Isolated one-phonon mixed-symmetry 2+ state of the radioactive neutron-rich nuclide 132Te

A. N. Ionescu; C. Costache; C. M. Nickel; C. R. Nita; G. Rainovski; H. Mayr; I. E. Dinescu; K. E. Ide; L. Stan; N. M\u{a}rginean

REVIEW 2 major objections 5 minor 44 references

Isolated one-phonon mixed-symmetry 2+ state of the radioactive neutron-rich nuclide 132Te

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The 1665-keV second 2+ state of 132Te is the one-phonon mixed-symmetry state, established by a direct lifetime measurement and a strong M1 decay to the first 2+ state.

desk verdict Direct lifetime measurement resolves a 30-fold ambiguity and likely pins down 132Te's mixed-symmetry state, but an unaddressed ~2.5σ tension with the old Coulomb-excitation lower limit keeps the quantitative claim from being airtight. read the letter →

arxiv 2501.01436 v2 pith:VN2OQIBU submitted 2024-12-20 nucl-ex

T. Stetz , H. Mayr , V. Werner , N. Pietralla , Y. Tsunoda , T. Otsuka , G. Rainovski , T. Beck

show 15 more authors

R. Borcea S. Calinescu C. Costache I. E. Dinescu K. E. Ide A. N. Ionescu P. Koseoglou R. Lica N. Mărginean R. E. Mihai C. M. Nickel C. R. Nita L. Stan S. Toma R. Zidarova

This is my paper · ORCID

classification nucl-ex

keywords mixed-symmetrystateone-phonon2+132TeDoppler-shiftattenuationmethodB(M1)transitionstrengthN=80isotonesshellmodelneutron-richnuclei

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports a direct lifetime measurement of the second-excited $2^+$ state of the neutron-rich nucleus $^{132}\mathrm{Te}$, obtaining $\tau(2^+_2)=0.92(7)$ ps via the Doppler-shift attenuation method in a two-neutron transfer reaction. Combined with the known branching ratio, this gives $B(M1;2^+_2\to2^+_1)=0.18(2)\,\mu_N^2$, a magnetic dipole strength of the size expected for a one-phonon mixed-symmetry state. The paper argues that this strength, together with shell-model wave-function phases, unambiguously identifies the 1665-keV $2^+_2$ state as the isolated one-quadrupole-phonon mixed-symmetry $2^+$ state, with the neighboring $2^+_3$ state carrying essentially no $M1$ strength. If correct, $^{132}\mathrm{Te}$ is the smallest valence space -- two valence protons and two neutron holes -- in which a one-phonon mixed-symmetry state has been established, fixing a benchmark for proton-neutron collectivity near the doubly magic $^{132}\mathrm{Sn}$.

What carries the argument

The identifying mechanism is the magnetic dipole matrix element between the first two $2^+$ states: a one-phonon mixed-symmetry state is recognized by its strong $M1$ decay to the symmetric one-phonon state, with a matrix element near $1\,\mu_N$, whereas fully symmetric states decay only weakly by $M1$. Formally, the paper uses the two-configuration mixing scheme $|2^+_1\rangle=\alpha|2^+_\pi\rangle+\beta|2^+_\nu\rangle$ and $|2^+_{1,\mathrm{ms}}\rangle=-\beta|2^+_\pi\rangle+\alpha|2^+_\nu\rangle$, where the proton and neutron quadrupole excitations add in phase for the symmetric state and out of phase for the mixed-symmetry state. The experimental tool is a Doppler-shift attenuation lifetime measurement following a two-neutron transfer reaction, with the recoil velocity history simulated from stopping powers and the $\gamma$-ray line shapes fitted to extract $\tau(2^+_2)$. Shell-model wave functions then provide the phase analysis that connects the measured $B(M1)$ to the isovector character.

What would settle it

An independent measurement of the 1665-keV state's lifetime by a different method, such as recoil-distance Doppler shift after a fusion or transfer reaction, that yields a $B(M1;2^+_2\to2^+_1)$ outside roughly $0.1$--$0.3\,\mu_N^2$ would contradict the assignment, as would a measured $g$ factor of the $2^+_2$ state far from the shell-model value of about $0.36$.

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Extended reading notes

Core claim

The paper's central claim is that the $2^+_2$ state of $^{132}\mathrm{Te}$ at 1665 keV is the one-quadrupole-phonon mixed-symmetry state, the isovector counterpart of the fully-symmetric one-phonon $2^+_1$ state. In the two-configuration picture, these states are orthogonal combinations of a proton-quadrupole phonon and a neutron-quadrupole phonon, and the mixed-symmetry state is characterized by a large $M1$ decay to the symmetric state. The measured $B(M1;2^+_2\to2^+_1)=0.18(2)\,\mu_N^2$, derived from a directly measured lifetime of $0.92(7)$ ps, matches that fingerprint, and the $2^+_3$ state at 1788 keV has $B(M1;2^+_3\to2^+_1)<0.013\,\mu_N^2$, showing the strength is concentrated in one state. Shell-model calculations with a modern effective interaction reproduce the level energies and transition strengths, and a wave-function analysis shows the $2^+_1$ and $2^+_2$ states share the same dominant proton-neutron configurations with opposite relative phases -- the signature of isoscalar versus isovector character. The paper further places this result at the endpoint of an $N=80$ isotopic trend in which the $M1$ and $E2$ strengths of the mixed-symmetry state decrease toward the $Z=50$ shell closure.

Load-bearing premise

The result stands on the Doppler-shift analysis assuming that the simulated stopping of $^{132}\mathrm{Te}$ recoils in the $^{130}\mathrm{Te}$ target and $^{181}\mathrm{Ta}$ backing is accurate; if the true stopping powers differ by more than the 5% electronic and 10% nuclear variations already included in the systematics, the lifetime and hence the $B(M1)$ value, and with it the identification, would shift.

Editorial extensions

If this is right

The $2^+_2$ state of $^{132}\mathrm{Te}$ is established as the main fragment of the one-phonon mixed-symmetry state, with the $M1$ strength concentrated in it rather than shared with the nearby $2^+_3$ state.
The measured upper limit on the mixing matrix element, $V_{\mathrm{mix}}\le31$ keV, shows that mixed-symmetry and fully-symmetric configurations remain nearly unmixed even when their energies are within about 120 keV.
Along the $N=80$ isotones, the $B(M1;2^+_{\mathrm{ms}}\to2^+_1)$ and $B(E2;2^+_{\mathrm{ms}}\to0^+_1)$ strengths decrease toward $Z=50$, with $^{132}\mathrm{Te}$ showing the lowest values.
The shell-model reproduction of the $^{132}\mathrm{Te}$ data benchmarks the effective interaction in a minimal valence space, supporting its use for nearby neutron-rich isotopes relevant to the $r$-process.
A lifetime measurement of the $N=84$ nucleus $^{136}\mathrm{Te}$ would test whether the same minimal-valence-space pattern of isolated mixed-symmetry strength appears with two valence protons and two valence neutrons.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial extension: The near-perfect opposite-phase structure of the two leading configurations suggests $^{132}\mathrm{Te}$ may be the cleanest two-configuration mixed-symmetry case known; measuring the $g$ factor of the $2^+_2$ state would directly test the predicted proton-neutron balance beyond the $B(M1)$ value.
Editorial extension: Because the mixing upper limit was derived under the idealized assumption of zero $M1$ strength between fully symmetric states, the true mixing is likely smaller than 31 keV, implying an even purer mixed-symmetry character than the limit suggests.
Editorial extension: The successful shell-model description in this minimal space invites predictions for $^{136}\mathrm{Te}$ and other $N>82$ tellurium isotopes; a deviation there would signal missing collectivity relevant to the $r$-process path.
Editorial extension: The data do not directly constrain the $2^+_2\to0^+_1$ $E2$ strength beyond an upper limit; a dedicated Coulomb-excitation experiment with a $^{132}\mathrm{Te}$ beam could measure this small $E2$ directly, providing a further test of the destructive-interference prediction.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Johan, you should know two things. First, this paper reports the first direct DSAM lifetime of the 2+2 state in 132Te, τ = 0.92(7) ps, giving B(M1; 2+2→2+1) = 0.18(2) μN^2. That replaces the absurd literature value of 5.4(35) and, more importantly, it is the first quantitative M1 strength for a mixed-symmetry candidate in a radioactive neutron-rich nucleus. Second, the new value sits ~2.5σ below the lower limit B(M1) > 0.23 μN^2 that the same group's earlier Coulomb-excitation paper (Ref [12]) placed on the same transition, and the manuscript never explains why. That is a real soft spot, not a nitpick.

What is genuinely good: the measurement is mature. They gate on the 2+1→0+1 transition, use a multiplicity filter to suppress feeding, see no feeding transitions, fit forward and backward rings simultaneously, and bound the mixing ratio δ < 0.38 so the M1 extraction is robust. The 2+3 lifetime and the fragmentation limit (< 0.013 μN^2 to 2+1) are new and useful; the mixing calculation gives Vmix ≤ 31 keV, consistent with prior N=80 systematics. The shell-model comparison is honest: SN100PN with standard effective charges reproduces energies and g(2+1) well, overpredicts the new B(M1) by ~50%, and the authors note an alternative g-factor choice would bring it down. That is fine, but it underscores that the theoretical side carries no error bars and inherits effective operators from fits.

The load-bearing issue is the discrepancy. The old lower limit came from detection sensitivity, so it is a one-sided statement, and one-sided limits from low-statistics experiments can overclaim. But the authors know this number, cite it in the introduction, and then never reconcile it. If the old limit is right, the DSAM lifetime is systematically too long by more than 25%, meaning the SRIM stopping-power uncertainties (varied by 5% electronic, 10% nuclear) are underestimated. If the new lifetime is right, the old limit must be flawed, and it would be good to say how. Either way, the qualitative assignment of 2+2 as the one-phonon mixed-symmetry state survives: 0.18 μN^2 is still large, the E2 to ground is small, and the wave-function analysis supports the proton-neutron phase structure. But the claim of "unambiguous" quantitative identification is not yet airtight.

Data are not public, so independent reanalysis is impossible. That is a minor limitation for a beam experiment, but worth saying.

Who should read this: anyone working on mixed-symmetry states, N=80 systematics, or shell-model M1 operators near 132Sn. It deserves a serious referee. My recommendation: engage with it, but send it back with a request to either reconcile the Ref [12] limit or explicitly soften the "unambiguous" language.

Referee Report

2 major / 5 minor

Summary. The paper reports a Doppler-shift attenuation lifetime measurement of the 2+2 (1665 keV) and 2+3 (1788 keV) states of 132Te populated via the 130Te(18O,16O) two-neutron transfer reaction. The measured lifetime of the 2+2 state, tau = 0.92(7) ps, is combined with a branching-ratio upper limit (<2.4%) and a bound on the E2/M1 mixing ratio (delta < 0.38) to obtain B(M1; 2+2 -> 2+1) = 0.18(2) mu_N^2. On this basis, together with shell-model calculations, the authors identify the 2+2 state as the one-quadrupole-phonon mixed-symmetry state of 132Te, report a small upper limit for fragmentation into the 2+3 state, and discuss the N = 80 isotonic trends of M1 and E2 strengths.

Significance. If the B(M1) result is correct, the paper provides the first direct, quantitative M1 strength for the lowest mixed-symmetry 2+ state in 132Te, the smallest valence space (two protons, two neutron holes) in which an isolated one-phonon mixed-symmetry state is established. The experimental work contains several careful checks: a multiplicity filter to suppress feeding, no observed feeding transitions, a simultaneous line-shape fit with contaminants, and a bounded mixing ratio. The shell-model analysis adds wave-function phase information that supports the mixed-symmetry assignment. However, the new B(M1) is in tension with the previous Coulomb-excitation lower limit B(M1) > 0.23 mu_N^2 from Ref. [12], and the manuscript does not address this tension. The qualitative mixed-symmetry identification would probably survive either resolution, but the quantitative claim and the 'unambiguous' wording are not yet secure.

major comments (2)

[Section IV and Table II] The new value B(M1; 2+2 -> 2+1) = 0.18(2) mu_N^2 is below the lower limit B(M1) > 0.23 mu_N^2 from the Coulomb-excitation work of Ref. [12] by about 2.5 sigma (difference 0.05, quoted uncertainty about 0.02). The manuscript quotes both values in Table II but never discusses their compatibility. If the old detection-limit bound is valid, the DSAM lifetime is too long by more than 25%, which would point to an underestimated stopping-power systematic; if the new lifetime is correct, the basis of the old bound should be re-examined. Because the abstract and conclusion rest on a directly measured quantitative B(M1) and an 'unambiguous' identification, this unresolved discrepancy is load-bearing. The authors should add a quantitative reconciliation, or state explicitly under which assumptions the two results can be compared.
[Section III] The systematic uncertainty on the DSAM lifetime is estimated by varying the electronic and nuclear stopping powers by 5% and 10%, respectively. Given the tension with Ref. [12], these ranges may be narrower than the actual uncertainty of the SRIM stopping-power calculation. The authors should justify the 5%/10% ranges, ideally by benchmarking the DSAM lifetime on a state with an independently known lifetime in the same target/backing combination, or enlarge the systematic uncertainty to cover the Coulomb-excitation lower limit.

minor comments (5)

[Section IV] The sentence 'The magnetic moment operator operator ...' contains a duplicated word 'operator'.
[Section IV] The phrase 'fully-symmetric and mixed-symmteric 2+ configurations' contains a typo: 'mixed-symmteric' should be 'mixed-symmetric'.
[Reference [33]] The author name 'N. Schimizu' should be 'N. Shimizu' for consistency with the KSHELL code reference.
[Abstract] The abstract states that the result is 'in agreement with shell-model calculations', but the adopted SN100PN calculation gives B(M1) = 0.27 mu_N^2, about 50% above the measured value of 0.18(2); the text itself acknowledges this excess. Please rephrase to avoid overstating the agreement.
[Section III and Table II] Please clarify how the 0.01 mu_N^2 systematic uncertainty from the unknown mixing ratio is derived. For the quoted bound delta < 0.38, the M1 fraction is >87%, which would reduce B(M1) by roughly 0.02 mu_N^2 relative to a pure-M1 assumption, larger than the stated systematic.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the B(M1) value is derived from a direct DSAM lifetime measurement and is not an input to the shell-model comparison that is used as confirmation.

full rationale

The central claim rests on the lifetime tau(2+2)=0.92(7) ps extracted from Doppler-shift line shapes with APCAD/StopSim; B(M1;2+2->2+1)=0.18(2) uN^2 then follows from the lifetime, the measured <2.4% ground-state branching-ratio upper limit, and the bounded mixing ratio delta<0.38. None of these inputs is the mixed-symmetry assignment itself or a shell-model prediction. The shell-model calculations enter after the experimental value: effective charges and g factors are adopted from Ref. [30] rather than fitted to the new data, and the paper explicitly reports that the calculation overpredicts B(M1) by about 50%, with a post-hoc alternative g-factor choice that would improve agreement to 0.19 uN^2. That alternative is a comment, not the source of the measurement. Self-citations (Refs. [5,12,14,18,25]) provide context, analysis software, and prior data; the new result is not forced by them. In fact, the measured 0.18(2) sits below the prior Coulomb-excitation lower limit >0.23 from Ref. [12], so the present paper does not simply reproduce its cited input; the unaddressed discrepancy is a physical compatibility concern, not evidence of circularity. No equation in the paper reduces the target B(M1) to an assumed mixed-symmetry property, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The experimental B(M1) is extracted from measured lifetimes and branching-ratio limits, not from fitted parameters. The shell-model comparison inherits effective charges and g factors from prior literature; the DSAM result rests on stopping-power and no-feeding assumptions with quantified systematics.

free parameters (3)

Proton effective charge e_pi = 1.7e
Adopted from prior shell-model studies in this region (Refs [34,35]); used for all E2 transition strengths and wave-function matrix elements. Not fitted in this paper.
Neutron effective charge e_nu = 0.8e
Adopted from the same regional fits; enters the E2 strengths and the classification of configurations.
Effective g factors (g_l,eff, g_s,eff, g_p,eff) = Adopted from Ref [30]
Used for M1 strengths and g factors. The paper notes that a different set (free g_l, g_s quenched by 0.7) would bring the calculated B(M1) from 0.27 to 0.19 mu_N^2, closer to data, which shows sensitivity of the comparison.

assumptions (4)

domain assumption SRIM/StopSim stopping powers accurately describe the slowing of 132Te ions in the 130Te target and 181Ta backing.
DSAM line shapes depend on the velocity profile; systematic uncertainties were probed by varying stopping powers by 5%/10%, but the simulation itself is assumed valid. Section III.
domain assumption No significant unobserved feeding populates the 2+2 state.
No feeding transitions were observed, and a multiplicity filter test showed no change in the lifetime, but direct population is an assumption; a 0.05 ps systematic was added. Section III.
domain assumption The shell model with SN100PN interaction and the chosen valence space gives reliable wave functions for the low-lying 2+ states.
Used for energies, B(E2), B(M1), g factors, and the overlap analysis that classifies 2+1 and 2+2 as symmetric and mixed-symmetric. Section IV.
domain assumption Vibrational limit B(E2;2+2->2+1) <= 2 B(E2;2+1->0+1) constrains the multipole mixing ratio.
Used to derive delta < 0.38 and hence predominance of M1 in the 2+2->2+1 transition. Section III.

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Cite this review

Pith. "Pith review of Isolated one-phonon mixed-symmetry 2+ state of the radioactive neutron-rich nuclide 132Te." pith.science (2026). https://pith.science/paper/VN2OQIBU

@misc{pith2026250101436,
  author       = {Pith},
  title        = {Pith review of: Isolated one-phonon mixed-symmetry 2+ state of the radioactive neutron-rich nuclide 132Te},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VN2OQIBU}},
  note         = {Machine review of arXiv:2501.01436}
}

abstract

The $M1$ transition strengths between excited $2^+$ states of the neutron-rich, radioactive nuclide $^{132}$Te have been studied through direct lifetime measurements using the Doppler-shift attenuation method in a two-neutron transfer reaction on a $^{130}$Te target. An unambiguous identification of the lowest-lying mixed-symmetry $2^+$ state has been achieved on the basis of the large $B(M1;2^+_2\rightarrow2^+_1$)=0.18(2) $\mu_\mathrm{N}^2$ transition strength, in agreement with shell-model calculations. Results are compared to the shell model, and the analysis of both, data and calculations, unambiguously identifies the second-excited $2^+$ state of $^{132}$Te as the one-quadrupole phonon mixed-symmetry state of this isotope. A lowering of the energy and $B(M1;2^+_\mathrm{ms}\rightarrow 2^+_1)$ strength within the $N$=80 isotones toward the $Z$=50 shell closure is observed, which goes alongside with the lowering of the $E2$ collectivity approaching the magic proton shell.

Figures

Figures reproduced from arXiv: 2501.01436 by the authors.

**Figure 1.** FIG. 1. A particle-gated, background-subtracted spectrum, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 3.** FIG. 3. Calculated amplitudes (left, solid bars) and their [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: FIG. 5. The mixing matrix element V [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: The mixing matrix element is relatively small between about 10 keV and 20 keV [36, 41], which is a sign for the purity of the 2+ 1,ms states. In contrast to this, it maximizes at Ce [18] where the closure of the π(g7/2) proton sub-shell at proton number Z = 58 leads to…

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