Dragos » Dobre

Gérard Morel

Jean-Franc ˛ois

P Étin

Eddy Bajic
email: eddy.bajic@cran.uhp-nancy.fr

Improving digital interaction for operator-driven process-plant operation

Keywords: Process Plant Operation, Ambient Intelligence, SysML, Simulation, Modelica

Operating process plants to control, maintain and manage them remains a complex activity driven by skilled operators. Despite the increasing capabilities of automation and information technologies, only a part of the technical objects of a process plant digitally interact with human beings when performing their tasks. This paper present preliminary work based on the Ambient Intelligence concept in order to improve the digital interaction between human beings and technical devices when sharing common activities.

INTRODUCTION

In industry, physical systems have become more and more complicated due to the multitude of components and their sizes. Thus they became more difficult to control, to survey and to maintain. For security reasons, we have to be capable of predicting their behavior in all situations, and for all possible environmental perturbations. This is a difficult task and solutions are needed to improve the security and the dependability, to prevent serious accidents due to the incomplete understanding of the complex system. Solutions based on active components are available, transforming instrumented components in components with a reactive behavior. In spite of these advances we are still dealing with non-resolved problems of non-instrumented components.

The technological evolution and the microcontroller miniaturization have created new concepts like ubiquitous computing (the expanding of microcontrollers in everyday objects). Ambient Intelligence concept relies on ubiquitous computing in order to help people to accomplish their activities, being assisted by the surrounding environment itself.

Ambient Intelligence brings new visions in industrial applications which are based on permanent human to system interactions.

This article discusses preliminary results obtained using Ambient Intelligence concept in operating process plants. This work is motivated by the difficulties encountered in the process of controlling a complex system, considering as example a nuclear power plant.

The problem statement and the motivations will be presented in section 2. Section 3 deals with a brief introduc-tion to Ambient Intelligence, stressing its main advantages. A discussion of the results is provided before to conclude.

MOTIVATION

Recently, the exchange of knowledge and information between different actors of a production plant has become a necessary ingredient in complex systems' control and maintenance. An integrated organization requires that information from the process is made available for common use by the Control, Maintenance and technical Management (CMM) activities.

In 1998, [START_REF] Pétin | Distributed intelligent actuation and measurement (IAM) system within an integrated shop-floor organisation[END_REF] proposed a solution to integrate the "intelligence" into a physical system, especially for instrumented components. They present a distributed Intelligent Actuation and Measurement (IAM) system that helps in providing an informational representation of the production process as efficiently as is possible. This representation is distributed through field-bus architecture to all integrated activities of CMM.

The intelligent actuator representation (see fig. 1) incorporates four functional modules: the objective validation, Fig. 1. Visible and interoperable architecture Fig. 2. Plant operation: a complex system [START_REF] Galara | Roadmap to master the complexity of process operation to help operators improve safety, productivity and reduce environmental impact[END_REF] the report elaboration, the observation validation and the action execution. This solution is already implemented in industry and there are companies that propose it (i.e. PREDICT France). However, it applies only to the instrumented components (about 20% in case of a nuclear power plant). Our research problem is related to the noninstrumented components.

It would be incensed to consider that the physical system associated to a Nuclear Power Plant (NPP) can be nondeterministic. The complexity of a NPP resides mainly on human to physical system interaction. Therefore, this system can become not only complex, but also nondeterministic.

This issue is illustrated by [START_REF] Galara | Roadmap to master the complexity of process operation to help operators improve safety, productivity and reduce environmental impact[END_REF]. He proposed an explicit representation of the plant operation in order to help operators to improve safety, productivity and reduce environmental impact. Considering the plant operation as a complex system, Galara considers the NPP control as a system-of-systems (see fig. 2):

• The world of physics is a set of interconnected field technological devices supporting transformations of primary energy and material into products and wastes: the physical system (ϕs); • The computer science, also called "abstract layer", is a set of interconnected automata: Control, Maintenance, technical and financial Management system (CMMs); • The psychological layer is the human organization and information processing (ΨLs).

Therefore, considering this representation as a basis for our work, we tried to describe and offer solutions to plant operation problems.

The process layer (ϕs) is composed by all physical components of a NPP, counting more than 10.000 components to be controlled. A general problem is that about 80% of components are non-instrumented (without actuators or sensors), mainly due to cost and communication problems (cables).

The human organization layer (ΨLs) is composed by a hierarchy of personnel working in the NPP. Two categories can be distinguished: the Control Room Operators (CRO) and the Field Operators (FO). The CRO controls, at distance, not only the systems' components but also the FOs' actions. The FO work within the physical system and controls all non-instrumented components. This system is The Control, Maintenance, technical and financial Management system (CMMs) is composed by all means used to make a NPP work. There are control operations, maintenance operations, financial operations, etc. Our research objectives are related to this system, and more particular to complex systems control. In the next paragraphs we describe the problems related to our research.

To control a NPP, the personnel use pre-specified procedures. These Operating Procedures (OP) are a set of operations/actions that must be executed consecutively. They are written by the design engineers who must anticipate all possible states of the process and its environment. The procedures are usually implemented in the construction step, but it is essential to evolve in time. To respond to system's complexity, a realistic plant simulation could prevent undesired events. This simulation should also take into account the entire OPs associated to each physical system, called Operating Guides (OG).

Spangler and Peters ( 2001) have established a framework for an explanatory model of organizational knowledge and behavior in environments where procedures are an important influence on system behavior. Their solutions to operating problems is an ontology that models the explicit knowledge structures and their interactions. They validate the model in a computer simulation that explains and predicts human interventions in real-world scenarios.

Figure 3 illustrates the FO's working context, showing interactions and constraints that influence the quality of work.

The operators' cooperation and good synchronization is a key point in controlling a nuclear power plant. To conduct a safety and reliable component manipulation the interaction between FO and CRO must be done in realtime and permanent.

Fig. 4. OP execution by a field operator

A FO works in one physical system and controls mainly non-instrumented components. In some cases, the FO uses a portable computer to help accomplish his job, but in many cases the OP information is represented on a printed paper. The problems using printed papers are related to paper degradation due to different causes.

Moreover, the efficiency of the FO's work can be influenced by environmental constraints (like temperature, noise, whether) and internal constraints (like stress, experience, knowledge acquired during formations). These constraints can influence the quality of work and the reactions to different problems.

A step in the OP contains information about the component and the action, but it is the FO's job to locate and to identify the component, and to execute the action. However, the most important is action validation (the proper action on the right component at good moment). Nevertheless, the OP does not contain information about all possible cases. Therefore, the FO has to reorganize his work in collaboration with CRO in order to satisfy the constraints.

The activities done by the FO to execute the OPs are represented in figure 4. It is given by an activity diagram using SysML representation.

It all begins in control room where the operator chose to execute an OP. In most of cases, to accomplish an OP, the operator must collaborate with a FO. So, he searches one available. The FO, which surveys the system, stops his work and begins to communicate with the CRO. The communication is based on DECT telephone or walkietalkie. Some communication constraints are the cable lines and the wireless link specification that could interfere with sensible devices within the systems.

Because the OPs are paper-based, the FO must go and recuperate them from Control Room (CR). So, there is a waste of time from the moment the FO begins to communicate and the moment he begins the OP execution.

The OP execution is done in two (or more if necessary) steps. First, the CRO begins to execute his list of actions. At a specified time, in order to continue, he must synchronize with the FO. The FO begins his work and at the end he will write a report that will be sent to CRO. This can take from hours to days, depending on system evolution and operator motivation. Due to this delay, we could discover some inconsistencies between the logical situation and physical situation.

These different situations are explained in [START_REF] Galara | Process control engineering trends[END_REF]. The process is evolving from one steadystate process operation to another steady-state process operation. The situation described by the components' state can be different for the CRO and FO, as their activity can be done in serial or in parallel. The problem is how to map the physical situation into logical situation to eliminate the inconsistencies.

There are actually some works to computerize the operators in order to facilitate their work and to communicate information faster and safer. In O'Hara et al. ( 2004), the authors discuss the presentation of information in computer-based control rooms. Several approaches to information design are presented, specifically addressing: (1) monitoring, detection, and situation assessment;

(2) routine task performance;

(3) teamwork, crew coordination, collaborative work.

Pirus have done studies in using computers in field operation [START_REF] Pirus | Field operation computerization study[END_REF]). The informatics systems could respond at the difficulty of using paper documents, but must be well studied because the FO must have free hands, must allow audio and video communication, must facilitate interaction, etc. This is why there is a necessity to find solutions in physical systems control and mainly to test new technologies and concepts that could bring new visions to this domain. Ambient Intelligence is one concept that could change the way of thinking about operators' work.

AMBIENT INTELLIGENCE IN WORK ENVIRONMENTS

It all started in early 1990s. The ubiquitous computing was invented by [START_REF] Weiser | The computer for the 21st century[END_REF]. This concept refers to an environment where objects are given the information processing capability. The Ambient Intelligence is based on ubiquitous computing concept.

An Ambient Intelligence (AmI) environment is a surrounding computing space that is spontaneously and proactively supporting the user's needs [START_REF] Rigole | Task-driven automated component deployment for ambient intelligence environments[END_REF]). The principle [START_REF] Vasilakos | Ambient Intelligence, Wireless Networking, Ubiquitous Computing[END_REF]) is to integrate different computer science backgrounds together with psychology and social sciences in order to create a network of intelligent devices (with sensors and actuators) able to enhance the quality of people life.

There are many research projects on AmI. [START_REF] Friedewald | Privacy, identity and security in ambient intelligence: A scenario analysis[END_REF] have done scenario analysis in different applications • providing communication between people;

• support the mobility of workers;

• providing access to work-related information at any time and from any location, improving knowledge sharing and co-operation; • providing efficient working tools;

• controlling diverse working appliances;

• increasing safety and security;

• domain-specific functionalities such as diagnostics of equipment, factory automation, etc.

The scenario proposed by [START_REF] Aarts | IC design challenges for Ambient Intelligence[END_REF] contains three basic AmI functions. Firstly, the environment is contextual aware, which means that there are sensors integrated into the environment which communicate events that can be combined to determine meaningful states and actions, like person identification, position detection, and query interpretation. Secondly, audio, video, and data can be streamed wirelessly to any access device present in the environment, thus enabling ubiquitous wireless access to information, communication, services, and entertainment. Thirdly, users in an Ambient Intelligent environment interact with their surrounding through natural modalities such as speech, gesture, and tactile movements, thus enabling hands free interaction with their environment.

Researches of AmI in industrial application are not very frequently. [START_REF] Müller | An ambient intelligence information infrastructure for production-tomaintenance processes[END_REF] is studying the use of ambient technologies to solve informational problems in Process-to-Maintenance processes. The activity domain is the production, transport, installation and maintenance of machines and plants. The point of interest is the overview on ambient hardware and software technologies relevant to their domain.

Ambient Intelligence concept can help us improving human to system interaction. As we are interested more in field operator system control, we study AmI by taking him as the central actor of the system.

We can assimilate AmI to an interface between the FO and the system he controls. This interface helps him to improve work quality by offering personalized services. In figure 5 we illustrate some services examples that could be implemented to assist operators.

We have three interactions types: CRO -FO, CRO -PS and FO -PS. The interaction between CRO and FO is done to cooperate, coordinate and synchronize their work. AmI can improve the communication between the two using audio, video and data transmission, wirelessly, anytime and everywhere. The audio transmission is used for verbal communication, video is used to send images from the system for diagnostics, and data transmission is used to transfer information like OP and additional documents about OP execution. Also, automatic reporting could reduce the report time after OP execution.

In AmI, the physical objects are given the possibility to "think" and to have a behavior of their own. Wong et al. ( 2002) presents five characteristics of an intelligent product:

• Possesses a unique identity;

• Is capable of communicating effectively with its environment; • Can retain or store data about itself;

• Deploys a language to display its features, production requirements, etc.; • Is capable of participating in or making decisions relevant to its own destiny. [START_REF] Bajic | Ambient services modelling framework for intelligent products[END_REF] add another characteristic: offers objects advanced services along its life cycle.

Using advanced technologies, like RFID and Wireless Sensor Network, we can enhance the possibilities of an ordinary object, implementing reactive behavior, and increase the security of work. Implementing services like identification and localization of a physical component could eliminate the component mistake error. Automatic data acquisition about components' state could minimize the surveillance time. Action verification and validation, done by the component itself, could assist the FO in his work and could eliminate manipulation errors. Automatic traceability will help and improve the maintenance process.

The situation awareness could eliminate the incoherences between the physical situation and the logical situation. All these services are intended to be transparent to the FO and used by natural ways.

SYSTEM ENGINEERING FOR COMPLEX SYSTEMS

In our research we have chosen to adopt the System Engineering project life-cycle. This article presents some of our results: the problem state model and the simulation of a physical system. The simulation recreates the scale factor of a real physical system. The modeling part is made using SysML. The simulation has been implemented using Modelica language.

Modeling Complex Systems: System Engineering

SysML 1 is a UML2 profile that customizes the industry standard for modeling software-intensive systems for sys-tems engineering requirements. It supports the specification, analysis, design, verification and validation of a broad range of systems and systems-of-systems. These systems may include hardware, software, information, processes, personnel, and facilities.

In System Engineering, the project development is realized using the V cycle, starting with system's requirements analysis. There are User Requirements and Functional Requirements. The User Requirements are requirements given by the final user: to improve the operators work in controlling physical components. From these requirements and from the environment study we can extract the Functional Requirements.

After the requirement analysis, we have modeled the physical system on which we will test our concepts. It is a hydrodynamic installation containing all kind of components, instrumented and not instrumented.

First we have implemented a taxonomy classification for all physical components we are using in our system. Using these components, we implemented the technical infrastructure by instantiation. The technical infrastructure helps us to oversee the dimensions and parameters for each component. In parallel with the model we have worked on system simulation.

Using SysML we have modeled the OPs related to our system. They are implemented using Activities Diagrams. The OPs set forms the Operating Guide, implemented as a Block Definition Diagram.

Simulating Complex Systems: Modelica

The Modelica 2 language is widely used in industry for modeling and simulation of physical systems. Example application areas include industrial robotics, automotive applications and power plants. Typical for models of such systems is that they are of large scale, commonly up to 100.000 equations. There are also extensive standard libraries for e.g., mechanical, electrical, and thermal models.

The primary objective of formulating a model of a complex physical system is most often simulation. That is, prediction of the response of a model, given a specified input stimuli, and the state of the model. If the model is sufficiently accurate, the simulation results may be used to draw conclusions about the behavior of the true physical system ( Åkesson (2007)).

The ModelicaML unified language for modeling and simulation of complex systems combining both SysML and Modelica is the work of [START_REF] Pop | Towards unified system modeling with the ModelicaML UML profile[END_REF] The environment used for creating and simulating Modelica is Dymola. Using Modelica Fluid library we have created a hydrodynamic system. In figure 6 we show our model. It is based on a real physical system that is intended to be installed in order to test all proposed concepts and 2 Modelica Association -www.modelica.org Because the Modelica language supports both physical equation and algorithmic procedures, the combination of the two allows to create multi-domain models and simulations. The physical system is described using different equations. In addition, we can implement algorithmic entities to simulate technologies like WSN or RFID, even to implement different AmI services.

A multi-domain simulation involves some requirements to be fulfilled. First of all, there are lots of objects from different domains, like hydrodynamic, networking, automatic control, etc. An object oriented simulation environment like Modelica allows the reuse of components. Furthermore, it is an open language and there are lots of free libraries.

To visualize system's behavior, the environment must allow the real-time simulation. With Modelica this is possible using the Dymola real-time option or using the free real-time library from [START_REF] Wagner | Hardware-in-the-loop simulations with temporarily too slow simulation models[END_REF].

Another useful feature for a simulating environment is the reuse of libraries and code used in programming real objects. In Dymola it is possible to use C and Java code and to bypass any limitation given by Modelica language.

Last but not least, the simulation environment must permit the interaction with components, to change states and to receive situations. [START_REF] Olsson | External interface to modelica in dymola[END_REF] presents some of the possible interfaces to Modelica using Dymola. Besides external C/Java code that can implement any socket communication, there is the possibility to interact from Matlab or using any application with DDE (Dynamic Data Exchange).

Ambient Intelligence is described by an environment where objects have capacities to react to changes and to commu-nicate with each other and with peoples. We can simulate such environments with Modelica by creating behavioral objects and enabling any user to interact with virtual simulated physical components.

CONCLUSION

This article describes preliminary results on our research, concerning the problems of controlling complex systems. Complex systems are very large systems where the number of elements implies costs and communications issues.

In such systems, the good communication, coordination and synchronization of working personnel is essential to conduct a safety and reliable system manipulation.

Ambient Intelligence describes an environment in which the human is assisted by the surroundings and manipulated objects to improve his work. Using advanced technologies and personalized services, we could enhance the interactions between operator and the system he controls.

We have given some service examples like localization, identification and transparent action verification and validation.

The first results of this work are mainly situated in the modeling and simulation step. For modeling we have chosen to use the System Engineering process and for the complex system model, SysML is the most appropriate modeling language. For the simulation we have used Modelica, an object oriented language for modeling and simulation of large physical systems.

Our approach based on Ambient Intelligence can improve the digital interaction between human beings and technical devices when sharing common activities. Using System Engineering project process we can model advanced systems and with Modelica we can verify the correctness and the feasibility of modeled systems.

The next step in our research is to implement different Ambient Intelligence services within Modelica simulation. This will allow us to verify the feasibility of using such concepts. One issue will be the possibility to recover the implemented services to external computers and to test the interactions between the FO and the system by using advanced services.

The most important step will be the construction and implementation of these services using advanced technologies on the physical platform itself.

Fig. 3 .

 3 Fig. 3. Field operator's working context

Fig. 5 .

 5 Fig. 5. Ambient Intelligence services

Fig. 6 .

 6 Fig. 6. Modelica model for simulation technologies. In order to model and to verify the good construction of the platform we have chosen to simulate it using Modelica. Also, we can verify and validate the OPs' coherence of action execution.

OMG SysML -www.omgsysml.org

Scientific American 265, 3, 94-104. Wong, C., McFarlane, D., Zaharudin, A., and Agarwal, V. (2002). The intelligent product driven supply chain. In IEEE International Conference on Systems, Man and Cybernetics. Hammamet, TUNISIE.

ACKNOWLEDGEMENTS

This work is realized within the French LABIME (LAngage d'expression des Besoins en Informations des Métiers d'Exploitation) project of the research consortium (GIS) Surveillance, Sûreté et Sécurité des Grands Systèmes (3SGS) with CRAN, LORIA and EDF as partners.


S Calinescu

O Sorlin

I Matea

F Carstoiu

D D Dao

F Nowacki

G De Angelis

R Astabatyan

S Bagchi

C Borcea

R Borcea

L Cáceres

M Ciemála

E Clément

Z Dombrádi

S Franchoo

A Gottardo

S Grévy

H Guerin

M N Harakeh

I M Harca

O Kamalou

M Kmiecik

A Krasznahorkay

M Krzysiek

I Kuti

A Lepailleur

S Lukyanov

A Maj

V Maslov

K Mazurek

P Morfouace

J Mrazek

F Negoita

M Niikura

L Olivier

Y Penionzhkevich

L Perrot

C Petrone

Z Podolyák

C Rigollet

T Roger

F Rotaru

D Sohler

M Stanoiu

I Stefan

L Stuhl

J C Thomas

Z Vajta

M Vandebrouck

O Wieland

Coulomb and nuclear excitations of 70 Zn and 68 Ni at intermediate energy

Keywords: numbers: 24.50.+g., 25.60.-t, 21.10.Tg

published or not. The documents may come

I. INTRODUCTION

The 68 28 Ni 40 nucleus is, as 14 6 C 8 and 34 14 Si 20 , composed of a doubly-closed shell originating from the spin-orbit interaction for protons and from the harmonic oscillatorlike shape of the mean-field potential for neutrons. As for 14 C and 34 Si, 68 Ni lies at the verge of a so-called island of inversion where the cost of promoting pairs of neutrons across the shell gap is lower than the gain through quadrupole and pairing correlations.

The doubly-closed shell effect can be best viewed by the sudden increase of the energy of the first 2 + 1 state, that goes in concert with a decrease of the reduced transition probability B(E2; 0 + 1 → 2 + 1 ) to excite it. Adding two protons to these nuclei preserves a significant effect of double magicity in 16 O and 36 S, and single magicity in 70 Zn, whose structure resembles, according to Ref. [1], to a vibrator with some single-particle features. On the other hand, when removing two protons from these nuclei, no increase in the 2 + 1 energy is observed and the B(E2; 0 + g.s. → 2 + 1 ) values are increasing: 12 4 Be 8 , 32 12 Mg 20 and 66 26 Fe 40 nuclei are deformed (see, e.g., Refs. [2][3][4]). As discussed in Ref. [5], these nuclei lie in regions where the hierarchy between the proton-neutron forces in presence plays a crucial role in changing the spacing (and even the ordering) between orbits, thus favoring the breaking of magicity at N =8, 20 and 40.

The 34 Si and 68 Ni nuclei carry fingerprints of this proximity to the island of inversion through the presence of a 0 + 2 state below the 2 + 1 state. In these two cases, the determination of the reduced transition probabilities ρ(E0) and B(E2; 0 + 2 → 2 + 1 ) suggests a shape coexistence between spherical 0 + 1 and deformed 0 + 2 configurations (see, e.g., [6] for 34 Si and [7][8][9] for 68 Ni). Their weak B(E2; 0 + 1 → 2 + 1 ) values [10,11] have been interpreted as due to the fact that the 2 + 1 state mainly comes from neutron excitation(s). As neutrons carry a much smaller effective charge than protons, e ν 0.5 as compared to e π 1.5, the resulting neutron contribution to the B(E2) value, which scales with e 2 , is small compared to a similar excitation involving protons.

In the three nuclei, 14 8 C, 34 20 Si and 68 40 C, neutron excitations across the shell gap involve a change of parity from the normally occupied to the valence states. Therefore, the structure of the 2 + 1 state must involve 2p2h excitations, with the breaking of a pair. Consequently, the energy of the 2 + 1 state is not directly related to the size of the neutron shell gap but to a more complex energy balance that involves pairing and quadrupole correlations, which reduce its excitation energy as compared to the size of the shell gap. The size of the N = 40 shell gap can be more directly inferred from the energy of negative parity states coming from the (1p1h) excitation across the gap. In 68 Ni, the long-lived (0.86 ms) 5 -state at 2.849 MeV [12], formed by νp 1/2 or νf 5/2 excitations to the νg 9/2 orbit, is such a candidate.

Contrary to neutrons, proton excitations across the gap in 34 Si and 68 Ni occur between orbits of the same parity, e.g., between the 0f 7/2 and (1p 3/2 , 0f 5/2 ) orbitals in 68 Ni. Therefore, a proton 2 + p state can be constructed already at the 1p1h level and should be existing in the spectra of 34 Si and 68 Ni. The corresponding B(E2; 0 + 1 → 2 + p ) value could be larger than that for the 2 + 1 state, depending on the rigidity of the proton shell gap against ph excitations, the fragmentation of the strength, as well as the proton ph content of the ground state. In the case of 34 Si, similar B(E2) values have been predicted for the 2 + 1 and 2 + p states [13], but a firm identification of 2 + p state is still lacking. In 68 Ni, shell-model calculations of Langanke et al. [14] have predicted that a large fraction (about twice as large as that of the 2 + 1 state) of the B(E2) strength goes to 2 + p states present above 4 MeV. In the present work, we wish to confirm the low B(E2; 0 + g.s. → 2 + 1 ) value in 68 Ni, found to be 255(60) in [11] and 280 +120

-100 e 2 fm 4 in [15], and explore if significant B(E2) strength exists at higher excitation energy. We have also remeasured the [16].

The puzzling discrepancy between the determined B(E2) values in 70 Zn could point to a side-feeding of the 2 + 1 from the 2 + 2 state. If its contribution was large and not subtracted, it would artificially enhance the measured B(E2; 0 + g.s. → 2 + 1 ). However, with a branching ratio from the 2 + 2 to the 2 + 1 of 60% [18] (the remaining going to the g.s), and a low B(E2; 0 + g.s. → 2 + 2 ) of about 50 e 2 fm 4 [1, 19], a possible contamination would be only of about 0.6×50 = 30 e 2 fm 4 . This would therefore not explain the discrepancies on the reported B(E2; 0 + g.s. → 2 + 1 ) values observed in Table I.

The B(E2) values of 70 Zn and 68 Ni were obtained in the present work by Coulomb interaction with a 208 Pb target, using the same experimental technique as in Ref. [20]. In the following, we describe the production methods of the beams of interest, followed by a brief presentation of the experimental set-up and of the methodology to extract the Coulomb and nuclear quadrupole excitation strengths, which is then applied to the two nuclei. The search for measurable B(E2) strength at higher excitation energies in 68 Ni is addressed in the last experimental part of this work, followed by a theoretical interpretation of the structure of 70 Zn and 68 Ni using shell-model calculations.

II. EXPERIMENT

The 68 Ni nuclei were produced at GANIL in fragmentation reactions of a 60•A MeV 70 Zn 29+ beam, with an average intensity of ∼1.2 µAe, on a 145 µm 9 Be target. They were separated from other reaction products by the LISE3 spectrometer [21], using a wedge-shaped Be degrader of 221 µm inserted at its intermediate focal plane. Coulomb excitation was induced on a 200 mg/cm 2 208 Pb target, placed at the image focal plane of the spectrometer. In addition, a 146.4 mg/cm 2 12 C target was used to study more specifically the nuclear contribution. In total, 2.6×10 9 68 Ni nuclei were produced for the 208 Pb target study with a purity of 80% at energies of 47.68 and 40.8•A MeV before and at mid-target depth, respectively,

The 70 Zn primary beam was also used at a reduced intensity with an energy of 51. The incoming beam profile and interaction point on target were determined by using two sets of positionsensitive gas-filled detectors (CATS) [22] located 140 cm and 75 cm upstream of the Pb target.

46 hexagonal BaF 2 crystals of the Château de Cristal were placed in two hemispheres at a mean distance of 25 cm from the 208 Pb target for the detection of the inflight γ-rays, emitted within a 3-ns time window [27] with respect to the passage of the ions through the CATS detectors. The efficiency of this array was first determined using calibration sources up to 1.4 MeV, and cross checked using GEANT4 simulations. Then, the in-flight efficiency was simulated by taking into account the angular distribution of the emitted E2 γ-rays, calculated by the DWEIKO code [28] for the different cases under study. We confirmed a-posteriori that these distributions agree with the experimental ones. A photo-peak efficiency of 25(1)% was found at 885 keV, that is the energy of the 2 + 1 →0 + 1 transition in 70 Zn. As this transition has been seen in each individual crystal of BaF 2 , it has also been used to optimize the Doppler-shift correction by comparing the observed γ peak for each crystal, to the known energy at rest. It was assumed that the γ-ray emission occurred at mid-target depth to apply Doppler corrections, which is a good approximation for states with short lifetimes (here shorter than 4 ps). According to the simulations, the intensity of the photopeak signal is still dominant at γ-ray energies below 8 MeV, above which the single-escape peak becomes dominant.

The deflected nuclei were identified by their time-offlight and energy loss in a Double Sided Silicon-Strip annular Detector (DSSSD), located 50 cm downstream of the target. The DSSSD consisted of four quadrants having on the front side 16 annular strips of 1.9 mm width each, and on the back side 24 radial strips of 3.4 • pitch, each grouped three by three. With a central hole of 3 cm, this geometry allowed to detect and identify ions scattered between 1 • and 6.5 • in the laboratory frame. The efficiencies of the DSSSD to detect nuclei that underwent Coulomb excitation were determined using GEANT4 simulations by shooting the target with beam particles having the measured position and energy profiles. Their angular distributions were calculated with the DWEIKO [28] and ECIS [29] codes corresponding to 2 + state excitations. They were folded to account for the angular straggling (≈ 0.6 degrees) induced by interactions between the beams and the Pb target. After having removed the few dead strips from the analysis, DSSSD detection efficiencies of 62% and 72% were found for 70 Zn and 68 Ni, respectively.

The nuclei that passed through the central hole of the DSSSD were identified in an ionization chamber (CHIO) and stopped in a plastic detector, which was surrounded by two HPGe detectors, used to determine the isomeric content of the 68 Ni beam. The production of two isomeric states of 68 Ni, 5 -with T 1/2 of 860(50) µs [12] and 0 + 2 with T 1/2 of 268 (12) ns [8], was quantified from the characteristic delayed γ-ray transitions observed in Fig. 1 after the implantation of 68 Ni nuclei. The 815 keV transition that connects the 5 -state to the 2 + state at 2034 keV was used to determine that 31(2)% of the incoming 68 Ni were in the 5 -isomeric state. The number of counts in the 511-keV peak was used to infer an isomeric ratio of 2.45(2)% for the 0 + 2 at 1604 keV [7,8], obtained after correcting for the fact that only 2/3 of its decay occurs by pair creation [33]. The other γ-ray transitions observed in Fig. 1 come from the β-decay of 68 Ni [34].

III. EXPERIMENTAL RESULTS

A. Coulomb excitation of 70 Zn

The Coulomb interaction dominates over the nuclear interaction at small deflection angles, where the impact parameter b of the reaction is larger than the range of the nuclear force. Using semi-classical trajectories [36], a minimal impact parameter b min , above which nuclear excitations can be neglected, has been derived in Refs. [37,38]. It is linked to a maximal scattering angle θ max lab , up to which Coulomb excitation dominates, that can be approximated by [START_REF] Jackson | Classical Electrodynamics[END_REF]:

θ max lab = 2Z p Z t e 2 b min M p c 2 β 2 γ , (1)
where the subscripts 'p' and 't' stand for the projectile and target, respectively. In this equation, the minimal impact parameter b min is obtained as follows: The result of the best fit procedure is illustrated with blue circles.

b min = R p + R t + 6 + πa 2γ f m, (2)
with

R p(t) = r 0 A 1/3 p(t) f m, (3)
where r 0 =1.3 fm, A p(t) is the mass of the projectile and target, respectively, and

a = Z p Z t e 2 M p c 2 β 2 ; γ = 1 1 -β 2 (4)
Using the present mean velocity value < β > of 0.298, it is found that the Coulomb process is dominant for impact parameters larger than b min = 20.29 fm, i.e. for deflection angles lower than θ max lab = 3.3 • . This is significantly smaller than the grazing angle of the reaction that is here 4.5 • . However, as we shall discuss later, at this intermediate energy regime, there is no angular range in which the nuclear part is totally negligible.

The Doppler-corrected and background-subtracted γray spectrum of 70 Zn, displayed in Fig. 2, has been obtained using the full angular range up to 6.5 • . The background spectrum was obtained by collecting radiations out of the prompt time-window, which mostly displays structures arising from the intrinsic radioactivity of the BaF 2 crystals (see, e.g., Ref. [27]). Two γ-peaks are seen in Fig. 2, an unresolved doublet at around 880 keV and a single-peak at 1759-keV. The latter transition results from the de-excitation of the 2 + 2 state to the ground state. This level decays directly to the g.s., with a branching ratio of 68/168, and to the 2 + 1 state via a cascade of two γrays of 874 keV and 885 keV, with a ratio of 100/168 [18], both ratios having 10% error. Therefore, when extracting the reduced transition probability for the 2 + 1 state, the feeding from the 2 + 2 state has to be subtracted, which was not done in most of the works presented in Table I.

The B(E2; 0 + g.s. → 2 + 1 ) and B(E2; 0 + g.s. → 2 + 2 ) values of 70 Zn are obtained from the comparison between experimental and simulated differential cross sections, the latter being obtained from the DWEIKO [28] and ECIS [29] codes. The use of these two codes allows to estimate the error made in the derivation of the B(E2) values with two different methods. As there exists no optical potential available for our target/projectile/energy combination, the parameters derived from the 86 Kr+ 208 Pb reaction at 43 MeV/A [30] were used in our fits. In order to see the influence of the choice of potential on the fit of experimental data, two additional potentials 40 Ar+ 208 Pb at 44MeV/A [31] and 17 O+ 208 Pb at 84 MeV/A [32] were used. Very similar values (with less than 4% difference) were found in the determination of the nuclear parameter β N using these 3 optical potentials. This stability of the extracted nuclear parameter over the choice of optical model potential parameters is due to the fact that only the extreme tail of the potential influences the reaction mechanism.

Since the energy resolution of Château de Cristal (typically 18% at 885 keV) does not allow a discrimination between the 885 and 874 keV transitions emitted in the 2 + 2 → 2 + 1 → 0 + 1 cascade, the best approach is to first fit the experimental angular distribution of the 2 + 2 state, obtained by gating on the 1759-keV γ-ray, that corresponds to the direct decay to the g.s. Once the Coulomb (β C2 ) and nuclear (β N2 ) deformations of this 2 + 2 state are determined, they can be used to constrain the fit of the angular distribution gated on the (874, 885)-keV doublet in order to determine the β C1 and β N1 values of the 2 + 1 state.

The Coulomb and nuclear processes are present at all scattering angles and interfere. However, as the Coulomb excitation at intermediate energy is usually the dominating contribution below the 'safe' scattering angle, the fit of the angular distribution was first done using only β C2 up 3 • in Fig. 3. The β N2 parameter was set in order to reach a qualitative agreement for the high angular range of the spectrum. This way, a first couple of approximated β C2 and β N2 values was derived and used as initial parameters of a χ 2 minimization procedure applied to the full angular distribution. The values of β C2 and β N2 , obtained after convergence of the fit, are listed in Table II. The same procedure has been applied for other cases described later in the text.

The best agreement between the simulated (continuous red line) and the experimental (black crosses) amplitude of the angular distribution, gated on the 1759-keV γ-ray, is obtained for B(E2; 0 + g.s. → 2 + 2 ) = 62(7) e 2 fm 4 (β C2 = 0.045(3)), and a nuclear contribution of β N2 of 0.054 (3) with the DWEIKO code. The best fit with ECIS is for B(E2; 0 + g.s. → 2 + 2 )= 55(6) e 2 fm 4 (β C2 = 0.042(3)) and β N2 = 0.049 (3). The resulting simulations of the angular distributions of the deflected 70 Zn nuclei for the two codes are shown in Fig. 3.

At this relatively high energy of the scattered ions, the double-step excitation of the 2 + 2 state through the intermediate 2 + 1 state is expected to be small. It has been estimated to be 0.7 mb using the GOSIA code [35], as compared to the presently measured 0 + g.s. → 2 + 2 cross section of 7.8(9) mb over the 1 • -3.3 • angular range. Subtracting this estimated contribution from the mean value of the two fits, 58(7) e 2 fm 4 , leads to 53(7) e 2 fm 4 , which is in excellent agreement with the values of 50 (13) and 50(10) e 2 fm 4 , obtained in [19] and [1]. The present experimental results are reported in Table II.

The experimental cross-section for the 2 + 1 state is found to be 228 (20) mb in the angular range between 1 • and 3.3 • . The angular distribution corresponding to the excitation of the 2 + 1 state includes the contamination of the 2 + 2 state that has just been derived earlier and for which we keep the contributions (β C2 , β N2 ) as fixed. The fit of the global angular distribution with the DWEIKO code (continuous red line) in Fig. 4(a) includes a Coulomb part with β C1 = 0.215 (8), which corresponds to a B(E2; 0 + g.s. → 2 + 1 ) value of 1419(120) e 2 fm 4 , and a nuclear contribution of β N1 = 0.288 (12). When using the ECIS code instead (Fig. 4(b)), a comparable B(E2) value of 1447(127) e 2 fm 4 is found. While the β C1 value is very similar to that obtained with the DWEIKO code, the fitted β N1 value of 0.241 is significantly smaller and not compatible with the value of 0.288 obtained with DWEIKO.

Our adopted B(E2; 0 + g.s. → 2 + 1 ) of 1432(124) e 2 fm 4 corresponds to the mean value extracted using the DWEIKO or ECIS codes (see Table II). It agrees, within the error bars, with those of Refs. [11,23,25,26] and with the evaluated value of 1525(75) e 2 fm 4 [16]. It confirms that the B(E2) values above 2000 e 2 fm 4 obtained from inelastic scattering of electrons [19] and protons [24] are too large. The reduced transition probability B(E2) to the 2 + 1 state at 2.034 MeV in 68 Ni has been obtained using the same procedure as described above for 70 Zn. The fraction of 68 Ni fragments produced in an isomeric state has been subtracted from the number of incoming 68 Ni nuclei. In this assumption, we neglect the contribution of their excitation to higher excited states (especially for the 5 -isomeric state whose beam fraction is large) that would decay through the 2 + 1 state. This hypothesis is further justified by the fact that we do not see any γ-ray in coincidence with the line at 2.034 MeV.

With a mean < β > = v/c value of 0.286 and b min = 20.3 fm, a value of θ max lab = 3.4 • is calculated from Eq. 1. The Doppler-corrected background-subtracted γ-ray spectrum in Fig. 5 (a), obtained by including the angular distribution of the ejectile up to 6.5 degrees, clearly shows a 2.034 MeV line corresponding to the excitation of the 2 + 1 state. The integrated cross section between 1 • and 3.4 • is 55(7) mb. The complex fit of the high-energy part of the spectrum will be discussed in Sect. III B 3. 208 Pb, for which a B(E2) value of 3025(421) e 2 fm 4 is measured, compatible with the adopted value of 3010(160) e 2 fm 4 [16]. In the high-energy tail of the in-flight component of the 2 + 1 state in 68 Ni, the excitation of the 3 -state in 208 Pb is also observed for which a B(E3; 0 + g.s. → 3 - 1 ) value of 652000(9000) e 2 fm 6 was found, in agreement with [17]. 7) 312 [START_REF] Lenzi | [END_REF] 301 (38) a The calculated double-step feeding contribution to the 2 + 2 state has been subtracted from the B(E2) value of 58(7) e 2 fm 4 , obtained from the mean results of the two codes, leading to the adopted value of 53(7) e 2 fm 4 (see text for details). The number of counts in the 2 + 1 state at 2.034 MeV was extracted by using the simulated response function of the detection system (dashed magenta line). The curve in blue circles corresponds to the global fit, which includes an exponential decay (long-dashed gray line), the excitations of the 3 -and 2 + states in 208 Pb, and high-energy contributions discussed in Sect. III B 3. (b): Same as (a), but for the non Dopplercorrected spectrum. The decays of the 3 -and 2 + 1 states in 208 Pb are visible at 2.614 and 4.085 MeV (with single-escape), respectively, for which our measured B(E3) and B(E2) values agree with the ones of the literature.

The fit of the angular distribution of the ejectiles, observed in coincidence with the γ-ray (red curve in Fig. 6) from the 2 are obtained when using the DWEIKO and ECIS codes, respectively. The adopted B(E2) value of 301(38) e 2 fm 4 from these two results agrees, within one sigma, with the B(E2) values of 255(60) and 280(60) e 2 fm 4 obtained in Ref. [11] directly and relative to 70 Zn, respectively. It also agrees with the less accurate value of 280 +120

-100 e 2 fm 4 from [15].

Excitation of the 2 + 1 state in Carbon

Interactions between the 68 Ni nuclei and a C target were also studied in order to confirm the small nuclear contribution β N 0.1, derived from the study with the Pb target. As seen in Fig. 7, the experimental Dopplercorrected γ-ray spectrum associated with the C target (solid black histogram) does not show evidence of the 2 + 1 state excitation at 2.034 MeV. This indicates that the β N value is below the sensitivity of the present measurement. This hypothesis is confirmed by the fact that the spectrum shown in magenta stars of Fig. 7, which displays the result of a GEANT4 simulation including the experimental background contribution and a β N value of 0.10 derived from the excitation with the 208 Pb target, does not exhibit any peak at 2 MeV. As shown in the dashed blue spectrum of Fig. 7, a γ transition at the energy of the 2 + 1 state would have been seen in case of β N 0.2. . The adopted value of βN = 0.102 (8), as deduced from the study with the Pb target, is too small for a peak to be seen when 68 Ni scatters off the C target.

Excitation of the higher energy states

The structures that appear between 2.5 MeV and 8 MeV in the Doppler-corrected spectrum of Fig. 5(a) come from some processes that are discussed now. 1 and 3 - 1 states in the 208 Pb target (orange triangles). Note that, as the singleescape component dominates above 8 MeV, the two latter peaks are observed 511 keV lower than the value used in the fit. We do not find evidence of transitions that cascade through the 2 + 1 state. By assuming that the 4 states below S n = 7.8 MeV belong to E2 excitations, strengths of 15(2), 110(15), 42(5) and 16(2) e 2 fm 4 are found. As for the states above S n , they likely correspond to collective E1 excitations (likely to be Pigmy Dipole Resonance modes) whose much shorter lifetime, as compared to E2, make their γ decay not completely negligible as compared to neutron decay. Fig. 8 (b) corresponds to the non Doppler-corrected spectrum, fitted with the same components as the top spectrum. The consistent agreement of the fitting procedure for the top and bottom spectra gives more confidence in the proposed E2 components. This experimental distribution of E2 strength is compared in Fig. 11 to shell-model calculations, whose details will be discussed in Sect. IV B.

IV. DISCUSSION

In order to interpret the present experimental results, we performed Shell-Model (SM) calculations for the E2 response in 70 Zn and 68 Ni. These theoretical results are supplemented by deformed Hartree-Fock and beyond mean-field calculations in order to assess the collective features from a complementary approach. The valence space incorporates the needed degrees of freedom for the description of collectivity and the breaking of Z = 28 and N = 40 cores. It is composed of the pf shells for protons and 2p 3/2 1f 5/2 2p 1/2 1g 9/2 2d 5/2 orbitals for neutrons. We used the LNPS effective interaction [START_REF] Lenzi | [END_REF] with recent small adjustments to extend its reliability up to N = 50, including g 9/2 -d 5/2 particle-hole excitations, with minor consequences at N = 40. All electromagnetic properties are calculated using the microscopic effective charges (e p ,e n )= (1.31,0.46) from [41,42].

A. 70

Zn

The energies and E2 rates are compared to the full shell-model diagonalization in Fig. 9 (middle panel, level scheme labelled as 'Shell Model'). Note that the B(E2) values are indicated downwards in Fig. 9. They should be multiplied by 5 for the upwards values, such as for the 0 + → 2 + transition given in Table II.

The 70 Zn nucleus exhibits a rather complex spectrum with the observation of a low-lying excited 0 + 2 state (at 1.07 MeV excitation energy) and several 2 + states below 2.0 MeV (at 0.87 MeV, 1.76 MeV and 1.96 MeV excitation energy). The agreement is generally good for both the energies and B(E2) values: the calculations produce at the same time a strong B(E2;

2 + 1 → 0 + g.s.
) with a value of 314 e 2 fm 4 compared to 286 e 2 fm 4 experimentally, as well as hindered B(E2;

2 + 2 → 0 + g.s.
) and

B(E2; 2 + 3 → 0 + g.s.
) with values of 1 and 2 e 2 fm 4 , respectively, compared to the experimental value of 10.6 e 2 fm 4 for the 2 + 2 → 0 + g.s. transition. The branchings of the 2 + 2 state, either decaying directly to the ground state, or through a cascade to the 2 + 1 state are known to be of 68/168 and 100/168, respectively (see insert of Fig. 2). An upper value of the B(E2; 2 + 2 → 2 + 1 ) of 15.5 e 2 fm 4 can be derived from this ratio, assuming a negligible M1 contribution, and taking our experimental value of B(E2; 2 + 2 → 0 + 1 ) = 10.6 e 2 fm 4 . Any M1 contribution will further reduce this B(E2) value.

There is a large difference between the calculated decay rates of the 2 + 2 → 2 + 1 and 2 + 2 → 0 + 1 that are 412 e 2 fm 4 and 1 e 2 fm 4 , respectively. This is at variance with experimental values of ≤ 15.5 and 10.6, respectively. The calculated decay rate of the 2 + 3 → 2 + 1 transition (45 e 2 fm 4 ) is about 10 times smaller than that of the 2 + 2 → 2 + 1 transition. Therefore, from its decay properties, it it likely that the 2 + 3 state obtained in the SM calculation corresponds to the 2 + 2 state observed experimentally. The very small quadrupole moment value of the 2 + 3 state indicates its non-collective character. Because of this, predictions on its decay patterns and partial lifetimes are particularly sensitive to mixing with tiny components of the wave function.

The potential energy surface (PES) displayed in the upper panel of Fig. 9 is obtained from constrained Hartree-Fock calculations in the shell-model basis. At the mean-field level, the nucleus exhibits a spherical minimum in competition with a triaxial shape slightly higher (∼ 1.6 MeV) in energy. Angular momentum projection already favors the triaxial shape energetically and beyond mean-field mixing around the triaxial projected minimum stabilizes it.

The evolution of the obtained energy spectrum and associated B(E2) values for various approximations is shown in the middle panel of Fig. 9. From left to right, we present the projected triaxial solution (labelled as 'Triaxial AMP') extracted from the top panel, this solution correlated through a Generator Coordinate Method (GCM) mixing with 17 states, and the final correlated shell-model results. All three approximations reproduce the magnitude of the Yrast 2 + 1 → 0 + g.s. E2 transition. However, the gradual suppression of the 2 + 2 → 0 + g.s. transition occurs as correlations are added, although it is difficult to trace back which ones are the most relevant.

The Kumar Invariants method [43] has also been applied to the fully correlated shell-model calculations to extract the (β, γ) parameters in 70 Zn and their associated variances. As seen from Fig. 9 (c), 70 Zn exhibits a peculiar regime with a strong triaxial collectivity. This triaxial degree of freedom is in full agreement with what was obtained from the mean-field analysis discussed above.

B. 68 Ni

The 68 Ni nucleus has been described almost two decades ago as a mixture between a spherical closed shell and a superfluid nucleus [11]. In addition, although not clearly assigned yet, the occurence of a superdeformed state at low excitation energy has also been recently debated [7]. The PES shown in Fig. 10 reveals the occurence of three minima (spherical, oblate and prolate) within a range of 3-4 MeV excitation energy (0.0 MeV, 2.26 MeV and 3.53 MeV, respectively). These minima correspond to the first three low-lying observed 0 + states obtained in the shell-model calculations at 0.0 MeV, 1.4 MeV and 2.4 MeV, which are in very good agreement with the 0.0 MeV, 1.6 MeV and 2.5 MeV experimental values. This agreement between the full-space diagonalisation and the experimental excitation energies is striking as the theoretical spectrum is very sensitive to the details of the residual interaction. Analysis of the obtained wave functions shows configurations which can be interpreted in terms of particle-hole (ph) excitations: the first two 0 + states appear to be partially mixed, with leading components of N = 40 closed shell (CS) and 2p2h neutron excitations. As compared to the ground state, the 0 + 2 state has an additional component of proton 1p1h with the neutron 2p2h coupled to J=2. The 0 + 3 state appears as a 6p6h excitation composed of proton 2p2h and neutron 4p4h components. The Kumar deformation parameters from reference [43] agree very well with the present constrained minimization. This strengthens the complementarity between the two descriptions (the deformed Hartee-Fock in the intrinsic frame of 68 Ni, the SM in the laboratory).

In order to generate the E2 response from the 68 Ni ground state, we computed the E2 structure function and show the comparison with the experimental data in Fig. 11. Its E2 energy-dependent strength agrees relatively well with the experimental one up to the neutron separation energy value of 7.79 MeV. The largest contribution goes to the 2 + 1 state which has the same structure in terms of ph excitations as the 0 + 2 state. The remaining part of the strength is shared by several levels around 5 MeV, which are characterized by larger proton excita- tion contributions as well as by larger neutron excitations across the N = 40 gap, as compared to the structure of the ground state. These combined features lead to a relatively weak strength at high energies excited from the ground state of 68 Ni. Experimental values are about two times weaker than calculated.

As discussed above, we think that the remaining observed strength above S n is more likely due to E1 decays coming from the excitation of PDR states. We therefore do not make a comparison with E2 calculated strengths in this energy range.

V. CONCLUSIONS

Using the intermediate energy Coulomb-excitation technique, reduced transition probabilities B(E2; 0 + g.s. → 2 + 1 ) of 1432(124) e 2 fm 4 and B(E2; 0 + g.s. → 2 + 2 ) of 53(7) e 2 fm 4 have been determined for 70 Zn. The small but non zero B(E2; 0 + g.s. → 2 + 2 ) value confirms that 70 Zn does not behave like a good vibrational nucleus [1], for which the excitation of the second phonon would have been strictly forbidden in first order. Both the present beyond meanfield calculations and shell-model diagonalisation point to the development of a triaxial shape for the ground-state band of 70 Zn. These theoretical descriptions are in agreement with the Zn isotopes systematics recently obtained using beyond mean-field techniques and the Gogny force in Ref. [44].

As for 68 Ni, our adopted B(E2; 0 + g.s. → 2 + 1 ) value of 301(38) e 2 fm 4 is in very good agreement with the B(E2) values reported in Ref. [11,15] and with the shell-model calculations of the present work. The nuclear contribution to the 2 + 1 state in 68 Ni, extracted both from interactions with a Pb target beyond the 'safe' scattering angle and with a C target, has been found to be very small and comparable to the Coulomb contribution β N β C 0.10. This confirms the rigidity of 68 Ni against both nuclear and Coulomb excitations.

We have identified for the first time a significant B(E2) strength at high energy in 68 28 Ni 40 . It is centered around 5.6 MeV and amounts to about 2/3 of that to the 2 + 1 state. This strength can likely be attributed to proton excitations across the Z = 28 closed shell, whose experimental contribution is half of that calculated by Langanke et al. [14] and by the present shell-model calculations.

A comparison of the E2 strength distribution with those of 14 6 C 8 and 34 14 Si 20 nuclei, which also exhibit a combined proton and neutron magic numbers originating from the spin-orbit and harmonic-oscillator potentials, would be interesting. This unfortunately cannot be made as for the two latter nuclei, only the E2 strength to the first 2 + state has been measured so far.

Finally, combining the present experimental results, those of Refs. [7][8][9] and the present theoretical calculations, it is remarkable to see that four different shapes (spherical, oblate, prolate and triaxial) are present when considering the low-energy 0 + states of 68 Ni and the ground state of 70 Zn. This demonstrates the extreme sensitivity of the nuclear structure in this region to very small changes in degree of freedom (here by increasing slightly the excitation energy in 68 Ni or adding two protons to reach 70 Zn).

FIG. 1 .

 1 FIG. 1. (Color online) γ-ray spectrum of one HPGe detector associated with the de-excitation of 68 Ni implanted in the plastic detector. The lines corresponding to the decays of the 0 + 2 and 5 -isomers are indicated by arrows.

FIG. 2 .

 2 FIG. 2. (Color online) Doppler-corrected and backgroundsubtracted γ-ray spectrum of 70 Zn measured with Château de Cristal (black histogram). The intensities of the two peaks were determined using the simulated response function of the array (dashed magenta line) on top of two exponential functions accounting for the background (long-dashed gray line).The result of the best fit procedure is illustrated with blue circles.

FIG. 3 .

 3 FIG. 3. (Color online) Comparison between the experimental angular distribution (black crosses) of the deflected 70 Zn nuclei in the laboratory frame, gated on the 1759-keV peak of Fig. 2, with the simulated ones (continuous red lines) obtained with the DWEIKO (a) and ECIS (b) codes, leading to B(E2; 0 + g.s. → 2 + 2 ) values of 62(7) and 55(6) e 2 fm 4 , respectively. The Coulomb and nuclear contributions are shown with blue (long-dashed-dotted lines) and magenta (dotted lines), respectively. See text and Table II for the corresponding βC and βN parameters. The black vertical line marks the maximum 'safe' scattering angle of the reaction.

FIG. 4 .

 4 FIG. 4. (Color online) Same as Fig.3 but gated on the (874, 885)-keV doublet. The simulated angular distribution (continuous red line) is obtained using B(E2; 0 + g.s. → 2 + 1 )= 1419(120) e 2 fm 4 and B(E2; 0 + g.s. → 2 + 2 ) = 62(7) e 2 fm 4 with the DWEIKO code (a). Values of B(E2; 0 + g.s. → 2 + 1 ) =1447(127) e 2 fm 4 and B(E2; 0 + g.s. → 2 + 2 ) = 55(6) e 2 fm 4 are obtained with the ECIS code (b).

Fig. 5 (

 5 b) displays the non Doppler-corrected spectrum of 68 Ni (black histogram), together with the obtained fit (open blue circles). A clear photopeak is seen at about 4 MeV with the related single-escape peak. This doublepeak structure corresponds to the excitation of the 2 + 1 state at 4.085 MeV in

  fm 4 ) obtained with the DWEIKO and ECIS codes for 70 Zn and 68 Ni. Nucleus J π θ max lab 20) 0.215(8) 0.288(12) 1419(120) 0.217(9) 0.241(8) 1447(127) 1432(124) (7) 0.107(6) 0.102(8) 292(35) 0.110(7) 0.099(

3 FIG. 5 .

 35 FIG. 5.(Color online) (a): Doppler-corrected and background-subtracted γ-ray spectrum conditioned by the detection of scattered 68 Ni in the DSSSD (black histogram). The number of counts in the 2 + 1 state at 2.034 MeV was extracted by using the simulated response function of the detection system (dashed magenta line). The curve in blue circles corresponds to the global fit, which includes an exponential decay (long-dashed gray line), the excitations of the 3 -and 2 + states in 208 Pb, and high-energy contributions discussed in Sect. III B 3. (b): Same as (a), but for the non Dopplercorrected spectrum. The decays of the 3 -and 2 + 1 states in 208 Pb are visible at 2.614 and 4.085 MeV (with single-escape), respectively, for which our measured B(E3) and B(E2) values agree with the ones of the literature.

FIG. 6 .

 6 FIG. 6. (Color online) Same as Fig. 3 but for 68 Ni. B(E2; 0 + g.s. → 2 + 1 ) values of 292(35) and 312(40) e 2 fm 4 are obtained from the comparison between the experimental distribution (black crosses) with the DWEIKO (a) and ECIS (b) codes, respectively.

FIG. 7 .

 7 FIG. 7. (Color online)Comparison between the experimental Doppler-corrected energy spectrum for a 68 Ni beam on a C target (solid black histogram) and simulated spectra assuming βN = 0.1 (magenta stars) and βN = 0.2 (dashed blue histogram). The adopted value of βN = 0.102(8), as deduced from the study with the Pb target, is too small for a peak to be seen when 68 Ni scatters off the C target.

Fig. 8 (

 8 Fig.8(a) displays the Doppler-corrected68 Ni spectrum. The best fit (open blue circles of Fig.8) was obtained by introducing in-flight components at 3.3, 5.5, 6.3, 7.5, 8.7 and 9.3 MeV (magenta squares) and taking into account the excitation of the 2 + 1 and 3 - 1 states in the 208 Pb target (orange triangles). Note that, as the singleescape component dominates above 8 MeV, the two latter peaks are observed 511 keV lower than the value used in the fit. We do not find evidence of transitions that cascade through the 2 + 1 state. By assuming that the 4 states below S n = 7.8 MeV belong to E2 excitations, strengths of 15(2), 110(15), 42(5) and 16(2) e 2 fm 4 are found. As for the states above S n , they likely correspond to collective E1 excitations (likely to be Pigmy Dipole Resonance modes) whose much shorter lifetime, as compared to E2, make their γ decay not completely negligible as compared to neutron decay. Fig.8(b) corresponds to the non Doppler-corrected spectrum, fitted with the same components as the top spectrum. The consistent agreement of the fitting procedure for the top and bottom spectra gives more confidence in the proposed E2 components.

FIG. 8 .

 8 FIG. 8. (Color online) (a): Doppler-corrected experimental γray spectra of 68 Ni (black histogram) compared to GEANT4 simulations (open blue circles) including the excitation of several in-flight γ-ray components (magenta squares) discussed in the text and the excitation of the 2 + 1 and 3 - 1 states of the 208 Pb target (orange triangles). (b): same as (a) but non Doppler-corrected.

4 FIG. 9 .

 49 FIG. 9. (Color online) (top) Potential Energy Surface from constrained Hartree-Fock minimization in the shell-model basis for 70 Zn. (middle) Level scheme and B(E2↓) values (in MeV and e 2 fm 4 , respectively) for different theoretical models described in the text and from the present experiment (except for the 2 + 3 state observed in another work and whose B(E2) value is unknown). (bottom) 1σ contours in the β -γ sextant for the ground-state of 70 Zn. The red dot represents the effective β and γ value.

3 FIG. 10 FIG. 11 .

 31011 FIG. 10. (Color online) Potential Energy Surface from constrained Hartree-Fock minimization in the shell-model basis for 68 Ni. The three predicted 0 + minima of the PES, spherical, oblate and prolate, are shown with different symbols.

  As shown inTable I, four results cluster around 1600 e 2 fm 4 , while two others are above 2000 e 2 fm 4 . The last column gives the evaluated B(E2) values

B(E2; 0 + g.s. → 2 + 1 ) and B(E2; 0 + g.s. → 2 + 2 ) values in 70 Zn, for which various experiments gave rather inconsistent B(E2; 0 + g.s. → 2 + 1 ) values.

TABLE II .

 II Experimental cross sections, σ (in mb), between 1 • and θ max

lab , are reported together with βC , βN and B(E2; 0 + g.s. → 2 + ) (in e 2

  + 1 state, includes Coulomb and nuclear parts whose parameters β C and β N are listed in Table II.

B(E2; 0 + g.s. → 2 + 1 ) values of 292(35) and 312(40) e 2 fm 4

VI. ACKNOWLEDGMENTS

This work was supported by the Romanian National Authority grant for Scientific Research, CNCS -UE-FISCDI, project number PN-II-RU-TE-2011-3-0051, the ENSAR GA 654002 project, the National Research, Development and Innovation Fund of Hungary, financed under the K18 funding scheme with Project No. K128947 and by the European Regional Development Fund (Contract No. GINOP-2.3.3-15-2016-00034). We are grateful for the technical support provided by the GANIL facility staff. O.S. also wishes to thank D. Weisshaar for his useful comments on the paper.