Győző Gódor

Sándor Imre
email: imre@hit.bme.hu

Hash-based Mutual Authentication Protocol for Low-Cost RFID Systems

Keywords: RFID, lightweight, authentication

In the last decade RFID technology has become widespread. It can be found in various fields of our daily life. Due to the rapid development more and more security problems were raised. Since tags have limited memory and very low computational capacity a so-called lightweight authentication is needed. Several protocols have been proposed to resolve security and privacy issues in RFID systems. However, the earlier suggested algorithms do not satisfy all of the security requirements. In this paper we introduce our hash-based mutual authentication protocol which meets all the security requirements. Our solution provides an efficient mutual authentication method. Our protocol can defy the well-known attacks and does not demand high computational capacity.

Introduction

In the last few years the RFID (Radio Frequency Identification) technology has developed rapidly. Slather of applications were designed which steal into most of most fields of our daily life, e.g., personal identification in passports, medical identification of patients, access control, thief prevention, payment systems, tickets for transportation, supply-chain management, asset tracking, etc.

As in case of other radio frequency bases systems, e.g., wireless lans, bluetooth, cellular networks, the communication operates via the air-interface which raises many security issues. Since this kind of medium can be easily accessed by everyone the messages between the communication parties can be eavesdropped, observed or forged and further on fake messages can be composed and it can be replayed. Moreover, the communication parties can be impersonated, customers (possessing a tag) can be tracked or their transactions can be recorded.

In order to prevent the unauthorized access to protected databases or systems, or any sensitive data, authentication and encryption have to be applied. Since the tags have very limited computational capacity and low memory, new solutions are needed. Due to these conditions of RFID tags in the very beginning of the development of RFID authentication protocols only mathematical and logical operations could be used. After the computational capacity of tags increased, simple cryptographic functions, e.g., one-way hash functions could be used and many lightweight authentication protocols were developed.

In the last years numerous RFID authentication protocols have been proposed in order to resolve these privacy problems. For example, the hash-lock protocol [START_REF] Weis | Security and Privacy Aspects of Low-Cost Radio Frequency Identification Systems[END_REF], [START_REF] Lee | Efficient authentication for lowcost RFID systems[END_REF], the randomized hash-lock protocol [START_REF] Weis | Security and Privacy Aspects of Low-Cost Radio Frequency Identification Systems[END_REF], [START_REF] Liu | True random number generator in RFID systems against traceability[END_REF], tree-based protocol [START_REF] Molnar | Privacy and Security in Library RFID: Issues, Practices, and Architectures[END_REF], the hash-chain protocol [START_REF] Ohkubo | Cryptographic Approach to "Privacy-Friendly" Tags, RFID Privacy Workshop[END_REF] and the hash-based ID variation protocol [START_REF] Avoine | A Scalable and Provably Secure Hash based RFID Protocol[END_REF], [START_REF] Tsudik | Yet Another Trivial RFID Authentication Protocol[END_REF], [START_REF] Henrici | Hash-based Enhancement of Location Privacy for Radio-Frequency Identification Devices using Varying Identifiers[END_REF] are representative. However, the previous protocols do not resolve privacy problems since the previous protocols can not reuse tag or the previous protocols are vulnerable to replay and spoofing attacks, and tag can be tracked.

In this paper we introduce our hash-based mutual authentication protocol which meets all the security requirements. The protocol can defy the well-known attacks and does not demand high computational capacity.

Related Works

In the last decade the security issues of RFID systems got into the observed of all observers. Numerous protocols were proposed. Most of them are based on cryptographic hash functions, random number generation, mathematical and logical operations. These are the so-called lightweight protocols. In this section few significant protocols are introduced.

Hash-Based Access Control (HBAC)

The protocol, which can be implemented in low-cost RFID tags, was proposed by Weis [START_REF] Weis | Security and Privacy Aspects of Low-Cost Radio Frequency Identification Systems[END_REF] in 2003. The scheme is illustrated in Fig. 1. In case of Hash-Locking scheme, only the key k of each tag is stored in the database of the back-end server. In the followings the authentication process of the HBAC is presented.

4. The tag calculates the hash value of the key which is sent by the reader and compares it to the stored metaID. If the values match, the tag sends its own ID to the reader.

Security issues of HBAC protocol The hash-lock scheme is very elementary authentication protocol and very vulnerable. Since the key k is sent in plain-text over the air, thus an attacker can eavesdrop the key and it can be spoofed later or a given tag could be impersonated. Furthermore, since metaID is always constant each tag can be identify, and trace them, in order to avoid this the metaID should be changed frequently.

Randomized Access Control (RAC)

The RAC protocol [START_REF] Weis | Security and Privacy Aspects of Low-Cost Radio Frequency Identification Systems[END_REF] is an enhancement of HBAC. The aim was preventing the tracking of a given tag. While in this mode, a tag must not respond predictably to queries by unauthorized users, but must still be identifiable by legitimate readers. Tags are equipped with a one-way hash function, additionally also have a random number generator to make its constant variable randomized. Fig. 2 shows the authentication process of RAC. with the construction of R and each ID s which is stored in database, then authenticates itself by sending the unique identifier ID k back to the tag.

Security issues of RAC protocol This protocol can protect against tracking and replay attack effectively because the tag's response varies on each session. However, the tags' IDs are always constant so the tag can be traced if the tag's ID is leaked out. In addition, an adversary can easily obtain a valid message pair (h(ID ∥ R); R) from the tag and later the attacker can impersonate that tag to a legitimate reader. In order to identify a given tag back-end server needs to perform a brute-force search to verify the signature h(ID ∥ R). If there is a big amount of tags in the database, the computation load would be very high.

Tree-based RFID protocol

Molnar proposed a mutual authentication protocol for back-end server and tags in a private way which is based on key-tree [START_REF] Molnar | Privacy and Security in Library RFID: Issues, Practices, and Architectures[END_REF]. In Fig. 3 the tree-based authentication protocol can be seen.

Beginning of the authentication process, back-end server sends a random number r r to tag. Tag also generates a random number r t and computes σ = ID ⊕ f k (0, r r , r t ), where f k is a pseudo random function. Then tag sends r t and σ to the server. Based on the information received from the tag, the server could find the ID, k of the tag on the database. The search on the database server is the process of searching in key-trees.

A key-tree is a tree where a unique key is assigned to each edge. Each key is generated uniformly and independently. The server is assumed to know all keys. Each tag possesses the keys assigned to the edges of the path starting from the root and ending in the leaf that corresponds to the given tag.

For authenticating a reader it starts at the root and uses r r to check whether the tag uses the "left" key or the "right" key. If the reader and the tag successfully authenticate using one of these two keys, the reader and tag continue to the next level of the tree. If the reader fails to convince the tag on any level, the tag rejects the reader. If the reader passes all secrets in the path, the tag accepts the reader. If the server finds the ID of the tag, then the tag is authenticated. Server sends back τ = ID ⊕ f k (1, r r , r t ) to tag. Tag can thus verify the identity of back-end server by checking whether

ID = τ ⊕ f k (1, r r , r t ).
Security issues of the tree-based protocol The implementation of a treekey authentication protocol is very easy, moreover, this kind of protocol is very scalable, enlarging the system with additional tags is simply feasible. Since the total scheme requires O(logn) rounds of communication, O(logn) works for the reader, and O(logn) storage at the tag, where n denotes the number of tags. However, in this tree-based approach upper level keys in the tree are used by many members. This will cause problem if a member is compromised and its keys become known to the adversary, because in this case the adversary gains partial knowledge of the key of other members, too. This obviously reduces the privacy provided by the system to its members, since by observing the authentication of an uncompromised member, the adversary can recognize the usage of some compromised keys, and therefore its uncertainty regarding the identity of the authenticating member is reduced.

This scheme cannot provide backward security. Once a tag is compromised, the attacker can trace its past communication transactions, because a tag's identifier and secret key are static.

Hash-based Untraceable Protocol (Ohkubo protocol)

The main idea of this protocol is to modify the tag's identifier after each successful authentication process in order to prevent traceability and disclosure of the identifier and key. As it can be seen in Fig. 4 two hash functions are applied, one to refresh the secret of the tag, and the other to make responses of the tag untraceable by eavesdroppers [START_REF] Ohkubo | Cryptographic Approach to "Privacy-Friendly" Tags, RFID Privacy Workshop[END_REF]. Each tag has initial information s 1 . In the i th transaction when a reader queries tag, it sends an identification request to the tag and a i = G(s i ) is sent back, where s i is the current identifier of the tag. Tag refreshes its secret s i+1 = H(s i ) as determined from previous secret s i , where H and G are the two hash functions. The reader sends a i to the back-end database. From a i , the back-end database has to identify the corresponding tag.

In order to do this, the back-end database constructs a hash chain from each n initial value s 1 until it finds the expected a i , or until it reaches a given maximum limit m on the chain length. So the back-end database received tag's output a i from the reader and calculates a ′ i = G(H i (s 1 )) for each s 1 in the list, and checks if a i = a ′ i . If this holds, it returns the ID which is a pair of a ′ i . Ohkubo protocol is very weak in the resistance attacks by DoS. If the attacker impersonates the real tag and floods the server with fake a ′ i , the server should have to calculate thousands, even millions of hash function, thus it will occupy a lot of server resources and legitimate tags could not authenticate themselves.

Security issues of the

3 The Proposed Protocol

Main idea

In this section, we propose a robust privacy preserving mutual authentication protocol which utilizes hash function and synchronized secret information. The proposed authentication protocol, which can be realized in a low-cost tag, guarantees the privacy protection for a tag holder, which requires confidentiality, untraceability, anti-cloning, and integrity.

Usually, in RFID systems, synchronization of tag's identification information between tags and back-end servers can be violated by asymmetric communication channel of air interface between tags and readers. The replay attack is also enabled for tags and back-end servers, respectively. Moreover, as the characteristic of RFID systems, a tag can emit its data to everyone including adversaries. Adversaries thus can trace location and behaviors of tag holders without detection and impersonate a legitimate tag or a legitimate reader. To remove these security and privacy problems, our protocol is based on mutual authentication between tags and back-end servers guaranteeing freshness of tag's identification information. In addition, it is assumed that the communication channel between a reader and a back-end server is secure.

Our protocol works with the natural assumption that tag has a hash function, XOR gate, and the capability to keep state during a single session and the cryptographic hash function used in our protocol has the desirable security like preimage resistance, second preimage resistance, and collision avoidance. It is designed in order that tags do not have any real data and all messages would be random, hashed, and encrypted, so confidentiality is guaranteed even though the authentication messages are eavesdropped by adversaries.

In our protocol, the server stores the keys k 1 , k 2 , and h(k 1 ) of all the tags. When a tag sends its h(k 1 ) to the server, it tries to looking for this h(k 1 ) value in the database. At first sight, storing both k 1 and h(k 1 ) in the database seems to be wasteful because it is redundant, but in exchange for storing h(k 1 ) values in the database, the searching for a certain tag takes place extremely quickly. Generally, in real RFID systems there could be big amount of tags which can take part in the authentication process. The bigger the system is, the longer it takes to search for a certain tag, because more database entries need to be investigated. To speed up this process, it is reasonable to store the h(k 1 ) in the database because in this case we only have to read this value from the database instead of computing it every time a database entry needs to be investigated. It increases the effectiveness of the protocol.

After receiving h(k 1 ) from a tag, the server tries to search for this h(k 1 ) value in the database. Finding the h(k 1 ) value in the database only means that the message sender might be a tag in the system. The remaining part of the protocol is the mutual authentication between the tags and the server, as well as updating the keys. Notice that after the server has found h(k 1 ) value in its database, it generates such a random r 1 that h(k 1 ⊕ r 1 ) become unique in the database. This is required for the sake of the latter key update, because when the process of exchanging data has finished, the k 1 key of the tag would be updated to k new = h(k 1 ⊕ r 1 ).

The proposed protocol

Our proposed protocol can be seen in Fig. 5. In the followings our hash-based authentication protocol is described in detail.

= h(k 1 ⊕ k 2 ⊕ r 1 ), if t ′ 1 = t 1
then it has an identified and authenticated server. Tag computes: t 2 = h(k 2 ⊕ r 1 ⊕ r 2 ) and sends r 2 , t 2 message back to the back-end server.

The back-end server computes t

′ 2 = h(k 2 ⊕ r 1 ⊕ r 2 ), if t ′ 2 = t 2
then it has an identified and authenticated tag. After the successful authentication backend server updates k 1 and k 2 as follows:

-If h(k 1curr ) = h(k 1 ), in other words the received h(k 1 ) value corresponds to the stored ones in the current values table of database, then:

• k 1prev = k 1curr , k 1curr = h(k 1curr ⊕ r 1 ) • k 2 = h(k 2 ⊕ r 2 ) -If h(k 1prev ) = h(k 1 )
, which means the received h(k 1 ) value corresponds to the stored ones as in the previous values table of database, then:

• k 1curr = h(k 1prev ⊕ r 1 ) • k 2 = h(k 2 ⊕ r 2 )
This process seems a bit complicated because our goal is to prevent the loss of data when any kind of attacks happens. It protects the tags even in case of DoS attack in the last step of the protocol, while the server sends the "Update key" message to the tag. In this case the tag does not receive the "Update key" message, thus it does not update its keys, meanwhile the server has updated keys related to the tag, but the old information about the tag is still stored in the database as previous values. So the next time when tag want to authenticate with the server, the server would not be able to find the h(k 1 ) of the tag among the h(k 1 ) stored as current value in its database, but it could find it among the values stored as previous ones. Hereby this tag would be legal in the system. 6. After the server has updated the keys, sends "Update key" message to the tag. Tag updates his key as follows:

-

k 1 = h(k 1 ⊕ r 1 ) -k 2 = h(k 2 ⊕ r 2 )

Security Analysis

In this section the security analysis of our scheme is presented. We will show that our scheme is protected against the well-known attacks in an RFID environment. Moreover, attacks based on tampering with tags are also limited by updating secure information.

Tag information privacy When the server broadcasts Query messages a given tag sends back only its h(k 1 ) to the server, then waits for the server to replies the t 1 , r 1 message. After it is received by the tag, it could check whether t 1 is the right value, or not. In case that it is suitable the tag sends t 2 which contains k 2 to server. So, the server only has access to the tag information after it authenticated itself. A counterfeit server can only access to h(k 1 ) values which are freely accessible from anywhere.

Tag location privacy The responses from the tags are anonymous, the tag only sends h(k 1 ), t 2 , r 2 , which cannot be linked to any particular tag. In other words, the eavesdropper can neither link tag responses to previous responses from the same tag, nor distinguish one tag's responses from other's. It can be said that tracking the location of a tag is very difficult.

Eavesdropping Eavesdropper can collect information about h(k 1 ), t 1 , r 1 , and t 2 , r 2 during one authentication session. Since r 1 and r 2 are random values, they are useless to trace tags. After each successful authentication process, tags update their k 1 keys, therefore h(k 1 ) values can also be considered as random values. The t 2 = h(k 2 ⊕ r 1 ⊕ r 2 ) requires random numbers generated by two parties -the server and the tag. An impersonated server or impersonated tag cannot control the random number generated by the other party. Consequently, it is difficult for an eavesdropper to attack with t 2 . The

t 1 = h(k 1 ⊕ k 2 ⊕ r 1 )
value is computed from the two stored key values and a random value generated by server, the probability that the generated values among sessions are identical is negligible. Thus any useful information cannot be gained by eavesdropping.

Untraceability The server authenticates itself by sending the t 1 , r 1 message, while a tag authenticates itself by sending the t 2 , r 2 message. In each step, tag and server authenticate counterpart to remove traceability. In addition, despite the attacker knows k 1 , k 2 , a particular tag cannot be traced since tag responses in each session is different.

Cloning The secret information stored in a given tag is pertinent to that tag. Even if some tags are compromised, the obtained information is irrelevant for the others. Therefore, attacker cannot produce any other fake tag except the compromised tags.

Security against the spoofing attack Since each message is encrypted during the authentication process the spoofing attack is prevented. The attacker can only perform the following attack.

1. The attacker impersonate a real server and sends Query to the tag. 2. The attacker can acquire h(k 1 ) from the tag as a response.

In the subsequent session, when the real server transmits Query, the attacker responds with h(k 1 ) in order to disguise as a right tag and a server responses with t 1 = h(k 1 ⊕ k 2 ⊕ r 1 ), r 1 , but the attacker does not know the k 2 and it is not be able to computed, the t 2 = h(k 2 ⊕ r 1 ⊕ r 2 ) for replying to the server. Thus it can authenticate itself as a tag to the server. In our protocol, an attacker can only spoof a tag if the attacker knows both k 1 and k 2 , which happens very rarely. Consequently, the proposed protocol is secure against spoofing attack.

Security against the replay attack An attacker can eavesdrop the response message from a tag and may perform an attack as the followings.

1. After the server transmits t 1 = h(k 1 ⊕k 2 ⊕r 1old ), r 1old to the tag, the attacker eavesdrops the response of the tag t 2 = h(k 2 ⊕ r 1 ⊕ r 2 ), r 2 and the attacker block "Update key" message which is sent by the server, consequently the tag could not update its keys. 2. In the next authentication session, the attacker disguise as a legitimate tag and sends h(k 1 ) to the server. When the server transmits t ′ 1 = h(k 1old ⊕ k 2old ⊕ r 1new ), r 1new , the attacker responds with t 2 = h(k 2 ⊕ r 1old ⊕ r 2 ), r 2 . But since r 1new is a random number, r 1new is different from r 1old , the t ′ 2 = h(k 2 ⊕ r 1new ⊕ r 2 ) value computed by the server wolud be different from t 2 value which is possessed by the attacker, therefore the server could stop this authentication session. So the proposed protocol is secure against replay attack. Furthermore, if the one-way hash function such as MD5, SHA-1 is secure, the attacker does not know the keys of the tag due to the one-way property of hash function. So it is impossible to produce a right response h(k 2 ⊕ r 1 ⊕ r 2 ).

Forward and backward security Such an attack might happen that after an attacker obtains k 1 , k 2 by tampering with tag and has eavesdropped plenty of interactions between server and various tags, the attacker tries to infer the past or future secret information, but server and tag always update their keys using hash-function each time of the protocol, so it will never succeed.

Denial of Service Attack

If the server keeps only the current key per tag, the protocol is under the denial of service attack. The attack is possible as follows:

Attacker may try to do attack in order to desynchronize k 1 and k 2 between server and tag. We assume that attacker can relay the data between these two parties. When server starts the authentication process, attacker transfers t 1 , r 1 from server to tag and then transfers t 2 , r 2 to server. After that the server updates k 1 and k 2 in its database it sends the "Update key" message in order to update k 1 and k 2 in tag. At this time, if an attacker could block the delivery of "Update key" message, k 1 , k 2 values become different between server and tag.

If server uses only the latest k 1 , k 2 to authenticate a tag, this situation makes tag useless. However, in our protocol not only the current k 1 , k 2 values, but the previous k 1 and k 2 values are stored in the server database. In case a DoS attack happens server can still identify tag in a near future session by checking both the current and previous values in the database. Scalability In our protocol, the server can find the keys of a tag by searching for the h(k 1 ) received from the tag. In the database the k 1 , h(k 1 ), and k 2 values of each tag are stored. When a tag sends h(k 1 ) to the server the server can quickly find h(k 1 ) in the database, and so the server can find the appropriate k 1 , k 2 quickly and efficiently. So the system is scalable.

Comparison with other protocols

In Section 2 a brief overview about the security issues of previously proposed protocols were given, additionally in Section 3.3 our protocol's security analysis was presented. In this section the comparison from the point of view of security is given. In Table 1 we summarize the security and efficiency issues about the analyzed protocols.

The notations are the followings:

-The notation O means that the given protocol satisfies a given security requirement.

-The notation △ means the given protocol just only partially satisfy a given security requirement. -The notation X means that the given protocol does not satisfy a given security requirement. As it can be seen in Table 1 all schemes satisfy anti-cloning. Since all values emitted by tags are randomized and there is no data which reveals information of an object tag is attached in memory of tag, all schemes including our scheme satisfy data confidentiality. Because attacker cannot generate a legitimate response without any knowledge of secure information of tag, attacker cannot cloning tag without tampering it. HBAC is such a simple protocol that cannot resist any types of attack. In the tree-based protocol, the keys are not updated after each sessions, thus an attacker manages to obtain key of a tag, the attacker would know the behavior of the tag in the past. The Ohkubo protocol is very strong against tracking attack and replay attack, but the drawback of it is a lack of scalability. All protocols is very weak against desynchronization attack except our proposed protocol, where the previous keys are also stored.

Conclusion

In this contribution we pointed out the weaknesses of RFID systems which have to be solved. A brief overview about some well-known authentication protocols were given. It can be said that the major disadvantages are the decrease of anonymity level and the necessity of very high computational capacity.

We proposed our hash-based mutual authentication protocol for low-cost RFID environment. Our solution provides an efficient authentication method for the back-end and tags, furthermore, it resists against common RFID attacks, i.e., replay attack, impersonation, and forward security. Since in our solution every messages are randomized the location privacy is guaranteed, too.

Our future consideration is to implement our authentication protocol in order to make a comparison between our protocol and other authentication protocols by simulations in terms of security and performance.

Fig. 1 .

 1 Fig. 1. Hash-Locking: A reader unlocks a hash-locked tag

Fig. 2 .

 2 Fig. 2. Randomized Hash-Locking

Fig. 3 .

 3 Fig. 3. Privacy and Security in Library RFID

Fig. 4 .

 4 Fig. 4. Ohkubo protocol

Fig. 5 .

 5 Fig. 5. Proposed Authentication Protocol

  Ohkubo protocol Ohkubo protocol guarantees untraceability and forward secrecy, G is a one-way function, so if the adversary obtains tag output a i , it cannot know s i from a i . G outputs random values, so if the adversary watches the tag output, it cannot link a i and a i+1 . H is also a one-way function, so if the adversary tampers with a tag and obtains the secret information in the tag, it cannot know s i from s i+1 , but Ohkubo requires exhaustive search in the back-end server. The time complexity of this protocol is O(2mn) in terms of hash computations. The time complexity O(2mn) of Ohkubo is less scalable in comparison with Hash-Lock Scheme O(n).

  table, it should be searched in the previous values' table, too). In case it is found, the back-end server generates such a random number r 1 that h(k 1 ⊕ r 1 ) become unique among other h(k 1 ) values in the database. The back-end server then computes t 1 = h(k 1 ⊕ k 2 ⊕ r 1 ), and sends the r 1 , t 1 message to the tag. 4. The tag computes t ′ 1

Table 1 .

 1 Security comparison with other protocols

	Protocols	HBAC RAC Tree-based protocol Ohkubo protocol Our protocol
	Replay attack	X	X	O	O	O
	Prevent Spoofing R X	X	O	O	O
	Prevent Spoofing T X	X	O	O	O
	Forward Secrecy	X	X	X	O	O
	Untraceability	X	△	O	O	O
	Anti-Cloning	O	O	O	O	O
	DoS attack	X	X	X	X	△
	Eavesdropping	X	△	O	O	O
	De-synchronization △	△	O	△	O
	Scalability	△	△	O	X	O


András Tóth
email: toth@emt.bme.hu

Ferenc Vajda
email: vajda@iit.bme.hu

Autonomous Sensor Network Architecture Model

Keywords: role based, wireless sensor networks, sensors, sensor architecture model, maintenance free sensor networks, dynamic sensor network environment

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Nowadays, one of the main problems in sensor networks is to solve the problems that arise from network and resources maintenance. We need to optimize the efficiency and reliability of the systems. The main goal of a sensor networkis to gather measurement data from the environment. From a processing system point of view, it is a loss to maintain this kind of network. If the sensor network can handle these functions alone, then the processing network operation can be more reliable. There are two different control types. One, is a centralized control method, where the processor entities provide network guidance. These networks are more common than a non-centralized system, because the maintenance is taken on one side only, so problems and network errors are easier to recognize and repair. Therefore, most solutions use centralized control method based configuration.

In the current literature there are several system models and maintenance algorithms presented, which can handle large sensor networks. The main goal of these models is to verify system channels and other items in a fast and reliable fashion. The center of the system is usually one element of the sensor system or resides in the processing system and controls the network items using a selected administrator. In wireless sensor networks the relationships between entities (nodes) are changing dynamically. It is very difficult to use a static administrator entity, because some items often become disconnected and hidden within the environment. Developers and researchers implement many algorithms [START_REF] Casola | SeNsIM-Web: a Service Based Architecture for Sensor Networks Integration[END_REF][3] [START_REF] Han | A Dynamic Operating System for Sensor Nodes[END_REF] and functions to search and reconnect these "lost" items. There are numerous methods to recognize these events.

These solutions often mean additional work for the sensor administration and system maintenance side. It is necessary to poll the system elements frequently to see if the items have disappeared. If we could migrate this functionality to the entity side itself, these problems can be solved without adding overhead to the main system maintenance process.

Similar to a human community, it is normally expected that problems occurring can be solved by local members. If they cannot solve the problems, then the problems should escalate to a higher level, which can be, in this case, the system level. In this way we reduce the tasks and area of responsibility of the main system.

General weaknesses of the wireless sensor networks are the energy and communication reliability. The communication channels are often not static, so the problems with timing and energy management are much more complex. The relationships and network parameters are dynamically changing. If an element within the sensor network has to solve extra tasks, then extra energy is needed to be provided. If these items have spent all of the resources allocated to them, then their tasks should not be unfinished or incomplete.

There are studies [START_REF] Lombriser | Modeling Service-Oriented Context Processing in Dynamic Body Area Networks[END_REF][START_REF] Casola | SeNsIM-Web: a Service Based Architecture for Sensor Networks Integration[END_REF][START_REF] Jin | Application-Oriented Flow Control for Wireless Sensor Networks[END_REF][START_REF] Han | A Dynamic Operating System for Sensor Nodes[END_REF][START_REF] Bergstrom | Composing µSIC: A Lightweight Service Model for Wireless Sensor Networks[END_REF][START_REF] Kushwaha | OASiS: A Programming Framework for Service-Oriented Sensor Networks[END_REF][START_REF] Bai | MidCASE: A Service Oriented Middleware Enabling Context Awareness for Smart Environment[END_REF][START_REF] Foo | Service Oriented Architecture for Patient Monitoring Application[END_REF], which introduce novel methods and algorithms to solve the above mentioned problems. These methods are designed to provide an optimum between energy consumption and usability. There are some problems, which are not answered by these solutions. It is important to show that the problematic functions do not belong to the processing system or an administrator center, because one of the weakest point of the entire system could be that element itself. If the system contains the logic presented above in a distributed way, and most of the elements can recognize and handle these problems, then a more reliable solution is given. In addition, the reliability and speed of processing can be also increased.

This paper introduces such a novel sensor system architecture model that solves the problems associated with maintenance roles. A "role based" solution translates this subject in very different way. In this case, roles solve only a part of problems within the local sensor network. Only one operation is used for sensor data gathering, there are many others, which are dedicated to validate communication channels and routes and provide energy/resource management and maintenance sensor elements within separated parts of the environment.

This sensor network model focuses on wireless solutions, because that topic is more complicated and needs new/better solutions, however, wired networks can also benefit by using this model in implementation of operational functions.

The presented work is connected to a novel scientific program of the "Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" project. This project is supported by the New Hungary Development Plan (Project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002).

Our model can give a good base to build a simulation environment for the development process of a new sensor network. The work presented is not a simulation environment implementation. This model gives role based system architecture skeleton in a theoretical way. This system would provide the criterions mentioned before. Next sections will introduce the parameters and idea of this architecture model.

As mentioned before, the main goal of a sensor based system is to collect sensor information. A long-term usage network has many energy limitations. This forces engineers to develop more and more new algorithms, which make it possible to operate a network with higher reliability for a longer time with less energy.

In wireless sensor networks the parameters, which describe the environment of the sensor and the sensor itself have randomness and dynamism. This unpredictability means that the connections between the senders and receivers and their environment are not static. The neighborhood of the elements and the radio communication field can change all the time. Therefore, network searching and "keep alive" messages are necessary for reliable operations. However, the energy usage is high with every signal sent and received. It is also difficult to ensure that messages arrive to the target. Moreover, very important data security questions are arising.

First take a little look at relationships. Any connection between two network elements is temporary. For example, the physical movement element (node) can cause this phenomenon.

The provision of the available bandwidth in the network is very important. Of course, it is also important to prove that the communication routes are as short as possible and as "cheap" as possible. The system can reduce the needed bandwidth if the processing logic is partly placed within the sensor network itself. The only way this is possible, if the sensor network elements (nodes) has sufficient processing capacity to provide some preprocessing steps with raw sensor data.

Nowadays, sensor systems need to communicate with other networks. It can provide much higher efficiencies, if all members of these connected systems can use shared functions. This solution is possible if the system algorithms are well known and based on the same functional model. There are several research works, which describe a reliable base for future network standards [START_REF] Lombriser | Modeling Service-Oriented Context Processing in Dynamic Body Area Networks[END_REF][START_REF] Casola | SeNsIM-Web: a Service Based Architecture for Sensor Networks Integration[END_REF][START_REF] Jin | Application-Oriented Flow Control for Wireless Sensor Networks[END_REF][START_REF] Han | A Dynamic Operating System for Sensor Nodes[END_REF][START_REF] Bergstrom | Composing µSIC: A Lightweight Service Model for Wireless Sensor Networks[END_REF][START_REF] Kushwaha | OASiS: A Programming Framework for Service-Oriented Sensor Networks[END_REF][START_REF] Bai | MidCASE: A Service Oriented Middleware Enabling Context Awareness for Smart Environment[END_REF][START_REF] Foo | Service Oriented Architecture for Patient Monitoring Application[END_REF].

In a wireless sensor network environment, it is important to consider data and information security issues. The system administrator functions needs to verify that sent messages are arrived to the original requesters and the receivers are always trusted.

In the network architecture model of the current work, it is necessary to design all of these requirements at the level of the proposed model.

Design Trends

The earlier models [START_REF] Muruganathan | A centralized energy-efficient routing protocol for wireless sensor networks[END_REF] were based on some specific features of the sensors and the measured environment. Hardware limitations will determine the plan and the operation of the system. Almost all of these early systems are centralized, because it is easier to implement the defined functions and processes.

Nowadays, algorithms are controlled and developed by system informatics and mathematics. More computing capability is needed, as well as, logical resources within the sensor network nodes. This is possible because, currently hardware components are less expensive and more reliable due to better engineering, technology innovations, mass production and economies of scale. The newest sensor systems are focusing on energy consumption and long-term reliable operation. To reach these goals the system has to reduce the radio communication frequency and the actual size of the messages. The size of messages can be reduced with preprocessing and filtering.

The newer sensor systems are closer to the PC based networks. The new addressing, messaging and processing methods illustrate a good example of how to plan a new sensor network, function and architecture.

Database Style Service Based Networks.

In these solutions the wireless and wired sensor networks operate like databases. There is a special query language defined to get information from the sensor system. There is also a preprocessing layer, which translates the queries to control or maintenance messages in the network. This system is a demand driven architecture. In this case all of the functions are centralized. The system is focusing on ease of handling and implementation. The main goal is to hide the sensor system specialty and special functionality from the higher service layers. This could be very useful, if we do not want to see what is happening in the network, while we are working with it.

Task Oriented Solutions.

As in the database type systems, the task allocation process is dynamic in the network. The main feature of the system is a location based task allocation. The system can describe which part of the system will provide sensor information. This solution has some disadvantages. The system requires homogeneous sensor network items. So, it can exchange data with any other entity in the network. In distributed networks it is very significant limitation and it means the main issue. [START_REF] Kushwaha | OASiS: A Programming Framework for Service-Oriented Sensor Networks[END_REF] Service Oriented Networks.

The service oriented solutions has an inner and an outer control. This is the one of the main advantages, because these systems can operate independently from the administrator functions of the central control system. [START_REF] Lombriser | Modeling Service-Oriented Context Processing in Dynamic Body Area Networks[END_REF][2] But it is also possible to instruct the sensor networks entities from outside of the closed sensor network. There are functions for monitoring and verifying the system processes. This architecture successful in distributed sensor environment. The members of the network can handle and respond to the local problems independently, without the control of a central administrator. This approach is close to a service based solution. The main system has a built in operation process. This process has tasks, which are important for gathering information and maintaining the network. The tasks, which are related to one of the services in the system, are organized in a group. This group belongs to one role, which can be placed in any of the devices which is symbolized with an entity in the model. So the system maintenance is separated from the processing part (Figure 1). All of the roles have their own scope. The administrator role is able to send the control messages to the network, inside its scope or outside of it. It can also monitor and repair the system, but it can succeed only through maintenance messages for the special roles in the network. It is not necessary to know, where the processing roles are located. The system processes these queries, as it does with messages from the other roles.

One entity can provide more than one role, but it is limited by its resources. From the upper levels of the application, the sensor network seems to be one big sensing entity. This one entity is able to receive commands from the processing network, and able to serve monitoring information for the system control processes. From this information a system administrator can identify problems in the network.

The other main advantage is dynamism and modularity. The application code of the role can be run on all of the entities within the network. More roles function can run on the same entity parallel if it has enough resource. This roles location can be changed in the network as the optimal allocation needs. The administration role can control the displacements of roles in the network. One of the main criteria is to reduce energy consumption. Therefore, a solution that uses this model can be more energy efficient.

If one of the entities is running out of resources, then the nearest administration role should recognize this and try to select another place to run the needed role. This election is driven by the status of the known sensor parameters of entity. The developer can describe which roles are necessary in the sensor networks to work efficiently at the planning phase. The algorithm mentioned before, makes the system more reliable, because it will keep "alive" the roles of the system.

Two systems can cooperate with each other, because they have the same operation and protocol model. The difference could come from implementations, which can be solved by a translation protocol.

This version of the sensor system solutions can give more advantage than the others. It is more dynamic in operation. The functions solvers can change all the time and the system remains useful. The system can achieve its reliability in more cases than the others. The other advantage is to provide an energy efficient operation.

Roles Of The System

There are some base roles in the system. This set can be completed with implementation and simulation specific roles. These can make harder to plan cooperation between them. The root roles are dedicated to proper operation of the architecture. This solves the main tasks in the network. The models of the roles will be a set of usable applications and parameters in a specific configuration which can be run by the system members. The network members are different from each other and there are different versions from roles for the various types of entities. If the functions of the role could be modeled in one of the algorithm description language, then the running application modules can be generated after the planning phase.

All of the participants have a rating, which shows the capabilities for the running roles. This is the base of the implementation and the simulation side of the system. It describes the computing capacity and free resources. These can exist in a temporary storage, sensor item, extra logical unit or any other entity.

As stated, a critical criteria is the provision of an energy efficient operation. Communications consumes the majority of the overall energy. In this solution the units communicate with the nearest proximity entities. So the signal strength can be less than as it is at other network types. This network is using the "multi-hop" method at the higher layers, because members interact with their actual neighborhood. But in a bigger cluster the administration role gather data through its neighbors too. Alternatively, the administration processes can change a role location if the owner device is getting out of battery. Other devices can only nominate themselves for running the role if they have enough energy.

If the connection was lost between the two components, the administrator will start a new role owner selection. If the old owner device recognizes the lost connection, it will give up all of the services which belong to the actual authority.

If there is no usable role owner in the cluster, but it is necessary for the network, then the administrator module can transfer its task and request a new administrator runner election. If it is possible they will establish another cluster with other entities. If this does not give a reliable solution, then the role is going to get back to the processing system. After this, the process can be simulated until there is no appropriate entity to run it.

Basic Roles

The basic roles of the model are necessary to solve the maintenance and operational problems in a specific simulation environment. These contain the main rules for controlling and monitoring their neighborhood. The specific roles which come from the actual dependencies should implement near these. These entities provide the backbone of our sensor network.  Sensor data collector role: This role symbolizes the functions of sensing with measuring. An entity with this role can measure one of the parameters in the environment. These results can be converted after collecting all of them. Any entity can take on this function if it has a sensor and a basic preprocessing unit. These criteria are very basic requirements in sensor networks nowadays. (Figure 3.b)  Data transmission role: This role works like routers in a PC network. It has to transmit given data packets which arrive from a sensor data collector role or from another data transmission role. The destination state depends on the parameters of the data packet. E.g.: If the packet needs to be preprocessed somewhere, then the destination will be a preprocessor role, or a data transmission role, which is next to the closest preprocessor role.  Preprocessor role: This role has the function for preprocessing data directly. In addition to this, it can also provide a basic filtering process to recognize that there are unnecessary information in the raw sensor data. If we use filtering we can reduce the number of transmitted data packets. With preprocessing we can reduce the packet sizes in any given period of measurement. This processing step means specific energy cost. So, the actual implementation will decide the level of the processing logic.  Data saving role: In a wireless sensor network, it is a usual problem to lose connections between the sender and receiver. This connection should rebuild after a short period of time. Much depends on the features and the density of the network. If the communication connector does not have a usable route in direction to the destination role, then it can look for a storage role, which can temporarily store the data packets until the connection is made. In close proximity to this role there should be a data transmission role, because the stored message needs to be transmitted later.  Data access point: This role symbolize that device which is directly connected to the processing server side of the system. If there is more than one access point in the network, then the effective bandwidth can increase. This role is making snapshots about their neighborhood and transmits them to the process server of the system. The monitor data packets are similar to the sensor data ones in the network. The processing network will recognize and translate this information. These statistical trends and information can give a good base for upper level system maintenance in an implementation. The developers and administrators can follow the network operations and errors, which can be repaired.  Administrator role: This role is a key feature of the system. It can monitor all other roles and available entities in its authority. Its optimal location in the network depends on the other roles in the network. Of course since it is the most complex role in the network it needs the most complex resources. This role has to be online all of the time, because it has to provide the maintenance processes. If there is no entity left to handle this role, then it is goes back to the process center.

These roles provide the system features. These features are mobility and reliability. The model can give a more dynamic and adaptive solution for sensor systems. (e.g. in Figure 2) In large sensor systems there are a lot of usual problems with moving devices and the changing connections. At the start of the planning phase the developers have to imagine the system features before something is placed in the network. This system offers a good solution to simulate the members of the system before implementation. After evaluate a simulation from the theoretical model, then the developers can modify and optimize their composition. They can also plan the system for a longer term operation. The entity has to provide some own monitoring functions. It has to start its roles and functions regard to its features and parameters. (Figure 3

Dynamic Features

Within a wireless sensor system, there are many dynamic parameters. The sensor devices in the network can move and disappear at any time during operation. The mobile devices also have various changing parameters. If they are running roles then its power will become low with time elapsing. If they have no energy for this role, then they have to give the role up and forward it to the administrator process. The entities can thus handle any energy problems in a more reliable manner. Using these algorithms, all of the roles and processes are safe. The central logic can assign the functionality to the sensor network system and retrieve it when necessary. The developers can decide which level they would like to implement system logic within the sensor system which is using the role based model for developing.

Energy Features: The system can dynamically change system role configurations. Every entity has a list of possibilities and capabilities. These are based on the implemented functions of the symbolized device. But there is a very important parameter, which is the power buffer size. If the power level gets too low for a role, then the role has to be moved to another entity. The monitor role collects information about the systems energy level. The administrators can receive a signal if the power level is too low. The maintenance staff should then correct and repair the problem. After a real system startup, devices can determine an optimal energy spending algorithm. In optimal cases the system power level matches the rate of all devices in the network.

Scalability: If the developers plan a large sensor network in a large environment, they should use more sensors in smaller sensor networks. These will provide many roles to perform system operations. In many cases the solutions could be solved with fewer sensors. This architecture model would be a good solution since the required number of roles could be reduced. If an entity has exhausted its resources then it would return any running roles. These roles keep functioning within the central core of the system. If the system needs any roles then numbers can increase with new entities as they join. In this case, the administrator sees this new requirement as a failed transmission or network errors. Then the administrator can allocate more roles dynamically to the network. For example, if two networks are connecting in one environment, new router roles will appear on the boundary of thems. Of course the sensor data collecting roles cannot go to the processing center, because it needs a feature what must stay with the sensor entity. If they cannot do their sensing work they have to enter a suspend state upon receiving an alert message.

Autonomous Operation: In other service based models it is necessary to be a member, which can see the entire image of the network. This element stores something like service library. This list shows the entities, which belong to the actual services.

In this works case, the system could not see this image. The administration module sees its neighborhood. The members of a cluster or a group can reach an administrator role. They can address their messages with features. If they need a task from a specific role, then they send it to a route which contains the needed one. The role can disappear from the route, because it has been moved somewhere else. But on the route, the original owner exists, which had the old role and can give a new forward direction for message.

The system has to change a role location only if necessary. This change could be required for reasons of availability and/or energy needs. These movements are taken autonomously by the roles and entities. If one of them senses that a requirement for running a role is ending then it will release it and assign it to the closest administration logic. The roles can handle these problems within their local authority.

If an entity senses that, it has been removed from an environment, and it cannot reconnect to peers, then it will look for new connections with visible ones. It will request a link to the closest administrator role. The visible entities access the service list, discover what they can serve and route to them. This algorithm solves autonomously connection problems, and can enlist new elements to the network.

Advantages Of The Special Architecture Model

This model is a good base for the simulations and the modifications a sensor network before develop any hardware or software component. There are a few parameters, which have to be described for the model in the future, but with the exception these, the developers can plan and simulate the system easily after complete the model and calculate the parameters. These parameters are useful at a validation process too. With this platform the maintenance staff can follow system operations and events. The monitor role provides its data source.

During the planning of a project this model provides online simulation parameters to modify and optimize the system from the beginning. The developers can calculate the lifetime, processing and storage resources. The sensor network can give a reliable answer for connection errors and the operation deviances.

Future Work

There is a need to develop a newer version of the evaluation algorithm which is able to describe the roles location more efficiently. At this stage the location can be changed, if the requirements of connection change. We would like to integrate more points of view into the processes. The architecture can be more energy efficient and reliable if there is an independent process in the network which can collect information for this purpose. We will implement the specific features into an open source version, which will be usable all PC platforms. After this, we would like to test and upload it to a public site. It can be useful for engineers around the world and they can contribute their knowledge. This information is necessary to continue developing this architecture model. We will integrate the model simulation phase to existing sensor networks development process. We would like to measure the differences between the "typical" planned and the "role based" planned solutions.

Figure 1 :

 1 Figure 1: Role Based Sensor Architecture Model

Figure 2 :

 2 Figure 2: Distribution of the roles in a test design of the network  Monitoring role: This role is making snapshots about their neighborhood andtransmits them to the process server of the system. The monitor data packets are similar to the sensor data ones in the network. The processing network will recognize and translate this information. These statistical trends and information can give a good base for upper level system maintenance in an implementation.The developers and administrators can follow the network operations and errors, which can be repaired.  Administrator role: This role is a key feature of the system. It can monitor all other roles and available entities in its authority. Its optimal location in the network depends on the other roles in the network. Of course since it is the most complex role in the network it needs the most complex resources. This role has to be online all of the time, because it has to provide the maintenance processes. If there is no entity left to handle this role, then it is goes back to the process center.

  .a) In order to ensure reliable operation for providing roles it has to always monitor the available resources. If it is necessary the entity can change its configuration independently (Figure 3.c).

Figure 3 :

 3 Figure 3: a.) Role starter flowchart, b.)Sensing function flowchart, c.) Resource maintenance function flowchart

Acknowledgement.

I would like to thank my consultant Ferenc Vajda Dr. for monitoring and checking my work during the development phase of the model construction. Also many thanks to my supervisor Lóránt Vajda for the technical environment and the support meetings concerning this topic. And I am very grateful for the technical questions and the final proofreading of Randall Claywell, who also checked my research's direction.

This work was supported by TÁMOP-4.2.1/B-09/1/KMR-2010-0002.

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Isomeric states in 253 No

Keywords: 21, 10-k Properties of nuclei -21, 10, Tg Lifetimes -23, 20, Lv gamma transitions and level energies -23, 20, Nx Internal conversion

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Introduction

Isomeric states, i.e. states with strongly inhibited electromagnetic decay modes, occur when there is a secondary energy minimum for some values of shape elongation (shape isomers), total angular momentum of the nucleus (spin isomers) or for a certain value of the projection K of the total angular momentum of the nucleus onto the symmetry axis (K-isomers). Trapped in this pocket, it is difficult for the nucleus to change its shape, spin or its spin orientation relative to the axis of symmetry. In the transfermium region, one expects the occurence of spin-isomers because of the coexistence of high and low-j orbitals close to the Fermi surface [1][2][3][4][5][6]. K-isomers are also expected because of the combination of nuclear deformation and the presence of orbitals with large spin projections Ω on the symmetry axis. Isomeric states are therefore extremely revealing of the underlying structure of the nucleus: nature and ordering of single-particle states, deformation, configuration of quasiparticle states and magnitude of pairing and/or collective correlations.

K-isomers have been identified in several transfermium nuclei. The gamma-decay of a 70 ns K π =7 -isomeric state was observed by Hall et al. in 256 Fm [7]. The 1425 keV level, populated in the beta-decay of 256m Es, was also seen to fission with a half-life of 0.8 ms. A 0.28-second isomeric state in 254 No and a 1.8-second isomeric state in 250 Fm were reported by Ghiorso et al. [8] but their quantum numbers could not be determined. By analogy to the interpretation of isomeric states in the A=170-190 around the Hf isotopes, both isomeric states were interepreted as high-spin states, based on either two-proton or twoneutron configurations. It is only very recently, however, that the isomeric state in 254 No has been firmly identified as a two-proton K=8 -isomer via the properties of its electromagnetic decay [9,10].

Long-lived spin isomers have been observed in 257 Rf [11], 253 Lr and 257 Db [12], 251 No [13] and 255 Lr [14]. The isomers in 251 No, 253 Lr and 257 Db involve a low-spin singleparticle neutron (for No) or proton (for Lr and Db) state above a high-spin ground state. In 257 Rf and 255 Lr, the situation is reversed with a high-spin isomeric state above a low-spin ground state. On top of pinning down the sequence of single-particles states, the identification of isomeric states, especially the ones which alpha-decay, is important for the interpretation of the fine structure of alphadecay. Indeed, the non identification of an isomeric state in a nucleus may lead to the misinterpretation of its quan- tum structure and that of its daughter nucleus. As an example, the reinvistigation of 257 Rf revealed the presence of a 11/2 -isomeric state, which was responsible for the unusual alpha-decay pattern of 257 Rf compared to lighter isotones. This observation modified the spin and parity assignment of the ground state of 257 Rf and considerably changed the excitation energy of levels in the daughter nucleus, 253 No [11]. In particular, it established the excitation energy of the isomeric state reported by Bemis et al. [15] to be 124 keV above the ground state. This energy, however, is lower than the atomic K-binding energy in Nobelium and is incompatible with the delayed X-ray emission observed by Bemis. In this paper, we clarify the situation concerning the low-lying isomeric state in 253 No and report on the possible presence of a longer-lived isomeric state.

Experimental details 2.1 Experimental set-up

Excited states in 253 No were populated in the reaction 207 Pb( 48 Ca,2n) using 350 µg/cm 2 rotating PbS targets on 1.5 µm-thick Ti support foils. The 242 MeV, 0.7 pµA 48 Ca beam was provided by the U400 cyclotron of the FLNR, JINR, Dubna. A 2 µm-thick Ti degrader-foil was installed in front of the target in order to have a beam energy of ∼217 MeV at the center of the target. The fusionevaporation residues (mainly 253 No) were transported by the VASSILISSA separator [16,17] and implanted into the stop detector of the GABRIELA detection system [18] installed at the focal plane of the separator. Only nuclear states of the evaporation residues with lifetimes of the order of or larger than the time of flight through the separator (∼ 1µs) will be observed to decay at the focal plane. Evaporation residues are distinguished from the background of scattered beam particles and transfer products by a combined energy and time-of-flight measurement. The background of low-energy scattered particles detected in the stop detector is reduced by placing a mylar foil between the time-of-flight detector and the stop detector. This foil also serves another purpose: it slows down the evaporation residues to reduce their implantation depth in the stop detector. This increases the escape probability of conversion electrons emitted in the backward direction by the implanted nuclei and their daughter products. The conversion electrons are detected in four 4-fold segmented silicon detectors placed upstream from the implantation detector in a tunnel-like configuration. Gamma-ray emission is detected in seven germanium detectors from the French-UK Loan Pool. The signals from each detector are processed individually and time-stamped to a resolution of 1µs. The γ-ray efficiency reaches ∼9% at 120 keV and the electron-detection efficiency peaks at ∼17% for electron energies between 100 and 400 keV.

During the 144-hour experiment, 13000 evaporation residues were identified on the basis of their energy and time-of-flight. This corresponds roughly to half the total number of evaporation residues, which actually reach the stop detector. By requiring an anti-coincidence between the stop detector and the time-of-flight detector, a total of 10500 alpha-decays of 252-254 No were recorded. Using a search time of 10 minutes, 4800 alpha-particles were spatially correlated to recoil events in the stop detector (see Fig. 1). Finally, ∼2 10 6 electrons with energies below 200 keV were detected in the tunnel detectors.

Lifetime measurement method

The decay properties of a nuclear state can be characterised by the decay probability per unit time λ. If N r is the number of nuclei produced in such a nuclear state, then the number of decay events per unit time is given by:

dN (t) dt = N r λe (-λt) . (1)
In order to measure the lifetime τ = 1/λ or half-life T 1/2 = ln(2)τ of the state, decay times are generally sorted into a spectrum with time intervals of constant width ∆t. In this way, channel i contains the number of decay events observed between t i and t i + ∆t. Another way to proceed is to sort decay times into a spectrum with time intervals ∆t proportional to time (logarithmic time bins) [19]:

∆t t = constant. ( 2
)
By using a change of variables θ = log 2 (t) = ln(t)/ ln(2), the density distribution of decays per time bin is given by:

dN (θ) dθ = N r ln(2)λ × 2 θ × e (-λ2 θ ) (3)
This form has the advantage of peaking at θ max which is related to the lifetime of the state by the simple relation It also enables an easy inspection of decay times over a very large interval in time and is particularly well adapted to determine lifetimes in the case of low statistics.

τ = 2 θmax (4)
Figure 2 shows the energy spectra of electrons detected in the backward silicon detectors as a function of log 2 (∆t), where ∆t is the time difference between the detection of any recoil (panel a) or of a 253-254 No-alpha-positioncorrelated recoil (panel c) in the stop detector and the detection of an electron in the tunnel detectors. In both panels, the same delayed cluster of electrons is clearly visible at electron energies between 120 and 170 keV. A delayed structure around gamma-ray energy 120 keV is visible at similar time differences in panels b and d of Fig. 2. Even though the energy of the 254 No alpha-decay coincides with the energy range of the 253 No alpha-particle group, the delayed electron and gamma-ray emission seen in Fig. 2 is attributed to 253 No since in a dedicated run with a 208 Pb target, no such emission was observed in 254 No. From equation 4, one can estimate the lifetime of the emitting state to be of the order of τ = 2 5 -2 6 µs.

In order to measure the lifetime of the above-mentioned isomeric state, equation (1), and therefore also (3), need to be modified to take into account random recoil-electron (or recoil-gamma) correlations [20].

The number dN (t) of electrons detected between times t and t+dt following the implantation of a Nobelium recoil is given by the sum of two independent terms dN 1 (t) and dN 2 (t). The first term is the number of real decays multiplied by the probability that no other recoil is detected at the focal plane between t = 0 and t (i.e., the probability that the next recoil is detected after time t):

dN 1 (t) dt = N r λe (-λt) ∞ t σe (-σt) dt = N r λe (-(λ+σ)t) (5)
where σ is the recoil rate at the focal plane of VAS-SILISSA. The integral of this equation over the duration of the experiment yields the number of properly correlated electrons, N tot,1 . As the duration of the experiment is large compared to the sum of the time constants, N tot,1 = Nr λ λ+σ . Conversely, the number of randomly-correlated electrons is given by N tot,2 = N e -N tot,1 , where N e is the total number of electrons detected in the experiment.

The second term dN 2 (t) is the number of random electron events detected in the tunnel multiplied by the probability that no other recoil arrives between t = 0 and t. Since the number of random electron events per unit time is given by the product of the number of randomlycorrelated electrons N tot,2 and of the recoil rate σ:

dN2(t) dt = N tot,2 σ ∞ t σe (-σt) dt = N e -Nrλ λ+σ σe (-σt) (6)
Equation ( 3) therefore becomes:

dN (θ) dθ = N r ln(2)λ2 θ e (-(λ+σ)2 θ ) + N e -Nrλ λ+σ ln(2)σ2 θ e (-σ2 θ ) (7)
from which the lifetime of the isomeric state can be determined.

Electromagnetic properties

In Fig. 3 are displayed energy projections (taken between time bins 3 and 7, i.e. between 8 and 128 µs) of the matrices in the top panels of Fig. 2. The K α and K β Nobelium X-rays are clearly visible in the spectrum of γ-rays of Fig.

In the electron spectrum, two well-separated structures

Table 1. First row: Intensity of the 167 keV γ-ray line as determined experimentally and as determined from the product of the measured X-ray intensity and of the theoretical K-conversion coefficients taken from [22,23] appear at 138 and 161 keV. The nearly flat distribution of counts at lower electron energies corresponds to electrons which backscatter out of the tunnel detectors (see Fig. 4 of reference [18]).

The fact that K X-rays are emitted signifies that a transition of energy greater than the binding energy of K-electrons in Nobelium (150.5 keV) is converted. Furthermore, the energy difference of the two visible electron structures (23(3) keV) corresponds to the average difference in binding energies between the L and M shells in Nobelium (∼20.4 keV). The two electron structures observed in the top panel of Fig. 3 are therefore assigned to the L and M N + conversion of a 167(3) keV transition, which is highly converted. In the γ-ray spectrum of Fig. 3, there are 5(3) counts at 167 keV. In the Nobelium region, the fluorescence yield for a vacancy in the K shell is practically 1 [21]. This means that the observed X-ray intensity can be used as the experimental value for the K-conversion intensity. In Table 1, the expected intensity of the 167 keV γ-ray is reported as a function of the multipolarity and the electromagnetic nature of the 167 keV transition. The ratios of the experimental conversion coefficients are also shown in Table 1 together with the corresponding theoretical values [22,23]. Given all the experimental observations, the 167 keV transition is firmly established to be an M2 transition.

Lifetime properties

The time projection of the matrix of the top panel of Fig. 2 taken between electron energies 40 and 200 keV, is displayed in Fig. 4. In the bottom panel of Fig. 4, the same electron decay curve is shown using standard constant time bins. When only one decaying state is taken into account, the fit to the electron count distribution (according to equation 7) fails to account for all the intensity. In fact, in the top panel of Fig. 4, the presence of a second isomeric state appears clearly as a second bump around ln(∆T )/ ln(2)=10.

If a second isomeric state is included into the parameters of the fit, the lifetime of the isomeric state which decays by the emission of the 167 keV M2 transition, is found to be τ =44.9(3.1) µs. This corresponds to a half-life of T 1/2 =31.1(2.1) µs, which is in agreement with the value given by Bemis et al. [15]. The other electron-emitting state has a lifetime of τ =1.4(3) ms (T 1/2 =970(200) µs). Fig. 4. Distribution of time differences in logaritmic scale (top panel in counts per quarter bins) and linear scale (bottom panel) between the detection of recoils and electrons. The fits to these time distributions are shown for the cases where only the decay of one isomeric state is considered (dashed curves) and when the decay of a second isomeric states is taken into account (solid line).

A consistency check of the fit parameters can be made by comparing the values of (i) the number of recoils, N r , produced in the short-lived isomeric state, (ii) the total recoil rate, σ, and (iii) the total number of electrons, N e , detected in the experiment, obtained from the parameters of the fit and the same values obtained by other means. In the case of the shorter-lived isomer, the electron decay curve corresponding to electron energies greater than 120 keV was used to extract a value of N r = 190 (15). In order to find the total number of recoils which were produced in the isomeric state during the experiment, N r needs to be corrected for the electron-detection efficiency and for the fraction of the intensity of the 167 keV transition which is LM N +-converted. This yields N r = 2513(200). This is well in accordance with the value of N r which can be extracted from the electron spectrum of Fig. 3. From the intensity of the LM N + structure, the population of the isomeric state is found to be 2100(140). The total recoil rate obtained from the parameters of the fit is σ=2.8(1) 10 -8 µs -1 . This value also fits well with the total number of Nobelium recoils (mainly 253 No, but also 254 No and 252 No) identified during the experiment divided by the duration of the experiment: 2.5 10 -8 µs -1 . Finally, the total number of electrons detected during the experiment is extracted to be N e =1.7(1) 10 6 . This is in agreement with the 2 10 6 electrons actually detected in the tunnel with energies above the threshold and below 200 keV.

Discussion

The ground state of 253 No is known to be a 9/2 -state [13,24,25] so the observed excited state which decays to the ground state via an M2 transition must be either a 5/2 + or a 13/2 + state. The only possible neutron configuration for such a low-lying excited state is the 5/2 + [622] neutron hole state (see Fig. 6). This fits well into the systematics of the N=151 isotones [26][27][28][29], for which the first excited state can only decay to the ground state via an M2 transition and is therefore isomeric (see figure 5). The energy of the 5/2 + state is established to be 167 keV and not 296 keV as it currently tabulated in the Table of Isotopes [START_REF] Firestone | Table of Isotopes[END_REF] or 124 keV as is reported in reference [11]. The low energy of this isomeric state in the N=151 isotones is attributed to coupling with a low-lying octupole phonon state. In this experiment, the B(E3) rate and consequently, the degree of collectiviy of the 5/2 + state, could not be determined as it has been done for the lighter isotones 247 Cm [26] and 249 Cf [27]. This is because the uncertainties associated with the conversion coefficients are too large to determine a meaningful M2-E3 mixing ratio.

From the ratio of the number of recoils produced in the short-lived isomeric state of 253 No and of the total number of recoils, the population of the 31 µs isomeric state in the fusion-evaporation reaction is estimated to be at least 16(1)%. The rotational band built on the 5/2 + state must therefore be populated with similar intensity. This information cannot be ignored in the interpretation of the prompt γ-ray spectra obtained with the multidetectors Gammasphere [29] and Jurogam [START_REF] Greenlees | [END_REF]32] as well as the prompt conversion-electron spectrum obtained with the electron detector Sacred [24,32,33]. This is because the M1 transitions between members of the rotational band built on the 5/2 + state will dominate over the cross-over E2 transitions and will contribute to the observed X-ray, low-energy photon and conversion-electron intensities.

The longer-lived isomeric state is assigned to 253 No because its lifetime does not coincide with any of the lifetimes of the isomers observed in 254 No [9,10], and because the number of nuclei populated in such a state is larger than the number of observed 252 No recoils. The energy spectrum of the delayed electron emission is concentrated below 150 keV. The half-life of the state is measured to be 970(200) µs. Given the electron-background conditions and recoil rate, such a half-life is at the limit of the sensitivity of the current experimental setup. Indeed, the energy thresholds of the stop detector prevent the detection of any delayed electron emission below 500-1000 keV at the position of the implanted recoil. A clean and efficient tag on isomeric decays [34] is therefore not available. This is why, given the rather long lifetime of the longer-lived isomeric state and the low efficiency to detect electron-γ-ray coincidences, no γ-ray spectrum with reasonable statistics could be extracted from the background of random recoil-γ-ray correlations. Although we cannot study the details of the decay of the longer-lived isomeric state, we can exclude and suggest possible configurations based on the available singleparticle states shown in Fig. 6. The isomeric state cannot Fig. 6. Schematic representation of the available proton (left) and neutron (right) single-particle levels caclulated in reference [1]. The filled circles illustrate the filling of the orbitals in the ground state of 253 No.

be a spin isomer based on the 1/2 To conclude, the isomeric state first observed by Bemis et al. [15] has been shown to decay via an M2 transiton of 167 keV. The state is assigned the 5/2 + [522] Nilsson configuration. Its half-life is 31.1(2.1) µs and its popula-tion in the 207 Pb( 48 Ca,2n) reaction at mid-target beam energies of ∼217 MeV is estimated to be greater than 16%. There is evidence for another, longer-lived isomeric state in 253 No, but no spectroscopic information concerning the decay properties of this state could be obtained. To achieve this, tagging on the isomeric decay in the implantation detector is necessary.

Fig. 1 .

 1 Fig. 1. Energy spectrum of recoil-position-correlated alphaparticles.

Fig. 2 .

 2 Fig.2. Energy spectra of conversion electrons (a and c) and gamma-rays (b and d) as a function of ln(∆t)/ ln(2), where ∆t is the time difference between the detection of recoils and electrons or gamma-rays. The top panels show the case where all the identified recoils are considered. The bottom panels represent the time differences only for the recoils, which are followed within 10 minutes by the detection of a253-254 No alpha-particle at the same position in the stop detector. The boxes show the delayed electron and gamma-ray structures mentionned in the text. At large time differences, the spectra are dominated by random correlations.

Fig. 3 .

 3 Fig. 3. Energy spectra of conversion electrons (top panel) and γ-rays (bottome panel) emitted 8-128 µs after the detection of a recoil.

  . Second and third rows: Experimental and theoretical ratios of electronconversion coefficients for the 167 keV transition.

		experiment E1	E2	E3	M1 M2
	Iγ(167 keV) 5(3)	776 820	1035	9	3
	αK /αLMN+ 1.3(2)	2.8	0.04 0.002 3.3 1.27
	αL/αMN+	2.8(5)	3.0	2.6	2.4	3.0 2.67

  Systematics of low-lying levels in N=151 isotones obtained from references[26][27][28][29] and this work.

								620	(1/2 + )
						558	(1/2 + )
	1/2+[620]	404.9	1/2 +	416.8 379.4	1/2 + 7/2 +	354	(7/2 + )	355	(7/2 + )
	7/2+[624]	285.4	7/2 +
	5/2+[622]	227.4	5/2 +
						200	5/2 +
				145.0	5/2 +			167	5/2 +
	9/2-[734]	0.0	9/2 -	0.0	9/2 -	0.0	9/2 -	0.0	9/2 -	0.0	(9/2 -)
		Cm 247 96 151	Cf 249 98 151	Fm 251 100 151	No 253 100 151	255 Rf 102 151
	Fig. 5.

  + [631] or 11/2 -[725] single-particle neutron levels, as it is the case in251 No and 257 Rf, since it would readily decay to the 5/2 + state and ground state respectively. The same reasoning excludes the 1/2 + [620] and 3/2 + [622] neutron configurations. The isomer is therefore most likely a high-K isomer. In the neighbouring254 No, the K = 8 -isomeric state is based on the {9/2 + [624]π ⊗ 7/2 -[514]π} configuration[9,10]. A possible configuration for the isomeric state could therefore be the {9/2 + [624]π ⊗ 7/2 -[514]π ⊗ 9/2 -[734]ν} structure with K π = 25/2 + . If only neutron excitations are involved, the isomeric state could be based on the {9/2 -[734]ν ⊗ 7/2 + [624]ν ⊗ 7/2 + [613]ν} or {9/2 -[734]ν ⊗ 5/2 + [622]ν ⊗ 7/2 + [613]ν} configurations with K π = 23/2 -and K π = 21/2 -respectively.

The GABRIELA project is jointly funded by JINR (Russia) and IN2P3/CNRS (France). Work at FLNR was performed partially under the financial support of the Russian Foundation for Basic Research, contract N 05-02-16198 and JINR -BMBF (Germany), JINR -Polish, JINR -Slovak Cooperation Programmes. Financial support from the Norwegian Research Council and from the Bulgarian National Foundation, contract N MON-204/06, is also acknowledged.