Keywords: ecological connectivity, dispersal, graph theory, landscape genetics, R

In landscape genetics, habitat connectivity and population genetic structure have been analysed using graph-theoretic approaches to understand how landscape features influence demography (i.e. dispersal and population size). 2 -Despite substantial advances in enhancing both genetic and landscape graph use, a software tool bringing together a large range of construction and analysis parameters for these two types of graphs was lacking in the landscape genetic toolbox. Moreover, although these two types of graphs appear complementary for answering landscape genetic questions, methods for comparing them have not been forthcoming. 3 -We have developed an R package to improve and encourage the use of these graphs. It includes functions for converting and importing genetic data and for genetic distance computing. It also implements time-efficient geodesic and cost-distance calculations from spatial data. A large range of parameters can be used to create genetic and landscape graphs from these data, including several graph pruning methods. We made available to R users the command-line facilitaties of Graphab software to easily model landscape graphs in R. The package functions perform preliminary analysis to adapt methodological choices to research questions. Landscape and genetic graphs created can be analysed with node-level metrics as well as link-level and modularity analyses. Users can compare and visualise these graphs and export them to shapefiles to facilitate interpretation and subsequent analyses. 4 -graph4lg contributes to expanding landscape and genetic graph potential for analysing ecological connectivity while encouraging further investigations on methodological implications related to these tools.

Introduction

Landscape genetic studies aim at understanding how landscape characteristics such as habitat spatial distribution and matrix quality shape population genetic structure [START_REF] Balkenhol | Landscape genetics: concepts, methods, applications[END_REF][START_REF] Manel | Landscape genetics: combining landscape ecology and population genetics[END_REF]. In this recent field, new methods have been developing at a sustained pace to describe landscape structure (e.g. [START_REF] Galpern | Grains of connectivity: analysis at multiple spatial scales in landscape genetics[END_REF]), population genetic structure (e.g. [START_REF] Al-Asadi | Estimating recent migration and populationsize surfaces[END_REF]; [START_REF] Prunier | Contribution of spatial heterogeneity in effective population sizes to the variance in pairwise measures of genetic differentiation[END_REF]; [START_REF] Shirk | sgd: software for estimating spatially explicit indices of genetic diversity[END_REF]) and to bring landscape and genetic data together in multi-level analyses [START_REF] Hall | A practical toolbox for design and analysis of landscape genetics studies[END_REF][START_REF] Wagner | A conceptual framework for the spatial analysis of landscape genetic data[END_REF]. Among these methods, graph-theoretic approaches were identified as particularly relevant [START_REF] Manel | Ten years of landscape genetics[END_REF] because they grasp interactions between sets of habitat patches or populations in a comprehensive way [START_REF] Dale | From graphs to spatial graphs[END_REF][START_REF] Dale | Applying Graph Theory in Ecological Research[END_REF][START_REF] Fortin | Spatial statistics -spatial regression, and graph theory in ecology[END_REF].

A graph is basically a set of nodes connected by a set of links. In landscape ecology, the use of landscape graphs dates back to the 2000s [START_REF] Galpern | Patch-based graphs of landscape connectivity: a guide to construction, analysis and application for conservation[END_REF][START_REF] Urban | Landscape connectivity: a graph-theoretic perspective[END_REF] and has developed through the availability of free software tools such as Graphab [START_REF] Foltête | A software tool dedicated to the modelling of landscape networks[END_REF] or Conefor [START_REF] Saura | Conefor sensinode 2.2: a software package for quantifying the importance of habitat patches for landscape connectivity[END_REF]. The nodes of landscape graphs are habitat patches and their links correspond to potential dispersal paths, e.g. identified by computing least-cost paths across resistance surfaces. From these graphs, a large range of connectivity metrics can be computed [START_REF] Rayfield | Connectivity for conservation: a framework to classify network measures[END_REF] and used for inference [START_REF] Pereira | Using spatial network structure in landscape management and planning: a case study with pond turtles[END_REF] or conservationoriented decision making [START_REF] Foltête | A methodological framework for the use of landscape graphs in land-use planning[END_REF]. Besides, landscape graph nodes can be partitioned through modularity analyses to identify management units or perform analyses at a coarser grain [START_REF] Fletcher | Network modularity reveals critical scales for connectivity in ecology and evolution[END_REF][START_REF] Foltête | Using landscape graphs to delineate ecologically functional areas[END_REF].

Although landscape graphs enable close investigation of habitat connectivity, their construction often relies upon expert-based opinion and combining them with biological data can improve this approach [START_REF] Foltête | A methodological framework for the use of landscape graphs in land-use planning[END_REF]. Landscape graph modelling software tools already make possible the import of biological data [START_REF] Foltête | A software tool dedicated to the modelling of landscape networks[END_REF] and genetic data are a relevant candidate for such a combination [START_REF] Luque | Landscape connectivity analysis for conservation: insights from combining new methods with ecological and genetic data[END_REF]. Thus, this approach would benefit from being performed in a statistical software where genetic data processing and complex statistical analyses can both be done.

Similarly, migration models theorised in population genetics [START_REF] Kimura | The stepping stone model of population structure and the decrease of genetic correlation with distance[END_REF][START_REF] Wright | Evolution in mendelian populations[END_REF] often rely upon topological network representations and even if these models rarely reflect real situations [START_REF] Greenbaum | Application of network methods for understanding evolutionary dynamics in discrete habitats[END_REF][START_REF] Milligan | Disentangling genetic structure for genetic monitoring of complex populations[END_REF], population geneticists have developed a large range of genetic graph construction methods that can potentially fit all the observed migration networks [START_REF] Greenbaum | Application of network methods for understanding evolutionary dynamics in discrete habitats[END_REF]. Thus, population genetic structure has been frequently represented as genetic graphs in which nodes correspond to sampled populations and links to substantial gene exchanges between them [START_REF] Arnaud | Metapopulation genetic structure and migration pathways in the land snail helix aspersa: influence of landscape heterogeneity[END_REF][START_REF] Excoffier | Analysis of molecular variance inferred from metric distances among dna haplotypes: application to human mitochondrial dna restriction data[END_REF].

When building a genetic graph, the construction method should always be guided by the specific research question [START_REF] Miele | Nine quick tips for analyzing network data[END_REF]. For example, an important step in this process is graph pruning, which consists in removing some links and should be performed differently if the aim of the analysis is (i) to identify single generation (direct) dispersal paths [START_REF] Boulanger | Spatial graphs highlight how multi-generational dispersal shapes landscape genetic patterns[END_REF][START_REF] Dyer | Population graphs and landscape genetics[END_REF] or (ii) to infer landscape effects on dispersal from the genetic differentiation measurements between populations connected on the graph (Savary, P. et al., in correction;[START_REF] Van Strien | Consequences of population topology for studying gene flow using link-based landscape genetic methods[END_REF]). Indeed, in the first case, paths that are not within reach of individuals given their dispersal capacities should be removed in order to represent the dispersal network topology.

Accepted Article

In the second case, links corresponding to multi-generational indirect dispersal can be conserved given that they reflect the genetic connectivity emerging over generations due to stepping-stone dispersal [START_REF] Boulanger | Spatial graphs highlight how multi-generational dispersal shapes landscape genetic patterns[END_REF][START_REF] Saura | Stepping stones are crucial for species' long-distance dispersal and range expansion through habitat networks[END_REF]. In both cases, several graph pruning methods can be used and must be chosen accordingly [START_REF] Greenbaum | Application of network methods for understanding evolutionary dynamics in discrete habitats[END_REF][START_REF] Van Strien | Consequences of population topology for studying gene flow using link-based landscape genetic methods[END_REF]. Apart from these link-level analyses, once genetic graphs have been constructed, they can be analysed at the node-and boundary-levels [START_REF] Wagner | A conceptual framework for the spatial analysis of landscape genetic data[END_REF], according to the research question. For example, node-level metric calculations and module partitions are possible to assess genetic diversity and relative genetic differentiation at the population level (e.g. [START_REF] Koen | Node-based measures of connectivity in genetic networks[END_REF] and to identify population clustering patterns (e.g. [START_REF] Fortuna | Networks of spatial genetic variation across species[END_REF]), respectively.

Then, comparing genetic graph characteristics such as node-level indices, graph topology, link weights and module partitions to the exact same characteristics derived from a landscape graph could contribute to a better understanding of the effect of habitat spatial patterns on population genetic structure. It has therefore been claimed that genetic graphs and landscape graphs should complement each other [START_REF] Foltête | Using landscape graphs to delineate ecologically functional areas[END_REF][START_REF] Galpern | Patch-based graphs of landscape connectivity: a guide to construction, analysis and application for conservation[END_REF][START_REF] Manel | Ten years of landscape genetics[END_REF][START_REF] Murphy | Graph theory and network models in landscape genetics[END_REF]. However, a practical tool for building, analysing and comparing these graphs was still lacking. Accordingly, we have developed the R package graph4lg to bridge all these gaps in the implementation of landscape and genetic graphs. It provides graph users with a software tool facilitating their choice and implementation of graph construction and analysis methods and builds on previous developments of R packages for landscape genetic and graph-theoretical analyses such as igraph [START_REF] Csardi | The igraph software package for complex network research[END_REF], gstudio [START_REF] Dyer | R package gstudio: analyses and functions related to the spatial analysis of genetic marker data[END_REF] or adegenet [START_REF] Jombart | adegenet: a r package for the multivariate analysis of genetic markers[END_REF].

Workflow

graph4lg package functions can be divided into four categories following the steps of landscape genetic analyses:

1. The package allows for genetic and spatial input data processing in preparation for graph construction, calculating intra-population genetic indices and inter-population genetic and landscape distances and performing preliminary analyses through diagnostic plots.

2. It provides users with functions for building genetic graphs and analysis tools for these graphs.

3. In parallel, some 'wrapper functions' run command-line functionalities of Graphab software [START_REF] Foltête | A software tool dedicated to the modelling of landscape networks[END_REF] directly from R to construct and analyse landscape graphs.

4. Finally, genetic and landscape graphs can be compared, plotted and exported to other formats.

This workflow is described in the following sections and depicted in Figure 1. All the package functions are also listed in Table S1 with their dependencies on other R packages.

Input data processing

Genetic data

Studies of gene flow pattern and/or intensity and of landscape influence on it rely upon neutral genetic markers which reflect genetic variation due to demographic changes and are supposedly independent from adaptive processes [START_REF] Holderegger | Adaptive vs. neutral genetic diversity: implications for landscape genetics[END_REF]. Microsatellite loci assumed or identified as being neutral are the most frequent type of markers used in landscape Accepted Article genetics [START_REF] Storfer | Landscape genetics: where are we now?[END_REF]. Besides, SNP markers are now becoming widespread and can also be used to perform these analyses provided that loci under selective pressures (identified as outliers) have been discarded [START_REF] Cushman | The least cost path from landscape genetics to landscape genomics: challenges and opportunities to explore ngs data in a spatially explicit context[END_REF][START_REF] Foll | A genome-scan method to identify selected loci appropriate for both dominant and codominant markers: a bayesian perspective[END_REF]. Accordingly, graph4lg functions use genetic data with 2-or 3-digit allele coding to fit the common microsatellite coding. SNP data can also be used when loaded as genind object in R, because R objects with the genind class attribute from the adegenet package [START_REF] Jombart | adegenet: a r package for the multivariate analysis of genetic markers[END_REF] are the input of genetic data processing functions from graph4lg. Landscape genetic analyses performed with graph4lg are population-based and like most applications in this field rely on the a priori delineation of populations [START_REF] Milligan | Disentangling genetic structure for genetic monitoring of complex populations[END_REF][START_REF] Waits | Basics of population genetics: quantifying neutral and adaptive genetic variation for landscape genetic studies[END_REF]. Populations are identified by the pop strata of genind objects and usually correspond to sampling units.

We included conversion functions (gstud_to_genind, loci_to_genind, structure_to_genind, genepop_to_genind) to easily get genind objects from formats used in other software tools such as gstudio [START_REF] Dyer | R package gstudio: analyses and functions related to the spatial analysis of genetic marker data[END_REF], pegas [START_REF] Paradis | pegas: an r package for population genetics with an integrated-modular approach[END_REF], structure [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF] or genepop [START_REF] Raymond | Genepop: Population genetics software for exact tests and ecumenism. vers. 1.2[END_REF]. We also made possible the creation of external text files in genepop format from genind objects (genind_to_genepop) for users willing to perform analyses with this commonly used R package and executable software.

The mat_gen_dist function computes eight different inter-population genetic distances from genind objects (Table 1). However, 'external' genetic distance matrices or dist objects imported by users can be the input of the functions described in the next sections.

Spatial data

Two kinds of pairwise landscape distance matrices can be computed from point spatial coordinates and resistance surface raster layers:

• mat_geo_dist function computes geodesic distances from point sets with either projected or polar coordinate reference systems using Euclidean distance or great circle distance formulas, respectively.

• mat_cost_dist function computes pairwise cost-distance matrices from a point set, a categorical resistance surface raster layer and a data.frame indicating the cost associated with each cell value. This function depends on gdistance package (Van Etten, 2012), but can also use an external .jar file which substantially reduces computation times for large rasters (Table S2), providing R users with a time-efficient alternative to gdistance for cost-distance computing.

Preliminary analyses

When the study objective is to infer landscape effects on dispersal from the relationship between genetic and landscape distances associated with graph links, visualising a scatterplot using complete distance matrices (scatter_dist) can be a first step before graph construction. Isolation by distance patterns due to limited dispersal are common in population genetics [START_REF] Wright | Isolation by distance[END_REF]. However, if the studied species has low dispersal capacities or after a decrease in landscape connectivity, the increase of genetic differentiation with distance is only observed at a small scale, which tends to expand over time [START_REF] Slatkin | Isolation by distance in equilibrium and non-equilibrium populations[END_REF]. In that case, drift will be more important than migration as a driver of genetic differentiation between populations separated by large distances. This results in a non-linear relationship between landscape and genetic distances exhibiting a plateau beyond a given landscape distance threshold [START_REF] Hänfling | Concordant genetic estimators of migration reveal anthropogenically enhanced source-sink population structure in the river sculpin cottus gobio[END_REF][START_REF] Hutchison | Correlation of pairwise genetic and geographic distance measures: inferring the relative influences of gene flow and drift on the distribution of genetic variability[END_REF]. Conversely, a linear relationship is expected when equilibrium is established at the scale of the study area. Because migration-drift equilibrium is a pre-requisite for genetic differentiation to reflect landscape effects on dispersal, inference ignoring it may be Accepted Article biased [START_REF] Bradbury | Non-linear genetic isolation by distance: implications for dispersal estimation in anadromous and marine fish populations[END_REF][START_REF] Van Strien | Isolation-by-distance in landscapes: considerations for landscape genetics[END_REF]. Genetic graph pruning method determines population pairs included in the inference and should therefore be chosen after consideration of the scale at which populations verify this equilibrium. Similarly, genetic distances based on fixation indices require equilibrium assumptions to be confirmed so that derived inferences are reliable [START_REF] Neigel | Is fst obsolete?[END_REF][START_REF] Whitlock | Indirect measures of gene flow and migration: Fst̸ = 1/(4nm+ 1)[END_REF]. [START_REF] Van Strien | Isolation-by-distance in landscapes: considerations for landscape genetics[END_REF] estimated the threshold distance between population pairs maximizing the correlation between genetic differentiation and landscape distance. This distance of maximum correlation (DMC) can be viewed as an estimate of the scale at which populations verify migration-drift equilibrium, i.e. their neighborhood size [START_REF] Addicott | Ecological neighborhoods: scaling environmental patterns[END_REF][START_REF] Kierepka | Differing, multiscale landscape effects on genetic diversity and differentiation in eastern chipmunks[END_REF]. It is computed by the dist_max_corr function (Figure 2A), which can help choosing among pruning methods (cf. section 2.2.1).

When the objective is to recover direct dispersal paths by taking into account landscape resistance and maximum dispersal capacities of the study species, it is important to know how species dispersal distances expressed in geodesic distance units convert into cost-distance values, especially if geodesic distance thresholds are used to prune the graphs. To that purpose, the convert_cd function performs a linear or log-log linear regression of cost-distance values against geodesic distance values [START_REF] Tournant | Evaluating the effect of habitat connectivity on the distribution of lesser horseshoe bat maternity roosts using landscape graphs[END_REF].

Genetic graph construction and analysis

Genetic graph construction

The graph4lg package implements a wide range of pruning methods for constructing genetic graphs. Some of these methods can equally apply to landscape graphs. First, graphs can be pruned by removing the links between populations separated by genetic or landscape distances above or below a specified threshold value (gen_graph_thr). Such an approach can be efficient for identifying direct dispersal paths provided maximum dispersal distance is known. It has also been used to select population pairs to include in the inference of landscape effects on dispersal [START_REF] Angelone | Where movement happens -scale-dependent landscape effects on genetic differentiation in the european tree frog[END_REF][START_REF] Keller | Spatial scale affects landscape genetic analysis of a wetland grasshopper[END_REF]. In that case, the distance threshold can be the DMC if a clear plateau is identified in the IBD pattern.

Second, when the study species is assumed to have stepping stone dispersal or when migrationdrift equilibrium establishes at short distance, graphs can be pruned depending on topological constraints (gen_graph_topo), thereby constructing minimum spanning trees, planar graphs, k-nearest-neighbour graphs and Gabriel graphs [START_REF] Arnaud | Metapopulation genetic structure and migration pathways in the land snail helix aspersa: influence of landscape heterogeneity[END_REF][START_REF] Bunn | Landscape connectivity: a conservation application of graph theory[END_REF][START_REF] Keller | Spatial scale affects landscape genetic analysis of a wetland grasshopper[END_REF][START_REF] Naujokaitis-Lewis | Implications of incomplete networks on estimation of landscape genetic connectivity[END_REF]. The topological constraints can be applied to matrices of landscape distances as well as genetic distances. Similarly, the edge-thinning method, linked to percolation theory, identifies the distance threshold above which graph thresholding breaks the graph into more than one connected component [START_REF] Urban | Landscape connectivity: a graph-theoretic perspective[END_REF][START_REF] Rozenfeld | Network analysis identifies weak and strong links in a metapopulation system[END_REF] and creates a thresholded graph using this threshold.

Finally, the gen_graph_indep function creates genetic graphs directly from genetic data stored in genind objects, in the same way as the popgraph function from the popgraph package. This approach prunes graphs by conserving links between populations that are dependent on each other based on the covariance of their allelic frequencies, after having looked at the covariance with allelic frequencies from all the other populations. This use of the conditional independence principle [START_REF] Whittaker | Graphical models in applied multivariate statistics[END_REF] is supposed to conserve links between populations directly exchanging migrants through single generation dispersal events [START_REF] Dyer | Population graphs: the graph theoretic shape of genetic structure[END_REF]. This function expands the original popgraph function by implementing p-value adjustments 6

This article is protected by copyright. All rights reserved. [START_REF] Benjamini | Controlling the false discovery rate: a practical and powerful approach to multiple testing[END_REF][START_REF] Holm | A simple sequentially rejective multiple test procedure[END_REF], among other options compared by Savary et al. (in correction).

Accepted Article

Genetic graph analyses

Once genetic graphs have been created, the compute_node_metric function computes graphtheoretic metrics such as the degree, closeness and betweenness centrality indices, which identify keystone hubs of genetic connectivity [START_REF] Cross | The genetic network of greater sage-grouse: Range-wide identification of keystone hubs of connectivity[END_REF]. It also computes the average and sum of the inverse genetic distance weighting the links. [START_REF] Koen | Node-based measures of connectivity in genetic networks[END_REF] showed that these relative genetic differentiation indices can be good proxies of connectivity. Apart from these metrics depending on graph topology, population-level genetic diversity indices such as allelic richness and heterozygosity rates can be computed with the pop_gen_index function from genind objects. All these metrics can be added as node attributes with the add_nodes_attr function.

Link weights are used to partition nodes into modules (compute_graph_modul) and identify population clusters possibly delineated by sharp dispersal limitations [START_REF] Fortuna | Networks of spatial genetic variation across species[END_REF][START_REF] Garroway | Applications of graph theory to landscape genetics[END_REF]. We implement several modularity algorithms: fast greedy [START_REF] Clauset | Finding community structure in very large networks[END_REF], louvain [START_REF] Blondel | Fast unfolding of communities in large networks[END_REF], optimal [START_REF] Brandes | On modularity clustering[END_REF] and walktrap [START_REF] Pons | Computing communities in large networks using random walks[END_REF] from the igraph package. Link weights can also be exported into data frames for subsequent link-level analyses using the graph_to_df function.

Landscape graph construction and analysis

The graph4lg package integrates the graph construction and analysis options of Graphab software [START_REF] Foltête | A software tool dedicated to the modelling of landscape networks[END_REF] by implementing its command-line functionalities. Thus, both the package documentation and Graphab software manual can be of substantial help for users.

First, the graphab_project function creates a Graphab project from a categorical raster layer. It defines habitat patches as contiguous cells with a given cell value and creates a directory containing this project in the user's machine. Then, the least cost paths between these habitat patches are computed (graphab_link). Once the Graphab project and link set have been created, users can create complete, thresholded or planar graphs (graphab_graph). A large range of connectivity metrics can be computed at the graph or node levels (graphab_metric). Delta-metrics can also be computed, e.g. for prioritisation analyses. These metrics have been extensively tested and compared in the literature [START_REF] Baranyi | Contribution of habitat patches to network connectivity: redundancy and uniqueness of topological indices[END_REF][START_REF] Rayfield | Connectivity for conservation: a framework to classify network measures[END_REF].

Users can either import planar graphs created in Graphab as igraph objects (graphab_to_igraph) in order to compute metrics in R, or only import link weights or node-level metrics computed with Graphab (get_graphab_metric, get_graphab_linkset). In cases when users want to relate punctual field observations to connectivity metrics, they can get the metrics of the nearest habitat patches from a set of points (graphab_pointset). Finally, users can partition habitat patches through modularity analyses in Graphab (graphab_modul).

Landscape and genetic graph comparisons

Although landscape and genetic graphs have each been repeatedly used, their direct comparison has rarely been performed [START_REF] Draheim | Detecting black bear source-sink dynamics using individual-based genetic graphs[END_REF][START_REF] Schoville | Preserving genetic connectivity in the european alps protected area network[END_REF]. To facilitate the interpretation of their respective topology and the formulation and test of hypotheses regarding their similarities, the plot_graph_lg function allows users to visualise the topology and connectivity of the created graphs (Figure 2D). It maps graphs in a spatially-explicit way or implements an attraction-repulsion algorithm based on link weights [START_REF] Fruchterman | Graph drawing by force-directed placement[END_REF] to assess whether nodes cluster together independently from their spatial locations. Node metrics,

Accepted Article

link weights and module partitioning can also be visualised with this function. Moreover, the link weight distribution can be plotted as a histogram (plot_hist_w)(Fig. 2C) and the pruning intensity can be visualised by representing population pairs in a different color on the scatter plot relating genetic distance with landscape distance (scatter_dist_g).

To test the formulated hypotheses, when landscape and genetic graphs share the same nodes, the correlation between population-or patch-based indices can be assessed (graph_node_compar) in order to understand the relationship between i) landscape attributes (habitat surface area or connectivity) and ii) genetic attributes (genetic differentiation or local diversity).

Similarly, the graph_topo_compar function compares the topologies of two graphs (linkbased analysis) by creating a contingency table (based on the presence/absence of corresponding links in both graphs) and computing indices commonly used to assess classifications (e.g. Matthews' correlation coefficient, false discovery rate, accuracy). The congruence of two graph topologies can be visualised by plotting them on the same map while colouring their links to indicate whether they occur in both graphs or just one of them (graph_plot_compar). Mismatches between genetic and landscape graph topology can provide insights regarding the realised connectivity in the study area or the modelisation method itself.

Finally, quantifying how many node pairs classified in the same module in one graph are also classified together in the modules created from another graph indicates us how far these graphs reflect the same real-world situation. This boundary-based analysis is made possible by the graph_modul_compar function which computes the Adjusted Rand Index [START_REF] Hubert | Comparing partitions[END_REF] to compare partitions.

Export facilities and included data

The graphs can be exported to shapefile layers for integration into a GIS (graph_to_shp) and analyses involving other types of geographical data. Included genetic and spatial data can be used to discover the functionalities of the package. We included a data set created from simulations with cdpop [START_REF] Landguth | Cdpop: a spatially explicit cost distance population genetics program[END_REF] on a simulated landscape (data_simul_genind). It consists of 1500 individuals from 50 populations genotyped at 20 microsatellite loci. This dataset exhibits a typical type-IV pattern of IBD and was used to create Figure 2 and the tutorial presenting the package.

Limits and conclusion

Landscape and genetic graphs have great potential for analysing ecological connectivity and we do not claim to have compiled an exhaustive set of graph construction and analysis methods. Other pruning methods have been developing [START_REF] Brooks | Quantifying population substructure: extending the graph-theoretic approach[END_REF][START_REF] Greenbaum | Inference and analysis of population structure using genetic data and network theory[END_REF][START_REF] Kininmonth | Determining the community structure of the coral seriatopora hystrix from hydrodynamic and genetic networks[END_REF]Milligan, prep;[START_REF] Peterson | Spatially-structured statistical network models for landscape genetics[END_REF] and could be expanded to directed graphs for example. Besides, a large range of local metrics inspired from the metapopulation theory have been developed for landscape graphs and could similarly inspire genetic graph local metrics. Graph-based analyses could also benefit from significance testing approaches through permutations to enhance their robustness. Finally, although Graphab software can efficiently handle very large spatial data sets [START_REF] Foltête | A software tool dedicated to the modelling of landscape networks[END_REF], genetic graph modelling can involve higher computational costs, thereby limiting this approach to smaller spatial and genetic datasets. Further development of the package could introduce improvements.

Accepted Article

Our first goal in developing graph4lg is to bring together and make accessible a large range of methods currently used in landscape genetics for constructing and analysing graphs. We hope this package will foster the use of genetic and landscape graphs as well as further investigation regarding theoretical as well as methodological aspects.

Graphab project

Habitat patches, links

Graph construction and analysis Input data processing

Graph comparison and processing

16

This article is protected by copyright. All rights reserved.

Figure 2 :

 2 Figure1: graph4lg workflow. Functions are represented by arrows linking their arguments to their output. Their names are written in red. Light beige boxes correspond to input data whereas grey boxes correspond to final output that can be exported to figures or files. Light blue boxes indicate analysis output that are used to construct graphs or derived from them. Dark blue boxes correspond to the two types of graphs that can be constructed with the package. The green box corresponds to diagnostic plots that can be assessed to help choose among the construction methods. Orange boxes indicate the analyses that can be carried out at several levels using both landscape and genetic graphs.

Table 1 :

 1 Inter-population genetic distances computed with the mat_gen_dist function. The 'Eq.' column indicates whether the genetic distance implies that migration-drift equilibrium assumptions are made. The 'Depend.' column indicates the R packages on which the function depends for each genetic distance.

	Accepted Article	genind object	(msats, SNPs)	Genetic distance	Fixation indices,	Euclidean genetic distances

-En génétique du paysage, la connectivité des habitats et la structure génétique des populations ont été analysées à l'aide d'approches basées sur la théorie des graphes pour comprendre comment les éléments du paysage influencent la démographie (i.e. la taille des populations et la dispersion).

-Bien que des progrès conséquents aient amélioré l'utilisation des graphes génétiques et paysagers, un outil informatique réunissant une large gamme de paramètres de construction et d'analyse de ces deux types de graphes faisait défaut parmi les outils de la génétique du paysage. Par ailleurs, malgré l'intérêt potentiel de la complémentarité de ces deux types de graphes pour répondre aux questions de génétique du paysage, des méthodes permettant de les comparer n'ont pas encore été proposées.

-Nous avons développé un package R pour améliorer et encourager l'utilisation de ces graphes. Il intègre des fonctions de conversion et d'import de données génétiques et de calcul de distances génétiques. Il permet aussi de calculer des distances géodésiques et des distances-coût à partir de données spatiales. Une importante gamme de paramètres peut être utilisée pour créer des graphes génétiques et paysagers à partir de ces données, parmi laquelle on trouve plusieurs méthodes d'élagage. Nous avons rendu accessible l'utilisation du logiciel Graphab en lignes de commande aux utilisateurs du logiciel R pour faciliter la modélisation de graphes paysagers dans cet environnement. Les fonctions du package permettent des analyses préliminaires ayant pour but d'adapter les choix méthodologiques aux questions de recherche. Les graphes génétiques et paysagers créés peuvent être analysés avec des métriques calculées au niveau des noeuds ou avec des analyses des liens ou des modules de ces graphes. Les utilisateurs peuvent comparer et visualiser les graphes et les exporter sous forme de couches shapefile pour faciliter l'interprétation et les analyses ultérieures.

-graph4lg contribue à étendre le potentiel des graphes génétiques et paysagers pour l'analyse de la connectivité écologique tout en encourageant de futures recherches sur les aspects méthodologiques relatifs à ces outils.

This article is protected by copyright. All rights reserved.

Acknowledgements

We thank the editor and referees, as well as the CRAN volunteers for their constructive comments. This study is part of a PhD project supported by the ARP-Astrance company under a CIFRE contract supervised and partly funded by the ANRT (Association Nationale de la Recherche et de la Technologie). We are particularly grateful to ARP-Astrance teams for their support throughout the project. We thank Ahmed Jebrane, Catherine Labruere and Catherine Laredo for their help with mathematical aspects.

Data availability

No empirical data were used in this article. The graph4lg package, all the R source codes, documentation files and vignettes can be downloaded by users under the GPL-2 license from the CRAN repository (https://cran.r-project.org/web/packages/graph4lg/index.html).

7 Authors' contributions J.C.F., S.G. and H.M. obtained the funding for the project. P.S. and G.V. designed the package and developed the codes. P.S, J.C.F. and S.G. wrote the manuscript with significant contributions and remarks from all co-authors.


J E E Riley

A M M Laird

N De Séréville

A Parikh

S P P Fox

F Hammache

I Stefan

P Adsley

M Assie

B Bastin

† A Parikh

‡ M Assié

F Boulay

A Coc

S Franchoo

R Garg

S A Gillespie

V Guimaraes

C Hamadache

N Hubbard

J Kiener

A Lefebvre-Schuhl

F De Oliveira

Santos

A Remadi

L Perrot

D Suzuki

G Verde

V Tatischeff

M Williams

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I. INTRODUCTION

Classical novae outbursts are phenomena taking place in a binary system made up of a white dwarf accreting material from its companion star [START_REF] Bode | Classical Novae[END_REF]. This material is progressively heated and compressed at the surface of the white dwarf until it reaches the ignition temperatures for hydrogen burning in degenerate conditions. During this explosive burning, nucleosynthesis takes place in a fully convective envelope and the newly synthesized material is ejected into the circumstellar medium.

The most intense γ-ray line emission from classical novae is predicted to come from the β + -decay of 18 F producing a signature at and below 511 keV from positron annihilation. Due to the short 18 F half-life (T 1/2 = 110 min) similar to the transparency time of the ejected envelope to γ-rays, the γ-ray emission at ≤ 511 keV would give unique insights into the details of the expanding shell (velocity, material profile). Precise knowledge of the yield of 18 F produced during the explosion is therefore crucial for interpreting future observations. After several decades of experimental and theoretical work the main remaining nuclear physics uncertainty affecting model predictions of the 18 F yield arises from the 18 F(p,α) 15 O reaction rate.

Due to its importance, considerable experimental effort has been expended in studying the 18 F(p,α) 15 O reaction. The astrophysically-relevant energy range covers 50 -350 keV in the center of mass, and a number of direct measurements have been performed down to energies of 250 keV (see [START_REF] Bardayan | [END_REF][3][4][5][6]). Measurements at lower energies, however, are limited by the currently available 18 F beam intensities.

In the absence of direct measurements across the full energy range, a variety of indirect techniques have been arXiv:2011.13222v1 [nucl-ex] 26 Nov 2020 exploited to determine the 19 Ne level information necessary to allow the 18 F(p,α) 15 O reaction rate to be calculated. Resonant elastic scattering studies were performed by Bardayan et al. [7], Murphy et al. [8] and Mountford et al. [9] and parameters for several resonances at and above E c.m. r = 665 keV were determined. Transfer reaction studies have also been performed, including 18 F(d,p) 19 F [10,11], 18 F(d,n) 19 Ne [12] and 20 Ne(p,d) 19 Ne [13] to explore the region close to the proton threshold. A detailed summary of the known level information will be presented in a future paper [14], but here we summarise the situation relevant for the present work.

Due to the presence of broad states at E c.m. r = 665 keV (3/2 + ) and around 1468 keV (1/2 + ), 1/2 + and 3/2 + states close to the proton threshold at 6.411 MeV can have a significant impact on the S-factor, despite being narrow. The interference between these states and the tails of the broad states can significantly change the predicted S-factor in the energy region between 50 and 300 keV (between 300 and 350 keV the E c.m. r = 331 keV, J π = 3/2 -resonance dominates). Therefore it is critical to constrain the location of these states. From the mirror nucleus, 19 F, level scheme two 3/2 + states and one 1/2 + state are expected in the region around the proton threshold (E x = 6.0 -6.6 MeV).

Just below the p+ 18 F threshold, an = 0 state was observed at around 6.290 MeV by Adekola et al. using the 18 F(d,n) 19 Ne reaction [15]. The state was subsequently identified as a 1/2 + state by Bardayan et al. through the 20 Ne(p,d) 19 Ne reaction [13]. More recently Laird et al. [16] and Parikh et al. [17] performed high resolution 19 F( 3 He,t) 19 Ne measurements of states above 6 MeV, particularly focusing on the near proton threshold region. These works found the state around 6.290 MeV to be inconsistent with a single low-spin assignment and suggested a doublet with at least one high spin component.

Kahl et al. [18] also used the 19 F( 3 He,t) 19 Ne reaction to populate 19 Ne states but at intermediate energies with triton detection at very forward angles, to specifically identify ∆L = 0 transitions indicating 1/2 + and 3/2 + states. A state at 6.13 MeV was thus observed, agreeing with one of the two possible spin assignments suggested by Laird et al.. A possible ∆L = 0 contribution to the region around 6.289 MeV was also reported. Based on the required energy shift from the possible analogue states in 19 F, Kahl et al. concluded that the 6.13 MeV is most likely 1/2 + , rather than 3/2 + , and the component around 6.289 MeV is therefore 3/2 + . This is in contradiction to the findings of Bardayan et 19 Ne reaction is inconsistent with a 3/2 + assignment. It should also be noted that the neutron threshold in 19 F is at 10.432 MeV, around 4 MeV higher than the proton threshold in 19 Ne. The Thomas-Ehrman shift on such states could therefore be substantial.

Visser et al. [19] studied the proton and α-particle decay of excited states in 19 Ne populated via the 19 F( 3 He,t) 19 Ne reaction. Here, a 25 MeV 3 He beam was incident on a CaF 2 target and the resulting tritons were detected at the focal plane of the Yale Enge magnetic spectrometer. Coincident decay particles were detected in an array of single sided silicon detectors. Decay probability distributions were extracted and 19 Ne level parameters deduced (see Section IV.B for further details). However, no results for the region just below the proton threshold were reported.

Finally, Hall et al. [20] also used the 19 F( 3 He,t) 19 Ne reaction to populate 19 Ne states and then studied the γ-decays from the de-excitation of these states. A 30 MeV 3 He beam was incident on a CaF 2 target and the resulting tritons were detected with the ORRUBA silicon array. Coincident γ-rays were detected in the Comptonsuppressed high-purity germanium detector array Gammasphere. Triton-γ-γ coincidences suggested two 3/2 + states at 13 and 31 keV above the proton threshold. These assignments suggests either disagreement with the assignments of Laird et al. for this energy region or the presence of additional states not resolved in previous studies. Furthermore, as only two 3/2 + states are known in 19 F in this energy region, either the Hall et al. and Kahl et al. assignments are in contradiction, or there are unobserved = 0 states present in 19 F.

Hall et al. also observed decays from the sub-threshold state at 6.292 MeV and suggested an 11/2 + assignment based on the similarity to the decay scheme of the 6.500 MeV in 19 F. This assignment indicates an energy shift of 208 keV. Such a large energy shift suggests, therefore, that the average shift of 50 ± 30 keV estimated by Nesaraja et al. should be considered with caution.

It is clear, therefore, that the location, and indeed number, of 3/2 + and 1/2 + is still uncertain. The situation is further confused by the prediction of a broad 1/2 + around 6 MeV by Dufour and Descouvement [21] which is as yet unobserved.

Here we report on a study of the 19 Ne level scheme for excitation energies between 6-and 7.5-MeV. The 19 F( 3 He,t) 19 Ne reaction was used to populate and identify the relevant states. From the coincident detection of α-particles from the decay of 19 Ne, information on the spin-parity and branching ratios was extracted, which did not depend on the charge exchange reaction model assumed. Section II below describes the experimental setup and technique used, and Section III details the data analysis methodology for singles and then coincidence events. The results are presented in Section IV and the interpretation given in Section V. We summarise and conclude in Section VI.

II. EXPERIMENT

The 19 F( 3 He,t) 19 Ne reaction was studied using the tandem accelerator at the ALTO facility in Orsay, France. A beam of 3 He was produced by the duoplasmatron ion source, accelerated to 25 MeV and transported to the object focal point of an Enge Split-pole magnetic spectrometer [22] with a typical intensity of 70 enA where it impinged upon the targets. Two CaF 2 targets with a thickness of 100 µg/cm 2 and 200 µg/cm 2 were used during the course of the experiment, both backed onto a foil of nat C. Light reaction ejectiles entered the Split-pole spectrometer positioned 10 • from the beam line through a rectangular aperture. Though the nominal aperture covers 1.7 msr, it was opened to an extent covering 3.3 msr to maximise the triton yield, and corresponding to an angular acceptance of ±3 • . However the presence of optical aberrations in these conditions degraded the energy resolution, which was measured to be ≈85 keV (FWHM). Moreover, due to the horizontal asymmetry of the aperture, the effective detection angle was 12 • . Light reaction particles were momentum analyzed and focused on the focal-plane detection system [23], consisting of a position sensitive gas chamber (where the position (P os) and anode wire signal (W ire) are recorded), a ∆E proportional gas counter and a plastic scintillator to measure the remaining energy.

In addition to measuring tritons, α-particle and proton decays from unbound 19 Ne states were detected in a silicon array placed around the target at backward angles in the laboratory frame (see Fig. 1). Six double sided silicon strip detectors (DSSSDs) were mounted on three independent mechanical supports, each holding a pair of detectors, one positioned above the other. Each DSSSD is a square detector of 5 × 5 cm 2 with 16 strips on each side (W1 models from Micron Semiconductor Ltd) with thicknesses of 140 µm or 300 µm. The mechanical mounts were located upstream of the target at 113 • (D1 and D2), (-) 135 • (D5 and D6) and 155 • (D3 and D4) in the laboratory frame, providing an angular range of 91 • (5 • at the extreme were obscured by the target mount) and a total solid angle of Ω = 1.44 sr. A 1-cm thick steel shield was placed in a vertical median plane defined by the target ladder so that the DSSSD array was shielded from the activation of the 0 • Faraday cup inside the reaction chamber. Energy calibration of the DSSSD array was undertaken using a triple α-source placed at the target position.

Since the Split-pole is positioned at an angle of 10 • , the 19 Ne recoil direction is between 26 • and 30 • (see Fig. 1) depending on the excited state considered within the Spit-Pole acceptance. The determination of the center of mass angle (θ c.m. ) of the decay particles detected in the DSSSD array should then account for the 19 Ne recoil direction. In the present case θ c.m. covers a range between 90 • and 172 • covering the full possible decay range angle. Such a wide angular coverage allows for a complete measurement of the angular correlation and a reliable determination of the branching ratios.

The Split-pole plastic scintillator was used to trigger the data acquisition system. Information from the Splitpole focal plane detectors and DSSSDs were recorded along with timing information, relative to the event trigger, from the W1 detector front strips. To compensate for the flight time of the tritons, the signals from the DSSSDs were stretched using the shaping time of the Mesytec STM-16+ shaping amplifiers, such that triton recoil and 19 Ne* decay products corresponding to the same event appeared within the 2 µs DAQ timing window.

III. DATA ANALYSIS A. Singles Events

Several combinations of measured quantities in the focal-plane detectors (residual energy v.s. W ire, residual energy v.s. P os, P os v.s. W ire and P os v.s. ∆E) were used to identify the tritons from deuterons. Fig. 2 shows the residual energy versus position measurement. Given the Q-values of ( 3 He,t) reactions on possible target contaminants ( nat C, 16 O and nat Ca) and the magnetic field considered for the present measurement (1.42 T) only tritons from the 19 F( 3 He,t) 19 Ne reaction reached the focal plane.

Once the tritons were identified and selected in the focal-plane detector data, their position spectrum was obtained (see Fig. 3). Six well-known isolated and well populated 19 Ne states [4379. 1 (22), 5092 (6), 6013 (7), 6742 (2), 6864 (2) and 7076 [START_REF] Bardayan | [END_REF] keV] across the whole focal plane were used to calibrate the focal-plane position detector. A relation between the radius of curvature ρ and the focal-plane position was extracted, and well described with a one-degree polynomial function.

A functional including peak and background components was constructed to describe the triton magnetic rigidity spectrum and the best fit was obtained after a least-squares minimization procedure (see Fig. curve). Owing to the extended spectrometer acceptance used in the present experiment the triton peaks exhibit a low energy tail, and the line shape was therefore described by a skewed normal distribution. In most cases the analyzed 19 Ne states have a natural width smaller than the experimental resolution, and a common width was therefore used as a free parameter in the fitting procedure. In the case of 19 Ne states having a natural width larger than the resolution the width of the skewed normal distribution was set to the natural width, with an allowed variation during the fitting process equal to its documented uncertainty. The centroid of the peak was allowed to vary within the uncertainty associated to the corresponding 19 Ne state energy.

The main source of background in the triton magnetic rigidity spectrum comes from deuterons produced by the ( 3 He,d) reactions. Indeed deuteron events were observed to bleed into the triton selection cut, as can be seen in Fig. 2. Deuteron magnetic rigidity spectra obtained by gating on events immediately above and below the triton locus showed the same shape. This shape was then used as a template for the deuteron background in the fitting procedure with its amplitude as a unique free parameter. The background contribution obtained in the best fit (see Fig. 3, purple line) was found in good agreement with that expected, based on the amplitude of the deuteron magnetic rigidity spectra aforementioned.

The states included in the fit were taken from references [8, 15-17, 24, 25]. The best fit of the triton magnetic rigidity spectrum (see Fig. 3; red line) provides a very good description of the data, with the exception of the region at the lower excitation energy side of the 19 Ne state at 6014 keV, and the region at slightly lower excitation energies than the 6742 keV state. The former region will be discussed in further detail in Sec. IV A. For the latter, the fit is improved by the inclusion of two additional states. Nesaraja et al. [24] does indeed predict two states in this region, at 6504 and 6542 keV, one of which is consistent with that found by Cherubini et al. [26].

B. Coincident Events

Particle decays coincident with triton detection were selected on the basis of timing, whereby true coincidences were identified by a prominent peak above a background of unrelated decays within the reaction chamber as can be observed in the inset of Fig. 4. Valid decaying events in the DSSSD array were additionally selected when a similar energy deposit (within 2-σ) between the p-and n-side of the semiconductor was recorded. The energy deposited in the DSSSD array for coincident events, fulfilling the previous two conditions, as a function of the corresponding triton magnetic rigidity is shown in Fig. 4. Two kinematic loci with different slopes are observed corresponding to coincident α-particle decays to the ground state of 15 O (J π = 1/2 -) and coincident proton decays to the ground state of 18 F (J π = 1/2 + ). Software gates associated to each type of events are represented in red.

In order to correctly extract the angular distribution of the 19 Ne* decay particles, the geometry of the DSSSD array was rotated and boosted into centre of mass (c.m.) coordinates. As reaction kinematics are dependant on the 19 Ne state populated, this procedure was performed separately for each state of interest since the associated 19 Ne recoil direction is changing. These data were then separated into a number of distinct but equal angular ranges, the number of which depended on the population of the state. Focal plane spectra of tritons with a confirmed α-particle or proton coincidence were plotted for each angular bin and fitted with the same function used for the triton singles, allowing only peak normalization to vary.

The yield of each angular bin was extracted by integrating the function used to fit the state. The background of coincidences (seen in the inset of Fig. 4) was then subtracted proportionally from each angular yield. Finally the geometrical efficiencies for each bin were calculated by performing Geant4 [27] simulations of the experiment (assuming an isotropic distribution of 19 Ne* decays) constructed using the NPTool package [28].

High energy thresholds in the DSSSD array along with the lower decay probability from astrophysically relevant states meant that resonance parameters could not be extracted with confidence from the proton coincidence data for states below 7500 keV. Alpha-particle decay data were sufficient, however, for the analysis of 19 Ne states both above and below S p relevant to the 18 F(p,α) 15 O reaction. The angular probability distributions of the emitted αparticles for the 6289, 6742, 6864, 7076 and 7500 keV states in 19 Ne have been extracted and are discussed in Section IV B. It was not possible to extract these distributions for any other states due to the resolution of the focal plane data.

IV. RESULTS

A. Evidence for a broad state at Ex = 6 MeV

The triton magnetic rigidity spectrum is described extremely well by the best fit, performed as detailed in Section III A, with the exception of the region on the lower excitation energy side of the 6014 keV state. Here, the best fit underestimates the low energy (high magnetic rigidity) side of the triton peak and a significant excess of counts can be observed at a magnetic rigidity of 0.987 Tm as shown in the upper panel of Fig. 5. This region is, however, well described if an additional state, characterized by three independent parameters associated to a skewed normal distribution, is included in the minimization procedure. Results are shown in Fig. 5 (lower panel) and the goodness of fit is largely improved with a reduced chi-squared χ 2 /ndf = 1.98 instead of 3.65. The improved fit therefore suggests the presence of an additional state in 19 Ne at an energy of 6008 (20) keV with a total width of Γ = 124 (25) keV. A similar analysis of the total coincident spectrum also indicates the presence of a state with compatible energy and total width.

Although the evidence for this additional state in the present work is tentative, further investigation into the properties of this state is justified to constrain its possible impact on the 18 F(p,α) 15 O cross section.

It should be noted that the present work was performed at the same incident beam energy as that of Laird et al. [16] but with a larger angular acceptance, centred at a slightly different angle. A comparison can be made with Fig. 1 in that work, bearing in mind the different detection angle and therefore different relative population of states. Although the energy resolution is significantly better and the known states are well separated, the limited statistics prevent any conclusion regarding the existence of the broad state.

The events, neither in singles nor coincidences, corresponding to this possible new state cannot be unambiguously separated from those of the 6014, 6072, and 6100 keV states, and so an angular correlation could not be reliably extracted. Therefore, no constraint can be deduced on the spin-parity of this state from such an approach. However comparison of the extracted width of this state with the Wigner limit does provide stringent constraints. Since the 6008 keV state is below the p+ 18 F threshold, its total width is equal to its α-particle partial width. The Wigner limit, defined as Γ W igner α = 3 2 /(µr 2 ) × P (r, E) where µ is the reduced mass of the α+ 15 O channel and P (r, E) is the penetrability for the Coulomb and centrifugal barriers, was calculated for various transferred angular momentum . The experimental width (Γ = 124 keV) exceeds the Wigner limit for ≥ 2 giving strong constraints on the spin and parity of this broad state. In the α+ 15 O channel, = 0 corresponds to J π = 1/2 -and = 1 corresponds to J π = 1/2 + or 3/2 + . The Wigner limits are Γ W igner α ( = 0) = 265 keV and Γ W igner α ( = 1) = 165 keV. In either case, the broad state at 6008 keV would therefore be a strong α-cluster state since its dimensionless α-particle reduced width θ 2 α = Γ/Γ W igner α is greater than 50%.

B. Angular correlations

Formalism and method

The angular variation in decay product emission is governed by the orbital angular momentum l transferred to the decay particle and the spin J of the originating state. Particle decay distribution from isolated nuclear levels are described by a summation of even terms of the Legendre polynomials, P k (cos(θ)), truncated at a maximum value k max = min(2l, 2J). Following the formalism derived by Pronko & Lindgren [29], the correlation function W (θ) in its most general form reads

W (θ) = mll skr P (m) A(Jll smk) (2 -δ ll ) × X r (ll ) Y (s) Q(k) P k (cos(θ)). ( 1
)
The population of each (2J + 1) magnetic substate m is given by P (m), while the population of each exit channel spin s is given by Y (s). The orbital angular momenta l and l = l + 2 of the decaying particle represent the different possible values when several exit channel spins are allowed. The interference from the competing orbital angular momenta is accounted by the mixing ratio X r (ll ).

The term A(Jll smk) is a product of Clebsch-Gordon and Racah coefficients which is evaluated numerically, and the solid angle correction Q(k) is equal to 1 given the very small detection angle of the decaying particles subtended by a pixel of the DSSSD array [29].

In case of α-particle (0 + ) decays from 19 Ne excited states to 15 O ground state (1/2 -) a single channel spin s = 1/2 is allowed, and only a single orbital angular momentum l is possible for a given spin J of the 19 Ne decaying state. The general form of Eq. 1 then simplifies to

W α (θ) = m,k P (m) A(Jll 1 2 mk) P k (cos(θ)). (2)
Owing to the properties of the A(Jll 1 2 mk) term in case of a channel spin s = 1/2, it evaluates to the same value for decaying states having the same spin independently of their parity [29]. It is also worth noting that the A(Jll smk) term gives identical results if m is replaced by -m. Therefore, experimental α-particle angular correlations were fitted using Eq. 2 where the sum of the population of magnetic substates P (m)+P (-m) were considered as free parameters. In addition the magnetic substate population should fulfill the two following relations: 0 ≤ P (m) + P (-m) ≤ 1 and m P (m) = 1. For a given 19 Ne state there are (2J -1)/2 free parameters, and an additional overall scaling factor (not present in Eq. 2).

The case of proton (1/2 + ) emission from 19 Ne excited states to 18 F ground state (1 + ) is more complicated since two channel spin s = 1/2 and s = 3/2 are possible. In this case the general angular correlation function given by Eq. 1 is used. The fitting of the experimental proton angular distribution is then performed as for the α-decay case with one additional free parameter Y (1/2) and the condition s Y (s) = 1. The minimum value of the orbital angular momentum which couples the proton to the 19 Ne decaying state is chosen, which sets the mixing term X r (ll ) equal to one.

Results

The minimum order of Legendre polynomial needed to fit the data was decided on the goodness of fit achieved with progressively higher values of k max whilst maintaining a reasonable number of degrees of freedom. The best fits are shown in Fig. 6, together with the data from Visser et al. [19] for comparison (see Section IV C for discussion). The theoretical fits provide an overall very good description of the experimental angular correlation. Each 19 Ne state is now discussed individually.

The 19 Ne state at E x = 6742 keV is the first above the proton threshold to be meaningfully analysed. This state was first observed in the 20 Ne( 3 He, 4 He) 19 Ne reaction and its angular distribution indicates a J π = 3/2 -, (1/2 -) assignment [30]. Based on mirror symmetry arguments the J π = 3/2 -assignment was confirmed [31]. The maximum order of the summation in Eq. 2 for a state having J π = 3/2 -is k max = 2, and the corresponding best fit (χ 2 ν = 13.8/7) of the experimental data is represented by the solid line in Fig. 6. Such value for the reduced χ 2 corresponds to a p-value of 0.054 slightly greater than 0.05. This indicates that the present data is compatible with a J π = 3/2 -assignment even though the angular correlation would be better described if one would consider k max = 4 (implying J ≥ 5/2) as shown by the dashed line curve in Fig. 6.

The level at 6864 keV in 19 Ne has been assigned a spin and parity J π = 7/2 -based on mirror symmetry arguments [31], which was further confirmed by the angular correlation analysis of Visser et al. [19]. The sum over the Legendre polynomials in Eq. 2 is limited to k max = 6 in case of a J π = 7/2 -19 Ne state decaying in the αparticle channel. The best fit (χ 2 ν = 4.7/5) presented as a solid line in Fig. 6 shows a remarkably good description of the experimental data which confirms the spin and parity assignment J π = 7/2 -.

The 7076 keV state is one of the best studied resonance in the p+ 18 F system. It is known to have a spin parity of 3/2 + with well measured partial and total widths [START_REF] Bardayan | [END_REF]. The only possibility for the orbital angular momentum of the emitted α-particle is l = 1, which implies k max = 2. The best fit (χ 2 /ν = 0.7) in these conditions is represented by the red solid line which supports an assignment of J = 3/2 for the 19 Ne state at 7076 keV. Unfortunately, proton decay from the state was only partially observed in the D1 and D2 DSSSDs preventing a comprehensive analysis of its distribution.

The 7420 keV state was observed in a proton resonant elastic scattering experiment, and the subsequent R-matrix analysis found that it had most likely a spin and parity assignment J π = 7/2 + [7]. As in the case of the 19 Ne state at E x = 6864 keV the angular correlation must be described with k max = 6. The best fit (χ 2 ν = 4.3/5) shown in Fig. 6 as a solid red line compares very well the experimental angular correlation, thus supporting the spin and parity assignment J π = 7/2 + . Note that this level was not observed in another proton resonant elastic scattering and was concluded not to exist [8]. However no other known 19 Ne levels could constitute the observed peak in the current data. The spin and parity assignment obtained in this work being consistent with previous determination also adds support to its concluded existence from this work.

The 7500 keV state is strongly populated and it is the first 19 Ne level with sufficient proton decay strength to allow the t -p angular correlation to be extracted. This state was first observed with the 19 F( 3 He,t) 19 Ne reaction [31] and its J π = 5/2 + assignment comes from pairing with a known 5/2 + state in 19 F based on similar excitation energies [24]. This spin and parity assignment was later confirmed by an R-matrix analysis of proton resonant elastic scattering data [8], and in another coincidence measurement [25]. For both the proton and α-particle decay channels, the angular correlation is limited by k max = 4 for a J π = 5/2 + emitting state. Best fits are represented as solid red lines in Fig. 6 and the excellent agreement with the experimental data supports a J π = 5/2 + assignment.

C. Branching ratios

For each experimental angular correlation analysed in Fig. 6 the associated α-particle or proton branching ratio for the corresponding 19 Ne state was obtained by integration of the theoretical correlation function over the full solid angle. We found that our branching ratios are consistently lower than previous values reported in the literature [7,19,31]. This observation is consistent with the present angular correlations being usually lower than those of Visser et al. [19] reported in Fig. 6. The origin of this issue has been pinned down to an electronic problem affecting the coincidence event efficiency. This effect was found to be independent of both the focal plane position and the energy deposited in the silicon. The well studied 19 Ne state at 7076 keV was therefore used as a benchmark for the branching ratio. Considering partial and total widths Γ p = 15.2 (1) keV, Γ α = 23.8 (12) keV and Γ = 39.0 (16) keV [START_REF] Bardayan | [END_REF]7], the multiplication factor which must be applied to our data in order to reproduce the known α-particle branching ratio (Γ α /Γ = 0.61 (2)) for the 19 Ne state at 7076 keV is 1.58 ± 0.14.

Branching ratios from the present work are reported in Tab. I together with results from previous works. The uncertainty associated to our branching ratio determination arises from the combined effect (quadratic sum) of the correction factor uncertainty and from the propagation of uncertainties of the angular correlation fit parameters when integrating over 4π sr. The comparison between different data sets is shown in Fig. 7 andgood agreement is observed between our data and previous measurements.

The only exception is the 19 Ne state at 7500 keV for which the present determination of the α-particle branching ratio Γ α /Γ = 0.47 ( 6) is in agreement within 2σ with the measurement of Murphy et al. [8] but disagrees with Utku et al. [31] who obtain Γ α /Γ = 0.16 [START_REF] Bardayan | [END_REF]. The proton branching ratio for the 7500-keV state could also be extracted from the corresponding angular correlation shown in Fig. 7 and we obtain Γ p /Γ = 0.66 (7), while Utku et al. [31] obtain Γ p /Γ = 0.84 (4). The present proton and α-particle branching ratios sum to 1.13 (9) which is compatible within two sigma with unity, and strengthens the reliability of the present analysis.

One possibility for this discrepancy could originate from the angular correlation analysis in Ref. [31]. The experimental angular correlations for the 7500 keV state (not shown in their paper) is restricted to a small angular range sampled by three detectors centered at laboratory angles of 90°, 110°and 145°. The angular correlations are then independently fitted with a linear combination of the first three Legendre polynomials, thus implying three free parameters for three data points. The 7500 keV state is now known to have J π = 5/2 + [8], which implies k max = 4 and thus limits the sum in Eq. 1 to the first three Legendre polynomials, confirming the number of free parameters used in Utku et al. analysis. However in their procedure Utku et al. don't consider the m P (m) = 1 relation between the magnetic substate population which can lead to erroneous shape of the angular correlation function and biased determination of the branching ratios.

Another reason for the origin of the discrepancy with Utku et al. may be related to a possible contamination in the present data from the neighbouring state at 7531 keV. If one combines the individual branching ratio determined by Utku et al. [31] for the two 19 Ne states at 7500-and 7531-keV with their relative population as observed (FWHM = 24 keV) in their Fig. 1, one would get for these two states combined branching ratios of Γ α /Γ = 0.27(3) and Γ p /Γ = 0.73(4), in much better agreement with the results from the current work. A similar effect may also affect the data of Murphy et al [8] where the energy resolution does not allow to separate both states. The angular correlation of the 19 Ne 6289 keV state is represented in Fig. 8. While there are evidences of a close doublet at this energy [17,20] separated by about 12 keV [17], the energy resolution and the line shape asymmetry of the present data does not allow to separate them. Then the angular correlation in Fig 8 embeds the two possible contributions and a combined analysis is performed. The minimum value of k max providing a good description of the angular correlation was determined using χ 2 ν p-value hypothesis testing. The null hypothesis was first chosen to correspond to an isotropic correlation (k max = 0) and was accepted if the χ 2 ν pvalue was greater than 0.05. For a smaller p-value the null hypothesis (isotropic angular correlation) was rejected and k max = 2 was considered as the new null hypothesis. This procedure was repeated until p > 0.05 and the corresponding k max was considered as the minimum value providing a good description of the data. The isotropic case (k max = 0), which would imply J = 1/2, is clearly rejected as can be observed in Fig 8 (solid black line) with p = 1.5 × 10 -3 . The first case compatible with the experimental angular correlation is obtained for k max = 6 (red solid line) with p = 0.16. According to the definition of k max a value of 6 corresponds to a spin of 7/2. We therefore conclude from the current analysis that the peak corresponding to excitation energies about 6289 keV behaves as a state with a rather high spin J ≥ 7/2. The calculation of the correlation function with k max = 10, corresponding to an initial spin J = 11/2, is also shown in Fig. 8 for comparison (dashed black line). As expected the angular correlation is better reproduced (p = 0.39) since additional free parameters are considered in the fitting procedure. As for the other 19 Ne states, the α-particle branching ratio is calculated with the same procedure and yields Γ α /Γ = 0.92 ± 0.11 for this E x = 6289 keV doublet. As expected the branching ratio is compatible with 1 since at this energy only the α-particle decay channel is open.

As suggested [17,20], the existence of a second state close in energy is readily explained by all measurements of the state performed to date. Data by Adekola et al. [32] and Bardayan et al. [13] were taken using 18 F(d,n) 19 Ne and 20 Ne(p,d) 19 Ne respectively. Data in this work and that of Laird et al. [16] as well as Kahl et al. [18], populated 19 Ne through 19 F( 3 He,t) 19 Ne. It is expected that different reaction mechanisms may preferentially populate different states depending on the required l-transfer. Two possibilities remain, therefore, for interpreting the angular distributions in this work. Either the J π = 1/2 + is far lower in intensity and the distributions represent the spin from the second state, or both are populated to a non-negligible proportion and the αparticle decay measurements are mixing from both. Unfortunately, given the resolution and asymmetry of the focal plane, resolving two peaks at Bρ = 0.975 Tm with the predicted 12 keV difference was not possible. The analysis from this work can confirm, however, that the observed resonance cannot be a single state of J π = 1/2 + .

V. ASTROPHYSICAL S-FACTOR

An analysis of the 18 F(p,α) 15 O reaction at novae temperatures was conducted using the R-matrix formalism [START_REF] Lane | R-matrix Theory of Nuclear Reactions[END_REF] with the AZURE2 code [START_REF] Azuma | [END_REF]. While the focus is on the impact of sub-threshold states at 6.008-, 6.132-and 6.286 MeV, the contribution of influential resonances in the Gamow window is also calculated. This includes the 3/2 + states just above the p+ 18 F threshold [20], the 3/2 -state at 6.740 MeV [3], the 3/2 + state at 7.075 MeV [START_REF] Bardayan | [END_REF] and the 1/2 + state at 7.879 MeV [15].

A. The doublet at Ex = 6. 29 MeV

Taking together all the experimental data available, it is clear that in the region of 6.29 MeV two states are present, one of high spin, the other low spin. It is assumed that the high spin component is 11/2 + as reported by Hall et al. [20], this assignment being supported by the present analysis. However, a high spin component will not contribute to the astrophysical reaction rate and so a firm assignment is not required. For the low spin state, we prefer a spin assignment of 1/2 over 3/2, based on the clear signature from the 20 Ne(p,d) 19 Ne study [13]. Although Kahl et al. [18] prefer a 3/2 assignment based on the required mirror energy difference, we find this argument less compelling given the large shifts already observed, e.g. the 208 keV between the 11/2 + states at 6.292 and 6.500 MeV in 19 Ne and 19 F, respectively. Furthermore Dufour and Descouvemont [21] found large differences to be possible for swave states (i.e. 1/2 + or 3/2 + ) with large spectroscopic factors. Alpha-particle widths and Asymptotic Normalization Coefficients (ANC) for the 1/2 + states is taken from Ref. [18].

B. The level at Ex = 6.132 MeV This state has been populated by the 19 F( 3 He,t) 19 Ne reaction [16,17,31] and its angular distribution found to be indicative of a (3/2 + ) or (5/2 -) state [16]. A ∆L = 0 transition was observed at 6130 (5) keV by Kahl et al. and a J π = 1/2 + assignment favored, though J π = 3/2 + is not discarded [18]. Furthermore, the analysis of the p -α angular correlation of this state populated through the 19 Ne(p,p ) 19 Ne(α) 15 O reaction favors a J = 3/2 assignment [START_REF] Dalouzy | Spectroscopie du 19 Ne par diffusion inélastique[END_REF]. All observations can, therefore, be reconciled if this level is a J π = 3/2 + state, and we have used this assignment in the R-matrix calculations. This assignment, however, implies that either there is an, as yet, unidentified 3/2 + state in 19 F, or one of the two 3/2 + states suggested by Hall et al. is mis-assigned.

Alpha-particle widths and ANC for this state is taken from Ref. [18].

C. The broad state at Ex = 6.008 MeV Based on the extracted width, the spin-parity is J π = 1/2 -, 1/2 + or 3/2 + , and we consider possible analogue states in 19 F for each case here. In the case of a J π = 1/2 -assignment the only possibility for a mirror connection with a known state would be with the 6.429 MeV state in 19 F. This connection would require a rather large, but not prohibitively so, mirror energy difference (more than 400 keV). There is some evidence, however, that the 6.429 MeV state is paired with the 6.439 MeV state in 19 Ne based on the work of Utku et al. [31].

If the broad state has a J π = 1/2 + assignment, this raises the question of whether it can be associated to the broad 1/2 + state at 6.001 MeV (Γ = 231 keV) predicted using the Generator Coordinate Method (GCM) [21]. The energy and total width of the predicted state rely on the association of the theoretical GCM 1/2 + state in 19 F with the experimentally known 1/2 + state at 5.94 MeV. It should, in fact, be associated to the known α-cluster state at 5.34 MeV (θ 2 α = 0.53) [START_REF] Descouvemont | [END_REF], which then modifies the parameters predicted by Dufour et al. [21] such that the state is not now expected to be broad. Experimentally, there is strong evidence that in this energy region the 19 F state at 5.34 MeV has a much stronger α-particle clusterization than the 5.94 MeV state. First, the α-particle width for the 5.34 MeV state has been determined experimentally (Γ α = 1.3 (5) keV) and compared to single-particle width calculated with a potential model, leading to θ 2 α ≈ 0.4 [37], in agreement with theoretical predictions [START_REF] Descouvemont | [END_REF]. Other experimental work finds Γ α = 2.51 (10) keV [38] also supporting a strong αcluster contribution for the 5.34 MeV state. Second, the 15 N( 7 Li,t) 19 F reaction was studied at bombarding energies of 15 MeV and 20 MeV [START_REF] Middleton | Nuclear reactions induced by heavy ions[END_REF]. In both cases the 5.34 MeV state is very well populated, and while the 5.94 MeV is not labeled (see Figs. 7 and 10 in Ref. [START_REF] Middleton | Nuclear reactions induced by heavy ions[END_REF]) it can be estimated from these energy spectra that its α-particle spectroscopic factor is at least three times lower than for the 5.34 MeV. This indicates that the 5.94 MeV state has a much smaller α-cluster configuration than the 5.34 MeV state. The large θ 2 α deduced for the broad state under consideration (see Sec. IV A) could be an indication for being the mirror of the 5.34 MeV in 19 F, however this would require a very large energy shift of 1.15 MeV with respect to their respective α-particle threshold. Even though large energy shift are possible for strongly clusterized s-wave states [21], a shift of 1.15 MeV would be surprising and the above mentioned analog pairing is very unlikely.

Finally, considering the case of a J π = 3/2 + assignment a counterpart should have been predicted by the GCM since its experimental dimensionless reduced width is large. Indeed the GCM predicts a 3/2 + state in 19 F which is associated to the experimentally known 3/2 + at 5.501 MeV [21]. However there is some evidence that this state is the analog of the 5.463 MeV state in 19 Ne [18].

Given the lack of knowledge of the spin and parity assignment of the tentative broad state at E x = 6.008 MeV, all three possible assignments have been considered in order to evaluate its potential contribution above the p+ 18 F threshold. Its reduced proton width can be calculated using the following relation [START_REF] Iliadis | Nuclear Physics of Stars[END_REF] γ 2 p = θ 2 p ×γ 2 p,W igner , where γ 2 p,W igner = 3 2 /(2µr 2 ) = 2.246 MeV is the Wigner limit for the proton reduced width evaluated at a channel radius a p = 5.4 fm. A dimensionless proton reduced width θ 2 p = 1.8 × 10 -3 is considered using the results from the systematic study of Ref. [START_REF] Pogrebnyak | [END_REF]. This leads to ANC values of 1.19 fm -1/2 and 0.64 fm -1/2 in case of a proton in the s-or p-shell, respectively.

The proton transfer reaction 18 F(d,n) 19 Ne(α) 15 O [12] can also be used to assess the potential importance of the E x = 6.008 MeV state. In that work there is no evidence of any significant proton strength between E x = 5.49 and 6.09 MeV (see Fig. 5(b)). We roughly estimate that a number of coincident events greater than ≈ 30 for the contribution of the E x = 6.008 MeV state would have been detected. Assuming a similar angular distribution for the E x = 6.008 MeV state as the known swave state at E x = 6.289 MeV, a spectroscopic factor (2J + 1)S p 0.03 is deduced for the E x = 6.008 MeV state. The single-particle proton ANC for this state was calculated assuming a Woods-Saxon potential well with geometry (r, a) = (4.5 fm, 0.53 fm) and this gave ANC s.p. = 17.1 fm -1/2 . This leads to ANC values of 1.47 fm -1/2 and 2.08 fm -1/2 for a J π = 3/2 + and 1/2 + assignment, respectively.

D. Results and discussion

R-matrix calculations using channel radius a p = 5.4 fm (entrance) and a α = 6.1 fm (exit) are presented in Fig. 9 for the above mentioned 19 Ne states with the exception of the 6.132 MeV state whose contribution is lower than 1 MeVb for all center of mass energies. The dashdotted line represent the expected contribution for the sub-threshold state at 6.008 MeV with the ANC values computed using the experimental constraints from the work of Ref. [12], while the solid lines are estimates based on the systematic study of Ref. [START_REF] Pogrebnyak | [END_REF]. Given the magnitude of the S-factor it is very unlikely that this state has a strong impact in the 18 F(p,α) 15 O reaction rates since the contribution of other resonances (solid black lines) in the Gamow window dominate. It is worth noting that the proton ANC values used for the estimate of the 6.008 MeV state based on the systematic study of Ref. [START_REF] Pogrebnyak | [END_REF] can be uncertain by large factors. This is related to the scatter of the dimensionless proton widths reported in that study, and this could have significant impact on the potential role of the 6.008 MeV state. (Colour online) Astrophysical S-factor for the 18 F(p,α) 15 O reaction as a function of the center-of-mass energy. R-matrix calculations for the 6.008 MeV state are represented in color lines for different spin-parity assumptions. Calculations with three different ways of estimating the proton ANC values are presented in case of a 1/2 + assignment (see labels in the legend and text for discussion). The contribution of the most influential resonances is represented in solid black lines for comparison purposes.

Although it is not clear whether or not the 6.008 MeV state can be associated to the broad 19 Ne state predicted theoretically using the GCM [21], the consequences of such a possibility can still be explored. A theoretical partial width γ 2 p = 1.95 × 10 -3 is reported for a channel radius a p = 10.1 fm [21] which corresponds to an ANC of 4.3 fm -1/2 . The contribution to the S-factor of the 6.008 MeV state using this ANC value has been calculated and is shown in Fig. 9 by the dashed blue curve. As expected the contribution of the 6.008 MeV state to the 18 F(p,α) 15 O reaction rate could be much more important with these parameters.

The broad state at E x = 6.008 MeV will not play a role unless it has a large proton reduced width, similar to that of the GCM prediction. Such a value is not necessarily in contradiction to the systematic study of Pogrebnyak et al. [START_REF] Pogrebnyak | [END_REF] given the large scatter in those data and the trend of increasing reduced width for lower mass number. Similarly, the GCM predictions are not necessarily in contradiction with the estimate based on the Adekola et al. work [12] given the rater crude estimate of the maximum contribution of the E x = 6.008 MeV state given here.

VI. CONCLUSION

The level scheme of 19 Ne has been studied through the coincident detection of tritons and α-particles from the 19 F( 3 He,t) 19 Ne * (α) reaction. The results support the presence of a doublet at around 6.29 MeV consisting of a high spin (likely 11/2 + ) state and a low spin (1/2 + ) state. The state at 6.130 MeV was observed but due to the ex-perimental resolution, the angular correlation could not be separated from the much stronger 6.014 MeV state. The 6.130 MeV has been assumed to be 3/2 + but experimental confirmation of this assignment is needed. Evidence for a broad state at 6.01 MeV was found. Due to the large observed width, this state is likely to be low spin. Branching ratios were determined for states between 6.289 and 7.5 MeV, and are in good agreement with the literature. R-matrix calculations have been performed showing the contribution of key states in 19 Ne compared to estimates of the possible contribution of the tentative broad (Γ = 124 keV) state at 6.008 MeV. These calculations indicate that, if it is to be significant for the 18 F(p,α) 15 O reaction rate, the state must be 1/2+ or 3/2+ and its reduced proton width of similar magnitude to that predicted by Dufour and Descouvemont. Given the tentative evidence presented here, a high-resolution, high-statistics measurement is needed to provide clarification on the origin of the excess of counts observed in this region.

It is clear that significant gaps in our knowledge of the level scheme of 19 Ne and indeed 19 F remain, below the proton threshold as well as above. The connection of analogue states above 5 MeV is far from complete and the data suggest there may be unobserved and/or misassigned states in both nuclei. Not all of the missing information is required to constrain the 18 F(p,α) 15 O reaction rate however. The important parameters remain the proton widths of the 3/2 + states above the proton threshold and the interference terms between l = 0 states with the same spins. However, as the interference terms can only be determined by a direct measurement, higher statistics measurements below the 331 keV resonance are most critical to reducing the uncertainty on the 18 F(p,α) 15 O reaction rate at nova temperatures.

FIG. 1 .

 1 FIG. 1. Schematic diagram of the reaction chamber in front of the Split-pole. The z axis points along the beam. The 19 Ne recoil direction causes a rotation to the reference frame of ≈ 28 • from which θc.m. is calculated.

FIG. 2 .

 2 FIG. 2. (Colour online) Split-pole Plastic against Position signals to separate particles at the focal plane by Z and A. The triton selection cut is highlighted in red. Background from partial energy deposition of deuterons 'bleeds' into the triton region.

FIG. 3 .FIG. 4 .

 34 FIG. 3. (Colour online) Split-pole focal plane showing the gated triton spectrum. Also shown are events with α-particle detection (blue) and proton detection (red). The result of the fit function has been shown in red with individual states in yellow. The only source of background in the focal plane originating from ( 3 He,d) has been shown in blue.

FIG. 5 .

 5 FIG. 5. (Color online) Fitted Split-pole focal plane spectra focussed on the -400 keV sub-threshold region. The inclusion of an additional broad state to the fit function in panel b shows a marked improvement to the goodness of fit.

  FIG.6. (Colour online) Triton-alpha and triton-proton angular correlation probabilities from the 19 F( 3 He,t)19 Ne(α)15 O and 19 F( 3 He,t)19 Ne(p)18 F reactions for the19 Ne states listed above. The squares (blue) are experimentally determined values with associated uncertainty. Error bars in θc.m. represent the width of the angular bin. Even legendre polynomial terms are fitted to the data and the maximum order of the summation kmax is indicated. The best fit is shown by the solid line (red). Circles (black) are from a similar experiment performed by Visser et al.[19].

FIG. 7 .

 7 FIG. 7. (Colour online) Alpha-particle decay branching ratios from the present work (red) are displayed with previous results from the literature for comparison.

FIG. 8 .

 8 FIG. 8. (Colour online) Triton-alpha angular correlation from the decay of the 19 Ne doublet at Ex = 6289 keV. The blue squares are experimentally determined values with associated uncertainty. Error bars in θc.m. represent the width of the angular bin. Best fits of the angular correlation function are represented for three different values of kmax (see text).

  FIG. 9.(Colour online) Astrophysical S-factor for the 18 F(p,α)15 O reaction as a function of the center-of-mass energy. R-matrix calculations for the 6.008 MeV state are represented in color lines for different spin-parity assumptions. Calculations with three different ways of estimating the proton ANC values are presented in case of a 1/2 + assignment (see labels in the legend and text for discussion). The contribution of the most influential resonances is represented in solid black lines for comparison purposes.

  al.. Indeed the angular distribution presented by Bardayan et al. (Fig 2 in that work) from the 20 Ne(p,d)

TABLE I .

 I Alpha-particle branching ratios from the present work, and comparison with values reported in the literature. Excitation energies and spin and parity assignment comes from literature unless otherwise stated. Resonance energies are given with respect to the p+ 18 F threshold (Sp = 6410.0 (5) keV). This state is probably a doublet, see text for discussion.

	Ex	E cm r	J π			Γα/Γ branching ratio
	(keV)	(keV)		Present	Utku et al. [31]	Visser et al. [19]	Bardayan et al. [7]	Murphy et al. [8]
	6289 a	-121	> 7/2 b	0.92 (11)
	6742	332	3/2 -	0.92 (9)	1.04 (8)	0.901 +0.074 -0.031
	6864	454	7/2 -	0.81 (9)	0.96 (8)	0.932 +0.028 -0.031
	7076	666	3/2 +	0.62 (7)	0.64 (6)	0.613 (16)	0.61 (2)
	7420	1010	7/2 +	0.76 (12)			0.72 (14)
	7500	1090	5/2 +	0.47 (6)	0.16 (2)			0.60 (5)

a b From the present analysis.

D. The sub-threshold state at Ex = 6289 keV

ACKNOWLEDGMENTS

The continued support of the staff of the Tandem-Alto facility is gratefully acknowledged. NdS and AML acknowledge very fruitful discussions with Pierre Descouvemont about the properties of sub-threshold 19 Ne states, and with Michael Bentley on mirror energy differences. AML acknowledges the support of the Science and Technology Facilities Council and the Royal Society. This article is based upon work from the "ChETEC" COST Action (CA16117), supported by COST (European Cooperation in Science and Technology).