Evidence for shape coexistence in 52 Cr through conversion-electron and pair-conversion spectroscopy

, Abstract. Electric monopole ( E 0) transitions are a highly sensitive probe of the charge distribution of an atomic nucleus. A large E 0 transition strength ( ρ 2 ( E 0)) is a clear indicator of nuclear shape coexistence. In the region between doubly magic 40 Ca and 56 Ni, E 0 transitions have never been observed in the Ti or Cr isotopes, nor in the heavier iron isotopes ( 56 , 58 Fe). We have performed the ﬁrst measurements of the E 0 transitions in 52 Cr via conversion-electron and pair-conversion spectroscopy using the Super-e spectrometer at the Australian National University Heavy Ion Accelerator Facility. We present the ﬁrst spectra obtained for 52 Cr, including the ﬁrst observation of the E 0 transition from the ﬁrst-excited 0 + state in 52 Cr, in both electron-positron pairs and conversion-electron spectroscopy. The preliminary values for the E 0 strength in the 1531-keV 2 + 2 → 2 + 1 transition in 52 Cr is ρ 2 ( E 0) × 10 3 = 470(190), and for the 1728-keV 2 + 3 → 2 + 1 transition, it is ρ 2 ( E 0) × 10 3 = 1800(1200). The large E 0 strengths observed are consistent with shape coexistence in this region. However, despite the relatively precise observation of the conversion-electron and electron-positron pair intensities, the E 0 strengths have large uncertainties. More precise determinations of relevant spectroscopic quantities, such as the state lifetimes and transition mixing ratios for mixed M 1 + E 2 transitions, are needed to determine the E 0 strength more precisely.


Introduction
Nuclear shape coexistence is a phenomenon in which the atomic nucleus can take different shapes at low excitation energy [1]. Nuclear shape coexistence appears to be a phenomenon that is present across the nuclear landscape [1][2][3] with important implications for our current understanding of nuclear structure. For example, recent work on Cd isotopes casts doubt on the widely-held notion of spherical, quadrupole vibrations in these nuclei [4,5] and instead explains their behaviour by multiple shape-coexisting rotational bands [5].
The presence and behavior of 0 + states in even-even nuclei, and their association with nuclear shapes play a pivotal role in understanding shape coexistence [1]. E0 transitions, the only possible decay path between two J π = 0 + states, provide a unique probe into these nuclear shapes. The nuclear E0 transition strength (ρ 2 (E0)) is large when there is a sizable change in the nuclear meansquare charge radius, and when there is also strong mixing between states of different deformation [6]. The measurement of E0 transition strengths is then a direct experimen-tal tool to investigate nuclear shape coexistence and shape mixing.
Large E0 strengths have been recently observed in the Ni isotopes (Z = 28) [7,8], but it is unknown if shape coexistence is present in the N = 28 isotones between doubly magic 48 Ca and 56 Ni. Theoretically, shape coexistence has been predicted in the N = 28 isotones [9], resulting from the excitation of a neutron pair across the N = 28 closed neutron shell from the f 7/2 shell into the f p shell. This creates a deformed prolate band above a spherical ground state, possibly mixing with the spherical, seniority states in these nuclei [9][10][11][12][13]. There are candidates for the shapecoexisting band in 50 Ti, 52 Cr and 54 Fe, but no E0 transitions have been reported in 50 Ti or 52 Cr [14,15].
In this article, we report the preliminary results of our investigation into E0 transitions in 52 Cr.

Experiment
The experiments were performed at the Heavy Ion Accelerator Facility at the Australian National University (ANU) using the Super-e spectrometer [16] to measure the electron-positron pair, conversion-electron, and γ-ray transitions. The Super-e is a superconducting magnetic-lens spectrometer for the measurement of conversion electrons and electron-positron pairs, with excellent background suppression [16][17][18]. It consists of the Miel detector array, two HPGe detectors, a superconducting solenoid, and central HeavyMet baffles. An image of the Super-e rendered from the engineering drawings is shown in Fig. 1.
The Miel detector array consists of six Si(Li) detectors, each with an active area of 260 mm 2 and a thickness of 9 mm, allowing measurement of electron and positron energies up to 3.5 MeV and nuclear pair transitions up to 8 MeV in energy. The Miel detector array along with accompanying electronics has a time resolution of 10 ns and an energy resolution of 2.5 keV at an electron energy of ≈ 1.1 MeV. Each Si(Li) detector is separated from its neighbours by HeavyMet barriers to prevent cross-talk.
There are two HPGe detectors mounted as part of the experimental apparatus. The first is Compton suppressed and positioned at ≈ 135 • relative to the beam axis and ≈ 25 cm from the target; the second is not Compton suppressed, positioned at ≈ 135 • to the beam axis and 1.5 m from the target and is collimated, positioned within a polyethylene and lead radiation shield to provide beamcurrent normalization in high beam-current experiments [18].
The central HeavyMet baffles, along with the axial magnetic field of the solenoid, define an acceptance window for the emitted conversion electrons and electronpositron pairs as a function of take-off angle and energy. Only those particles with energies and take-off angles that lie within the acceptance window will reach the detector. The Super-e can only observe electron-positron pairs where the electron and positron have similar energy and separation angles up to 84 • . The trajectories of the electrons and positrons that reach the detector are helical, making 2.5 orbits between the target and the detector; such orbits can be seen schematically in Fig 1. More details of the operation of the Super-e can be found in a number of recent papers [  The 14UD pelletron accelerator at the ANU Heavy Ion Accelerator Facility delivered a 5.4-MeV proton beam to the Super-e pair spectrometer. The nuclear states of interest in 52 Cr were excited with the (p, p ) reaction. The 52 Cr target had a thickness of 1.3 mg/cm 2 and was isotopically enriched to 99.9(1)%, and mounted at 45 • to both the beam axis and the solenoid axis as shown in Fig. 1.
Data was collected in two modes: singles mode collecting electron singles with the Miel detector array and both HPGe detectors; and doubles mode, with only the far HPGe detector, and collecting only Miel coincidence events. The Super-e was operated in swept-field mode, scanning the magnetic field between an upper and lower value continuously. The solenoid current for each of the modes was different. For the singles mode, the solenoid current range was 1.700 -11.569 A, while for the doubles mode was 2.712 -7.720 A; these correspond to transitions of energy 200 -2500 keV in singles mode and 2200 -4352 keV in doubles mode.
The relative efficiencies of the HPGe detectors were determined from the measurement of well-known calibration sources: 152 Eu, 56 Co, and 170 Lu. 152 Eu and 170 Lu sources were also used to calibrate the relative efficiency of the Super-e spectrometer in singles by sweeping the solenoid current over the same current range used in the singles measurement. The efficiency of the Super-e to pair conversion was determined via Monte-Carlo simulation of the trajectories of the electrons and positrons inside the bore of the Super-e using PENELOPE and Poisson Superfish [20,21]. The Miel detector efficiency was then also determined via Monte Carlo simulation, using PENE-LOPE. More details are given in Refs. [14,18,19].

Results
The transitions observed in conversion electrons and electron-positron pairs are shown in Fig. 2 along with the populated levels of 52 Cr. The observed γ-ray, conversionelectron, and electron-positron pair spectra are shown in Figs. 3a, b, and c, respectively. We have observed the transitions from the second-and third-excited 2 + states to the first-excited 2 + state at energies of 1531 and 1728 keV in both internal conversion and γ-ray spectroscopy, see     (9) Figs. 3a and b. The 2647-keV E0 transition can also be clearly observed from the first-excited 0 + state in 52 Cr to the ground state in both conversion electrons and electronpositron pairs which can be seen in Figs. 3b and c. Note that there is no strong γ-ray line at 2647 keV in the γ-ray spectrum, clearly indicating that the 2647-keV transition corresponds to a 0 + → 0 + transition. Table 1 shows the E0 strengths determined in this work. These use the determined detector efficiencies, adopted values for the transition mixing ratios, branching ratios, and state lifetimes from Nuclear Data Sheets [22], conversion coefficients from the BrIcc database [23], electronic factors from the recent tabulation [24], and the measured conversion-electron and electron-positron pair intensities from the present work. Unfortunately, without a lifetime for the 2647-keV first-excited 0 + state in 52 Cr, the E0 transition strength cannot be determined [15]. Instead, we report the X(B(E0)/B(E2)) value -a measure of the relative strength between the E0 and E2 transitions depopulating the 0 + state [25].

Discussion
We have observed large E0 strengths in the mixed M1 + E2 + E0 transitions from the second and third-excited 2 + states in 52 Cr to the first-excited 2 + state. An expected E0 strength for a nucleus of A = 52 from a simple shell-model picture is 36 milliunits [6], while the largest reported E0 strength across the nuclear chart is 500(81) milliunits from the Hoyle State in 12 C [15].
The 1531-keV M1 + E2 + E0 transition is from the second-excited 2 + state in 52 Cr. This state is suggested to be the first-excited 2 + state in the shape-coexisting band in 52 Cr [9][10][11]. If there is strong mixing and a large change in nuclear shape, a large E0 strength is expected [1,6]. The large observed E0 strength in this transition, see Table 1, supports the shape-coexistence picture of 52 Cr.
The very large E0 strength in the 1728-keV 2 + 3 → 2 + 1 M1 + E2 + E0 transition of 1800(1200) milliunits is unprecedented [15], however the uncertainty in the value is equally large. The E0 strength in this transition is consistent with zero within two standard deviations. Along with the experimental conversion-electron and electronpositron pair intensities, the determination of the E0 strength of a mixed M1 + E2 + E0 transition relies on three factors: the parent level lifetime, the transition mixing ratio (δ(E2/M1)), and the transition branching ratio. All of these factors must be known to high precision in order to extract a precise ρ 2 (E0) value. The E2/M1 mixing ratio for the 1728-keV 2 + 3 → 2 + 1 M1 + E2 + E0 transition is -0.18(7) [27] and the branching ratio is 0.909(66) [22]. The E0 intensity is determined from the difference between the experimental conversion electron and electron-positron pair intensity and that which is theoretically predicted for a mixed M1+E2 transition. Uncertainty in the mixing ratio exacerbates the uncertainty in the E0 intensity. The E0 strength is inversely proportional to level lifetime, ρ 2 (E0) ∝ 1/τ(E0). The level lifetime (T 1/2 = 0.035(7) ps [22]) is short and has large uncertainty; as smaller lifetimes increase the E0 strength non-linearly, this uncertainty amplifies the possible E0 strength.
In order to determine precise values for the E0 strength in the 1531-keV and 1728-keV transitions, precise determinations of the state lifetimes as well as the transition branching ratios and mixing ratios are needed. Without this information, our ρ 2 (E0) values for these transitions remain tentative. In order to resolve these limitations, an experimental campaign investigating these properties of 52 Cr is planned to take place at the University of Kentucky Accelerator Laboratory (UKAL). The inelastic neutron scattering reaction, (n, n ), has been successfully used to measure nuclear lifetimes via the Doppler-shift attenuation method (DSAM) and mixing ratios via angular distributions in the Ni isotopes, which were needed for accurate E0 strength determination [7,8,28].

Conclusion
We report the observation of the E0 transition from the first-excited 0 + state to the ground state of 52 Cr for the first time. We also report the first values for the E0 strength in the mixed M1 + E2 + E0 transitions from the secondand third-excited 2 + states to the first-excited 2 + state in 52 Cr. The large E0 strengths in these transitions support the current theoretical picture of shape coexistence in the N = 28 isotones, particularly in 52 Cr [9]. The observed E0 strengths are the first experimental evidence for shape coexistence in 52 Cr, suggesting a quadrupole deformation for the excited band of β 2 = 0.49 (5). Using this preliminary E0 strength, the predicted lifetime of the first-excited 0 + state is ≈ 0.6 ps, within the lifetime range for DSAM measurement. Unfortunately, there is a large uncertainty on the reported E0 strengths in this work due to the uncertainty in the state lifetimes, and the transition branching and mixing ratios. The unprecedented strength in this region (Ca -Ni) [7,8,14,15] is still not understood, and further measurements of both the E0 transition strengths, along with other spectroscopic quantities like mixing ratios, are needed to reduce the uncertainty on the E0 transition strengths and to understand the structure of these nuclei.