PHYSICAL REVIEW C 88, 024317 (2013) Level lifetimes in the stable Zr nuclei: Effects of chemical properties in Doppler-shift measurements E. E. Peters, 1 A. Chakraborty, 1,2,* B. P. Crider, 2 B. H. Davis, 3 M. K. Gnanamani, 3 M. T. McEllistrem, 2 F. M. Prados-Est´ evez, 1,2 J. R. Vanhoy, 4 and S. W. Yates 1,2 1 Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506-0055, USA 2 Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055, USA 3 Center for Applied Energy Research, University of Kentucky, Lexington, Kentucky 40511-8479, USA 4 Department of Physics, United States Naval Academy, Annapolis, Maryland 21402, USA (Received 15 June 2013; published 20 August 2013) The lifetime of the second excited 2 + state of 94 Zr at 1671 keV was determined with the Doppler-shift attenuation method (DSAM) following the (n, n ′ γ ) reaction on scattering samples of Zr metal and ZrO 2 of natural isotopic abundance. The measured lifetime, τ = 368 +27 −23 fs, is considerably longer than the previous measurement, as are measured lifetimes of other levels in 94 Zr. However, lifetimes of low-lying, low-spin states in 90,91,92,96 Zr were also determined and found to be in good agreement with measurements employing non-DSAM methods. Possible reasons for the discrepant lifetimes measured for 94 Zr are discussed and focus on the chemical properties of the scattering sample, specifically, the effects of using amorphous materials, or those composed of small particles as scattering samples. These properties have been investigated by x-ray powder diffraction and scanning electron microscopy. The effects of using these materials for lifetime measurements were investigated by employing, as scattering samples, Zr(OH) 4 (a known amorphous material) and ZrO 2 with various crystalline domain sizes. DOI: 10.1103/PhysRevC.88.024317 PACS number(s): 21.10.Tg, 21.10.Re, 25.40.Fq, 27.60.+j I. INTRODUCTION In the studies of 94 Zr by Elhami et al. [1,2] with the (n, n ′ γ ) reaction, the lifetime of the second 2 + state (2 + 2 ) at 1671 keV was determined to be 183 +13 −12 fs using the Doppler-shift attenuation method (DSAM). With this lifetime, the B (E2) of the transition to the ground state has an unusually large value of 7.8(7) W.u., greater than B (E2; 2 + 1 → 0 + 1 ) of 4.9(11) W.u. [3], distinguishing this nucleus as the only case in which a higher-lying 2 + state has a larger B (E2) to the ground state than the first excited 2 + state. Recent shell model calculations have reproduced the aforementioned inversion of the E2 strengths, although not the magnitudes [4]. To examine this anomaly and the large number of collective excitations observed in 94 Zr, we and others have focused on characterizing this nucleus more fully. For example, we investigated the β − decay of 94 Y into 94 Zr with the powerful arrays for β − , internal conversion electron, and γ -ray detection available at the 8π spectrometer at TRIUMF-ISAC. Our focus was to obtain additional information about the feeding and decay behavior of the 1671-keV 2 + 2 state. The large data set obtained from this experiment has exposed important new information and provides input to reveal the structural behavior of this semimagic nucleus and the role of subshells in shape coexistence [5]. Recently, colleagues informally reported preliminary re- sults from other experiments which indicate the prior lifetime measurements [1,2] were in error [6,7]. Electron scattering measurements at T. U. Darmstadt by Scheck, Pietralla et al. indicate the ratio B (E2; 2 + 2 → 0 + 1 )/B (E2; 2 + 1 → 0 + 1 ) is ap- * Present Address: Department of Physics, Krishnath College, Berhampore 742101, India. proximately 0.9 [6], in agreement with Coulomb excitation measurements by Werner et al. [7]. This B (E2) ratio would re- quire that the lifetime of the 1671-keV level be approximately twice as long as previously reported. These new findings, along with the added significance of the results of the β − decay measurements at TRIUMF, motivated us to re-examine the earlier data [1,2] on the lifetime of the 1671-keV state. Except for a small inaccuracy in the crystalline density used by Elhami et al. [1,2], which would increase the lifetime by a few percent, the analysis was determined to be otherwise valid—i.e., no problems with the previous 94 Zr(n, n ′ γ ) measurements or the data analysis were discovered that would lead to a level lifetime consistent with the new value suggested by Scheck [6] and Werner [7]. In view of these results, however, we felt it imperative to remeasure the lifetime of the 1671-keV 2 + 2 state of 94 Zr and possibly reassess the structure of this nucleus. II. THE DOPPLER-SHIFT ATTENUATION METHOD FOLLOWING INELASTIC NEUTRON SCATTERING While a detailed description of the DSAM following inelastic neutron scattering (INS) can be found in Ref. [8], a few relevant comments are in order. The DSAM-INS measurements rely on careful determinations of γ -ray energy as a function of the detection angle with respect to the direction of the incident neutrons. From this information, the attenuation factor, F (τ ), which describes the slowing-down process of the recoiling nucleus within the material, may be extracted from E γ (θ ) = E 0  1 + F (τ ) v c.m. c cos θ  , (1) where E γ (θ ) is the γ -ray energy as a function of the angle of detection with respect to the direction of the incident neutrons, 024317-1 0556-2813/2013/88(2)/024317(10) ©2013 American Physical Society