Experimental evidence of (M1+E2) mixed character of the 9.2 keV transition in ^{227}Th and its consequence for spin-interpretation of low-lying levels
A. Kovalík, A. Kh. Inoyatov, L. L. Perevoshchikov, M. Ryšavý, . D. V. Filosofov, P. Alexa, J. Kvasil
EExperimental evidence of (M1+E2) mixed character of the 9.2 keV transition in
Th and its consequence for spin-interpretation of low-lying levels
A. Kovalík a,b , А.Kh. Inoyatov a,c , L.L. Perevoshchikov a , M. Ryšavý b , D.V. Filosofov a , P. Alexa d ,J. Kvasil ea Dzhelepov Laboratory of Nuclear Problems, JINR, 141980 Dubna, Moscow Region, Russian Federation b Nuclear Physics Institute of the ASCR, CZ-25068 Řež near Prague, Czech Republic c Institute of Applied Physics, National University,
University Str. 4, 100174 Tashkent, Republic of Uzbekistan d Department of Physics, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00 Ostrava, Czech Republic e Institute of Particle and Nuclear Physics, Charles University, CZ-18000, Praha 8, Czech Republic
Keywords:
Internal conversion electron spectroscopy; Nuclear transition; Transition multipolarity;Spin-Parity;
Ac;
ThThe 9.2 keV nuclear transition in
Th populated in the -decay of Ac was studied bymeans of the internal conversion electron spectroscopy. Its multipolarity was proved to be of mixedcharacter M1+E2 and the spectroscopic admixture parameter δ (E2/M1)=0.695±0.248 (|δ(E2/M1)|=0.834±0.210) was determined. Nonzero value of δ(E2/M1) raises a question about the existingtheoretical interpretation of low-lying levels of Th.
1. Introduction
The interpretation of the level structure of
Th is still a major problem mainly due to thelack of experimental information on the low-lying levels of
Th and a long-standing controversy[1] about the spin-parity of the
Th ground state, which represents the basis for all other level spin-parity assignments. Until recently only two excited levels at 9.3 and 24.5 keV were known from theβˉ-decay of
Ac [2] and an additional one at 77.7 keV from the α-decay study of
U [3] feedingthe former two.In earlier compilations [4,5], the spin-parity 3/2 + was suggested for the Th ground state. Insubsequent compilations (including the most recent ones [6,7]), the spin-parity 1/2 + wasrecommended for it. Nevertheless, this assignment contradicted the observed distributionanisotropies for the gamma rays following the α decay of U in the α-γ nuclear orientationexperiment [8] in which the 3/2 + spin-parity for the Th ground state was assumed. However, laterthe authors [9] came to a conclusion that the
Th ground-state spin is consistent with 1/2 (thoughtheir data did not strictly exclude spin≠1/2). This was done on the basis of the measurements [3,10]and results of their investigation [9] of the α-decay of
U and the angular distribution of α particlesin the decay of low-temperature oriented
Th. They deduced that the above-mentioned nuclear-orientation experiment [8] was in error and thus the only experimental evidence for a
Th ground-state spin≠1/2 was eliminated. The present spin-parity assignments of the
Th levels are based on the assumption of spin-parity 1/2 + , 5/2 + and 3/2 + for the ground state, 9.3 keV and 24.5 keV levels, respectively. Thisinterpretation supposes the pure E2 multipolarity for the 9.3 keV gamma-ray transition(depopulating the lowest excited state of Th). Such a multipolarity was determined as the “mostlikely” one in Ref. [2] from the conversion-electron data in the study of the decay of Ac but the uthors [2] did not excluded a considerable admixture of the M1 multipolarity . The above spin-parity assignments were first proposed in Ref. [11] and are also assumed in the most recent nucleardata compilation [7].Thus, it is obvious that the adopted interpretation [7] of the lowest Th levels is not yetstrictly established by experiment. It needs additional experimental data, in particular, reliable andaccurate multipolarity determination of the 9.3 keV transition on which the whole spin sequence andband structure above the ground state depends. Therefore, we performed a new study of the low-energy electron spectrum generated in the - decay of Ac (in which the ground state and thelowest three excited levels of
Th are populated [7], see Fig. 1) using the internal conversionelectron spectroscopy (ICES). Results obtained on the 15.1 keV (M1+E2) transition in
Th werealready published in Ref. [12]. In this work, results on the multipolarity determination of the 9.3keV transition depopulating the 9.30(3) keV 5/2 + (assumed) level of Th [7] are given.2.
Experiment and analysis of the spectra.
The
Ac source for the investigation was produced by a sorption of slightly soluble formsof actinium (AcF ) on a carbon polycrystalline foil and its activity was 690 kBq just after thepreparation (for details see Ref. [12]).The electron spectra were measured in sweeps at the 14, 21, and 35 eV instrumental energyresolution with the 2, 3, 5, 6, 8, and 10 eV scanning step by a combined electrostatic electronspectrometer [13,14]. Examples of the measured spectra are shown in Figs. 2, 3.To decompose the measured conversion electron spectra into the individual components, theapproach and the computer code SOFIE (see, e.g., Ref. [15]) was applied. In this approach, thespectral line profile is expressed by a convolution of the Lorentzian (describing the energydistribution of the investigated electrons leaving atoms) with an artificially created function basedon the Gaussian. The aim of the latter function is to describe both the response of the spectrometerto the monoenergetic electrons and the observed deformation of the measured electron lines on theirlow-energy slopes caused by inelastically scattered electrons in the source material. The MonteCarlo procedure is, therefore, involved in the code.
3. Transition multipolarity determination.
It should be noted that if one accepts arguments of the most recent nuclear data compilation[7] that the 9.3 keV transition in
Th depopulates the first excited state 5/2 + to the ground state 1/2 + ,then any mixture containing the M1 multipolarity is excluded but the M3 multipolarity is possible inprinciple (e.g. E2+M3 multipolarity mixture). For the multipolarity determination, thirteen independent experimental values (i.e., obtainedfrom different measurements) of the M- and N-subshell conversion line ratios were used: M /M =0.031(11), 0.027(9); M /M = 0.025(9), 0.023(7); M /M =0.852(10); M /M = 0.019(6), 0.021(4);M /M = 0.019(4), N /N = 0.02(3), 0.012(13); N /N = 0.84(7), 0.84(2); and N /N = 0.044(17).The theoretical internal conversion coefficients for the M1, M3, and E2 multipolarities andfor transition energy of 9245 eV [16] were calculated employing the computer code NICC [17]using the potential [18] for a neutral thorium atom and the thorium electron binding energies [19].They are presented in Table 1 (marked as NICC). In order to minimize a possible influence of thetheoretical ICC evaluation approach on the multipolarity determination , we applied also another(widely used) method BrICC [20] using the internet calculator [21]. These ICC’s are also presentedin Table 1 (marked as BrICC). The transition multipolarity was then determined using the program CFIT [22] which fits thetheoretical ICC’s and/or ICC ratios into the experimental values by means of the least-squaresmethod. s can be seen from Table 1, the s / to p / subshell ratio values of theoretical M1-ICC arearound 8 (for the both ICC sets), while our corresponding experimental ratios do not exceed 0.03(see our experimental data above). This clearly proves that the 9.2 keV transition cannot be of pureM1 multipolarity.Then we tested (only with the use of the NICC set) a possibility of a multipolarity mixture ofE2+M3. In such a case the ICC α i is given by the formula α i =(1 − Δ)α i ( M3 )+Δα i ( E2 ), where thesubscript i marks the atomic (sub-)shell and Δ is the admixture of the E2 multipolarity (connectedwith the δ (E2/M3) admixture parameter commonly used in the gamma ray spectroscopy by therelation Δ=δ /(1+δ )). We obtained Δ=1.0±(1.0x10 -6 ) and the χ ν value the same as for the pure E2multipolarity (see Table 2).Finally we performed analysis with both sets of theoretical ICC’s for the assumedmultipolarities, i.e. the pure E2 and the mixture M1+E2 ( in the latter case the theoretical ICC isexpressed as α i =(1 − Δ) α i ( M α i ( E . The results obtained are presented in Table 2. As can beseen from the table, the received χ ν values indicate that the NICC set of the theoretical ICC’s is inbetter agreement with the experiment than the BrICC one. But what is more important, thedifference between the χ ν = 0.89 for the mixed multipolarity M1+E2 and χ ν = 1.18 for the pure E2in the case of the NICC set (and correspondingly χ ν =1.03 and 1.35 for the BrICC set) stronglyindicates that the 9.2 keV transition is of the mixed multipolarity. To prove such a statement, weapplied the statistical method presented in Ref. [23].The essence of this method is as follows: We have a set of experimental values, F = ( F ±σ ,F ±σ , ..., F n ±σ n ). We have also two hypotheses explaining the experiment, f and f , which give thecorresponding theoretical values, f = ( f , f , ..., f n ) and analogically f . We should decide which oneis true, i.e. which one can be rejected. Let us assume f be null hypothesis and we seek theprobability that – rejecting it – we reject the true hypothesis. The method consists of study of theexpression M − M where M i = ∑ j = n ( F j − f ij ) σ j as a function of independent statistical variables F j .The result is, that the probability P to reject the true hypothesis (i.e. f ) is P ≤ [ − Erf ( √ η exp ) ] .Here η exp = M − M evaluated with the experimental values F , i.e. a difference of the χ ’s not normalized for one degree of freedom, and Erf is the error function,
Erf(x) = √ π ∫ x exp ( − t )dt.In our case, f is the hypothesis “mixed multipolarities” and f is “pure E2”. Then η exp =15 . − .
68 = 4.66 (for the NICC set). The probability, that rejecting “pure E2” we reject the truehypothesis is
P ≤ . Th might be of pure E2 multipolarity. We thus conclude that this transition isof the mixed multipolarity of M1 with the admixture Δ=0.41±0.12 (i.e., δ (E2/M1) = 0.695±0.248; |δ(E2/M1)|=0.834±0.210) of E2.
4. Calculations and Interpretation
Th belongs to the Ra-Th isotopic region where octupole correlations are very important fortheoretical description of low-lying excitations (see e.g. [27],[28],[29]). From theoretical point ofview there are two types of approaches for treating the stronger octupole correlations in this region. In the first one it is supposed that octupole correlations of single-nucleon states near theFermi level are sufficiently strong for the formation of stable octupole deformation (e.g. [27],[28], K=1) interaction betweenrotational bands. This mixing is very important for the interpretation of the experimental odd-Anucleus spectrum (see [10],[29],[30]). As concerns nucleus
Th, the interpretation in Ref. [10] wasbased on the calculation of the strongly Coriolis mixed rotational bands built on the lowest K=1/2 + ,K=3/2 + and K=5/2 + intrinsic reflection symmetric states involving octupole vibrational components.This strong Coriolis mixing together with relatively high positive decoupling parameter for theground K=1/2 + rotational band lead to the interpretation of the lowest positive parity levels 0.0 keV,9.2 keV, 77.7 keV and 88.0 keV to be members of the ground rotational band with the non-standardsequence of spins I = 1/2 + , 5/2 + , 3/2 + , and 9/2 + , respectively, and levels 24.3 keV and 127.3 keVbeing 3/2 + - and 5/2 + - members of rotational band built on the lowest K=3/2 + intrinsic state. Thisinterpretation was also in agreement with the former reflection asymmetric mean field calculationsin [27] where the presence of mutually close neutron orbitals with K = 1/2 + and 3/2 + near theneutron Fermi energy was found. However, there are no calculations of Coriolis mixing rotationalbands based on the reflection asymmetric mean field in [27] and in the literature at all.As it was mentioned in the Introduction from experimental point of view the spin-parityascription 1/2 + to the Th ground state, I = 5/2 + for 9.2 keV level and I = 3/2 + for 24.3 keV levelcannot be considered as unambiguous. Nevertheless, from systematic investigation of low-spinspectra of odd-A nuclei from Ra-Th region in the connection with the intrinsic single-neutronscheme near the Fermi level (see e.g. [10] and citations therein) one can expect that at least one ofthe levels 0.0 keV, 9.2 keV, 24.3 keV corresponds to I = 1/2 + . If it is so then the nonzero mixing (E2/M1) obtained in this paper for the transition 9.2 keV (E2/M1)parameters for transitions 24.3 keV + for any of these levels (0.0 keV, 9.2 keV and 24.3 keV) isexcluded. By other word it means that the presence of level with 5/2 + in the lowest part of the Thspectrum is in contradiction with the measured mixing ratios (E2/M1) for transitions mentionedabove. In view of these facts, we tried to modify the Coriolis mixing calculations performed in [10]with the aim to shift the 5/2 + - level above 50 keV in order the levels 0.0 keV, 9.2 keV and 24.3 keVcorrespond to 1/2 + or 3/2 + and in such a way to be consistent with observed mixed E2+M1transitions among them. Simultaneously we want to keep reasonable agreement betweenexperimental and theoretical energies of higher lying levels in Th similarly as was done in [10].We used very similar approach as in [10], that means the Quasiparticle-Phonon Model (QPM) of theintrinsic Hamiltonian with the reflection symmetric Nilsson mean field, monopole pairinginteraction and long-range quadrupole-quadrupole and octupole-octupole residual interaction.Rotational degrees of freedom were described within the standard axially symmetric rotor modelwith Coriolis coupling involved. Detailed description of the model can be found in [26]. In order to obtain more realistic values of deformation parameters and than those used in[10] the equilibrium deformation of the Th (even-even core of
Th) was searched for by theminimizing the Skyrme-BCS total mean field energy with the SV-bas Skyrme interactionparametrization (see [24]) for two situations: i) Only deformation parameters and were allowed to be changed. In this case reflectionsymmetric equilibrium deformation was found.(ii) Deformation parameters and were simultaneously varied. Then the reflectionasymmetric equilibrium values were obtained.Equilibrium values of the total mean field energy for these two cases were practically thesame. This means that it is not possible to conclude if the mean field is reflection symmetric orasymmetric.In the next step the eigen problem of the intrinsic QPM Hamiltonian was solved withdeformation parameters from the case (i) above. The lowest five eigenstates of the intrinsicHamiltonian are listed in the Table 3. One can see that all these eigen states have octupolevibrational components.In the last step the total Hamiltonian in the laboratory frame involving the standard axially-symmetric rotor with Coriolis coupling and fixed inverse moment of inertia, ℏ /2J = 10 keV for allrotational bands was diagonalized (see [26] for details). In the calculation of electromagnetictransitions fixed effective charges (taking into account CoM motion (see [25],[26]) and the value ofthe intrinsic quadrupole moment Q = 821 e fm calculated from the known Th B(E2, +¿¿ → +¿¿ )core transition) and the rotation gyromagnetic factor g R = Z / A were chosen. We then investigated the effect of different Coriolis and recoil attenuation factors, h cor and h rec , on the spin and parity sequences of the lowest states in Th in the laboratory frame. The recoilinteraction pushes (K=3/2 - ) up and the fourth excited intrinsic state (K=1/2 + ) down. For h rec < 0.12we get the 3/2 - ground state, for 0.12 < h rec < 0.64 the 3/2 + ground state (the first excited intrinsicstate) and for h rec > 0.64 the 1/2 + ground state. The sequence of the lowest three states is controlledby h cor . For lower values of h cor there exist two regions with sequences 3/2 + , 1/2 + , and 3/2 + ( h rec ~ 0.4– 0.63, h cor < 0.55) and 1/2 + , 3/2 + , and 3/2 + ( h rec > 0.63, h cor < 0.55 – 0.6). For higher values of h cor one of the two 3/2 + states is replaced by a 5/2 + state. The obtained model energies slightly favor thefirst sequence because for higher values of h rec the lowest 3/2 - state lies too high in energy that is incontradiction with the experimental value of 37.9 keV. However, the theoretical values of theadmixture parameter δ (E2/M1) fit better the second sequence (see Table 4).
4. Conclusion
Highly efficient low-energy nuclear electron spectroscopy technique developed in the JINRDubna was applied for the analysis of the 9.2 keV transition in
Th populated in the - decay of Ac. The mixed multipolarity M1+E2 proved for this transition in the present work together withthe same multipolarity character determined experimentally in Refs. [12] and [16] for the 15.1 keVand 24.3 keV transitions in
Th, respectively, cause doubts for existing spin assignments 1/2 + , 5/2 + and 3/2 + for the lowest levels 0.0 keV, 9.2 keV and 24.3 keV, respectively, of Th (see [10]).Particularly, the assignment /2 + for any of these levels is excluded in such a case.Up to date interpretation of low-lying spectrum of Th is influenced by strong Corioliscoupling of rotational bands built on the lowest intrinsic /2 + or /2 + states which pullsdown the /2 + state (see [10]). We tried to play with parameters of the rotor + QPM Hamiltonian(the same Hamiltonian as in [10]) with the aim to shift the /2 + level up in the spectrum andsimultaneously to keep relatively good agreement of the calculated and experimental spectra also forhigher-lying levels. Particularly, we varied the strength of the Coriolis coupling and found that for areduced strength by the attenuation factor of h cor ~ 0.6 the three lowest states (1/2 + , 3/2 + , and 3/2 + ) re compatible with the present experimental data but we failed to reproduce the position of thelowest negative parity states.In order to prove the new interpretation of the current experimental data it is necessary to usemore precise theoretical approaches, e.g., an approach with the laboratory Hamiltonian involvingCoriolis mixing of rotational bands based on reflection asymmetric intrinsic states (which has notbeen used in practice up to now) and that could solve the problem of the position of the lowestnegative parity states. From experimental point of view more information about low-energytransitions connecting low-lying levels is also desirable (for instance data about E1 transitionsbetween low-lying levels of opposite parity rotational bands with given K because such strong E1transitions are indications of stable octupole deformation). Acknowledgement
We highly appreciate Dr. Balraj Singh (McMaster Univ., Hamilton, Canada) for initiating ofthis investigation, permanent support and valuable discussions. This work was partly supported by Project founded by the MEYS of the Czech Republicunder the contract LTT18021 and by projects founded by the Czech Science Agency (Project No.19-14048S). able 1 Theoretical subshell internal conversion coefficients for the M1, M3 and E2 multipolaritiescalculated in the present work for the 9.245 keV [16] transition in
Th using both the computercode NICC [17] with the potential [18] (for a neutral thorium atom) and the BrICC approach[20,21]. Atomicsubshell M1 M3 E2NICC BrICC NICC NICC BrICCM a a Table 2
The results of the transition multipolarity determination for the 9.2 keV transition in
Th obtainedin the present work using the computer code [22] for two different sets of ICC’s, namely NICC[17,18] and BrICC [20,21].ICC calculations M1 + E2 E2Δ χ ν b ν a χ ν b ν a NICC 0.41±0.12 0.89 12 1.18 13BrICC 0.38±0.11 1.03 12 1.35 13 a ν is the number of degrees of freedom. b χ ν is normalized χ per one degree of freedom. able 3 Energy and structure (single-quasiparticle and quasiparticle + even-even core vibrational phononcomponents) of the lowest five intrinsic excitations (eigenstates of the intrinsic Hamiltonian).Intrinsic state Energy[keV] Structure of intrinsic excitations[individual components with percentage]gr. state K=3/2 -
21 3/2[761] (71%) 3/2[501] (3%) 3/2[642] +Q (15%) 3/2[631] +Q (2%)1-st exc. state K=3/2 +
35 3/2[631] (37%) 3/2[642] (29%) 3/2[761] +Q (17%) 3/2[501] +Q (7%)2-nd exc. state K=5/2 -
69 5/2[752] (53%)5/2[633] +Q (42%)3-rd exc. state K=1/2 +
77 1/2[631] (57%) 1/2[640] (13%) 1/2[761] +Q (9%) 1/2[770] +Q (8%) 4-th exc. state K=1/2 +
127 1/2[640] (47%) 1/2[631] (19%) 1/2[770] +Q (13%) 1/2[510] +Q (9%) Table 4
Comparison of theoretical and experimental values of the admixture parameter δ (E2/M1)Transition Exp. value Theor. value h cor =0.50, h rec = 0.54 Theor. value h cor = 0.59, h rec = 0.809.2 keV → 0 keV 0.695±0.248 1/2 + (8.5 keV) → 3/2 + (0 keV):0.0008 3/2 + (9.2 keV) → 1/2 + (0 keV):0.8124.3 keV → 0 keV 0.0116±0.0004 3/2 + (39.2 keV) → 3/2 + (0 keV):0.0040 3/2 + (40.4 keV) → 1/2 + (0 keV):0.003524.3 keV → 9.2 keV 0.035±0.006 3/2 + (39.2 keV) → 1/2 + (8.5 keV):0.0030 3/2 + (40.4 keV) → 3/2 + (9.2 keV):0.0064 eferences [1] E. Browne, Nucl. Data Sheets B65 , 669 (1992). DOI: 10.1016/0090-3752(92)80016-D[2] G. I. Novikova, E. A. Volkova, L. L. Gol’din, D. M. Ziv, and E. F. Tret’yakov, Zh. Eksp. Teor. Fiz. , 928 (1959); Sov. Phys. JETP , 663 (1960).[3] C.F. Liang, R.K. Sheline, P. Paris, M. Hussonnois, J.F. Ledu, and D.B. Isabelle, Phys. Rev. C, , 2230 (1994). (DOI: 10.1103/PhysRevC.49.2230)[4] C.M. Lederer and V.S. Shirley, Table of Isotopes, 7th ed. (Wiley, New York, 1978).[5] C. Maples, Nucl. Data Sheets , 275 (1977). DOI: 10.1016/S0090-3752(77)80008-2[6] E. Browne, Nuclear Data Sheets , 970 (2001). (DOI:10.1006/ndsh.2001.0016)[7] Filip Kondev, Elizabeth Mc Cutchan, Balraj Singh, Jagdish Tulid, Nuclear Data Sheets for A=227 , 331 (2016). DOI: 10.1016/j.nds.2016.01.002[8] Ch. Briançon, S. Cwiok, S. A. Eid, V. Green, W. D. Hamilton, C. F. Liang, and R. J. Walen, J. Phys. G , 1735 (1990). DOI: 10.1088/0954-3899/16/11/021[9] U. Müller, P. Sevenich, K. Freitag, C. Guünther, P. Herzog, G. D. Jones, C. Kliem, J. Manns, T. Weber, B. Will, and the ISOLDE Collaboration, Phys. Rev. C , 1199 (1995). (DOI: 10.1103/PhysRevC.51.1199 ) [11] G. A. Leander and Y. S. Chen, Phys. Rev. C , 2744 (1988). DOI:10.1103/PhysRevC.37.2744[12] A. Kovalík, А.Kh. Inoyatov, L.L. Perevoshchikov, M. Ryšavý, D.V. Filosofov, J.A. Dadakhanov, Eur. Phys. J. A , 131 (2019). ( DOI: 10.1140/epja/i2019-12812-5) [13] Ch. Briançon, B. Legrand, R.J. Walen, Ts. Vylov, A. Minkova, A. Inoyatov, Nucl. Instrum. Methods , 547 (1984). (DOI: 10.1016/0167-5087(84)90062-0)[14] V.M. Gorozhankin, V.G. Kalinnikov, A. Kovalík, A.A. Solnyshkin, A.F. Novgorodov N.A. Lebedev, N.Yu. Kotovskij, E.A. Yakushev, M.A. Mahmoud and M. Ryšavý, J. Phys. G: Nucl. Part. Phys.
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Th as presented in Ref. [7].
Fig. An example of the L and M subshell conversion electron lines of the 24.3 keV and the 9.2keV transitions, respectively, in
Th (shown without correction for the spectrometer transmissiondependence on the electron retarding voltage [13,14] and the
Th half-life). The spectrum wasmeasured at the absolute instrumental energy resolution of 14 eV and the energy step of 2 eV in twosweeps with the exposition time of 100 s per spectrum point in each sweep. The structure of themeasured conversion electron spectra is complicated by a presence of the MNX group of Augerelectrons of Th (indicated by the oblique lines in the picture).
Fig. 3
An example of the N and L subshell conversion electron lines of the 9.2 keV and 24.3 keVtransitions, respectively, in Th. The spectrometer was set to the 21 eV absolute instrumentalenergy resolution. The spectrum was scanned with the 2 eV step in four sweeps at the expositiontime per spectrum point of 75 s in each sweep. The measured conversion electron lines aresuperimposed on the LMM Auger-electron spectrum of Th. ig. 1 The decay scheme of Ac to
Th as presented in Ref. [7]. ig. An example of the L and M subshell conversion electron lines of the 24.3 keV and the 9.2keV transitions, respectively, in
Th (shown without correction for the spectrometer transmissiondependence on the electron retarding voltage [13,14] and the