PHYSICAL REVIEW C 71, 044303 (2005) Energy of the 3/2 + state of 229 Th reexamined Z. O. Guimar˜ aes-Filho and O. Helene Instituto de F´ ısica, Universidade de S ˜ ao Paulo, CP 66318-CEP 05315-970, S ˜ ao Paulo, Brazil (Received 25 March 2004; revised manuscript received 17 December 2004; published 12 April 2005) 229 Th has an isomeric state of unusually low energy, whose adopted value is by now 3.5(10) eV. This value was determined indirectly, based on several very precise γ -ray energies, between 25 and 217 keV, from the α decay of 233 U. Two recent works suggest that the decay pattern of the transitions that link the low-energy levels of 229 Th is different from that assumed in earlier works, but there also is a difference between them. In this article we investigate the effect on the value determined for the excitation energy of that isomeric state if those different assumptions regarding the γ -ray transitions in 229 Th are considered. We use published data and a statistical method that takes into account both variances and correlations between data. Adopting the statistically most acceptable assumption regarding the decay pattern of 229 Th, we deduced the value of 5.5(10) eV for the excitation energy of that isomeric state, with consequences for both theoretical and experimental studies related to that level. DOI: 10.1103/PhysRevC.71.044303 PACS number(s): 21.10.−k, 23.20.Lv, 27.90.+b INTRODUCTION The existence of a 3 2 + excited state quite close to the 5 2 + ground state of 229 Th was put into evidence about three decades ago [1]. In 1990, the energy difference between these levels was shown to lie below 7 eV (at the 2σ level) [2]. A few years later the excitation energy of the 3 2 + state, hereafter cited as , was determined from a very detailed energy measurement of many γ rays emitted in the α decay of 233 U [2,3]. Thereafter, the accepted value, calculated by Helmer and Reich [3], is  = 3.5(10) eV. This unusually low excitation energy is of great interest in many experimental and theoretical studies, for which the results depend critically on the knowledge of  [4–9]. For instance, the nuclear half-life of the 3 2 + level by an M1 elec- tromagnetic transition depends strongly on . Investigation of the consequence of different  values on the nuclear-spin mixing shows that the 3 2 + half-life, the energy of the emitted photon, and the mixing ratio of the 3 2 + level and the ground state in a hydrogenlike 229 Th 89+ ion also strongly depend on  (see Ref. [4] and others cited therein). If the isomer excitation energy is greater than the ionization potential energy of Th, ∼5.9 eV, the 3 2 + state would rapidly decay to the ground state by internal conversion [7]. Because there is no an unambiguous measurement of the electromagnetic transition from the 3 2 + excited state to the ground state [8,9], the determination of the 3 2 + excitation energy depends not only on the precise measurement of the γ -ray energies, which feed each of those levels, but also on some assumptions about other relevant level energies and the γ -ray transition pattern of 229 Th. Recent experimental and theoretical studies of the nuclear structure of 229 Th [10,11] suggest a pattern of γ -ray transitions different from that assumed in Refs. [2] and [3], but there also is no complete agreement between their claims. Specially, the decays of the 29- and 71-keV levels must be considered. Formerly [2,3], these were assumed to feed only the 3 2 + , whereas the nuclear model calculation of Ref. [10] indicates that both levels decay also to the ground state (see Fig. 1). To study the consequence of the different assumptions on the determination of the excitation energy of the 3 2 + level, we extended the work of Refs. [2] and [3], including more experimental data and new values of standard γ -ray energies [12]. We used the least-squares method in a matrix formalism that considers in the fit the totality of the available experimental information. So, the standard γ -ray energies, the experimental data from Refs. [3] and [13], and the energies of all the relevant levels and γ -ray transitions in the nucleus under study are taken into account on the same footing [14,15]. ANALYSIS The energy of the 3 2 + level was fitted using the same general procedure adopted in Refs. [2] and [3], that is, considering multiple cascade/crossover relations between the γ rays of 229 Th. However, through the matrix formalism [14,15], both the calibration standards and the precise thorium γ -ray energies were considered in an equivalent manner. This method delivers best values, variances, and covariances that are consistent, in a statistical sense, for the whole set of experimental quantities subjected to the fit, as may be retrieved by consulting Refs. [14] and [15]. The use of the covariances is an important upgrading in the statistical analysis with respect to previous work. The level scheme of 229 Th is shown in Fig. 1: those transitions, which are by now well established, are identified by continuous arrows; dashed and dotted lines indicate the transitions that may be allocated to different final states, following the different experimental and theoretical results to be presented later. (The dotted lines correspond to transitions that were not used to the determination of .) The fit was performed using all experimental data from Tables III and V of Ref. [3] and from Table 3 of Ref. [13], after reducing all energy values by 5.8 ppm to update them to the 1986 fundamental constant values [12]. (Data related to the 0556-2813/2005/71(4)/044303(4)/$23.00 044303-1 ©2005 The American Physical Society