Interplay between shape-phase transitions and shape coexistence in the Zr isotopes

A. Leviatan; F. Iachello; N. Gavrielov

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Interplay between shape-phase transitions and shape coexistence in the Zr isotopes

N. Gavrielov, A. Leviatan, F. Iachello

Nuclear Theory · Submitted 18 Sep 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We demonstrate the role of two concurrent types of quantum phase transitions, sharing a common critical point.

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arXiv ID1909.08305 (version 2)

Pith ID6J6WA7CV, Pith's permanent record of this paper and its review

CitationA. Leviatan, F. Iachello, N. Gavrielov. "Interplay between shape-phase transitions and shape coexistence in the Zr isotopes." arXiv:1909.08305 (2019). https://pith.science/paper/6J6WA7CV

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,180 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.37 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We investigate the evolution of structure in the zirconium isotopes where one of the most complex situations encountered in nuclear physics occurs. We demonstrate the role of two concurrent types of quantum phase transitions, sharing a common critical point. The first type, involves an abrupt crossing of coexisting normal and intruder configurations. The second type, involves a gradual shape-phase transition within the intruder configuration, changing from weakly-deformed to prolate-deformed and finally to gamma-unstable. Evidence for this scenario is provided by a detailed comparison with experimental data, using a definite algebraic framework.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the evolution of structure in the zirconium isotopes where one of the most complex situations encountered in nuclear physics occurs.	background 0.60	0.54	0.04	asserted 0.92
s1	We demonstrate the role of two concurrent types of quantum phase transitions, sharing a common critical point.	result 0.68	0.91	0.63	asserted 1.00
s2	The first type, involves an abrupt crossing of coexisting normal and intruder configurations.	result 0.83	0.56	0.16	asserted 0.98
s3	The second type, involves a gradual shape-phase transition within the intruder configuration, changing from weakly-deformed to prolate-deformed and finally to gamma-unstable.	result 0.90	0.73	0.20	asserted 1.00
s4	Evidence for this scenario is provided by a detailed comparison with experimental data, using a definite algebraic framework.	method 0.78	0.87	0.09	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from analysis of existing data 0.96.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We investigate the evolution of structure in the zirconium isotopes where one of the most complex situations encountered in nuclear physics occurs. We demonstrate the role of two concurrent types of quantum phase transitions, sharing a common critical point. The first type, involves an abrupt crossing of coexisting normal and intruder configurations. The second type, involves a gradual shape-phase transition within the intruder configuration, changing from weakly-deformed to prolate-deformed and finally to gamma-unstable. Evidence for this scenario is provided by a detailed comparison with experimental data, using a definite algebraic framework.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 5 papers

We demonstrate the relevance of IQPTs to the Zr isotopes, with such coexisting Type I and Type II QPTs, and ground state shapes changing from spherical to prolate axially deformed and finally to gamma-unstable.

Intertwined Quantum Phase Transitions in the Zr Isotopes · 0.99
The good agreement of our calculation with the vast empirical data along the chain of isotopes demonstrates the relevance of IQPTs to the zirconium isotopes, and can serve as a case study to set path for new investigations of IQPTs in other nuclei and other physical systems.

Zr Isotopes as a region of intertwined quantum phase transitions · 0.97
The results suggest a remarkable interplay of multiple quantum phase transitions (QPTs).

Multiple quantum phase transitions in the Zr isotopes · 0.95
A detailed analysis in the framework of the interacting boson model with configuration mixing, provides evidence for this scenario in the Zr isotopes.

Intertwined quantum phase transitions in the Zr chain · 0.90
The algebraic framework of the interacting boson model with configuration mixing is employed to demonstrate the occurrence of intertwined quantum phase transitions (IQPTs) in the $_{40}$Zr isotopes with neutron number 52-70.

An algebraic approach to intertwined quantum phase transitions in the Zr isotopes · 0.88

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