Isomerism in the "south-east" of 132 Sn and a predicted neutron-decaying isomer in 129 Pd
Cenxi Yuan, Zhong Liu, Furong Xu, P. M. Walker, Zs. Podolyak, C. Xu, Z.Z. Ren, B. Ding, M.L. Liu, X.Y. Liu, H.S. Xu, X.H. Zhou, Y.H. Zhang, W. Zuo
aa r X i v : . [ nu c l - t h ] S e p Isomerism in the “south-east” of
Sn and a predicted neutron-decaying isomer in Pd Cenxi Yuan a, ∗ , Zhong Liu b, ∗∗ , Furong Xu c,d , P. M. Walker e , Zs. Podoly´ak e , C. Xu f , Z. Z. Ren f , B. Ding b , M. L. Liu b , X.Y. Liu b ,H.S. Xu b , Y.H. Zhang b , X.H. Zhou b , W. Zuo b a Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, 519082, Guangdong, China b Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China c State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China d Center for Theoretical Nuclear Physics, National Laboratory for Heavy Ion Physics, Lanzhou 730000, China e Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom f Department of Physics, Nanjing University, Nanjing 210093, China
Abstract
Excited states in neutron-rich nuclei located south-east of
Sn are investigated by shell-model calculations. A new shell-modelHamiltonian is constructed for the present study. The proton-proton and neutron-neutron interactions of the Hamiltonian areobtained through the existing CD-Bonn G matrix results, while the proton-neutron interaction across two major shells is derivedfrom the monopole based universal interaction plus the M3Y spin-orbit force. The present Hamiltonian can reproduce well theexperimental data available in this region, including one-neutron separation energies, level energies and the experimental B ( E , , Sn,
Cd, and
Pd. New isomers are predicted in this region, e . g . in Sn,
Cd,
Pd, , In and
Ag, in which almost no excited states are known experimentally yet. In the odd-odd , In and
Ag, the predicted very long E − states are discussed, demanding more information on the related proton-neutron interaction. Thelow-lying states of In are discussed in connection with the recently observed γ rays. The predicted 19 / − isomer in Pd coulddecay by both electromagnetic transitions and neutron emission with comparable partial life-times, making it a good candidate forneutron radioactivity, a decay mode which is yet to be discovered.
Keywords:
1. Introduction
On the journey towards the neutron drip-line one needs areliable theoretical model which incorporates the known fea-tures of the nuclear many-body system and has enough pre-dictive power for a range of unexplored nuclei. The nuclearshell model is one such, providing the basic framework for un-derstanding the detailed structure of complex nuclei as arisingfrom the individual motion of nucleons and the e ff ective nuclearinteractions between them. In the shell model, doubly magicnuclei, especially those far from the line of stability, such as Sn, act as cornerstones for exploring the unknown regions.Experimentally, the observation of isomers has been key tothe understanding of the shell structure and the development ofthe shell model [1]. Recently, nuclei around
Sn have beenthe subject of intensive experimental studies with respect to thepersistence of the N =
82 shell gap and its relevance to theastrophysical r -process path. Early β -decay results seemed toindicate a substantial shell quenching [2], while isomeric spec-troscopy studies gave evidence for the persistence of the N = Z = Pd [3, 4, 5]. Along the Z =
50 lineisomeric states were also observed in , , Sn [6, 7], andmixing between seniority-2 and -4 configurations was revealed ∗ [email protected] ∗∗ [email protected] for the 6 + isomer of Sn [7]. Furthermore, mass measure-ments have been crucial for experimental determination of theshell gaps [8, 9].In addition, isomers in the region far from the β -stabilityline could serve as stepping stones towards the drip-lines. Forexample, the high-spin (19 / − ) isomer in Co provided thefirst example of proton radioactivity [10]. Similarly in thevery neutron-rich region, a neutron may “drip” from an iso-mer before the neutron drip-line itself is reached, if the iso-mer’s excitation energy takes it above the neutron separationenergy [11, 12].In this paper, shell-model calculations are performed to in-vestigate the isomerism in the south-east quadrant of
Sn, i.e.with Z ≤
50 and N ≥
82, including the possibility of neutronradioactivity from such isomers.
2. E ff ective Hamiltonian The construction of an e ff ective Hamiltonian is one of thekey elements in a shell-model study. The model space forthe present work is π f / , π p / , π p / , π g / , and ν f / , ν p / , ν p / , ν h / , ν f / , ν i / , corresponding to the Z = −
50 and N = −
126 major shells, respectively.Below
Sn, the robustness of the N =
82 shell gap hasbeen experimentally examined and confirmed down to Cd andPd [3, 5, 8, 9]. The core excited states in
In are found to be
Preprint submitted to Physics Letters B November 9, 2018 t nearly 4 MeV [4], thus this model space is suitable for the in-vestigation of the low-lying states around or lower than 2 MeVin Sn, In, Cd, Ag, and Pd isotopes with N >
82. So far there isno well established e ff ective Hamiltonian for this model spacedue to the lack of experimental data on the excited states in thismost neutron-rich region around Sn. An e ff ective Hamilto-nian for this model space is proposed below. In a very recentwork, shell-model calculations for In were performed em-ploying a modern realistic e ff ective interaction and two-bodymatrix elements deduced from the Pb region [13].The single-particle energies for the four proton orbits and thesix neutron orbits in the present model space are fitted to thereported energies of the single-particle states of
In and
Sn,respectively. These energies are from Ref. [14] and the recentlydiscovered π p / and π p / single-hole states in In [15,16]. The single-particle energy for the ν i / orbit in Ref. [14]is estimated from the excitation energy of the 10 + state in Sb[17]. The present Hamiltonian fixes the relative single-particleenergies to the observed excited states. It is reasonable as thepresent work concentrates on the excitation energies of levelsand neutron separation energies.The proton-proton interaction is based on the proton-protonpart of jj45pna Hamiltonian, which has been derived fromthe CD-Bonn potential through the G matrix renormalizationmethod by Hjorth-Jensen and is included in the OXBASH pack-age [18]. The theoretical method to derive the jj45pna e ff ectiveinteraction and its application in the A ∼
100 region is describedin Ref. [19]. Recently, the Hamiltonian jj45pna was also usedto investigate the β decay of Cd and
In [20], and the low-lying states of In isotopes around A =
125 [21]. The strengthof this interaction is modified by a factor 0 .
74 to reproduce thelow-lying states of
Cd. The neutron-neutron interaction isfrom the neutron-neutron part of CWG Hamiltonian, which isderived from the CD-Bonn renormalized G matrix and used tostudy nuclei around Sn [22].The proton-neutron interaction is calculated through an ef-fective nucleon-nucleon, monopole-based universal interactionV MU [23] plus a spin-orbit force from M3Y [24](V MU + LS).The validity of the V MU + LS interaction in shell-model calcu-lations has been examined in di ff erent regions of the chart ofnuclei. The structure features of neutron rich C, N, O [25],Si, S, Ar, Ca [26], Cr, and Fe isotopes [27] have been nicelydescribed by shell-model calculations by taking V MU + LS asthe proton-neutron interaction between the p proton shell andthe sd neutron shell [25], the sd proton shell and the p f neu-tron shell [26], and the p f proton shell and the gds neutronshell [27], respectively. For example, the neutron drip-lines forcarbon, nitrogen and oxygen isotopes are simultaneously ex-plained, revealing the impact of the proton-neutron interactionon the evolution of the nuclear shell [25]. Recently, the first 4 + state of S has been identified as a high- K isomer [28] throughthe Hamiltonian suggested in Ref. [26]. In the heavier region,close to Sn, the change of the energy di ff erence between the10 + and 7 − yrast levels in the N =
80 isotones down to
Pd iswell explained by V MU + LS [29]. Thus it is natural and reason-able to use this interaction as the proton-neutron interaction inthe present study.
Table 1: One neutron separation energies of experiments S ( expt ) n from Ref [30]except Cd from [8], predictions S ( AME n of AME2012 [30], calculationsthrough the finite range liquid drop model S ( FRDM ) n [32] and the present work S ( jj n . (All values are in MeV.) Nuclei S ( expt ) n S ( j j n S ( AME n S ( FRDM ) n Sn 2.402(4) 2.408 2.651
Sn 3.629(4) 3.732 4.281
Sn 2.271(4) 2.405 1.871
Sn 3.795 3.340 3.741
Sn 2.339 1.960 1.611
Sn 3.834 3.140 3.561
In 2.450(60) 2.364 2.701
In 3.418 3.130 3.781
In 2.370 2.270 1.771
Cd 2.169(103) 1.984 1.870 2.031
Cd 3.324 3.000 3.671
Cd 1.977 1.730 1.321
Ag 1.902 1.780 2.001
Pd 1.524 1.461In the present Hamiltonian the strength of the central-forceparameters of V MU is enhanced 1 .
07 times the original one inRef. [23] to give a better description of the one-neutron sepa-ration energies S n . It should be noted that the original form ofV MU comes from the e ff ective Hamiltonian in the sd and p f regions. In psd region, the strength of its central part is reducedby a factor of 0 .
85 to reproduce the binding energies of the B,C, N, and O isotopes. The new Hamiltonian is named as j j
Sn has fully occupied valence protons and no valenceneutrons in the present model space. Starting from
Sn, theproton-hole energies of
In and the neutron-particle energiesof
Sn are not directly taken as the single particle energies inthe Hamiltonian, but are modified by the residual proton-protonand proton-neutron interactions, respectively. The proton-holestates in the present work are a ff ected by the missing corre-lations due to the removal of protons from the fully occupied28-50 shell. In the following discussion, the configurations arewritten in the proton-hole neutron-particle scheme for simplic-ity.
3. Results and Discussion
With the j j
46 Hamiltonian described above, the propertiesof − Sn, − In, − Cd, − Ag, and − Pd areinvestigated. One-neutron separation energies calculated usingthe present Hamiltonian are listed in Table 1 together with thepredictions of AME2012 [30], the finite range droplet model(FRDM) [32] results, and experimental values available. Thepresent calculations reproduce the few experimental neutron2 Sn Expt. jj46 E ne r g y ( M e V ) Sn Expt. jj46 E ne r g y ( M e V ) Sn Expt. jj46 E ne r g y ( M e V ) Expt. jj46 E ne r g y ( M e V ) Sn Figure 1: Comparison between the calculated levels in − , Sn in thepresent work and those observed experimentally [7, 14]. separation energies [30] in this region nicely. Both the single-particle energy of the ν f / orbit and the proton-neutron inter-actions involving the fully occupied proton orbits contribute to S ( j j n of Sn. Its value together with the other observed S n values are used to constrain the strength of the proton-neutroninteraction in the present Hamiltonian as discussed in the pre-vious section.The levels of neutron-rich Sn isotopes are presented in Fig. 1.The present Hamiltonian reproduces the known low-lying statesof , , Sn well, especially the positions of the 2 + statesin , , Sn and the increasing trend of the energies of 4 + and 6 + states from Sn to
Sn. The dominant configurationsof the 8 + states in Sn and
Sn are 99.55% ν (1 f / )(1 h / )and 41.83% ν (1 f / ) (1 h / ), respectively. This state in Sn /2 Sn Sn Sn Sn /2 ESPE ( M e V ) Figure 2: Calculated neutron e ff ective single-particle energies (ESPE) for Snisotopes (Color online). is dominated by the ν (1 f / ) configuration (84.34%). If allthe yrast 6 + and 4 + levels in , , Sn were dominated bya pure seniority-2 configuration, the B ( E
2; 6 + → + ) value in Sn would be expected to be the lowest among these threeisotopes, but their experimental results are decreasing from
Sn to
Sn. The seniority scheme of the low-lying states inthese three isotopes can be discussed through the comparisonbetween the experimental results and the shell model calcula-tions. The observed B ( E
2; 6 + → + ) value indicates a mixingof seniority-2 and -4 configurations in the 4 + state of Sn bycomparing the results from a realistic e ff ective interaction andthe empirical modification of ν (1 f / ) matrix elements [7, 33].The present calculation also gives the decreasing B ( E
2) valuesbetween 6 + and 4 + states from Sn to
Sn, which will beshown later.The large energy di ff erences between the 6 + and 8 + states inthese three nuclei suggest that the 8 + states are not isomeric.However the small energy di ff erence between the 17 / − and21 / − states in Sn implies a 21 / − metastable state. Detailsfor this possible isomer in Sn will be given later. However,no such isomer is predicted in
Sn (not shown in Fig. 1). Thefirst 21 / − state of Sn is dominated by a ν (1 f / ) (0 h / ) con-figuration (96.7%). Compared with Sn the first 21 / − levelin Sn is expected to be more mixed because of the increas-ing number of valence neutrons and / or the change of the shellstructure. Fig. 2 presents the e ff ective single-particle energies(ESPE) of the neutron orbits in Sn isotopes. ESPE are definedas [31], ε j = ε corej + X j ′ V j j ′ h ψ | b N j ′ | ψ i , (1)where ε core j is the single-particle energy relative to the core, h ψ | b N j ′ | ψ i is the shell-model occupancy of the j ′ orbit and V j j ′ is the monopole part of the two-body interaction. Asshown in Fig. 2, the single particle energies do not changemuch in the Sn isotopes. Therefore the main di ff erencebetween the 21 / − states in Sn and
Sn arises fromthe two additional valence neutrons in
Sn. The con-figuration of the first 21 / − level in Sn is a mixtureof ν (1 f / ) (0 h / ) (61.3%), ν (1 f / ) (2 p / ) (0 h / ) (9.97%), ν (1 f / ) (2 p / )(0 h / ) (9.05%), and ν (1 f / ) (1 f / ) (0 h / )(3.38%), very di ff erent from the almost pure ν (1 f / ) ν (0 h / )configuration in Sn.Levels of the , In, , Cd, and , Pd isotopes arepresented in Fig. 3. Some of them are possibly isomers. Theground state of
In is found to be 7 − with a configuration of π (0 g / ) − ν (1 f / ), in agreement with the experimental assign-ment [14]. Our calculations indicate a very low 5 − state in In,which can be a candidate for an isomer. With two more neu-trons and two more proton holes respectively,
In and
Aghave similar structure, 7 − for ground state and very low 5 − forfirst excited state. These results depend on the details of theproton-neutron interaction between π (0 g / ) − and ν (1 f / ) or-bits, for which the experimental information is still rare.Recently six γ rays were observed following the β -delayedneutron emission from Cd and assumed to be emitted fromthe excited states of
In [13]. Due to the low statistics and3 .00.4 In Expt. jj46 E ne r g y ( M e V ) (9/2+) 17/2+7/2+ Expt. jj46 E ne r g y ( M e V ) In Cd Expt. jj46 E ne r g y ( M e V ) Expt. jj46 E ne r g y ( M e V ) Cd Pd Expt. jj46 E ne r g y ( M e V ) Expt. jj46 E ne r g y ( M e V ) Pd Figure 3: The same as Fig. 1, but for , In, , Cd, and , Pd. g ) -1 (2p )p ) -1 (1f ) g ) -1 (2p )p ) -1 (1f )g ) -1 (1f ) spin ( ) E x ( M e V ) Figure 4: Calculated excitation energies of the π − ν multiplets in In as func-tion of spin. -3-2-10 ESPE ( M e V ) Sn In Cd Ag Pd0123 Sn In Cd Ag Pd /2 ESPE ( M e V ) /2 Figure 5: Proton hole and neutron particle ESPEs for N =
82 isotones calcu-lated in the present work (Color online). the lack of γ - γ coincidence, it was di ffi cult to establish a levelscheme with those observed γ rays [13]. The spin parity of theground state of Cd is 7 / − from Ref. [14] and the presentshell-model calculation. As the β decay energy ( ∼
13 MeV) of
Cd is much larger than the neutron separation energy ( ∼ In, the ground state of
Cd can decay to manyhigh excited states beyond the neutron emission threshold of
In, with spin parity 5 / − to 9 / − through Gamow-Teller tran-sitions and 3 / + to 11 / + through first forbidden transitions.Thus many states in In could be populated in the β -delayedneutron emission of Cd.The low-lying states of the π − ν configurations in Incalculated by the present Hamiltonian are shown in Fig. 4.The present shell-model results are similar to those shown inFig. 4(a) of Ref. [13], especially for the π (1 p / ) − ν (1 f / ), π (0 g / ) − ν (2 p / ), and π (1 p / ) − ν (1 f / ) multiplets, thoughthe proton-neutron interaction is calculated through V MU + LSin this work, while it is derived from the CD-Bonn potentialwith V low − k approach in [13].In both calculations the 7 − state is the lowest and 1 − the high-est among the π (0 g / ) − ν (1 f / ) multiplets, however the otherstates are slightly di ff erent. The present work predicts that 5 − is first excited state and a little lower than 6 − state, while theshell-model calculation in Ref. [13] gave opposite prediction.Similarly the present shell-model results may also explain mostof the observed γ rays in In [13]. Because of the uncer-tainty of the shell-model calculations and extra complexity in-troduced by the low-lying π (1 p / ) − ν (1 f / ) multiplets, more4xperimental information on the excited states of In,
Inand
Ag are highly desired and crucial in understanding theproton-neutron interactions in this region.The ESPE for proton-hole and neutron-particle orbits alongthe N =
82 closed shell are shown in Fig. 5, where it can beseen that the π (0 g / ) and π (1 p / ) proton orbits are quite closeto each other. So the 1 / − states in odd-Z N =
82 isotones arepredicted to be the first excited state beyond ground state 9 / + and are long-lived isomers, consistently with the experimen-tal observation that in both In and
Ag the low-lying 1 / − states are β -decaying isomers [15, 14]. The ground state of Cd is found to be a mixture of π (0 g / ) − and π (1 p / ) − . Thelow-lying positive-parity states of Cd are formed throughthe coupling of π (0 g / ) − . The present calculations show thatthe 2 + and 4 + states of Cd are dominated by the π (0 g / ) − configuration with 93.0% and 99.2%, respectively. The contri-bution from other configurations such as π (1 p / ) − (1 p / ) − , π (1 p / ) − (0 f / ) − , or π (1 p / ) − , is very small as they havemuch higher energies. In the present model space, the 6 + and8 + states can only be formed from the π (0 g / ) − configura-tion. Previous shell-model work showed similar results [34]for Cd. As expected from the seniority scheme, the yrast 8 + state in Cd was found to be isomeric [3]. Similarly the 8 + seniority isomer in Pd was recently identified at RIKEN [5].All the seniority isomers experimentally observed in , , Sn,
Cd and
Pd are well reproduced. Their semi-magic nature validates the neutron-neutron and proton-protonparts of the shell-model interactions in the present work. Insome other nuclei in this region, some of the levels are possi-bly isomeric because of the slow transition rates resulting fromlow transition energies. These isomer candidates are listed inTable 2 together with those experimentally confirmed in Sn iso-topes and N =
82 isotones. τ E is the mean life-time of E B ( E
2) values and predicted transition energies. The ex-perimental B ( E expt values of , , Sn are from Ref. [7].The two B ( E expt values of Cd are due to the two possibledecay transition energies [3]. The e ff ective charges for calcu-lation of B ( E
2) values for protons and neutrons are e p = . e and e n = . e , respectively, which are similar to those used inRef. [7].The 21 / − isomer in Sn is analogous to the 6 + isomer in Sn, but its B ( E
2) value is much larger than that of
Sn, asshown in Table. 2. The one-body transition density of the neu-tron 1 f / orbit from 6 + to 4 + in Sn is almost the same asthat from 21 / − to 17 / − in Sn, and the B ( E
2) enhancementin
Sn is mainly due to the transition from 0 h / to 1 f / and1 f / to 1 p / . Although the occupancies of 1 f / and 1 p / inthe 17 / − state are small, the large number of 0 h / and 1 f / particles in the 21 / − state result in a large one-body transi-tion density. The transition energy between 21 / − and 17 / − in Sn is predicted to be almost the same as that between 6 + and 4 + in Sn. τ E around 100 ns is predicted for the 21 / − isomer in Sn.The yrast 5 − states in , In and
Ag are predicted to beclosely below the 6 − levels and only around 70 keV above the7 − ground states, as shown in Fig. 4 for In, leading to long life-times. A much larger τ E in In is predicted because ofthe small B ( E
2) value caused by the cancellation between theproton and neutron contributions. It should be noted that dueto the lack of experimental information on the proton-neutroninteraction in this quadrant of
Sn, large uncertainties relatedto the isomerism in these odd-odd nuclei are not unexpectedin the present shell-model calculations. For example, the 5 − isomer will disappear if it is higher than the 6 − state. Or alter-natively the 4 − state could be isomeric, if it lies below the 5 − state.19 / − isomers are predicted in the N =
83 isotones
Cdand
Pd, with τ E ∼
100 ns and ∼ µ s, respectively. The ex-citation energy of the predicted 19 / − isomer in Pd is around0 . Pd by emitting a neutron withan orbital angular momentum of l = ~ (not to 2 + state of Pdbecause of its 1 .
311 MeV excitation energy). The half-life ofneutron emission is calculated by using the widely-used for-mula of the two-potential approach [35], in which both the pre-exponential factor and exponential factor are explicitly defined.The potential that the emitted neutron feels is a sum of the nu-clear potential, the spin-orbit potential and the centrifugl poten-tial. The form of both the Woods-Saxon nuclear potential andthe spin-orbit potential and the parameters used are taken fromtextbook [36], V = V central ( r ) + λ r ∂ V central ( r ) ∂ r −→ l · −→ s , (2)where V central ( r ) = − V + e r − Ra , R = . A / fm, a = . λ = − . ~ M ω , ~ ω = A / (1 + N − ZA ), and M is the av-erage mass of a nucleon. The depth of the nuclear potential V is determined by the Bohr-Sommerfeld condition to ensure aquasi-bound state [37], Z r r s µ ~ ( Q n − V − ~ µ l ( l + r ) dr = ( G − l + π , (3)where µ is the reduced mass of the neutron, Q n is the decayenergy, r and r are classical turning points defined by Q n = V + ~ µ l ( l + r , and G is the global quantum number. The predictedlife-time for neutron emission from the 19 / − state of Pdto the ground state of
Pd ranges from 0 . µ s with thedecay energy Q n =
4. Summary
In summary, a shell-model study has been performed in thesouth-east of
Sn to search for possible isomeric states. A newshell-model Hamiltonian has been constructed for the presentinvestigation. The proton-proton and neutron-neutron interac-tions, which are each limited to one major shell, have beenobtained from existing CD-Bonn G matrix calculations. The5 able 2: Excitation energies (MeV), transition energies (MeV), observed [3, 5, 7] and calculated B ( E
2) values ( e f m ), calculated E µ s ), and thedominant configurations for possible isomeric states. Nuclei J π i → J π f E i ∆ E B ( E th τ E B ( E Expt
Configuration
Sn 6 + → + ν (1 f / ) (96.3%) Sn 21 / − → / − ν (1 f / ) (0 h / )(96.7%) Sn 6 + → + ν (1 f / ) (75.5%) Sn 6 + → + ν (1 f / ) (53.13%) In 5 − → − π (0 g / ) − ν (1 f / )(99.0%) In 17 / + → / + π (0 g / ) − ν (1 f / ) (93.9%) In 5 − → − π (0 g / ) − ν (1 f / ) (72.5%) Cd 8 + → + / π (0 g / ) − (100.0%) Cd 19 / − → / − π (0 g / ) − ν (1 f / )(99.7%) Ag 5 − → − π (0 g / ) − ν (1 f / )(74.3%) Pd 8 + → + π (0 g / ) − (71.1%) Pd 19 / − → / − π (0 g / ) − ν (1 f / )(74.2%) Pd 6 + → + π (0 g / ) − ν (1 f / ) (54.6%)proton-neutron interaction across two major shells is calculatedthrough the V MU plus M3Y spin-orbit interaction. The presentHamiltonian, j j
46, is able to reproduce well the one-neutronseparation energies, level energies, and B ( E
2) values of thealready observed isomers in this region. New isomeric statesare predicted and their structures are discussed. The predicted19 / − isomer in Pd could be a candidate for neutron radioac-tivity.
5. Acknowledgements
This work has been supported by the National NaturalScience Foundation of China under Grant Nos. 11235001,11305272, 11375086, 11405224, 11435014, 11575007,11535004, and 11320101004, the Special Program for Ap-plied Research on Super Computation of the NSFC Guang-dong Joint Fund (the second phase), the Specialized Re-search Fund for the Doctoral Program of Higher Educationunder Grant No. 20130171120014, the Guangdong NaturalScience Foundation under Grant No. 2014A030313217, theFundamental Research Funds for the Central Universities un-der Grant No. 14lgpy29, the Pearl River S&T Nova Programof Guangzhou under Grant No. 201506010060 and Hundred-Talent Program (Chinese Academy of Sciences), and the UnitedKingdom Science and Technology Facilities Council undergrant No. ST / L005743 / References [1] E. Segre and A.C. Helmholz, Rev. Mod. Phys.
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