J Ha

T Sumikama
email: sumikama@ribf.riken.jp

F Browne

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P Doornenbal

G Lorusso

P.-A Söderström

H Watanabe

R Daido

Z Patel

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Z Li

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Zs Podolyák

P H Regan

O J Roberts

H Sakurai

H Schaffner

G S Simpson

H Suzuki

H Takeda

M Tanaka

J Taprogge

V Werner

O Wieland

Shape evolution of neutron-rich 106,108,110 Mo isotopes in the triaxial degree of freedom

  L'archive ouverte pluridisciplinaire

to triaxial motion [START_REF] Casten | Nuclear Structure from a Simple Perspective[END_REF]. In the case of axially-symmetric quadrupole deformation, a rotational band built on a γvibrational state constitutes the γ band. The energy of its band head is related to the softness of the vibrational motion in the γ direction. When the potential energy surface (PES) has a deep minimum between γ = 0 • (prolate) and 60 • (oblate), the nucleus takes on a static triaxial shape and rotates about all three axes of the intrinsic body. The rigid triaxial rotor model by Davydov et al. [START_REF] Davydov | [END_REF] predicts that the 2 + 2 state lies below the 4 + 1 state at the maximum triaxiality of γ = 30 • . Another model of the triaxial shape is the γ-unstable rotor by Wilets

and Jean [3], where PES has a γ-independent valley at a given β. The γ-unstable model predicts degenerate 2 + 2 and 4 + 1 states. A transitional rotor between the γvibrational band and the γ-unstable rotor is the γ-soft rotor, of which the PES has a moderate path between prolate and oblate [4].

The neutron-rich Mo isotopes are good candidates to investigate shape evolution in the γ degree of freedom.

Calculations using the liquid-drop or the finite-range liquid-drop model using particle number projection or Bardeen-Cooper-Schrieffer methods predict the coexistence of prolate and oblate shapes, a prolate-to-oblate shape transition at N = 68 or 70, and triaxial ground states in 104 Mo, 106 Mo, and 108 Mo [5]. Hartree-Fock-Bogoliubov (HFB) calculations with the D1S-Gogny interaction [START_REF] Hilaire | AIP Conference Proceedings[END_REF] predict a gradual transition from γ-soft rotor in 102 Mo to oblate in 112 Mo. A calculation using the global Skyrme energy density functional UNEDF0 predicts triaxial ground-state deformation in 106,108 Mo [START_REF] Zhang | [END_REF].

Calculations of two quasi-particle states are used to investigate quasi-particle configurations near the proton and neutron Fermi surfaces [8].

From the lifetime measurement of the ground-state band in 100-108 Mo [9], the quadrupole deformation was indicated to reach a maximum at 106 Mo. More precise measurements are awaited to obtain a certain conclusion, since uncertainties of transitional quadrupole moments are larger than a change among isotopes. The measured 2 + 2 -state energy, E(2 + 2 ), in the neutron-rich Mo isotopes decreases as mass number, A, increases. It becomes almost equal to E(4 + 1 ) at A = 108 and drops below E(4 + 1 ) at A ≥ 110 [10][11][12][13][14][15][16]. The low-lying 2 + 2 state in the neutron-rich Mo isotopes has been interpreted in terms of the rigid triaxial shape [12], γ vibration [13,14],

and γ-soft rotor [15] based on the measured values of the energies of the 2 + 1 , 4 + 1 , and 2 + 2 states and the γ-decay branching ratio from 2 + 2 state. The interpretation of the 2 + 2 state attracts controversy due to its similarity between the three models, since the γ-vibrational state and γ-soft rotor have a finite root-mean-square value of γ as a result of a dynamic motion.

The energy staggering of the 2 + 2 band is a good signature to distinguish among the three models which describe axial asymmetry [START_REF] Casten | Nuclear Structure from a Simple Perspective[END_REF]17]. The rigid-triaxial and γ-soft rotors show an energy staggering which deviates from the J(J + 1) dependence of the rigid axial rotor.

The staggering of the rigid triaxial rotor is opposite to 101 that of the γ-soft rotor; for example, the 3 + γ state is close 102 to the 2 + γ and 4 + γ states of the rigid triaxial and γ-soft the existence of β-decaying isomeric states. For exam-194 ple, in Ref. [32], the β-γ spectrum of 102 Zr was observed

217

In the previous β-γ spectroscopic study [12], the ground

FIG.

2. The proposed level scheme of 106 Mo obtained from the β-decay chain 106 Zr→ 106 Nb→ 106 Mo. The Q(β -) of 106 Nb is taken from the atomic mass evaluation (AME2016: [33]). The arrow width is proportional to the relative intensity Iγ (Zr → Mo, given in Table II). Red lines are the new levels and transitions. Spin-parities of the known states are taken from ENSDF [START_REF]ENSDF database[END_REF]. indicates an allowed transition with ∆J = 0 or 1 and ∆π = 0, or a first non-unique forbidden transition with ∆J = 0 or 1 and ∆π = 1 [40]. was also roughly half of that reported in Ref. [21]. This for the transitions to these states, the spin-parity of the a The absolute intensity per 100 β-decays is 0.448(23)Iγ .

b Internal conversion coefficients, calculated using the BrIcc code [START_REF] Kibédi | [END_REF], were adopted for three transitions with 192.8, 196.0, and 197.9 keV.

second unique forbidden transition with ∆J = 3 and ∆π = 0. The log f t value of the 5 -state was recalculated to be 11.6(2) and within the typical range from 10.6 to 18 for the second unique forbidden transition [40].

Therefore, the spin-parity of the 108 Nb was assigned to be 2 -. The quasi-particle state configuration of 108 Nb is described in Sec. IV F.

C. Neutron-emission probability in 108 Nb β decay

The zero-neutron emission probability, P 0n , of the

P n = 1 -P 0n = ∑ i≥1 P in , ( 1
)
where i is the number of the emitted neutrons.

∑ I L β (E i ) + I L β (0) + P L n = 100%, ( 4
) ∑ I H β (E i ) + P H n = 100%, (5)
(E i ) = r ∑ I L β (E i ) + (1 -r) ∑ I H β (E i ). ( 6
)
From the assumption that the 828. The logf t values were determined from the half-lives, I β and Q β = 12230(840) keV [33] for the low-and highspin states, (as summarized in Tables IV andV), respectively. The excitation energy in 110 Nb was not taken into account, which would be negligible in comparison with its

Q β .
First, the spin-parity of the low-spin state in

663

for 106 Mo are 0.54 (8) [47,48], 1.08 (22) [49], 1.73 (24) [50], 664 and 1.93 (14) ns [START_REF] Cheifetz | Proc. Conf. Nucl. Spectr. Fission Products[END_REF]. The present lifetime (τ = 1.86 (13) 665 ns) is consistent with the values in Refs. [50,[START_REF] Cheifetz | Proc. Conf. Nucl. Spectr. Fission Products[END_REF]. The 666 result of τ = 1.21 [START_REF] Zhang | [END_REF] ns for 108 Mo is consistent with the 667 previously reported value of 0.72 (43) ns [21] 681 values using the formula given in the review paper [48] 682 as 0.349(13), 0.327 (10) ) values of the even-even Mo isotopes. The experimental values were calculated by the use of the relation in Ref. [START_REF] Raman | [END_REF]. The open circles are taken from Ref. [48]. The theoretical values were calculated using the five-dimensional collective Hamiltonian with the pairing-plus-quadrupole interaction parameters determined from the two kinds of the Skyrme-interaction parameters (SLy5+T and SLy4). for the Mo isotopes. Filled squares for the Zr isotopes are the results from the same data set [53], but the values were recalculated from B(E2; 2 + 1 → 0 + 1 ) by using the formula given in the review paper [48]. Open circles and squares are taken from the review paper [48] and a later work [54].

the energy staggering of the 2 + 2 band [START_REF] Casten | Nuclear Structure from a Simple Perspective[END_REF]:

695 E s (J) E(2 + 1 ) = ∆E J -∆E J-1 E(2 + 1 ) , ( 9
)
where ∆E J = E γ (J) -E γ (J -1), and E γ (J) is the 696 energy of the 2 + 2 band member with the spin J. The of J for the Mo, Ru, and Pd isotopes. The difference 714 among the isotopes is more apparent than in Fig. 12.

715

The J-dependence of E s (J)/E(2 + 1 ) is shown to have a ). The flat pattern indicates the γ-vibrational band, while the staggering pattern with low values at even and odd J indicates the γ-soft and rigid triaxial rotor, respectively, [4]. TABLE VI. The experimental and theoretical B(E2) ratios. The M1/E2 mixing ratio of δ = 6.2 +1.0 -0.8 [56] was used for 106 Mo. A pure E2 transition was assumed for 108 Mo and 110 Mo. The theoretical calculation using the SLy5+T interaction is given. The squared wave functions of the 0 + 2 state in [64] and the quasiparticle level in the Woods-Saxon potential [66] for each nucleon. The left and right values show the spin-parity of the parallel-and antiparallel-spin coupling, respectively. The parallel-spin coupling state becomes lower-lying state [65].

Alaga 106 Mo 108 Mo 110 Mo B(E2; 2 + 2 → 2 + 1 ) B(E2; 2 + 2 → 0 + 1 ) exp. 4.5(6) 8.3(6) 17.3(4)
B(E2; 2 + 2 → 2 + 1 ) B(E2; 2 + 2 → 0 + 1 ) th.
The spins of the assigned configurations for the low and highspin states are written in bold text.

π1/2 + [431] π5/2 + [422] π5/2 -[303] π3/2 -[301] ν5/2 + [402] 2 + /3 + 5 + /0 + 0 -/5 - 4 -/1 - ν1/2 + [411] 1 + /0 + 2 + /3 + 3 -/2 - 1 -/2 - ν7/2 -[523] 3 -/4 - 6 -/1 - 1 + /6 + 5 + /2 + ν1/2 -[541] 1 -/0 - 2 -/3 - 3 + /2 + 1 + /2 +
proton and neutron levels in the deformed nucleus 962 were calculated according to the Nilsson diagram [64] 963 and by using the Woods-Saxon potential [66] It is interesting to investigate whether the disagreement between the experiment and prediction for 110 Mo is enhanced at heavier Mo isotopes or not. The low-lying 2 + 1 , 4 + 1 , and 2 + 2 states are known in 112 Mo [16]. In order to study the triaxial motion, measurements of the higher spin states in the 2 + 2 band are awaited.

195A. β decay to 106 Mo 208 Figs. 1 (

 2081 Figs.1 (a-b). The proposed level scheme of 106 Mo, illus-211 212

218

  band was observed up to 6 + , and the 2 + 2 and 4 + 3 bands 219 up to 4 + . In the present study, γ rays from the 5 + states 220 in the 2 + 2 and 4 + 3 bands were observed. These γ rays 221 are consistent with the results obtained from the spon-222 taneous fission of 252 Cf [35-37]. The placement of the 223 784.6-keV and 1106.7-keV γ rays were reassigned from 224 those of Ref. [12] based on the following arguments. The 225 0 + 2 state was previously assigned at 956.6 keV based on 226 the 784.6-keV transition feeding only the 171.4-keV level. 227 However, the high statistics of the present study allowed 228 us to observe additional coincidences with the 784.6-keV 229 transition, which are shown in Fig. 1 (d). Based on this 230 information, the assignment of the 784.6-keV γ ray as the 231 transition between the 5 + 1 and 4

FIG. 4 .

 4 FIG. 4. (a-b) The β-delayed γ-ray spectrum of 108 Nb obtained from the β-decay chain 108 Zr→ 108 Nb→ 108 Mo. The range of the time window was set to be 80 ms < tion -t β < 280 ms. The labeled peaks belong to 108 Mo. The identified background peaks are marked with asterisks. Other unknown peaks are mainly associated with parent 108 Zr decays. (c-d) The coincidence spectra gated on 192.8 keV and 700.7 keV.

366 1 375 and 4 + 1

 141 may be due to a 50% uncertainty of the 108 Nb yield ex-367 trapolated as a function of the atomic number [21]. Al-368 though the uncertainty of the previous I β was not eval-369 uated, the present I β (3 + 1 ) of 5.1(6)% is 1/10 of the re-370 ported 53% [21] owing to yield uncertainties and the pre-371 vious non-observation of the cascade transitions to the 372 3 + 1 state.373The log f t values were determined from T 1/2 , I β , and374 Q β = 11210(12) keV[33]. The log f t values of the 0 + states were 5.8(3) and 6.4(1) and are too small 376 for any transitions with ∆J ≥ 2[40]. This is the same 377 situation as for the 106 Nb decay. If the first unique for-378 bidden transition with ∆J = 2 and ∆π = 1 is considered 379

405N

  β ( 108 Nb) was determined to be 5.20(13) × 10 4 from 406 a fit to the β-decay time curve obtained following the 407 implantation of 108 Nb. The fit used the decay half-lives 408 and neutron-emission probabilities of the parent 108 Nb, 409 daughters 107,108 Mo, granddaughters

FIG. 6 .

 6 FIG. 6. (a-b) The β-delayed γ-ray spectrum of the implanted 110 Nb. The time window after the implantation of 110 Nb was set to be less than 400 ms. The labeled peaks belong to 110 Mo. The identified background peaks are marked with asterisks. (c-d) The coincidence spectra gated on 213.4 keV and 828.8 keV. (e) The β-delayed γ-ray spectrum obtained from the β-decay chain 110 Zr → 110 Nb→ 110 Mo, where ∆t β-ion from 30 to 250 ms was selected.

decay of 110

 110 Zr was analyzed using the observation of the 95-keV γ ray as time zero. The observation of the 213.4-, 280.2-, and 493.8-keV γ rays shows that the low-spin state in 110 Nb is selected by the gate on the 95-keV γ ray. The ratio of the number of the measured β decays and 213.4-keV γ rays was determined from this subsequent βdecay analysis. The conversion factor from I γ to absolute intensity was determined to be 0.41(14) using the 213.4-keV γ ray. The I γ values corresponding to the high-spin state were determined by subtracting the low-spin contribution from the results given in Table V under the assumption that the ground and second 0 + states are directly populated only by the low-spin β decay. The I β values for low-and high-spin β decays were determined and are summarized in Tables IV and V. The I β value of the 110 Mo ground state corresponding to the low-spin state and P n values corresponding to the low-and high-spin states were determined by combining the following five equations. First, the P n value has a relation to I β (E i ) for the γ-decaying states at the energy E i and I β (0) for the ground state as,

of the 110

 110 Mo β decay was obtained using the 121.0-keV γ ray emitted from 110 Tc. From R(121.0 keV) = 0.0375(16), N γ (121.0 keV) = 2.279(44) × 10 4 , and N β ( 110 Nb) = 7.39(7)×10 5 , P L+H 0n = 82(4)% and P L+H n = 18(4)% were determined. Based on the above values and Eqs. (4-8), the remaining values were determined as P L n = -5(41)%, P H n = 31(15)%, I L β (0) = 47(26)%, and ΣI H β (E i ) = 69(15)%. Since the P L n value must be positive, an upper limit is given as P L n < 36%. The large uncertainties were propagated mainly from the uncertainty of I L γ,abs (828.8 keV). The separate P n determination of the low-and high-spin states was made for the first time in the 110 Nb β decay. The previous P L+H n value of 40(8)% [43] is larger than the present result. In the previous work, 110 Nb was produced by bombarding a U target with a 50 MeV H + 2 beam. The low-spin fraction r may be different due to the different production reaction and energy.

FIG. 8 .

 8 FIG. 8. The time spectra of 2 + 1 → 0 + 1 γ-ray transition in 106 Mo, 108 Mo, and 110 Mo. ∆T is the time from β-particle detection by the plastic scintillator to γ-ray detection by the LaBr3(Ce) array. The solid red lines are the best-fit curves using an exponential function and fixed constant background to the region indicated by the dashed red lines. The constant backgrounds, shown by the orange lines, were determined by fitting the region of 15 < ∆T < 25 ns, 10 < ∆T < 25 ns, and 8 < ∆T < 25 ns for 106 Mo, 108 Mo, and 110 Mo, respectively.

Fig. 10 .FIG. 9 .

 109 Fig. 10. The present results with small uncertainties 672

FIG. 11 .

 11 FIG. 11. Quadrupole deformation parameter β for Zr (square) and Mo (circle) isotopes. Filled circles are the present results for the Mo isotopes. Filled squares for the Zr isotopes are the results from the same data set[53], but the values were recalculated from B(E2; 2 + 1 → 0 + 1 ) by using the formula given in the review paper[48]. Open circles and squares are taken from the review paper[48] and a later work[54].

697 E s ( 4 )/E( 2 + 1 )FIG. 12 .Figure 13

 4211213 FIG. 12. The Es(4)/E(2 +1 ) ratio around neutron-rich A = 110. The black-dashed lines represent the ideal values of three models; rigid-triaxial rotor, γ-unstable rotor, and γvibrational band. Filled square, circles, triangles and inverted triangles represent Zr, Mo, Ru, and Pd isotopes, respectively.

716

  relation to the triaxial motion from the calculation us-717 ing the Bohr Hamiltonian with a γ-dependent potential 718 [4]. While the γ-vibrational band shows a flat pattern, 719 the γ-soft and the rigid triaxial rotors show a staggering 720 pattern with low values at even and odd J, respectively.

FIG. 13 .

 13 FIG.13. The staggering pattern of Es(J)/E(2 + 1 ). The flat pattern indicates the γ-vibrational band, while the staggering pattern with low values at even and odd J indicates the γ-soft and rigid triaxial rotor, respectively,[4].

  a γ-vibrational band. model which introduces the Coriolis mixing between two 756 bands with ∆K = 2 [1]. In Sec. IV E, the B(E2) ratio is 757 compared with beyond-mean-field calculations.

FIG. 14 .

 14 FIG.14. The kinematic moment of inertia for the ground band (black line with filled squares), K π = 2 + band (blue line with filled triangles for even J and green line for odd J), and K π = 4 + band (red line with open circles for even J and orange line for odd J) in (a)106 Mo, (b) 108 Mo, and (c) 110 Mo.

6 FIG. 16 . 5 FIG. 17 .

 616517 FIG.16. Same as Fig.15, but with the SLy4 interaction.

1029 2 1049

 2 figurations of the parent nuclei were assigned by referring the Nilsson diagram for the prolate shape.

1089 ACKNOWLEDGEMENTS 1090

 1090 We would like to express our gratitude to the 1091 RIKEN Nishina Center accelerator staff for provid-1092 ing a stable and high intensity 238 U primary beam. 1093 This work was supported by JSPS KAKENHI Grants 1094 Nos. 24740188, 25247045, 26800117, and 16K17680, 1095 NRF Grant No. 2016K1A3A7A09005575, STFC Grant 1096 Nos. ST/J000132/1, ST/J000051/1 and ST/K502431/1, 1097 DOE Grant No. DE-FG02-91ER-40609, and Span-1098 ish Ministerio de Ciencia e Innovación under Contracts 1099 No. FPA2009-13377-C02 and No. FPA2011-29854-C04. 1100 P.H.R. acknowledges support from the UK National Mea-1101 surement Office (NMO). P.-A.S. was financed by JSPS 1102 Grant No. 23 01752 and the RIKEN Foreign Postdoc-1103 toral Researcher Program. We acknowledge the EU-1104 ROBALL Owners Committee for the loan of germa-1105 nium detectors and the PreSpec Collaboration for the 1106 readout electronics of the cluster detectors. NH ac-1107 knowledges the JSPS-NSFC Bilateral Program for the

TABLE I .

 I The number of106,108,110 Zr and 106,108,110 Nb ions implanted in WAS3ABi and their implantation rate.

		Isotope	The number of	Implantation rate
			implanted ions	(pps)
		106 Zr	1.9 × 10 6	3.5
		108 Zr	2.1 × 10 6	3.8
		110 Zr	3.2 × 10 4	0.059
		106 Nb	7.1 × 10 4	16
		108 Nb	1.3 × 10 5	0.24
		110 Nb	1.9 × 10 6	3.5
		tecting the cross-talk signal induced to the DSSSD down-
	188	decay of 106,108,110 Nb were studied. The daughter decays
	189	of Zr isotopes were also analyzed to increase statistics
	190	and to search for β-decaying isomeric states. The num-
	191	ber of implanted Nb and Zr isotopes are summarized in
	192 193	Table I. Daughter-decay analysis provides evidence on

  106 Nb→ 106 Mo and 106 Zr→ 106 Nb→ 106 Mo.

	Counts/0.5 keV 106 40	3 (a) 10 × + 0 66 Zr 25 15	β	-	171 188 106 Nb 65 41 223 =1.10(5) s 1/2	351 357 363	421	5 539 × 511 545 550 517	710 714 724	783 & 785 773	869	896	932	978 998 1009
			100		200	300		400	500	600	700		800		900	1000
	Counts/0.5 keV	1013 1022 (b) 1052	1107 1113		1263		1364 1359		1471 & 1474	1624	1677	1752	1780	1850	1913 1930
			1100		1200	1300		1400	1500	1600	1700		1800		1900	2000
	Counts/1.0 keV	(c)					363 357 351	421	539 545 550 517 511	714 724	896 171 keV gate 783 & 785 773 869	932	978	1009
			100		200	300		400	500	600	700		800		900	1000
	Counts/1.0 keV				171		351					783 785 keV gate
			100		200	300		400	500	600	700		800		900	1000
									Energy (keV)
									232	+ 1 states is preferred. The observation of the transition from 5 + 1 to 3 + 1 supports this
									106 Mo 64 42
									270	Two relevant transitions, 2 + 1 → 0 + 1 and 2 + 2 → 0 + 1 , were
									271	observed. The sum of the absolute intensities of these two
									272	transitions was 92.2(51)%, which included contributions
									273	of possible undetected transitions, due to low intensities,
									274	through the 2 + 1 or 2 + 2 states. The remaining 7.8(51)%
									275	contribution is the sum of I β to the ground state, and
									276	the β-delayed neutron emission probability, P n . When a
									277	previously measured P n of 4.5(3)% [34] is subtracted, the
									278	I β value to the ground state is given as the upper limit
										< 8.4%.
									283
	269								255

233

assignment. The previous assignment of the 1106.7-keV 234 γ ray was the transition between a 1279.9-keV state to 235 the 2

+

1 state

[12]

, but it was reassigned to a known tran-236 sition

[START_REF]ENSDF database[END_REF]

from the 1816.9-keV state, since a coincidence 237 with 710.2 keV was observed. The half life of 106 Nb was 238 determined to be 1.10(5) s from the decay curve of the 239 171.4-keV γ ray for the 106 Nb→ 106 Mo decay as shown in 240 Fig. 3 (a). The obtained half life was consistent with the 241 evaluated value of 1.02(5) s [34]. 242 Table II summarizes the relative γ-ray intensity, I γ , 243 following the β decay from 106 Nb to 106 Mo from the two 244 decay chains, 245 Since I γ of the major peaks was consistent between both 246 decay chains, there was no evidence on the existence of a 247 second β-decaying state in 106 Nb. The absolute γ-ray in-248 tensities per 100 β decays were determined from the data 249 of the 106 Nb→ 106 Mo decay for the first time. Here, we 250 used the number of the detected β particles emitted from 251 the 106 Nb decay, which was determined from the decay-252 curve integral of the parent component in the fitting func-253 tion to the β-particle counts as a function of time. The 254 conversion factor from the relative to absolute γ-ray in-(d) FIG. 1. (a-b) The β-delayed γ-ray spectrum of 106 Nb obtained from the β-decay chain 106 Zr→ 106 Nb→ 106 Mo. The range of the time window was set to be 180 ms < tion -t β < 2200 ms. The labeled peaks belong to 106 Mo. The identified background peaks are marked with asterisks. Other unknown peaks are mainly associated with parent 106 Zr decays. (c-d) The coincidence spectra gated on 171.4 keV and 784.6 keV. tensities was obtained from the absolute intensity of the 256 largest γ-ray peak at 171.4 keV in the 106 Nb→ 106 Mo de-257 cay. The relative systematic uncertainty of the absolute 258 γ-ray detection efficiency was adopted into the uncer-259 tainty of the conversion factor as 0.696(38). 260 The β-decay intensities, I β , to excited states, given in 261

Table II, were determined by combining results obtained 262 from the Zr→ 106 Nb→ 106 Mo and 106 Nb→ 106 Mo decay 263 chains so as to take into account small β-decay branches. 264 The decay schemes and I γ values were obtained from 265 the 106 Zr→ 106 Nb→ 106 Mo decay chain, which provided 266 higher statistics. The total I β of all γ-decaying excited 267 states is given by summing the absolute transition in-268 tensities of excited states decaying to the ground state. 279 Table II summarizes the logf t value of each excited 280 state calculated using Q(β -) = 9931

(10)

keV from the 281 atomic mass evaluation (AME2016)

[33]

and the calcula-282 tion tool of Ref.

[START_REF]Calculation program of logf t[END_REF]

. The logf t of the 6 + 1 state, 6.6(1),

TABLE II :

 II decay from the implanted 106 Nb to 106 Mo. (Zr→Mo) indicates the β decay to 106 Mo in the decay chain of the implanted 106 Zr, i.e. 106 Zr→ 106 Nb→ 106 Mo. (allowed/non-UF) indicates the calculation is for the allowed or non-unique forbidden transitions. (1UF) is for the first unique forbidden transition from 4 -to 2 + or 6 + states.

	Ei(keV)	J π	Eγ(keV)	Iγ a	Iγ	I β (%) b	logf t	logf t
				(Nb→Mo)	(Zr→Mo)		(allowed/non-UF)	(1UF)
	0.0	0 +				< 8.4
	171.4(2)	2 +	171.4(2)	100(2)	100.0(5)	7.3(8)	6.7(1)	9.1(1)
	521.9(2)	4 +	350.5(2)	37.9(16)	43.8(5)	9.1(14)	6.5(1)

The level energy, Ei, spin-parity, J π , γ-ray energy, Eγ, relative γ-ray intensity, Iγ, β-decay intensity, I β , and log f t of the excited states in 106 Mo. (Nb→Mo) indicates the β

TABLE II

 II

					: (continued)
	Ei(keV)	J π	Eγ(keV)	Iγ a	Iγ	I β (%) b	logf t	logf t
				(Nb→Mo)	(Zr→Mo)		(allowed/non-UF)	(1UF)
	710.2(1)	2 +	188.4(4)	2.9(7)	0.3(2)	2.8(6)	7.0(1)	9.3(1)
			538.8(2)	16.6(12)	15.6(3)
			710.2(2)	14.4(15)	15.2(3)
	884.7(2)	3 +	174.7(3)		1.0(4)	8.7(7)	6.5(1)
			362.5(3)	1.7(7)	0.7(2)
			713.5(2)	30.1(17)	31.9(4)
	1032.8(3)	6 +	510.9(2)	5.3(12)	8.2(15)	5.5(11)	6.6(1)	8.9(1)
	1067.4(1)	4 +	357.4(2)	3.9(8)	2.1(2)	7.9(5)	6.5(1)
			545.4(2)	5.3(10)	7.6(2)
			896.0(2)	6.1(10)	6.1(2)
	1149.5(2)	(2 + )	978.1(2)		2.3(2)	1.6(2)	7.1(1)	9.4(1)
	1306.2(2)	5 +	421.3(2)	3.1(7)	3.5(2)	5.4(8)	6.6(1)
			784.6(2)	3.4(8)	5.5(7)
	1434.3(1)	4 +	549.5(2)	5.1(9)	6.9(2)	7.0(5)	6.4(1)
			724.3(2)	11.7(12)	14.0(3)
			1262.7(3)		1.4(2)
	1535.1(3)	(4 + )	1013.2(2)		1.5(3)	1.0(2)	7.2(1)
	1657.2(3)	5 +	772.5(2)		1.4(2)	1.0(1)	7.2(1)
	1719.2(2)		1009.0(2)		1.3(2)	0.9(1)	7.2(1)

β decay to 108 Mo The

  β-delayed γ-ray spectrum of 108 Mo obtained from the 108 Zr→ 108 Nb→ 108 Mo decay chain is shown in

	unique forbidden transitions, the log f t values need to be calculated by taking into account the different energy dependence of the shape factor from that of the allowed decay [38, 41]. The log f t of the 6 + 1 state becomes 8.9(1) for the first unique forbidden transition with ∆J = 2 and ∆π = 1. This value is consistent with the typical range from 8 to 11 [40]. This indicates that the spin-parity of type to other states. Since the β decay to the 2 + states is 100 200 300 400 500 106 Nb is 4 -. This assignment determines the transition Counts/0.5 keV 193 371 393 391 414 65 ( 107 Mo) 196 & 198 (a) 3 10 ×	×	5	0 1000 2000 3000 4000 5000 6000 7000 8000 700 800 900 1000 =1.10(5) s 1/2 T + 1 0 → + 1 171.4 keV (2 Mo 106 → Nb 701 966 818 840 836 944 (a) 639 622 600 Counts/80 ms 1 10 2 10 3 10 586 590 595 106	)
	also a first unique forbidden transition, the log f t values of the 2 + states with 171.4, 710.2, and 1149.5 keV were recalculated as 9.1(1), 8.9(1), and 9.4(1), respectively. These values are consistent with the typical range of the first unique forbidden transition. The log f t values of the 3 -, 4 -, and 5 -states are consistent with the allowed transition with ∆J = 0 or 1 and ∆π = 0, and those of Counts/0.5 keV 1158 1213 1355 1142 1056 1265 1426 1062 1258 1163 (b)	1535 1527	Counts/20 ms	10 2 10 3 10 1598 1622	108 (b)	Nb	→	Time (ms) 1/2 T 192.8 keV (2 =186(8) ms → + 1 Mo 1770 108 1753	0	+ 1	)
	3 + , 4 + , and 5 + states are consistent with the first non-1100 1200 1300 1400 1500		1 1600		1700	1800	1900	2000
	unique forbidden transition with ∆J = 0 or 1 and ∆π = 1. Thus, providing further evidence that the spin-parity of 106 Nb is 4 -. The quasi-particle state configuration of 106 Nb is discussed in Sec. IV F. 100 200 300 400 500 414 Counts/1.0 keV 371 391 & 393 (c)			10 600 Counts/10 ms 2 10 3 10 4 10 622 590	0 110 (c)	700 Nb 701	Time (ms) 1000 800 1/2 900 1500 =75(1) ms T 531.5 + 462.6 + 563.3 + 563.4 keV 2000 1000 Mo 966 836 193 keV gate 500 110 →
	Figs. 4 (a-b). The proposed level scheme illustrated in Fig. 5 was constructed through the use of γ-ray co-incidences, examples shown in Figs. 4 (c-d), energy sums, and intensity balances. In the previous β-decay study [21], the ground band was observed up to 4 + and the 2 + 2 band was up to 3 + . In this work, the 2 + 2 band was observed up to 4 + , and the band head of the 4 + band was namely the observed 700.7-keV transition was measured from the typical γ decay pattern of a low-lying 0 + state, 2 fied, of which the lowest at 893.4 keV was assigned to 0 + observed at 1422.1 keV. Fifteen new levels were identi-Energy (keV) 100 200 300 400 500 Counts/10 ms 600 -200 1 1 10 2 10 (d) 0 Counts/1.0 keV 193	Time (ms) 400 Time (ms) 400 600 1/2 T 800 900 600 =94(9) ms 800 800 1000 1000 + 1 0 → + 1 213.4 keV (2 Mo 110 → 701 keV gate 200 Nb 110 200 → 700 0 Zr 110	)
	to be in strong coincidence with the 2 + 1 → 0 + 1 transition,
	as shown in Fig. 4 (c), and without an observed γ de-cay to the 0 + 1 state. The spin-parity of the 1158.4-keV state was assigned to be 2 + , and those of the 1404.8-,			FIG. 3. The time spectra of β-delayed γ rays in the Mo isotopes. Dashed lines indicate the fitting region of the decay curve to determine the β-decay half life, T 1/2 . Orange lines
	and 1727.6-keV states were to be 3 or 4 + by assuming			are the constant background, which was determined by fitting
	the transition type from those states is E1 or M1/E2. The half life of the 108 Nb decay was determined to be T 1/2 = 186(8) ms from the decay curve of the 192.8-keV			to the negative-time region. The β-delayed γ rays with 531.5, 462.6, 563.3, and 563.4 keV from the implanted 110 Nb were selected as the β decays of the high-spin state in 110 Nb.
	γ ray, as shown in Fig. 3 (b), and is consistent with the
	evaluated value of 198(6) ms [34].
	The I γ values were determined for the two decay chains, 108 Nb → 108 Mo and 108 Zr → 108 Nb→ 108 Mo, as summarized in Table III. The consistent I γ values be-tween two decay chains indicate no β-decaying isomeric state in 108 Nb. The conversion factor from the relative	351 352 353 354 355	was determined to be 62.8(33)% from the sum of abso-lute transition intensities of three transitions from the 2 + 1 , 2 + 2 , and 2 + 3 states to the ground state. The zero-neutron emission probability of the 108 Nb decay, P 0n , which is the probability decaying to 108 Mo without a delayed-neutron
	to absolute γ-ray intensities was determined from the ab-	356	emission, was determined by using a new method de-
	solute 192.8-keV intensity in the 108 Nb→ 108 Mo decay.	289 357	dicates allowed or first non-unique forbidden transitions. scribed in Sec. III C as, P 0n = 82(11)%. The difference
	Three 2 + states have The I β values were determined from the absolute inten-sities and the decay scheme. As described in Sec. III A,	290 358 291 359	However, the transitions with ∆J ≤ 1 can not populate of these two values gave the ground-state I β of 19(12)%. both the 2 + and 6 + states. Therefore, transitions with The I γ values obtained in this work are inconsistent
	similar logf t values ranging from 6.7 to 7.1 which also in-the total I β of the γ-decaying excited states in 108 Mo	292 360	at least ∆J = 2 are required for these states. For the with the previous results [21] with the exception of the

B.

TABLE III :

 III Same as TableII, but for 108 Mo. (1UF) is for the first unique forbidden transition from 2 -to 0 + or 4 + states. (2UF) is for the second unique forbidden transition from 2 -to 5 -states.

	Ei(keV)	J π	Eγ(keV)	Iγ a	Iγ	I β (%) b	logf t	logf t	logf t
				(Nb→Mo)	(Zr→Mo)		(allowed/non-UF) (1UF)	(2UF)
	0.0	0 +				19(12)	5.8(3)	8.2(3)
	192.8(2)	2 +	192.8(2)	100(2)	100.0(9)	6.7(10)	6.2(1)
	563.8(2)	4 +	371.1(2)	18.2(10)	14.5(5)	3.7(6)	6.4(1)	8.8(1)
	586.0(1)	2 +	393.1(2)	28.3(13)	27.8(10)	13.2(12)	5.8(1)
			586.1(2)	25.0(12)	26.4(7)
	783.0(2)	3 +	197.9(6)		3.4(1)	5.1(6)	6.2(1)
			590.1(2)	27.4(12)	26.1(6)
	893.4(2)	(0 + )	700.7(2)	4.7(16)	9.7(5)	4.3(3)	6.3(1)	8.7(1)

TABLE III

 III

					: (continued)
	Ei(keV)	J π	Eγ(keV)	Iγ a	Iγ	I β (%) b	logf t	logf t	logf t
				(Nb→Mo)	(Zr→Mo)		(allowed/non-UF) (1UF)	(2UF)
	978.3(2)	4 +	196.0(2)		5.0(1)	5.4(7)	6.1(1)	8.5(1)
			391.2(3)	7.0(9)	4.5(14)
			414.4(3)	2.1(5)	2.3(6)
	1158.4(1)	(2 + )	594.8(3)	1.2(5)	1.5(4)	3.8(4)	6.3(1)
			965.7(2)	4.2(7)	4.4(4)
			1158.3(2)	3.2(6)	2.5(4)
	1404.8(2)	(3, 4 + )	622.3(3)		1.7(4)	2.1(3)	6.5(1)
			818.1(4)		0.8(3)
			839.7(3)		0.7(3)
			1212.5(3)		1.4(4)
	1422.1(2)	(4 + )	638.8(4)	0.6(1)	0.5(3)	0.9(2)	6.8(1)	9.2(1)
			836.2(3)		1.4(3)
	1547.5(3)		1354.7(2)		2.1(4)	0.9(2)	6.8(1)
	1727.6(2)	(3, 4 + )	944.0(5)		0.4(3)	1.5(3)	6.5(1)
			1141.7(3)		1.4(3)
			1163.4(6)		0.5(5)
			1535.3(4)		1.1(3)
	1839.0(5)		1056.0(4)		0.8(3)	0.4(1)	7.1(1)
	1844.4(2)	(3 -)	1061.5(2)	2.2(1)	3.6(4)	4.1(4)	6.1(1)
			1258.3(2)	7.5(6)	5.6(5)
	1962.3(2)		1769.5(2)		0.8(1)	0.4(1)	7.1(1)
	2048.4(3)		1265.4(2)	3.3(5)	3.1(4)	1.4(2)	6.5(1)
	2161.8(4)	(5 -)	1598.0(3)		1.2(5)	0.5(2)	6.9(2)		11.6(2)
	2208.4(2)	(3 -)	1425.9(7)		1.1(3)	2.4(3)	6.2(1)
			1622.3(2)		4.2(4)
	2309.7(3)		1526.7(3)		1.8(3)	0.8(1)	6.7(1)
	2339.6(2)		1753.4(3)		3.3(5)	2.8(3)	6.1(1)
			2147.1(3)		3.0(4)
	3093.4(5)		2900.6(4)		1.6(4)	0.7(2)	6.6(1)
	3104.1(4)		2911.3(3)		2.3(5)	1.0(2)	6.4(1)
	3550.1(5)		3357.3(4)		1.6(6)	0.7(3)	6.4(2)

  ( 108 Mo) can be derived from the number of counts 416 of the 268.3-keV γ ray, N γ (268.3 keV), emitted from the 417 108 Mo → 108 Tc decay using the relation, Mo decay. In order to evaluate N β ( 108 Mo), In the previous works of the 110 Nb β decay and

	418	×I γ,abs (268.3 keV), 200 300 N γ (268.3 keV) = N β ( 108 Mo)ε γ (268.3 keV) 100 400 280 385 & 386 206 421 315 276 182 241 Counts/0.5 keV 3 × 10 213 (a)	(2) 500 472 473 466 467 468 469 in Fig. 7. 470 471 band up to 10 + and the 2 + 2 band up to 5 + were reported. 600 700 800 900 1000 the 248 Cm spontaneous fission decay [15, 45], the ground the coincidence spectrum of the 2 + 1 → 0 + 1 transition is shown in Fig. 6 (c). The proposed level scheme is shown 494 486 532 463 544 750 563 606 821 592 652 553 634 882 829 824 965 875 693 661 703 948 935 977 655 5 × Mo 110 → Nb 110
	where ε γ (268.3 keV) is the γ-ray detection efficiency, which is sensitive to the implantation position, and I γ,abs (268.3 keV) is the absolute intensity of 268.3 keV per one 108 422 419 420 421 we define the ratio, 423 Counts/0.5 keV 1104 1082 1466 1300 1401 1019 1051 1088 1128 1246 1269 1292 1325 1350 1439 1075 1494 474 475 476 477 478 479 1524 In the present work, thirty new levels are identified and the 2 + 2 band is extended up to its 7 + state. A new band based on a 1243.8-keV state was observed and from its interband transitions to the 2 + 2 band, a spin-parity of 4 + was assigned to its band head. The spin-parities of the band members with 1520.1 keV and 1796.2 keV were as-1544 1584 1591 1995 1924 1213 1110 1303 Mo 110 → Nb 110 (b)
		R(268.3 keV) = 1100	N γ (268.3 keV) N β ( 108 Mo) 1200 1300	,	1400	480 481 1500 (3)	signed as 5 + and 6 + , respectively. A state at 1042.2 keV was measured based on the observation of a 828.8-keV γ 1600 1700 1800 1900 2000
		which should be the same for the 108 Nb → 108 Mo → 280 206 486 421 315 463 182 241 Counts/1.0 keV 386 (c)	ray coincident only with the 213.4-keV γ ray, as shown in 532 544 750 563 606 821 592 652 553 634 829 693 661 703 213 keV gate
		100	200	300		400	500	600	700	800	900	1000
		Counts/1.0 keV	213								829 keV gate
		100	200	300		400	500	600	700	800	900	1000
	451
	452	ternal conversion for the E2 transition. It is reasonable	508
	453	that this is less than P n = 18(11)%, given above, as there	509	termined separately for the low-and high-spin states in
	454	exist unobserved one-or multi-neutron emission chan-	510	110 Nb. To evaluate T 1/2 for the high-spin state, the γ
	455	nels. The minimum value reported here is larger than a	511	rays with 462.6, 531.5, 563.3, and 563.4 keV from the
	456	previously reported P n value of 6.2(5)% [43] and equal	512	5 + 1 , 6 + 1 , or 6 + 2 states were used as they are emitted only
		to 8(2)% of Ref. [44]. The previous P n values were de-	513	in the β decay of the high-spin state. The half-life of the
									high-spin state in 110 Nb was determined to be 75(1) ms
								519

106,107,108

Tc and 410 great granddaughters

107,108

Ru from the literature

[START_REF]ENSDF database[END_REF]

411 except for

108

Nb where the half-life of 186

(8)

ms mea-412 sured in this work was used. It was assumed that the 413 probability of the emission of two or more neutrons is 414 negligibly small so that P 1n = 1 -P 0n . 415 N β 424 108 Tc and 108 Mo → 108 Tc decays, if the position of 425 the 108 Nb and 108 Mo parent in WAS3ABi is the same. 426 To satisfy this requirement, we consider only events 427 where the implanted ion is 108 Nb. To obtain a value of 428 R(268.3 keV) from the 108 Mo → 108 Tc decay, we use the 429 detection time of the 192.8-keV γ ray emitted from the 430 2 + 1 state in 108 Mo as a time-zero of the decay of 108 Mo. 431 N β ( 108 Mo) was then obtained from the β-decay time 432 curve using the same method as described for 108 Nb. The 433 number of 108 Tc 268.3-keV γ rays was obtained from the 434 γ-ray peak integral to give R(268.3 keV) = 0.0558(65). 435 To obtain a value of N γ (268.3 keV) for the 108 Nb → 436 108 Mo → 108 Tc decay, a time gate of 400-3000 ms af-437 ter the 108 Nb implantation in WAS3ABi was applied 438 to optimize the γ rays emitted from the 108 Mo de-439 cay. This yielded a 268.3-keV peak containing 1695(43) 440 counts. The expected number of 268.3-keV γ rays ob-441 served without time restriction is evaluated as N γ (268.3 442 keV) = 2380(140), which, using Eq. (3), equates to 443 N β ( 108 Mo) = 42700(5600). 444 By using the relation, P 0n = N β ( 108 Mo) N β ( 108 Nb) , we obtain 445 P 0n = 82(11)%, giving P n = 18(11)%. Observation of 446 the known 65.4-keV γ ray [42] from the isomeric state 447 in 107 Mo in Fig. 4 (a) provides a direct evidence of the 448 β-delayed neutron emission of 108 Nb. The absolute γ-ray 449 intensity of the 65.4-keV γ ray corresponds to a minimum 450 P 1n of 8.1(7)%, which includes the contribution of the in-457 rived from measurements of β-delayed neutrons with 3 He 458 ionization chamber tubes [43], or a combination of 3 He 459 and B 3 F proportional gas-counter tubes [44]. Neutron-460 detection efficiencies of these configurations, which have 461 a possible energy dependence, could have been affected 462 by unknown β-delayed neutron energy distributions.

463 D. β decay to 110 Mo 464 The β-delayed γ-ray spectrum of 110 Mo obtained from 465 the β decay of 110 Nb is shown in Figs. 6 (a-b), and 482 Fig. 6 (d). Direct γ decay from the 1042.2-keV state to 483 the ground state was not observed. Based on this typical 484 γ-decay pattern of a low-lying 0 + state, the 1042.2-keV 485 state was assigned to 0 + . The I γ values are summarized 486 in Table IV. 487 The β-delayed γ-ray spectrum of 110 Mo obtained from 488 the 110 Zr → 110 Nb → 110 Mo decay chain is shown in 489 Fig. 6 (e). Only five excited states were observed, which 490 were the 2 + and 4 + states in the ground band, the 2 + 491 and 3 + states in the 2 + 2 band, and the 0 + 2 state. This 492 β-decay feeding pattern and the I γ values, given in Ta-493 ble V, are different from those of the 110 Nb → 110 Mo 494 decay. These differences indicate the existence of two β-495 decaying states in 110 Nb. Since the spin-parity of the 496 even-even nucleus 110 Zr is 0 + , it is expected that the 497 low-spin states in 110 Nb are populated by the β decay of 498 110 Zr. This expectation is consistent with the β-decay 499 feeding pattern to the lower-spin states in 110 Mo by the 500 110 Zr → 110 Nb → 110 Mo decay chain. On the other hand, 501 the 110 Nb → 110 Mo decay has contributions of the low-502 and high-spin states in 110 Nb because the in-flight fission 503 reaction populates both states. 504 E. Extraction of β-decay properties for low-and 505 high-spin states in 110 Nb 506 Beta-decay properties, namely T 1/2 , relative and ab-507 solute γ-ray intensities, I β , and logf t, need to be de-514 from the sum of the decay curves of these four γ rays 515 using the data of the 110 Nb → 110 Mo decay as shown in 516 Fig. 3 (c). The 213.4-keV γ ray obtained in the 110 Zr 517 → 110 Nb → 110 Mo decay chain was used for the half-life 518 measurement of the low-spin state in 110 Nb. The decay

  FIG.7. The proposed level scheme of 110 Mo obtained from the β-decay of 110 Nb isotopes implanted into WAS3ABi. Red lines are the new levels and transitions.

	=94(9) ms =75(1) ms 1/2 T ( )=12230(840) keV [AME2016] 1/2 T	2218.7 2371.4 2376.0 2421.6 2431.7 2454.8 2480.8 2569.1 2594.6 2624.5 2654.1		3036.1 2838.6	3036.1 655.4 1924.3 1523.7 1494.1 1074.5 1110.2 1438.9 1350.4 934.7 976.5 1292.4 1324.6 1268.7 1302.9 240.6 1213.4 1245.8 1127.6	2822.6
													2142.6 2170.8 2181.0 2183.1 2191.0 2208.0		1999.8	1300.0 1543.6 693.1 1400.8	1050.5 1018.6 703.1 660.9 384.8 181.5 1584.1 1591.3 947.6 1994.6 1088.3
	1782.7	(8	+	)	1754.3	591.8	(7	+	) 1796.2	881.9 633.6	552.5 276.1 (6	+	)	1466.4 1081.5
	5 652.2			699.8 914.4 1162.4 1477.7	486.4 206.0 420.7 315.4 563.4 563.3	(3 (4 (5 462.6 (6	+ + + +	) ) ) 1243.8 ) 1520.1	750.1 544.0 820.5 605.6 276.3		(4 (5	+ +	) )	1042.2 1317.3 1458.5 1574.7 1680.1	828.8 1103.5 823.7 964.8 874.9	(0	+	)
					493.7	493.8	280.2	(2	+	)
	213.4

β Q

TABLE IV :

 IV Same as TableII, but for the 110 Mo results obtained from the β decay of the implanted 110 Nb. (high) indicates the β decay of the high-spin state in 110 Nb. The low-spin contribution was subtracted by combining with the results in TableVand the assumption that the 0 + states at 0 and 1042.2 keV are populated only from the low-spin β decay. (1UF) is for the first unique forbidden transition from 6 -to 4 + or 8 + states.

	Ei(keV)	J π	Eγ(keV)	Iγ a	Iγ b	I β (%) c	logf t	logf t
				(Nb→Mo)	(high)	(high)	(high)	(high)
							(allowed/non-UF)	(1UF)
	0.0	0 +				0
	213.4(2)	(2 + )	213.4(2)	100.0(5)	100(11)	<1.5
	493.7(1)	(2 + )	280.2(2)	23.5(4)	21.6(33)	-5.4(45)
			493.8(2)	23.1(3)	18.9(38)
	599.0(2)	(4 + )	385.5(2)	39.0(7)	52.7(14)	6.2(16)	5.9(2)	8.5(3)
	699.8(1)	(3 + )	206.0(2)	8.5(2)	11.3(3) e	1.5(6)	6.5(2)
			486.4(2)	26.2(3)	34.9(8)

TABLE IV

 IV

					: (continued)
	Ei(keV)	J π	Eγ(keV)	Iγ a	Iγ b	I β (%) c	logf t	logf t
				(Nb→Mo)	(high)	(high)	(high)	(high)
							(allowed/non-UF)	(1UF)
	914.4(2)	(4 + )	420.7(2)	18.8(3)	27.0(4)	4.8(15)	6.0(2)	8.5(3)
			315.4(2)	2.9(2)	4.2(3)
	1042.2(2)	(0 + )	828.8(2)	1.8(1)	0	0
	1130.4(3)	(6 + )	531.5(2)	19.7(3)	28.3(4)	8.2(20)	5.7(2)
	1162.4(2)	(5 + )	462.6(2)	19.7(3)	28.3(4)	6.5(17)	5.8(2)
			563.4(3)	1.8(4)	2.6(6)
	1243.8(1)	(4 + )	544.0(2)	2.9(2)	4.2(3)	3.5(9)	6.1(2)	8.5(3)
			750.1(2)	5.9(2)	8.5(3)
	1317.3(2)		823.7(2)	1.3(1)	1.9(1)	1.4(3)	6.5(2)
			1103.5(3)	0.5(1)	0.7(1)
	1458.5(2)		964.8(2)	1.1(1)	1.6(1)	0.5(2)	6.9(2)
	1477.7(2)	(6 + )	563.3(2)	10.0(10)	14.4(14)	4.8(14)	5.9(2)
	1520.1(2)	(5 + )	276.3(3)	0.3(4)	0.4(6)	3.8(11)	6.0(2)
			605.6(2)	2.9(2)	4.2(3)
			820.5(2)	4.9(2)	7.0(3)
	1574.7(3)		874.9(3)	0.9(1)	1.3(1)	0.7(2)	6.7(2)
	1680.1(2)		1081.5(3)	0.4(1)	0.6(1)	0.9(2)	6.6(2)
			1466.4(3)	0.8(1)	1.2(1)
	1754.3(3)	(7 + )	591.8(2)	3.3(3)	4.7(4)	2.5(7)	6.1(2)
	1782.7(3)	(8 + )	652.2(2)	2.8(2)	4.0(3)	2.2(5)	6.2(2)	8.6(3)
	1796.2(1)	(6 + )	276.1(3)	0.8(4)	1.2(6)	1.7(7)	6.3(2)
			552.5(2)	2.7(2)	3.9(3)
			633.6(2)	2.1(2)	3.0(3)
			881.9(2)	1.6(1)	2.3(1)
	1999.8(2)		1300.0(2)	2.3(2)	3.3(3)	0.5(3)	6.8(3)
			1400.8(4)	0.3(1)	0.4(1)
	2142.6(3)		1543.6(2)	1.6(2)	2.3(3)	1.2(3)	6.4(2)
	2170.8(3)		693.1(2)	0.9(1)	1.3(1)	0.7(2)	6.6(2)
	2181.0(1)		181.5(2)	1.9(2)	2.7(3)	10.1(25)	5.4(2)
			384.8(2)	5.0(6)	7.2(9)
			660.9(2)	1.4(1)	2.0(1)
			703.1(2)	2.4(1)	3.5(1)
			1018.6(2)	5.0(2)	7.2(3)
			1050.5(2)	1.6(1)	2.3(1)
	2183.1(3)		1584.1(2)	1.4(2)	2.0(3)	0.4(2)	6.8(3)
	2191.0(3)		947.6(3)	0.6(1)	0.9(1)	1.0(3)	6.4(2)
			1591.3(4)	0.7(2)	1.0(3)
	2208.0(4)		1994.6(3)	0.8(1)	1.2(1)	0.6(2)	6.6(2)
	2218.7(4)		1088.3(3)	0.5(1)	0.7(1)	0.4(1)	6.8(2)
	2371.4(4)		1127.6(3)	0.6(1)	0.9(1)	0.5(1)	6.7(2)
	2376.0(3)		1213.4(3)	0.9(1)	1.3(1)	0.9(2)	6.4(2)
			1245.8(3)	0.3(1)	0.5(1)
	2421.6(2)		240.6(2)	4.2(7)	6.0(10)	3.2(9)	5.9(2)
	2431.7(3)		1268.7(3)	0.7(1)	1.0(1)	0.8(2)	6.5(2)
			1302.9(6)	0.4(1)	0.6(1)
	2454.8(2)		934.7(3)	0.5(1)	0.7(1)	2.0(5)	6.1(2)

TABLE IV

 IV

					: (continued)
	Ei(keV)	J π	Eγ(keV)	Iγ a	Iγ b	I β (%) c	logf t	logf t
				(Nb→Mo)	(high)	(high)	(high)	(high)
							(allowed/non-UF)	(1UF)
			976.5(3)	0.4(1)	0.6(1)
			1292.4(2)	1.0(1)	1.4(1)
			1324.6(3)	0.7(1)	1.0(1)
	2480.8(4)		1350.4(3)	0.7(1)	1.1(1)	0.5(2)	6.7(3)
	2569.1(3)		1110.2(3)	0.4(1)	0.6(1)	0.8(2)	6.5(2)
			1438.9(3)	0.6(1)	0.9(1)
	2594.6(5)		1074.5(5)	0.4(1)	0.6(1)	0.3(1)	6.9(2)
	2624.5(4)		1494.1(3)	0.9(3)	1.3(4)	0.7(3)	6.5(3)
	2654.1(4)		1523.7(3)	0.6(1)	0.9(1)	0.5(1)	6.6(2)
	2838.6(2)		655.4(2)	0.9(1)	1.3(1)	1.4(4)	6.2(2)
			1924.3(3)	0.9(2)	1.3(3)
	3036.1(2)		2822.6(3)	1.1(1)	1.6(1)	2.1(5)	5.9(2)
			3036.1(3)	1.6(2)	2.3(3)

a The absolute intensity per 100 β-decays is 0.492(25)Iγ . b The absolute intensity per 100 β-decays is 0.54(19)Iγ . c Internal conversion coefficients

[START_REF] Kibédi | [END_REF]

were adopted for two transitions with 213.4 and 206.0 keV. e Branching ratio of the 206.0-and 486.4-keV transitions and Iγ (486.4 keV) in Table V were used to subtract the low-spin β decay contribution.

TABLE V .

 V From the data of the 110 Nb → 110 Mo → 110 Tc decay Same as TableII, but for the 110 Mo results obtained from the β-decay chain 110 Zr→ 110 Nb→ 110 Mo, where the low-spin state in 110 Nb is populated by the β decay of the 0 + ground state in 110 Zr. (1UF) is for the first unique forbidden transition from 2 -to 0 + or 4 + states.

	Ei (keV)	J π	Eγ (keV)	Iγ a	I β (%)		log f t	log f t
			(low)	(low)	(low)		(low)	(low)
							(allowd/non-UF)	(UF)
	0.0	0 +			47(26)		5.2(3)	7.8(4)
	213.4	(2 + )	213.4	100(4)	25.0(88)		5.5(2)
	493.7	(2 + )	280.2	28.0(24)	25.0(87)		5.4(2)
			493.8	33.0(27)
	599.0	(4 + )	385.5	7.0(13)	2.9(11)		6.4(2)	8.9(3)
	699.8	(3 + )	486.4	6.0(4)	2.5(9)		6.4(2)
	1042.2	(0 + )	828.8	6.0(15)	2.5(10)		6.3(2)	8.8(3)
				576
				577	as,
					r =	I L+H γ,abs (828.8 keV) I L γ,abs (828.8 keV)	= 0.36(15),	(7)
				578	where I γ,abs (828.8 keV) is the absolute intensity of the
					828.8-keV γ ray.
				580
				581	chain, the P L+H 0n	value can be determined following the
					procedure described in Sec. III C. It is given by

8-keV γ ray is emitted 575 only from the β decay of the low-spin state, r was given 579 582

1 -P L+H 0n = rP L n + (1 -r)P H n ,

(8)

Here, only the differences from Sec. III C are de-583 scribed. The 213.4-keV γ ray was used for the iden-584 tification of the 110 Nb → 110 Mo decay. The number 585 a The absolute intensity per 100 β decays is 0.41(14)Iγ .

Lifetime measurement of 2 + 1 states in

  110 Nb is discussed. Positive-parity states with spins ranging from 0 to 4 are populated by the β decay of the lowspin 110 Nb. Because this decay pattern and the logf t values are similar to the 108 Nb decay, the spin-parity of the low-spin 110 Nb is assigned to be 2 -. The logf t values of 0 + and 4 + states were recalculated as the first unique

		2 10			Mo, 106	τ	=1.86(13) ns
	Counts/0.3 ns	1 10
		2 10	0	2	4 108 Mo, 6	τ	8 =1.21(7) ns 10	12
	Counts/0.2 ns	1 10
			0	2	4		6	8	10	12
			0	2	4	∆	6 T [ns]	8 10 12
								635
								8.6(3) for the 4 + 1 , 4 + 2 , 4 + 3 , and 8 + 1 states, respectively, are
								642
								643	106,108,110 Mo
								644	The mean lifetimes, τ , of the 2 + 1 states in 106,108,110 Mo
								645	were measured from the time between the observation
								646	of a β particle in a plastic scintillation detector and a
								647	γ ray corresponding to the 2 + 1 → 0 + 1 transition in the
								648	LaBr 3 (Ce) detector array. Figure 8 shows the time-
								649	difference distributions for the three nuclei and Fig. 9
								650	shows the corresponding γ-ray spectra with the regions
								651	used to make the time spectra highlighted in gray. The
								652	time spectra show a clear single exponential decay on
	forbidden transition to be 7.8(4), 8.8(3), and 8.9(3) for 0 + 1 , 0 + 2 , and 4 + 1 , respectively. These are consistent with the typical range from 8 to 11 [40].	653 654	a very low background. The γ-ray spectra in Fig. 9 do not show any evidence for delayed feeding of the 2 + 1 state from higher-lying states and indeed, the lifetime of the 4 + 1
								660

For the β decay from the high-spin state, it is impossible to interpret the logf t values of both the 3 + and 8 + states, even if the first unique forbidden transition is considered. Because the I β to the 3 + state, 1.5

[START_REF] Hilaire | AIP Conference Proceedings[END_REF]

, is smaller than the other states, missing feedings from higher excited states may cause a significant deviation 625 from the actual logf t. On the other hand, it is reason-626 able that the 8 + state, which is the largest spin among 627 the measured states, is directly populated. Therefore, the 628 3 + state is considered to be mainly fed from the higher 629 excited states. The logf t values of the 4 + , 5 + , 6 + , 7 + , 630 and 8 + states are in the range from 5.7 to 6.3. This case 631 is similar to the situation above. When the spin-parity of 632 the high-spin state in 110 Nb is 6 -, the transitions to 4 + 633 or 8 + states become the first unique forbidden transition. 634 The recalculated logf t values, 8.5(3), 8.5(3), 8.5(3) and 636 consistent with the typical range. For the other positive 637 parity states, the logf t values are consistent with the first 638 non-unique forbidden transitions from the 6 -state. As 639 a result, the spin-parity of the high-spin state is assigned 640 to be 6 -. 641 F. 655 state in 108 Mo was recently measured as τ = 29.7 +11.3 -9.1 656 ps [9]. Its effect can be ignored, since the lifetime is 657 one order of magnitude smaller than the time resolution 658 of 0.61 ns at 200 keV. The lifetimes of the 2 + 1 states 659 were determined from fitting the slope with a single ex-

  , and 0.305[START_REF] Zhang | [END_REF] for 106 Mo, 108 Mo,

			0.4
	]	0.35	Mo isotopes		SLy5+T
	+ 0 1 2 b 2 e ) [	0.25 0.3					SLy4
	→	0.2
	+	1
	B(E2;2		0.1 0.15
			0.05
			0	58	60	62	64	66	68
						Neutron number
	FIG. 10. Experimental and theoretical B(E2; 2 + 1 → 0 + 1
								683
								684 685	and 110 Mo, respectively. Figure 11 shows the neutron-
								686	number dependence of β for Mo and Zr isotopes. While
								687	the Zr isotopes have a clear peak structure at N = 64
								688	and reach β = 0.46(1), the Mo isotopes have almost con-
								689	stant β ∼ 0.32 between N = 60 and 68. A comparison
								with microscopic calculations is described in Sec. IV E.
								694

690 B. Triaxial motion in 2 + 2 band 691 The low-lying 2 + 2 state is a signature of a softness 692 against γ vibration, a γ-unstable rotor, or a rigid triaxial 693 rotor. The three models are distinguished by means of

  • . For the comparison with the experimental re-+ component, since the odd-spin states are not 891 allowed in the K π = 0 + band. This means that the ex-FIG.15. The potential-energy surface and the collective-wave functions squared (with a factor of β 4 ) of low-lying states in 106 Mo, 108 Mo, and 110 Mo. The pairing-plus-quadrupole interaction and spherical single-particle energies used in the CHFB+LQRPA calculations were fitted to the mean-field results obtained with the SLy5+T interaction.

	106 Mo		60		γ (deg) 40	3.6 4.8		0 + 1			2 + 1			2 + 3	3 + 1	0 + 2
	0 108 Mo	0.2	β 60	0.4	20 0 0.6 20 γ (deg) 40	2.4 1.2 0.0 2.4 3.6 4.8	(MeV) (MeV)	0 0 + 1	β	0.6	0 2 + 1	β	837 838 839 840 841 0.6 sults, the B(E2; 2 + 1 → 0 + 1 ) value was used instead of β. The B(E2; 2 + 1 → 0 + 1 ) values were calculated by adopting the effective charges, e π = 1.5e, and e ν = 0.5e, for the two major-shell single-particle model space as shown in β 0 0.6 β 0 0.6 0 0.6 β Fig. 10. The theoretical values with SLy5+T are roughly 842 double those with SLy4 and agree well with the exper-843 imental ones. The energy of 2 + band, which has a strong correlation to B(E2) [52], is 845 an observable closely related to β. The energies of the 846 1 state for the rotational 844 2 + 2 3 + 1 0 + 2
						1.2							847	ground-state band are well reproduced by the calcula-
	0	0.2	β	0.4	0 0.6	0.0		0	β	0.6	0	β	tions with SLy5+T, as shown in Fig. 17. The good agree-ment with the theoretical values using the SLy5+T in-0.6 848 849 β 0 0.6 β 0 0.6 β 0 0.6
	110 Mo		60		20 γ (deg) 40	2.4 3.6 4.8	(MeV)	0 + 1			2 + 1		850 851 852 853	teraction indicates that the ground state in 106,108,110 Mo has a prolate shape. The B(E2) values for SLy5+T shows rather constant. The PES of 106 Mo has a gentle slope an increase at N = 64, while the experimental ones are 2 + 2 3 + 1 0 + 2
	0	0.2	β	0.4	0 0.6	1.2 0.0		0	β	0.6	0	β	toward β ∼ 0.45, which may increase β compared with 108 Mo. Because the largest β was observed at N = 64 in the Zr isotopes [53] and the energy of the 2 + 1 state 0.6 854 855 856 β 0 0.6 β 0 0.6 β 0 0.6
													857	becomes minimum at N = 64 for both isotopes [61], the
													858	soft potential toward the large β might be consistent with
													859	the experimental results. But a less-soft potential would
													860	be necessary for a better agreement.
													861	The energies of the 2 + 2 band in 106 Mo are well repro-
													862	duced by the calculation with SLy5+T. The wave func-
													863	tions of 2 + γ and 3 + γ are localized on a finite γ value, reflect-
													864	ing the dynamical triaxial deformation induced by the γ
													865	vibration of the prolate shape. While the band-head en-
													866	ergy in 108 Mo is overestimated, the excitation energies
													867	measured with respect to the 2 + 2 state are well repro-
													868	duced and the wave functions show the γ vibration ex-
													869	pected from the experimental odd-even staggering. Thus,
													870	the calculations for 106 Mo and 108 Mo are consistent with
													871	the interpretation in Sec. IV B, that is, the rotational
													872	band of the γ vibrational state. On the other hand, the
													873 874	calculated 2 + 2 band in 110 Mo shows considerable energy staggering. The 3 + γ and 5 + γ states converge toward the
													875	4 + γ and 6 + γ states, respectively. The degeneracy of these
													876	states is predicted in the γ-unstable model. The wave
													877	function of 2 + γ is prolonged in the γ direction as expected
													878	in the γ-unstable model. It is caused by the flatness of the
													879	PES between γ = 20 • and 60 • . Conversely, the experi-
													880	mental results indicate γ vibration in the stiffer potential.
													881	It is noticed that the calculated wave function of the 3 + γ
													882	state is similar to those of the lighter Mo isotopes and in-
													883	dicates γ vibration. The characteristics of the wave func-
													884	tions with higher spins change depending on if the spin
													885	is even or odd. This is also noticed in the calculations
													886	with SLy4. It is suggested that the energy staggering
													887	with the close degeneracy of E(3 γ ) and E(4 γ ) might de-
													888	pend not only on the prolonged wave function toward the
													889	γ direction, but also on the difference between the even
														and odd spins. The odd-spin states cannot mix with the
													892

890

K π = 0

TABLE VII .

 VII Candidates of the quasiparticle-state configurations of two β-decaying states in 110 Nb. Four quasiparticle states are selected from the Nilsson diagram

		949
		950	posed for the ground state [63]. In the Nilsson dia-
		951	gram [64], these quasiparticle states are predicted for
		952	the prolate shape with β ∼ +0.35 measured in 106 Mo.
		953	The Gallagher-Moszkowski (GM) rule [65] predicts that
		954	the state with the antiparallel spin-coupling becomes a
	106,108,110 Mo with SLy5+T indicate β vibrational mo-	955	higher-lying state. Therefore, the observed β-decaying
	tion. On the other hand, the calculation with SLy4 indi-		state was assigned to be a high-spin K π = 4 -isomeric
	cates the possibility of shape coexistence of prolate and
	oblate shapes. Since the energy difference between the
	0 + 2 and 2 +

3 states in 108 Mo is consistent with the prediction with SLy5+T, the 0 + 2 state in 108 Mo is suggested to be a β vibrational state. There is no experimental in-formation providing a favored origin for the 0 + 2 state in 934 110 Mo. Additional experimental and theoretical works 935 are awaited for further discussions. 936 F. Structure of parent nuclei 106,108,110 Nb 937 Configuration of 106 Nb: The spin-parity of the β-938 decaying state in 106 Nb was assigned to be 4 -, and 939 there were no experimental indications of the existence 940 of a second β-decaying state. From the prompt γ-941 ray spectroscopy of the 252 Cf spontaneous fission [63], 942 the spin-parity of the ground state in 106 Nb was as-943 signed as 1 -. Owing to the relatively strong popula-944 tion of high-spin states in 106 Mo and the fact that no 945 known γ rays of 106 Nb are observed following the de-946 cay of 106 Zr, it is likely that the β-decaying state of 947 106 Nb is not the 1 -ground state. The configuration 948 of π3/2 -[301] ⊗ ν5/2 + [413] with K π = 1 -was pro-956 state of the GM partner in the π3/2 -[301] ⊗ ν5/2 + [413] 957 configuration. 958 Configuration of 108 Nb: The spin-parity of the 108 Nb 959 ground-state was assigned to be 2 -, and there was no 960 evidence of a β-decaying isomeric state. The single-961

  -state by a M1 transition. Therefore, the ground 986 state of108 Nb was assigned to be the 2 -state with the -state by an M1 transition. For the low-spin 1005 2 -state, there are three candidates as given in TableVII. 1006 Since the spin difference between the GM pair is 1 for all 1007 three candidates, the lower energy state with the parallel 1008 spin becomes the β-decaying state. Thus, the parallel 1009 spin-coupling state of the π5/2 + [422] ⊗ ν1/2 -[541] con-1010 figuration was assigned to the β-decaying 2 -state. The difference between the assigned configurations of 1012 the two β-decaying states is the neutron quasiparticle 1013 state. It is indicated that the ν7/2 -[523] and ν1/2 -[541] 1014 states are near the Fermi surface and close to each other. The assigned 1019 configurations of 106 Nb, 108 Nb, and 110 Nb are consistent 1020 with the Nilsson diagram given in Ref. [64]. On the other 1021 hand, the π5/2 + [422] state in the Woods-Saxon potential 1022 is located below Z = 40 [66], even though it is used in the 1023 configuration of 108 Nb and 110 Nb. From comparison with 1024 the Nilsson diagram, it is suggested that the π3/2 -[301] 1025 state in the Woods-Saxon potential may need to lower in 1026 energy so as to cross the π5/2 + [422] state at β ∼ 0.3.

		1015
		1016	There was no experimental evidence to select the ground
			state from these two states.
	987
		π5/2 + [422] ⊗ ν1/2 -[541] configuration.
	989
	990	observed. The spin-parities were assigned to be 2 -and
	991	6 -. The quasiparticle states are selected from the Nilsson
	992	diagram [64] at around β = +0.305 for 110 Mo or the
	993	single particle levels in the Woods-Saxon potential [66]
	994	as π1/2 + [431], π5/2 + [422], π5/2 -[303], and π3/2 -[301]
	995	for the proton, and ν5/2 -[402], ν1/2 + [411], ν7/2 -[523],
	996	and ν1/2 -[541] for the neutron. The spin-parities of the
		configuration coupled with these quasiparticle states are

. A ma-964 jor difference of the level orderings between these two 965 is the negative parity states of the protons. Can-966 didates of the valence proton and neutron configura-967 tions were selected based on these two predictions. 968 These are, π1/2 + [431], π5/2 + [422], π5/2 -[303], and 969 π3/2 -[301] for the proton configuration, and ν1/2 + [411], 970 ν5/2 + [413], and ν1/2 -[541] for the neutron configura-971 tion at around β = +0.33 for 108 Mo. The spin-parity 972 of the π5/2 -[303] ⊗ ν1/2 + [411] configuration is 2 -and 973 3 -with the antiparallel-and parallel-spin couplings, re-974 spectively. The lower-lying state is the 3 -state based 975 on the GM rule. The 2 -state would not form a β-976 decaying isomeric state because of a fast M1 transi-977 tion to the 3 -state. Thus, the expected β-decaying 978 state is not the 2 -state, but the 3 -state. The 2 - 979 state of the π3/2 -[301]⊗ν1/2 + [411] configuration is also 980 antiparallel-spin coupled, therefore the 1 -state with the 981 parallel-spin coupling would be the β-decaying state. The 982 π5/2 + [422] ⊗ ν1/2 -[541] configuration can generate a β-983 decaying 2 -state with the parallel-spin coupling. The 984 3 -state with the antiparallel-spin coupling will decay to 985 the 2 988 Configuration of 110 Nb: Two β-decaying states were 997 summarized in Table VII

.

998 999 The 6 -state is only generated by the parallel-spin cou-1000 pling of the π5/2 + [422] ⊗ ν7/2 -[523] configuration. The 1001 anti-parallel spin coupled 1 -state of this configuration, 1002 which has a higher energy based on the GM rule, would 1003 not be a β-decaying state, because it can decay to the β-1004 decaying 2 1011 1017 Comparison between Nilsson diagram and single-1018 particle levels in Woods-Saxon potential:

were performed in part using the COMA Oakforest-PACS provided by Multidisciplinary Coopera-1112 tive Research Program in Center for Computational Sci-

1113

The flat pattern of the 106,108,110 Mo isotopes indicates The ratio B(E2; were performed for the low-lying states in 106,108,110 Mo.

814

The PES and the kinetic terms (vibrational and rota-815 tional masses) were microscopically calculated using the 816 CHFB+LQRPA approach using pairing-plus-quadrupole 817 (P+Q) interactions whose parameters, such as spherical