Ancient documents bleed-through evaluation and its application for predicting OCR error rates

Keywords: Document Image analysis, Quality, bleed through quantification, Ocr Prediction

This article presents a way to evaluate the bleed-through defect on very old document images. We design measures to quantify and evaluate the verso ink bleeding through the paper onto the recto side. Measuring the bleed-through defect alows us to perform statistical analysis that are able to predict the feasibility of different post-scan tasks. In this article we choose to illustrate our measures by creating two OCR error rate predicting models based bleed-through evaluation. Two models are proposed, one for Abbyy FineReader * which is a very power-full commercial OCR and OCRopus † which is sponsored by Google. Both prediction models appears to be very accurate when calculating various statistic indicators.

INTRODUCTION

In scanning and indexing document chains, quality evaluation of the scanned document is a concerning issue. One could need to evaluate the image quality in order to : readjust the scanner parameters, predict the Optical Character Recognition (OCR) error rate, annotate a document image of quality meta-datas. Studies [START_REF] Cannon | Quality assessment and restoration of typewritten document images[END_REF][START_REF] Blando | Prediction of ocr accuracy[END_REF][START_REF] Rice | An evaluation of ocr accuracy[END_REF][START_REF] Cannon | An automated system for numerically rating document image quality[END_REF] were made on quality image evaluation in which metrics on characters degradations were introduced. These studies were made on modern documents suffering from holes in characters, broken and touching characters, and background speckle noise. Prior to this paper, image quality evaluation did not account for either the bleed-through defect nor ancients document images.

Bleed-through is a defect from which a lot of ancient documents suffer. The bleed-through defect can be explained by two combined reasons : the light reflected by the scanner backing, [START_REF] Knox | Show-through correction for two-sided documents[END_REF] and the ink of the verso side which is diffusing into the paper. Several bleed-through models [START_REF] Knox | Show-through correction for two-sided documents[END_REF][START_REF] Moghaddam | Low quality document image modeling and enhancement[END_REF] and restoration algorithms [START_REF] Dubois | Reduction of bleed-through in scanned manuscript documents[END_REF][START_REF] Moghaddam | Rsldi: Restoration of single-sided low-quality document images[END_REF][START_REF] Tonazzini | Fast correction of bleed-through distortion in grayscale documents by a blind source separation technique[END_REF][START_REF] Nishida | Correcting show-through effects on document images by multiscale analysis[END_REF] exists. In Rsldi 8 document image classifiers are used to restore all background defects including bleed-through. This technic is very efficient but cannot be applied to our need since measuring the difference between the old image and the restored one will not only measure the bleed-through ; G. Shama 11 models the bleed-through with optical densities and applies a linear filter adapted (with the least mean squares) where recto pixels are ink on the verso side. We inspired ourselves with the method introduced by E.Dubois, [START_REF] Dubois | Reduction of bleed-through in scanned manuscript documents[END_REF] whom proposes an effective bleed-through restoration algorithm in which recto pixels that have an ink pixel on the verso side are replaced with an background estimation. Using this method implies studying the influence of the verso side ink diffused onto the recto side. Indeed, we evaluate the likely recto side bleed-through with different measures applied to the binarized recto and verso side of a document image page.

The bleed-through effect is a major issue when binarizing a very old document image. Indeed, with a global binarization method some bleed-through pixels will be identified as ink pixels which will undoubtedly lead to Optical Character Recognition (OCR) errors. Worst, some adaptive binarization methods will identify bleedthrough pixels as ink pixel in any zone of the page where only bleed-through is present. On the other hand, optical character recognition of very old documents is a major need, while the OCR error rate is a real economic issue. The quality of OCR softwares results are depending on the quality of the document image given as input.

It is now stated that for good and moderns document, the average OCR recognition rate is close to 100%, unlike on poor quality documents where the recognition rate drops alongside quality. Since the binarization phase is critical for the OCR, the bleed-through defect is to be considered when predicting OCR results. Depending on the origin of the bleed-through , its cancellation can be hard : if it comes from the quantity of light used to digitize the document, it can be faded by tuning the scanner parameters. But, if it also comes from the ink diffusion into the paper, one can only cancel the bleed-through defect by applying a restoration process to the document. By measuring the bleed-through defect and predicting the OCR error rate, we could be able with statistic analysis, to tell whether or not a bleed-through restoration algorithm needs to be applied or if the scanner's parameters needs to be changed before trying to give the document to an OCR software. In our experiments we used two different OCR systems : OCRopus which is open source, and Abbyy FineReader. Even if it appears that Abbyy's OCR gives better results on very old document than OCRopus we decided to use both of them.

From observations made on a realistic corpus, we present in section 2 six measures able to efficiently evaluate the bleed-through defect. This vector of measures is then used in section 3, as an application, to create an OCR error rate predicting model. Finally, our research perspectives are discussed in section 4

BLEED-THROUGH EVALUATION

In order to measure the verso's ink pixel influence on the recto, we need to identify three classes of pixels : ink, bleed-through and background. We inspired ourselves with a bleed-through restoration method in which the registered [START_REF] Dubois | Reduction of bleed-through in scanned manuscript documents[END_REF] binarized verso and recto are needed. From the binarized verso P v and recto P r , we introduce I r and I v the set of ink pixels on respectively the recto side and the verso side, I v is the projection of I v onto the verso image. We also define T r which is made out of all the pixels on the recto background that corresponds to an ink pixel on the verso side.

T r can be defined by the folowing equation where p is a pixel of co-ordinated (x, y).

T r = {p ∈ I v , p / ∈ I r }
Finaly, B r is introduced as the set of pixels corresponding to the background without any pixels likely to be bleed-through ones.

B r = P r \ [T r ∪ I r ]
Our document image quality measures are designed to quantify the document bleed-through defect which we observed on a corpus of ancient documents. Bleed-through has three principals characteristics : the intensity of the bleed through pixels, the amount of pixels and, at last, the location of the bleed through.

The bleed-through intensity

The intensity of bleed-through corresponds to the average bleed-through pixels grayscale level and varies from very light gray (close to the background level) to low dark gray (close to the ink level). The intensity of bleedthrough is a major issue when trying to identify pixels corresponding to text in very old documents where that intensity is low, and we believe that it exists a value where the intensity of bleed-through is so low that the OCR will identify those pixels as ink pixels. This value must be in function of the average ink intensity and the average background intensity. Figure 1 shows the zones identified as text by the OCR on the same document images with different bleed-through intensity, and as we can see the OCR identifies some bleed through pixels as text pixels. To evaluate the bleed through intensity we consider two measures MI i which corresponds to the distance to the average ink intensity and MI b the distance to the background intensity. In the following equations let µ Tr , µ Ir and µ Br be the average intensity of respectively T r , I r and B r .

MI i = µ Tr -µ Ir 255 MI b = µ Br -µ Tr 255

The bleed-through quantity

The bleed through intensity is not the only parameter that may produce OCR errors. Indeed, OCR systems will make more errors on a document with a lot of bleed-through that on one with just a few. Therefore, we also need to measure the quantity of bleed-through that may appear by introducing MQ, the ratio of ink verso pixels that appear as bleed-through pixels on the recto side.

MQ = T r I r

The bleed-through location

We observed from our corpus of document images that the bleed-through letters location is also a caraceristic that needs to be considered and measured. Depending on the OCR used binarization methods and parameters (global or adaptative, widow-size, usage od dictionaries or not), the bleed-through location will create less or more OCR errors. Therefore, we propose measures to quantify three different bleed-through component locations. Let E and K two letters from respectively the recto and the verso image, we denote three different locations that gives different OCR outputs when the binariztion method fails :

• if E and K do not overlap (figure 2.a) : the component resulting from the wrong binarization of the letter K, will have the same characteristic (size, stroke-width) as the real text components. The result will be two ink connected components instead of one. The quantity of non-touching components is measured by MA (location measure 2.3.a).

• if E and K do overlap (figure 2.b) : the original letter will be altered. This leaves the OCR with one connected component that does not match any letter in the current page's font. The quantity of touching connected components is measured by MS (location measure 2.3.b).

• if E and K are completely overlapped (figure 2.c) : the original letter is completely modified. In this case, the OCR recognition phase is harder. The alteration's size is measured by MSG (location measure 2.3.c)

For the folowing measures, we define T C the set of connected components that are overlapping on the recto side where r and v are two connected components :

T C = {c = v ∪ r | ∃v ⊂ I v , ∃r ⊂ I r , r ∩ v = ∅} T C = {c = v ∪ r | ∃v ⊂ I v , ∃r ⊂ I r , r ∩ v = ∅}
Let also be I r and I v the set of connected components of respectively I r and

I v . a) MA = T C I v
MA is the ratio between the cardinal of the ink connected components on the verso side that are not overlapping any recto side ink components and the number of connected components on the verso side. In other words, MA measures the quantity of letters that may be added by the bleed-through defect onto the recto. This measure is not defined if the verso has no ink components. Otherwise, 0 means that no verso component will be added to the recto, and 1 means that all verso components will be added to the recto.

b) MS = T C I r

On the opposite MS is the ratio between the ink connected components that may be expended by any ink connected components from the verso and the total number of ink connected components on the recto side. if MS = 0 no recto letters will be modified, if MS = 1 all letters on the recto side will be modified.

c) MSG = 1 T C r⊂Ir,v⊂Iv,r∪v⊂T C r ∪ v -r ∩ v 1 Ir r⊂Ir r
As said, MSG will quantify the way the two letters overlaps by dividing the expended components mean area by the ink's components mean area. In other words, MSG measures the average expansion rate. The higher MSG is, the less the two connected components have pixels in common.

Table 1 shows the values of the three location measures on figure 2. MA is equal to 1 since 1 letter over 1 is added to the verso. The same reasoning can be done on MS. MSG equals to 0 on figure 2.a since no black-component are overlapping. Latter lowers the more the two overlapping components have pixels in common.

Measures experiments on document images

Table 2 shows that our measures cover all the aspects of the bleed-through. In the first case (table 2.a), even though the locations and quantity measures are not good (MQ indicates that there are as many bleed-through as ink pixels on the recto side and MS that about 60% of the text will be modified) MI i tells us that the bleedthrough intensity is not close to the ink and as MI b indicates that the bleed-through is close to the background, a global binarization method such as for example, Otsu, 12 can successfully identify ink pixels. The second (table 2.b) case as similar quantity and location measures, but MI i and MI b shows that the bleed-through pixel are equal distance from the ink and the background color, the global binarization fails. The third case shows that even if the MI i is similar to the second case, much more errors will appear : MQ shows that 300 times more bleed-through pixels will be added to the recto side and since MA equals 1, that none of the verso letters overlaps a recto letter. Two more cases are not shown on table 2 : the verso is a white page, the verso and the recto are white pages. In those two last cases no bleed-through from the verso can appear on the recto. A document where the bleedthrough will not produce OCR errors, b. An other document with much more bleed-through that will produce OCR errors, and c. the worst case, all bleed-through pixels will be identified as ink pixels by a binarization method

USING THE MEASURES TO PREDICT THE OCR ERROR RATE

In this section our goal is to create an OCR error rate prediction model in order to prove the relevance of our measures. We used two OCR systems : the OCR Abbyy FineReader ‡ and OCRopus § giving us two different prediction model since both OCR do not have the same results. In order to correctly calculate the OCR error rate, we used an application of the Levenshtein string distance statistic presented in. [START_REF] Soukoreff | Measuring errors in text entry tasks: an application of the levenshtein string distance statistic[END_REF] Creating a prediction model can be done in several steps :

• first, a dataset is created containing for each document image its ground truth (the text) and its measures. This dataset must be as heterogeneous as possible. Latter is then randomly separated in two sub-set: the prediction corpus and the validation corpus.

• secondly, a stepwise regression is done on the prediction corpus. This statistical technic will create an optimal prediction model based on our measures.

• finally, the prior prediction model is tested on the validation corpus in order to test its sharpness.

An heterogeneous ancient document image dataset and measures annalysis

The lack of OCR truth on the corpus of old document that is in our possession forced us to work on synthetic documents. We chose to use a software ? able to create old documents with the truth associated. We extended this software to generate large amounts of random old documents :

• for the text we used the web service Lorem Ipsum ¶ which is simply random text,

• we varied the size of the margins from 50 to 200 pixels,

• the line spacing from 30 to 50 pixels,

• the number of columns and rows from 1 to 3, in order to have multi-column and multi-row documents, the space between rows and columns was also random and varied from 30 pixels to 100 pixels.

• the percentage of text on the over all resulting page, randomly chosen from 0% (white page with only bleed-through ) and 100%.

• the background was chosen randomly in a directory of realistic backgrounds (white pages from ancients documents),

• the font was chosen randomly between a set of three fonts.

• the quantity of bleed-through was created using a model 6 based on the diffusion of different layers : the recto ink, the background and the verso ink.

Where articles like Prediction of OCR accuracy 2 in which 21 pages are used to train their model, we created a set of 191 ancients documents. This set is divided in two subsets : the prediction corpus ( 90 %) and the validation corpus (10%) in which the documents were chosen randomly in the original set.

Measures

Mean Table 3. Measures distribution on the prediction corpus (90%) on the over all dataset (best and worst cases are theoritical).

Concerning the measures, our dataset is heterogeneous. It is worth noting the mean error rate difference between Abby and OCRopus. OCRopus poorer performance suggest that a training could be done. MQ and MSG worst case values is due to the fact that both are normed but not between 0 and 1.

The study of table 3 on which the measures distribution is shown indicates that our dataset has heterogeneous bleed-through caracteristics. Indeed, measures have their values well distributed around their mean, minimums and maximums are close to best case and worst case theoretical values. Worst Case is the measure value that is likely to give a lot of OCR errors, and on the contrary Best Case is the measure value that is likely to give no OCR errors.

Prediction model of OCR error rate trained on 90% of our dataset

An univariate linear regression is done in order to analyze the correlation between each measure and the OCR error rate. This shows that all of the measures are linked to the OCR errors but none of them are able to individually predict the OCR error rates. Indeed, The proportion of variability Rsquare was often close to 0 instead of 1. This fact indicates that each measures has its relevance concerning the OCR errors rates. A stepwise regression includes regression models in which the choice of predictive variables is carried out by an automatic procedure. [START_REF] Thompson | Selection of variables in multiple regression: Part i. a review and evaluation[END_REF] This leads to a pure causality model without any confusion between our measure and the OCR error rate presented in table 4. ¶ http://www.lipsum.com/

The stepwise regression method could be detailed and explained in the final manuscript.

OCR Abbyy

Predicting Model Validation on 10% of our dataset

In order to test if the prediction model can predict OCR error rates, it needs to be validated. The validation corpus corresponds to 10% of the original dataset. These documents were chosen randomly and are not used for the prediction model. From our prediction equations we create scores of OCR error rate for our validation corpus. This leads us with two set of values per OCR : the prediction, the OCR error rate truth. Slope Coefficient R-square Adjusted R-square RMSE OCR Abbyy FineReader 1.006 0.97 0.97 11,03 OCROpus 0.99 0.99 0.99 7

Table 5. Indicators show that our predictions using the two models are very close to the real OCR error rate.

A linear regression between the prediction scores and the truths shows that both prediction models are accurate enough to work on other documents (table 5). For Abbyy FineReader, the linear regression gives a slope coefficient of 1.006 (where a perfect correlation has a coefficient equal to 1), a R-square of 0.97, and a RMSE of 11.03. The prediction on the validation corpus is very accurate. [START_REF] Draper | Applied regression analysis[END_REF] OCRopus validation is also very good : the slope coefficient is 0.99, R-Square equals 0.99, and RMSE equals 7.

CONCLUSION AND RESEARCH PERSPECTIVES

This paper introduce 6 measures able to measure the bleed-through defect on very old documents. Based on these measures, we are able to create prediction models of OCR error rates. Two models are given : one for Abbyy FineReader a commercial and very powerfull OCR and one for OCRopus, sponsored by google. The accuracy of the two models proves the relevance of our 6 measures concerning bleed-through evaluation. Therefore, we are able to predict OCR error rates from digitized very old documents.

We have many perspectives around this work, OCR error rate prediction is just one of many usages that can be done with these measures. It could also be interesting to study the effect of bleed-through on more simple tasks such as binarization methods. An other perspective is to run our measures on real ancient documents to create OCR prediction models that are even more accurate. To do so, and since we need the registered verso and recto, we will interest our-selves in future works with registration algorithms and the search of a corpus of very old documents with their OCR ground truth.

Figure 1 .

 1 Figure 1. OCR identified text zones (highlighted) : a. high value of intensity, the OCR correctly identifies the texts blocks, b. the same document with a lower intensity, the OCR fails to identify the text blocks. Green zones are recognized text-blocks, and red zones are unrecognized text-blocks.

Figure 2 .

 2 Figure 2. The different locations of a bleed-through letter on the page: a.the two letters do not overlap, b. the letters overlap, c.the letters are more overlapped than in b.

Figure 2

 2 Figure 2.a Figure 2.b Figure 2.c MA 1 0 0 MS 0 1 1 MSG 0 2,04 1.62

Table 1 .

 1 Example of the location measures on previous examples images. MA is none 0 in only the first case. MSG is higher the less the two connected components have pixels in common

Table 2

 2

	Test Image	Verso	Measures	Value	Otsu Binarization
	a.		MI i	0.716498
			MI b	0.103556
			MQ	1.19191
			MA	0.238095
			MS	0.606061
			MSG	1.93156
	b.		MI i	0.327205
			MI b	0.38078
			MQ	0.948104
			MA	0.461538
			MS	0.215385
			MSG	1.16205
	c		MI i	0.341211
			MI b	0.266451
			MQ	300.3
			MA	1
			MS	0
			MSG	0

. Experiments of measures document imagessorted from best (a) to worse (c) : a.

Table 4 .

 4 Prediction model of the two OCRs (OCRopus and Abbyy Fine Reader). It is worth noting that for OCRopus, all of our measures are highly significant when trying to explain the OCR error rate. The lower the p-value, the less likely the result is if the null hypothesis is true, and consequently the more significant the result is.Abbyy FineReader : The Measures MI i , MA, MSG and MI b are selected in the Abbyy FineReader prediction model. The fact the MQ and MS are removed does not indicates that those two are not significant. They are removed because they do not improve the model (to predict Abbyy FineReader error rate, MA and MSG are enough). Various indicators are calculated. Firstly, the R-square[START_REF] Draper | Applied regression analysis[END_REF] which provides a measure of how well future outcomes are likely to be predicted by the model, equals to 0.96. Secondly, the Adjusted R-square which unlike the R-square, increases only if the new term improves the model more than would be expected by chance equals 0.96. Finally Root Mean Squared Error (RMSE ) which measures the average of the square of the error, equals to 12.77. These values are very good, R-square best value is 1 and since the lower the RMSE value is the better the model is, we can say that our prediction model is very accurate. The stepwise regression on OCRopus error rates create a prediction model in which all measures are kept. Moreover, both model are a little different implies that both OCR error rates are not correlated. This is confirmed with a Pearson 16 correlation test and indicates that both OCRs use different methods (binarization, dictionaries). The same indicators have been calculated on this model : R-square and Adjusted R-square equal 0.99 and the RMSE equals to 7.5. These indicators show[START_REF] Draper | Applied regression analysis[END_REF] that the prediction model is even more accurate the Abbyy FineReader's one.

	Measures	prediction equation coefficient	p-value	prediction equation coefficient	p-value
	MI i	97,11	<0.0001	74,12	<0.0001
	MI b	195,25	<0.0001	147,09	<0.0001
	MQ	-	-	0.16	0.003
	MA	19,8	<0.0001	-16,99	0.02
	MS	-	-	-74,5	<0.0001
	MSG	-22,19	0.0008	16,08	<0.0001

15 P rediction = 97, 11 * MI i + 195, 25 * MI b + 19 * MA -22.19 * MSG OCRopus : P rediction = 74, 12 * MI i + 147, 09 * MI b + 0.16 * MQ -16, 99 * MA -74 * MS + 16, 08 * MSG

‡ http://france.abbyy.com/ § http://code.google.com/p/ocropus/

ACKNOWLEDGMENTS

We would like to thanks Arkhenum * * for letting us observe, analyze and study the bleed-through defect on real digitized ancient documents. This work is done in the Polinum project context † † .


Niels Hald

Sudip K Sarker

Paul Ziprin

Pierre-Frederic Villard

Fernando Bello

Open Surgery Simulation of Inguinal Hernia Repair

Keywords: Virtual reality, open surgery, hernioplasty, simulation, e-learning

Inguinal hernia repair procedures are often one of the first surgical procedures faced by junior surgeons. The biggest challenge in this procedure for novice trainees is understanding the 3D spatial relations of the complex anatomy of the inguinal region, which is crucial for the effective and careful handling of the present anatomical structures in order to perform a successful and lasting repair. Such relationships are difficult to illustrate and comprehend through standard learning material. This paper presents our work in progress to develop a simulation-based teaching tool allowing junior surgeons to train the Lichtenstein tension-free open inguinal hernia repair technique for direct and indirect hernias, as well as to enforce their understanding of the spatial relations of the involved anatomy.

Introduction

An inguinal hernia is an unnatural protrusion of abdominal contents through a weakness in the abdominal wall of the inguinal area. The treatment of inguinal hernias is one of the most common surgical procedures in the US and Europe [START_REF] Primatesta | Inguinal Hernia Repair: Incidence of Elective and Emergency Surgery, Readmission and Mortality[END_REF], with open mesh repair being the preferred method of treatment in many European countries [START_REF] Simons | European Hernia Society guidelines on the treatment of inguinal hernia in adult patients[END_REF]. Improvements in patient safety in recent years has lead to increased supervision of training surgeons, which in turn prevents the junior surgeons from performing surgical tasks independently [START_REF] Sarker | Constructing hierarchial task analysis in surgery[END_REF]. While these improvements are a clear benefit for the safety of the patients, it increases the burden on senior surgeons and obstructs junior surgeons from gaining the confidence from performing procedures independently [START_REF] Sarker | Constructing hierarchial task analysis in surgery[END_REF]. From our literature review and discussions with surgeons, it has become apparent that one of the hardest and most crucial challenges in repairing inguinal hernias is understanding the three dimensional spatial relations of the complex anatomy in the inguinal region [START_REF] Townsend | Sabiston Textbook of Surgery: The Biological Basis of Modern Surgical Practice 16th[END_REF]. It is our belief that these spatial relations are best taught using three-dimensional models in order to minimize the level of abstraction required by the trainee. A wide range of teaching tools utilizing 3D or pseudo 3D are available for teaching the anatomy of the inguinal region and hernias, ranging from paper cut [START_REF] Mann | Teaching Three-dimensional Surgical Concepts of Inguinal Hernia in a Time-effective Manner Using a Two-dimensional Paper-cut[END_REF] and plastic models, to simple animation based simulators such as the one provided by Simbionix (http://www.etrinsic.com/). However, the level of interaction and user involvement in the currently available tools is restricted.

Our goal is to develop a system that can contribute to the confidence, skills and knowledge of the training surgeons, with a special focus on teaching the anatomy and its spatial relations, as well as the tasks involved in the repair procedure. By doing so, we aim to optimise training by senior surgeons and further improve patient safety by helping trainee surgeons progress through the learning curve faster. We are building our system around the Lichtenstein repair technique. This technique has been chosen over other open repair techniques due to the wide acknowledgement and scientific evidence supporting it [START_REF] Primatesta | Inguinal Hernia Repair: Incidence of Elective and Emergency Surgery, Readmission and Mortality[END_REF]. The ultimate goal is to deploy our system as an e-learning application, allowing surgeons easy access to the application, without the dependence of expensive specialized hardware. Based on our initial analysis and goal, we have arrived at the following overall specifications for our system:

• The system should be web-based and ensure easy and independent accessibility • The system should require a minimum of hardware -this means no requirements of specialized equipment, such as haptic devices and the possibility to run the application on a standard laptop • The system should not require supervision to use and only require basic knowledge of the anatomy and the procedure • The system should be intuitive, allowing trainees to use it independently • There is a high emphasis on realistic anatomical models and the ability to explore these

The remainder of the paper details the analysis and design of the system, current implementation and results, as well as future planned work.

Methods

Our system has been designed around a hierarchical task analysis (HTA) [START_REF] Sarker | Constructing hierarchial task analysis in surgery[END_REF], as well as in continuous correspondence with expert surgeons and observations made in the operating theatre. Using a HTA of the Lichtenstein procedure as a foundation, we have compiled an implementation plan detailing A) the virtual environment, B) the user interactions and C) the requirements of deformable models. The implementation plan has then been used to guide the system development according to the overall specifications outlined above. The next sections will cover the use of the HTA, the virtual environment, the user interactions and the deformation models.

HTA in system design

The HTA is a systematic chronological breakdown of a procedure, detailing tasks, subtasks, roles and branching of tasks. We decided to use the HTA as a foundation for an implementation plan in order to have a solid framework for our discussions with surgeons during the design phase of our project. The HTA for the Lichtenstein procedure used here is presented in [START_REF] Sarker | Constructing hierarchial task analysis in surgery[END_REF]; it contains 16 tasks and 46 sub-tasks. Since the individual subtasks require various skills, it has been our goal to determine the most suitable implementation for each individual task that would allow our system to convey the crucial details of the surgical procedure. In collaboration with surgeons resident at St Mary's and Whittington Hospitals (London, UK), the HTA was used to iteratively develop and expand the implementation plan on which the simulation system was based.

The final version of the implementation plan encompasses the HTA itself, input from the literature review, observations from video recordings of inguinal hernia repair surgery (eleven open and one laparoscopic), observations from hernia repair procedures (three laparoscopic, two open), and continuous feedback, discussions and input from expert surgeons. The plan contains details on how we intend to implement the 46 subtasks of the procedure.

Environment

Our environment is implemented in Java, using Java3D (https://java3d.dev.java.net/) for 3D rendering. The 3DScience (http://www.3dscience.com/) models by the Zygote Media Group are used as a basis for the anatomical models of skin, muscles, intestine, ligament, bone, blood vessels and nerves. Whilst these models are of high quality and suitable for general visualization and rendering purposes, the level of anatomical detail present does not accurately reflect the anatomy of the inguinal region: the inguinal canal is not present, while the spermatic cord is in a position that bears little resemblance to where it is expected through normal growth and development. We have undertaken the careful modification and extension of the 3DScience models to correctly reflect this anatomy in close collaboration with surgeons. Modification of the 3D models and generation of additional models has been carried out using the Blender 2.5 software package (http://www.blender.org/).

User interactions

Our implementation plan contains a wide range of different user interactions, such as selection and application of the correct tool, selection from multiple interaction choices (e.g. location of incision), 3D navigation and manipulation and exploring the anatomy.

We have carefully designed the individual interactions to focus on the key elements to be taught to the trainees. For instance, when incising the external oblique muscle, we focus on teaching the trainee where to cut, not how to cut. As a result, rather than cutting freely, we present the user with a series of incision sites, where the user will have to choose the correct location for the incision, thus allowing the system to easily detect and feedback to the user when he/she tries to perform an incision in an erroneous location. Other tasks, such as the mobilization of the spermatic cord, give the user freedom to drag, twist and explore.

The chronological flow of the procedure is controlled using state machines. The purpose of the state machines is both to ensure that the user does not divert from the correct order of execution of the tasks in the procedure, as well as to determine when the different deformation models should be active or paused to minimize computational load. One general state machine governs the overall flow of the tasks in the procedure, while a number of sub-state machines govern the progression between the different interactions in the procedure.

When the execution of all the state machines comes to an end, the procedure has been completed and the user is presented with feedback on her/his performance. A very important aspect of feedback is to highlight any erroneous actions, together with recommendations of how to execute the same action correctly. Examples of wrong actions could be: placing the polypropylene mesh at a wrong angle with respect to the spermatic cord, or attempting to perform the incision in the skin with disregard to anatomical landmarks.

Deformation modelling

The anatomy of the inguinal region differs greatly in its geometric and physical properties. We have put much consideration into choosing deformation models that are well suited to handle the properties, geometry and interaction that are required in our simulation system.

The anatomy to be modelled has very different geometries and properties. As a consequence, various models are required to simulate them. They can be categorized in terms of their geometry as follows:

• Rods -The spermatic cord and, to some extend the hernia sack, are both cylindrical structures • Surfaces -The external oblique is a very thin surface • Volumes -The layer of skin and fat is a thick layered volume • Bundles -The fibrous net in the inguinal canal consists of a chaotic network of fibres attached to the spermatic cord

The CoRdE or Cosserat rod model [START_REF] Spillmann | CoRdE: Cosserat Rod Elements for the Dynamic Simulation of One-Dimensional Elastic Objects[END_REF][START_REF] Spillmann | Cosserat Nets[END_REF] was chosen for the spermatic cord as this model encompasses the geometry of the cord, while supporting the necessary pulling and twisting that the cord is subject to while the surgeon mobilises it and explores its contents. Direct and indirect hernias are also modelled using the CoRdE model. We have explored methods for linking the indirect hernia sack to the spermatic cord. One method investigated is the use of simple springs, but Cosserat elements turned out to be a more feasible method. The Cosserat elements allow the models not only move together, but also bend and twist together.

We extended the CoRdE model to a surface in a similar way to the net described in [START_REF] Spillmann | Cosserat Nets[END_REF] in order to yield the surface models required for the external oblique muscle, and the polypropylene repair mesh. To ensure coherence with the interactions required for the external oblique in our system, we developed a cutting scheme for this Cosserat surface model, which is performed by splitting a control point into two control points and reassigning local elements to ensure no exchange of bending or translational forces between the two points, resulting in the control points coming apart.

Simple individual randomly generated springs were used to simulate the chaotic network of fibres holding the anatomy of the inguinal region in place. Each fibre-spring connects one of the deformation models to the walls of the inguinal canal and holds them in place until the user dissects the fibres.

We chose a spring-based Free-Form Deformation (FFD) model, similar to the dynamic FFD model of SOFA (http://www.sofa-framework.org/), to simulate the deformation and cutting of the skin and the underlying adipose tissue. Cutting is enabled by aligning two spring-based blocks over the incision site, locking the mass points together and letting the user gradually dissolve the locks using a cutting tool.

Results

One of our key goals was to make the virtual environment simple and recognizable to the trainees to ensure that they will be able to intuitively understand and interact with it. To achieve this, we have made our virtual operating theatre a close, but simpler, recreation of a real operating theatre. This involved building 3D models of the necessary tools and equipment in the operating theatre. Our virtual operating theatre and adapted 3D models can be seen in Figure 1. A selection of the various interactions possible is shown in Figure 2. Based on our experiments, a Cosserat rod model of only twenty elements suffices to define the centreline of the spermatic cord and provide a fast and realistic biomechanical deformation. Our initial validation of this model by surgeons has indicated that it performs in a convincing manner. We have mapped a textured cylindrical mesh and animations onto the model, as shown in Figure 3. From the top left: the cord, the cremasteric muscle opened, the hernia partly separated, the hernia separated, the hernia sack opened, the contents of the hernia sack reduced and the hernia sack incised.

The Cosserat surface resulting from our extension of the CoRdE model is highly stable and an abundance of physical parameters allow us to modify the surface to yield the desirable behaviour and configuration. Figure 4 compares the polypropylene mesh and the Cosserat surface subject to gravity. Whilst our method for cutting the Cosserat surfaces described above is limited to splitting control points, it satisfies our needs well, as the correct incision will be predefined, and the emphasis is on choosing the correct incision site from a set of multiple possible locations, rather than performing the actual cut manually.

Discussion and conclusion

This paper presents the design and initial implementation of a virtual reality system for open inguinal hernia repair. Our use of a HTA in the design and implementation phase of the project assures its clinical relevance and authenticity. The subdivision of the surgical tasks in the HTA proved useful in the design phase of our system -not only did the HTA break down a complex operation to simpler tasks and sub-tasks, it also provided the foundation for useful and productive discussions between clinical staff and developers.

We have found the CoRdE model to be a flexible and powerful model. While the per-element computations are relatively heavy, the model requires only very few elements to handle complex and large deformations. At the same time, the quantity of adjustable physical parameters in the model allows us to simulate a wide range of materials with the same model. Our extension of the rod model to a surface model has resulted in a very stable surface. While the cutting scheme in our Cosserat surface can only be performed at control points, it is suitable for our purposes.

Our future work on this system will encompass further validation and the final stages of development, including summative and formative feedback. Validation of the modifications made to the anatomical 3D models is required to ensure that the models correctly reflect the anatomy of the inguinal region. Validation of the interactions, deformation models, and integrated system to evaluate its value as a teaching and learning tool are all planned. Further development of the tasks involved in the procedure is required to ensure the natural and correct flow of the procedure.

The ultimate aim of this work is to assist trainees progression through the learning curve and, as a result, improve patient safety, the quality of future surgeons, while relieving some of the pressure on senior consultants.

Figure 1 .

 1 Figure 1.To the left, the initial view of the virtual operating theatre. To the right, the 3D anatomical models, including muscle, vessels, ligaments, bone and facia.

Figure 2 .

 2 Figure 2. Clockwise from top left: The untreated patient, betadine applied, drape applied, incision in the fat, retraction of the fat, incision in the external oblique, lifting the external oblique with clips, grabbing the spermatic cord.

Figure 3 .

 3 Figure 3. The Cosserat rod based spermatic cord and attached hernia.From the top left: the cord, the cremasteric muscle opened, the hernia partly separated, the hernia separated, the hernia sack opened, the contents of the hernia sack reduced and the hernia sack incised.

Figure 4 .

 4 Figure 4. To the left the polypropylene mesh, to the right the un-textured Cosserat surface under gravitational pull. The spheres in the Cosserat surface represents control points, while the grid and lines represents bending elements.

Corresponding Author: Fernando Bello, f.bello@imperial.ac.uk

Acknowledgement

This research is funded by the London Deanery (http://www.londondeanery.ac.uk/).


Alain Astier

Marie-Geneviève Porquet

First observation of high-spin states in 214 Po: Probing the valence space above 208 Pb

Keywords: numbers: 25.70.Hi, 27.80.+w, 23.20.-g, 21.60.Gx

Excited states in 214 Po have been populated using the 18 O + 208 Pb reaction at 85 MeV beam energy and studied with the Euroball IV γ-multidetector array. The level scheme has been built up to ∼ 2.7 MeV excitation energy and spin I = 12 from the triple γ coincidence data. Spin and parity values of most of the observed states have been assigned from the γ-angular properties. The configurations of the yrast states are discussed using results of empirical shell-model calculations and by analogy with the neighbouring nuclei. The 214 Po level scheme established in this work constitutes an important step for the determination of the effective nucleon-nucleon interactions beyond N = 126.

I. INTRODUCTION

The knowledge of the excited levels of nuclei lying north-east of 208 Pb remains fragmentary since most of these nuclei with Z > 82 and N > 126 cannot be populated via the standard reactions because of the lack of suitable stable projectile-target combinations. In many cases, one can only rely on decay studies (α and/or β) which unfortunately give access to a very restricted range of spin values. Such a situation prevents us to follow the behaviours along whole isotopic or isotonic series, while it is so fruitful for the identification of the involved configurations. This is for instance the case for the study of the filling of the νg 9/2 orbital which is expected to play the major role in 211-220 Po. Whereas the highspin states of 210,212 Po isotopes could be investigated by fusion-evaporation reactions [START_REF]ENSDF data base[END_REF] and the states up to 8 + of 216,218 Po by the β-decay of Bi isotopes [START_REF] Kurpeta | [END_REF]3], there was, up to now, no candidate for the medium-spin states of 214 Po. Because of the low spin of the parent 214 Bi (I π = 1 -), the spin values of the observed states in 214 Po are mainly 0, 1 or 2 [START_REF]ENSDF data base[END_REF]. The synthesis of this nucleus, with 2 protons and 4 neutrons above the heaviest stable nucleus, is not an easy task since such a transfer of 6 nucleons is a very peculiar exit channel of reactions induced by heavy ions, having likely a very low cross section.

We have performed a very detailed identification of all the nuclides produced in the 18 O+ 208 Pb reaction at 85 MeV thanks to their gamma decays, the great sensitivity and high efficiency of the Euroball IV germanium array being decisive for that purpose. In addition to the ∼150 fission fragments, which were the main objective of the experiment [4], as well as the 222-224 Th isotopes corresponding to the expected fusion-evaporation reaction, we have found γ-ray cascades emitted by several trans-lead nuclei produced by various transfer reactions.

Our results on 212 Po have been recently published [5,6]. In the present paper, we report on high-spin excited states in 214 Po, which are identified for the first time. In addition to the usual analysis of the high-fold coincidences to build the level scheme, the angular distributions and anisotropy ratios of γ-rays have been mea-sured to assign the spin values. Moreover the existence of isomeric states has been looked for from the Ge detector timing information. The yrast states of 214 Po which have been obtained up to I π = 12 + are discussed using an empirical shell-model approach.

II. EXPERIMENTAL METHODS AND DATA ANALYSIS

We have used the 18 O+ 208 Pb reaction, the 18 O beam with an energy of 85 MeV being provided by the Vivitron tandem of IReS (Strasbourg). A 100 mg/cm 2 selfsupporting target of 208 Pb was employed, which was thick enough to stop the recoiling nuclei. It is worth noting that due to this large thickness, the 18 O beam was stopped in the Pb target too, and therefore the incident energy covered a large range of values, above and below the Coulomb barrier. The de-exciting γ-rays were recorded with the EUROBALL IV array consisting of 71 Compton-suppressed Ge detectors [7] (15 cluster germanium detectors placed in the backward hemisphere with respect to the beam, 26 clover germanium detectors located around 90 • , 30 tapered single-crystal germanium detectors located at forward angles). Each cluster detector is composed of seven closely packed large-volume Ge crystals [8] and each clover detector consists of four smaller Ge crystals [9]. The 239 Ge crystals of the Euroball array could be grouped into 13 rings, with the following angles with respect to the beam axis, 15.5 Events were recorded on tape when at least 3 unsuppressed Ge detectors fired in prompt coincidence. In this way, a set of ∼ 4 × 10 9 three-and higher-fold events were available for subsequent analysis, but only a small part of these data corresponds to 214 Po events. Indeed the main objective of the experiment was actually the study of the fusion-fission channel which leads to the production of the high-spin states of ∼ 150 fragments, mainly located on the neutron-rich side of the valley of stability [4]. The 214 Po study became itself a goal when it turned out that its main γ lines were strong enough in our data set to be identified and precisely analyzed. The production of 214 Po in the 18 O+ 208 Pb reaction comes from a channel which likely involves two steps, the breakup of the 18 O projectile and the fusion of the light partner and the target. From our data set, we have estimated that the cross section of this channel is 0.5-1 mb.

Various procedures have been used for the offline analysis in order to fully characterize the excited levels of 214 Po (excitation energy, spin and parity values). Both multi-gated spectra and three-dimensional 'cubes' have been built and analyzed with the Radware package [10], starting from the first transition deexciting the 2 + state [START_REF]ENSDF data base[END_REF] in order to identify the new transitions and to build the level scheme.

The angular distributions of the γ-rays with respect to the beam axis have been analyzed to determine their multipole orders. In order to characterize the transitions having too weak intensity to be analyzed in that way, their anisotropies have been determined using the intensities measured at two angles relative to the beam axis, R ADO =I γ (39.3 • )/ I γ (76.6 • ), these two angles being the average angle of the tapered and cluster detectors in the one hand, and the average angle of the clover detectors in the other hand, when taking into account the symmetry of the distribution around 90 • .

The timing information from the germanium detectors have been used to measure the half-life of the 8 + yrast state. The procedures were checked using the delayed coincidences of isomeric states of various nuclei produced in this experiment, as described in ref. [11].

III. EXPERIMENTAL RESULTS

The study of the β -decay of 214 Bi goes back to the early days of nuclear physics. This remained the sole source of information for 214 Po, since their excited levels have not reached by any nuclear reaction to date [START_REF]ENSDF data base[END_REF]. Because of the low spin of the parent 214 Bi (I π = 1 -), the spin values of the observed states are mainly 0, 1 or 2. The second excited state at 1015 keV was assigned a most probable I π of 4 + from the directional correlation coefficients for the 406-609 keV cascade [12], while the gamma intensity imbalance found for this level led to logf t = 9.6 ± 0.1, which is strongly at variance with the value expected for a third forbidden transition (logf t ∼ 18).

In order to identify the unkown transitions depopulating the yrast states of 214 Po, we have first looked into spectra gated by the K α1 X-rays 1 of Po. The spectrum 1 Low-energy transitions, such as the X-rays of Po, are clearly of γ-rays in coincidence with two K α1 X-rays of Po displays, in addition to the strong transitions emitted by 212 Po [5,6], the 2 + → 0 + transition of 214 Po (609 keV). We have then analyzed the spectrum in double coincidence with this transition and the K α1 X-ray of Po (see Fig. 1(a)). Three transitions of 244, 324, and 405 keV are clearly observed and assigned to 214 Po. We have then analyzed all the spectra in double coincidence with them (see, as examples, the spectra displayed in Figs. 1(b) and 1(c)), as well as many spectra in triple coincidence with the newly identified γ-rays. It is worth noting that some of the double-gated spectra display contaminants, as ∼ 150 nuclei are produced at high spin in the fusionfission reaction 18 O+ 208 Pb [4], that gives several thousands of γ-lines close in energy. In particular, two strong transitions of 109 Rh (324 and 242 keV) produce many contaminant lines in the spectrum of Fig. 1(c): They are emitted either by 109 Rh or by its complementary fragments, 110-111-112 Rh (see refs. [13,14]).

The level scheme built from all the analysed coincidence relationships is shown in Fig. 2. A 671 keV line is observed in our work since we used a very low threshold for triggering the CFD discriminator of each Ge channel. This was allowed by the VXI electronic cards of the Euroball array. For that purpose, the lower thresholds of the 239 channels were carefully checked at the beginning of the data acquisition. clearly seen in the spectrum gated by the two first yrast transitions (609 keV and 405 keV). Nevertheless, in the absence of any other confirmation of its origin, it is not firmly attributed to 214 Po.

In order to determine the spin values of the 214 Po states, we have firstly analyzed the angular distributions of the four most intense transitions. The results, displayed in Fig. 3, indicate that the 405, 324 and 244 keV transitions are quadrupole transitions with ∆I = 2, such as the 609 keV one (2 + → 0 + ), already known. Thus the yrast cascade of 214 Po is newly identified up to spin 8 + , at 1583 keV. The location of the 4 + state at 1014 keV is then fully confirmed, in agreement with the suggestion of ref. [12], the feature of the logf t value mentioned above likely comes from the incompleteness of the βdecay scheme of 214 Bi. It is worth recalling that the intensity imbalance of the 1015-keV 4 + state was only 0.094(19) per 100 β-decays [START_REF]ENSDF data base[END_REF].

We have gathered in Table II all the properties of the transitions assigned to 214 Po from this work. In particular, the third column gives the R ADO values which allow us to determine the spin values of most of the states lying above 1.6 MeV.

The 240 keV transition is located jut above the 8 + yrast state (see Fig. 2). Without any experimental result on its multipole order at hand, we could assume that it is the next ∆I = 2 transition, leading to the 10 + 1 state at 1823 keV. The actual result is more complex, as the R ADO value of the 240 keV transition is slightly less than 1.0 (see Table II) and not around 1.3, the value of the ∆I = 2 transitions, such as the 244 keV transition which depopulates the 8 + yrast state. The contrasting behaviour of the 240 keV and 244 keV transitions is clearly demonstrated in Fig. 4, the intensity ratio of these two transitions is not the same in the two spectra registered at different detection angles, θ mean = 39.3 • (tapered and cluster detectors) and θ mean = 76.6 • (clover detectors) respectively. A weak anisotropy, such as that displayed by the 240 keV transition, is foreseen when a transition is of mixed multipole type (dipole + quadrupole), for particular values of the mixing ratio, the transition being either stretched, ∆I = 1, or non-stretched, ∆I = 0.

To go further, we have extracted the internal conversion electron coefficients of some transitions of 214 Po by analyzing the relative intensities of transitions in cascade. The intensity imbalances of the 244 keV and the 240 keV γ-rays measured in spectra in double coincidence with at least one transition located above them in the level scheme lead to α tot (244 keV)=0.25(5) and α tot (240 keV)=0.7 [START_REF]ENSDF data base[END_REF]. While the first value is in good agreement with the theoretical value for E2 multipolarity [15], the second one implies that the 240 keV transi-tion is strongly mixed, 65(15)% M1 + 35(15)% E2.

Using the theoretical coefficients of angular distribution of gamma rays from aligned nuclei [16], we have computed the parameters of such a strongly mixed transition assuming either ∆I = 1 or ∆I = 0, and taking into account the two possible signs of the mixing ratio. A weak anisotropy is obtained when the transition is nonstretched, with a negative mixing ratio. Thus the spin value of the 1823 keV level is unambiguously assigned,

I π = 8 + .
Noteworthy is the fact that the large value of the internal conversion electron coefficient of the 240 keV transition is confirmed by the loss in intensity of its γ line in the spectra when gated by the X-rays of Po. A first example is given in Fig. 1, the intensity of the 240 keV line is weaker in Fig. 1(a) than in Fig. 1(b), as compared to the intensity of the 244 keV line. A second example is shown in Fig. 5, the 240 keV line is stronger than the 357 keV one in the spectrum gated by the 554 keV and the 405 keV transitions (see Fig. 5 a behaviour corroborates the method of γ-ray identification by means of the K α1 X-ray of Po, used in the present work.

The spin and parity values of the levels lying above the 1583 keV and 1823 keV states have been chosen according to the R ADO values of the involved γ-rays (see Table II). Aside from a few levels with odd spin values, the yrast structure comprises two states with I π = 10 + and two states with

I π = 12 + .
The timing information from the germanium detectors have been used to look for isomeric states in the 10-300 ns range. The time distributions between the γ-ray emissions of all the yrast states have been systematically analyzed. Typical spectra are shown in Fig. 6, they are compared with the case of prompt coincidences (curve filled in gray) measured for the 4 + yrast state of 212 Po, obtained in the same work [5,6]. In Fig. 6(a), the green spectrum is the time distribution between the emission of the 324 keV γ-ray and that of either the 405 keV or the 609 keV γ-rays, while the red spectrum is the time distribution between the emission of the 244 keV γ-ray and that of either the 324 keV or the 405 keV or the 609 keV γ-rays. They show that the decays of the 4 + and 6 + states are prompt. In Fig. 6(b), Fig. 6(c), and Fig. 6(d), the blue spectra are the time distributions between the emission of the 240 keV, 554 keV, and 449 keV transitions, respectively, and that of one transition located below the 1583 keV state. They establish that the half-life of the 8 + 1 state is 13(1) ns. Then the value of the B(E2) reduced transition probability of the 244 keV transition is 41(3) e 2 f m 2 , i.e. 0.54(4) W.u., taking into account the theoretical value of its internal conversion coefficient (α tot (E2)=0.24). This result will be discussed in the next section.

It is noteworthy that none of the γ-ray of 214 Po measured in the present work exhibits Doppler shift or broadening, meaning that none of the observed states have lifetimes shorter than 1 ps. This is at variance with the 212 Po results obtained in the same experiment [5,6]. Nevertheless it cannot be excluded that states decaying by very enhanced E1 transitions also occur in 214 Po, but being much less populated than the yrast states, their identification would need much more statistics than that obtained in the present work.

IV. DISCUSSION

With two protons and four neutrons more than the doubly-magic 208 Pb, 214 Po would display a low-lying structure coming from the excitations of a few singleparticle states in the mean field of the core, i.e. πh 9/2 and πf 7/2 on the one hand, νg 9/2 and νi 11/2 on the other hand. Using the experimental results of the neighbouring nuclei and assuming that the various configurations do not mix, we easily get the energies of some unperturbed states in 214 Po, as shown in Fig. 7 using different symbols:

• Eigtheen states are expected from the (νg 9/2 ) 4 configuration: One seniority-0 state (0 + ), four seniority-1 states (2 + , 4 + , 6 + , 8 + ) and thirteen seniority-2 states (up to 12 + ). Their relative energies are computed using the energies of the (νg 9/2 ) 2 multiplet (known in 210 Pb [START_REF]ENSDF data base[END_REF]) and the coefficients of fractional parentage (CFP), assuming that the shell-model Hamiltonian contains at most twobody interactions (see for instance ref. [START_REF] Talmi | Simple Models of Complex Nuclei[END_REF]). The energies of the yrast states are drawn with the red full circles (among the seniority-2 states, we have only reported those with the highest spin values, 8 + , 9 + , 10 + , and 12 + ).

• The two-neutron configuration, (νg 9/2 ) 1 (νi 11/2 ) 1 , gives rise to a multiplet with I π = 1 + to 10 + . The 8 + and 10 + states are known in 210 Pb (see the stars in magenta).

• The energies of the 2 + , 4 + , 6 + , and 8 + states from the two-proton configuration (πh 9/2 ) 2 come from 210 Po [START_REF]ENSDF data base[END_REF] (see the blue filled diamonds).

• The two-proton configuration, (πh 9/2 ) 1 (πf 7/2 ) 1 , gives rise to a multiplet with I π = 1 + to 8 + . The 8 + state is known in 210 Po (see the violet filled square).

Then we compare the experimentally observed states of 214 Po (Fig. 2) to the results given in Fig. 7. As for the yrast states up to 8 + , the involved configurations are certainly more complex than (νg 9/2 ) 4 , since the measured 4 + , 6 + , and 8 + states are not so close in energy. It is worth recalling that the first yrast states of 212 Pb have been identified [START_REF]ENSDF data base[END_REF] and the level spectrum (see the right part of Fig. 7) is in good agreement with the prediction of the (νg 9/2 ) 4 work. As for the higher spin states, the breaking of two-nucleon pairs being not fully considered in the computation leading to Fig. 7, several other 10 + and 12 + states are foreseen, such as from the (νg 9/2 ) 3 (νi 11/2 ) 1 and (νg 9/2 ) 2 (πh 9/2 ) 2 configurations. In summary, the structure of the high spin states of 214 Po identified in this work likely involve the breaking of one and two pairs of nucleons in the four orbits above the magic gaps, πh 9/2 and πf 7/2 , νg 9/2 and νi 11/2 . It would be instructive to compare our experimental results to shell-model (SM) calculations using realistic effective interactions. This is discussed below.

In this second part of the discussion, we compare the first excited states of 214 Po to the ones of the neighbouring isotopes. Fortunately the spin value of the β-decaying state of 216,218 Bi is high, > 6 [START_REF]ENSDF data base[END_REF] (the one of 214 Bi is 1 -, as said above). The study of these decays [START_REF] Kurpeta | [END_REF]3] gave the first results on the medium-spin states of 216,218 Po, with I π up to 8 + . The evolution of these levels in the 210-218 Po isotopes and in 210 Pb is shown in the bottom part of Fig. 8, the energies of the 8 + 1 states being adjusted to a constant value in order to enhance the typical pattern of states due to a two-nucleon configuration, if any. The yrast states of the three isotopes 214,216,218 Po have quasi-constant relative energies, showing that their configurations do bear strong resemblance. According to the SM calculations based on the Kuo-Herling interaction, performed in ref. [3], the sequence of the 4 + 1 , 6 + 1 , and 8 + 1 states of 218 Po should be very compressed (as those of 210 Po), at variance with the experimental results. This calls for a review of the realistic effective interactions to improve the predictions in this mass region. The first levels of 212 Po do not follow the trend of the heavier isotopes, even though the distance in energy between the 0 + and the 8 + states is almost the same. It is worth recalling that 'α+ 208 Pb' cluster structures have been recently found in 212 Po, which coexist (and eventually mix) with single-particle excitations [6]. Such mixings are likely responsible of the large variation of the level energies shown in the bottom part of Fig. 8.

To go further and to have a deeper insight into the wave functions of the yrast states of heavy Po isotopes, we use the values of the reduced transition probabilities, particularly these of B(E2; 8 + 1 → 6 + 1 ) which have been measured in four cases (see the top part of Fig. 8). As expected, the value of 210 Po is above that of 210 Pb, owing to their different excitation processes, π 2 versus ν 2 . The large value measured in 212 Po can be explained by the 'α+ 208 Pb' cluster content of the wave functions [6]. As regards 214 Pb, it is worth pointing out that the B(E2; 8 + → 6 + ) value measured in the present work (0.54(4) W.u.) is of the same order of magnitude than the one of 210 Pb, with the ν 2 configuration. Thus a one-neutron-pair breaking is likely the main excitation process of the 8 + 1 state in the heavy Po isotopes. Such an assumption could be checked by measuring the half-life of the 8 + 1 state of 216,218 Po. Taking into account the energies of the E2 decaying transition (223 keV and 263 keV, respectively) and their conversion coefficient, and assuming B(E2; 8 + → 6 + )= 0.5 W.u., we expect T 1/2 (8 + 1 ) = 20 ns and 10 ns respectively. At least, the measurement of the first one could be easily performed using the timing information from germanium detectors.

V. SUMMARY AND CONCLUSIONS

High spin states of 214 Po up to 12 + have been identified for the first time. This neutron-rich isotope has been produced in the 18 O+ 208 Pb reaction, the γ-rays being detected using the Euroball IV γ-multidetector array. Spin and parity values of most of the observed states have been assigned from the γ-angular distributions and DCO ratios. An isomeric state which decays by an E2 transition has been established at spin 8 + . The configurations of the yrast states have been discussed using results of empirical shell-model calculations. Moreover, the first four excited states measured in 214 Po have been found very similar to those known in 216,218 Po , showing that it does not matter whether the number of neutrons beyond the N = 126 magic number is 4, 6 or 8. On the other hand, because of the influence of the 'α+ 208 Pb' cluster, 212 Po has a peculiar behaviour and its states should not be used to better characterize the two-body effective interactions at work in this mass region. A rather large amount of experimental data is now available in the major shell quadrant to the "north-east" of 208 Pb. They would deserve to be used in order to improve the SM predictions in the mass region between the doubly-magic 208 Pb core and the well-deformed actinides.

FIG. 1 :

 1 FIG. 1: Spectra of γ-rays in double coincidence with (a) the first transition of 214 Po (609 keV) and the Kα1 X-ray of Po, (b) the 405 keV and 324 keV transitions, and (c) the 324 keV and 244 keV transitions. The lines, marked with a star, are contaminants due to several Rh isotopes (see text).

FIG. 4 :

 4 FIG. 4: Low energy part of the γ-ray spectra showing the yrast transitions of 214 Po detected at a mean angle of 39.3 • by the tapered and cluster detectors (a) and at a mean angle of 76.6 • by the clover detectors (b).

FIG. 5 :

 5 FIG. 5: Spectra of γ-rays in double coincidence with (a) the 554 keV and 405 keV transitions, (b) the 554 keV transition and the Kα1 X-ray of Po.

FIG. 6 :

 6 FIG. 6: (color online) Time distributions between the emissions of γ-rays of 214 Po showing either prompt coincidences -curves in red and green, panel (a)-or delayed ones corresponding to the decay of the 1583 keV state -curves in blue, panels (b), (c), and (d)-, they are compared with an example of γ-rays of 212 Po in prompt coincidences, shown with the curve filled in gray (see text).

  • (5 crystals), 34.6 • (10), 52.3 • (15), 72.2 • (26), 80.9 • (26), 99.1 • (26), 107.5 • (26), 122.6 • (10), 130.5 • (30), 138.7 • (25), 148.1 • (15), 155.9 • (15), and 163.5 • (10), i.e. 3 rings forward, 4 rings close to 90 • and 6 rings backward with respect to the beam axis.

TABLE I :

 I Angular distribution coefficient (a2) and multipole order of the most intense γ-rays of 214 Po. The number in parenthesis is the error in the last digit.

	Eγ	a2 a	multipole order spin sequence
	609.0 +0.34(5) ∆I=2 quadrupole 2 + → 0 +
	405.4 +0.25(5) ∆I=2 quadrupole 4 + → 2 +
	324.4 +0.3(1)	∆I=2 quadrupole 6 + → 4 +
	244.1 +0.30(15) ∆I=2 quadrupole 8 + → 6 +
	a

TABLE II :

 II γ-ray transition energies (Eγ), relative γ intensities (Iγ), angular distribution ratios (RADO), and level and spin assignments for the 214 Po nucleus. Intensities measured in this experiment (i.e. with the requirement that a minimum of three unsuppressed Ge detectors fired in prompt coincidence) are normalized to the value of the transition populating the 2 +

	Eγ a	Iγ b c	RADO	Ei	E f	I π i	I π f
	(keV)			(keV) (keV)
	239.6	15(2)	0.95(5) 1822.5 1582.9 8 + 8 +
	244.1	44(5)	1.31(7) 1582.9 1338.8 8 + 6 +
	250.2 2.0(8)		1589.0 1338.8		6 +
	292.4 1.2(6)		2669.3 2376.9		10 +
	324.4	70(5)	1.30(8) 1338.8 1014.4 6 + 4 +
	333.0 2.0(8)		2604.5 2271.5		9
	356.8	4(1)	1.3(3)	2733.8 2376.9 12 + 10 +
	398.0 1.8(6)		1736.8 1338.8
	405.4	100	1.26(8) 1014.4 609.0 4 + 2 +
	433.2 2.5(10)	1.2(2)	2611.9 2178.7 12 + 10 +
	449.0 7.4(12) 0.76(11) 2271.5 1822.5 9	8 +
	503.5	3(1)		1842.3 1338.8
	554.5 8.5(13) 1.34(17) 2376.9 1822.5 10 + 8 +
	574.4 3.8(11)	0.8(2)	2157.3 1582.9 9	8 +
	595.8	11(1)	1.32(15) 2178.7 1582.9 10 + 8 +
	609.0	-	1.24(8)	609.0	0.0	2 + 0 +
	642.9 3.7(11)	0.6(2)	1981.7 1338.8 7	6 +
	670.5 3.8(12)		1684.9 1014.4		4 +
	a Uncertainties in transition energies are typically between 0.1 and
	0.5 keV.

b 1 state, Iγ (405.4 keV) = 100. c

The number in parenthesis is the error in the last digit.

  configuration. Since at least four 8 + states are expected close in energy in 214 Po, this could explain why two 8 + states are populated in the yrast decay studied in the present FIG.7:(color online) Energies for expected states in214 Po, (i) from the (νg 9/2 ) 4 configuration calculated using empirical shell model (red full circles), (ii) from the (νg 9/2 ) 1 (νi 11/2 ) 1 configuration measured in 210 Pb (stars in magenta), (iii) from the (πh 9/2 ) 2 configuration measured in 210 Po (blue filled diamonds), (iv) from the (πh 9/2 ) 1 (πf 7/2 ) 1 configuration measured in 210 Po (violet filled square). The experimental states of 212 Pb are shown for comparison (red empty circles).

		2500
						12 +
		2000	10 1 (πf 7/2 ) (πh 9/2 )	+	8 + 10 + 9 +	8	+
							10 +
	Excitation energy (keV)	1000 1500	8 + 6 + 4 + 2 +			2 + 4 + 6 + 8 + (νg 9/2 ) 1 (νi 11/2 ) 1	2 + 4 + 6 + 8 +
		500
		0	0 +			0 +	0 +
			(πh 9/2 ) 2	(νg 9/2 )	4	212	Pb

1

  Evolution of the first energy levels in the even Po isotopes, 210-218 Po, and in 210 Pb. The energies of the 8 + 1 states are adjusted to a constant value (see text). Top: Experimental values of the reduced transition probabilities B(E2; 8 + → 6 + ) for 210 Pb, 210 Po, and 212,214 Po. Data are taken from refs. [1-3, 5, 6] and this work.

	B(E2; 8 -> 6) (W.u.)	ν 2	π	2	π 2 ν 2 +α	(π 2 )ν

4

FIG.

8

: (color online) Bottom:

Acknowledgments

The Euroball project was a collaboration between France, the United Kingdom, Germany, Italy, Denmark and Sweden. We are very indebted to our colleagues involved in the EB-02/17 experiment devoted to the fission fragments, in which the present data on 214 Po were recorded. We thank the crews of the Vivitron, as well as M.-A. Saettle for preparing the Pb target, P. Bednarczyk, J. Devin, J.-M. Gallone, P. Médina and D. Vintache for their help during the experiment.