Beta-Decay Strength Measurement, Total Beta-Decay Energy Determination, and Decay-Scheme Completeness Testing by Total Absorption γ-ray Spectroscopy *

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1 Physics of Atomic Nuclei, Vol. 67, No. 1, 24, pp From Yadernaya Fizika, Vol. 67, No. 1, 24, pp Original English Text Copyright c 24 by Izosimov, Kazimov, Kalinnikov, Solnyshkin, Suhonen. Proceedings of the International Conference Nuclear Structure and Related Topics Beta-Decay Strength Measurement, Total Beta-Decay Energy Determination, and Decay-Scheme Completeness Testing by Total Absorption γ-ray Spectroscopy * I. N. Izosimov 1)**,A.A.Kazimov 1), V. G. Kalinnikov 2),A.A.Solnyshkin 2), and J. Suhonen 3) Received January 21, 24 Abstract Applications of total absorption γ-ray spectroscopy and its combination with high-resolution nuclear spectroscopy methods for measurements of a β-decay strength function S β (E), determination of the total β-decay energy Q β, and testing of decay-scheme completeness are presented. c 24 MAIK Nauka/Interperiodica. 1. INTRODUCTION Total absorption γ-ray spectroscopy (TAGS) is based on summation of cascade gamma-quantum energies in 4π geometry [1 11]. TAGS may be applied for measurements of a β-decay strength function S β (E), determination of the total β-decay energy Q β, and testing of decay-scheme completeness. The combination of TAGS with high-resolution γ spectroscopy may be applied in studies of S β (E) fine structure as well as in constructing detailed decay schemes [3, 1, 11]. Total absorption spectrometers (TAS) are used in many laboratories and their constructions are based on large-size NaI(Tl) crystals [1 11]. Comparing the TAGS spectra with the existing data on decay schemes, one may estimate the degree of decay scheme completeness. It was shown that more than 3 5% of β decays to the high-lying nuclear levels (i.e., levels with excitation energies higher than 2 3 MeV) in medium and heavy nuclei may not have been identified in decay schemes [1, 5, 7, 1, 11]. The principles of construction of more complete decay schemes by using the combination of TAGS spectroscopy with high-resolution γ spectroscopy are presented for both neutron-deficit (β + /EC decay) and neutron-rich nuclei (β decay). The possibilities of TAGS applications in testing of completeness of decay schemes of fission products and more complete data using decay-heat calculations [6] are discussed. This article was submitted by the authors in English. 1) Khlopin Radium Institute, St. Petersburg, Russia. 2) Dzhelepov Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia. 3) Department of Physics, University of Jyväskylä, Finland. ** izosimov@atom.nw.ru 2. β + /EC- AND β -DECAY STRENGTH FUNCTIONS For the Gamow Teller beta transition, the level occupancy I(E) with the excitation energy E of the daughter nucleus after β + /EC and β decay and the half-life T 1/2 canbewrittenas[1] I(E) =S β (E)T 1/2 f(q E), (1) Q ( ) 1 T1/2 = S β (E)f(Q E)dE, (2) where S β (E) describes the nuclear part of the transition; f(q E) is the Fermi function, which describes the lepton part of the transition; and Q is the total energy of the β decay. The function S β (E) is proportional to the squared matrix elements of β-decay type between the initial i and final f nuclear states S β (E)dE = 1/(ft) (3) E E = [ D(gV 2 ] 1 /g2 A B(GT,E), E B(GT,E)= [ D(gV 2 /ga] 2 /(ft) (4) =4πB ± (GT,E)/gA 2 2 / = I f t ± (k)σ µ (k) I i (2I i +1). k,µ In Eqs. (3), (4), I i and I f are nuclear spins, g A and g V are the constants of the axial-vector and vector components of the β decay, D = 6 ± 7 s, and t ± σ is the product of the isospin and spin operators /4/ $26. c 24 MAIK Nauka/Interperiodica

2 BETA-DECAY STRENGTH MEASUREMENT 1877 The value S β (E) is in units of MeV 1 s 1, whereas B(GT,E) is in ga 2 /4π units and ftis in seconds. The Fermi function f(q E) decreases with increasing E. As a rule, the more intensive beta decays populate the levels with low (lower than 2 3 MeV) excitation energies. But from the nuclear structure point of view, the most interesting beta transitions populate the levels with excitation energies higher than 3 4 MeV, where strong resonances or at least their tails may be observed in S β (E). Also, a lot of nuclear levels and γ transitions may not be identified in decay schemes because of relatively weak beta transitions to the levels with high excitation energies. To study beta transitions to the high-lying levels, total absorption γ spectroscopy may be used [1 11]. The combination of TAGS with high-resolution γ spectroscopy can be applied to study a fine structure S β (E) as well as a detailed decay-scheme construction [3, 4, 1]. To this end, it is necessary to have Z-separated (element separation) and M-separated (mass separation) sources. For nuclei with T 1/2 > 3 min, we applied radiochemistry methods of element separation and after them a mass separator for production of isobaric pure sources [5, 11]. In our experiments, a total absorption γ-ray spectrometer (Fig. 1) is used, which consists of two NaI(Tl) crystals with the sizes 2 11 mm and 2 14 mm. The larger crystal has a 7 8 mm well, into which nuclei under investigation are supplied and where a Si(Au) detector is installed for β-particle detection [5]. Isolating total absorption peaks in the TAS spectrum, one can find the occupancy of levels I(E) and then using (1) (4) find the strength function S β (E) [1, 5]. The end-point energy of the TAS spectrum is related to the total β-decay energy Q β [1 4]. The TAS spectrum and S β (E) can be calculated from decay-scheme data. For decay-scheme construction, high-resolution nuclear spectroscopy methods are used [11]. Comparing the TAGS spectroscopy data (TAS spectrum and S β (E)) with the data obtained from decay schemes, one may estimate the degree of decay-scheme completeness and determine the energy regions where a decay scheme is not sufficiently complete [1, 3, 7, 1]. Beta-decay strength functions S β (E) for β + /EC and β decays are schematically shown in Fig. 2. The strength functions of β + /EC and β Gamow Teller decays are qualitatively different [1]. According to the Ikeda sum rule [12], the total sums S + and S are related to each other as S S + 3(N Z), where S ± = i B ±(GT,E i ). The total sum of β transitions in N>Znuclei is larger than that for Beam of nuclei Tape X Y PMT NaI(Tl) Be D NaI(Tl) PMT Fig. 1. Total absorption γ-ray spectrometer: D βparticle detector, X X-ray detector, Y γ-ray detector. β + /EC transitions. However, a large part of the total strength of β transitions is concentrated in the Gamow Teller resonance with µ τ = 1 (i.e., in the state which is a coherent superposition of simple excitations with isospin projection µ τ = 1, e.g., proton-particle neutron-hole ones) and is out of the Q β energy window, where the observed strengths of β + /EC decay and β decay may be comparable. The Gamow Teller resonance with µ τ = 1 is in principle unattainable in β decay of N>Znuclei, whereas the Gamow Teller resonance with µ τ =+1 or its tail may be observed in β + /EC decay of N> Z nuclei. In β decay of N>Znuclei, so-called satellites ofthegamow Teller resonance (back spinflip and/or core polarization states) may be observed (Fig. 2). 3. β + /EC DECAY Using our TAGS spectrometer, we detected [3, 5, 1] the Gamow Teller resonance with µ τ =+1 (Fig. 3) in g Tb (T 1/2 1.6 h) as a strong peak at E 4 MeV. The β + /EC transitions to levels with excitation energies higher than 2 MeV were not identified in the decay scheme (Fig. 4) from [13]. This means that the decay scheme of g Tb (T 1/2 1.6 h) in [13] is very incomplete. The more complete decay scheme of g Tb (T 1/2 1.6 h) was constructed in [11] (Fig. 5). The most interesting region for study of the beta-strength function is at an excitation energy higher than 3 4 MeV. The β + /EC-decay strength function (Fig. 6) deduced from the more complete decay scheme was constructed in [3, 1]. The strength functions (Figs. 3 and 6) are in good

3 1878 IZOSIMOV et al. τ = 1, µ τ = +1 τ = 1, µ τ = 1 SF SF CP BSF j < j < j > j j j > j < j > p n p n p n p n GT(T > ) GT(T < ) GT (n, p) (p, n) SF IAR ZA N CP SF β + /EC β BSF Z 1A N +1 Z + 1 A N 1 Fig. 2. Aschemeofβ-decay strength function in nuclei with N>Z. The strength function of Fermi-type transitions is concentrated at the isobar-analog resonance (IAR). The components of the Gamow Teller resonance with different isospins (T <, T >)andtheconfigurations forming the strength function of Gamow Teller β transitions are indicated [1, 1]. BSF is abackspin-flip configuration; CP, a core polarization configuration; SF, a spin-flip configuration. Isovector excitations are characterized by isospin τ and isospin projection µ τ ( denotes a particle, and denotes a hole). S β+ec (E), 1 6 MeV 1 s TAS detector Energy, MeV Fig. 3. The β + /EC-decay strength function for g Tb (T 1/2 1.6 h) deduced from the TAGS spectra [3, 5, 1]. The Gamow Teller µ τ =+1resonance was observed as astrongpeakate 4 MeV. agreement and one may conclude that the decay scheme of g Tb (T 1/2 1.6 h) β + /EC decay in [11] is sufficiently complete. This demonstrates that the decay schemes for transitions to the levels with excitation energies higher than 2 3 MeV in medium and heavy nuclei may be very incomplete. To estimate the degree of incompleteness of the decay scheme by using TAGS spectroscopy, it is necessary to have Z- and M-separated sources and about one day for measurements and data analysis. For detailed decayscheme construction, it is necessary to have a much longer time of measurements and data analysis. Theoretical analysis of the observed Gamow Teller resonance with µ τ =+1and its fine structure was done in [3]. Only qualitative agreement between experimental and theoretical fine structure (Fig. 6) was observed. Theory predicts more strength than was experimentally observed. This is a typical situation for both β + /EC and β decays. In β + /EC-decay of g Tb, not all the strength is in Q EC window. For a more detailed analysis of β + /EC-decay strength in this region, experimental data on S β (E) in nuclei,

4 BETA-DECAY STRENGTH MEASUREMENT h (1/2 + ) 65 Tb ~.42 ps <.2 ns <.2 ns <.2 ns (1/2) (1/2) + 7/2 + (1/2) + 3/ M M E M1 + E E M E E Q EC = 469 5% 2.5% 4.7% 1.4% 9.8% 23% h 7/2 64 Gd Fig. 4. g Tb decay scheme from [13]. The β + /EC transitions to the region where the excitation energy is higher than 2 MeV are not indicated. This decay scheme is not complete and does not agree with TAGS data. (Level energies and Q EC are in kev.) where all the β + /EC strength lies within the Q EC window, are needed. Such a possibility exists for β + /EC decays of 145,143,141 Tb nuclides. The end point of the TAS spectrum is connected with the total energy Q β of the β decay. TAG spectroscopy can be used for measurements of Q β with accuracy up to 2 kev [1, 4]. As a rule, the most informative region for determination of the TAS spectrum end point has a low counting per channel and determining it directly is very difficult. The part of the TAS spectrum with sufficiently high statistics is not so informative for this purpose. So there is an optimal interval of the TAS spectrum for a determination of Q EC.Weusetheχ 2 criterion for selecting the optimal energy interval [4]. In the fitted region, the errors of the intensity determination δi were more than the maximum value of the pileup spectrum intensity. The results of determination of Q EC from TAS spectra of β + /EC decay of 156 Ho (T 1/2 56 min) using the maximum-likelihood method [4] are presented in Figs. 7 and 8. The obtained value Q EC = 5.5 ±.2 MeV for 156 Ho (T 1/2 65 min) is in good agreement with the systematics [14]. 4. β DECAY, COMPLETENESS OF DECAY SCHEMES OF FISSION PRODUCTS, AND DECAY-HEAT CALCULATIONS The population of levels at excitation energies higher than 2 3 MeV after β decay is related to the resonance structure in S β (E) (Fig. 2). Information about the β -decay strength function and the possibility of testing decay-scheme completeness is very important for correct calculations of decay heat especially for fission products [6]. The β-andγ-decay energies realized through the natural decay of fission products may exhaust up to 13% of the total energy generated during the fission process and becomes a dominate component following a reactor shutdown [6, 15]. This energy source is commonly called decay heat. There exist some discrepancies between calculations of decay heat with different libraries like JNDC, JEF2.2, ENDF/B-VI and experiments connected with γ and β radiation of the fission products. This discrepancy is seen in equivalent studies of 239 Pu (Fig. 9) and 233,235,238 U fission products [6, 15]. Correct calculations of decay heat is a very important factor in operation with radioactivity. In [7], by using TAG spectroscopy, it was demonstrated that more than 5% of the intensity of β decay to high-lying states was not identified for some fission products in nuclear spectroscopic studies. To improve agreement between calculations and experiments, more complete decay schemes of fission products are needed. The combination of TAGS with highresolution nuclear spectroscopy methods may be effectively used for construction of more complete decay schemes of fission products and understanding of the reason of the γ discrepancy in decay heat (Fig. 9). 5. CONCLUSION In many fundamental and applied studies, sufficiently complete decay schemes of nuclei and data

5 188 IZOSIMOV et al. (a) + (3/2 5/2) (3/2 5/2) (3/2 5/2) + + 5/2 5/2 (3/2 5/2) (5/2 7/2) (5/2) 5/2 1/2 1/2 + 5/2 + 1/2 + 3/ E E E M1+E E M E M E M M M (M1) E (M1) (M1) E M (M1) (M1) M E E E Tb 1/ h EC + β (3) 7. 7/ h EC + β + (b) (1/2) (1/2) (1/2) (1/2 ) (1/2 + 3/2 ) (3/2) (1/2+) (1/2 + ) (3/2 5/2) (3/2 5/2) ( 5/2 + ) (1/2 + ) 5/2 5/2 + (1/2 + ) (3/2 5/2 ) (5/2 7/2) (5/2 ) Gd (M1) E [kev]. I EC+β [%] log (ft) 1/ Tb 1.64 h /2 + 1/2 1/2 + 5/2 + 1/2 + 3/2 7/2 64 Gd E [kev] I EC+β [%] log (ft) Fig. 5. g Tb decay scheme from [11]. (a) Low energy levels of Gd. (b)highenergylevelsof Gd. There are many β +/EC transitions to the region where the excitation energy is higher than 2 MeV. This decay scheme is quite complete and is in good agreement with the TAGS data.

6 BETA-DECAY STRENGTH MEASUREMENT 1881 B(GT), g A 2 /4π.18 Experiment Q EC = 4.6 MeV.14 (a) B(GT) =.12 in energy window 4.43 MeV B(GT), g A 2 /4π Theory B(GT) = (b) Energy, MeV Fig. 6. (a) A strength function S β (E) of β + /EC decay deduced in [3, 1] from the more complete decay scheme [11]. (b) A theoretical fine structure of S β (E) [3]. Intensity 2 (a) Intensity 4 (b) Calculation Experiment Energy, kev Fig. 7. Experimental (a)andfitted (b)tasspectraof 156 Ho (T 1/2 56 min) β + /EC decay. on S β (E) and Q β are needed. This information may be obtained by using TAGS or TAGS in combination with high-resolution nuclear spectroscopy methods. The degree of decay-scheme incompleteness may be quite high at excitation energies higher than 2 3 MeV in medium and heavy nuclei. The degree of the decay-scheme completeness and energy regions where the decay scheme is incomplete can be effectively estimated by a comparison of the experimental TAS spectra with the TAS spectra calculated from the decay scheme and by a comparison of the β-decay strength functions deduced from the TAS spectra and the decay scheme. For a more complete decay-scheme construction, the combination of TAGS with high-resolution γ-spectroscopy methods must be used. To use TAG spectroscopy, it is necessary to have both Z(element)- and M(mass)-separated sources.

7 1882 IZOSIMOV et al. χ (a) Q EC, kev (b) % limit 5 54 Q EC, kev ln of likelihood function Parabola 95% C.L. Fig. 8. (a) χ 2 and (b) natural logarithm of a likelihood function versus the total EC energy in 156 Ho. The number of degrees of freedom for the fitted region is ν = 15, χ 2 min/ν =.81. Decay heat ft(t), MeV/fission Yayoi ORNL Lowell JNDC-V2 (thermal) JNDC-V2 (fast) JEF2.2 (thermal) ENDF/B-6 (thermal) Cooling time, s Fig. 9. Gamma-decay heat (multiplied by cooling time) for 239 Pu fission products as a function of cooling time after fission [6]. The curves represent results of calculations using a different database. There is a γ discrepancy in the cooling period 3 3 s. Results are from [6, 15, 16] and references therein. ACKNOWLEDGMENTS This work is supported by the Russian Foundation for Basic Research, project nos and REFERENCES 1. Yu.V.Naumov,A.A.Bykov,andI.N.Izosimov,Fiz. Elem. Chastits At. Yadra 14, 42 (1983) [Sov. J. Part. Nucl. 14, 175 (1983)]. 2. G. D. Alkhazov, A. A. Bykov, V. D. Witmann, et al., Nucl. Phys. A 438, 482 (1985). 3. I. N. Izosimov, V. G. Kalinnikov, A. A. Solnyshkin, and J. Suhonen, Phys. Part. Nucl., Lett., No. 2 [11], 4 (2). 4. I. N. Izosimov, A. A. Kazimov, V. G. Kalinnikov, and A. A. Solnyshkin, Phys. Part. Nucl., Lett., No. 4 [111], 36 (22). 5. I. N. Izosimov, V. G. Kalinnikov, M. Yu. Myakushin, et al.,j.phys.g24, 831 (1998). 6. A. Algora, J. L. Tain, B. Rubio, et al., JYFL-177 Proposal (22). 7. R. C. Greenwood, R. G. Helmer, M. H. Putnam, and K. D. Watts, Nucl. Instrum. Methods Phys. Res. A 39, 95 (1997).

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