Decay spectroscopy of $^{50}$Sc and $^{50m}$Sc to $^{50}$Ti

TL;DR

This study investigates the beta decay of $^{50}$Sc to $^{50}$Ti using gamma-ray spectroscopy, revealing new decay pathways and providing detailed data that enhance understanding of nuclear structure near semi-magic nuclei.

Contribution

It provides the first detailed gamma-ray decay scheme for $^{50}$Sc to $^{50}$Ti, including new transitions and branching ratios, and compares results with advanced shell-model calculations.

Findings

Discovered 16 excited states linked by 38 gamma-ray transitions.

Measured gamma-ray intensities down to 0.001% of the strongest transition.

Data agree with shell-model calculations, validating theoretical models.

Abstract

The $\beta$ decay of the isomeric and ground state of $^{50}$Sc to the semi-magic nucleus $^{50}_{22}$Ti$_{28}$ has been studied using a $^{50}$Ca beam delivered to the GRIFFIN $\gamma$-ray spectrometer at the TRIUMF-ISAC facility. $\beta$-decay branching ratios are reported to 16 excited states with a total of 38 $\gamma$-ray transitions linking them. These new data significantly expands the information available over previous studies. Relative intensities are measured to less than 0.001$\%$ that of the strongest transition with the majority of $\gamma$-ray transitions observed here in $\beta$ decay for the first time. The data are compared to shell-model calculations utilizing both phenomenologically-derived interactions employed in the ${\it pf}$ shell as well as a state-of-the-art, ${\it ab~initio}$ based interaction built in the valence-space in-medium similarity renormalization group framework.

Tables

Table 1. Table 1: Energies, intensities and branching ratios of γ 𝛾 \gamma rays measured in the beta decay of 50 Sc. I γ subscript 𝐼 𝛾 I_{\gamma} is expressed relative to the 1554 keV transition to the ground state of 50 Ti determined using a γ − γ 𝛾 𝛾 \gamma-\gamma coincidence matrix except where noted. Data are compared to previous measurements where available. See text for details.

	This work					Previous Works
$E_i$111Ref. Chen and Singh (2019) except for 6237 and 6625 keV states which are determined using the (weighted) average energies of depopulating transitions, corrected for nuclear recoil. (keV)	$J_i^{\pi }$222Ref.Chen and Singh (2019) or current work.	$E_{\gamma }$333Systematic and statistical uncertainties added in quadrature. (keV)	$E_f$ (keV)	BR	$I_{\gamma }$	BR	$I_{\gamma }$
						Ref.Chen and Singh (2019)	Ref.Alburger et al. (1984)
1553.8	2+	1553.8(2)444$I_{\gamma }$ obtained in singles mode using $\gamma -$ray addback energy spectrum.	0.0	100	100	100	100
2674.9	4+	1121.0(2)44footnotemark: 4	1553.8	100	100.1 22	100	99.54 90
3198.7	6+	523.7(2)44footnotemark: 4	2674.9	100	88.5 17	100	88.74 150
4147.2	4+	1472.3(2)555$I_{\gamma }$ from coincidence gate placed at 1121 keV.	2674.9	100	0.630 14	100	0.61 4
4171.9	3+	1497.1(2)55footnotemark: 5	2674.9	41.1 31	0.0365 26	48 3	<0.10
		2618.0(2)666$I_{\gamma }$ from coincidence gate placed at 1554 keV.	1553.8	100.0 28	0.0889 28	100 6	<0.30
4310.0	2+	2756.0(2)777$I_{\gamma }$ obtained in singles mode using $\gamma -$ray single-hit energy spectrum.	1553.8	100.0 60	0.00381 24	100 10
		4307.8(11)77footnotemark: 7	0.0	26.8 35	0.00102 12	19.6 21
4880.6	5+	733.4(2)888$I_{\gamma }$ from coincidence gate placed at 1472 keV.	4147.2	2.14 6	0.02683 70	2.12 20
		1682.0(2)999$I_{\gamma }$ from coincidence gate placed at 524 keV.	3198.7	16.96 44	0.2131 52	8.3 24	0.28 3
		2205.8(2)55footnotemark: 5	2674.9	100.0 18	1.256 30	100 6	1.27 3
5186.1	4+	1014.6(8)101010$I_{\gamma }$ from coincidence gate placed at 2618 keV.	4171.9	2.24 37	0.00152 25
		2511.3(2)55footnotemark: 5	2674.9	100.0 21	0.0678 18	100 7
		3631.5(10)66footnotemark: 6	1553.8	38.2 13	0.02588 83	40.4 24
5379.9	4+	1207.7(2)1010footnotemark: 10	4171.9	49.5 31	0.0531 33	54.8 31	<0.10
		2705.1(2)55footnotemark: 5	2674.9	100.0 19	0.1071 27	100 7	0.105 16
		3825.1(10)66footnotemark: 6	1553.8	11.28 58	0.01209 61	12.8 10	0.044 10
5440.7	4+	1130.4(3)111111$I_{\gamma }$ from coincidence gate placed at 2756 keV.	4310.0	2.13 23	0.00245 25
		1268.9(8)1010footnotemark: 10	4171.9	1.31 24	0.00152 28
		2765.7(2)55footnotemark: 5	2674.9	100.0 42	0.1152 51	100	0.145 18
		3885.5(10)66footnotemark: 6	1553.8	18.67 98	0.02151 77
5547.8	(2, 3)+, (4)+121212Spin and parity assignments based upon $\beta$ feeding from the 50mSc and 50Sc parent states, respectively. See Table III.4.	2872.8131313Not observed. 1.22$\times I_{\gamma }^{3993keV}$ from Ref.Ruyl et al. (1984).	2674.9	100.0 168	0.00075 13	100 6
		3993.2(11)44footnotemark: 4	1553.8	81.7 63	0.00061 9	82 5
5806.5	4+	1635.2(8)1010footnotemark: 10	4171.9	0.91 9	0.00249 25
		3132.2(2)55footnotemark: 5	2674.9	100.0 22	0.2747 75	100	0.251 15
		4251.8(10)66footnotemark: 6	1553.8	12.3 12	0.0338 32
6123.1	(4)+	1242.4(2)141414$I_{\gamma }$ from coincidence gate placed at 2206 keV.	4880.6	100.0 35	0.0512 20	100 7
		1975.6(2)88footnotemark: 8	4147.2	24.6 11	0.01262 42	<15
		2924.3(2)99footnotemark: 9	3198.7	31.5 16	0.01615 67	31 7
		3448.4(2)55footnotemark: 5	2674.9	24.8 14	0.01272 57	20 5
6156.4	4+	1983.4(8)1010footnotemark: 10	4171.9	4.88 103	0.00044 9
		2008.9(2)88footnotemark: 8	4147.2	100.0 34	0.00903 34
		3481.4(3)55footnotemark: 5	2674.9	58.5 41	0.00528 34
		4600.6(12)44footnotemark: 4	1553.8	12.6 13	0.00114 11	100
6236.9(2)	(4,5)+	2064.8(8)1010footnotemark: 10	4171.9	2.97 44	0.00066 10
		3038.1(2)99footnotemark: 9	3198.7	61.1 27	0.01355 52
		3560.9(10)55footnotemark: 5	2674.9	100.0 27	0.02217 69
6625.4(3)	(4,5,6)+	3426.6(3)44footnotemark: 4	3198.7	63.7 86	0.00132 15
		3950.1(10)44footnotemark: 4	2674.9	100.0 72	0.00208 15

Table 2. Table 3: Transition strength, B ​ ( E ​ 2 ) 𝐵 𝐸 2 B(E2) , values are given in e 2 ​ f ​ m 4 superscript 𝑒 2 𝑓 superscript 𝑚 4 e^{2}fm^{4} and quadrupole moments, Q 𝑄 Q , are given in e 2 ​ f ​ m 2 superscript 𝑒 2 𝑓 superscript 𝑚 2 e^{2}fm^{2} . Experimental data are taken from Ref. Chen and Singh ( 2019 ) .

	Exp.	KB3G	GXPF1A	VS-IM-SRG
$B(E2:2_1-0_1)$	58(2)	99.9	100.4	38.2
$B(E2:4_1-2_1)$	60(13)	98.2	98.0	36.1
$B(E2:6_1-4_1)$	34(1)	46.7	47.0	16.9
$B(E2:2_{2p2h}-0_{2p2h})$	-	10.1	39.5	26.7
$Q\left(2_1\right)$	8(16)	6.77	6.53	4.69
$Q\left(2_2\right)$	-	-19.61	-12.77	-11.36
$Q\left(2_3\right)$	-	13.51	13.30	9.76

Full text

I Introduction

Nuclei in the vicinity of magic neutron (N) and proton (Z) numbers, often display simple patterns of low-energy excitations which can be well described in a spherical shell model approach. The structure of these lowest-lying excited states may be deduced by considering the behavior of a single nucleon or pair of nucleons occupying just a few single-particle orbits near the Fermi surface in a spherically-symmetric potential. However, this simple picture does not describe the nature of all excitations observed at low energies. Most notably, the limitations in the number of basis states included in this approach means that it usually does not capture deformed configurations or collective behaviors which can coexist along side the spherical single-particle structures and typically involve breaking the core. Particle-hole excitations across major shell gaps are energetically costly, requiring several MeV of energy. However, the additional correlation energy, coming primarily from the neutron-proton quadrupole-quadrupole interaction Heyde et al. (1982), which becomes possible with this release of particles from the core makes such cross-shell excitations energetically competitive with the lowest-lying states Heyde et al. (1982); Heyde and Wood (2011).

Recently, the rapid development of new theoretical methods and the availability of increased computational power have extended the reach of ab initio methods to medium-mass nuclei Epelbaum et al. (2009); Machleidt and Entem (2011); Bogner et al. (2007, 2010). The need to include three-nucleon forces in the interactions for an accurate description of excitations has become evident Hebeler et al. (2015). In order to support the further development of these methods, detailed spectroscopic information of excited nuclear states and transitions is necessary.

The even-even N=28 isotones above 48Ca provide a good example, where protons fill the $0f_{7/2}$ orbital. The seniority=2 (V=2), J=$2^{+}$,$4^{+}$,$6^{+}$ states in ${}^{50}_{22}$Ti, ${}^{52}_{24}$Cr and ${}^{54}_{26}$Fe with Ex $\approx$1.5-3 MeV show very little change in excitation energy as additional pairs of protons are added to the $0f_{7/2}$ orbital. In contrast the J=$0_{2}^{+}$,$2_{2}^{+}$ excited states originating from neutron two-particle, two-hole ($\nu$2p-2h) excitations across the N=28 shell gap to the $1p_{3/2}$ orbital show an abrupt change beyond 50Ti. There is a rapid lowering in excitation energy as more proton pairs are added to increase the attractive correlation strength, and these states begin to intrude upon the $\pi 0f_{7/2}$ ground state structure at $\leq$ 3 MeV in 52Cr and 54Fe Rowe and Wood (2018). In addition, below 48Ca, the N=28 shell gap has been shown to vanish upon the significant removal of protons Sorlin and Porquet (2013).

The electric quadrupole transition strength B(E2; $0_{1}^{+}$ $\rightarrow$ $2_{1}^{+}$) is frequently used to probe the evolution of collectivity near closed shells, appearing enhanced at mid-shell and at a minimum at the shell closure, for example the B(E2) for the $2^{+}_{1}\rightarrow 0^{+}_{1}$ transition measured in 52Cr is around twice that of 50Ti Poves et al. (2001). In general, constraints on the decay intensities observed between the mainly non-yrast states and the V=2 seniority states are valuable targets for experiments aiming to understand the microscopic behaviors in *A$\approx$*50 semi-magic nuclei, particularly the B(E2; $0_{2}^{+}$ $\rightarrow$ $2_{2}^{+}$) transition strength for the $\nu$2p-2h configuration. A deeper insight into the interplay between configurations will be obtained from a detailed comparison between calculations and experimental data.

In this article we report on the most sensitive study of the $\beta$ decay of 50Sc to 50Ti performed to date, using the GRIFFIN spectrometer at TRIUMF-ISAC Svensson and Garnsworthy (2013); Rizwan et al. (2016); Garnsworthy et al. (2017a); Garnsworthy et al. (2019). The analysis of the excited states in 50Sc populated from the $\beta$ decay of the 50Ca beam in this work have been previously reported in Ref. Garnsworthy et al. (2017b). The new data for 50Ti presented here are compared to shell-model calculations utilizing both phenomenologically-derived interactions employed in the pf shell as well as an ab initio based interaction built in the valence-space in-medium similarity renormalization group framework.

II Experimental details

The isotope 50Ca ($T_{1/2}$ = 13.9(6) s Warburton et al. (1970)) was produced from reactions induced in a 22.49 g/cm2 Ta target by a 500 MeV proton beam delivered by the TRIUMF Cyclotron Bylinskii and Craddock (2013). The position of the 60 $\mu$A proton beam on the ISOL target was continuously rastered such that a tighter proton beam spot could be used to induce a higher localized power density in the Ta material. The calcium atoms created in the target that diffused out of the material were ionized using resonant-laser ionization and accelerated to 20 keV, mass separated and delivered to the experimental station. The typical beam intensity of 50Ca was $\sim 10^{6}$ ions/s. Small amounts of surface-ionized 50K ($T_{1/2}$=472(4) ms Langevin et al. (1983)) and 150Tb ($T_{1/2}$=3.5 hrs Basu and Sonzogni (2013); Haenni and Sugihara (1977)) were also present in the beam.

The ions were stopped in a mylar tape at the central focus of the Gamma-Ray Infrastructure For Fundamental Investigations of Nuclei (GRIFFIN) spectrometer Svensson and Garnsworthy (2013); Rizwan et al. (2016); Garnsworthy et al. (2017a); Garnsworthy et al. (2019). GRIFFIN consists of an array of 16 high-purity Germanium (HPGe) clover detectors coupled to a series of ancillary detectors. Fifteen HPGe clovers were used in the present work. An array of plastic scintillator paddles (SCEPTAR) was used for the detection of $\beta$ particles. Four cerium-doped lanthanum bromide (LaBr3(Ce)) scintillators were installed in the array but the data from them was not used in this work. The GRIFFIN clovers were positioned at a source-to-detector distance of 11 cm from the implantation point. A 20 mm thick delrin plastic absorber shell was placed around the vacuum chamber to prevent $\beta$ particles from reaching the HPGe detectors while minimizing the flux of Bremsstrahlung photons created as the $\beta$ particles were brought to rest.

In order to study the longer-lived 50Sc daughter (T1/2 = 102.5(5) s) activity, the beam was continuously delivered to the experimental station with the tape stationary. Data were collected in this way for a period of 5 hours. As previously reported Garnsworthy et al. (2017b), a series of short cycles were collected to clearly distinguish the activity of the 50Ca beam. In addition, a longer tape cycle of 1 min 50Ca implantation and 10 min decay was collected for a short time and used in the current analysis.

Energy and timing signals were collected from each detector using the GRIFFIN digital data acquisition system Garnsworthy et al. (2017a), operated in a triggerless mode. HPGe energy and efficiency were calibrated using standard radioactive sources of 133Ba, 152Eu, 60Co and 56Co with the necessary corrections for coincidence summing applied.

III Data analysis and results

III.1 Gamma-ray energy spectra

Events observed by individual GRIFFIN clover detectors were time-correlated to produce $\gamma$-ray addback spectra and provided the principal tool for offline analysis of 50Sc decay. Time-correlated $\gamma$-ray addback hits were used to construct $\gamma$-$\gamma$ matrices in order to establish branching ratios and coincidence relationships in 50Ti, with the option of requiring coincidences with $\beta$ electrons detected in SCEPTAR.

An addback energy spectrum is shown in Figure 1 for $\gamma$-ray energies below 1.6 MeV, encompassing the most intense transitions observed following the decay of 50Ca and 50Sc. The intensity of the 1554 keV 2*+* $\rightarrow$ 0*+* transition in 50Ti yields a total of $\approx$ 2.8 $\times$109 50Sc decays. The fraction of contaminant nuclei in the beam was assessed using $\gamma$ rays emitted following $\beta$-decay and $\beta$-delayed neutron emission of 50K and the EC decay of 150Tb, transmitted to GRIFFIN as $Q=1^{+}$ and 3*+* charge states, respectively. The total contaminant activity detected in the chamber was $\approx$ 1 $\%$ relative to the 1554 keV transition.

III.2 Level scheme

The level scheme observed in the decay of 50Sc to 50Ti was constructed on the basis of a $\gamma-\gamma$ coincidence analysis. Examples of $\gamma$-ray gated addback energy spectra are shown in Figure 2. Figure 3 shows the placement of $\gamma$ rays observed in the current work into the 50Ti level scheme. The width of the arrows indicates the intensity relative to that of the 1554 keV transition. In addition to the 1554 keV decay from the first excited state, only one other transition is observed to decay directly to the ground state, de-exciting the $J^{\pi}$=$2_{2}^{+}$ state at 4310 keV (Figure 2 (a) gated on the 1130 keV feeding transition). Otherwise all excited states eventually feed the yrast, $J^{+}$=$2^{+}$,$4^{+}$ and $6^{+}$ states. For this reason, gates placed upon the $\gamma$ ray of interest (i.e. gating from above) were often the most useful concerning placement in the level scheme. Transitions were placed according to their observed coincidence (or non-coincidence) with the strongest transitions in 50Ti, notably the 524, 1121 and 1554 keV $\gamma$ rays, and via comparison of $\gamma$-ray energies with the energy difference $\Delta E$ between previously known excited states. Feeding transitions were observed in a few cases above the 3199 keV $6^{+}$ state (at 4147, 4172 and 4310 keV) helping to constrain the measurement of direct $\beta$ decay branching to these states.

The 3132 keV $\gamma$ ray de-exciting the 5807 keV state to the 2675 keV $4^{+}$ state is observed to interfere with a different transition (the 2618 keV transition de-exciting the yrast $3^{+}$ state at 4172 keV) through an energy-coincidence of the associated single-escape peak at 2621 keV. This was confirmed by gating on the 2618 keV transition (Figure 2b) where strong coincidences are observed with both a 511 keV escape photon and the 1121 keV transition. The intensity of the 2618 keV $\gamma$ ray has been corrected for this contribution (Section III.3).

There is good agreement between the current work and that from a previous $\beta$-decay study reported by Alburger et al. Alburger et al. (1984) as well as with Ruyl et al. Ruyl et al. (1984) who utilized thermal neutron capture on metallic titanium targets. In the present work, the level scheme has been expanded with a number of levels and transitions observed for the first time in $\beta$ decay. This is discussed in detail in the following Sections.

III.3 Gamma-ray relative intensities

Intensities of $\gamma$ rays observed following the decay of 50Sc are given in Table III.3. Branching ratios of $\gamma$ rays from each excited state are also provided. $\gamma-\gamma$ coincidence requirements have been applied where possible in order to isolate the transitions of interest and obtain the optimum peak-to-background ratio for extracting relative intensities. This is especially important for weaker branches obscured by the Compton-scattered background arising from more intense transitions (mainly the 1121 and 1554 keV $\gamma$ rays). A procedure similar to the ‘gating from below’ method employed by Kulp et al. Kulp et al. (2007) has been used here to obtain the normalized intensity $I_{\gamma}$ for the transitions of interest. Modifications to the overall detection efficiency due to coincidence timing restrictions and the angular coverage of GRIFFIN compared to singles data are assumed to be $\approx$ 1.0 (see for example, Ref. Garrett et al. (2012)). The gating transition was chosen to de-excite states below that of the transition of interest with the 524, 1121 and 1554  keV $\gamma$ rays being the most common choice due to their well-characterized branching ratios. The transition of interest directly feeds the level depopulated by the gating transition in all cases.

All intensities provided in Table III.3 have been corrected for summing effects using an empirical method described in Ref. Garnsworthy et al. (2019). In cases where transition intensities are extracted from $\gamma$-ray addback hits or $\gamma$-ray single hits without any coincidence conditions applied (i.e. the 524, 1121, 1554, 3427, 3950, 3993 and 4601 keV transitions and the 2756 and 4308 keV transitions respectively), summing corrections are obtained using a $\gamma-\gamma$ coincidence matrix with the requirement that HPGe clovers be located at 180 ∘ with respect to each other. A normalization factor is included to reconcile the difference in combinatorial efficiency between the intensity obtained in singles and the summing correction. This may arise due to asymmetries in the detector array where the availability of single crystals (clovers) differs from the number of crystal (clover) pairs at 180 ∘. A similar method is employed to extract summing corrections for the remaining transitions in Table III.3 extracted from coincidence measurements. In the coincidence case the summing correction factors are specific to the transition of interest as well as the choice of the gating transition. Much care must be taken when constructing the necessary coincidence matrices used to determine these factors in order that the same experimental conditions are applied to them as to the experimental data.

Data in Table III.3 are compared to previously reported measurements where available. A total of 38 transitions have been identified in 50Ti. The vast majority of the $\gamma$-ray intensity ($\approx$ 99 $\%$) is contained in the 524, 1121 and 1554 keV transitions. The remaining $\approx$ 1 $\%$ includes many weak transitions, 25 of which are observed here in $\beta^{-}$ decay for the first time, with around half of these transitions having not been reported in any previous experiment. Relative intensities are determined to below 10*-3* $\%$ that of the 1554 keV transition to the ground state, which is a factor of $\approx$15 lower than that of the 3825 keV transition identified by Alburger et al Alburger et al. (1984).