A fast-timing study of neutron-rich yttrium nuclei has filled in several missing lifetime measurements used to examine changes in nuclear shape and configuration. The measurements cover 16 excited states in 93Y, 95Y, 97Y and 99Y, and the results place four states once known only to have lifetimes below 2 to 4 nanoseconds in the low-picosecond range. Five of the measured lifetimes had not previously been known.
The work addresses whether competing shapes and configurations can be tracked as yttrium approaches neutron number 60. The paper compares the new measurements with calculations based on the interacting boson-fermion model with configuration mixing, known as IBFM-CM. That framework treats odd-A yttrium as one unpaired proton coupled to monopole and quadrupole bosons, while allowing normal and intruder configurations to mix through off-diagonal interactions.
The clock inside an excited nucleus
The experiment used fast-timing gamma-ray coincidence spectroscopy with fast scintillation detectors at the LOHENGRIN recoil separator. Lifetimes were extracted with the generalized centroid difference method, which compares the timing centroids of delayed and anti-delayed spectra after accounting for the detectors' energy-dependent prompt response.
Because some signals were weak or background-sensitive, several lifetimes were reported as upper limits rather than precise central values. The 97Y results also included a tentative question-mark state, while other investigated levels had uncertain or tentative assignments. These qualifications matter when lifetime measurements are converted into transition strengths.
What the four isotopes revealed
In 93Y, the adopted lifetimes were no more than 5 picoseconds for the first 3/2− state, 16(5) picoseconds for the first 5/2− state and 15(3) picoseconds for a tentative level. In 95Y, the corresponding results were no more than 9 picoseconds, 27(2) picoseconds and no more than 15 picoseconds. An ionization-chamber-gated analysis gave 29(3) picoseconds for the first 5/2− state in 95Y.
The 97Y results were no more than 11 picoseconds for a state assigned as 3/2− or 5/2−, 24(4) picoseconds for the first 5/2+ state, no more than 10 picoseconds for a tentative state, 15(7) picoseconds for the first 13/2+ state, no more than 10 picoseconds for a 1/2+ or 3/2+ state, and no more than 13 picoseconds for the first 17/2+ state.
In 99Y, adopted lifetimes were 64(10) picoseconds for the 7/2+ state, 28(9) picoseconds for the 9/2+ state and no more than 14 picoseconds for the 11/2+ state. A 29(6)-picosecond result for the 13/2+ state was not adopted because slight contamination was reported for the 272.9- and 269.6-kiloelectronvolt transitions.
As a check, the paper reports that every measured lifetime was consistent with earlier measurements within one standard deviation. The study therefore adds five previously unknown lifetimes while moving four former nanosecond-scale limits into the low-picosecond range, although some results remain limits rather than precise lifetime determinations.
A model of mixed nuclear shapes
The calculations suggest that 97Y does not have one simple structural character across its low-lying positive-parity states. The 9/2+ and 11/2+ states were calculated to be 98.2% and 98.9% normal, while the 5/2+ and 13/2+ states were 93.4% and 83.8% intruder. Selected calculated electric-quadrupole transition strengths were 4.41, 31.43 and 5.8 Weisskopf units, the transition-probability unit used in the paper.
For negative-parity transitions in 93Y and 95Y, the calculation gave a magnetic-dipole strength of about 0.66 Weisskopf units for the 3/2− to 1/2− transition, while values obtained by assuming a purely magnetic-dipole transition were smaller. For the 5/2− to 3/2− transitions, the calculated electric-quadrupole strengths were 1.25 and 1.27 Weisskopf units. The authors report agreement after applying assumed mixing ratios of 0.341 and 0.112, treating the transitions as mixtures of different electromagnetic types.
The comparison in 99Y was more favorable for one key transition. Its experimental electric-quadrupole strength was 45 with an upper uncertainty of 23 and a lower uncertainty of 13 Weisskopf units, compared with a calculated 58 Weisskopf units, and the paper reports the two as consistent. Calculated in-band strengths ranged from 108 to 190 Weisskopf units, while assumed mixing ratios of 0.118 and 0.233 were used for other transitions.
Why neutron number 60 matters in the paper
The authors interpret 99Y at neutron number 60 as having a 5/2+ intruder rotational-band head. In their reading, two structural changes occur together: a crossing between normal and intruder configurations, described as a Type II quantum phase transition, and an evolution of the intruder configuration from more spherical to more deformed, described as Type I. They call the combination an intertwined quantum phase-transition scenario.
That conclusion is a model-based interpretation, not a unique reading of the raw timing data. Many transition probabilities depend on assumed multipolarities or mixing ratios, and the calculations do not remove the uncertainty around every state assignment. The study covers yttrium only through 99Y, so it cannot show how the pattern develops in more neutron-rich isotopes. Better statistics, firmer spin and parity assignments, direct mixing-ratio measurements and wider calculations are needed to test the picture further.
Preprint status
The document is an arXiv preprint, version 1, dated 28 August 2026, and is identified as arXiv:2608.28259. It states that the recorded experimental data can be found in references 34 to 36. The work was supported by the Deutsche Forschungsgemeinschaft under grants JO 391/18-1 and JO 391/18-2, with the ILL nuclear-reactor team acknowledged.
Paper data and sources
Original title: Lifetime measurements in neutron-rich odd-A yttrium isotopes ($^{93-99}$Y): Investigation of shape coexistence and the intertwined quantum phase transition
Authors: A. Pfeil, N. Gavrielov, U. Köster et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text