The boson number hypothesis and the boson number odd-even effect in $^{196-204}$Hg

Chun-xiao Zhou; Lorenzo Fortunato; Tao Wang

REVIEW 4 major objections 5 minor 2 cited by

The boson number hypothesis and the boson number odd-even effect in $^{196-204}$Hg

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Mercury isotope data confirm that low-lying nuclear states alternate with the parity of the boson number N.

desk verdict The Hg odd-even pattern is real, but N is locked to A here, so the boson-number verification claim overshoots. read the letter →

arxiv 2412.14881 v2 pith:RWD6KFYW submitted 2024-12-19 nucl-th

Tao Wang , Chun-xiao Zhou , Lorenzo Fortunato This is my paper · ORCID

classification nucl-th PACS 21.60.Fw21.10.Re

keywords bosonnumberhypothesisSU3-IBMSU(3)third-orderCasimiroperatoroblatenuclearshapesodd-eveneffectinteractingmodelmercuryisotopes

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

The paper claims that an odd-even effect in the low-lying spectra of $^{196-204}$Hg is caused by the parity of the boson number $N$, the model count of valence-nucleon pairs. In the SU3-IBM, the oblate shape is generated by the SU(3) third-order Casimir operator, and for finite $N$ the first excited band's bandhead angular momentum alternates between $0$ and $2$ as $N$ runs through 6, 5, 4, 3, 2. The measured $0_2^+$ and $2_2^+$ energies in the five mercury isotopes show the same alternation that this finite-$N$ structure predicts. If the paper is right, low-lying collective excitations are genuinely sensitive to the exact boson number, which would verify the boson number hypothesis for the first time since the interacting boson model was proposed.

What carries the argument

The load-bearing object is the SU(3) third-order Casimir operator $\hat C_3[\mathrm{SU}(3)]$ inside the Hamiltonian (1), together with the other SU(3) higher-order terms. For finite boson number $N$, this operator's ground representation alternates between $(0,N)$ for even $N$ and $(2,N-1)$ for odd $N$, forcing the first excited bandhead angular momentum to alternate between $0$ and $2$. A single parameter set ($\eta=0.4$, $\alpha=1.65$, $\beta=0.05$, $\gamma=-1.9$, $\delta=-12.0$) with only the global scale $c$ adjusted per nucleus carries the whole calculation, so the $N$-parity alternation is the mechanism that explains the data.

What would settle it

Measure, or reanalyse with higher resolution, the ordering of the $0_2^+$ and $2_2^+$ bandheads in $^{200}$Hg and $^{202}$Hg: if $^{200}$Hg showed a $2_2^+$ state below its $0_2^+$ state, or $^{202}$Hg showed a $0_2^+$ state below its $2_2^+$ state, the predicted $N$-parity alternation would be directly contradicted.

Watch

Extended reading notes

Core claim

The central claim is that the boson number odd-even effect predicted by the SU3-IBM really exists in $^{196-204}$Hg. For the third-order Casimir interaction, the ground-state SU(3) representation is $(0,N)$ for even $N$ and $(2,N-1)$ for odd $N$, so the bandhead of the first excited band has angular momentum $0$ for even $N$ and $2$ for odd $N$. The paper shows that a fixed five-parameter Hamiltonian, Eq. (1), with only the boson number $N$ changed from isotope to isotope, reproduces the measured evolution of the $0_1^+$, $2_1^+$, $4_1^+$, $0_2^+$, $2_2^+$, and $0_3^+$ states, including the anomalous low $0_2^+$ energy in $^{200}$Hg. This is presented as the first verification of the boson number hypothesis and as direct evidence for the validity of the SU3-IBM.

Load-bearing premise

The argument assumes that one fixed five-parameter Hamiltonian, with only the boson number changing between isotopes, fully accounts for the odd-even pattern; the paper itself says that effects it left out, such as distinguishing protons from neutrons, adding higher-spin bosons, and including individual-particle motion, are also needed near the heavier mercury isotopes.

Editorial extensions

If this is right

The low-lying $0_2^+$ and $2_2^+$ bandheads in $^{196-204}$Hg become a direct readout of the boson number $N$: even $N$ favors a $0_2^+$ bandhead, odd $N$ a $2_2^+$ bandhead.
A single Hamiltonian with fixed parameters, only the scale $c$ changed, reproduces the measured level evolution for five isotopes, implying the spectra are sensitive to the exact value of $N$.
The SU(3) third-order Casimir operator is identified as the correct finite-$N$ description of oblate shapes, and the O(6) limit is judged inadequate for the $\gamma$-softness of these nuclei.
The calculation predicts a $4_2^+$ state in $^{200}$Hg that future experiment should be able to find.
The odd-even effect is absent in the large-$N$ limit and in earlier IBM treatments, so the finite-$N$ representation structure of SU3-IBM is the essential ingredient.

Reading between the lines

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

Beyond the paper: if the $N$-parity interpretation is right, the alternation should weaken as $N$ grows toward the large-$N$ limit, so heavier mercury isotopes or neighbouring platinum isotopes should show a fading of the effect; this is a testable extension the authors do not state.
Beyond the paper: the fit is worst exactly where the paper invokes missing degrees of freedom (single-particle excitations, g bosons, proton-neutron distinguishability), so a cleaner test is to measure the $2_2^+ \to 2_1^+$ transition rate in $^{198}$Hg, where the calculation overshoots experiment by a large factor; a small measured value would implicate non-collective mixing rather than $N$ parit
Beyond the paper: the same logic predicts an $N$-parity ordering in the neighbouring $^{192-200}$Pt nuclei mentioned as a future platform, turning the five-isotope coincidence into a region-wide prediction.
Beyond the paper: the evidence that $N$ alone controls the effect could be sharpened by perturbing the five parameters within their uncertainties; if the $N$-parity ordering survives only for the one tuned set, the case that $N$ is the controlling variable becomes much weaker.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

Colleague,

The paper identifies a real odd-even staggering in the 0+2 and 2+2 bandheads of 196-204Hg and shows that a fixed-parameter SU3-IBM Hamiltonian can track the energy trend quite well. That is the genuinely new part, and the authors deserve credit for looking at this chain through that lens and for reporting failures (196Hg bandhead, bad B(E2)s) rather than hiding them.

The soft spot is the interpretation, and it is load-bearing. The claim is that because only N varies, this verifies the boson number hypothesis. But in this region N is not an independent variable: counting valence holes gives N = (208-A)/2, so every step in A changes N by exactly one. The odd-even effect in A is automatically an odd-even effect in N. That does not mean the observation is worthless, but it cannot uniquely fingerprint N as the cause. The paper needs to compare with other models, e.g., the O(6)-U(5) descriptions it dismisses in Refs. [41,43], and ideally with chains where N and A decouple.

The fit itself has more knobs than the text suggests. Five structure parameters plus per-isotope scale c (733, 743, 602, 549, 613 keV) and per-isotope effective charges. The B(E2) failures are severe: in 198Hg the 2+2 -> 2+1 rate is off by a factor of fifty, which makes it hard to claim the calculated 2+2 state is the experimental one.

I would send this to review, because the empirical pattern and the model application are worth airing, but the referee should require the authors to moderate the 'verification' and 'proof' language, add at least one alternative-model comparison, and quantify uncertainties. A revised version with those changes would be a solid contribution.

Worth reading if you work on IBM or shape evolution. I wouldn't cite it in its current form.

Referee Report

4 major / 5 minor

Summary. The paper claims to identify a boson number odd-even effect in the low-lying 0+2 and 2+2 bandheads of 196-204Hg and interprets it as a verification of the IBM boson number hypothesis and of the SU3-IBM. The authors use a Hamiltonian (Eq. 1) with five fixed structural parameters (eta=0.4, alpha=1.65, beta=0.05, gamma=-1.9, delta=-12.0), per-isotope energy scales c, and per-isotope effective charges e, and show that the calculated bandhead energies reproduce the observed alternating pattern of 0+2 and 2+2 states. They also compare selected B(E2) values and quadrupole moments.

Significance. If the central claim were established, the paper would provide a rare empirical test of the finite-N predictions of an algebraic model, and the odd-even pattern predicted from the SU(3) third-order Casimir operator (Ref. [34]) predates the present data fit, which is a genuine strength. The authors are also transparent about the deficiencies of the B(E2) description and about the need for extensions such as proton-neutron distinction and g bosons. However, the evidence presented is not sufficient to support the strong conclusions in the abstract and conclusion, and the manuscript needs substantial additional analysis before the claim of verification can be accepted.

major comments (4)

[Eq. (1) and 'Now we explain this effect'] The statement that 'for this specific Hamiltonian, the only variable is the boson number N' is not supported, because the energy scale c is adjusted per isotope (733.5, 743.1, 602.0, 548.6, 613.2 keV) and the effective charge e also takes five different values in Table I. The five structural parameters are fixed, but the model still contains ten isotope-dependent scaling parameters, so the comparison is not parameter-free. The paper should report the sensitivity of the odd-even pattern to the per-isotope scales and demonstrate that the pattern is not an artifact of tuning c_N and e_N.
[Paragraph 'The boson number for 196−204Hg are 6,5,4,3,2'] For these Hg isotopes the boson number is N=(208-A)/2, so N is an exact linear function of the mass number A; every step A to A+2 changes N by exactly one. Consequently, any odd-even staggering in A automatically appears as an odd-even staggering in N, and the Hg chain alone cannot discriminate the boson number hypothesis from any other mechanism that produces an A-parity effect. The authors do not fit an alternative model to the same data, do not provide a statistical significance test, and dismiss the O(6)-U(5) descriptions in Refs. [41,43] without a quantitative comparison. The conclusion that the effect 'verifies the boson number hypothesis' therefore goes beyond what a single isotope chain can establish.
[Table I and discussion near Fig. 2] The B(E2) comparison contains order-of-magnitude failures for the 2+2 states: in 198Hg the calculated 2+2→2+1 value is 32.7 W.u. versus 0.63(8) W.u. experimentally, and 2+2→0+1 is 3.44 versus 0.0216(4); in 200Hg the 2+2→2+1 value is 19.1 versus 2.2(5). The authors themselves state that the collective nature of the 2+2 state is greatly reduced. If the calculated 2+2 states are not the same as the experimental states, the agreement of the bandhead energies in Fig. 2 cannot be used as evidence for the predicted odd-even effect of the 2+2 bandhead.
[Paragraph 'For only this third-order interaction...'] The pure SU(3) third-order Casimir term predicts a 0+2 first-excited bandhead for 196Hg (N=6), but the experimental bandhead is 2+2. The authors state that other higher-order interactions change 196Hg from 0 to 2 while keeping the heavier nuclei unchanged. Thus the full five-parameter Hamiltonian, not the C3 term alone, reproduces the observed pattern, and the assertion that 'the main interaction is the C3 operator' is not established by the fit. A decomposition showing the separate effect of each term in Eq. (1) is needed to support the attribution.

minor comments (5)

[Abstract and Conclusion] There are typos: 'hgiher-order' in the conclusion and 'pevious' in the penultimate section; these should be corrected.
[Fig. 4 caption] The caption should read 'Black squares' and 'blue spheres' rather than 'Black square' and 'blue sphericity'.
[Eq. (1)] The operators Omega and Lambda are described only verbally; explicit expressions or precise equations from Refs. [47,48] should be provided.
[References] Reference [58] is missing the journal name, and the volume number in Ref. [20] appears inconsistent; please check all entries for completeness.
[Discussion of Fig. 2] The sentence 'the theoretical results of the 2+2 states in Fig. 2 also suffer from deficiencies' should be quantified, since those deficiencies are relevant to the identification of the states.

Circularity Check

2 steps flagged · score 4.0 of 10

The model's structural odd-even prediction is independently grounded in Ref. [34], but the 'verification' is weakened by fitting c to the 0+2 bandheads and by the definitional identity N_boson=(208-A)/2 in this mass region.

fitted input called prediction [Section 'Now we explain this effect with the SU3-IBM' (p.3), after Eq. (1); Fig. 2 and Table I]
"To make the energy of the 0+2 state be equal to the experimental data, the parameter c are 733.5 keV, 743.1 keV, 602.0 keV, 548.6 keV, 613.2 keV for 196−204Hg, respectively. Thus for this specific Hamiltonian, the only variable is the boson number N."

The 0+2 bandhead is one of the two quantities whose odd-even alternation is presented as evidence (Fig. 1). Setting c_n so that E_th(0+2)=E_exp(0+2) for every isotope makes the staggered 0+2 curve in Fig. 2 an input, not an output; the subsequent statement that 'theoretical calculations reproduce the evolutional behaviors at a high level' is therefore partly true by construction. The independent part, the 2+2 bandhead, is admitted to be 'somewhat quantitatively worse', and the B(E2) rates for 2+2→2+1 disagree by factors of 10-50 (Table I), so the data do not independently confirm the fitted 0+2 pattern. This is a fitted input presented as a verified prediction.
other [Section 'The boson number for 196−204Hg are 6,5,4,3,2' (p.3) and Conclusion (p.5)]
"The boson number for 196−204Hg are 6,5,4,3,2. ... Because these results are very sensitive to the boson number N, they also verify the basic boson number hypothesis of the IBM, which was considered impossible in the past 50 years."

N_boson is not an independent variable in this chain: with Z=80 and neutrons counted as holes to N=126, N_boson=(208−A)/2, so the listed values 6,5,4,3,2 are exactly linear in A. Consequently every odd-even staggering in A is automatically an odd-even staggering in N under the very hypothesis ('N is half the number of valence nucleons') that the paper claims to verify. The test therefore cannot distinguish N-sensitivity from ordinary mass-number or valence-neutron-number sensitivity; no alternative model (e.g., keeping N fixed while changing other degrees of freedom) is compared. The claimed verification is partly a restatement of the definitional link between A and N, not an independent confirmation of the boson number hypothesis.

full rationale

The paper's internal derivation is not overtly circular at the level of the SU(3) representation: the alternating bandhead angular momenta (0,2,0,2,0) for N=6..2 are a structural property of the third-order Casimir operator reported in Ref. [34], which is independent of the present data fit and not authored by the current paper's authors. That gives the central model prediction real, independently published content. However, the empirical validation is substantially weakened by two construction-related issues. First, the per-isotope energy scale c is chosen to force each 0+2 bandhead to exactly equal experiment, so the 0+2 component of the odd-even effect is fitted, not predicted; the remaining 2+2 comparison is admitted to be quantitatively worse and its B(E2) values fail by large factors. Second, the boson number hypothesis itself defines N from the valence-nucleon count, and in 196-204Hg this gives N_boson=(208-A)/2, so an A-parity staggering is automatically an N-parity staggering; the paper's 'only variable is N' statement is thus a re-labeling of the mass-number dependence rather than an independent experimental control. The manuscript also concedes the need for proton-neutron distinction, g bosons, single-particle excitations, and reduced collectivity of the 2+2 states, further weakening the directness of the claimed verification. There is no load-bearing self-citation chain that forces the result, and the structural prediction is not equivalent to its inputs by definition. The appropriate finding is therefore partial circularity: score 4.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the standard IBM valence-space counting, the validity of the SU3-IBM Hamiltonian truncation, the group-theoretic bandhead structure of the cubic Casimir operator, the triaxial-rotor mapping for the extra terms, and the correctness of the experimental 0+2 and 2+2 assignations. All are inputs from previous work or data; none are derived in this paper.

free parameters (7)

eta = 0.4
Hamiltonian structure parameter fixed by hand to reproduce the Hg spectra; no first-principles derivation is given.
alpha = 1.65
Hamiltonian structure parameter fixed by hand to reproduce the Hg spectra; no first-principles derivation is given.
beta = 0.05
Hamiltonian structure parameter fixed by hand to reproduce the Hg spectra; no first-principles derivation is given.
gamma = -1.9
Hamiltonian structure parameter fixed by hand to reproduce the Hg spectra; no first-principles derivation is given.
delta = -12.0
Hamiltonian structure parameter fixed by hand to reproduce the Hg spectra; no first-principles derivation is given.
c_N (energy scale per isotope) = 733.5, 743.1, 602.0, 548.6, 613.2 keV for 196-204Hg
Fitted per isotope so the theoretical 0+2 energy equals the experimental value; not a predicted quantity.
e_N (effective boson charge per isotope) = 2.395, 2.542, 2.829, 2.801, 3.471 (W.u.)^1/2 for 196-204Hg
Chosen to reproduce B(E2; 2+1 to 0+1) for each isotope; all other B(E2) values then deviate strongly from experiment.

assumptions (5)

domain assumption Standard IBM valence boson count for 196-204Hg gives N=6,5,4,3,2.
This is the counting the paper uses to map isotopes to N; it is also the assumption the conclusion claims to verify, so it enters as an input.
domain assumption The SU3-IBM Hamiltonian with only the U(5) and SU(3) limits is an adequate low-energy model space for these nuclei.
Equation (1) restricts the Hamiltonian; the paper offers no first-principles justification for omitting O(6), g-boson, or proton-neutron terms.
standard math The SU(3) cubic Casimir yields (0,N) ground states for even N and (2,N-1) for odd N, giving bandhead angular momenta 0 and 2 respectively.
Group-theoretic result cited from Ref. [34]; used to construct the odd-even prediction.
domain assumption The Omega and Lambda terms are the SU(3) images of the rigid triaxial rotor.
Taken from Refs. [47,48]; these terms are used to fix the 196Hg exception.
domain assumption The experimental 0+2 and 2+2 assignments in 196-204Hg are correct.
Data from ENSDF and Bernards et al.; if the assignments are wrong, the odd-even pattern could be an artifact. The paper does not re-analyze the raw data.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The boson number hypothesis and the boson number odd-even effect in $^{196-204}$Hg." pith.science (2026). https://pith.science/paper/RWD6KFYW

@misc{pith2026241214881,
  author       = {Pith},
  title        = {Pith review of: The boson number hypothesis and the boson number odd-even effect in $^196-204$Hg},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RWD6KFYW}},
  note         = {Machine review of arXiv:2412.14881}
}

abstract

In the SU3-IBM the oblate shape is described by the \textrm{SU(3)} third-order Casimir operator in the large-$N$ limit. However for finite $N$, this interaction can produce a boson number odd-even effect. In this Letter, we find that, the unique odd-even effect really exists in the nuclei $^{196-204}$Hg. This finding implies that realistic low-lying excitations are sensitive to certain boson number $N$. The boson number hypothesis is verified for the first time since the advent of the interacting boson model. This also proves the accuracy and validity of the SU3-IBM directly. The SU(3) symmetry and the higher-order interactions are both indispensable for understanding the nuclear quadrupole deformations.

Figures

Figures reproduced from arXiv: 2412.14881 by the authors.

**Figure 2.** FIG. 2. Experimental data (top) [46] and the theoretical re [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. Experimental data [46] and the theoretical results o [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. Experimental (Black square) [46] and theoretical [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Typical new spherical-like $\gamma$-soft spectra in $^{104,106,108}$Pd
nucl-th 2025-01 reject novelty 5.0 of 10

The author fits an interacting boson model with many parameters to low-lying data for 106Pd and concludes it confirms a new gamma-soft mode, but the evidence is mostly fitting, not prediction.
SU(3) rigid triaxiality in $^{154}$Sm
nucl-th 2025-09 conditional novelty 4.0 of 10

Applying the SU3-IBM with ground-state irrep (18,2) to 154Sm reproduces many energy levels, B(E2) values, and quadrupole moments, but with significant deviations in key transitions and a γ angle outside the experiment...

Reference graph

Works this paper leans on

62 extracted references · 33 canonical work pages · cited by 2 Pith papers

[34]

F. Pan, T. Wang, Y. S. Huo, and J. P. Draayer, J. Phys. G: Nucl. Part. Phys. 35, 125105 (2008)

2008
[1]

Iachello and A

F. Iachello and A. Arima, The Interacting Boson Model , (Cambridge University Press, Cambridge, 1987)

1987
[2]

Arima and F

A. Arima and F. Iachello, Phys. Rev. Lett. 35, 1069 (1975)

1975
[3]

Wang, EPL 129, 52001 (2020)

T. Wang, EPL 129, 52001 (2020)

2020
[4]

Wang, Chin

T. Wang, Chin. Phys. C 46, 074101 (2022)

2022
[5]

The large- N limit of this new model was ﬁrst discussed by one of the authors (L

and the higher-order interactions [6, 7]. The large- N limit of this new model was ﬁrst discussed by one of the authors (L. Fortunato) and his collaborators [8]. In the SU3-IBM, the SU(3) symmetry is suggested to domi- nate over the onset of quadrupole deformations, and only the U(5) limit and the SU(3) limit are included. So, in a sense, the SU3-IBM is b...

work page
[6]

V. K. B. Kota, SU(3) Symmetry in Atomic Nuclei , (Springer Nature, Singapore,2020)

2020
[7]

Van Isacker and J

P. Van Isacker and J. Q. Chen, Phys. Rev. C 24, 684 (1981)

work page 1981

Show all 62 references

[8]

Vanden Berghe, H

G. Vanden Berghe, H. E. De Meyer and P. Van Isacker, Phys. Rev. C 32, 1049 (1985)

1985
[9]

Fortunato, C

L. Fortunato, C. E. Alonso, J. M. Arias, J. E. Garc ´ ıa- Ramos and A. Vitturi, Phys. Rev. C 84, 014326 (2011)

2011
[10]

T. Wang, B. C. He, C. X. Zhou, D. K. Li and L. Fortu- nato, Chin. Phys. C 48, 094102 (2024)

2024
[11]

Arima and F

A. Arima and F. Iachello, Phys. Rev. Lett. 40, 385 (1978)

1978
[12]

J. A. Cizewski, R. F. Casten, G. J. Smith, M. L. Stelts, W. R. Kane, H. G. B¨ orner et al., Phys. Rev. Lett. 40, 167 (1978)

1978
[13]

Zhang, Y

Y. Zhang, Y. W. He, D. Karlsson, C. Qi, F. Pan and J. P. Draayer, Phys. Lett. B 834, 137443 (2022)

2022
[14]

Wang, Phys

T. Wang, Phys. Rev. C 107, 064303 (2023)

2023
[15]

Zhang, S

Y. Zhang, S. N. Wang, F. Pan, C. Qi and J. P. Draayer, Phys. Rev. C 110, 024303 (2024)

2024
[16]

F. Pan, Y. Zhang, Y. X. Wu, L. R. Dai and J. P. Draayer, Phys. Rev. C 110, 054324 (2024)

2024
[17]

W. Teng, Y. Zhang and C. Qi, Chin. Phys. C 49, 014102 (2025)

2025
[18]

Zhang and W

Y. Zhang and W. Teng, Phys. Rev. C 111, 014324 (2025)

2025
[19]

Y. X. Cheng, D. H. Zhao, Y. Y. Shao, T. Wang and X. S. Kang, in preparation
[20]

T. Wang, X. Chen and Y. Zhang, Chin. Phys. C 49, 014107 (2025)

2025
[21]

T. Wang, B. C. He, D. K. Li and C. X. Zhou, Phys. Rev. C 78, 064322 (2023)

2023
[22]

C. X. Zhou and T. Wang, Phys. Rev. C 108, 024309 (2023)

2023
[23]

C. X. Zhou, T. Wang, D. K. Li, B. C. He and L. Fortu- nato, in preparation
[24]

Wang, arXiv:2501.10925v2

T. Wang, arXiv:2501.10925v2

arXiv
[25]

Heyde and J

K. Heyde and J. L. Wood, Rev. Mod. Phys. 83, 1467 (2011)

2011
[26]

Heyde and J

K. Heyde and J. L. Wood, Phys. Scr. 91, 083008 (2016)

2016
[27]

P. E. Garrett, J. L. Wood and S. W. Yates, Phys. Scr. 93, 063001 (2018)

2018
[28]

C. X. Zhou and T. Wang, in preparation
[29]

Otsuka, Y

T. Otsuka, Y. Tsunoda, T. Abe, N. Shimizu and P. Van Duppen, Phys. Rev. Lett. 123, 222502 (2019)

2019
[30]

Tsunoda and T

Y. Tsunoda and T. Otsuka, Phys. Rev. C 103, L021303 (2021)

2021
[31]

Otsuka, Y

T. Otsuka, Y. Tsunoda, Y. Utsuno, N. Shimizu, T. Abe and H. Ueno, arXiv:2303.11299v5

arXiv
[32]

A. M. Shirokov, N. A. Smirnova and Y. F. Smirnov, Phys. Lett. B 434, 237 (1998)

1998
[33]

Cejnar, S

P. Cejnar, S. Heinze, and J. Jolie, Phys. Rev. C 68, 034326 (2003)

2003
[35]

Zhang, F

Y. Zhang, F. Pan, Y. X. Liu, Y. A. Luo and J. P. Draayer, Phys. Rev. C 85, 064312 (2012)

2012
[36]

Jolie, R

J. Jolie, R. F. Casten, P. von Brentano and V. Werner, Phys. Rev. Lett. 87, 162501 (2001)

2001
[37]

Jolie, P

J. Jolie, P. Cejnar, R. F. Casten, S. Heinze, A. Linne- mann and V. Werner, Phys. Rev. Lett. 89, 182502 (2002)

2002
[38]

Warner, Nature 420, 614 (2002)

D. Warner, Nature 420, 614 (2002)

2002
[39]

Jolie and A

J. Jolie and A. Linnemann, Phys. Rev. C 68, 031301(R) (2003)

2003
[40]

Bonatsos, A

D. Bonatsos, A. Martinou, S. K. Peroulis, T. J. Mertz- imekis and N. Minkov, Phys. Scr. 99, 062003 (2024)

2024
[41]

Nomura, R

K. Nomura, R. Rodr ´ ıguez-Guzm´ an and L. M. Robledo, Phys. Rev. C 87, 064313 (2013)

2013
[42]

J. E. Garc ´ ıa-Ramos and K. Heyde, Phys. Rev. C 89, 014306 (2014)

2014
[43]

X. Q. Yang, L. J. Wang, J. Xiang, X. Y. Wu and Z. P. Li, Phys. Rev. C 103, 054321 (2021)

2021
[44]

Sahoo, P

S. Sahoo, P. C. Srivastava, N. Shimizu and Y. Utsuno, Phys. Rev. C 110, 024306 (2024)

2024
[45]

Bernards, R

C. Bernards, R. F. Casten, V. Werner, P. von Brentano, D. Bucurescu, G. Graw et al. , Phys. Rev. C 87, 024318 (2013)

2013
[46]

Bernards, R

C. Bernards, R. F. Casten, V. Werner, P. von Brentano, D. Bucurescu, G. Graw et al. , Phys. Rev. C 87, 064321 (2013)

2013
[47]

ENSDF: https://www.nndc.bnl.gov/ensdf/
[48]

Y. F. Smirnov, N. A. Smirnova and P. Van Isacker, Phys. Rev. C 61, 041302(R) (2000)

2000
[49]

Zhang, F

Y. Zhang, F. Pan, L. R. Dai and J. P. Draayer, Phys. Rev. C 90, 044310 (2014)

2014
[50]

Chakraborty, H

S. Chakraborty, H. P. Sharma, S. S. Tiwary, C. Ma- jumder, P. Banerjee, S. Ganguly et al. , Eur. Phys. J. A 55, 46 (2019)

2019
[51]

Olaizola, A

B. Olaizola, A. B. Garnsworthy, F. A. Ali, C. Andreoiu, G. C. Ball, N. Bernier et al. , Phys. Rev. C 100, 024301 (2019)

2019
[52]

Bonatsos, I

D. Bonatsos, I. E. Assimakis, N. Minkov, A. Martinou, S. Sarantopoulou, R. B. Cakirli et al. , Phys. Rev. C 95, 064326 (2017)

2017
[53]

Bonatsos, A

D. Bonatsos, A. Martinou, S. K. Peroulis, T. J. Mertz- imekis, N. Minkov, Symmetry 15, 169 (2023)

2023
[54]

Martinou1, D

A. Martinou1, D. Bonatsos, N. Minkov, I. E. Assimakis, S. K. Peroulis, S. Sarantopoulou et al. , Eur. Phys. J. A 56, 239 (2020)

2020
[55]

Bonatsos and A

D. Bonatsos and A. Klein, Ann. Phys. 169, 61 (1986)

1986
[56]

J. P. Elliott and J. A. Evans, J. Phys. G: Nucl. Part. Phys. 25, 2071 (1999)

1999
[57]

Bernards, S

C. Bernards, S. Heinze, J. Jolie, C. Fransen, A. Linne- mann and D. Radeck, Phys. Rev. C 79, 054307 (2009)

2009
[58]

Bernards, S

C. Bernards, S. Heinze, J. Jolie, M. Albers, C. Fransen and D. Radeck, Phys. Rev. C 81, 024312 (2010)

2010
[59]

Bernards, W

C. Bernards, W. Urban, M. Jentschel, B. M¨ arkisch, J. Jolie, C. Fransen et al. , 84, 047304 (2011)

2011
[60]

Esmaylzadeh, L

A. Esmaylzadeh, L. M. Gerhard, V. Karayonchev, J.-M. R´ egis, J. Jolie, M. Bast et al. , Phys. Rev. C 98, 014313 (2018)

2018
[61]

Alimohammadi L

M. Alimohammadi L. Fortunato and A. Vitturi, Eur. Phys. J. Plus 134, 570(2019)

2019
[62]

R. Kern, R. Stegmann, N. Pietralla, G. Rainovski, M. P. Carpenter, R. V. F. Janssens et al. , Phys. Rev. C 99, 011303(R) (2019)

2019

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [34]

F. Pan, T. Wang, Y. S. Huo, and J. P. Draayer, J. Phys. G: Nucl. Part. Phys. 35, 125105 (2008)

2008

[2] [1]

Iachello and A

F. Iachello and A. Arima, The Interacting Boson Model , (Cambridge University Press, Cambridge, 1987)

1987

[3] [2]

Arima and F

A. Arima and F. Iachello, Phys. Rev. Lett. 35, 1069 (1975)

1975

[4] [3]

Wang, EPL 129, 52001 (2020)

T. Wang, EPL 129, 52001 (2020)

2020

[5] [4]

Wang, Chin

T. Wang, Chin. Phys. C 46, 074101 (2022)

2022

[6] [5]

The large- N limit of this new model was ﬁrst discussed by one of the authors (L

and the higher-order interactions [6, 7]. The large- N limit of this new model was ﬁrst discussed by one of the authors (L. Fortunato) and his collaborators [8]. In the SU3-IBM, the SU(3) symmetry is suggested to domi- nate over the onset of quadrupole deformations, and only the U(5) limit and the SU(3) limit are included. So, in a sense, the SU3-IBM is b...

work page

[7] [6]

V. K. B. Kota, SU(3) Symmetry in Atomic Nuclei , (Springer Nature, Singapore,2020)

2020

[8] [7]

Van Isacker and J

P. Van Isacker and J. Q. Chen, Phys. Rev. C 24, 684 (1981)

work page 1981