Review
Electric monopole transitions in nuclei

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Abstract

Electric monopole, E0 transitions in nuclei are reviewed. Values for ρ2(E0)×103, X(E0/E2) and qK2(E0/E2) are tabulated. Particular attention is paid to a complete re-evaluation of all reported values starting from raw input data, i.e. none of the adopted values are taken from the literature without evaluation. Values for JJ transitions for J=0, J=2, and some selected J=4 transitions are given. The 22 transitions involve evaluation of δ(E2/M1) mixing ratios. These were usually assessed from values given in ENSDF. Asymmetric uncertainties and multiple sources of error are handled using up-to-date, Monte Carlo-based procedures. All conversion coefficients and electronic factors are taken from the latest tabulations. As a second major component of the review, a detailed illustration of the association of E0 transition strengths with the manifestation of shape coexistence in nuclei is made. This demonstrates that large E0 transition strengths are a strong indication of the presence of shape coexistence in nuclei. In many cases this is shown to be directly corroborated by B(E2) data. Some details of experimental techniques behind the input data are given. The connection between E0 transition strengths and mean-square charge radii, isotope and isomer shifts is sketched.

Introduction

Electric monopole, E0 transitions are unique to nuclei; they are not observed in any other manifestations of matter. The reason for this “isolated” manifestation is because photons have spin one, and nuclei are well isolated from their environment by atomic electrons. Thus, electromagnetic decay by single-photon emission is forbidden for a transition between two states with spin zero.1 However, decay is possible through the interaction between the nucleus and its atomic electrons: the so-called internal conversion process. While the formation region of higher multipole order transitions (E1, M1, E2, etc.) is dominantly outside the nucleus, the formation region of E0 transitions, involving a different set of nuclear matrix elements, takes place inside the nuclear volume. Decay is also possible through the creation of electron–positron pairs (if the decay energy exceeds the mass of the pair, i.e., ΔE> 1.022 MeV): the so-called internal pair formation (IPF).

States with spin zero in nuclei are of particular interest. This has always been true; but has acquired enhanced significance in the last twenty years. The reason is that they are a sensitive indicator of structure. In particular, at low energy, excited states with spin zero and positive parity, 0+ states are associated with either changes in pair-correlated structure or changes in deformation (shape) relative to the ground state of the nucleus. The largest E0 transition strengths are consistent with changes in deformation: thus, we consider them a compelling spectroscopic fingerprint of shape coexistence in nuclei. The issue of shape coexistence in nuclei has progressively become an evermore fundamental one over the past fifty years: it may be said, along with the domination of nuclear structure by deformed shapes, to have become a leading indicator of the fundamental defining characteristics of atomic nuclei.

In this review we present an up-to-date summary of the status of E0 transitions in nuclei. About twenty years have passed since this topic was last reviewed [1], [2]. We pay special attention to the major advances in the computation of internal conversion and internal pair coefficients [3], [4], which require the need to re-evaluate all data. We also formally extend this review to E0 transitions between states with spins differing from zero (as will become evident, this requires careful evaluation of mixing ratios for the competing E2 and M1 radiative transitions). The significance of this is that such transitions are a spectroscopic signature of coexisting “bands”, i.e., excited states with monotonic changes in spin that arise because of the different shapes that nuclei can possess and the consequent emergence of structure such as rotational bands. This was reviewed most recently, ten years ago [5].

Section snippets

Experimental determination of E0 transition strengths

The E0 transition probability is given by the expression W(E0)=1τ(E0)=Wic(E0)+Wπ(E0),where τ(E0) is the partial mean life of the initial state for E0 decay. The quantities Wic(E0) and Wπ(E0) are the transition probabilities for internal–conversion electron and electron–positron pair emission, respectively. They are given by the expression Wic(E0)+Wπ(E0)=ρ2(E0)×[Ωic(E0)+Ωπ(E0)],where Ωic(E0) and Ωπ(E0) are electronic factors defined by Church and Weneser [6]. They are functions of atomic number,

Manifestation of E0 transitions in nuclei

In this section we present illustrations of E0 transition strength and, where relevant, the connection of such strength to shape coexistence. Note that ρ2(E0)103 values given in the figures are rounded off to avoid cluttering the figures: Table 1, Table 2 should be consulted for actual values.

Conclusions

The present work is an update of reviews appearing in 1999 [1] and in 2005 [2]. We retain the major features of these earlier works while combining the nuclear structure and the evaluation procedure components of them. As such we go to a greater depth of detail than was achieved in either of these earlier reviews.

The evaluation procedures have used the latest protocols for handling errors and uncertainties. This is critical in view of the multiple input data, viz. lifetimes, branching ratios

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported in part by the Australian Research Council Grant Nos. DP140102896, No. DP170101673 and Natural Sciences and Engineering Research Council of Canada (NSERC). TRIUMF receives federal funding via a contribution agreement through the National Research Council Canada (NRC) .

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