Conversion electrons from high-statistics β-decay measurements with the 8π spectrometer at TRIUMF-ISAC

The 8π spectrometer, located at TRIUMF-ISAC, was the world’s most powerful spectrometer dedicated to β-decay studies until its decommissioning in early 2014 for replacement with the GRIFFIN array. An integral part of the 8π spectrometer was the Pentagonal Array for Conversion Electron Spectroscopy (PACES) consisting of 5 Si(Li) detectors used for charged-particle detection. PACES enabled both γ − e− and e− − e− coincidence measurements, which were crucial for increasing the sensitivity for discrete e− lines in the presence of large backgrounds. Examples from a 124Cs decay experiment, where the data were vital for the expansion of the 124Csm decay scheme, are shown. With sufficient statistics, measurements of conversion coefficients can be used to extract the E0 components of J → J transitions for J 0, which is demonstrated for data obtained in 110In→110Cd decay. With knowledge of the shapes of the states involved, as obtained, for example, from the use of Kumar-Cline shape invariants, the mixing of the states can be extracted.


Introduction
Prior to its decommissioning, the 8π spectrometer, located at the TRIUMF-ISAC radioactive beam facility in Vancouver, Canada, was the world's most powerful HPGe array routinely used for β-decay studies.This status was achieved because the spectrometer and its auxiliary detector systems were dedicated to β-decay studies only, al- lowing it to be optimized for that singular purpose.The 20 Compton-suppressed HPGe γ-ray detectors were configured in a truncated icosahedral geometry and achieved ≈ 1% photopeak efficiency at the energies of the 60 Co γ rays.Surrounding the beam-implantation point onto a FeO or Al coated mylar tape of the Moving Tape Collector at the center of a vacuum chamber were up to 20 plastic scintillator detectors of the SCintillating Electron-Positron Tagging Array (SCEPTAR).A different configuration involved the removal of the upstream hemisphere of SCEPTAR and its replacement with the Pentagonal Array for Conversion Electron Spectroscopy (PACES).Finally, the downstream SCEPTAR hemisphere could be removed and replaced with a single fast-plastic scintillator.These detector systems were coupled to a high-throughput and high-precision data acquisition system capable of triggering in excess of 30 kHz that enabled the collection of highstatistics data sets in a reasonable amount of beam time, but also enabled the half life and branching ratio measurements to a level of precision of better than 0.1% required for studies of Fermi superallowed β + emitters.Additional details of the spectrometer can be found in Refs.[1][2][3].
The 8π spectrometer was decommissioned in the early part of 2014 and replaced with the much more powerful GRIF-FIN array [1,4].Consisting of 16 large-volume HPGe clover detectors, GRIFFIN utilizes all of the existing auxiliary detectors and in addition can be coupled with the DESCANT neutron detector array [5] for studies of βdelayed neutron emitters.
One of the main goals of the science program carried out with the 8π spectrometer was the investigation of collectivity in nuclei, especially those located on or near the valley of stability.For these studies, high sensitivity to weak, low-energy γ-ray branches from highly-excited states is necessary.Studies to date have included, for example, the decay of 110 In [6][7][8][9], 112 In/ 112 Ag [10,11], and 122,124,126 Cs [12,13] into 110 Cd, 112 Cd, and 122,124,126 Xe, respectively.The 8π spectrometer proved itself a valuable tool for these studies since, for the above species, the high intensity of the radioactive beams delivered by TRIUMF more than compensated for the low absolute efficiency (by modern standards) for γ-ray detection.
In addition to the detection and measurement of weak γ-ray decay branches, in many of the experiments the 8π spectrometer was augmented with PACES for the purpose of conversion-electron detection and to seek possible E0 branches.As is well known, the measurement of E0 strengths, in the form of ρ 2 (E0) values, provides crucial information concerning the mixing of states with different intrinsic shapes.Such measurements, however, prove to be especially challenging requiring the ability to extract E0 branches in the presence of large backgrounds from β particles and Compton scattering of γ rays.Further, high statistics for J π → J π transitions with J π 0 must be acquired since the M1/E2 contribution to the electron intensity must be subtracted.

E0 conversion electron studies
E0 transitions are sensitive to the changes in the nuclear charge-squared radii since the E0 operator is [14] where the sum extends over the A bodies in the nucleus with their charges e i and radial position r i .The usual quantity quoted when referring to an E0 transition is the ρ 2 (E0) value, defined via [14] where Γ(E0) is the partial width for the decay, τ(E0) the partial lifetime, and Ω(Z, E e ) the electronic factor that depends on the atomic number Z and the energy of the transition ΔE.The quantity ρ(E0) is defined by, with R = 1.2A 1/3 fm, and carries all of the nuclear structure information.A successful measurement of the ρ 2 (E0) value thus requires a measurement of the branching fraction of the total transition intensity that proceeds through the E0 decay, i.e., where the summation extends over all possible branches (neglecting very small possible contributions from twophoton decay, internal pair formation, etc.) and also a measurement of the level lifetime τ.The number of ρ 2 (E0) values known is still rather limited [14,15].The ρ 2 (E0) values can be expressed in terms of the collective variables from the Bohr model.The operator is [16] so that in a two-level mixing solution with quadrupole deformation parameters (β 1 , γ 1 ) and (β 2 , γ 2 ) the E0 strength is given by [14,16] The first term, proportional to the differences in the squares of the quadrupole deformation parameters β, is the usual expression that one sees for the ρ 2 (E0) values.The second term shows the leading order term involving the shape parameter γ; since it enters as the cube of the deformation β, its contribution is usually small.What is clear from Eqn. 6 is if information on the shape parameters β are known, the mixing of states can be determined.

The PACES Apparatus
PACES, shown in the photograph in Fig. 1, is installed internally in the vacuum chamber that is surrounded by the HPGe detectors of the 8π spectrometer.The 5 Si(Li) detectors have a 5 mm thickness, with a surface area of ≈ 200 mm 2 , and are located at a distance of 3 cm from the beam deposition position.The Si(Li) detectors are in thermal contact with an Al plate that is cooled by an annular Cu cold finger of 0.75 m length.The annular cold finger is placed inside the beam line, with the annular opening allowing the beam to pass through.The Si(Li) detectors have a typical resolution of 2.5 keV at 1 MeV.The available active area of PACES covers ≈ 7% of 4π solid angle, making it an efficient device for coincidence studies.Further details can be found in Refs.[1,8].

Conversion electron spectroscopy with PACES
Inclusion of conversion-electron data may reveal not only E0 transitions, indicative of shape coexistence effects, but also provides multipolarity information.In studies of nuclei with a large number of levels at low-excitation energy, as is often encountered in odd-odd nuclei or in the actinide region, the ability to detect low-energy conversion electrons and γ rays is vital in the construction of accurate decay schemes.
As mentioned above, a limitation on the measurement of E0 transitions, for J 0 states, is that both the back-  ground level and the contribution of the M1/E2 electrons to the observed intensity of the transition must be subtracted.This requires much higher statistics than a measurement of the 0 + → 0 + transitions.Figure 2  The fact that PACES consists of multiple, independent Si detectors enables e − −e − coincidence spectroscopy.During a portion of a measurement to study the decay of 124 Cs, the observation of the decay of the t 1/2 = 6.3s (7 + ) 124 Cs isomeric state was enhanced relative to the t 1/2 = 30.8-s 1 + ground state by employing a beam-on and tape movement cycling consisting of 1 s of beam implantation followed by 12 s of decay.This cycling minimized the build-up of the longer-lived ground state on the collection tape.Figure 3 shows the projection of the e − − e − coincidence matrix collected during this portion of the experiment.Compared with data presented in Fig. 2, which was obtained using a beam/tape cycling appropriate for the long-lived 124 Cs ground state, the background in Fig. 3 is much lower due to the lower relative intensities of the high-energy γ rays in 124 Xe and the β + particles.Figure 4 displays e − − e − coincidence spectra from gates with the 65-keV M conversion electrons (top panel) and 97-keV L electrons (bottom panel) from the 124 Cs isomer decay.Of particular note is the presence in the bottom panel of the 25-keV peak from the 31-keV L conversion electron, clearly resolved from the Cs K α X-ray; the 31-keV transition was previously unobserved.Using data such as this, the decay scheme of the 124 Cs isomer was significantly modified and is shown in Fig. 5.

E0 transitions in 110 Cd
A high-statistics data set for the decay of 110 In→ 110 Cd was collected with the dual goals of measuring weak, lowenergy γ-ray decay branches from highly-excited states, and observing additional E0 branches.The high-intensity ion beam of 1.2 × 10 7 ions/s of 110 In in the 7 + ground state with a 4.9-hr half life, and 1.7 × 10 6 ions/s of 110 In in the 2 + isomeric state with a 69-min half life was delivered to the center of the 8π spectrometer.The internal conversion coefficients were extracted from the γ − e − and γ − γ coincidence data.The γ-ray coincidence gates were taken from above or below the decay of interest.When gating from below, the number of (3) (5) γ − e − coincident counts measured can be expressed as where K is an overall normalization factor, I e − is the conversion electron intensity ( f is the feeding and d the draining transition), e − is the detector efficiency for the conversion electron, γ is the detector efficiency for the γ ray, BR γ is the γ-ray branching ratio, c is the coincidence efficiency and η(θ γe − ) is an angular correlation factor.The number of γ − γ coincident counts can be similarly written as where I γ is the γ-ray intensity.Rearranging for the intensity of γ rays and the intensity of conversion electrons from Eqns. 7 and 8, the internal conversion coefficient, in accordance with its definition, can be written as An internal efficiency calibration was adopted (see Fig. 4 in Ref. [9]), using the conversion coefficients for well- known E2 and E1 transitions or those determined in the present work to be essentially pure M1 or E2 transitions.Shown in the top panel of Fig. 6 are examples of partial e − spectra obtained by placing coincidence gates on the 658-(left) and 885-keV (right) γ rays.The bottom panel displays the corresponding γ-ray coincidence spectra with the same γ-ray coincidence gates applied.Fitting of the corresponding electron and γ-ray peaks provides the number of coincidence counts used in Eqn. 9.

Implications of ρ 2 (E0) values
As shown in Eqn.6, the determination of experimental ρ 2 (E0) values enables the admixtures between states to be determined provided that the underlying intrinsic shapes are known.In many cases this is not possible since the shapes have typically not been determined for excited states.However, when Coulomb excitation has been performed with sufficient sensitivity and statistics such that the Kumar-Cline [17,18] shape invariants can be constructed, the shapes of the states can be extracted in a model-independent way.Such a case is 114 Cd [19].
The Coulomb excitation experiment performed by Fahlander et al. [19] provided a sufficient number of matrix elements that enables the shape invariant Q 2 to be de- The coincidence with the 245-keV γ ray shows the 397-keV K-conversion electron peak, which is weak, and some much stronger peaks that result from Compton scattering of the 511-keV annihilation radiation and the 582-and 642-keV γ rays.The coincidence spectrum with the 626-keV γ ray shows the 708-keV K-conversion electron peak.termined from where M(E2) is the transition matrix element and {} is a 6 j symbol.While the sum extends over the complete set of states I j , it generally is determined by a few key matrix elements.The Q 2 invariant extracted from the experimental data, Q 2 , can be related to the β shape parameter with q 0 = 3 4π ZR 2 0 with R 0 = 1.2AThe upper limit for the 0 + → 0 + transition is due to a lower limit on the lifetime for the 1473-keV 0 + level.e 2 b 2 , respectively, leading to β values of 0.187(2) and 0.27 (1).In 114 Cd, ρ 2 (E0; 0 + 2 → 0 + 1 ) = (19 ± 2) × 10 −3 , and with the above values of β, Eqn.6 leads to an admixture of a 2 = 0.08 of the intruder 0 + wave function in the ground state.

Conclusions
Conversion electron spectroscopy is a powerful tool for the elucidation of level schemes, especially those involving highly-converted, low-energy transitions that are not always observed with γ-ray detectors.Furthermore, they provide a way to measure the E0 components of J π → J π transitions.The PACES array, employed at TRIUMF-ISAC with the 8π and GRIFFIN spectrometers, has provided such data.Examples of electron data from the decay of 124 Cs m have been given that led to a modification of the decay scheme of this isomer.Data from the decay of 110 In were used to extract new E0 values, and a new ρ 2 (E0) value was determined for the decay of the 4 + deformed intruder band to the 4 + member of the ground-state band.Combining data from a previous Coulomb excitation study of 114 Cd with the available ρ 2 (E0) values permitted the admixture of the intruder 0 + state in the ground state to be determined.
a e-mail: pgarrett@physics.uoguelph.cab present address: DESY Photon Science, Notkestrasse 85 D-22607 Hamburg, Germany c Present address: Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, ON K1N 6N5, Canada d Present address: Instituut voor Kern-en Stralingsfysica, K.U.Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium e Present address: Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA f Present address: Department of Physics, Tennessee Technological University, Cookeville, Tennessee 38505, USA g Present address: National Superconducting Cyclotron Laboratory, Michigan State University, 640 South Shaw Lane, East Lansing, Michigan 48824, USA h Present address: Diamond Light Source Ltd., Diamond House, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom

Figure 1 .
Figure 1.Photograph showing the detail of the PACES array of Si(Li) detectors located on the upstream side of the vacuum chamber of the 8π spectrometer.Details of the positioning are listed in Ref. [8].

Figure 2 .
Figure2.Example of a spectrum of conversion electrons obtained with the Si detectors of the 8π spectrometer in the β + /EC decay of 124 Cs.The background is due to β + -particle interactions in the detector, as well as Compton-scattering of γ rays.The main discrete lines observed are from Cs X-rays, transitions from the internal decay of the 124 Cs 7 + isomeric state, and the most intense transitions in124 Xe.

Figure 3 .
Figure 3. Projection of the e − -e − coincidence matrix obtained during a measurement of the decay of 124 Cs m .
displays a spectrum observed with the Si detectors of PACES in a recent measurement of the 124 Cs β + /EC decay[13].The sudden increases in the level of the background observed at 210 keV and 340 keV are Compton edges from intense 354-keV γ rays and the 511-keV annihilation radiation.

Figure 4 .
Figure 4.Examples of e − -e − coincidence spectra from the decay of 124 Cs m .The top panel displays the coincidence spectrum with a gate taken on the 65-keV M conversion electron peak, whereas the bottom panel displays the coincidence spectrum with the 97-keV L conversion electron peak.The 97-keV L gate includes a small contribution from the 90-keV γ-ray photopeak.

Figure 5 .
Figure 5. Level scheme deduced for the isomeric decay of 124 Cs m .Levels are labelled with their energies in keV, and their J π values.The transitions are labelled with their energies in keV.Arrows in blue are previously unobserved transitions in the decay of the isomer, with those in red new transitions.

Figure 7 .
Figure 7. Portions of the spectra of the conversion electrons in coincidence with the 245-(top) and 626-keV (bottom) γ rays.The coincidence with the 245-keV γ ray shows the 397-keV K-conversion electron peak, which is weak, and some much stronger peaks that result from Compton scattering of the 511-keV annihilation radiation and the 582-and 642-keV γ rays.The coincidence spectrum with the 626-keV γ ray shows the 708-keV K-conversion electron peak.

Figure 8 .
Figure 8. Partial level scheme for 110 Cd showing the ρ 2 (E0) • 10 3 values for transitions from the deformed intruder band to the ground-state band.The upper limit for the 0 + → 0 + transition is due to a lower limit on the lifetime for the 1473-keV 0 + level.