PHYSICAL REVIEW C 81, 024302 (2010)

Spectroscopy of 144 Ho using recoil-isomer tagging
P. J. R Mason,1,* D. M. Cullen,1 C. Scholey,2 P. T. Greenlees,2 U. Jakobsson,2 P. M. Jones,2 R. Julin,2 S. Juutinen,2 S. Ketelhut,2 M. Leino,2 M. Nyman,2 P. Peura,2 A. Puurunen,2 P. Rahkila,2 P. Ruotsalainen,2 J. Sorri,2 J. Sar´ n,2 J. Uusitalo,2 and F. R. Xu3 e
Schuster Laboratory, University of Manchester, Manchester M13 9PL, United Kingdom 2 Department of Physics, University of Jyv¨ skyl¨ , Jyv¨ skyl¨ FIN-40014, Finland a a a a 3 Department of Technical Physics, Peking University, Beijing 100871, People’s Republic of China (Received 30 November 2009; published 4 February 2010) Excited states in the proton-unbound odd-odd nucleus 144 Ho have been populated using the Mo(54 Fe,pn)144 Ho reaction and studied using the recoil-isomer-tagging technique. The alignment properties and signature splitting of the rotational band above the I π = (8+ )144m Ho isomer have been analyzed and the isomer conﬁrmed to have a π h11/2 ⊗ νh11/2 two-quasiparticle conﬁguration. The conﬁguration-constrained blocking method has been used to calculate the shapes of the ground and isomeric states, which are both predicted to have triaxial nuclear shapes with |γ | ≈ 24◦ .
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DOI: 10.1103/PhysRevC.81.024302

PACS number(s): 21.10.Re, 23.20.Lv, 23.35.+g, 27.60.+j

I. INTRODUCTION

Ho is a proton-unbound [1] odd-odd nucleus lying close to the limits of nuclear existence at the proton drip line. The extremely neutron-deﬁcient A = 130–150 region of the nuclear chart in which it lies is at the boundary between regions with prolate and oblate nuclear shapes and is predicted to show numerous axially asymmetric, γ -soft nuclei [2]. This asymmetry is driven by the competing effects of the proton and neutron h11/2 orbitals, which both lie close to the Fermi surface for these nuclei. Protons in the lower part of the h11/2 shell drive the nucleus toward a prolate-deformed shape [3,4] with γ ∼ 0◦ . Neutrons in this region ﬁll the upper part of the h11/2 shell and favor an oblate-deformed nuclear shape [3,4] with γ ∼ −60◦ . This predicted triaxiality necessitates the inclusion of freedom with respect to γ deformation in any theoretical predictions made when studying 144 Ho. Isomeric I π = (8+ ) states have been established in the neutron-deﬁcient odd-odd N = 77 isotones, 140 Eu [5], 142 Tb 63 65 [6,7], and 144 Ho [6,8]. The source of hindrance for decays 67 from these isomers has been predicted to be based largely on structural changes within the nucleus [5,6]. In this work, the shapes of the isomeric and ground-state conﬁgurations in 144 Ho were calculated using the conﬁguration-constrained blocking method [9]. These calculations predict similar shapes for these states, despite the different underlying quasiparticle conﬁgurations. This suggests that some hindrance may be generated by conservation of the K quantum number, deﬁning the projection of the total angular momentum of the nucleus onto its symmetry axis. In a triaxial nucleus, K is not a good quantum number and there will be substantial mixing of different K values, which might be expected to preclude any K hindrance. The role of K hindrance in a nucleus without axial symmetry is discussed in this work. In this article, we present the results of an experiment utilizing recoil-isomer tagging to study the excited states above

144

and below the 144m Ho isomeric state, which has been conﬁrmed to have a π h11/2 ⊗ νh11/2 two-quasiparticle conﬁguration. The prompt bands above the isomer are discussed in terms of their alignment and signature-splitting properties and are systematically compared with the analogous bands in the neighboring N = 77 isotones.
II. EXPERIMENT AND DATA ANALYSIS

Present address: Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom. 0556-2813/2010/81(2)/024302(8) 024302-1

*

Excited states in 144 Ho were populated with the Mo(54 Fe,pn)144 Ho fusion-evaporation reaction using a 226-MeV beam provided by the K130 cyclotron at the University of Jyv¨ skyl¨ , Finland. The beam was incident on a a a 550 µg/cm2 92 Mo target and the experiment ran for 46 h, during which the average beam intensity was 12 particle-nA. A total of 2 × 109 recoil-gated prompt events were recorded and 2 × 105 prompt events were correlated to 144 Ho-delayed decays at the focal plane. Prompt γ rays from the reaction were detected in the JuroGam array, consisting of 43 Compton-suppressed HPGe detectors surrounding the target chamber with a total photopeak efﬁciency of ∼4.2% at 1332 keV [10]. The recoiling reaction products passed into the RITU (recoil ion transport unit) gas-ﬁlled separator [11], where they were separated from the unreacted beam and transported to the GREAT (γ recoil electron alpha tagging) focal-plane spectrometer. In the GREAT spectrometer, the recoils passed through a multiwire proportional counter (MWPC) and implanted in two double-sided silicon strip detectors (DSSDs). Energy-loss and time-of-ﬂight measurements were made between the MWPC and the DSSDs to distinguish the reaction products from any scattered beam transported through the RITU. Delayed γ -ray decays occuring after implantation were measured in the GREAT planar Ge detector. The planar detector has an absolute efﬁciency of up to 30% at 100 keV [12], making it very suitable for the spectroscopy of low-energy γ rays from the decay of isomeric states. The data from the JuroGam and GREAT spectrometers were acquired using the triggerless total data readout (TDR) system, where every measured decay is recorded with a time stamp generated by a global 100-MHz clock.
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PHYSICAL REVIEW C 81, 024302 (2010) III. RESULTS

The data from this experiment were sorted into a series of two-dimensional matrices using the GRAIN software package [13] and were analyzed using the UPAK [14] and RADWARE [15] software suites. Initially, a matrix of prompt γ rays measured in the JuroGam array against correlated delayed γ rays measured in the GREAT planar detector was created with the condition that the decays must be associated with a recoil implantation in the DSSDs at the focal plane. A time condition of 0–2 µs between a recoil implantation in the DSSDs and a γ ray being detected in the planar detector was also applied, corresponding to approximately four times the half-life of the 144m Ho isomeric state [8]. The matrix was background subtracted in time, which removed the peaks associated with longer-lived isomers or β-delayed γ rays from the spectra. By gating on the known delayed decays beneath the 144m Ho isomer, the correlated prompt decays above this state were observed. A sum of spectra showing prompt γ rays in coincidence with decays from beneath the 144m Ho isomer is shown in Fig. 1(a) and the result of gating on the observed prompt transitions to conﬁrm the correlation is shown in Fig. 1(b). Additionally, the available statistics allowed a recoil-isomer-tagged prompt γ -γ matrix to be created, incrementing only those prompt γ -γ coincidences correlated to a delayed 144 Ho γ ray detected in the GREAT planar detector within 0–2 µs of a recoil implantation. This allowed construction of the prompt level scheme for 144 Ho. Finally, a recoil-gated delayed γ -γ matrix was constructed to allow veriﬁcation of the delayed level scheme and measurement of the internal conversion coefﬁcients of the delayed transitions through the intensity of the Ho x-ray peaks.

COUNTS / 0.5 keV

10000
502

8000 6000

(a)

The Ho isomeric state was ﬁrst observed by Scholey et al. [8] and tentatively assigned an I π = 7+ spin and parity. In a study by Tantawy et al. [6], the isomer was reassigned as having an I π = (8+ ) spin parity and the lower-lying longlived state was assigned an I π = (5− ) spin parity based on the systematics of the lower-mass N = 77 nuclei, 140 Eu [5] and 142 Tb [6]. No evidence for an I π = (1+ ) ground state, expected from extrapolation of the level systematics from 140 Eu and 142 Tb, was observed. It is suggested in Tantawy et al. [6] that the I π = 1+ conﬁguration may be absent for 144 Ho due to ﬁlling of the d5/2 proton orbital. In the present work the I π = (5− ) state is assumed to be the ground state of 144 Ho. The study by Scholey et al. [8] established a rotational band above the 144m Ho isomer and a tentatively placed signature partner to this band. However, the placement of prompt states was based largely on the intensities in the isomer-tagged spectrum, as the statistics were not sufﬁcient to allow extensive prompt isomer-tagged γ -γ coincidence measurements to be examined. The study by Scholey et al. tentatively linked the strongest 502-keV γ ray from this singles spectrum to the isomeric state through two transitions of 299 and 348 keV [8]. Gating on the 502-keV transition in the isomer-gated prompt γ -γ matrix in the present work did not show the 299- and 348-keV γ rays in coincidence with the 502-keV transition, which was determined to feed directly into the 144m Ho isomer. The rotational sequence, assigned as Band 1a in the present work, was extended to spin I π = (22+ ) and the placement of all the transitions in this band was conﬁrmed through single gates set in the recoil-isomer-tagged prompt γ -γ matrix. Figure 2(a) shows a spectrum of γ rays in coincidence with the 869-keV transition from Band 1a and shows the other transitions belonging to this band. The properties of the 144 Ho γ rays observed in the present work are summarized
300

144m

430 468

4000
363 141

724 745 762 813 + 817 842 857 869 885 + 889 915 928

(a)
200
502

531 569

2000 0 0 (b)

645 662

COUNTS / 0.1 keV

COUNTS / 1 keV

47

8000 6000 4000 2000 0

54

57

61

0
502

57

149

300 200

(b)

87

123

210

61

474

100

430 468

FIG. 1. (a) Sum of γ -ray spectra showing the prompt γ rays in coincidence with the 57-, 61-, 149-, and 210-keV γ rays below the 144m Ho isomeric state. (b) The delayed γ -ray spectrum for 144 Ho, created by gating on the 363-, 430-, 468-, 502-, 724-, 857-, 869-, 885-, and 889-keV prompt transitions. The inset to (b) shows the low-energy delayed transitions expanded for clarity. The 47- and 54-keV peaks are the Ho Kα and Kβ x rays, respectively, aiding veriﬁcation of the assignment of the observed transitions to 144 Ho.

0 0 200 400 600 800 1000 1200

ENERGY (keV)

FIG. 2. (a) Prompt spectrum of γ rays in coincidence with the 869-keV γ ray in the isomer-gated prompt γ -γ matrix, showing the transitions in Band 1a. (b) Spectrum of γ rays in coincidence with the 915-keV γ ray in the same matrix, showing the transitions in Band 1b and linking transitions to Band 1a.

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762

ENERGY (keV)

100

813 857 889

0

50

100

150

200

250

300

350

724

817 857 885 928

200
47

400

600

800 1000 1200 8000 6000 4000 2000 0 45 50 55 60

724

SPECTROSCOPY OF 144 Ho USING RECOIL-ISOMER . . .

PHYSICAL REVIEW C 81, 024302 (2010)

TABLE I. Delayed γ -ray energies, intensities, internal-conversion coefﬁcients, multipolarities, and initial and ﬁnal spins for 144 Ho deduced in this work. Eγ (keV) 56.8(3) 61.0(2) 86.8(4) 122.8(5) 148.9(2) 209.6(4) Iγ 86(9) 11(2) 4(2) 5(2) 100(6) 53(5) αK (exp.) 1.1(2) 8(1) 3(1) 3(1) 0.6(1) <0.2 αK (calc.) 1.1(E1), 11(M1), 2.1(E2) 0.94(E1), 9.1(M1), 2.3(E2) 0.38(E1), 3.3(M1), 1.5(E2) 0.15(E1), 1.2(M1), 0.65(E2) 0.09(E1), 0.71(M1), 0.38(E2) 0.04(E1), 0.27(M1), 0.14(E2) Adopted multipolarity E1 M1/E2 M1/E2 M1/E2 M1/E2 E2
π Jiπ → Jf

(8+ ) → (7− ) (6− ) → (5− ) (6− ) → (5− ) (7− ) → (6− ) (7− ) → (6− ) (7− ) → (5− )

in Tables I and II and the deduced level scheme is shown in Fig. 3. The intensities of the prompt and delayed transitions are normalized separately. The placement of Band 1b, which appears to form a signature partner to Band 1a, was conﬁrmed and the band was extended to spin I π = (21+ ). A number of transitions linking Band 1b to Band 1a were also observed. The 842-keV transition depopulating the I π = (21+ ) state is assigned tentatively as its placement could not be directly conﬁrmed through coincidence measurements. However, summing gates on Band 1b, excluding the 813- and 889-keV doublets, shows that the 842-keV γ ray is coincident with this band. Figure 2(b)
TABLE II. Prompt γ -ray energies, intensities, initial and ﬁnal spins, and angular coefﬁcients for 144 Ho deduced in this work. Eγ (keV) 140.6(5) 293.7(5) 363.3(2) 387.4(7) 429.9(1) 468.1(2) 474.4(5) 500.0(5) 501.9(1) 530.8(6) 569.3(3) 645.4(5) 662.3(4) 723.7(1) 745.4(5) 762.3(2) 812.7(8) 816.7(7) 833.8(5) 842.0(5) 856.6(2) 869.2(5) 884.8(6) 889.3(8) 915.3(3) 927.5(3)
a

Iγ 2(1) 1(1) 14(2) 3(1) 25(2) 17(2) 3(1) 10(4) 100(6) 6(2) 9(2) 12(3) 15(2) 62(4) 6(2) 14(2) 7(3) 8(3) 2(1) 3(1) 43(4) 16(2) 26(10) 10(4) 11(2) 6(2)

π Jiπ → Jf

A2

A4

(10+ ) → (9+ ) (12+ ) → (11+ ) (9+ ) → (8+ ) (14+ ) → (13+ ) (11+ ) → (10+ ) (13+ ) → (12+ ) (19+ ) → (18+ ) (15+ ) → (14+ ) (10+ ) → (8+ ) (17+ ) → (16+ ) (11+ ) → (9+ ) → (13+ ) (12) → (11+ ) (12+ ) → (10+ ) (13+ ) → (11+ ) (19+ ) → (17+ ) (20+ ) → (18+ ) (21+ ) → (19+ ) (14+ ) → (12+ ) (18+ ) → (16+ ) (16+ ) → (14+ ) (15+ ) → (13+ ) (17+ ) → (15+ ) (22+ ) → (20+ )

−0.2(1) −0.4(1) −0.4(1) 0.31(2)a 0.31(2)a

0.0(2) 0.0(1) 0.0(1) 0.09(16)a 0.09(16)a

−0.2(1) 0.45(8) 0.6(2)

0.3(2) −0.2(1) 0.1(2)

0.5(1) 0.4(2)

−0.3(2) 0.0(2)

Value represents the combined intensity for the 500/502-keV doublet.

shows the spectrum of γ rays in coincidence with the 915-keV peak in the isomer-gated prompt γ -γ matrix, showing the other members of Band 1b and several linking transitions to Band 1a. Angular distributions were measured for the most intense transitions in Bands 1a and 1b by creating prompt isomertagged singles spectra for each ring of the JuroGam array. The transition intensities were measured as a function of beamto-detector angle and ﬁtted with a series of Legendre polynomials of the form W (θ ) = A0 + A2 P2 cos(θ ) + A4 P4 cos(θ ) as described by Yamazaki [16]. The Ak coefﬁcients were compared to theoretically calculated coefﬁcients, assuming a substate population distribution of width σ/I = 0.3 [17], to deduce the spin changes associated with the γ -ray transitions. The 363-, 430-, and 468-keV transitions were found to have angular coefﬁcients consistent with stretched dipole transitions and are assumed to be of M1 character, forming the linking transitions between the signature partner bands, 1a and 1b. The coefﬁcients for the 724-, 762-, 857-, and 869-keV transitions are found to be consistent with stretched quadrupole transitions and these γ rays are assumed to be of E2 character. As the peak for the 502-keV transition could not be resolved from the peak at 500 keV, the measured angular distribution is the combined distribution for the 500/502-keV doublet. The measured distribution for this doublet is seen to be consistent with a pure stretched quadrupole. Because the 502-keV contains ∼90% of the intensity for the doublet, the distribution is assumed to be representative of this transition. No multipolarity can be inferred for the weaker 500-keV transition. The measured angular coefﬁcients are summarized in Table II and sample angular distributions are shown in Fig. 4. The prompt-delayed matrix reveals two previously unobserved delayed transitions at 87 and 123 keV (see Fig. 1). Analysis of the delayed γ -γ matrix shows that these transitions are in coincidence with the 57-keV γ ray depopulating the 144m Ho isomer. Because the 87- and 123-keV transitions are in coincidence with each other, but show no coincidences with the 61-, 149-, and 210-keV γ rays below the isomer, it is clear that these transitions form a decay branch parallel to the 210-keV transition. K-shell internal conversion coefﬁcients were measured from x-ray intensities in the delayed γ -γ matrix and compared to theoretically calculated values from the BRICC internal conversion coefﬁcient database [18] to assign multipolarities to the transitions below the 144m Ho isomer. The measured

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PHYSICAL REVIEW C 81, 024302 (2010)

Band 1a Band 1b
(21 ) 928 (22 )

1.5

1

W(θ)

0.5 1.5

(a) (c)

(b) (d)

(842)

(20 )

144

Ho77

(19 ) 817 474 813 (17 ) 869 531 915 (16 ) (18 )

1

0.5 0 0.4 0.8 0 0.4 0.8

cos θ

2

(834)

(15 ) 885 500 889 (14 ) 387 (13 ) 857 468 662 (11 ) 569 (9 ) 762 294 724 430 (10 ) (141) 363 210 (6 ) 502 57 149 61 (12 )

FIG. 4. Angular distributions measured for the (a) 363-, (b) 430-, (c) 724-, and (d) 857-keV transitions of 144 Ho. The solid lines and dashed lines show the theoertically calculated distributions for pure stretched dipoles and pure stretched quadrupoles, respectively. A substate distribution width of σ/I = 0.3 [17] was chosen for the theoretical distributions.

745 (12)

645

half-life of the 144m Ho isomeric state to be 519(5) ns. This is in agreement with measurements of 500(20) ns [8] and 564(60) ns [6] from previous studies. The sum of time spectra for the 57-, 61-, 87-, 123-, 149-, and 210-keV transitions is shown in Fig. 5.
IV. DISCUSSION

519(5)ns

8 123 87 (5 )

The shapes of the ground state and isomeric state were determined using the conﬁguration-constrained blocking method [9] to calculate the potential-energy surface (PES) of the quasiparticle states. The method is based on a nonaxial deformed Woods-Saxon potential and treats β and γ as dynamical variables. Average Nilsson quantum numbers for

FIG. 3. The level scheme for 144 Ho deduced from this study. The widths of the arrows are proportional to the intensities of the γ -ray transitions and the white part of the arrows represents the calculated internal conversion component.
Counts / 10 ns

10

4

internal conversion coefﬁcients are summarized in Table I, along with the assigned multipolarities for each transition. The assigned multipolarities give a maximum spin change between the ground state and isomer of I = 3, which is consistent with the assumed spins of I π = (5− ) and I π = (8+ ) for the ground state and isomer, respectively. The half-life of the 144m Ho isomer was measured by creating a two-dimensional energy-time matrix for the planar detector. The time was deﬁned as the time difference between a recoil implantation in the DSSDs and a correlated γ ray being detected in the planar detector. Gating on a particular γ -ray peak in the energy spectrum allowed the exponential time spectrum of that γ ray to be observed. Half-lives were measured for the 57-, 61-, 87-, 123-, 149-, and 210-keV transitions and a weighted averaged of these results gave the

10

3

10

2

10

1

10

0

0

2

4 Time (µs)

6

8

10

FIG. 5. (Color online) The sum of the individual time spectra for the 57-, 61-, 87-, 123-, 149-, and 210-keV γ rays in 144 Ho. The solid line represents the ﬁt to this data with a half-life of 519(5) ns. Here the “time” axis is deﬁned by the time difference between a recoil implantation in the GREAT DSSDs and the γ ray being detected.

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