-Lying Excited 0+ States in 160Dy NucleusNew 0+ States in the 160Dy

0 4 8 12 16 200.0

0.5

1.0

1.5

2.0

2.5

0 4 8 12 16 200.0

0.5

1.0

1.5

2.0

2.5

0 8 16 240.0

0.5

1.0

1.5

2.0

2.5

3.0

0 4 8 12 16 20 240.0

0.5

1.0

1.5

2.0

2.5

3.0

MeV

a = 0.438b = 0.0206

= 0.002 MeV

180W 178Hf

a = 0.531b = 0.0261

= 0.004 MeV

MeV

a = 0.59797b = 0.0279573

= 0.006 MeV

158Gd

n

a = 0.42b = 0.0158

= 0.0007 MeV

n

162Dy

Figure 1. (Color online) Energy distribution of the known experimental energies of 0+

states in 180W, 178Hf, 158Gd, and 162Dy as functions of the number of monopole bosons.

the respective dynamical symmetry of the IVBM [14], where even a relation be-tween the two classification numbers n of the monopole bosons and N = 4n ofthe vector bosons was obtained. Although exact harmonic phonon excitationshave never been observed, there are numerous examples of nuclei exhibitingunharmonic vibrational motion. More theoretical work is needed in order to un-derstand the effects responsible for the wide range of observed unharmonicities.

4

Figure 1. (Color online) Energy distribution of the known experimental energies of 0+

states in 180W, 178Hf, 158Gd, and 162Dy as functions of the number of monopole bosons.

collectivity, i.e., by the number of monopole bosons n, building the correspond-ing state. In other words, each particular excited 0+ state is associated with thenumber of monopole bosons n that determine the structure of this state. In allthe considered cases the experimentally observed energies of the 0+ states aredistributed on a parabola and show rather good agreement with the theory.

It should be pointed out that similar results are obtained in the application ofthe respective dynamical symmetry of the IVBM [14], where even a relation be-tween the two classification numbers n of the monopole bosons and N = 4n ofthe vector bosons was obtained. Although exact harmonic phonon excitationshave never been observed, there are numerous examples of nuclei exhibitingunharmonic vibrational motion. More theoretical work is needed in order to un-derstand the effects responsible for the wide range of observed unharmonicities.In general, if we use a Hamiltonian in a second quantized boson or fermion form

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0 4 8 12 16 200.0

0.5

1.0

1.5

2.0

0 10 20 300

1

2

3

4

n

a = 0.410505b = 0.0217586

= 0.0009 MeV

160Dy

MeV

MeV

n

166Era = 0.518956b = 0.0166255

= 0.007 MeV

Figure 2. Distribution of the experimentally observed energies of the 0+ states in 166Er(left) and in 160Dy (right) as function of the monopole boson number. The solid curveis the model calculation with (4), the stars are the experimentally known 0+ states, andopen circles are theoretically predicted 0+ states in 160Dy.

In general, if we use a Hamiltonian in a second quantized boson or fermion formwith one– and two–body interactions such a second order function of their num-ber will appear. Hence, we do not consider the second term in the Hamiltonian,depending on b, as a perturbation of the harmonic vibrations, described by thefirst one. It is rather a mixture with the rotational motion, as discussed in themore elaborate version of this approach - the application of the algebraic IVBM(see [14] and [16]). In it other collective states with fixed angular momentumL = 1, 2... are described and show very similar behavior. There, it is obviousthat as N - the number of vector bosons that build the states is proportional tothe angular momentum L of the states, so N2 ∼ L2 introduces rotations in thecollective motion, which for some nuclei could be prevailing.

In view of the ability of this approach to predict the positions of the 0+ ener-gies with an accuracy within 7 keV, we tried to search for new model-predicted0+ states among the excited low lying states of the deformed 160Dy nucleus(∆ = 1keV ). To this end, we performed model calculations (found the modelparameters a and b (4) given on the right side of Fig. 2, from a fit to the exper-imentally known 0+ level’s energies) and evaluated the energies of the missinglow lying 0+ states (to each n a corresponding 0+ state should exist). The laterare presented with circles on the right hand side of Fig. 2, thus determiningthe energy region in which the search of the new excited 0+ state should befocussed.

5

Figure 2. (Color online) Distribution of the experimentally observed energies of the 0+

states in 166Er (left) and in 160Dy (right) as function of the monopole boson number. Thesolid curve is the model calculation with (4), the stars are the experimentally known 0+

states, and open circles are theoretically predicted 0+ states in 160Dy.

with one- and two-body interactions such a second order function of their num-ber will appear. Hence, we do not consider the second term in the Hamiltonian,depending on b, as a perturbation of the harmonic vibrations, described by thefirst one. It is rather a mixture with the rotational motion, as discussed in themore elaborate version of this approach – the application of the algebraic IVBM(see [14] and [16]). In it other collective states with fixed angular momentumL = 1, 2... are described and show very similar behavior. There, it is obviousthat as N – the number of vector bosons building the states – is proportional tothe angular momentum L of the states, so N2 ∼ L2 introduces rotations in thecollective motion, which for some nuclei could be prevailing.

In view of the ability of this approach to predict the positions of the 0+ ener-gies with an accuracy within 7 keV, we tried to search for new model-predicted0+ states among the excited low lying states of the deformed 160Dy nucleus(∆ = 1 keV). To this end, we performed model calculations (found the modelparameters a and b (4) given on the right side of Figure 2, from a fit to the exper-imentally known 0+ level’s energies) and evaluated the energies of the missinglow lying 0+ states (to each n a corresponding 0+ state should exist). The laterare presented with circles on the right hand side of Figure 2, thus determiningthe energy region in which the search of the new excited 0+ state should befocussed.

3 Experiment and Discussion

One of the main approaches in the search of excited 0+ states in nuclei is basedon the investigation of the spectra of internal conversion electron (ICE), obtainedin their β decay. This investigation in practice gives the E0 transitions betweenthese states. In this paper, our new results on the investigation of the strongly

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New Low-Lying Excited 0+ States in 160Dy Nucleus

deformed 160Dy nucleus are presented. Its excited levels’ scheme is quite wellstudied experimentally [21–24] and theoretically as well [15]. In addition, aswas already mentioned the energy distribution of the experimentally known 0+

states in 160Dy, indicated by stars on the right of Figure 2, was obtained withthe accuracy within 1 keV in the theoretical approach described in the previousSection.

Before these investigations were started, five zero-spin positive-parity states (in-cluding the ground state) of this nucleus were reliably known from experiment.In the figures in Section 2, the vertical axis is the excitation energy of states andthe horizontal axis is the number of monopole bosons forming these states. Inthe right side of Figure 2 the states that earlier were not observed experimentallyare presented with circles.

We decided to investigate thoroughly the ICE spectrum arising from the β de-cays of 160Ho−→ 160Dy and 160Er−→ 160Ho−→ 160Dy, in order to search fornew E0 transitions in 160Dy that could be associated with the 0+ states shownin the right of (Figure 2). It is known that only transitions due to internal con-version of γ rays can be observed, i.e. γ transitions are forbidden and betweenzero-spin states only E0 transitions can occur. Therefore, observation of new E0transitions allows to determine new 0+ states. Investigations of this kind wereperformed for many years at the proton accelerator of the Dzhelepov Laboratoryof Nuclear Problems (DLNP, JINR, Dubna) (http://nuweb.jinr.ru/en/) for sys-tematic studies of rare-earth and actinide nuclei in the scope of the YASNAPPnuclear spectroscopy program [25, 26].

The necessary radioactive isotopes were produced at the accelerator by bom-barding a tantalum target. Fractions of the radioactive elements for further spec-troscopy were extracted from the target by the chromatographic method devel-oped at DLNP [25]. The ICE spectra were investigated using a set of β spectro-graphs with a constant magnetic field [26], one of which is shown on the upperpanel of Figure 3. The extracted fraction was deposited on the surface of a plat-inum wire 50−100 µm in diameter and placed in the chamber of a spectrograph.The ICE were detected using a thin layer of nuclear photoemulsion on a glassplate (blackening at the electron hit points). The plates were 400 × 15 mm2 insize with a layer of P -type emulsion (50 µm thick) manufactured by the FoMosCompany. One of the main problems was the processing of the spectrogramsin order to find the energies and the intensities of particular ICE spectral linesfrom the location and the degree of blackening of the nuclear emulsion. Thetechnique practiced in Dubna (photometric measurements) did not allow for theobservation of low-intensity ICE lines. The lines corresponding to the new tran-sitions, predicted by the model distribution, which could be associated with thenew 0+ states in 160Dy, were expected to be among them.

A solution to this problem was found in the new experimental setupMAS − 1 developed at the Institute of Theoretical and Experimental Physics,

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J. Adam et al.

New 0+ States in the 160Dy

Figure 3. (Color online) (left) β spectrograph with a constant magnetic field (Dubna,JINR); (right) The MAS−1 setup (Moscow, ITEP).

3 Experiment and discussion

One of the main approaches in the search of excited 0+ states in nuclei is basedon the investigation of the spectra of internal conversion electron (ICE), obtainedin their β decay. This investigation in practice gives the E0 transitions betweenthese states. In this paper, our new results on the investigation of the stronglydeformed 160Dy nucleus are presented. Its excited levels’ scheme is quite wellstudied experimentally [21], [22], [23], [24] and theoretically as well [15]. Inaddition, as was already mentioned the energy distribution of the experimentallyknown 0+ states in 160Dy, indicated by stars on the right of Fig.2, was obtainedwith the accuracy within 1 keV in the theoretical approach described in the previ-ous section. Before this investigations was started, five zero-spin positive-paritystates (including the ground state) of this nucleus were reliably known from ex-periment. In the figures in section 2, the vertical axis is the excitation energy ofstates and the horizontal axis is the number of monopole bosons forming thesestates. In the right side of Fig. 2 the states that earlier were not observed inexperiment are presented with circles.

We decided to investigate thoroughly the ICE spectrum arising from the β de-cays of 160Ho −→ 160Dy and 160Er −→ 160Ho −→ 160Dy, in order to search fornew E0 transitions in 160Dy that could be associated with the 0+ states shownin the right of (Fig. 2). It is known that only transitions due to internal con-version of γ rays can be observed, i.e. γ transitions are forbidden and betweenzero-spin states only E0 transitions can occur. Therefore, observation of new E0transitions allows to determine new 0+ states. Investigations of this kind wereperformed for many years at the proton accelerator of the Dzhelepov Laboratoryof Nuclear Problems (DLNP, JINR, Dubna) (http://nuweb.jinr.ru/en/) for sys-tematic studies of rare-earth and actinide nuclei in the scope of the YASNAPPnuclear spectroscopy program [25], [26]. The necessary radioactive isotopeswere produced at the accelerator by bombarding a tantalum target. Fractions ofthe radioactive elements for further spectroscopy were extracted from the target

6

New 0+ States in the 160Dy

Figure 3. (Color online) (left) β spectrograph with a constant magnetic field (Dubna,JINR); (right) The MAS−1 setup (Moscow, ITEP).

3 Experiment and discussion

One of the main approaches in the search of excited 0+ states in nuclei is basedon the investigation of the spectra of internal conversion electron (ICE), obtainedin their β decay. This investigation in practice gives the E0 transitions betweenthese states. In this paper, our new results on the investigation of the stronglydeformed 160Dy nucleus are presented. Its excited levels’ scheme is quite wellstudied experimentally [21], [22], [23], [24] and theoretically as well [15]. Inaddition, as was already mentioned the energy distribution of the experimentallyknown 0+ states in 160Dy, indicated by stars on the right of Fig.2, was obtainedwith the accuracy within 1 keV in the theoretical approach described in the previ-ous section. Before this investigations was started, five zero-spin positive-paritystates (including the ground state) of this nucleus were reliably known from ex-periment. In the figures in section 2, the vertical axis is the excitation energy ofstates and the horizontal axis is the number of monopole bosons forming thesestates. In the right side of Fig. 2 the states that earlier were not observed inexperiment are presented with circles.

We decided to investigate thoroughly the ICE spectrum arising from the β de-cays of 160Ho −→ 160Dy and 160Er −→ 160Ho −→ 160Dy, in order to search fornew E0 transitions in 160Dy that could be associated with the 0+ states shownin the right of (Fig. 2). It is known that only transitions due to internal con-version of γ rays can be observed, i.e. γ transitions are forbidden and betweenzero-spin states only E0 transitions can occur. Therefore, observation of new E0transitions allows to determine new 0+ states. Investigations of this kind wereperformed for many years at the proton accelerator of the Dzhelepov Laboratoryof Nuclear Problems (DLNP, JINR, Dubna) (http://nuweb.jinr.ru/en/) for sys-tematic studies of rare-earth and actinide nuclei in the scope of the YASNAPPnuclear spectroscopy program [25], [26]. The necessary radioactive isotopeswere produced at the accelerator by bombarding a tantalum target. Fractions ofthe radioactive elements for further spectroscopy were extracted from the target

6

Figure 3. (Color online) (up) β spectrograph with a constant magnetic field (Dubna,JINR); (down) The MAS−1 setup (Moscow, ITEP).

(http://www.itep.ru/), Moscow. This setup was used for the investigation ofneutrino interactions in nuclear emulsion [27] and search for neutrino oscilla-tions [28]. Its principle of operation is described in details in [29]. On the lowerpanel of Figure 3, a photo of this setup is presented. This setup was adapted [29]to scan spectrograms (emulsion plates with ICE spectra exposed in the β spec-trographs) for the investigations of the E0 transitions in nuclear spectra. Twoemulsion plates with spectrograms of Er-fractions and one spectrogram with theHo-fraction were exposed in the β spectrographs in Dubna in the 1970s. Anexample of ICE lines on an emulsion plate scanned at MAS − 1 is presented inFigure 4.

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New Low-Lying Excited 0+ States in 160Dy Nucleus

Figure 4. Fragment of ICE lines as seen in the process of scanning the emulsion plate onMAS − 1

New 0+ States in the 160Dy

in the β spectrographs) for the investigations of the E0 transitions in nuclearspectra. Two emulsion plates with spectrograms of Er fractions and one spec-trogram with the Ho fraction were exposed in the β spectrographs in Dubna inthe 1970s. An example of ICE lines on an emulsion plate scanned at MAS − 1is presented in Fig.4.

An intense vertical ICE line is distinctly seen at the center of the photo and onits right a weaker line is distinguishable. The intensity of this line is too low tobe observed by standard photometry methods.

With the new technique we first reviewed the ICE spectra from the three plates,which proved that it works well. One of the obtained spectra is shown in Fig.5.The other two are not shown because they are identical to that one. We observedall known 160Dy ICE lines, and their energies and intensities did not differ withinthe error limits from the previously known values [22]. Three of them are shownin Fig. 6.

Then the regions of interest predicted from the theoretical energy distribution of0+ states were investigated in more details in the ICE energy spectrum.

First the region from 600 to 800 keV, was studied thoroughly with the expecta-tion to find new E0 transitions. And indeed they were observed, as could be seenin Fig.6. At the left of this figure there is a doublet of K672.35 keV and K673.09keV. The K673.09 keV line has long been known from experiment. The onlyproblem is that it was slightly broadened in all investigated spectra, and the rea-son for this was not clear for a long time. It was assumed that there is an E0

Figure 5. Fragment of the 160Dy ICE spectrum (Ee = 578−1078 keV) from the MAS−1scanning of the emulsion plate.

8

Figure 5. Fragment of the 160Dy ICE spectrum (Ee = 578−1078 keV) from the MAS−1scanning of the emulsion plate.

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J. Adam et al.

...

transition between the known 1952.3 keV and 1280.0 keV 0+ states in the spec-trum of 160Dy. As is evident from Fig.6, we managed to observe this K672.35E0 transition and evaluated its intensity. In Fig.6 we see the known K682.3 keVICE line, and on its left there is a distinct new K681.3 keV line found by us.After thorough analysis we ascribed this line to the E0 transition to the groundstate in 160Dy and thus introduced a new 0+ state with an energy of 681.3 keV.Note that it is of the same order of magnitude as the energies of two 0+ states in160Dy, which the theory predicts (see Fig.2).

Further we managed to establish the other model-predicted 0+ level with anexcitation energy of 703.0 keV (see Fig.2). Next to the known K707.6 keVline in the ICE spectrum we found the corresponding K703.0 keV E0 transition,which we also assumed to be the E0 transition to the 0+ ground state in 160Dy.Figure 7 shows the 160Dy ICE spectrum region where this transition is observed.We also observed other E0 transitions, both earlier known and newly introducedby us, between zero-spin excited states, e.g., the K1271.0 keV transition (seeFig.8) and a number of others.

In Fig.9, the scheme of the excited 0+ states in 160Dy with the transitions con-firming their existence is presented. The two new 0+ states first establishedin our investigations are colored in purple. It is clear that 0+ states in 160Dy,including the 681.3 and 703.0 keV states established by us, cannot be directlypopulated by the β decay according to the selection rules, e.g. the 160Ho daugh-

Figure 6. Fragment of the 160Dy ICE spectrum (Ee = 615.4 − 631.4 keV) from theMAS−1 scanning of the emulsion plate

9

Figure 6. Fragment of the 160Dy ICE spectrum (Ee = 615.4 − 631.4 keV) from theMAS−1 scanning of the emulsion plate

An intense vertical ICE line is distinctly seen at the center of the photo and onits right a weaker line is distinguishable. The intensity of this line is too low tobe observed by standard photometry methods.

With the new technique we first reviewed the ICE spectra from the three plates,which proved that it works well. One of the obtained spectra is shown in Fig-ure 5. The other two are not shown because they are identical to that one. Weobserved all known 160Dy ICE lines, and their energies and intensities did notdiffer within the error limits from the previously known values [22]. Three ofthem are shown in Figure 6.

Then the regions of interest predicted from the theoretical energy distribution of0+ states were investigated in more details in the ICE energy spectrum.

First the region from 600 to 800 keV, was studied thoroughly with the expec-tation to find new E0 transitions. And indeed they were observed, as could beseen in Figure 6. At the left of this figure there is a doublet of K672.35 keV andK673.09 keV. The K673.09 keV line has long been known from experiment.The only problem is that it was slightly broadened in all investigated spectra,and the reason for this was not clear for a long time. It was assumed that thereis an E0 transition between the known 1952.3 keV and 1280.0 keV 0+ states inthe spectrum of 160Dy. As is evident from Figure 6, we managed to observe thisK672.35 E0 transition and evaluated its intensity. In Fig.6 we see the knownK682.3 keV ICE line, and on its left there is a distinct new K681.3 keV linefound by us. After thorough analysis we ascribed this line to the E0 transition tothe ground state in 160Dy and thus introduced a new 0+ state with an energy of681.3 keV. Note that it is of the same order of magnitude as the energies of two

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New Low-Lying Excited 0+ States in 160Dy Nucleus

New 0+ States in the 160Dy

ter nucleus has spin and parity Jπ = 2− in the isomeric state and Jπ = 5+ inthe ground state). They can only be populated via γ transitions from the statessituated higher in energy. In the existing experimental data [22] we found theappropriate γ transitions with energies 1594.5(4)keV and 1822.4(3) keV and in-tensities 0.8(3) and 0.24(5) rel. un. respectively. These γ transitions were notearlier placed in the 160Ho →160 Dy decay scheme [22]. We assumed thatboth these γ transitions proceed from the known [22] 2297.5 Jπ = (2)+ and2503.8 Jπ = 2+ keV states and populate the 681.3 and 703.0 keV 0+ states re-spectively, since they fit well the energy differences between the correspondinglevels (see fig 9).

Moreover, the 1594.5(4) and 1822.4(3) keV γ transitions fully compensate forthe deexcitation of 681.3 and 703.0 keV 0+ states within the errors and thusprovide zero intensity balance for these states. The states are deexcited viathe 681.3 and 703.0 keV E0 transitions to the ground state and via compet-ing E2 transitions to the 86.8 keV 2+ level of the ground state band. Accord-ing to the scheme (Fig.9), the energies of these γ transitions are 594.5 and616.2 keV. Unfortunately, they are masked by the existing [22] low-intensity593.48(15), 595.32(10), and 616.18(10) keV γ transitions. Under these condi-

Figure 7. Fragment of the 160Dy ICE spectrum (Ee = 641.5 − 655.5 keV) from theMAS − 1 scanning of the emulsion plate.

10

Figure 7. Fragment of the 160Dy ICE spectrum (Ee = 641.5 − 655.5 keV) from theMAS − 1 scanning of the emulsion plate.

0+ states in 160Dy, which the theory predicts (see Figure 2).

Further we managed to establish the other model-predicted 0+ level with anexcitation energy of 703.0 keV (see Figure 2). Next to the known K707.6 keVline in the ICE spectrum we found the corresponding K703.0 keV E0 transition,which we also assumed to be the E0 transition to the 0+ ground state in 160Dy.Figure 7 shows the 160Dy ICE spectrum region where this transition is observed.We also observed other E0 transitions, both earlier known and newly introducedby us, between zero-spin excited states, e.g., the K1271.0 keV transition (seeFigure 8) and a number of others.

In Figure 9, the scheme of the excited 0+ states in 160Dy with the transitionsconfirming their existence is presented. The two new 0+ states first establishedin our investigations are colored in purple. It is clear that 0+ states in 160Dy,including the 681.3 and 703.0 keV states established by us, cannot be directlypopulated by the β decay according to the selection rules, e.g. the 160Ho daugh-ter nucleus has spin and parity Jπ = 2− in the isomeric state and Jπ = 5+ inthe ground state). They can only be populated via γ transitions from the statessituated higher in energy. In the existing experimental data [22] we found theappropriate γ transitions with energies 1594.5(4) keV and 1822.4(3) keV andintensities 0.8(3) and 0.24(5) rel. un. respectively. These γ transitions werenot earlier placed in the 160Ho→ 160Dy decay scheme [22]. We assumed thatboth these γ transitions proceed from the known [22] 2297.5 Jπ = (2)+ and

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J. Adam et al.

...

tions we could only evaluate the intensities of the 594.5 and 616.2 keV γ tran-sitions and calculate the experimental values of the dimensionless Rasmussenparameter B(E0)/B(E2) for the 681.3 and 703.0 keV 0+ states. Table 1 be-low presents the ratios B(E0)/B(E2) calculated from the experimental datafor each 0+ level in comparison with the theoretical estimate of the Rasmussenparameter [30] for 160Dy. In the first two rows the new data obtained by us isgiven.

Figure 8. Fragment of the 160Dy ICE spectrum (Ee = 1215.1 − 1218.1 keV) from theMAS−1 scanning of the emulsion plate.

11

Figure 8. Fragment of the 160Dy ICE spectrum (Ee = 1215.1 − 1218.1 keV) from theMAS−1 scanning of the emulsion plate.

2503.8 Jπ = 2+ keV states and populate the 681.3 and 703.0 keV 0+ states re-spectively, since they fit well the energy differences between the correspondinglevels (see Figure 9).

Moreover, the 1594.5(4) and 1822.4(3) keV γ transitions fully compensate forthe deexcitation of 681.3 and 703.0 keV 0+ states within the errors and thusprovide zero intensity balance for these states. The states are deexcited viathe 681.3 and 703.0 keV E0 transitions to the ground state and via compet-ing E2 transitions to the 86.8 keV 2+ level of the ground state band. Accord-ing to the scheme (Fig.9), the energies of these γ transitions are 594.5 and616.2 keV. Unfortunately, they are masked by the existing [22] low-intensity593.48(15), 595.32(10), and 616.18(10) keV γ transitions. Under these condi-

20

New Low-Lying Excited 0+ States in 160Dy NucleusNew 0+ States in the 160Dy

Figure 9. (Color online) Fragment of the 160Dy excited state scheme. The new levels arecolored in purple and the transitions in red

Table 1. The calculated and experimental ratios B(E0)/B(E2)

E(0+) IK(E0) ΩK Eγ(E2) Iγ(E2) B(E0)B(E2)

B(E0)B(E2)

keV rel.un. keV rel.un. exp. theor.681.3 0.024 4.0891010 594.5 < 0.3 > 0.3703.0 0.086 4.2081010 616.2 ∼ 0.4 ∼ 0.61280.0 0.053 7.7781010 1193.2 13.8 0.3 0.61456.7 − 9.0681010 1369.9 40 −1708.2 0.033 1.1031011 1621.4 12.7 0.61952.3 0.015 1.311011 1865.6 6.1 0.9

The Rasmussen parameters were calculated and estimated using the expressions:

Xexp =B(E0)

B(E2)exp.=

2.56 · 1010 · A4/3 · IK(E0) · E5γ

ΩK · Iγ(E2)(6)

12

Figure 9. (Color online) Fragment of the 160Dy excited state scheme. The new levels arecolored in purple and the transitions in red

tions we could only evaluate the intensities of the 594.5 and 616.2 keV γ tran-sitions and calculate the experimental values of the dimensionless Rasmussenparameter B(E0)/B(E2) for the 681.3 and 703.0 keV 0+ states. Table 1 be-low presents the ratios B(E0)/B(E2) calculated from the experimental datafor each 0+ level in comparison with the theoretical estimate of the Rasmussenparameter [30] for 160Dy. In the first two rows the new data obtained by us isgiven.

Table 1. The calculated and experimental ratios B(E0)/B(E2)

E(0+) IK(E0) ΩK Eγ(E2) Iγ(E2) B(E0)B(E2)

B(E0)B(E2)

keV rel.units keV rel.units exp. theor.

681.3 0.024 4.0891010 594.5 < 0.3 > 0.3703.0 0.086 4.2081010 616.2 ∼ 0.4 ∼ 0.61280.0 0.053 7.7781010 1193.2 13.8 0.3 0.61456.7 − 9.0681010 1369.9 40 −1708.2 0.033 1.1031011 1621.4 12.7 0.61952.3 0.015 1.311011 1865.6 6.1 0.9

21

J. Adam et al.

The Rasmussen parameters were calculated and estimated using the expressions:

Xexp =B(E0)

B(E2)exp .=

2.56 · 1010 ·A4/3 · IK(E0) · E5γ

ΩK · Iγ(E2)(6)

Xtheory =B(E0)

B(E2)theory= 17 ·A−2/3 (7)

HereB(E0) andB(E2) are the reduced probabilities of the corresponding tran-sitions, A is the mass number, IK(E0) is the relative intensity of the E0 tran-sition, ΩK is the electron factor, and Eγ(E2) and Iγ(E2) are the energy andrelative intensity of the E2 transition.

In conclusion we could summarize that the predictive power of the proposedtheoretical approach was proved by the new thorough investigation of the ICEspectra in the low energy region of the 160Dy, which resulted in the locationof two new excited 0+ states. These states are rather close in energy, but areclearly distinguished through their assigned value of the distribution parameterintroduced in the model. This approach could be used for prediction of addi-tional 0+ states in other rotational nuclei, in particular in the low energy region.This requires a systematic investigation of the behavior these states in sequencesof nuclei, where some interesting effects are observed [31]. Also since the 0+

states are band-head configurations it is worth investigating their distributions incomparison to other excited states with Jπ = 2+, 4+, 6+, . . . and in respect toother excited bands, which requires the use of a more general algebraic modellike the IVBM [14], where the energy distribution of states with fixed angularmomentum and the band structure of the collective spectra can be described.

Acknowledgments

The authors from INRNE would like to acknowledge hospitality and fruitfulcollaboration with the colleagues from BLTP and DLNP, JINR, Dubna, Ho-ria Halubei National Institute for Nuclear Research and Engineering (IFIN-HH) in Bucharest, Magurele and Department of Physics, Notre Dame Uni-versity, Notre Dame, Indiana, USA. This work was partially supported by theBulgarian National Foundation for Scientific Research under Grants No DID-02/16/17.12.2009, DNTS02-21, the grant for collaborative research with JINR,Dubna on the subject “Nucleus-Nucleus Collisions and Nuclear Properties atLow Energies” and NSF, US under grant number PHY-1068192.

References

[1] A. Aprahamian, R.C. de Haan, H.G. Borner, H. Lehmann, C.Doll, M. Jentschel,A.M. Bruce, R. Piepenbring (2002) Phys. Rev. C 65 031301.

22

New Low-Lying Excited 0+ States in 160Dy Nucleus

[2] X. Wu, A. Aprahamian, S. M. Fischer, W. Reviol, G. Liu, J. X. Saladin (1994) Phys.Rev. C 49 1837-1844

[3] S. R. Lesher, A. Aprahamian, L. Trache, A.Oros-Peusquens, S. Deyliz, A. Goll-witzer, R. Hertenberger, B. D. Valnion, G. Graw (2002) Phys. Rev. C 66 051305

[4] D. Bucurescu et al., (2006) Phys. Rev. C 73 064309[5] D. A. Meyer et al., (2006) Phys. Rev. C 74 044309[6] D. Bucurescu (2011) private communication[7] C. Bernards et al., (2013) Phys. Rev. C 87 024318 and 064321[8] B. Silvestre-Brac, R. Piepenbring (1977) Phys. Rev. C 16 1638 and (1978) Phys.

Rev. C 17 364[9] A. Passoja et al (1983) Phys. Lett. 124 B 157

[10] J. Kantele, M. Luontama, W. Trzaska, R. Julin, A. Passoja (1986) Phys. Lett. 171 B151

[11] N. LoIudice, A. V. Sushkov, N. Y. Shirikova (2004) Phys. Rev. C 70 064316[12] C. Bahri, J. Escher, J. P. Draayer (1995) Nucl. Phys. A 592 171[13] V. P. Garistov (2000) e-Print Archive: nucl-th/0008067 and (2003) nucl-th/0309058[14] H. G. Ganev, V. P. Garistov, A. I. Georgieva, J. P. Draayer (2004) Phys. Rev. C 70

054317[15] A. A. Solnyshkin, V. P. Garistov, A. Georgieva, H. Ganev, V. V. Burov (2005) Phys.

Rev. C 72 064321-1[16] A. I. Georgieva, H. G. Ganev, J. P. Draayer and V. P. Garistov (2009) Physics of

Elementary Particles and Atomic Nuclei 40 461[17] T. Holstein, H. Primakoff (1940) Phys. Rev.58 1098[18] R. Marshalek (1980) Phys. Lett. B 97 337[19] A. Arima, T. Otsuca, F. Iachello and I. Talmi (1977) Phys.Lett. B 66 205[20] J P. Elliott (1985) Rep. Prog. Phys, 48 171[21] C W. Reich (2005) Nuclear Data Sheets 105, 557[22] J. Adam et al., (2002) Izv. RAS 66 1384[23] A. Jungclaus et al., (2002) Phys. Rev. C 66 014312[24] V. G. Kalinnikov et al., (1992) Nucl. Instr. and Meth. B 70 62[25] F. Molnar, V. Halkin, E. Herrmann, (1973) Physics of Elementary Particles and

Atomic Nuclei 4 1077[26] A. Abdurazakov, K. Gromov, G. Umarov (1972) β-spectrographs with constant

magnets Tashkent, printing house FAN () (in russian)[27] Yu. D. Aleshin, T. A. Islamov, V. G. Kalinnikov, N. T. Kambarova, V. V. Kolesnikov,

V. I. Silaev, A. A. Solnyshkin (2001) Instruments and Experimental TechniquesVolume 44 Issue 3 pp 347-351

[28] Yu. D. Aleshin, V. V. Kolesnikov, V. I. Silaev (1995) Preprint ITEP 5-95 Moscow[29] O. K. Egorov, T. A. Islamov, V. G. Kalinnikov, N. T. Kambarova, V. V. Kolesnikov,

T. M. Muminov, V. I. Silaev, A. A. Solnyshkin (2003) Tech. Phys. 48 Issue 3 pp 370[30] T. O. Rasmusen (1960) Nucl. Phys. 19 85[31] G. Popa, A. Georgieva, J. P. Draayer (2004) Phys. Rev. C 69 064307

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