Ali El-Amine

Hussein Al

Haj Hassan
email: hhajhassan@aust.edu.lb

Loutfi Nuaymi

Services KPI-based Energy Management Strategies for Green Wireless Networks

Complex green wireless networks including smart grid, renewable energy and batteries need precise energy management strategies in order to realize some of the defined objectives. Although these networks have different services (streaming, web, voice call, etc.) with different requirements, most research work slightly covered the specific contribution of each of these services and their effect on the network energy consumption. In this paper, we consider advanced KPIs (Key Performance Indicators) putting forward each service contribution to energy consumption. Using these new KPIs, we propose to adapt some energy management strategies, leading to performance amelioration and new energy savings, under renewable energy and smart grid environment. Simulations indicate the efficiency of our proposed adaptation, achieving 11.45% enhancement in these new KPIs, and outperforming several benchmark algorithms with a gain up to 8% points in terms of energy savings reduction. We analyze the benefits of the services KPIs and also their limits, leading to possible new services-based efficient energy management strategies in the considered framework.

I. INTRODUCTION

The radical surge of Information and Communication Technology (ICT) devices and services has pushed corresponding energy consumption to grow at a staggering rate. Followed by an increased awareness of environmental protection and strict regulations on pollutant emissions, there is a growing attention to reduce the energy consumption associated with ICT equipment [START_REF] Heddeghem | Trends in worldwide ICT electricity consumption from 2007 to 2012[END_REF]. For instance, it is estimated that ICT consumes around 4.7% of the world's electrical energy, releasing into the atmosphere about 1.7% of the global CO 2 emissions [START_REF] Gelenbe | The impact of information technology on energy consumption and carbon emissions[END_REF].

Cellular networks, a significant component of ICT energy consumption, have drawn considerable attention of many researchers from both academia and industry. With roughly 80% of network energy being consumed by base stations (BSs) [START_REF] Holtkamp | Minimizing base station power consumption[END_REF], most efforts to improve energy efficiency (EE) in mobile radio networks focus on BSs.

A. Related Work

EE is becoming a significant key performance indicator (KPI) in evaluating next generation cellular networks. It is defined as the amount of information that can be reliably transmitted per Joule of consumed energy [START_REF] Kwon | Channel capacity in bits per joule[END_REF]. Due to its simplicity, this metric is widely used in the evaluation of the EE of telecommunication networks including cellular networks [START_REF] Wu | Energyefficient base-stations sleep-mode techniques in green cellular networks: A survey[END_REF]. In the literature, recent efforts have been made investigating EE and energy savings of cellular networks. Among the different approaches existing in the literature, sleep mode strategies and the deployment of heterogeneous networks have been proven to be the most effective in improving energy savings and EE in cellular networks [START_REF] Han | Survey of strategies for switching off base stations in heterogeneous networks for greener 5G systems[END_REF], [START_REF] Elsawy | Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wireless networks: A survey[END_REF]. Nevertheless, providing BSs with renewable energy (RE) sources is another effective approach to enhance the EE of cellular networks by acquiring clean and cheap energy from ambient surrounding. A detailed survey on powering cellular BSs with RE can be found in [START_REF] Hassan | Renewable energy in cellular networks: A survey[END_REF].

In order to benefit more from RE, intelligent energy management is required to yield a higher EE in cellular networks. In [START_REF] Hassan | Classification of renewable energy scenarios and objectives for cellular networks[END_REF], we showed that intelligent usage of harvested energy results in higher cost savings in a variable electricity price environment. Based on state of charge (SoC) of the battery and electricity price, we introduced SPAEMA, an energy management algorithm, that decides whether to store or use RE. The work, however, is limited to one BS, and it does not study the impact on EE metric. In [START_REF] Liu | Small cell base station sleep strategies for energy efficiency[END_REF], the design of energy efficient heterogeneous cellular networks is investigated. Using a stochastic geometry-based model, the authors derived the EE with different sleep modes for small cells. However, the study was done in the absence of RE. In [START_REF] Ramamonjison | Energy allocation and cooperation for energy-efficient wireless two-tier networks[END_REF], maximizing the EE in a 2-tier wireless network powered by both RE and power grid is considered through power allocation. An offline algorithm based on parametric optimization is proposed. The work, however, ignores sleep mode strategies. In [START_REF] Hu | Optimal energy-efficient transmission in multiuser systems with hybrid energy harvesting transmitter[END_REF], EE in a multiuser energy harvesting system is considered. The authors developed an offline algorithm that maximizes the EE of the system by jointly varying the users' transmission time and power. Despite their analytical work, the model is limited to only one BS.

In most prior efforts, the emphasis was on maximizing cost savings or EE of the network. In [START_REF] Yoro | Sharing of energy among service categories in wireless access networks using shapley value[END_REF], the authors assessed the sharing of energy consumption among the different service categories provided by the network. An energy sharing model based on Shapley value, is proposed and proven to be a good balance between the service categories, in terms of fairness compared to uniform and proportional sharing. To the best of our knowledge, the study of the impact of RE and energy management strategies on services KPIs has not been well investigated in the literature, and it is still an open problem.

B. Paper Contributions

In this paper, we propose an EE metric that evaluates the performance of the network. In contrast to the definition given by ETSI [START_REF] Etsi | Measurement method for power consumption and energy efficiency of wireless access network equipment[END_REF], which limits the evaluation of the EE to operational BSs, we suggest an extension that includes inactive BSs (in sleep mode) and RE. Then, we assess this EE-KPI over all the services the network is providing by putting forward their contribution to energy consumption under RE sources. Finally, we propose to adapt some energy management techniques with the objective of having better energy indicators for each of these services.

While most studies assume BSs fully equipped with RE sources, our model considers a more realistic scenario where a percentage of sites is equipped with energy harvesters. This renders the model economically viable when the network operator has thousands of deployed BSs.

The rest of the paper is outlined by the following sections: Section II describes the system model. Section III explains the different KPI metrics understudy and states the problem formulation. Then, we propose two algorithms to enhance this EE-KPI in Section IV. In Section V, simulation results are presented and analyzed. Finally, Section VI concludes the discussion and future work.

II. SYSTEM MODEL

A. Network Description

We consider a wireless cellular network overlaid with M macro BSs having an inter-cell distance D and K mobile users. We denote the set of BSs by B = {1, ... , m, ... , M }, and the set of users served by BS m by U m = {1,...,u,...,k m }. Initially, the users are associated with and served by the BSs, based on best signal-to-interference-plus-noise ratio method (Best SINR) that is managed by a centralized energy management unit (EMU). Each user measures the SINRs by using pilot signals from all BSs and sends it to the EMU. These BSs are providing different services to the users (streaming, web, voice call, etc.). We further consider two sets of BSs. One is solely powered by conventional power grid, e.g. smart grid (SG), and is denoted by BS grid . The other set of BSs is equipped with RE and energy storages (batteries); hence, it is powered by a mix of hybrid energy sources (SG+RE) and is denoted by BS mix . The total bandwidth of the system W is shared among the BSs with a frequency reuse factor of one. We consider that the traffic load, on-grid energy price and RE are all varying over time.

B. Dynamic Network Operations

As illustrated in Fig. 1, we divide our observation time T into multiple one hour-periods, each with L time slots. Each slot s has a duration of 1/L hour. At each slot, we allocate RE and set the state of each BS (active or sleep) following the energy management strategies explained below.

1) RE allocation:

The decision of allocating RE is managed through a local EMU installed at each BS ∈ BS mix . Based on the current traffic load and SoC of the battery, the EMU decides whether to use or store the harvested energy. The decisions of managing RE are detailed in Section IV.

2) BS sleep scheme: Based on the SINR measurements collected by all users, the centralized EMU controls the operational mode of the BSs (active or sleep) following our sleep mode strategy presented in [START_REF] Amine | Analysis of energy and cost savings in hybrid base stations power configurations[END_REF]: SINR threshold-based method. This algorithm aggressively switches off candidate BSs (B c ) according to an SINR Switch-Off Threshold (SINR SOT ). While this algorithm considers only BSs ∈ BS grid to be switched off, we extend the set B c to include BSs ∈ BS mix . However, not all BSs ∈ BS mix are candidates to switch off. In Section IV-B, we detail the required conditions for a BS ∈ BS mix to join B c . The motivation behind this selection is to give the BSs consuming energy solely from the grid the priority to switch off, in order to increase the utilization of RE.

A candidate BS m switches off if the SINRs measured by the users served by BS m from neighboring BSs m are above the SINR SOT :

SINR m (u) ≥ SINR SOT , ∀u ∈ U m , m ∈ B c and m ∈ {B\m}. (1)
Finally, we evaluate the hourly KPI metric for BS m at time t, KP I m (t), that is defined as the ratio between the total data volume (DV) transmitted and the energy consumed (E) during one hour.

RE allocations and BSs

states decisions

C. Energy Consumption Model

In order to calculate the power consumption of the wireless cellular network, we use the power model provided by EARTH [START_REF] Auer | How much energy is needed to run a wireless network?[END_REF]. Accordingly, the power consumption of a BS consists of a static part P 0 and a traffic dependent part P out . Moreover the power demand depends on the number of active RBs. Because of the nearly linear relationship that exists between the RF power and the BS power consumption, the power consumed by a BS at time slot i can be expressed as follows:

Pin,i =    Ntrx(P0 + n (i) RB n T otal RB ×∆p ×P (i) out ), 0 < Pout ≤ Pmax, NtrxP sleep , Pout = 0.
(

) 2
where N trx is the number of transceivers. ∆ p and P sleep are the load dependent parameter and the power con-sumption of the BS in sleep mode, respectively. n

(i)
RB and n T otal RB are the number of active RBs at time slot i and the maximum number of RBs available to the BS, respectively.

D. Downlink Transmission Model

We measure the downlink transmission quality between a BS m and a user u based on the SINR as follows:

SINR m (u) = P m h m (u) σ 2 + m ∈B,m =m P m h m (u) (3)
where P m is the transmitted power of BS m, h m (u) is the channel gain from BS m to user u, which accounts for the path loss and shadowing effect, and σ 2 is the additive white Gaussian noise power density.

We can express the rate offered to a user u and served by BS m using Shannon-Hartley theorem as follows:

R m (u) = n RB (u)×BW RB ×log 2 (1+SINR m (u)) (4)
where n RB (u) is the number of RBs allocated to the user u, and BW RB is the bandwidth of one RB.

E. Renewable Energy Generation and Traffic Variation

We consider the use of solar panels due to their flexibility. In addition, we provide these sites with battery storages in order to store the excess harvested energy for future transmission. The amount of harvested energy varies depending on the location and panel size. In Fig. 2, we illustrate an example of the harvested energy generated by a solar panel having a surface area of 12.5 m 2 in the city of Marseille (France) [START_REF]PVWatts calculator[END_REF].

The traffic load on the other hand manifests both temporal and spatial diversities. On the temporal diversity, the traffic load of a BS dynamically changes over time as shown in Fig. 2. We assume that the users are uniformly distributed in the given area. Fig. 2: Variations of the average traffic load and the average RE power [START_REF] Auer | How much energy is needed to run a wireless network?[END_REF], [START_REF]PVWatts calculator[END_REF].

III. ADVANCED ENERGY KPIS AND PROBLEM FORMULATION

The focus in our work is on EE-KPIs for wireless communications. Therefore, the bits per Joule metric understudy is given as follows:

KP I = DV E (bit/J) (5)
where DV represents the overall volume of transmitted data in bits and E is the consumed energy in Joules. Let us first define the following new EE-KPIs that take into consideration the usage of RE (in the rest of the paper, we often refer to EE-KPI as KPI for the sake of abbreviation):

Definition 1 (Global KPI): We denote by global KPI, the hourly performance evaluation of the EE of a BS including all the services it is providing. It is calculated as follows:

KP I m (t) = DV m (t) E m (t)-RE m (t) (6)
where RE m (t) is the allocated RE for BS m at time t, and it depends on the energy harvesting policy.

Definition 2 (Service KPI): The service i KPI is the hourly EE evaluation of service i provided by BS m as follows:

KP I i m (t) = DV i m (t) E i m (t)-RE i m (t) (7)
where DV i m is the volume of the transmitted data by service i, and E i m is the energy consumed by this service. The latter is evaluated based on Shapley model presented in [START_REF] Yoro | Sharing of energy among service categories in wireless access networks using shapley value[END_REF] and is summarized in the next subsection.

We now extend the above mentioned KPIs by defining a new metric scale under which we evaluate our EE-KPIs: Network KPI. This metric can be used to evaluate either global or services KPIs.

Definition 3 (Network KPI):

The network KPI, KPI(t 1 ,t 2 ) is defined as the hourly average EE of the entire network including BSs in sleep mode, between times t 1 and t 2 , where KPI(t 1 ,t 2 ) [KP I(t)] t1≤t≤t2 and:

KP I(t) = 1 M M m=1 DV m (t) E m (t)-RE m (t) (8)
Since this metric is evaluated hourly, it takes hourly discrete values. For example, KPI(1, 24) = [KP I(1), KP I(2), ... , KP I(24)], where KP I( 1) is evaluated at time = 1 hour.

A. Shapley Model for Energy Sharing among Services

While it is easy to monitor the traffic volume consumed by service i, its specific energy consumption, E i , is not intuitive. In order to evaluate the energy consumed by each service, we use the model proposed in [START_REF] Yoro | Sharing of energy among service categories in wireless access networks using shapley value[END_REF] that estimates this energy based on Shapley Value, a coalition game concept.

The energy consumption of the network is composed of two components: a variable one (E v ) that varies with the traffic load and a fixed one (E f ) independent of the network load. These two components can be easily monitored using appropriate energy consumption models such as EARTH model (summarized in Section II-C). Similarly, we can evaluate the energy consumed by service i as follows:

E i = E f i +E v i (9)
While the variable part is shared among the services with proportion to the service traffic, i.e., E v i = DV i /DV T ×E v (DV T is the total data volume), the fixed part is estimated following Shapley Value as follows:

E f i = θ i ×E f (10)
θ i (N,p i ) = N s=1 1 sC s N p i + N s=2 (C s-2 N -1 -C s-1 N -1 )C s-2 N -2 C s-1 N -1 C s-2 N -1 sC s N (1-p i ) (11)
where θ i is the share of energy for service i following Shapley Value, N is the number of services (players), p i is the traffic portion (p i = DVi DV T ), and C s N is the binomial coefficient.

Compared to uniform and proportional sharing of fixed energy component, Shapley model achieves a trade-off among all services. That is to say, it does not penalize major services as much as proportional sharing, and it is also a good trade-off for small services as it does not condemn them with high fixed energy as in uniform sharing. By combining ( 7), ( 9) and ( 10), the EE-KPI of service i is evaluated as follows:

KP I i m (t) = DV i m (t) θ i ×E f m (t)+φ i ×E v m (t)-RE m (t) (12)
where φ i is the proportional share of the service variable energy, φ i = DV i /DV T . E f m and E v m are calculated using EARTH model in Section II-C.

B. Problem Formulation

Considering both QoS and battery capacity constraints, we aim at maximizing the EE-KPI by the efficient use of RE. We consider a network of LTE BSs having a percentage of its sites equipped with RE. We assume that the BSs always have data to transmit. Our goal is to maximize the average network KPI over a time duration T. We express the optimization problem as follows:

max RE(T ),S(T ) 1 T t2 t=t1 KP I(t) (13)
subject to:

Quality constraint:

r(u) ≥ R min ,∀u ∈ U m ,∀m ∈ B (14)
System constraint:

u∈Um w u W ≤ 1,∀m ∈ B ( 15
)
P m ≤ P max (16)
Renewable energy availability constraint: 13) is a non-convex fractional problem due to its objective function. In the next section, we propose a heuristic online algorithm that efficiently utilizes the harvested energy, and decides which BSs to switch to sleep state in order to improve the EE-KPI. The above formulated problem maximizes the network global KPI. The same problem can be formulated for the services KPIs.

RE m (t) ≤ B m (t) (17

IV. ADAPTATION OF ENERGY MANAGEMENT STRATEGIES

Enhancing the EE-KPI requires maximizing the throughput of the network while minimizing the on-grid energy consumption. The two parameters that directly affect this improvement are traffic load and RE. SPAEMA, an energy management algorithm described in [START_REF] Hassan | Classification of renewable energy scenarios and objectives for cellular networks[END_REF], is an online algorithm that decides how to manage RE (store it in battery or use it) based on the battery state of charge (SoC) and the price of electricity, in order to reduce the electric bill of the operator. Thus, it does not require any future knowledge of RE nor traffic load. In [START_REF] Hassan | Classification of renewable energy scenarios and objectives for cellular networks[END_REF], we showed that SPAEMA outperforms the traditional algorithm that uses RE whenever it is available. However, since the objective has shifted from reducing the electric bill of the operator to increasing our EE-KPIs, adaptation of our previously proposed algorithm (SPAEMA) is needed to match our new objective. Thus, we propose a new algorithm that adapts SPAEMA to satisfy the newly introduced objective. Then we extend the proposed algorithm for further enhancement.

A. Proposed algorithm 1 -STAEMA

We suggest a Simplified Traffic-Aware Energy Management Algorithm (STAEMA) that is an adaptation of SPAEMA. The major motivation behind this adaptation is to preserve the simplicity of SPAEMA and avoid high complexity. In contrast to SPAEMA that ignores the traffic load of the network, which is an important parameter in our studied KPIs, our proposed algorithm manages the use of RE by taking into account the SoC of the battery and the traffic load. Similar to SPAEMA, we quantify each of the traffic and battery storage states into 3 discrete levels: low, medium and high. Table I shows the applied decisions for different cases.

The decisions summarized in the table below are designed to store the harvested energy in the battery when its SoC is low, and then use it at high traffic load. This When a BS switches to sleep mode, its EE-KPI drops to zero, since it is not transmitting data anymore, and hence, affecting the network EE-KPI as shown in Fig. 3. At t 1 , both BSs are active (consuming energy and transmitting data) with different KPI values. At t 2 , BS 2 switches to sleep mode. During this time, the users offload to BS 1 , increasing its data transmitted volume, thus increasing its KPI, while the KPI of BS 2 drops to zero. In order to better handle this degradation in the network EE-KPI, we decide to put the BSs equipped with RE sources to sleep, in the case where the traffic load is high and the battery SoC is low. The motivation behind this is to preserve the energy stored in the battery for a longer period of time and to enhance the KPI of the neighboring BSs by transmitting more data to the newly offloaded users. We summarize the decisions in Table II. The decision of switching BS m ∈ BS mix to sleep mode, in the case when the SoC of its battery is low and the traffic is high, depends whether the condition of switching off m is satisfied (Eq.( 1)). If not, m will use its stored energy to power its components. In this section, we provide simulation results to assess the network performance by evaluating the EE-KPIs of the services provided by a cellular network under the proposed algorithms. We obtain our results via Monte-Carlo method using MATLAB. The month of June is considered as an example to harvest RE, due to its high solar potential (7.08KW h/day/m 2 ) [START_REF]PVWatts calculator[END_REF]. We assume that the load is randomly distributed among the BSs following the traffic load variation in Fig. 2. We further consider five service categories: two large ones (streaming and web) and three smaller ones (download, voice and other minor data services). We set T = 24 hours and evaluate the KP I(t) on an hourly basis. From Eq. ( 6), whenever the harvested energy (RE m (t)) is higher than the energy consumed by BS m (E m (t)), the excess RE is stored in the battery. In table III, we summarize the simulation parameters and traffic proportions of each service taken from a real European operator data set [START_REF] Yoro | Sharing of energy among service categories in wireless access networks using shapley value[END_REF]. In Fig. 4, we evaluate the network EE-KPI for the different services the network is providing. These values are calculated in the absence of RE and energy management strategies. From the obtained results, we observe that the EE-KPIs of the services are proportional to their traffic volumes, i.e., the larger the service is, the higher is its KPI. And even though Shapley energy model puts more weight on larger service categories, their EE-KPI is higher due to their increased traffic volume. In Fig. 5, we evaluate the impact of RE and sleep scheme under the Extended-STAEMA on the streaming service network EE-KPI. We will focus on streaming service due to its high impact on the KPI as shown in Fig. 4.

Using solar panels that only harvest 35% of the total energy demand at full load, we are able to enhance the EE-KPI by about a factor of 10 when 25% of the sites are equipped with RE and by roughly 40-times when all the BSs of the network are equipped with RE. This significant increase in the KPI is demonstrated in Eq. [START_REF] Hassan | Renewable energy in cellular networks: A survey[END_REF]. From this equation, this metric can go up to very large values when significant amount of RE is available, i.e., when this amount is equal to the energy required by the BS. However, and in order to handle these massive EE-KPIs, we set them to high values compared to the average network KPI. On the other hand, when sleep scheme is applied we observe a slight decrease in the network EE-KPI (∼ 9%). The reason behind this is twofold. First, the network EE-KPI takes into account operational and inactive (sleep) BSs having positive and zero KPIs, respectively. So the more inactive BSs we have, the less the network EE-KPI becomes. The second reason occurs when a BS goes to sleep mode and some of its users offload to another BS equipped with RE source. In this case, both the energy demand and the data volume transmitted by the latter BS will increase. However, if this happens at the end of the day, when the battery storage is suffering due to low RE, this increase in energy demand might force the BS to draw energy from the grid in order to compensate for this surge in energy consumption. This will result in a significant drop in its KPI, especially since it was solely relying on its green stored energy. We will show next that despite this inconvenience, some energy savings can be attained with sleep strategy.

B. Adaption of energy management techniques

We use greedy algorithm and SPAEMA as benchmarks to compare with our proposed algorithms. In greedy algorithm, the BS uses the harvested energy whenever available and stores the excess RE in the battery. Fig. 6 illustrates the performance of the network streaming EE-KPI for different percentages of sites equipped with RE without sleep mode. The system achieves the lowest EE-KPI when the energy allocation policy does not take into account traffic volume (greedy and SPAEMA). On the other hand, STAEMA results in an enhancement in the EE-KPI up to 11.45% in comparison with the other two. The reason behind the similar performances of greedy and SPAEMA algorithms is that they both ignore traffic load variations.

In Fig. 7, we present the results in the case of sleep scheme. Ext-STAEMA algorithm, that widens the candidate set of BSs allowed to switch to sleep mode to include BSs equipped with RE, performs slightly better than STAEMA (∼ 2%). This tells us that under these traffic-aware algorithms, our EE-KPI has reached its limit. The reason is because our metric does not valorize grid energy savings of the network. Despite having similar performances of EE-KPI, Ext-STAEMA saves more energy than the other algorithms (up to 8% more savings), as shown in Table IV. This can be explained by the wider set of BSs that can be put to sleep mode, and thus saving more energy. In this paper, we have studied advanced services-based energy KPIs. These metrics are important for the evaluation of future cellular networks by putting forward the contribution of each service to energy consumption. Our research focuses on the adaptation of energy management strategies with the objective of having better indicators for each of the services.

The context studied allows to investigate different parameter choices. For instance, we can study the impact of the type of batteries used, their capacities and their ageing calender on the performance of cellular networks in terms of EE.

  t): Data volume transmitted at time t by BS m. E m (t): Energy consumed at time t by BS m. EMU: Energy Management Unit.

Fig. 1 :

 1 Fig. 1: Dynamic network operations.

Fig. 3 :

 3 Fig. 3: Illustration of the problem: At t1, both BSs are active. At t2, BS2 switches to sleep mode, and its users offload to BS1.

Fig. 4 :

 4 Fig. 4: Evaluation of the network global and services EE-KPI in the absence of RE and energy management techniques.

Fig. 6 :Fig. 7 :

 67 Fig. 6: Network streaming EE-KPI without sleep scheme.

  )where w u is the bandwidth allocated for user u. RE and S are the RE utilization for each BS equipped with RE and the state of each BS (active or sleep) in the network at each time horizon, respectively. RE m (t) and B m (t) are the allocated harvested energy and the available energy stored in the battery for BS m,

	at the beginning of stage time t, respectively; where
	RE s m (t) = RE s m (t -1) + RE a m (t) -RE m (t), and RE s m (t) and RE a m (t) are the stored energy and the
	harvested energy allocated by BS m at time t, respectively.
	Problem (

TABLE I :

 I STAEMA decisions for different cases of battery and traffic load. BS mix to switch to sleep mode. In the next algorithm, we extend the latter algorithm to allow hybrid powered BSs to switch to sleep mode. B. Proposed algorithm 2 -Extended-STAEMA Extended-STAEMA (Ext-STAEMA) allows BSs equipped with RE sources to switch to sleep mode. It modifies the candidate set B c to include BSs ∈ BS mix .

	Battery/Traffic Low Medium High
	Low	store	store	use
	Medium	store	use	use
	High	use	use	use
	setup will minimize the waste of RE caused by battery
	overflow, and compensate for the increase in energy
	consumption caused by the increased traffic load.
	Both SPAEMA and STAEMA don't allow BSs
	∈

TABLE II :

 II Extended-STAEMA decisions for different cases of battery and traffic load.

	Battery/Traffic Low Medium	High
	Low	store	store	use/ sleep
	Medium	store	use	use
	High	use	use	use
	V. SIMULATION AND RESULTS

TABLE III :

 III Parameters' values and assumptions.

	Parameters	Values
	Number of BSs	25
	Number of sectors	3
	Bandwidth	10 MHz, FDD
	Maximum transmitted power	43 dBm
	Inter-cell distance	1000 m
	RB	50
	BW RB	180 KHz
	Number of users K	400
	User min. required rate	1 Mb/s
	Noise power	-174 dBm/Hz
	P 0	118.7 W
	∆ p	5.32
	Number	10
	of slots per hour period L
	Battery capacity	5 KWh
	Services	Traffic proportions
	Streaming	34%
	Web	30%
	Download	13%
	Voice	9%
	Other data	14%

A. Impact or RE and sleep scheme on EE-KPI

TABLE IV :

 IV Total energy savings of the network.

		Total Energy Savings (%)
	Algorithms	% of sites equipped with RE
		25% 50% 75% 100%
	Greedy	37.75 40.8 44.3	50.5
	SPAEMA	37.75 40.8 44.3	50.5
	STAEMA	38.13 40.8 44.3	50.5
	Ext-STAEMA 40.46 45.5 51.7	58.4
		VI. CONCLUSION

ACKNOWLEDGMENTS

The authors would like to acknowledge the support of the French Ministry of Industry for supporting this work under SooGREEN project.


G Sardin

About the symmetry of the deuteron structural charge density distribution

The distribution of the structural charge density of the deuteron is examined and its symmetry is analyzed on the basis of experimental data obtained from electron scattering experiments, in which the total symmetry of the deuteron structure is evidenced. Since according to the conventional nuclear model the deuteron is formed of a neutron and a proton, whose structural charge density is substantially different, it follows that the juxtaposition of the distribution of their charge density is asymmetrical, thus being in deep disagreement with that of the deuteron which is symmetrical. This incongruence is thus analyzed. The conventional model of a proton juxtaposed to a neutron is unable to provide a credible explanation of the symmetry of the deuteron charge distribution since it is composed of two different particles, one neutral and the other one charged, and with a highly dissimilar structural charge density. Consequently, an explanation for the structural symmetry of deuteron is proposed, based on a revised approach.

Introduction

Here, the symmetry of the density distribution of the deuteron (fig. 1,2,3) is examined by comparison with those of the neutron and the proton. Let us first consider the symmetry of the deuteron charge distribution in the context of the classical proton and neutron model as constituents of atomic nuclei [1-8]. The conventional model of a proton juxtaposed to a neutron does not reliably account for the total symmetry of the deuteron charge distribution since it is composed of two different particles, whose structural charge density is deeply dissimilar (fig. 5). It is therefore obvious that the conventional model is in default. In fact, such a model, without being retouched, is incompatible with the symmetry of the experimental distribution of the structural charge density of the deuteron given the dissymmetry of its two nucleons, one charged and one neutral.

The deuteron structural charge density distribution

The symmetry of the deuteron charge distribution is inspected on the basis of the experimental data shown in the following pictures: The two picks from fig. 1 and 2 are extremely identical, as well as the two parts from fig. 3. Thus, the question is: can such structural symmetry of the deuteron be explained by the conventional neutron-proton representation of the deuteron without resorting to an excess of intellectual acrobatics? How a charged particle juxtaposed to a neutral particle could produce such a symmetry? On fig. 3 the two red zones, which correspond to the maximal nucleonic densities, are identical and thus cannot correspond to the asymmetrical union of a proton and a neutron. Instead they can easily be seen as two protons (red zones) wrapped within a "shell" (blue zone) formed by the orbital of an integer electric charge.

By deduction between the mass of the deuteron and that of two protons, the enveloping orbital would be in a quantum state of energy -0.931 MeV. In effect, the structural energy of the deuteron is of 1875.612928 MeV, while that of the two protons is of 2 (938.272 0813) =1876.5441626 MeV [9, 10], so the difference is of -0.9312346 MeV. Since this energy has a negative value, it corresponds to a binding energy provided by the shell. Here we distinguish between bonding energy and dissociation energy. In effect, the disintegration energy into a proton and a neutron needs an extra energy of 1.29 MeV to form a neutron, so the energy of dissociation ends up being of 2.22 MeV, i.e. 0.93 MeV to brake the bond between the two protons plus 1.29 MeV for the shell to recombine with a single proton to form a neutron.

Incompatibility of the deuteron symmetrical charge distribution with the conventional model of the nucleus

Let us first point out that the conventional model of elementary particles is unsuitable with the high symmetry of the deuteron charge distribution since it preserves the integrity of nucleons within the nucleus. So, in the deuteron a proton and a neutron are juxtaposed, which leads to an asymmetrical structure where a neutral particle is paired with a charged one.

Let us also point out another failure of the standard model. In fact, this model cannot provide a realistic explanation for the slight separation of the proton and the neutron in the deuteron, as evidenced in fig. 3 and7. It brings no reason for such separation since there is no repulsion between a neutral and a positive particle.

An important clue is provided by the fact that the potential between nucleons is repulsive at short distance. Note that no repulsion is expected between a proton and a neutron. This clearly indicates that this repulsive potential comes from the electrostatic repulsion between protons. On the other hand, they are bound by the enveloping cloud of negative charges (the "shell") arising from the dissociation of neutrons. A quantum equilibrium is reached between the binding force and the dispersion force.

In view of these incongruities of the conventional neutron-proton model, let us briefly inspect the issue of the neutron and proton union in the deuteron. We know that the proton and the neutron are bound by the strong interaction. The question is: what is its true nature? Given its very short range it was interpreted by Yukawa as necessarily due to an exchange of a heavy particle whose range of interaction would be shorter as larger the mass.

Consequently, at the very beginning, the strong interaction has been interpreted as an exchange of the muon, just discovered. Very soon after, this interpretation was refuted in favor of an exchange of pions, which had been discovered by then. But as some experimental data resisted an adequate adjustment, some theorists proposed using a mixture of pions and kaons to obtain better fittings.

Currently, strong forces are rather interpreted from Quantum Chromo-Dynamics (QCD) as being mediated by a residual gluonic field, peripheral to the internal cohesive field of the nucleons. However, since from the QCD, strong forces cannot be solved quantitatively due to extreme complexity, their quantitative evaluation keeps to be done using pion exchange. How much uncertainty and gradual variation of the official point of view! Can it be trusted after so many fancy occurrences? A consensus on the nature of the strong interaction is still far away.

According to the QCD, the neutron would be composed of 3 quarks: two quarks "down" of electric charge 1/3 q-each one and a quark "up" of charge 2/3 q+, while the proton would be composed of a quark "down" of electric charge 1/3 q-and two quarks "up" of charge 2/3 q+. Since, according to the conventional model, the neutron and the proton preserve their individual structure in the nucleus, the structural symmetry of the deuteron cannot be explained from this model without resorting to a high dose of much risky mental acrobatics.

An essential difference with the QCD is that the neutron charged zones are not considered to be produced by fractional quark charges, but by integer electric charges q+ and q-, as supported by the neutron decay into a proton and an electron, both with an integer electric charge. In addition, according to the QCD, the distribution of the proton charge density should have two peaks, one positive corresponding to the two 2/3 q+ quarks and the other negative corresponding to the 1/3 qquark. Moreover, the positive peak should be four times larger than the negative peak, which is incongruent with fig. 4 showing only a positive part, but in contrast it is in full agreement with the model of the proton formed by one full positive charge. The fact that the proton has not two charge distributions, one positive and one negative, as the neutron, is clearly incoherent with their quark composition, since both having + and -quarks.

The neutron charge density distribution

In our publication of 1999 on the fundamental principles of the structure of elementary particles [START_REF] Sardin | Fundamentals of the Orbital Conception of Elementary Particles and of Their Application to the Neutron and Nuclear Structure[END_REF], the graph relative to the neutron and proton charge distribution (fig. 4) was already included, from which we deduced and represented the charge distribution of the negative component of the neutron ("the shell"). In addition, based on the decay of the neutron, it was deduced that its positive component ("the core") would simply be a proton. Moreover, since the distribution of the proton charge density has only one positive zone, it has been deduced that it is traced by a single positive integer charge.

Conversely, the graph (fig. 4) shows that if the distribution of the charge density of the shell is then superposed to that of the proton, the distribution of the resulting charge density corresponds to that of the neutron, which is dual, showing a positive zone (+) in the first part of the radius and a negative zone (-) in its second part. It thus appears that the charge density of the shell overlaps that of the proton, since its maximum is at a radius greater than that of the proton. This is why they have been called "core" and "shell", and correspond respectively to the structural distribution of a positive charge forming a proton and to the spatial distribution of a negative charge forming a shell. On its side, the charge distribution of the proton has only one positive zone, traced by a single positive charge.

Fig.4. Distribution of the charge density of the proton and the neutron, as well as that of the shell deduced from the first two. [11, 12]

It can be seen that the charge distribution of the shell has a shape similar to that of the proton but inverted. Both have a maximum of about the same height but at a different radius, that of the proton being smaller than that of the shell. Therefore, it can be deduced that most of the shell covers the proton, since its maximum is more distant than that of the proton. This explains the shape of the neutron charge distribution and why it has a positive part adjacent to a negative part, and also why their maximum and minimum have a lower height than the proton. The height of the charge distribution of the proton and that of the shell are both fixed by the electric charge which structures them and which has the same integer value but of opposite sign. This is in full coherence with the fig. 5 presented here below.

The deuteron charge density according to the conventional model of a neutron adjacent to a proton

Fig.5. Graph derived from fig.4 in which the charge distribution of the neutron and the proton have been juxtaposed, according to the conventional representation of the deuteron in which the neutron and the proton are adjacent.

It is therefore obvious that according to the conventional model, in which the neutron preserves its structure in the atomic nucleus, the deuteron would not be symmetrical, which is in contradiction with the experimental results of fig. 1, 2 and 3. Moreover the charge distribution of the neutron is in conflict with the two symmetrical peaks in fig. 1 and2, while one of them is assumed to correspond to a neutron, which is in formal disagreement with the neutron charge distribution of the fig. 4, differing substantially from that of the proton as it has two zones, one positive and the other negative. So, the charge distribution of a neutron juxtaposed to a proton is asymmetric as shown in fig. 5, which is in formal contradiction with the symmetry shown in fig. 1, 2 and 3.

The deuteron charge density according to the orbital model of two juxtaposed protons

Fig.6. Structural charge distribution of two juxtaposed protons

In contrast, the charge distribution of two adjoin protons is symmetric as shown in fig. 6. These two juxtaposed two-dimensional distributions of the electric charge of the proton are conformed to the three-dimensional distribution of the charge in fig. 1 and2, since it is evident that they show the same symmetry, corresponding to the charge distribution of two adjacent protons. This is a formal experimental proof that in the deuteron the neutron is dissociated into a proton and a negative electric charge wrapping then both protons. If the neutron would preserve its structure, the charge distribution of the deuteron could not be symmetrical.

It therefore appears clear that the charge distribution of the deuteron corresponds adequately to the model of the deuteron structure shown below in fig. 7, which is symmetrical and therefore in agreement with fig. 1, 2 and 6 and also coincides coherently with the charge density of fig. 3. This symmetry cannot be obtained by the conventional model of a neutron juxtaposed to a proton, but only by two adjacent protons, enveloped in the distribution of the negative electric charge bonding them.

Deuteron structure according to the orbital model

Fig.7. Formation of the deuteron by sharing the neutron shell with a proton [11]

The binding force is provided by the distribution of the neutron peripheral charge (that is, the enveloping orbital) which, in the atomic nucleus, is shared with the adjacent protons. This is why the incorporation of neutrons is indispensable for the cohesion of the atomic nucleus. Since the neutron is considered to dissociate in the nucleus into a proton and a shell, it follows that the nucleus is composed exclusively of protons held together by the negative charges forming a bonding shell.

Thus, it follows that there are no neutrons in the atomic nucleus since in it they dissociate. Neutrons emitted during induced nuclear reactions or spontaneous nuclear disintegrations are considered to be formed at the very moment of their escape, by recombination of a proton with a negative charge of the binding shell of the atomic nucleus. This process of neutron formation from a proton is endothermic and requires 1.29 MeV, energy extracted from the cloud of negative charges wrapping the atomic nucleus. The inverse process of the neutron decay into a proton and an electron corresponds to the detachment of the neutron shell, resulting in a proton and the release of the shell, which then mutates to the electron structural quantum state, with emission of an antineutrino draining the surplus of energy at the time that it preserves the total spin.

From the conventional neutron-proton model, with the proton being charged and the neutron being neutral, it is clear that their charge distribution must differ, as it has been experimentally demonstrated, the proton having a single positive charge distribution while the neutron has two charge distributions, a positive at the center and a negative at the periphery, as shown in fig. 4. These distributions accurately match with the proposed model.

From the standard model, how could the +2/3, +2/3, -1/3 fractional charges of the proton give the same charge distribution as that of the neutron with instead +2/3, -1/3, -1/3 fractional charges? How can it be explained without appealing to dubious arguments? Or as usual, what does not correspond with the QCD is ignored! Can we really believe that a charged particle, that is to say the proton, juxtaposed to a neutral particle, that is to say the neutron, could give such a symmetry of the structure of the deuteron? Moreover, it should be noted that in the conventional representation, proton-proton and neutronneutron nuclear structures should both be possible. Indeed, the cohesive force of the strong interaction is more than a hundred times stronger than the electrostatic repulsion, so a protonproton bond should be possible. In addition, the neutron-neutron assembly being neutral should be even more easily formed due to the absence of repulsive forces. The conventional point of view has no real answer to these problems and must resort to highly artificial explanations, in a vain attempt to solve the issue.

According to the proposed model the proton-proton nuclear structure is not possible since the proton has no cohesive element. On its part, in the atomic nucleus the neutron-neutron union cannot be as well, because of the electrostatic repulsion of its two enveloping charges. To compensate for this repulsion between the electric charges of the shell, the incorporation of more protons is necessary, which is however limited by an excess of repulsion between protons, which entails the shell ending to be able of maintaining the cohesion of the protons when they are in excess. To recover the cohesion it is then necessary to incorporate more electric charges in the shell, and so on. The balance between the cohesive strength of the shell and the inner repulsion strength between its electric charges, plus the repulsion between protons, governs the stability of nuclei.

The spin 1/2 of the neutron implies that the spin of its shell is equal to 1 and antiparallel to the spin 1/2 of the proton. In addition, the fact that the deuteron has a spin 1 implies that its shell has retained the spin 1 of the neutron shell. The deuteron may also be seen as a neutron whose shell has incorporated a second proton, while preserving its spin 1. This implies the spins of the two protons to be antiparallel and so neutralizing each other, while the spin 1 of the shell is preserved. Instead, if the deuteron would have a spin 0 it would imply the spins of the two protons to be parallel, and that of the shell to have the opposite orientation, which in fact does not occur because the spin 0 of the deuteron is not observed, thus leading to the exclusive state antiparallel of the proton spin. The deuteron spin is determined from the hyperfine transition having a value of 1, and a positive parity. Since the quadrupole moment does not cancel out, it follows that the nucleus is not round, therefore it cannot be in a pure S state with an orbital angular momentum l = 0.

The proton radius has been re-evaluated recently (the proton radius puzzle), obtaining a value of 0.84087 Fm, about 4% lower than the previous value of 0.8775 Fm, and corresponding to the value of the root-mean-square radius of the proton obtained from spectroscopic measurements of a Lamb-shift transition frequency in the muonic hydrogen atom [9, 10]. Anyway these values of the proton radius can represent only an average value since the proton is not a rigid body in view that its structure corresponds to a density of charge which spatial distribution has an extension of the order of the Fm (Fig 4). It should also be mentioned that from the size of atomic nuclei, the nucleons occupy a volume having an average radius of about 1.4 Fm. If this average radius of the nucleons is compared to that of the proton of 0.84 Fm, this means that the protons are somewhat distant (about 1 Fm) between them, as might be expected due to their electrostatic repulsion.

In this context, one might ask at first sight why the deuteron does not dissociate into two protons and an electron. The reason is simple and comes from the fact that once broken the -0.93 MeV bond between the two protons, the dissociation of the deuteron into a neutron and a proton is more favorable than its dissociation into two protons and an electron because the first process requires an additional energy input of only 1.29 MeV, while the second requires 0.51 MeV for the electrical charge to transit to the electron state, plus an energy of at least about 3 MeV to escape from the electrostatic attraction of the two protons, a process which requires thus an energy higher (~3.5 MeV) than the energy required by the n p dissociation (2.22 MeV). Moreover, during the disintegration of the deuteron into neutron and proton, the spin 1 of the deuteron shell is preserved by the neutron shell. In the energetically unfavorable case of two protons and one electron decay, the conservation of total spin would also imply the emission of a neutrino.

Complementarily, the equivalent diffusion experiment with positrons should be compared to that performed with electrons. Actually, they represent two different interactions of the structural charge distribution of the neutron with two different incident particles, an electron in one case and its anti-particle in the other case. Given the mutual attraction between the negative charge of the deuteron shell and the positive charge of the incident positron, it is to be expected that these two charges of opposite sign could be annihilated into a gamma photon, thus releasing a proton and a neutron, plus a positron by dissociation of a virtual photon.

Discussion

We have provided experimental evidence that there is no neutron in the atomic nucleus because of its dissociation into a proton and an enveloping negative charge, thus leading to a proton that adds to the adjacent protons. Neutrons are only protons covered by a shell formed by the distribution of a negative electric charge.

Considering that in the atomic nucleus the neutron dissociates into its two parts, namely a proton and a negative charge that spreads over all the protons present, acting as a binding carrier, it is therefore necessary to improve our understanding of the atomic nucleus because it does not contain neutrons. These can only be at the most regarded as virtual neutrons, since they are in a dissociated state. Neutrons are formed only when they escape from the nucleus by the recombination of a proton with an electrical charge of the nuclear bonding shell.

Aren't the two identical peaks of Fig. 5 and6 and the symmetry of Fig. 7 better explained by a nucleus of two protons wrapped in a bonding orbital rather than a proton juxtaposed to a neutron? Will experimental data diverging from the standard standpoint be ignored forever? The conventional representation of deuteron based on a proton juxtaposed to a neutron cannot lead to such a total symmetry of the structure of the deuteron since one particle is charged and the other is neutral.

Since the discovery of the neutron in 1932 by James Chadwick, the model of the neutron-proton nucleus has been formally established without questioning the presence of the neutron in the nucleus, even knowing that it is unstable. Nobody deeply wondered why the neutron would become stable once in the nucleus. This was admitted without knowing why. No one put in doubt its presence, and no one thought that it would only get formed at its escape from the atomic nucleus. Nobody thought that the neutron could be a disguised proton, resulting from the fusion of a proton and an electron, fusion in which the proton preserves its identity but not the electron, whose structural charge distribution mutates to a different quantum state, and whose new charge distribution covers the proton.

How is it that nobody has thought about the possibility that the neutron would not be present in the nucleus, but that it would just be formed when ejected from the nucleus, by recombination of a proton with a negative charge of the nucleus shell? Nobody thought that atomic nuclei could simply be composed of protons wrapped in a cloud of electric charges that would bond them. In fact, the old proton-electron model was closer to reality than the afterward proton-neutron model, however it has been rejected due to the confusion between electric charge and electron, instead of considering the electron as a quantum state of the electric charge. When the electron is substituted by the electric charge the difficulties that motivated the rejection of the former e-p model disappear, since unlike the electron, the electric charge has neither mass, nor magnetic moment, nor spin, but these are provided by each specific quantum state it acquires. Thus the arguments regarding the spin of the nucleus and the excess of kinetic energy of the nuclear electrons making them unable to sustain the cohesion of the nucleus are no longer valid for the electric charge.

And besides, how come no one has thought of the possibility that the neutron is a composite particle containing at its center a core formed by a proton, and wrapped by a negative charge forming a shell, since it dissociates into a proton and an electron. The emitted electron would come from the mutation of the neutron shell in detaching from its core proton, and the antineutrino would be emitted by the transition of the shell to its state of lower energy, from 1.29 MeV (structural energy of the neutron shell) at 0.51 MeV (structural energy of the electron). All this has been inhibited by the very fanciful composition of the neutron and the proton formulated by the QCD, including all hadrons, as well as by the gluonic nature of the strong interaction, equally far-fetched.

The inception in the 1920s of Quantum Mechanics and Heisenberg's indeterminacy principle led to the persuasion that electrons confined at the nuclear scale would have a kinetic energy overcoming the nuclear cohesion. Furthermore, some nuclei, such as e.g. the 14N has integer spin 1. In the nucleus model composed of protons and electrons, the 14N had 14 protons and 7 electrons, i.e. 21 entities of spin 1/2 and so the total spin would be half integer, in discrepancy with the experimental integer spin 1. These two arguments led to the rejection of the presence of electrons in the nucleus. Nevertheless, Rutherford maintained the subsistence of electrons by proposing that in the nucleus each electron would be bonded to a proton. The deficiency came from not having been able to differentiate between electron and electric charge, so his proposal could not be retained.

Consequently the e-p model has been rightly rejected but this is due to the confusion between electron and electric charge. The electric charge has no intrinsic mass, nor magnetic moment neither spin, but it gets a mutable extrinsic mass, magnetic moment and spin according the diverse quantum states it may acquire. For example, in its lowest quantum state represented by the electron it has a spin 1/2, but in other quantum states such has e.g. the μ-, π-, K-, p-, Ω-, etc. the electric charge has different mass, magnetic moment and spin. The point is that the extrinsic characteristics of the electric charge are quantized and mutable. Similarly, when the electric charge is incorporated into nuclei it may acquire different quantum states according to each specific nucleus.

However, a consequence of leaving behind the previous electron-proton nuclear model was the loss of the cohesive vehicle of the atomic nucleus represented by the electron, which required having to conceive another cohesion element for the new neutron-proton model, since without it they lack of cohesive power. This led to the then recently discovered muon being proposed as the cohesive vehicle between nucleons, which was later rejected in favor of the pion when discovered, and finally attributed to the gluons, of eight different types, fruits of the CDQ. However, the current introduction of the nuclear model q-p makes possible to recover the cohesion vehicle of the nucleus, lost when rejected the nuclear electron-proton model, but this time replacing the electron with the electric charge. So, within this revised framework, the electric charge can be afresh incorporated to the nucleus, leading now to the q-p model, where q is the electric charge, not the electron. In the nucleus the electric charge can acquire diverse quantum states and it also act as bonding element between nuclear protons. Note that this q-p model is nonetheless somewhat approximate with the n-p model since the union of an electric charge with a proton gives a neutron, however in the nucleus the neutrons may only be seen as virtual neutrons since they are dissociated into a proton, and an electric charge in different quantum states according to each specific nucleus. Sometimes an electric charge recombines with a proton leading to a neutron that is expelled. Instead in the βdecay, a q-charge is expelled alone acquiring then the electron state, but according to the energy released it may rather transit to the higher muon state.

It is surprising to note that the electric charge is still today assimilated in a wrong and atavistic way to the electron, simply because it has been the first charged particle discovered and that of all of them it has the smallest mass, without realizing that the electron only corresponds to a specific quantum state of the electric charge. Unlike the electron, the electric charge has neither mass nor magnetic moment, but it gets them via each quantum state it can acquire. Each of the quantum states that the electric charge can reach defines a specific elementary particle, with its mass, magnetic moment, spin, and so on.

Conclusions

We have demonstrated that in the deuteron, the neutron is dissociated into a positive charge distribution corresponding to a proton and a negative charge distribution that extends over the whole nucleus, and acts as a cohesive shell. Thus, the deuteron is in fact composed of two protons wrapped by the distribution of the negative electric charge, coming from the dissociation of the neutron. It is crucial not to confound the electric charge with the electron, which is a specific quantum state of the electric charge. In fact, all charged particles, such as the muon, the pion, the kaon, the proton, etc., correspond to different quantum states of the electric charge, each having a specific structural charge distribution defined by a wavefunction.

Obviously, something has not been wholly suitably conceived in regard to the atomic nucleus. In order to solve the problem, the structure of the neutron must be reconsidered. Consequently, the deuteron model should be revised in accordance with the experimental proofs here provided, supporting a two-proton nucleus and a cohesive shell. The great advantage of this model is that it offers a simple explanation of the nuclear cohesion, without calling for an exchange of imaginary gluons, but instead just resorting on the sharing of the long-known integer electric charge, which acts as a bonding carrier in accordance with the extended quantum state acquired. By extension, this model can be applied to all atomic nuclei and it can be considered that the neutron is always dissociated into a positive charge distribution corresponding to a proton and a negative charge distribution which extends over the whole nucleus, acting as a cohesive shell.

Fig. 1 :Fig. 2 :Fig. 3 :

 123 Fig. 1: Deuteron density ρM [fm-3] as a function of x, z for M = 0 (fig. extracted from ref. [1])