Touzé

Romain Touzé

Yann Heuzé

Matthieu P Robert

Dominique Brémond-Gignac

Syril James

Giovanna Paternoster

Eric Arnaud

Roman Hossein Khonsari

Extra-ocular muscle positions in anterior plagiocephaly; V-pattern strabismus 3 explained using geometric mophometrics

Keywords: Child health (paediatrics), Imaging, Muscles, Orbit, Treatment Surgery

113 contralateral deviation of the vomer and nasal pyramid. [1] 114 Ocular involvement is frequent in UCS and includes extra-ocular muscle (EOM) dysfunction 115 with cyclovertical strabismus, astigmatism -usually contralateral to the UCS, due to the 116 compensatory deformations of the contralateral bones -with anisometropia, and amblyopia.

117 The prevalence of ocular abnormalities ranges from 50 to 65% in this condition. [2][3][4] This high 118 prevalence underlines the need for a systematic ophthalmological clinical screening for patients 119 with UCS within multidisciplinary craniofacial teams, in order to prevent, detect, and treat the 120 amblyopia.

121 The most common type of strabismus in UCS is referred to as the V-pattern, which is defined 122 by a vertical incomitance with a distance between both eyes larger in upgaze than in 123 downgaze. [2,[START_REF] Samra | The prevalence of strabismus in unilateral coronal 349 synostosis[END_REF] Two hypotheses have been proposed in the literature in order to explain the 124 occurrence of V-pattern oculomotor anomalies in UCS: (1) excyclorotation of the rectus muscle 125 and (2) inferior oblique overaction associated with superior oblique underaction. [1,2,[START_REF] Dagi | Rectus muscle excyclorotation and V-351 pattern strabismus: a quantitative appraisal of clinical relevance in syndromic 352 craniosynostosis[END_REF][START_REF] Bagolini | Plagiocephaly Causing Superior Oblique Deficiency 355 and Ocular Torticollis: A New Clinical Entity[END_REF] 126 Here we assessed the positions of the EOM in patients with UCS and controls, based on MRI 127 data and geometric morphometric analyses, and screened for clinically relevant specificities of 128 the muscular anatomy of UCS orbits.

C o n f i d e n t i a l : F o r R e v i e w O n l y
129 Geometric morphometrics allowed us to acquire, process and analyze landmarks by preserving 130 their 3D inter-relationship. This approach was required as we had to compare non-trivial 131 shapes. [START_REF] Mitteroecker | Advances in Geometric Morphometrics[END_REF] The framework used to assess our data was Procrustes superimposition followed by 132 Principal Component Analysis (PCA). Procrustes superimposition allowed comparing different 133 shapes by freely adjusting the position, orientation and scale parameters using translations, 134 reflections and rotations. [START_REF] Rohlf | Extensions of the Procrustes Method for the Optimal Superimposition 360 of Landmarks[END_REF] PCA was used to reduce the large number of variables responsible 135 for shape differences into a small number of principal variables with geometric 136 correspondence. [START_REF] Jolliffe | Principal Component Analysis[END_REF] 137 Our aim was to find anatomical bases for the V-pattern strabismus. More precisely, we assessed 138 the 3D modifications in the positions of EOM in UCS and the effects of fronto-orbital 139 advancement surgery on these positions. 161 right and left superior oblique trochlea. One extra-orbital landmark was also defined: [START_REF] Kono | Active pulleys: magnetic resonance imaging of rectus 372 muscle paths in tertiary gazes[END_REF] 162 chiasma (Table 1). Landmarks 1-10 were placed using coronal views, on the plane immediately 163 behind the two globes (Figure 1). Pulleys of recti muscles were described in dynamic MRI 164 (IMROD) as encircling sleeves and rings of collagen in the tenon fascia. [START_REF] Kono | Active pulleys: magnetic resonance imaging of rectus 372 muscle paths in tertiary gazes[END_REF] Table 1. 167 168 These pulleys represented the functional vector of EOMs and were located more proximal 169 relative to muscle insertions. That's why we determined the coronal plane sectioning these 170 pulleys to place landmarks concerning recti muscles. Landmarks 11 and 12 were defined using 171 MPR after having localized the trochlea of the superior oblique muscle. Landmark 13 (chiasma) 172 was placed using coronal sections.

Number

173 We exported all landmark coordinates from Avizo to MorphoJ [START_REF] Klingenberg | MorphoJ: an integrated software package for geometric morphometrics[END_REF] in order to perform 174 geometric morphometric analyses. [START_REF] Mitteroecker | Advances in Geometric Morphometrics[END_REF] We extracted the shape information defined by the 179 We furthermore performed cephalometrics analyses in 2D defining angles and linear distances 180 between landmarks in using coronal and axial planes. These angles and distances were 181 determined using Euclidian distances and scalar products, and compared between UCS and 182 controls. We defined two vectors named u (landmark 2 to 4) and v (landmark 1 to 3) in the 183 coronal plane. Angle α between u and v was computed using the scalar product. We furthermore 184 computed the angles β between u and the x-axis, and the angle γ between v and the x-axis 185 (Resumed in the Figure 3). 193 agreement of Lin [START_REF] Lin | A Concordance Correlation Coefficient to Evaluate Reproducibility[END_REF] was computed for each operator and landmark. An overall concordance 194 correlation coefficient (OCCC) was also computed. [START_REF] Barnhart | Overall Concordance Correlation Coefficient for 380 Evaluating Agreement Among Multiple Observers[END_REF]

140

  Page 6 of 27 https://mc.manuscriptcentral.com/bjo British Journal of Ophthalmology 144 We retrospectively included patients with isolated UCS and with at least one available digital 145 pre-operative craniofacial magnetic resonance imaging (MRI), managed in our tertiary center 146 (French National Reference Center for Craniofacial Malformations -CRANIOST) between 147 2013 and 2018, using Dr Warehouse search engine.[11] We excluded patients with complex 148 and syndromic craniosynostosis and deformational plagiocephaly. Age-matched control 149 patients without craniofacial anomalies were also retrospectively included. We analyzed the 150 effects of fronto-orbital advancement surgery based on post-operative MRIs for included 151 patients, when available. For image analysis purposes, we mirrored patients with left UCS in 152 order to consider a cohort of patients with right UCS only.[12] All patients with UCS benefited 153 from fronto-orbital advancement. 154 155 Morphometrics 156 Landmarking was performed using Avizo 6.4.0 (Thermo Fisher Scientific, Waltham, 157 Massachusetts, USA). Landmarks were placed using Multi Planar Reconstruction (MPR) on 158 Cube T1-weighted or Cube T2-weighted sequences. Twelve bilateral orbital landmarks were 159 defined: (1; 5) right and left lateral rectus; (2; 6) right and left superior rectus; (3; 7) right and 160 left medial rectus; (4; 8) right and left inferior rectus; (9; 10) right and left optic nerve;(11; 12)

186 187

 187 Data analysis188 Data analysis was performed using R3.3.3.[15] Comparisons of means were performed using a 189 Wilcoxon test, depending on the data distribution and significance was defined for p<0.05. We 190 performed a reproducibility assessment based on a subset of 10 normal MRIs. Two operators 191 (for the interobserver reproducibility) (RT and RHK) landmarked these MRIs three consecutive 192 times (intraobserver reproducibility). The concordance correlation coefficient (CCC)

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. 3D positioning of the landmarks based on MRI images. A. Red line: section plane used to place rectus muscle landmarks. B. Rectus muscle landmarks (red dots) and optic nerve landmarks (dark green dots). C. Trochlea of superior oblique muscles (yellow circles). D,E. Trochlea of superior oblique muscles (yellow dots). F. Chiasma landmark (blue dot); rectus muscle landmarks (red dots); optic nerve landmarks (dark green dots); trochlea of superior oblique muscles (yellow dots).

Figure 4 .

 4 Figure 4. A. Coronal MRI section in anterior plagiocephaly before fronto-orbital advancement. B. Coronal MRI section in anterior plagiocephaly after fronto-orbital advancement. Qualitative correction of the position of the right trochlea of the superior oblique muscle (red arrow) and qualitative reduction of the excyclorotation of recti muscles.

100 Conclusion 101 Our results confirm that UCS-associated anomalies of the superior oblique muscle function are 102 associated with a malposition of its trochlea in the roof of the orbit. This clinical anomaly 103 supports the importance of MRI imaging in the surgical management of strabismus in patients 104 with UCS. 105

  This study reports statistically abnormal extra-oculomotor muscles positions within the orbit of 53 patients with anterior plagiocephaly using the geometric morphometrics, in order to better 54 understand strabismus in this pathology especially V-pattern. Ophthalmological involvement in anterior plagiocephaly (AP) due to unicoronal synostosis 82 (UCS) raises management challenges. Two abnormalities of the extra-ocular muscles (EOM) 83 are commonly reported in UCS without objective quantification: (1) malposition of the trochlea 84 of the superior oblique muscle and (2) excyclorotation of the eye. Here we aimed to assess the 85 positions of the EOM in AP, using geometric morphometrics based on magnetic resonance 86 imaging (MRI) data.87 Materials and Methods 88 Patient files were listed using Dr WareHouse, a dedicated big data search engine. We included 89 all patients with AP managed between 2013 and 2018, with an available digital pre-operative 90 MRI. MRIs from age-matched controls without craniofacial conditions were also included. We 91 defined 13 orbital and skull base landmarks in order to model the 3D position of the EOM. 92 Cephalometric analyses and geometric morphometrics with Procrustes superimposition and 93 principal component analysis were used with the aim of defining specific EOM anomalies in 94 UCS.95 Results96 We included 15 pre-operative and 7 post-operative MRIs from patients with UCS and 24 MRIs 97 from age-matched controls. Cephalometric analyses, Procrustes superimposition and distance 98 computations showed a significant shape difference for the position of the trochlea of the 99 superior oblique muscle and an excyclorotation of the EOM.

	Page 1 of 27 41 Corresponding Author: 42 43 Dr Romain Touzé 44 Service d'ophtalmologie, Hôpital Universitaire Necker -Enfants Malades, 149, Rue de British Journal of Ophthalmology 45 Sèvres, 75015 Paris. France 46 Email r.touze.rt@gmail.com Tel + 33629654980 50 Synopsis: 51 Page 3 of 27 British Journal of Ophthalmology 79 Abstract 80 Introduction British Journal of Ophthalmology 106 Introduction 81 Page 4 of 27 107 Craniosynostoses are often associated with strabismus. The management of these specific types 108 of strabismus is a clinical challenge, especially in anterior plagiocephaly (AP) caused by 52 55 C o n f i d e n t i a l : o r R v i e w O l y O n l y 29 Number of Figures: 4 30 Word count of Abstract: 243 31 Word count of Paper: 2440 33 y y 74 y y 32 O n l O n l 72 73 O n l l n O n R e v i e w 22 TeteCou ; Université de Paris, Sorbonne Paris Cité ; Paris, France 24 25 26 Keywords: Child health (paediatrics); Imaging; Muscles; Orbit; Treatment Surgery 27 28 Number of Tables: 1 e v i e w e v i e w 68 69 70 71 e v i e w w e i v e 23 R R 67 R R e : F o r 19 7. Service de chirurgie maxillo-faciale et chirurgie plastique, Hôpital Universitaire Necker 20 -Enfants Malades, Assistance Publique -Hôpitaux de Paris ; Centre de Référence des 21 Malformations Rares de la Face et de la Cavité Buccale MAFACE, Filière Maladies Rares : F o r : F o r 65 66 F o r r o F 64 : : F C o n f i d e n t i a l C o n f i d e n t i a l 109 unicoronal synostosis (UCS). UCS is the third most common single-suture craniosynostosis 47 48 49 C o n f i d e n t i a l 56 57 58 59 61 63 i a l l a i 62 e n t t n e 60 C o n f i d C 110 and is associated with the premature unilateral fusion of a coronal suture. Craniofacial o 111 anomalies in UCS include a larger orbit on the affected side, a shift of the petrous bone towards n f d i 112 the fused suture, compensatory growth of the contralateral forehead and temporal bone, and
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Table 1 .

 1 Orbital and extra-orbital landmarks used to model the 3D position of extra-ocular muscles in anterior 166 plagiocephaly.

	Anatomical definition

  We report the first detailed assessment of EOM positions in anterior plagiocephaly due to 310 unicoronal synostosis. Strabismus in unicoronal synostosis has repeatedly been explained by 311 weakness of the superior oblique muscle due to a malposition of its trochlea and excyclorotation 312 of rectus muscles. Our study provides a quantitative proof of these two anomalies and supports 313 the usual hypothesis formulated in the literature. It underlines the relevance of orbital imaging 314 in the management of strabismus in patients with UCS.

	Page 9 of 27 Page 15 of 27 Page 19 of 27 Page 21 of 27	British Journal of Ophthalmology British Journal of Ophthalmology British Journal of Ophthalmology British Journal of Ophthalmology British Journal of Ophthalmology British Journal of Ophthalmology British Journal of Ophthalmology	Page 16 of 27
	308 Conclusion 316 Funding Statement 410 435 Figure legends supplementary files
	CCC and OCCC values above 0.99 e r : t e f o C n i d n i a l F o R v i e w O n l C o n f i d e n t i a l : F o r R e v i e w O n l C o n f i d e n t i a l : F o r R e v i e w O n l C o n f i d e n t i a l : F o r R e v i e w O n l C o n f i d e n t i a l : F o r R e v i e w O n l C o n f i d e n t i a l : F o r R e v i e w O n l 317 This research received no specific grant from any funding agency in the public, commercial or 318 not-for-profit sectors. 319 411 412 436 Figure 1. Variance 437 A diagram showing the percentages of total variance for which the principal components (PCs) 438 account. The five first PCs represent more than 70% of the total difference between both groups. 309 315 C o n f i d e n t i a l : F o r R e v i e w O n l 320 Competing Interests 321 None authors have a competing interest 322 323 Contributorship Statement 324 All authors made substantial contributions to conception and design, analysis and interpretation 325 of data; drafted or critically revised the article; and gave final approval of the version to be 326 published. 327 328 Data Sharing 329 N/A 330 331 Acknowledgments 332 Special thanks to strabologists Drs Mitra Goberville and Marie-Andrée Espinasse-Berrod. 333 Ethical statement 334 Patients were informed of the use of their medical data for this study. 335 C o n f i d e n t i a l : F o r R e v i e w O n l C o n f i d e n t i a l : F o r R e v i e w O n l C o n f i d e n t i a l : F o r R e v i e w O n l C o n f i d e n t i a l : F o r R e v i e w O n l C 439 440 Figure 2. PCA C o o n 441 Principal component analysis with Procrustes superimposition of the two groups (UCS) and n f 442 control. We can observe difference with confidence ellipses concerning PC1 vs PC2; PC1 vs i f i 443 PC4; and PC1 vs PC5. d e d e n t n t i a i l : a l : F F o r o r R e R v e i e v i w e w O n l O l n y
	195 corresponded to excellent reproducibility of landmark placement.[16]	y y y y y y y y y y y y
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https://mc.manuscriptcentral.com/bjo https://mc.manuscriptcentral.com/bjo British Journal of Ophthalmology

British Journal of Ophthalmology


A Bello Garrote

G Etile

F Georgiev

L Giacoppo

M Grente

A Klintefjord

Kuşoğlu

A Goasduff
email: alain.goasduff@pd.infn.it

J Ljungvall

A Etile

G Georgiev

S Roccia

T R Rodríguez

F L Bello Garrote

M Klintefjord

L Grente

M.-D Salsac

A Kuşoglu

C Sotty

B(E2) anomalies in the yrast band of 170 Os

B(E2) anomalies in the yrast band of 170 Os

Methods:

The states of interest were populated via the fusion-evaporation reaction 142 Nd( 32 S,4n) at a bombarding energy of 170 MeV at the ALTO facility from IPNO (Orsay, France). Lifetimes of the 2 + 1 and 4 + 1 states in 170 Os were measured with the Recoil-Distance Doppler-Shift method using the OUPS plunger.

Results: Lifetimes of the two first excited states in 170 Os were measured for the first time. A very small B(E2; 4 + 1 → 2 + 1 )/B(E2; 2 + 1 → 0 + 1 ) = 0.38 (11) was found, which is very uncharacteristic for collective nuclei. These results were compared to state-of-the-art beyond mean-field calculations.

Conclusions: Although theoretical results give satisfactory results for the energy of the first few excited states in 170 Os and the B(E2; 2 + 1 → 0 + 1 ) they fail to reproduce the very small B(E2; 4 + 1 →

2 + 1 ) which remains a puzzle.

I. INTRODUCTION

The mechanisms of shape transitions remain a challenging topic in nuclear structure calculations, but are becoming experimentally more accessible. While the transition between shapes is generally gradual, the systems of interest are those that exhibit abrupt changes in observables with the addition or subtraction of a few nucleons. The osmium isotope chain provides such a test case, as it goes from a soft triaxial rotor in 168 Os to a mid-shell welldeformed prolate rotor in 180 Os, with the appearance of shape coexistence close to N = 96 in 172 Os. The osmium isotopic chain is the longest continuous chain of even-even isotopes with available spectroscopic data on the low-lying yrast states covering mass range from A = 162 to A = 198. The evolution of the energies of the yrast 2 + and 4 + for those isotopes is reported in the upper panel of Figure 1 together with the structural benchmark

E 4 + 1 /E 2 + 1 (R 4/2
) in the lower panel. A transition from vibrator-like structures for the most neutronrich nuclei to deformed prolate rotors close to the mid-neutron shell passing by γ-unstable or triaxial shapes is suggested by the data [1][2][3][4]. Moving close to the N = 82 shell closure at A = 158, the collectivity decreases and neutron deficient osmium isotopes pass through shape coexistence at A = 172 [5] to a single-particle like excitations in 162 Os [6].

Osmium isotopes with N ≈ 96 lie at the edge of the region of neutron deficient nuclei close to the Z = 82 shell closure where a large number of nuclei with shape coexistence [7] are found making it fertile grounds for nuclear structure research. A good example is 186 Pb with three 0 + states close in energy [8]. Shape-coexistence phenomenons have been evidenced in several nuclei in the lead region and recent lifetime measurements in Po [9], Pb [10][11][12],

Hg [13][14][15], and Pt [16]. These discoveries have allowed a deeper understanding of the shape-coexistence origins. The model-independent measurements of the B(E2) values in the yrast bands have given firm experimental evidence of several low-energy configurations highly mixed at low spins.

The question of shape coexistence in the neutron-deficient osmium isotopes has been addressed several times over the last few decades. The yrast sequence of 172 Os shows a sharp backbend near spin 14h originated from the i 13/2 neutron alignment [17]. At a spin of 6h, an up-bend can be observed. The shape coexistence in 170,172 Os was discussed based on a three-band mixing model [18] reproducing level energies and moments of inertia. The work suggested that shape coexistence is as well present in 170 Os although the deformed structure responsible for the anomaly seen in the moments of inertia in 172 Os is shifted upwards in 170 Os making its influence on the kinematic moments of inertia significantly smaller. In order to explain this variation in the moments of inertia around the 172 Os several approaches were employed based either on particle alignment or phenomenological shape coexistence [17].

Although no firm conclusions could be drawn, shape coexistence is presented as a plausible explanation. The question of shape coexistence in 172 Os [19] Beyond mean field calculations using the Gogny D1S force, allowing for triaxial shapes, have been used to investigate the shape coexistence phenomenon. For lighter nuclei such as Kr [30] and Se [31], it has been shown that triaxial shapes have to be included in the A∼ 70 region for a correct reproduction of the observables. The importance of triaxial degree of freedom has also been demonstrated in the neutron-rich osmium [1].

The work presented here was initiated to elude on the question of shape coexistence and shape evolution in neutron-deficient osmium isotopes. In this paper the result of an experiment where the lifetimes of yrast states in 170 Os have been measured via the RDDS method are presented. The results are compared to the state-of-the-art beyond mean field

calculations.

II. EXPERIMENT AND RESULTS

The experiment was performed at the ALTO facility (IPN Orsay, France) using the Tandem accelerator. Excited states in 170 Os were populated in the reaction 142 Nd( 32 S, 4n) 170 Os at a beam energy of 170 MeV. The isotopically enriched 142 Nd target had a thickness of 1 mg/cm 2 . The Nd was evaporated onto a 2 mg/cm 2 thick Ta fronting facing the beam. The energy loss of the beam inside the Ta backing was taken into account in the determination of the bombarding energy. A 5 mg/cm 2 Au thick foil was used as a stopper foil for the fusion-evaporation fragments. Target and stopper were mounted on the OUPS plunger [32]. The γ-rays were detected by the ORGAM germanium detector array composed of 10 Compton-suppressed HPGe detectors distributed over two rings at backward angles (133.5 and 157.6 degrees) and two additional detectors at forward angle (43 degrees).

The recoil velocity of the 170 Os nuclei was deduced from the Doppler shift of γ rays emitted in flight to be β = v/c = 1.62 ± 0.02%. Data were collected for 8 target-stopper separations between 18 and 740 µm. The normalization of the data for the different distances was obtained using the 278 keV line of 197 Au, resulting from the Coulomb excitation of the stopper foil. The normalization is thus directly proportional to the integrated beam current on the target. The γ -γ coincidences were reconstructed and used to avoid side-feeding effect on the lifetime determinations. Lifetimes of the two first excited states have been obtained using γ -γ coincidence and the DDCM method [33,34] gating on the in-flight component of the feeding transition. γ -γ were sorted ring wise and the background subtracted projection were then summed and used to extract the lifetimes of interest. The background subtracted spectra obtained by gating on the in-flight component of the 4 + 1 and 6 + 1 are presented in Fig. 2 and Fig. 4 for the detectors at 157.6 degree and Fig. 3 and Fig. 5 for the ones at 133.5 degree respectively. As the spectra were contaminated with peaks from other nuclei and there was not sufficient statistics to work with triple coincidences two independent methods were used to extract the lifetimes of interest: the traditionnal method in which the intensities of the peaks were extracted from the in-flight gated spectrum using analytic functions and a Monte-Carlo based approach. For the latter, GEANT4 Monte-Carlo simulations taking into account all the relevant aspects of the experimental setup such as the position and resolution of individual detectors, target and degrader thickness, reaction kinematics, etc., were used to determine the line shapes of the peaks. These line shapes were later used to extract the intensities of the stopped (I us ) and in-flight (I s ) in the spectra as a function of the lifetime (τ ) via the relation:

I us = dI s dt τ. (1)
I us (red square) and Is (black triangle), after renormalization to the Coulomb excitation of the Au-stopper, are given in the right panels of Fig. 2 and Fig. 4 for the 2 + and 4 + state respectively and for the detectors placed at 157.6 degrees. The same analysis was performed independently for the detectors at 133.5 degrees and the results are presented in Fig. 3 and Fig. 5. Lifetimes were extracted using background substracted spectra gated on the in-flight component of the feeding transition. Using such a gated-approach allows to get rid of the problem with long lived unseen feeding. Moreover, the second approach presents the advantage of taking into account the non-gaussian shape of the peaks due to the angular aperture of the detectors, the velocity distribution and slowing down of the recoiling nuclei in the target/stopper. For these reasons the more robust fit given by the second approach gives a more reliable determination of the lifetimes. The lines shapes were fitted to the experimental spectra using the Minuit2 package [35] and the asymmetric errors were extracted using the MINOS function included in Minuit2, leaving as free parameters only the number of counts in the two components. MINOS extracts the error on either side by varying the lifetime such that ∆χ 2 = 1 while minimising the χ 2 on all other free parameters. In Fig. 2 and 4 the γ-ray spectra obtained by projecting the γ -γ matrices on the in-flight component of the feeding transition (4 + 1 → 2 + 1 and 6 + 1 → 4 + 1 respectively) are presented (solid black line) for the distance in the sensitive range for the lifetime measurement. The corresponding fits are shown (dashed red line) for γ-ray spectra with detectors at the most backward angle, representing about half of the total statistic. Purple bands corresponding to the variations done by MINOS to find the two sided errors are also shown. It should be noted that the two methods yielded compatible results using the same background substracted spectra. While the result using the second methods are reported in Table I, the ones employing the first methods corresponds to 80 +11 -13 ps for the 2 + 1 and 20 +8 -5 ps for the 4 + 1 . Reduced electromagnetic transition probabilities were obtained from the measured lifetime (τ ) using the formula:

τ = 8.13 × 10 13 E -5 γ [B(E2) ↓] -1 (1 + α) -1 , (2)
where E γ is in units of keV, B(E2) ↓ in e 2 b 2 , τ in ps and α is the total internal conversion coefficient evaluated using [36]. The results are summarized in table I.

As this is a very unusual result the validity of the measured lifetime of the 4 + 1 state can be questioned. The data has been analyzed in an independent manner by several of the

III. DISCUSSION

The measured B(E2; 2 + 1 → 0 + 1 ) of 0.54(0.05) e 2 b 2 (97(8) W.u.) is in agreement with extrapolation from less neutron-deficient osmium isotopes. It is also in good agreement with earlier theoretical estimates [37]. The variable-moment-of-inertia (VMI) model [38] with the fitted parameters [18] gives an estimate of the B(E2; 2 + 1 → 0 + 1 ) of 170 Os, which is ∼ 40% lower than the experimental value. A similar underestimate is obtained for 172 Os, however, the VMI reproduces correctly the evolution of the B(E2; 2 + 1 → 0 + 1 ) going from 172 Os to 170 Os. Looking at the 2 + 1 state the 170 Os behaves as a transitional nuclei with the normal decrease in collectivity moving away from the neutron mid-shell. The B(E2; 4 + 1 → 2 + 1 ) of 0.21(0.05) e 2 b 2 is, in contrast to the "normal" B(E2; 2 + 1 → 0 + 1 ) surprisingly small, resulting in a B 4/2 ratio of 0.38 (11). Similar results were obtained in

J π E [keV] τ [ps] I π i → I π f B(E2) ↓ [e 2 b 2 ]
Exp. Theo. The reported theoretical values are the ones obtained in this work using the symmetry conserving configuration mixing method.

166 W [28], 168 Os [23], and 172 Pt [29]. Based on those measurements, Cederwall et al. [29] proposed a transition at N = 94 from a collective regime into a seniority-like scheme as a possible explanation for the B 4/2 < 1 , despite the presence of a large number of valence nucleons. The position of such a phase transition at N = 94 is supported by the present data. However, as 170 Os is rather collective the suggested explanation, i.e., a transition into a seniority-like scheme, is very surprising. Band mixing calculations for 170 Os [18] cannot explain this phenomenon, as the ground-state band should be pure at such low spins.

Moreover it is worth noticing that the 2 + 1 states of these four nuclei follow the expected correlations between the E(4 + 1 )/E(2 + 1 ) or the product of number of valence protons and neutrons and the B(E2; 2 + 1 → 0 + 1 ) [39].

To try to understand the small B 4/2 ratio, symmetry-conserving configuration mixing (SCCM) calculations were performed using the generator coordinate method framework with Hartree-Fock-Bogoliubov states found with variation after particle number projection (PN-VAP) [40,41]. In general the yrast states are given as close to prolate with a β ≈ 20 • and γ ≤ 20 • . For 172 Os, the yrast band is however tri-axial with γ ≈ 30 • . The energies for the lowest yrast and non-yrast states for 168,170,172 Os are presented in Fig. 1.

The agreement between experimental and theoretical excitation energies is satisfactory (see Ref. [42] and references therein). In Fig. 6

→ 0 + 1 ) (B 4/2 )
for the neutron-deficient osmium isotopes. The tabulated values for 172,174 Os values were taken from NNDC and from Ref. [43,[START_REF] Melon | Investigation of the X(5)-Structure in 176 Os using Aboslute Transition Probabilities[END_REF] for the 176 Os. The value reported for 168 Os is the one from the work of Grahn et al. [23]. The experimental value for 170 Os as well as the theoretical values for 168,170,172 Os are part of this work.

as well as those of 168,172 Os. Thus the observed discrepancy on the B 4/2 for 168,170 Os is solely originated by the B(E2; 4 + 1 → 2 + 1 ). Indeed a similar factor ∼4 is found between the experimental and theoretical B(E2; 4 + 1 → 2 + 1 ). While the experimental B 4/2 ratio is small, the resulting theoretical ratios are ∼ 1.5, close to that of a deformed rotor. The experimental B 4/2 ratio for 172 Os is 1.5(2), compatible with the present theoretical approach. The present results show that the structural change is more sudden than previously observed. Indeed the large drop in B 4/2 is already evidenced in 170 Os. A possible explanation for the observed B 4/2 ratio is that the yrast 4 + state does not belong to the same band as the 2 + 1 state. The origin for this mismatch could be the presence of a shape-coexistent rotational band whose 4 + member would be below the 4 + level of the ground state band. The symmetry conserving conguration mixing methods (SCCM) calculations performed in this work show no evidence for such a side band. In Fig. 7 the potential energy surface (PES) obtained using the PN-VAP method, and the collective wave functions for the 0 + 1 , 2 + 1 , and 4 + 1 state are plotted in the (β 2 , γ) plane. The PES exhibits only one minimum at a slightly triaxial deformation (β 2 , γ) ∼ (0.2, 15 • ) and the collective wave functions have all the same structure, revealing that they belong to the same rotational band. The second 4 + in the calculations (not shown) corresponds to a state in a γ-band. Another possibility is that the experimental yrast 4 + has a single-particle nature that could be produced, e.g., by the alignment of a pair at low spin as it was found in 44 S [42]. In order to search for such a state, calculations were expanded by performing PN-VAP calculations including cranking and by extending the range of triaxial quadrupole deformations to -60 • < γ < 120 • as done in Ref. [42]. The full configuration mixing was not performed due to the large computational burden. Nevertheless, a 4 + state with the sought after characteristics to reproduce the low B(E2; 4 + 1 → 2 + 1 ) value would manifest itself as a minimum for the projected J ≥ 4 PES's not present in the J = 0, 2 PES's computed at non-zero intrinsic rotation (cranking) frequency, ω = 0. Such a feature has not been found in the calculations and the origin of the observed transition probability remains unexplained within the employed formalism and/or variational space.

IV. CONCLUSION

The lifetimes of the first excited 2 + and 4 + states in 170 Os were measured for the first time using the RDDS method at the ALTO facility with the ORGAM γ-ray array coupled to the OUPS plunger. A surprisingly small B(E2; 4 + 1 → 2 + 1 ) value was found. To understand this value, the results were compared to the state-of-the-art beyond mean field calculations. The model accurately reproduced the energies of the lowest lying yrast states and the 2 + reduced transition probabilities in 168,170,172 Os. Although the model described correctly the properties of the yrast 4 + state of 172 Os, the sudden structural change observed when removing two neutrons is not present in the calculation. The question of the origin of the small B 4/2 in 168,170 Os remains open, and merits experimental efforts in order to validate these surprising results and expand the known lifetimes to higher spin yrast and yrare states.

FIG. 1 . 1 /

 11 FIG. 1. (Color online) The excitation energy systematic of the 2 + and 4 + yrast states in the osmium isotopes in the upper panel. The structural benchmark R 4/2 = E 4 + 1 /E 2 + 1

FIG. 2 .FIG. 3 .FIG. 4 .

 234 FIG. 2. (Color online, left panels) Background subtracted γ-ray spectra obtained by gating on the in-flight transition of the 4 + 1 → 2 + 1 for the detectors at 157.6 degrees. The γ-ray spectra show the stopped and in-flight components of the 2 + 1 → 0 + 1 . Only the distances in the sensitive range are presented. The stopped component is indicated by an arrow in the upper most panel, while the in-flight component with an arrow in the lowest panel. The large peak at 279 keV is the Coulomb excitation of the gold stopper. Spectra are background subtracted. The fit used to extract the integral of the two components are displayed for each distance with the red dashed line. The purple surfaces corresponds to the variations performed by the MINOS package to find the two sided error on τ . (Right panel) Normalized number of counts for the distances in the sensitive range used to extract the lifetime of the 2 + state.

FIG. 5 .

 5 FIG. 5. (Color online) Same as Fig. 4 for the 4 + 1 → 2 + 1 transition at 133.5 degrees obtained by gating on the 6 + 1 → 4 + 1 in-flight transition.

1 FIG. 7 .

 17 FIG. 7. (Color online) The PN-VAP potential energy surface for 170 Os (top left panel) and collective wave functions for the ground state (top right) as well as the yrast 2 + (bottom left) and + (bottom right) states. All calculated wave functions display a very similar structure.

48,50 Cr [24], 72,74 Zn [25], 114 Te [26], 114 Xe [27], 166 W [28], 168 Os [23] and 172 Pt [29]. These observations have not been reproduced so far by any type of state-of-art nuclear structure calculations

  , neither large-scale shell model nor beyond mean-field.

	was also addressed by the
	means of lifetime measurements using the Recoil-Distance Doppler Shift (RDDS) method
	giving access to the transition quadrupole moment Q t . A strong variation in the Q t with
	increasing spin in the ground state band was observed. This behavior could be explained
	by the model of three bands with strong mixing. Studing the spectroscopy of 168 Os [20] and
	using a similar theoretical approach of three band mixing model, a conclusion similar to
	that for 170 Os is reached concerning the presence of shape coexistence as the shaping force
	of the low spin spectroscopy.
	More recent studies concerning neutron deficient Os isotopes such as 162 Os [21], including
	a lifetime measurement of the 17/2 + state in 167 Os [22] and of yrast and non-yrast states
	in 168 Os [23], give evidences for a shape transition from prolate deformed via γ-soft nuclei
	to spherical shapes close to the N = 82 shell gap. It is worth pointing out that for the
	168 Os Grahn et al. [23] measured a reduced transition probability for the yrast 4 + resulting
	in a B 4/2 = B(E2; 4 + 1 → 2 + 1 )/(B(E2; 2 + 1 → 0 + 1 ) = 0.34(18). A B 4/2 < 1 is very rare
	throughout the nuclear chart with only a handful of examples away from closed shell nuclei,
	e.g.,

TABLE I .

 I Spin and parities of the yrast states in 170 Os together with their excitation energies, lifetimes, and reduced electromangnetic transition probabilities (experimental and theoretical).

	2 + 1	287 70 +6 -6 2 + 1 → 0 + 1 0.54 +0.05 -0.05 0.53
	4 + 1	750 18 +6 -4 4 + 1 → 2 + 1 0.21 +0.07 -0.04 0.81

  experimentally known B 4/2 are shown together with the results of the calculations. The experimental B 4/2 are presented in Fig.6for169-176 Os and compared for168-172 Os to the present theoretical calculations. The B 4/2 for 172 Os is well-reproduced by the model, however the ones of168,170 Os are overestimated by a factor ∼ 4. As shown in Tab. I, the B(E2; 2 + 1 → 0 + 1 ) of 170 Os is very well reproduced,

		2.5 3.0	Tab. Grahn This work			SCCM
	4/2 B	1.0 2.0 1.5					B 4/2 vib. B 4/2 vib. B 4/2 rot. B 4/2 rot.
		0.5
		0.0	168	170	172 Mass number A	174	176
	FIG. 6. (Color online) The ratio between the B(E2; 4 + 1 → 2 + 1 ) and the B(E2; 2 + 1

authors using more than one way of estimating the peak intensities. Results scatter slightly but within errors and the anomaly of a B 4/2 < 1 remains valid. ACKNOWLEDGMENTS The authors would like to thank the ALTO technical team for the good quality beam that was provided during the experiment. Dr. K.O. Zell and Dr. A. Blazhev from IKP Köln are thanked for the excellent quality Nd targets. We also thank the UK/France (STFC/IN2P3) Loan Pool and GAMMAPOOL European Gamma-Ray Spectroscopy Pool for the loan of the detectors for ORGAM. This work was supported in part by the 2214-TUBITAK (Scientific and Technological Research Council of Turkey) Programme, the Scientific Research Projects Coordination Unit of Istanbul University under Project No. 46811, the European Community FP7 Capacities-Integrated Infrastructure Initiative-Contract ENSAR No. 262010 This work has been partly funded (A.G.) by the P2IO LabEx (ANR-10-LABX-0038) in the framework Investissements d'Avenir (ANR-11-IDEX-0003-01) managed by the French National Research Agency (ANR). T. R. R acknowledges support from Spanish grants FIS-2014-53434-P MINECO and Programa Ramon y Cajal 2012 No. 11420, and computing time at GSI-Darmstadt.