102.

1. INTRODUCTION ln France there are 27,639 water supply facilities serving the population. On this total 931 are serving over 10,000 inhabitants corresponding to a total of 36.2 million of persons.

For these 931 units available data related to water quality are more numerous than for small facilities. For example the yearly frequency of the analyses varies from 0.5 to 4, for 500 inhabitants, to 144-720 for 300,000 inhabitants and over according to the parameters. Table 1 provides general information conceming the qualtity of drinkable water. If we consider supply facilities exceeding frequently the norms we can see that about 9% of the French population is served by a water of poor quality from a microbiological point of view and 2.8% by a water having more than 50 mg of nitrates per liter. If we now consider water quality of the 200 main French lakes (artificial and natural lakes) half are suffering of eutrophication. About 80% of the reservoirs used for public water supplies have also an excess of nutrient salts. Eutrophication is also observed in coastal waters. Lakes and reservoirs are affected by phosphorus originating mainly from municipal sources, then from agriculture, while problems in marine waters are primarly attributed to nitrate from agriculture. For example in the Bay of Brest it is estimated that 80% of the influx of nutrient salts originate from agriculture. At the national level the contribution of agriculture to nitrogen pollution is about two-thirds (Etat de L 'environnement, 1993).

Even if minerai emissions from agriculture also concern phosphorous and heavy metals, nitrate concentration in groundwater and surface water have received more attention in France. This emphasis is mainly due to the EC Directive relating to the quality of water { DL( Because arable land refers to land under temporary crops, temporary meadows for mowing or pasture and land temporarily fallow or Iying idle the impact of CAP reform is not c1ear. The total which was about 17 million of ha during the 1970s and the 1980 is now over 18 million. The high cereal priee support leaded to plough up pastures since the seventies.

Between 1970 and 1990 total permanent grassland decreased by 2.5 million and this decrease was greater between 1990 and 1994 (more than 1 million). The transformation of meadows and pastures used permanently, in arable land, and the intensification induced by high priees, leaded to a steady increase in the use of nitrogen, phosphates and potash (figure 1). This period is also characterised by the large-scale use of pesticides. In France, total pesticide use increased from 25,000 to 1 million tonnes in the 1971-1981 period.

Cereal cropping and water contamination

Cereals are mainly grown in regions characterized by water supply facilities using aquifers. There are few reliable long-terrn records of nitrate concentration, one such record does exist for a catchment located in the Paris area (la petite Traconne) for which data ara available since 1928. There is a high correlation between nitrate concentration and the use of minerai fertilizer (figure 2). Otherwise, there is a close relationship between cereal production and the consumption of commercial fertilizers. So there is a c1ear evidence that the increase in nitrate concentration in groundwater is partly due to the dramatic growth of cereal production.

(Ob

Intensive livestock rearing and water contamination

The development of intensive livestock rearing and its concentration in particular regions has created another important source of nitrogen pollution: that from animal wastes, The main part of organic nitrogen is deposited directly on grassland by grazing animais, and poses a lesser problem than high concentrations of organic nitrogen found where there is a high animal density due to intensive Iivestock rearing, namely pig production and poultry. In France, Brittany is the region where intensive animal husband.ry is the most important. In 1994, pig production in Brittany represented 51,2 % of French pig production. This proportion is lower for poultry where total chickens, turkeys and guinea fowls represented 30.4 % of the French total. For eggs this proportion is 28.6 %. Total agricultural output for Brittany represents 12 % of total French agricultural output, although the used agricultural area accounts for only 5 % of the corresponding French total. The comparison between 10 f. these Iwo figures (12 % of the .output and 5 % of thearea) gives an indication of environmental problems in Brittany.

Due to its geological features, Brittany has few aquifers, tertiary basins being the only exception. Water catches underground represent sorne 20 per-cent of total drinking water available, or 164,000 m3 per day from 450 boreholes. The 668,000 m3 of surface water per day from 108 draw-off points, are drawn directly from water courses or from larger or smaller reservoirs. In rural areas underground water accounts for a higher proportion. The quality of these water catchments is very poor, especially in areas where intensive animal rearing is combined with market gardening. For example, in the Finistère (which is one of the four "Dèpartements" of Brittany) 20 % of water catchments are over 100 mgll of nitrates.

Because of the importance of surface water to provide drinkable water and the intensification of agriculture, Brittany has one of the worst situation in France. For surface water a third of water supply facilities are exceeding occasionnally 50 mgll of nitrates. If physical constraints concerning the volume of water needed for fish and qualitative constraints concerning the evolution of the nitrate concentration are taken into account there will be a shortage by 2005 ; this will reach 22%.

OTHER ISSUES

Little information conceming other minerai emissions from agriculture is available.

Nevertheless we try to present here some data about problems caused by phosphates, heavy metals and ammonia.

Phosphates

As indicated in figure 1 the consumption of phosphate fertilizers in France has been decreasing since the beginning of the seventies. But phosphate is also supplied by organic manure. A phosphate balance estimated by difference belween the phosphate from manure production and from purchased phosphate fertilizer on the one hand, and phosphate uptake by crops on the other hand, shows a surplus reaching 65 kg at the national level. But in Brittany, where manure production is large, this surplus is 84 kg whereas in Limousin, with a low livestock density, this surplus-is only 30 kg [START_REF] Brouwer | Mineral balances at farm level in the European Union[END_REF]. The nitrogen balance at the national level indicates a 73 kg surplus but this surplus reaches 133 kg for Brittany and 10 kg for Limousin. ln fact the balance belween the supply and the removal of phosphorus by crops must be analyzed in relation with the accumulation of nutrients in the soil. Results conceming about 240,000 soil samples are available but not yet published. These analyses are related to acid soils using the Dyer method.. and to basic soils using the Joret-Hebert method. Table 4 gives genereal information conceming phosphorus contents in French acid soils. Table 4 shows that 14.0 % of the samples analysed in acid regions have a deficiency in phosphorus (Iess than 100 mg/kg), whereas the same percentage has an excess of phosphorus (more than 500 mg/kg). Moreover 21.5 % of the samples need more phosphorus (samples having contents between 100 and 200 mg/kg). The results for basic soils are more or less similar. From a geographical point of view the regions having the most important amounts of phosphorus are Brittany and Nord-Pas-de-Calais. The regions with a deficiency of phosphorus are Limousin and Meuse. Actually the regional average hides a wide diversity e.g. in Brittany, where there is a global excess, a quarter of the samples are characterised by a deficiency. The last information available is related to the dissolved concentration of total phosphorus in the main French rivers (table 5). The large difference in phosphorus amounts in the Seine compared to the other rivers, can be attributed to the domestic discharges, since treatment plants are not sophisticated enough to remove phosphorus.

Heavy metals

The concept of soil contamination by heavy metals is complex, so is that of soil pollution. But two ideas are underlying these concepts: (i) the increasing releases of heavy metals arising fro the economic activity, (ii) human health hazards through contamination of the food chain, and impacts on ecosystems. Less is known about heavy metal contamination in French soils. However 381 samples have been gathered coming from various types of soils. There are also results from a survey conceming the soil quality with data fram Lorraine, Bretagne, Nord-Pas-de-Calais and Aquitaine. A general overview of the French situation is given in table 6.

Results in table 6 are presented according to the content of clay in soils and with -maximum, minimum and median amounts of trace elements. To a large extent a good relationship exists between particle size and total amounts of heavy metals. This relationship is better for median and maximum values than for minimum contents. The sandy and silty horizons are the poorest, but for c1ayey horizon and horizon with over 35 % clay there is sorne uncertainty. This is due to the influence of the geological substratum. Median contents of trace elements are never excessing the AFNOR norrn except for Ni in very clayey soils.

The maximum contents are exceeding the norrn in many cases.

To be c1early demonstrated, the raie of agriculture in soil contamination needs a comparison between the superficial horizons and deeper horizons.

Ammonia emissions

The major component of increased acidification of the environment is sulfur from lignite-fired installations. But in Western Europe the contribution of nitrogen oxides, released by trafflc and power generation, is more important. In countries where agriculture remains an important activity there are emissions of N 2 0 from the decomposition of organic matter. This lI1 natural nitrogen oxid is non reactive in the lower atmosphere but contributes to global warming. In fact, ammonia from intensive cattle breeding represents "the most important contribution of agriculture to air pollution in France. Because of the winds acid depositions do not affect severely France.

Various authors have estimated the total ammonia emissions for the European countries including animal waste, minerai fertilizers and fertilizer processing plants. For

France the figures quoted by [START_REF] Moal | Volatilisation de l'azote ammoniacal des lisiers après épandage[END_REF] Precise results obtained during field studies exist for Brittany [START_REF] Moal | Volatilisation de l'azote ammoniacal des lisiers après épandage[END_REF]. Results

demonstrate the important variability of ammonia emissions, since after two days, 5 to 75% of the ammoniaca"I-N applied were observed after spreading. Half the experiments show ammonia 1055 over 30 % of the ammoniacal -N applied. NH 3 emissions are correiated to the temperature (soil and air temperature), to the slurry dry matter content, and at a lesser extent, to the slurry ammoniacal-N content. The role of temperature explains that NH 3 emissions are twice as important in summer as in winter.

THE FRENCH LEGAL CONTEXT

The legal background to pollution associated with agriculture contains both general and more specifie regulations which are considered successively.

General regulations

ln principle the enactments concerned do not apply to agriculture as such, but affect the ways in which any form of pollution associated with agriculture has to be dealt with. The two broad categories involve town planning and water protection.

b) Water protection

The Water Act of 16th December 1964 relates to the management and distribution of water and to the control of water pollution. This aet ereated the qualitative and quantitative management system for the six major French hydrographie networks through advisory basin eommittes and exeeutive basin agencies whieh are financially independent (The "Agences Financieres de Bassin" ie Water Authorities). Under that act, these agencies determine and define quality targets for watercourses. Quality and f10w problems are viewed economically through a system of charges, pollution discharges are also subject to strict standards.

A key feature of the Water Act of 1964 was the establishment of a system of charges on water pollutants. This new direction in water policy was in line with the polluter-pays principle but it was restrieted to point pollution sources. Charges cover a wide variety of pollutants and they are set through a complex procedure in eaeh Water Authority. Water

Authorities also collect the payment of charges whose revenues are then redistributed to the dischargers through the use of grants, soft loans and rewards for abating pollution. Where at a low level and were gradually raised to current levels. This graduai introduction resulted in a successful and weil accepted policy. Moreover il must emphasized that the French system is self-financing. Otherwise the water authorities, the "Agences Financières de

Bassin", have been charged in Water Agencies ie "Agences de l'eau" which take a more prominent part in water management even if they are less independent.

Specifie regulations

Here we examine specifie regulations conceming c1assified installations and the implementation of the EC Nitrate Directive.

a) Classified installations and intensive rearing

The Act of 19th July 1976 on classified installations for environmental protection, and its implementation orders supercedes the 1917 Act on hazardous establishments which did not coyer intensive rearing activities. An activity coming under this act has to be classified, Le. listed within a given nomenclature. This applies to livestock rearing installations of a certain size. According to size there is a reporting regime, ie, "déclaration" or a permission regime, ie, "autorisation" (table 8). The permission regime is more exigent, since the applicant has to provide an impact assessment giving details of the source, nature and magnitude of any disamenities liable to result from the installation concerned. Disamenities include noise, use and discharge of water, the protection of underground waters, and waste disposaI. b) The EC Nitrate Directive and its implementation Three administrative circulars have been elaborated by the French authorities, March 1992, June 1992 and November 1992 to implement the Nitrate Directive in France. The latter explains how to define the vulnerable areas at the regional level. A task force was set 1Jll up in each "département" to improve coordination and information. The zoning is based on the average level of nitrate concentration during the past year. Waters for which the level of N03 is over 50 mg per litre are automatically considered as polluted waters and consequently the area is classified vulnerable. Waters under 25 mg are supposed safe.

Special attention is paid to intermediate levels of nitrate concentrations. Time-series are set up in order to define any possible trend in an attempt to foresee any possible problem areas.

If the trend indicates in 2005 a level of N03 over 50 mg the aquifer or the river is c1assified as polluted. In the waters where nitrate concentration reaches 40 mg per litre and where time-series data do no exist the pollution is considered as apt to occur in the very near future.

NEW PERSPECTIVES FOR THE POUCY

According to the 1964 Water Act the basin agencies are empowered to levy charges on sources of pollution. The threshold is an equivalent of 200 inhabitants with a charge reduction when measures are taken to limit wastes. Since 1975 there has been a c1ear legal basis to levy charges on non-point sources. In 1982 the water authorities proposed a system of charges per pig according to the number of places available and slurry spreading quality.

However this system never entered into application because farmers unions were against it.

ln June 1991, the French govemment decided to combat against water pollution caused by nitrates from agricultural sources and to introduce a levy on nitric nitrogen. The aim was a progressive introduction of the polluter-pays principle into agriculture as was already the case for other activities. To achieve this purpose a special agreement was concluded between the Ministry of Environment and the Ministry of Agriculture on 11th march 1992. This agreement includes the various European Directives related to water quality and that concerning the protection of waters against pollution caused by nitrates from agricultural sources.

Even if priority is given to preventive means especially advice to farmers (more efficient application of fertilizers by more accurate timing or rates of application and a better use of animal wastes) the place of economic incentives is important. Subsidies are provided to encourage farmers-to reduce their pollution by using methods more compatible with the environment, by the prevention of water pollution by run-off and the leaching of liquids containing livestock manures and effluents from silage, and by the processing of manure.

We will first review research and extension programmes and we will further consider the charge system and the compliance scheme. Committee associates representatives from the agricultural unions, the fertilizer manufacturers, the extension services, the research institutes, the consumers' and environmentalists' unions, the water authorities, local councillors and regional bodies. In parallel the Ministry of Agriculture and the Ministry of Environment created a common bureau with responsabilities for ail the problems concerning nitrates and water in relation to the agricultural industry, the "Mission Eaux-Nitrates". This bureau serves as the bureaucratie arm of CORPEN.

The CORPEN has been made responsible for preparing programmes to improve certain agricultural operations in order to reduce the nitrate leaching and nitrate run-off.

CORPEN promotes research projects on technical issues and those areas which lack precise informations in order to obtain a better understanding and quantification of the N cycle; nitrate movement in soil and water ; the leaching in the root zone; the subsoil and the saturated and unsaturated parts of aquifers. CORPEN provides advice to agriculture through national and local farming press, talks and conferences, demonstrations, exhibitions. This committee has also elaborated codes of good agricultural practice adapted to local conditions leading to 16 specifie operations where bodies involved in the water management, extension services and farmers unions are associated.

Water effluent charges

The extension of the charge system achieves a process originated in the late sixties.

The basic principle to determine the amount of the charge remain the same. At the moment, these charges coyer four susbstances, for livestock farming : suspended solids, oxidisable matters, reduced nitrogen, phosphates. In the future, other substances e.g. heavy metals and some organic toxins would be taken into account. There are three steps in calculating the levy.

(i) Emission in physical units are calculated for each pollutant and each category of livestock (dairy cows, pigs, poultry ...). This is based on industry average since technical coefficients are used to transform number of animais into quantity of polluting substances.

Then monetary coefficients are used to obtain a gross charge per farm. These coefficients are poliutant specifie and do not vary according to the various industries.

lib

(ii) Farms are c1assified according to a number of parameters including manure storage facilities capacity, sitting of the buildings, run-off from buildings, manure spreading scheme and livestock density. This process leads to 9 environmental classes which are based on individual performances. The abatement of polluting emissions is then estimated for each farm. This outcome is converted into monetary terms in order to obtain a premium per farm.

(iii) Net charge is then obtained, this is the difference between gross charge and premium. The charge system and specially the technical coefficients result from negociations between parties and therefore bear the characteristics of a compromise. It must be underlined that net charges does not include either suspended solids or phosphates because a 100 per cent abatement is assumed for these two substances. Farmers will finally have to pay net charge minus a lump sum of FF 4000. This is the monetary equivalent of farmers' rights on the environment.

The charge system was planned to be gradually enforced, with the following calendar:

-for those rearing installations c1assified before 1st January 1991 charges will be paid from the 1st January 1993.

-for those rearing installations classified during 1992 charges will be paid from the 1st January 1994.

-for the whole of animal husbandry and crops the charges will be paid from the 1st January 1995.

For each category subsidies will be given during the year before the levies are charged to help the farmers to meet the standards required. This system was criticised from a theoretical point of view because the regulatory mechanisms to control non-point-source pollutants are more intricate to implement than those concerning point-source pollutants.

There exist differing cost structures for the acquisition of information and there are informational asymmetries between polluters and regulators. From a political point of view french farmers protest against the proposed calendar and also against the principle itself of Ali these elements lead the former government to delay the application of the taxation system. Finally, the biggest farms are entering the scheme in 1995. The process is expected to be achieved within a five-year period. Moreover in order to reduce the effect of the charge system, on farm income, there is a transitory period during which eligible farmers will only support a fraction of total amount. For example, in 1995 eligible farmers will have to pay 40 per cent of the total, in 2 000, 76 per-cent. This process is expected to be achieved in 2 003 when farmers will pay the total amount of the charge.

Compliance scheme

Ali the required information in calculating charges are provided by an environmental audit. This is a compulsory assessment of the farm in terms of its environmental impacts.

The statement is named DEXEL (diagnostic environment de l'exploitation d'élevage i.e.

environmental audit of the Iivestock farm). This statement includes two main sections.

(i) There is a detailed description of polluting emission flows with emphasis on building siting, storage facilities for manure, run-off, leaching and infiltration.

(ii) There is an assessment of agricultural practices whose main outcome is a nitrogen balance both on the plot level and on the farm level. This focuses on the sources of nitrogen surplus.

This statement is used to start a negociation between each eligible farmer and the basin agency. The objective is to achieve individual agreements whose prescriptions deal with the improvement of farm buildings and the promotion of better farming practices.

Investments while are agreed on, will be subsidized from the state, regional authorities and the basin agency. It must be emphasized that, in addition to the section on building improvements, any contract includes precise prescriptions on farming practices. There are financial and technical commitments involving a classification of the farm in a better environmental c1ass leading to a reduction in the charge amount. Thus before contracting with the agency, every eligible farmer has to trade-off between the extra-costs of compliance and the benefits in terms of charge payment.

Table of contents

Introduction

Figure 1 .

 1 Figure 1. Consumption of commercial fertilizers (Nitrogen, Phosphate, Potash) 1970-1992

Figure 2 .

 2 Figure 2. Nitrate concentration in the spring "La petite Traconne" and fertiliser nitrogen use in the region (Seine-et-Marne)

  des nitrates -Bulletin de liaison de la mission eau-nitrates du Ministère de l'Environnement n' 12 Juillet-AoOt 1985• Statistique agricole annuelle (fertiliser consumption)

lOi

  As a result, the French Ministry of Environment detines three types of land use and four levels of concentration. The three types of land use are related to : market gardening, other agricultural uses and non agricultural land use. The four levels of concentration are detined in reference to the maximum concentration in the standard soils. The tirst lever is used to detine the maximum lever of hevay metals beyond which sludge applications are not authorized (AFNOR nom U 44-04). Then there is a second threshold beyond which thorough investigations are necessary. This threshold is equivalent to twice the tirst level. The third threshold, equivalent to 5 times the tirst level, corresponds to remedial actions. The fourth threshold, equivalent to 10 times the tirst level, needs immediate c1ean-up.Even if heavy metal contamination arises fram domestic activities, run-off water and industrial discharges, a large part arises from agriculture mainly through sewage sludge spreading. But phosphate fertilizers also contain heavy metals, mainly cadmium the most dangerous one. Igneous phosphates from South Africa or Russia are very low in cadmium, whereas the Maghreb phosphates imported in France contain 10-70 ppm.. Manure and compost are another source of trace elements. Conceming manure, copper, zinc and cadmium are introduced in feeding stuffs to improve sow fertility and pig fattening.

a)

  Environmental protection and town planningThe main environmental problems caused by agriculture are due to the installation of intensive rearing plants. Environmental protection in the broad sense, including landscape and the incompatibility between productive activities and residential areas is considered as a problem for land use which cornes under town planning law. The land use plan (POS : Plan d'Occupation des Sols) sets out general rules for land use within communes and allows for specialisation of activities upon the local territory. The main categories are : urban sites and future urban sites, areas of natural beauty, agrieultural land, sensitive areas and areas of special interest from an eeological or aesthetie point of view. Intensive rearing installations may be located on agrieultural land or in sensitive areas when there is no special environmental problem. Other more specifie provisions apply, partieularly the "département" health regulations.

  eontrolling and monitoring are feasible at low eosts, charges are based on individual performance. Otherwise they are based on industry average. This applies to firms and to households and commercial enterprises as weil on which a sewage tax is levied. The Water Act of 3rd January 1992 is a more comprehensive act which proposes a balanced management of total water resources. The aim is the protection of the aquatic ecosystems and wetlands, the protection of the quality of surface waters and groundwaters, and a better use of water from an economic point of view. To aehieve this balanced management new watershed management schemes were set up.These Iwo acts provide the basis for regulations applying to any use of water and to ail types of discharge, direct and indirect of any type of material Iiable to cause -Qr increase water deterioration by modifying the physical, chemical, biological, bacteriological characteristics of any water. Any water means surface water, underground water and sea water within the limits of French territorial waters. In fact, the 1992 Water Act which provides more severe civil and criminal penalties has not yet been completely enforced since ail the previous ordinances have not yet been signed. Nevertheless the charge system has ln provided a significant source of water quality control. This mechanism has helped promote more efficient operation of treatment plants and invest in clean technology. Charges started

5. 1 .

 1 Research and extension Since 1984 the French Govemment has set out the Standing Committee for the Study of Nitrate Pollution (Comité d'Orientation pour la Réduction de la Pollution des Eaux par les Nitrates et les phosphates provenant des activités agricoles Le. CORPEN). This

  taxation. The farmers'unions argue that agriculture is a special case because of the particular circumstances of the farming economy, of agricultural pollution, and of agricultural policy. Concerning the levies on intensive animal rearing pig producers argue that the tax is unfair because minerai fertilisers are not taxed. From an economic point of view the large increase in European pig production has caused priees of pork to fall sharply from around 117-150 ECU/100 kg in the summer of 1992 to 125 ECU by mid-october before sinking to around 100 ECU in April 1993. Given the continuing increase in pig production foreseen in the EC, there seems to be Iittle prospect of prices increasing over the coming months. So their financial position has deteriorated and they refuse to accept any extra cost.

Table 1 .

 1 Drinkable water quality in water supply facilities serving over 10 000 inhabitants(data referto 1989 or 1990 or 1991)

		Supply facililies meeting the	Supply facililies exceeding the norms occasionnally
			norms
	Parameters			occasionnally		frequently
		number	million of persons	number	million of persons	number	million of
			served		served		persons served
	Microbiology	708	26.4	114	6.4	lOg	3.4
	Nitrates	842	32.3	65	3.4	24	0.5
	Iron	866	34.1	27	1.1	38	1.0
	Aluminium	892	35.0	4	0.2	35	1.0
	Fluor	920	36.0	0	0	11	0.2
	Turbidity	844	30.6	19	3.3	68	2.3

Source: IFEN, 1994 : L'environnement en France p. 20.

Table 2 .

 2 Evolution of arable land and permanent grassland (1,000 ha).

		1960	1965	1970	1975	1980	1990	1994
	arable land	19007	18267	17047	17 012	17221	17969	18316
	1 grassland	13062	13459	13934	13403	12884	11406	10361

Table 3

 3 The supplies where nitrate concentration exceeded 50 mg tend to be located in rural areas where intensive agriculture is dominant. This suggests that there has been an improvement in the quality of the water distributed. In fact, this improvement does not correspond to a decrease in nitrate concentration in raw water but is rather due to the blending of high nitrate supplies with low nitrate sources, the use of water of new aquifers, or the treating of water by chemical or biological way to remove nitrates. It is c1early demonstrated by the increase of the number of water supply facilities in which nitrate concentration exceeds 50 mg/l once a year.

the situation in 1980 is compared to the situation in 1988 and 1993 with the distribution of inhabitants according•to the quality of drinkingwater supplied (mean annual nitrate concentration). There was a decrease in the number of persons exposed to high nitrate concentrations.

Table 3 .

 3 Water Supply Facilities (WSF) and population served with a nitrate concentration over 50 mgll

			1981		1988		1993
		WSF	population	WSF	population	WSF	population
	average concentration over 50 mg!1	584	1 160000	707	860000	689	720000
	exceeding 50 mgll once a year	1 010	2180000	1074	1700000	1308	5100 000

Source: Eaux destinées à la consommation humaine-Ministére des Affaires Sociales-Direction Générale de la

Santé-Déc 1993

Table 4 .

 4 Distribution of acid soils according to the amount of prosphorus

		< 100 mgJkg	100 to 200 mgJkg	200 to 500 mgJkg	> 500 mgJkg
	%	14.0%	21.5%	50.4 %	14.9%
	Source: Walter personal communication.

Table 5 .

 5 Total phosphorus in the main French rivers (orthophosphate concentrations in mg pli)

		Loire	Seine	Garonne	Rhône
	1980	0.07	0.76	0.09	0.18
	1985	0.04	1.01	0.09	0.17
	1987	0.07	0.71	0.07	0.13
	Source: Eurostat -Statistiques de l'environnement 1991 .

Table 7

 7

displays such a situation on a polder in the region of Mont Saint-Michel, at the border between Norrnandy and Brittany. The comparison in table 7 between 41-69 cm and 69-76 cm horizons and the top soil indicates a cadmium contamination (0.90 mg/kg) in the top soil and 0.02 in the eiq deepest horizon due to the agriculture.

110

Table 6 .

 6 Trace elements in French soilsin mg/kg (g/100 9 for Fe) Maximum; minimum and median

	Trace elemenls	Cu	Co	Cr	Cd	Pb	Zn	Ni	Fe	Mn
	Type ofsoil
		Max	32.1	11.1	35.9	0.48	64.9	49	11.4	1.70	201
	Sandy	Mn	0.2	0	0.3	0.02	2.2	0	0.1	0.29	37
		Median	3.2	1.3	13.5	0.03	13.1	17	3.8	0.60	152
		Mu	71.0	18.0	104.0	0.90	152.0	115	53.2	3.11	1331
	Silly	Mn	2.1	0.8	14.0	0.01	10.0	16	2.1	0.64	50
		Median	6.3	5.7	36.3	0.08	22.8	35	11.1	1.28	393
		Max	56.6	107.0	221.0	1.20	578.0	436	198.0	6.11	5833
	Average Mn	3.9	2.8	24.0	0.01	8.2	23	5.1	1.53	69
		Median	11.6	12.9	58.0	0.10	26.9	56	24.8	2.48	507
		Mu	99.0	148.0	362.0	3.70	1560.0	3820	476.0	10.70	23440
	Clayey	Mn	3.5	1.6	38.3	0.01	13.1	31	14.4	1.83	38
		Median	13.3	16.5	76.2	0.17	35.2	88	36.1	3.55	924
		Mu	51.2	143.0	456.0	4.30	264.0	1999	478.0	12.15	24975
	Very	Min	3.2	3.2	62.9	0.01	13.0	42	12.1	2.45	41
		Median	16.7	17.3	99.4	0.19	37.9	128	55.1	5.47	861
	AFNOR		100,0	30.0	150.0	2.00	100.0	300	50.0
	nom NF
	U 44-041
	Source: Baize, 1994.

Table 7 .

 7 Trace elements in the polder of Beauvoir (Mont Saint-Michel) (market gardening)

	Trace	Cu	Zn	Cr	N	Co	Pb	Cd	Clay(%)
	elemenls
	Horizons
	0-33 cm	7.5	26	21.5	6.0	2.2	15.2	0.90	13.9
	33-41 cm	3.8	20	17.4	5.2	1.8	11.4	0.57	6.6
	41.Q9 cm	4.6	18	15.5	4.3	1.5	16.1	0.09	4.5
	69-76 cm	2.8	14	13.5	3.4	1.3	8.7	0.02	1.0
	Source: Baize, 1994.

Table 8 .

 8 Legal regime for classified livestock rearing installations according to species and size

	Reporting regime	Permission regime

II

Sorne comments

The new policy implemented in the livestock sector relies on the same basic principles which has steered water policy for three decades. Enforcing charges on polluting emissions from livestock farms is a straighforward application of the polluter-pays principle.

This could give farmers a good incentive to reduce emissions. But in contrast with other industries there is a huge number of farmers so establishing environmental audits and agreing on individual contracts are potentially very costly for the public budget.

Administrative and transaction costs could represent a significant proportion of total expenditures. Moreover control and monetary issues did receive Iittle attention. Future development of the policy will depend on future compromises between public authorities and farmer representatives. The present balance between farmers and public interest benefits farmers but things could change in response to different polilical and environmental pressures. The crucial issue will be the benefits (market and non-market) of this programme for society. A great attention will be devoted to the evolution of nitrate content of freshswater and of eutrophication of coastal waters. These are the key parameters for the general public.


B Maisonneuve

Y Bellec

S Souche

& H Lot

New resistance against downy mildew and lettuce mosaic potyvirus in wild Lactuca spp

Keywords: serriola, L. saligna, L. virosa, LMV, Bremia lactucae, resistance genes, genetics of resistance, accumulation of genes

New European isolates of B. lactucae and of LMV are able to overcome the disease resistance genes used in commercial varieties. Wild Lactuca spp. constitute a large pool for new genes. Several new resistance genes against European B. lactucae isolates were identified in wild Lactuca species and introduced in L. sativa lines. The resistance from two L. virosa accessions was efficient against every isolate. The results suggested at least 2 dominant genes in each accession controlled the resistance (2 independent in one accession, two tightly linked in the other one). A complete stable resistance was observed in artificial tests with absence of spores. Therefore, this resistance was assumed to be comparable to Dm gene. The spectra of resistance of lines derived from two L. saligna were similar with resistance from cv. Ninja. This mechanism seems more complex than Dm gene with apparition of late and sparse sporulation on many plants in some segregating populations. This late sporulation was also observed in some commercial varieties and other INRA resistant lines derived from L. serriola.

In a large collection of different Lactuca spp., one L. virosa (PIVT1398), was identified as resistant to different European LMV isolates overcoming mo1 1 or mo1 2 genes. A study of L. virosa segregating F 2 population suggested one major dominant gene for this resistance. Mo3 was proposed to designate this gene. Its expression in heterozygous plant was variable with different isolates. Its expression was consistent with a dominant gene against LMV-0, but incomplete dominant gene against LMV-13 (necrotic phenotype). The introgression of this gene in L. sativa is in progress despite several difficulties.

An accumulation in one genotype of several resistance genes against each disease could be a strategy to increase the durability of these new genes.

Introduction

Lettuce is an important vegetable crop for fresh market. For consumer, the leaves must be exempt of disease symptoms and of pesticide residues. Among the most important diseases, downy mildew (Bremia lactucae Regel) and lettuce mosaic potyvirus (LMV) are constant risks for this crop. For both diseases, resistance genes have been introduced in cultivars since 30 to 40 years [START_REF] Bannerot | Etude de lhérédité de la tolérance au virus de la mosaïque de la laitue chez la variété Gallega de Invierno[END_REF][START_REF] Crute | The role of resistance breeding in the integrated control of downy mildew (Bremia lactucae) in protected lettuce[END_REF][START_REF] Ryder | Inheritance of resistance to common lettuce mosaic[END_REF]. Nevertheless, several isolates identified in Europe can overcome the Dm and mo resistance genes used in commercial varieties.

For B. lactucae, several genes efficient against NL16 isolate were overcome in the last few years, e.g. resistance from Samourai (RZ), Ninja (S&G) or Bacarès (Vilmorin) (presented in a communication at this meeting). Likewise, European virus isolates can overcome the LMV tolerance conferred by mo1 1 and mo1 2 [START_REF] Pink | Novel pathotypes of lettuce mosaic virus breakdown of a durable resistance?[END_REF]. Therefore, we are looking in wild Lactuca spp. for new sources of resistance to both diseases.

Several genes from L. serriola have been introduced into some cultivars (e.g. several Dm genes; [START_REF] Crute | The role of resistance breeding in the integrated control of downy mildew (Bremia lactucae) in protected lettuce[END_REF]) because the two species can be easily crossed. The use of L. saligna and L. virosa has been more restricted; however, some resistance genes from L. saligna have been introduced into L. sativa [START_REF] Netzer | Lactuca saligna L. a new source of resistance to downy mildew (Bremia lactucae Reg.)[END_REF][START_REF] Provvidenti | A source of resistance to a strain of cucumber mosaic virus in Lactuca saligna[END_REF]. A possible method for overcoming the crossability barrier with L. saligna and L. virosa was achieved by in vitro rescue of immature hybrid embryos [START_REF] Maisonneuve | Utilisation de la culture in vitro dembryons immatures pour les croisements interspecifiques entre Lactuca sativa L. et L. saligna L. ou L. virosa L.; étude des hybrides obtenus[END_REF].

Investigations of new sources of resistance to B. lactucae in L. serriola, L. saligna and L. virosa have been in progress at INRA for several years. Some resistance efficient to NL16 have been introgressed into L. sativa and we are controlling their efficiency against new European isolates.

For LMV, we have recently screened a large collection of Lactuca with virulent isolates. One accession of L. virosa appeared interesting, consequently a program to study this resistance and introgress it into L. sativa has been investigated.

Material and methods

Plant material

Two morphologically different accessions of L. saligna (CR16 and CR17) received from I. Crute (NVRS, Wellesbourne) and two accessions of L. virosa collected by INRA (LS238 and LS241) were used for B. lactucae resistance studies. The interspecific crosses with L. saligna and the BC 1 [(L. sativa x L. virosa) x L. sativa] were made by in vitro culture of immature embryo [START_REF] Maisonneuve | Utilisation de la culture in vitro dembryons immatures pour les croisements interspecifiques entre Lactuca sativa L. et L. saligna L. ou L. virosa L.; étude des hybrides obtenus[END_REF]. The progenies obtained at INRA from 3 L. serriola resistant to NL16 were also tested with new European isolates. Lines derived from these interspecific crosses by backcrosses with several L. sativa (e.g. cv. Girelle, cv. Ravel) or crosses between interspecific progenies; and then selfpollination were generated. Evaluation of this resistance and its inheritance study were made on this material issued from four to seven cross generations before selfing; the genetic background could be considered as L. sativa one.

In contrast, the research on LMV resistance was achieved in wild species. In preliminary experiments, 116 L. sativa genotypes were screened for resistance to virulent LMV-E isolates. Because no interesting resistance was found, then 115 wild Lactuca accessions were screened. The most interesting accession, L. virosa (PIVT1398) received from CPRO (Wageningen, NL), was extensively studied for its LMV resistance. The study was made on L. virosa material: F 1 between susceptible L. virosa (PIVT280) and resistant PIVT1398 and derived F 2 and F 3 families.

Tests for resistance to B. lactucae

European isolates has been used in this study, NL16 and isolates overcoming NL16 resistant varieties. The new isolates SAR1, SAR3 and I3 attacking respectively Ninja, Samourai and Bacarès, were supplied by Novartis Seeds (France); 49/83, overcoming previously Mariska resistance [START_REF] Maisonneuve | Rapid mapping of two genes for resistance to downy mildew from Lactuca serriola to existing clusters of resistance genes[END_REF], was supplied by A. Lebeda. Lettuces were tested at seedling stage in closed plastic boxes with soil substratum. After sowing, the lettuce seeds were incubated at 6 °C for 24 h to 48 h to overcome seed dormancy; and then the boxes were transferred to a growth chamber for 3 weeks (16/12 °C day/night tempera-tures, 16 h per day). Isolates were multiplied on susceptible cultivar seedlings cultivated on filter paper moistened with a nutrient solution. Seven day-old seedlings were inoculated by spraying a spore suspension (2 x 10 5 spores/ml). Seven and 14 days after inoculation, presence or absence of asexual sporulation were scored.

Tests for LMV resistance

European isolates were used in this study, the common isolate (LMV-0) and some isolates identified on some tolerant varieties: LMV-E, LMV-1, LMV-13 (3). The inoculum was an extract from 2-3 week-old infected lettuce plants (cv. Trocadero for LMV-0 or cv. Mantilia for other isolates). One gram of infected leaf tissue was grinded in 4 ml buffer containing 100 mg/ml of activated charcoal and carborundum. Young plants were mechanically inoculated once or twice (day 0 and 2). Plants were maintained in a growth chamber (22 °C /12 to16 °C day/night temperatures, 16 h per day) for LMV-0 and LMV-E. Experiments using the other strains (LMV-1 and LMV-13) were conducted at Montfavet with plants in an insect-proof greenhouse. Symptom observation as well as DAS-ELISA (Double Antibody Sandwich-ELISA) was used to evaluate the plant resistance. One gram of leaf tissue was collected from different young leaves, grinded with a roller press in 4 ml of PBS-Tween-PVP buffer and tested by DAS-ELISA using polyclonal antibodies.

Results and discussion

New sources of resistance to B. lactucae

Seven sources of resistance to B. lactucae, previously identified against NL16 and 49/83, were tested against new European isolates in comparison with new resistance of commercial varieties (Table 1). Four out of these 7 lines were resistant to every isolate (two L. serriola and the both L. virosa). As expected, TTE, genitor of one of the resistance used by Vilmorin, was overcome by I3. Isolate SAR3, identified on Ninja, attacked the both L. saligna.

Observation of plants with sparse and late sporulation was made in several lines and varieties in our test conditions; this late sporulation was scored especially in interaction I3/R18, but also with different isolates on R38 and R36 resistance factors as well as on our lines derived from L. saligna, and sometimes on TTE and FHD.

In segregating population with resistance from CR16 or CR17, this phenotype with late and weak sporulation was screened 14 days after inoculation (dpi), and then increased the percentage of susceptible plants. For example, in F 2 (SaBV x Girelle) the ratio resistant to susceptible plants at 7 dpi (120 to 33 with NL16 and 110 to 42 with 49/83) was consistent with one dominant gene (? 2 = 0.96 and 0.56 respectively). But at 14 dpi, some sporulation was scored on more than 50% of plants (51 res to 92 susc with NL16 and 66 res to 83 susc with 49/83). In experiment with weaker inoculation (2 x 10 3 sp/ ml), the ratio at 14 dpi fitted with 3 : 1 in some segregating populations. These results suggested that the mechanism of resistance in these both L. saligna CR16 and CR17 as observed previously in other L. saligna (4) was different from the Dm gene mechanism. A difference of susceptibility between SaBV and SaAB observed with SAR2, isolate supplied by Novartis (results not shown), suggested that the both resistant factors must be different. In contrast, the interaction between B. lactucae and our progenies from L. virosa was similar with reaction of Dm genes. At 7dpi, a strong sporulation was observed on susceptible plants and often the same segregation was scored at 7 and 14 dpi. Segregating populations with these resistance were scored after inoculation with 4 isolates (Table 2). The results suggested that two tightly linked dominant genes in ViBK and two independant genes in ViCQ and one dominant gene in ViCP controlled the resistance.

Mariska R18 R + + R R * Samourai R + + R * Argelès R38 R * nd R * R + Bacarès R R R * R + Ninja R36 R R R + R * Angie Nd R R R + R INRA lines Resistance from L. serriola F 7 YYD LS102 (R17) R R R R R F 7 FHD LS162 R R R R R F 7 TTE Nd R R R R + Resistance from L. saligna F 6 SaAB CR16 73 R 73 R 27 R 20 + 20 R F 4 SaBV CR17 68 R 72 R 27 R 20 + 20 R Resistance from L. virosa F 6 ViAE LS241 197 R 340 R 349 R 410 R 143 R F 4 ViCQ LS238 250 R 357 R 383 R 413 R 219 R a R
The complete resistance of ViBK (315 tested plants) and ViCQ (170 tested plants) after inoculation with I3, what is Avr7, was an indication of the transfer into these genotypes of Dm7 from the different cultivars used in this cross. The segregation for resistance to I3 scored in ViCP (ratio 350 res to 71 susc) suggested that the gene from LS238 present in ViCP could be linked to Dm7. Complementary tests on larger populations would be necessary to confirm these hypothesis. These loci could be designated R39 to R42 if there is no allelic gene between LS238 and LS241. Allelism tests are in progress.

New resistance to LMV

In a collection of 116 L. sativa, 76 L. serriola, 11 L. saligna, 22 L. virosa and 6 other Lactuca spp. tested with LMV-E only few accessions did not show severe symptoms. These resistant genotypes were tested with LMV-0, LMV-1 and LMV-13. Only one L. virosa and some plants from L. perennis showed interesting resistance to the four isolates.

The resistance of the L. perennis must be fixed before any program of protoplast fusion in order to transfer it into L. sativa that could be a very laborious work [START_REF] Maisonneuve | Sexual and somatic hybridization in the genus Lactuca[END_REF]. Therefore, we initiated a study of the resistant L. virosa (PIVT1398). An immunity was observed with the different isolates (no virus detectable in ELISA in systemic but also in infected leaves). Because of the very low fertility of the interspecific crosses with L. virosa (hybrid sterile, very low fertility of the BC 1 ), the research on inheritance was initiated in segregating population derived of a cross between two L. virosa (PIVT280), a susceptible one (high virus multiplication) and PIVT1398. The F 1 and F 2 generation were inoculated with LMV-0 and LMV-13 (Table 3).

After inoculation with LMV-0, the results were consistent with one dominant gene. This hypothesis was confirmed by the study of F 3 families derived from F 2 tested plants, because the progenies of all susceptible F 2 plants were homogeneous for susceptibility and the progenies of resistant F 2 plants were resistant or in segregation (data not shown). The results after inoculation with LMV-13 was different. Indeed, the expression of resistance in the heterozygous plants was sometimes irregular with often a necrotic phenotype. The same expression was observed after inoculation with LMV-E (data not shown). The results suggested an hypothesis of one incomplete dominant gene with these virulent isolates; we designated this locus Mo3.

In our strong test conditions (mechanical inoculation, often twice on young plant), some PIVT1398 susceptible plants were identified (2 out 30 plants inoculated with LMV-13 in greenhouse, 0 out of 114 plants inoculated with LMV-0 in growth chamber). A control of the virus multiplied in these plants revealed a LMV variant able to systemically infect PIVT1398. When these variants were inoculated to susceptible lettuce (cv. Trocadéro), they can lose their ability to overcome Mo3. According to the possibility of variant of LMV, for a good evaluation of Mo3 in segregating population, the susceptibility of the plants must be checked by studying of the multiplied virus in back-inoculation on PIVT1398. A test of F 3 lines were made to know whether the same gene confers the resistance to LMV-0 and to LMV-13. The 13 lines fixed susceptible to LMV-0 (11 to 74 tested plants) were susceptible to LMV-13 (5 to 28 plants tested) and the 11 lines fixed resistant to LMV-0 (34 to 88 tested plants) were resistant to LMV-13 (13 to 33 tested plants). However, in three resistant F 3 lines, one or two susceptible plants were identified; but a control of the virus revealed a variant of the isolate. These results suggested the same gene controlled the resistance to the both isolates. For this reason, it is possible to inoculate the plants with the common isolate (LMV-0) in breeding program in order to score Mo3; that is less hazardous for environment than to use a virulent isolate, especially LMV-13 that it could be seed born.

The introgression of Mo3 into L. sativa were initiated [START_REF] Maisonneuve | Sexual and somatic hybridization in the genus Lactuca[END_REF] but it is a very laborious work due to the high mortality and to the low fertility of progeny maintained after several generations of BC with L. sativa.

Conclusions

Some new resistance genes were identified in L. virosa. Their introgression into L. sativa is more or less difficult with respect to the wild resistant accession. These resistance seem due to one or two dominant major genes in each accession that could be easy to use in breeding programs. For B. lactucae resistance, some other genes were identified in other species easier to cross with lettuce (L. serriola and L. saligna). But the expression of these genes with some partial resistance makes them not easy to screen and need very standardized conditions for the artificial test.

The main problem for disease resistance is the durability of the efficiency of the gene. For the both diseases, we were able in our test conditions to obtain variant of isolate that overcome some resistance (isolates of B. lactucae overcoming L. saligna resistance and variant of LMV overcoming Mo3). The durability of these resistance in natural conditions is not known. In absence of other resistance efficient against the new European isolates of these both diseases, we will continue these programs with complementary genetic studies as in one hand allelism tests between B. lactucae resistance, in the other hand the introgression of Mo3 in diversified cultivars. A strategy to increase the durability of the resistance could be the accumulation of the resistance genes in one genotype especially if mechanisms are different: for example, resistance against B. lactucae from L. saligna with genes from L. virosa or Mo3 with one allele of mo1 locus. Consequently, it will be important to identified some PCR based molecular markers of these genes; it is in progress for Mo3.

Table 1 .

 1 Interaction of NL16 resistant genotypes with European isolates of B. lactucae

	Variety/line	R factor a	Isolates of B. lactucae
		or source NL16	49/83	SAR1	SAR3	I3
		of resistance
	Commercial varieties b

Table 2 .

 2 Segregation of resistance in populations derived from crosses between resistant L. virosa and susceptible cultivars inoculated with 4 isolates of B. lactucae

factor proposed by IBEB (presented at this meeting); b test on 10 to 50 plants per variety; interactions were scored as R for no sporulation, score R * for a sparse and late sporulation on only few plants of resistant variety; score * for mixed reaction (5R, 7*, 3+); score + for profuse sporulation on all plants.

Table 3 .

 3 Resistance to different LMV isolates in segregating population of L. virosa

		LMV		Number of plants		? 2
	Genotypes	isolates	susceptible intermediate	resistant	1:2:1 or 1:3
	F 1 (PIVT1398 x PIVT280)
		LMV-13	0	10	0
	F 1 (PIVT280 x PIVT1398)
		LMV-13	3	8	7
		LMV-0	0	0	16
	F 2 (PIVT280 x PIVT1398)
		LMV-13	17	28	13	1.14
		LMV-0	26	4	56	1.25
	Inoculation of plants cultivated in a growth chamber for LMV-0 or in a greenhouse for
	LMV-13 and then assay by DAS-ELISA. OD of susceptible plants were similar with
	inoculated PIVT280, the OD of resistant plant similar with inoculated PIVT1398 and
	not inoculated plants. The intermediate score corresponded to necrotic plants and/or
	plants with low virus multiplication

Acknowledgements

We are grateful to E. Martin, F. Dauphin and M. Duteil for technical assistance with resistance tests. We wish to acknowledge the financial support to INRA provided previously by Societe Vilmorin for the generation of lines with B. lactucae resistance from L. serriola and by both Societies, Vilmorin and Tezier, for the study of LMV resistance from PIVT1398. The studies on LMV resistance of L. virosa were supported by AIP-INRA grant 4/4920 in 95-96.


est destinée au dépôt

  Influence des profils verticaux d'humidité et de température sur l'émission micro-onde d'un sol nu : conséquence sur l'estimation de la teneur en eau du sol S. Raju To cite this version: S. Raju. Influence des profils verticaux d'humidité et de température sur l'émission micro-onde d'un sol nu : conséquence sur l'estimation de la teneur en eau du sol. Life Sciences [q-bio]. Université Paris Diderot -Paris 7, 1997. English. NNT : . tel-02840796


Ludovic Pricoupenko

Resonant scattering of ultracold atoms in low dimensions

Keywords: numbers: 03.65.Ge, 03.65.Nk, 03.75.Ss, 05.30.Jp, 32.80.Pj, 34.10.+x, 34.50.-s

Low energy scattering amplitudes for two atoms in one-and two-dimensional atomic wave guides are derived for short range isotropic and resonant interactions in high partial wave channels. Taking into account the finite width of the resonance which was neglected in previous works is shown to have important implications in the properties of the confinement induced resonances. For spin polarized fermions in quasi-1D wave guides it imposes a strong constraint on the atomic density for achieving the Fermi Tonks Girardeau gas. For a planar wave guide, the charateristics of the 2D induced scattering resonances in p-and d-wave are determined as a function of the 3D scattering parameters and of the wave guide frequency.

Recent experimental progress in degenerate atomic gases make possible accurate studies of quasi-one (1D) [1,2,3,4,5,6] and quasi-two dimensionnal (2D) [6,7,8] configurations. These systems are interesting in view of future applications involving coherent manipulation of matter waves and can be used also for studying generic phenomenona in low dimensions [1,8]. One major interest of atomic gases is the precise knowledge and experimental control of the low energy interatomic collisions: the effective two-body interaction can be tuned with a Feshbach resonance [9] by applying an external magnetic field and/or with a Confined Induced Resonance (CIR) by varying the extension of the trap in the tight transverse direction [10,11,12]. These techniques open possibilities for achieving new types of strongly correlated quantum systems. For example, thanks to s-wave collisional properties in quasi-1D wave guides [10], it has been possible to observe the so-called Tonks Girardeau (TG) gas [13] where 1D hard-core bosons can be mapped onto a system of non interacting fermions [3,4]. For quasi-1D spin polarized fermions an analogous regime: the Fermionic Tonks Girardeau (FTG) gas is subject to intensive studies [14,15,16]. In this case, as a consequence of the Pauli exclusion principle, atoms interact predominantly in the p-wave channel and it has been predicted that the strongly interacting 1D polarized Fermi gas can be mapped onto a non interacting Bose gas.

In this letter, it is shown that the finite width of the high partial waves resonances is an essential feature in the properties of the corresponding CIR. As a consequence, the resonant fully polarized Fermi atomic gas in quasi-1D traps can reach the FTG regime in a very dilute limit only (which means that for realistic trap parameters, only few particles systems can undergo this regime) and is more generally described by a narrow BEC-BCS crossover. Violation of the fermion-boson mapping theorem [17] opens relevant issues on the quasi-1D resonant polarized Fermi gas such as the equation of state and the shift and damping of the collective modes which are only known at the FTG limit [16]. Motivated by the exciting predictions of exotic superfluid phases [18,19] with non-Abelian statisitics, the p-wave scattering amplitude in quasi-2D atomic wave guide induced by a resonant interaction is derived. The effective range parameter which were neglected in Ref. [20] appears essential for the determination of the 2D low energy scattering parameters. Due to the possibility of achieving d-wave resonances [21] in 3D systems, the quasi-2D d-wave scattering amplitude is also derived and the characteristics of this new CIR are depicted.

In the following, the true interatomic forces are supposed to be short range and isotropic. Moreover they are considered in the neighborhood of a resonance. The 3D low energy collisional properties of two atoms are then parameterized in each partial wave (l ≥ 0) by the following phase shift δ l (q):

q 2l+1 cot δ l (q) = - 1 w l -α l q 2 + O(q 4 ), (1)
in Eq.(1) q is the relative momentum of the two colliding atoms, and the resonant regime in the l-partial wave is achieved for |w l | ≫ R 2l+1 , where R is the characteristic radius of the pairwise potential (w 0 is the usual scattering length and w 1 is the scattering volume). The effective range parameter α l is linked to the width of the resonance: a large (small) value of α l R 2l-1 corresponds to a narrow (relatively broad) resonance. In the neighborhood of the resonance and for l ≥ 1, it has been shown recently that for a finite range potential [22,23,24]:

α l R 2l-1 (2l -3)!!(2l -1)!! . (2)
Thus α l |w l | ≫ R 2 , and -2 /(2µα l w l ) is a low energy scale (µ is the reduced mass) which is for large and positive values of w l , nothing but the shallow bound state energy (and the quasi-bound state energy for large and negative w l ). Hence, unlike s-wave broad resonances where α 0 ≡ O(R) can be neglected in the low energy limit, for l > 0 the effective range parameter α l which depends on the specific resonance considered, is an essential parameter involved in the low energy properties. In experiments the resonant regime can be achieved by using a Feshbach resonance [9] on the spin degree of freedom. An external magnetic field B modifies the detuning between an open and a closed channel of the two-body system, and in the vicinity of the resonance in the partial wave l where B ∼ B 0 , w -1 l ∝ -(B -B 0 ) while α l is almost constant. Due to the short range character of interatomic forces, we use the so-called zero range approximation. Hence, the pairwise interaction between particles is replaced by a source term of vanishing range ǫ → 0 in the Schrödinger's equation (it is assumed that the characteristic lengths of the trapping potential are ≫ R). Moreover, the trapping potentials considered in this letter are always harmonic, so that the center of mass and relative coordinates are decoupled each from the other. For a binary collision in the center of mass frame at energy E = 2 q 2 /µ, the Schrödinger's equation can be transformed into an integral equation for the wave function |Ψ :

|Ψ = |Ψ 0 + 2π 2 µ l≥0 d 3 k (2π) 3 k l δ ǫ (k) (R l •S l,k ) H 0 -E -i0 + |k , (3)
where H 0 is the free Hamiltonian which includes the external potential, and |Ψ 0 belongs to the kernel of H 0 -E. In Eq.( 3), the source term is introduced in the momentum representation:

δ ǫ (k) = exp(-k 2 ǫ 2 /4)
is the Fourier transform of a normalized Gaussian weight having a vanishing range ǫ [25], R l and S l,k are Symmetric Trace Free (STF) tensors of rank l, and the notation (R l •S l,k ) means a contraction between the two tensors. The tensors S l,k are eigenfunctions of the momentum operator and they appear in a standard multipolar expansion in Cartesians coordinates [22]:

S [αβ... ] l,k = (-1) l k l+1 ∂ kα ∂ k β . . . k -1 /(2l-1)!!,
where {k α } are the Cartesian components of the vector k (α ∈ {x, y, z}). Eq.(3) shows explicitly that the interacting wave function |Ψ is the superposition of a regular solution |Ψ 0 and of an irregular part generated by the source term [START_REF]For relative coordinates r → 0[END_REF]. The correct asymptotic behavior of the wave function (for relative coordinates |r| ≫ R) is obtained by the determination of the tensors R l which fixes the balance between the regular and irregular solutions. For this purpose, contact conditions (for r → 0) are imposed in each partial wave and are such that without external potential the phase shifts in a scattering process coincide exactly with the first two terms in the right hand side of Eq.( 1) [22]. In the momentum representation, the contact conditions can be written as:

Reg ǫ→0 d 3 k (2π) 3 k l k|Ψ S l,k = - l! R l a l (q)(2l + 1)! ! , (4)
where a -1 l (q) = (w -1 l + α l q 2 ). In Eq.( 4), Reg ǫ→0 means the regular part of the integral obtained when the formal range ǫ is set to zero. This way, the source term in Eq.( 3) is itself a functional of |Ψ , and a closed equation for R l is obtained by combination of Eqs. (3,4). In the next parts, the scattering problem for p-or d-wave channels is solved successively in 1D and 2D harmonic wave guides.

Linear atomic wave guide. -Two atoms are confined in a two-dimensional harmonic trap while they move freely along the third direction (z). In the center of mass frame, the non interacting Hamiltonian is:

H 0 = - 2 2µ ∆ r + 1 2 µω 2 ⊥ ρ 2 -ω ⊥ , (5)
where r = z êz + ρ are the relative coordinates. For a scattering process at energy E = 2 q 2 /2µ, the state |Ψ 0 in Eq.( 3) is: k|Ψ 0 = (2π)δ(k z -q) k 2D |φ 00 , where |φ 00 is the ground state of the 2D harmonic oscillator in Eq.( 5), and k = k 2D + k z êz . Hereafter, the system is in the monomode regime (E < 2 ω ⊥ ). At large distances |z| ≫ a ⊥ (where a ⊥ = /µω ⊥ ≫ R), the wave function factorizes as r|Ψ ≃ ρ|φ 00 ψ 1D (z), and for E > 0:

ψ 1D (z) = exp(iqz) + exp(iq|z|) f even + sign(z)f odd .(6)
In this situation, the system which is frozen along the transverse direction, can be considered as quasi-1D. The even (odd) scattering amplitude f even (f odd ) results from the asymptotic contributions (z ≫ a ⊥ ) in the different even (odd) 3D partial waves. Quasi-1D scattering in the s-wave channel has been thoroughly studied [10] and in the following we consider quasi-1D scattering of two spin polarized fermions in the vicinity of a p-wave resonance. Thus, one can restrict the source term in Eq.( 3) to the l = 1 contribution, where S 1,k = k/k, and the choice |Ψ 0 imposes that R 1 = P 1D êz . Computation of P 1D from Eq.( 4) is much simpler in the domain of negative energy E < 0 and using Eq.( 3) one can show that:

P 1D = -3qφ 00 (0) 1 a 1 (q) + 6 √ πa 3 ⊥ P.f. ∞ 0 du u 3/2 exp(τ u) 1 -exp(-u)
. (7) where τ = E/2 ω ⊥ < 0 and P.f. denotes the "partie finie de Hadamard" of the integral [START_REF] Schwartz | Théorie des distributions Paris[END_REF].

Interestingly, one recognizes the Riemann-Hurwitz Zeta function ζ H (-1/2, -τ ) in the regularized integral of Eq.( 7). Hence, by analytic continuation in the domain τ > 0, one obtains a simple expression of the scattering amplitude, and in the low energy limit qa ⊥ ≪ 1:

f odd p = 2iπP 1D φ * 00 (0) ≃ -iq 1 l p + iq + q 2 ξ p -1 , (8)
with the odd-wave scattering length l p and the effective range ξ p given respectively by:

l p = 6a ⊥ a 3 ⊥ w 1 -12 ζ(- 1 2 )
-1

and

ξ p = α 1 a 2 ⊥ 6 . (9)
Expression of l p in Eq.( 9) coincides with the result in Ref. [12], while the effective range ξ p and its physical implications was (up to our knowledge) not studied in previous works. However, ξ p is in general not negligible for all q ≪ a -1 ⊥ and crucially depends on the width of the 3D resonance and on a ⊥ . Indeed, the inequality ξ p ≫ a ⊥ is likely to occur as a consequence of Eq.( 2) (α 1 R 1) and also from the condition a ⊥ ≫ R which is needed from the hypothesis that scattering processes are studied at collisional energies ≪ 2 /µR 2 . The regime ξ p ∼ a ⊥ can be reached only for an extreme transverse confinement (a ⊥ ∼ 10R) and for the broadest p-wave resonances with α 1 R ∼ 1. In actual experiments, two p-wave resonances are used: the resonance for 6 Li atoms (R ≃ 3 nm) at B 0 ≃ 215 G with α 1 R ≃ 5 [START_REF] Frédéric Chevy | [END_REF] and the one at B 0 ≃ 198.8 G for 40 K atoms (R ≃ 7 nm) where α 1 R ≃ 3 [30]. For l p > 0 the scattering amplitude in Eq.( 8) has a pole at q = iκ with κ = (-1 + 1 + 4ξ p /l p )/2ξ p > 0 giving a shallow bound state energy at (-2 κ 2 /2µ). For large and positive values of l p ≫ ξ p , κ = l -1 p and the bound state has a vanishing energy (i.e. ≪ ω ⊥ ) [31]. The scattering amplitude in Eq.( 8) can be obtained from a 1D effective theory where the wave function ψ 1D in Eq.( 6) solves the non interacting Schrödinger equation and satisfies the following contact condition:

lim z→0 + 1 l p + ∂ z -ξ p ∂ 2 z ψ odd 1D (z) = 0, ( 10
)
where

ψ odd 1D (z) = [ψ 1D (z) -ψ 1D (-z)]/2
is the projection of the wave function onto its odd component [START_REF]Eq.(10) can be obtained also by use of a Λ-potential: z|VΛ|φ = -2 lpδ ′ (z) lim ǫ→0 + (Λ + ∂ǫ -ξp∂ 2 ǫ )(ǫ), where Λ is a free parameter[END_REF]. This approach can be generalized for few-and many-body systems by imposing the contact condition in Eq.( 10) for each pair of interacting particles. Without performing these calculations which are clearly beyond the scope of this letter, it is of importance to determine the conditions such that the fully polarized fermionic gas can reach the FTG regime or equivalently can be mapped onto non interacting 1D bosons [14]. Eq. (10) implies that this mapping is possible only at resonance (|l p | = ∞) and also if the effective range is negligible. The resonant condition is easily obtained by using a Feshbach resonance. However, the momentum distribution of the FTG gas has a large tail given by a Lorentzian of width 4n, where n is the 1D atomic density [15], thus ξ p can be neglected only in the dilute limit: nξ p ≪ 1. For N atoms trapped in a strongly anisotropic trap with a weak harmonic confinement along the z-direction (atomic frequency ω z ≪ ω ⊥ and axial length a z = /µω z ≫ a ⊥ ), in the FTG regime one has n ∼ N/a z and the condition nξ p ≪ 1 gives N ≪ 6a z /(α 1 a 2 ⊥ ). For example, considering 40 K atoms in a highly anisotropic trap with ω ⊥ = 2π × 70 kHz and ω z = 2π × 10 Hz, the FTG regime is obtained for N ≪ 14, which makes sense only for fewbody configurations (for 6 Li atoms with the same trap parameters, ξ p is of the order of a z and the mapping to a non interacting Bose system is a poor approximation even for the two-body ground state). Interestingly, if the condition nξ p ≪ 1 is not satisfied, the scale invariance in the linear wave guide is broken at low energy, hence the time-dependent many-body ansatz in Ref. [16] is no more an exact solution. To conclude this part, excepted specific configurations, the criterium nξ p ≪ 1 is in gen-eral not verified and the density corrections to the FTG properties are important issues for understanding the resonant gas. Moreover, following the reasoning of the box model in Refs. [23,34], one expects that by varying l p from large and positive values to large and negative values, the system experiences a narrow p-wave BEC-BCS cross-over, where the composite bosons in the dilute BEC phase (l p > 0) are dimers populating the quasi-1D shallow two-body bound state.

Planar atomic wave guide. -High partial wave superfluidity in quasi-2D geometries is interesting for its links with condensed matter physics like for example high-T c superconductivity and the possible applications for quantum computing [18,19]. These studies motivate a close investigation of quasi-2D scattering properties. In this geometry, the two colliding atoms are confined in a planar harmonic trap along the z-direction and move freely in the (xy) plane. The free Hamiltonian reads:

H 0 = - 2 2µ ∆ r + 1 2 mω 2 z z 2 - ω z 2 . ( 11
)
The homogeneous solution corresponding to a scattering process at energy E = 2 q 2 /2µ is: k|Ψ 0 = (2π) 2 δ(k 2D -q) k z |φ 0 , where |φ 0 is the ground state of the 1D harmonic oscillator in Eq.( 11). In the monomode regime (E < ω z ), the system can be considered as quasi-2D, and for large interparticle separation (ρ ≫ a z ), the wave function factorizes: Ψ(r) = φ 0 (z)ψ 2D (ρ). The 2D partial scattering amplitudes f [m] = f [-m] can be defined by the following expansion:

ψ 2D (ρ) = ρ≫az e (iq.ρ) - i 4 m=∞ m=-∞ f [m]
H (1) m (qρ)e (imθ) , (12) where θ = π/2 + ∠(ρ, q) and H

(1) m

is the Hankel's function.

Using Eqs. (3,4,12) the scattering amplitude for two atoms interacting in the s-wave channel is: [START_REF]The functions Jm(τ ) are defined in the domain τ[END_REF], and B ≃ 0.9049 [36]. In the p-wave channel, Eq.( 2) implies the existence of a small parameter η 1 = (α 1 a z ) -1 ≪ 1 which plays a central role in the scattering properties [37]. For q = qê x , the p-wave regular part in Eq.( 3) is related to the 2D p-wave scattering amplitude f [1] by R 1 = -f [1] (q)ê x /[2πqφ * 0 (0)]. Using the contact condition in Eq.( 4) where S 1,k = k/k gives:

f [0] = 4π[a z √ π/a 0 (q) + J 0 (τ + i0 + )] -1 , with τ = E/2 ω z , J 0 (τ ) = ln(-B/(2πτ )) + ∞ n=1 ln(n/(n - τ ))(2n -1)!!/(2n)!!
f [1] (q) = 6πq 2 |φ 0 (0)| 2 1 a 1 (q) + 6J 1 (τ + i0 + ) √ πa 3 z -1 , (13)
where |φ 0 (0)| 2 = 1/(a z √ π). In the low energy limit |τ | → 0 then J 1 (τ ) = J 1 (0) + τ ln(-eB/2πτ ) + O(τ 2 ), where J 1 (0) ≃ -5.4722 × 10 -2 [START_REF]The functions Jm(τ ) are defined in the domain τ[END_REF], and the logarithmic term ensures the unitarity condition in Eq.( 13). A similar calculation can be done for atoms interacting resonantly in the 3D d-wave channel. In this case, the small parameter related to the resonance width is

η 2 = α -1
2 a -3 z ≪ 1. For q = qê x , the l = 2 regular part is given by: k

2 (R 2 •S 2,k ) = S 2D (2k 2 z -k 2 2D )+ D 2D (k 2 x -k 2 y )
, where S 2D contributes to the m = 0 2D partial wave channel and D 2D contributes to the |m| = 2 channel (2Dd-wave). The scattering amplitude in the |m| = 2 channel is f [2] (q) = -2πq 2 φ * 0 (0)D 2D , and using Eq.( 4):

f [2] (q) = 15πq 4 |φ 0 (0)| 2 2 1 a 2 (q) + 60J 2 (τ + i0 + ) a 5 z √ π -1 , (14)
where J 2 (τ ) = J 2 (0) + τ J 1 (0) + O(τ 2 ) for τ → 0, and J 2 (0) ≃ -2.2752 × 10 -2 [START_REF]The functions Jm(τ ) are defined in the domain τ[END_REF]. From Eqs. (13,14), several conclusions can be drawn on the quasi-2D scattering in m = 1 and m = 2 partial wave channels: i) At small collisional energy (q → 0), f [m] (q) ∝ q 2m /(w -1 m -w ⋆-1 m ) where w ⋆ 1 ≃ 5.39 × a 3 z and w ⋆ 2 ≃ 1.3 × a 5 z . Hence, the 2D confinement induces a shift w ⋆ m in the generalized scattering length w m , which grows as the confinement increases. ii) By modifying the trap frequency and/or the external magnetic field it is possible to drive the system from a regime with a 2D m-wave quasibound state (w -1 m < w ⋆-1 m ) to a regime with a shallow bound state (0 < w m w ⋆ m ), in both cases the (quasi-) bound state energy is E b ∼ -2 (w -1 m -w ⋆-1 m )/(2µα m ) [38], thus having an expression similar to the 3D case: E 3D b ∼ -2 /(2µw l α l ). iii) Resonance in the scattering cross section σ = |f m | 2 /4q occurs at a collisional energy E ∼ E b , that is only for positive values of E b : in presence of a quasi-bound state. The resonance width is given by ∆E/E b ∝ η m (E b / ω z ) m-1 ≪ 1. iv) Consequently, α l appears as a crucial parameter for the low energy scattering properties. For example, by neglecting α 1 (η 1 = ∞) in Ref. [20], the resonant collisional energy and resonance width of the p-wave CIR are found with other order of magnitudes. v) Following the reasoning in Ref. [34], these scattering properties open the possibility of observing high partial waves BEC-BCS transitions in quasi-2D fermionic gases by varying (w -1 m -w ⋆-1 m ) from positive to negative values.

Acknowledgments

It is a pleasure thank Y. Castin, M. Holzmann, M. Jona Lasinio, A. Minguzzi, P. Pedri and F. Werner for discussions. LPTMC is UMR 7600 of CNRS.

Jm(τ ) = P.f. ∞ 0 du u -(m+1) exp(τ u)[1 -exp(-u)] -1/2 , and appear in the computation of f [m] . The expression of Jm(τ +i0 + ) are deduced using an analytical continuation.

[36] The constant B is obtained from: ln

where γ is the Euler's constant. This value slightly differs from the one in Ref. [11]. However, a close investigation shows that it coincides with the evaluation of the slowly converging series in Ref. [11].

[37] For the resonances considered previously and a wave guide with ωz = 2π × 70 kHz, η1 ≃ 3 × 10 -2 for 40 K atoms and η1 ≃ 7 × 10 -3 for 6 Li atoms.

[38] For m = 1, this expression of E b neglects the logarithmic correction which is vanishingly small if η1 ln a 3 z (w -1 1 -w ⋆-1

1

) ≪ 1.


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