Lucie Dalibert
email: lucie.dalibert@univ-lyon1.fr

Agathe Camus

Striving to live well with chronic neuropathic pain managed by a neuromodulation technology: A phenomenological exploration

Introduction

Pain is a widely shared experience. It is, in fact, the main reason why people consult their general practitioner or go to the emergency department (Inserm, 2008;[START_REF] Jackson | Pain and Bodies[END_REF]SFETD, 2017). While acute pain is a healthy and useful warning signal that indicates that something is wrong with one's body, when it is chronic, that is, when it lasts for more than three months, pain has no warning function anymore. Rather, pain itself becomes the problem that demands attention. It is estimated that between 20 and 30% of the European adult population suffers from chronic pain [START_REF] Bouhassira | Prevalence of Chronic Pain with Neuropathic Characteristics in the General Population[END_REF][START_REF] Breivik | Survey of Chronic Pain in Europe: Prevalence, Impact on Daily Life, and Treatment[END_REF][START_REF] Van Hecke | Chronic Pain Epidemiology and its Clinical Relevance[END_REF][START_REF] Queneau | Les douleurs chroniques en France. Recommandations de l'Académie nationale de médecine pour une meilleure prise en charge des malades[END_REF]. Among them, one out of three people, i.e., 7 to 10% of the adult European population, suffers from neuropathic pain [START_REF] Bouhassira | Prevalence of Chronic Pain with Neuropathic Characteristics in the General Population[END_REF][START_REF] Colloca | Neuropathic Pain[END_REF][START_REF] Chenaf | Prevalence of Chronic Pain With or Without Neuropathic Characteristics in France Using the Capture-Recapture Method: A Population-Based Study[END_REF], which is pain caused by a lesion or disease of the somatosensory nervous system (IASP, 1994;[START_REF] Colloca | Neuropathic Pain[END_REF]. Although it is a rather common 1 neurological disorder, neuropathic pain is very difficult to treat with medication (De Vos 2 2013). Indeed, besides analgesics having little effect on it (with the exception of certain opioids), less than 50% of the individuals who receive the most frequent treatments, which consist of repositioned drugs (mainly anticonvulsants and antidepressants), achieve a Somatosensory 'refers to information about the body per se, including visceral organs, rather than information 1 about the external world (e.g., vision, hearing, or olfaction)' (IASP, 1994). As for the somatosensory system, it 'allows for the perception of touch, pressure, pain, temperature, position, movement and vibration' (Colloca et al, 2017, p. 2).

The difficulties related to pain management and treatment are not restricted to neuropathic pain. As observed 2 by Harald Breivik and his colleagues in their survey of chronic pain in Europe, 'one-third of the chronic pain sufferers were currently not being treated' (Breivik et al, 2006, p. 287). Among those who received treatment, 40% 'had inadequate management of their pain,' be it neuropathic, musculoskeletal or other, with 'only 2% […] treated by a pain management specialist' (Ibid.). Even more alarming, the French society for the evaluation and the treatment of pain estimates that 'more than 70% of chronic pain patients do not receive appropriate treatment for their pain, and less than 3% of them receive care in a specialised centre' (SFETD, 2017, p. 9, my translation).

significant reduction of their pain [START_REF] Chenaf | Prevalence of Chronic Pain With or Without Neuropathic Characteristics in France Using the Capture-Recapture Method: A Population-Based Study[END_REF], Inserm, 2008). In this context, alternative forms of therapy are being researched and used to treat or manage neuropathic pain.

Spinal cord stimulation is one of them. Based on the gate control theory elaborated in 1965 by Ronald Melzack and Patrick Wall that postulates that pain can be (electrically) inhibited by non-painful stimuli [START_REF] Rossi | The History of Electrical Stimulation of the Nervous System for the Control of Pain[END_REF], spinal cord stimulation (SCS) is a neuromodulation technology that acts directly upon neural tissue. More specifically, composed of one or two electrodes implanted on the dorsal columns of the spinal cord and of a pulse generator (a neurostimulator) implanted under the skin of the lower abdomen or upper buttock, the technology administers electrical pulses that interrupt pain signals, thus reducing neuropathic pain perception [START_REF] De Vos | Spinal Cord Stimulation and Modulation of Neuropathic Pain[END_REF]. In addition to these internal components, an external remote control enables the person living with SCS to regulate the intensity of the stimulation. While obstructing pain signals, the technology does not however cure the cause of pain: rather, it replaces pain perception by paraesthesia, a 'more pleasant sensation' generally described as tingling or pricking (pins and needles).

In this article, I aim to explore life with chronic pain as it is managed by spinal cord stimulation. More particularly, how is bodily intentionality affected and effected in such experience? If anthropologists, sociologists and philosophers have inquired into the experience of/with chronic pain as well as into the strategies and coping mechanisms that people living with chronic pain implement daily [START_REF] Scarry | Livre blanc sur la douleur 2017: État des lieux et propositions pour un système de santé éthique, moderne et citoyen[END_REF][START_REF] Baszanger | Pain: Its Experience and Treatments[END_REF][START_REF] Jackson | Chronic Pain and the Tension between the Body as Subject and the Body as Object[END_REF][START_REF] Jackson | Pain and Bodies[END_REF][START_REF] Richardson | Is Chronic Widespread Pain Biographically Disruptive?[END_REF][START_REF] Zeiler | A Phenomenological Analysis of Bodily Self-awareness in the Experience of Pain and Pleasure: On Dys-appearance and Eu-appearance[END_REF][START_REF] Breton | Anthropologie de la douleur. Edition revue et complétée[END_REF]& 2016), fewer have attended to its 'technological care,' to use Mathilde Lancelot (2019)'s apt expression, especially when such care is performed by implanted technologies [START_REF] Kaufman | Ironic Technology: Old Age and the Implantable Cardioverter Defibrillator in US Health Care[END_REF][START_REF] Dalibert | Posthumanism and Somatechnologies: Exploring the Intimate Relations between Humans and Technologies[END_REF][START_REF] Dalibert | Living with Spinal Cord Stimulation: Doing Embodiment and Incorporation[END_REF][START_REF] Haddow | Everyday cyborgs[END_REF][START_REF] Oudshoorn | Sustaining Cyborgs: Sensing and Tuning Agencies of Pacemakers and Implantable Cardioverter Defibrillators[END_REF][START_REF] Oudshoorn | Resilient Cyborgs: Living and Dying with Pacemakers and Defibrillators[END_REF]. Both medical studies and the philosophy, anthropology and sociology of health underline how chronic pain severely impairs people's lives, having a negative influence on almost all aspects of life: on one's sleep and physical abilities, on one's mental health and wellbeing, on one's social and professional life -on one's world [START_REF] Jackson | Chronic Pain and the Tension between the Body as Subject and the Body as Object[END_REF][START_REF] Jackson | Pain and Bodies[END_REF][START_REF] Breivik | Survey of Chronic Pain in Europe: Prevalence, Impact on Daily Life, and Treatment[END_REF][START_REF] Bouhassira | Prevalence of Chronic Pain with Neuropathic Characteristics in the General Population[END_REF]van 3 Hecke et al., 2013;[START_REF] Breton | Anthropologie de la douleur. Edition revue et complétée[END_REF]. Pain has famously been described by Elaine Scarry as a 'destruction' or 'unmaking of the world' [START_REF] Scarry | Livre blanc sur la douleur 2017: État des lieux et propositions pour un système de santé éthique, moderne et citoyen[END_REF]. That is, from a phenomenological perspective, being is always being in, as well as to, the world [START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF]. In Drew Leder's words, 'the lived body […] is an openness upon the world. It is a centre from which the rays of intentionality radiate outward ' (1990, p. 74). In everyday life, in the normal course of one's life, one is rarely concerned with his or her pain-free body; rather, s/he is projected outside from it, towards the world. Bodily intentionality is thus characterised by agency -'I can.' Conversely, in pain, one is no longer directed towards the world but called, instead, towards his or her painful body (-part). The latter becomes the object of one's concern and attention, thereby impacting one's perception and action (Zeiler, 2010, p. 336). Being a bodyin-pain enacts a world in which one's field of possibilities is hindered -'I can' gives way to 'I cannot' -and such a world can be experienced as shattered and shattering. In fact, it has to be emphasised that 'I can' and 'I cannot,' or the degree of possibilities for the embodied subjects, can only be understood in relation to the latter's environnement or lifeworld. In this respect, Iris Marion Young (1980) and Sara [START_REF] Ahmed | A Phenomenology of Whiteness[END_REF] have powerfully, and respectively, shown that women who live in a sexist society and are taught to protect and restrict their body might experience an 'I cannot' while a black person who lives in a white world might experience being 'stopped' (Ahmed, 2007, p. 61) or an 'I cannot.' Therefore, one's degree of bodily intentionality does not reside solely in one's body; rather, it is also affected and effected by one's lifeworld. In (chronic) pain too, one's 'I cannot' is not an exclusive property of one's body .

4

When attending to chronic pain and chronic illness, 'disruption' is a recurring term or theme in academic work. Accompanied by an 'intentional disruption' (Leder, 1990, p. 73) or causing a 'disrupted intentionality' (Zeiler, 2010, pp. 337-339), chronic pain also constitutes a 'biographical disruption' [START_REF] Richardson | Is Chronic Widespread Pain Biographically Disruptive?[END_REF]. Initially formulated in the context of chronic illness by Michael Bury, biographical disruption conveys that, in one's life, chronic illness 'mark[s] a biographical shift from a perceived normal trajectory through relatively

Epidemiological and medical research also frequently emphasise the socio-economic burden of chronic pain.

3 Due to its impact on healthcare, absence from work and job loss, it is evaluated at more than €200 billion per year in Europe (van Hecke et al, 2013; see also [START_REF] Eschalier | Prevalence and Characteristics of Pain and Patients Suffering from Pain in France: An Epidemiological Survey National Health and Wellness Survey in 15,000 adults[END_REF]. I thank one of the anonymous reviewers for inviting me to make that point stronger.

predictable chronological steps, to one fundamentally abnormal and inwardly damaging ' (1982, p. 171). It throws into confusion one's 'taken-for-granted assumptions and behaviours [and] the person's biography and self-concept' (Ibid., p. 169). For S. Kay Toombs (1987), this disruption caused by chronic illness presents itself as five losses: the loss of wholeness, of certainty, of control, of freedom and of the familiar world. Similarly, for Havi Carel, it materialises as 'bodily doubt,' where one's ' [b]asic tacit beliefs about bodily abilities that were previously taken for granted are suddenly, and sometimes acutely, made explicit and thrown into question […] [It] gives rise to an experience of unreality, estrangement, and detachment. From a feeling of inhabiting a familiar world, the ill person is thrown into uncertainty and anxiety' (Carel, 2016, p. 92). It is, in fact, one's sense of being-in-the-world that is affected -disrupted (Ibid.: 94).

Chronic illness, chronic pain, and accounts thereof bear substantial similarities. As it has been underlined, chronic illness frequently entails pain and suffering, while, conversely, chronic pain might stem from chronic illness, such as neuropathy [START_REF] Bury | Chronic Illness a Biographical Disruption[END_REF][START_REF] Charmaz | Stories of Suffering: Subjective Tales and Research Narratives[END_REF][START_REF] Carel | Phenomenology of Illness[END_REF]. Additionally, as Isabelle [START_REF] Baszanger | Pain: Its Experience and Treatments[END_REF] draws attention to, their chronic nature means that they share two characteristics: duration and clinical management. Chronic pain, like chronic illness, is not short-lived, but rather 'lasts for months, years, or often a life-time

[…] Instead of a cure, the chronic condition has to be managed day after day' (Ibid., p. 425).

Living with chronic pain therefore requires adjustment and adaptation, but also the acquisition of new skills to live a life as 'normal,' as 'ordinary,' or as little hampered by the (bodily, social, material, and so forth) constraints that the condition entails, as possible [START_REF] Carel | Phenomenology of Illness[END_REF][START_REF] Winance | Histoires de normes. Articuler récits biographiques et analyses des processus de normalisation par les sciences sociales[END_REF].

Joseph W. Schneider and Peter Conrad write that '[a] bona fide illness experience perspective 5 must consider people's everyday lives lived with and in spite of illness » (1983, p. 9, quoted in Baszanger, 1989, p. 428, emphasis in original). Thus, to explore life with chronic pain as it is managed by spinal cord stimulation, this article will rely on fieldwork I realised in 2012 at a Dutch regional hospital. There, I interviewed 15 people living with the neuromodulation technology as well as the nurse and the neurosurgeon who take care of people (to be) The latter is structured in three parts. After having presented what it means to be living with, or in, chronic neuropathic pain in the first part, in the second one, I will attend to how chronic neuropathic pain, as it is managed by analgesic medication and spinal cord stimulation, is experienced. When doing so, particular attention will be paid to the way one's being in the world is affected in these different configurations. While living with chronic neuropathic pain and chronic neuropathic pain managed by medicine are characterised by 'I cannot,' SCS is experienced as a 'reworlding' marked by 'I can.' In the third and last part, I will show, however, that demanding work is necessary to achieve and maintain bodily intentionality and to live well with SCS.

Living in chronic neuropathic pain: Inhabiting a world of shattered possibilities

Living with chronic neuropathic pain means experiencing some body parts as distinctively painful. For people whose symptoms are treated with spinal cord stimulation, pain is located in the lower-back, legs and feet. Diagnosed with tools such as the 'Douleur Neuropathique 4 (DN4)' questionnaire, neuropathic pain is generally described as burning, painfully cold or electric-like shock sensations, which can be associated with tingling, pins and needles, numbness and itching [START_REF] Bouhassira | Development and Validation of the Neuropathic Pain Symptom Inventory[END_REF][START_REF] Colloca | Neuropathic Pain[END_REF]. Other sensations, such as pain brought by brushing as well as reduced sense (hypoaesthesia) upon touch or pinprick, can be experienced by people living with neuropathic pain (Ibid.). In contrast to its dry clinical characterisation, people experiencing it use much more vivid, visceral even, images to describe it. As expressed by these three men living with chronic neuropathic pain, the latter is ceaseless.

There is no respite from it, even at night. All evoke the pain they feel in their feet through the action of walking barefoot on particularly unpleasant materials -pebbles, a rope, broken glass -and doing so constantly. Pain, be it burning or shooting, is also exacerbated through contact with matter and objects that are part of daily life -socks, shoes, a blanket, sand or water. Unavoidable, it is also conjured up as the impossibility to do certain things, nothing less than sleeping. Acutely felt in one's body (the feet in Mr Koopman, Mulder and Meijer's case), chronic neuropathic pain has significant repercussions on one's being in the world.

Recalling how life was before he was implanted with SCS, Mr van Houten, 61 years old, explains that

[w]hen I don't have this [SCS], I am in a lot of pain. I'm always lying in bed or I'm sitting in a wheelchair, all day. And I sit down, and I look outside, I don't do anything -maybe, yes, get some coffee, at home.

As it overwhelms Mr van Houten, chronic neuropathic pain also engulfs his world: it 'unmakes' it [START_REF] Scarry | Livre blanc sur la douleur 2017: État des lieux et propositions pour un système de santé éthique, moderne et citoyen[END_REF] all the while it disrupts his bodily intentionality [START_REF] Leder | The Absent Body[END_REF][START_REF] Zeiler | A Phenomenological Analysis of Bodily Self-awareness in the Experience of Pain and Pleasure: On Dys-appearance and Eu-appearance[END_REF]. That is, as previously mentioned, in good health and without pain, the body is experienced as an absent presence (Leder, 1990, p. 36-68).'Most of the time, most of us, walk to the door without a thought. And as we walk, we think thoughts without a thought of the body that transparently makes not only out walking but also out thoughts possible,' writes Vivian Sobchack (2004, p. 190, emphasis in original). In other words, the lifeworld of healthy, pain-free people is a world characterised by agency -I can. Mr van Houten's experience is fundamentally different. Brought to the forefront of his consciousness and attention, that is, having 'dys-appeared' or having become an 'absent absence,' his painful body is experienced as a strange, disturbing presence: as alien [START_REF] Leder | The Absent Body[END_REF]. As Kristin Zeiler phrases it, 'I no longer experience that I am my body, but that I have a body ' (2010, p. 337). Objectified, and even alienated, the body becomes a hermeneutical problem (Sobchack, op. cit). In this respect, Havi Carel's account of bodily doubt is illuminating to understand the extent to which chronic pain can throw existing trust in one's body and bodily abilities in disarray: as one lives and becomes aware of the failings of his or her body-in-chronic-pain, s/he starts experiencing 'anxiety on a physical level, hesitation with respect to movement and action, and a deep disturbance of existential feeling' (Carel, 2016, p. 96). Such realisation, and loss of bodily intentionality and agency in general, are experienced as highly distressing: it is with sorrow that Mrs Bloemen, 45 years old, remembers that 13 years ago,

[w]hen the children were 3 and 7 years old, we… with one of his aunts [she points to her husband] who's twenty years older than me, we went to the zoo in Rotterdam, and she took my children [her voice trembles as she fights back tears] to the playground because I couldn't do it.

Because pain is tying her to her 'here-and-now' body (Leder, 1990, p. 76), Mrs Bloemen is unable to perform movements and actions as well as to undertake activities that a much older woman can realise. In chronic pain, one's lifeworld or habitual world becomes characterised by 'I cannot.'

In it, space and time are constricted (Leder, 1990, p. 73-76). Mr van Houten's horizon, for instance, is reduced to his home, while Mrs Bloemen's stops at the playground's borders. In chronic pain, with the painful body having become the thematic object of her attention, '[s]pace loses its normal directionality as the world ceases to be the locus of purposeful My world, and the world of those who are close to me, has shrunk. For me, the trap is permanent. There is no release from it (Carel, 2016, p. 71).

Where once accessible places have become out of reach, doing anything now demands planning. This changed state of affairs not only involves herself but also her loved ones, those who share her life (e.g. her partner, children, friends). As pain (or illness) is chronic, there is however no break nor turning back, which also affects one's relation to time. A certainty is that pain is not only present -and constantly so -today, but that it also lasts and requires that one attends to his or her bodily sensations throughout the day, before and when engaging in particular activities (Zeiler, 2010, p. 336). In echo of Carel, Mrs Bloemen recounts that 'before [living with SCS], I really have to think about what I am going to do today. Now I just do it.' As for the future, as one no longer trusts his or her body, it is foreseen, and feared, that it might hold a worsening of the pain (Le Breton, 2016, p. 132). Finally, if such dread pervades future plans as well as present considerations, pain also colours one's past, insofar as 'while knowing intellectually that we were once not in pain we have lost the bodily memory of how this felt,' explains Leder (1990, p. 76). Bodily doubt envelops one's present and future as well as one's past.

With chronic pain offering no respite days and nights but tainting one's existence and undoing one's world with disrupted bodily intentionality, bodily doubt and a constricted space-time, quest for a treatment or a solution to restrain or ease its effects becomes an important part of one's life (Baszanger, 1989, p. 428). Chronic neuropathic pain is progressive, as Mrs Jansen, 63 years old, reminds us:

You have the feeling that you are reasonably healthy, weirdly enough, because everything happens so gradually and you get so used to the pain, so you go one step further and then you think, well this [increase of pain] I can also still take.

When pain becomes eventually unbearable, alleviating it becomes one's, or rather one's and one's partner's focus.

Mr Meijer: I was only searching for pain reduction.

Mrs Meijer: He was in so much pain, everyday, every hour. So much pain… It was the solution to be implanted.

The men and women I interviewed all mentioned not only the different medical professionals, hospitals and specialised pain centres they have visited and consulted, often in different parts of the country, but also, for some, the clinical trials in which they took part. Implantation with spinal cord stimulation occurs after a long journey with pain and various pain medications.

The technology is indeed used as last resort in cases of refractory chronic neuropathic pain [START_REF] Colloca | Neuropathic Pain[END_REF].

Living in chronic neuropathic pain, that is, constantly experiencing burning, shooting, painfully cold or electric-like shock sensations is disruptive. It has significant repercussions on one's being in the world, as one's bodily intentionality is hindered and one's projection in the world shattered. Seized by bodily doubt, one's existence endures a constriction of space and time and a reduced agency. One's lifeworld is marked by 'I cannot.' In this context, people look for remedies against their pain, and it is only after medication proves ineffective that spinal cord stimulation is offered as a last resort treatment. It is against this backdropi.e., the experience of chronic pain and the experience of chronic pain managed by drugsthat what it means to live with chronic pain managed with spinal cord stimulation has to be understood.

Managing chronic pain with medication and spinal cord stimulation: From a world of 'I cannot' to a world of 'I can'

Eliminating or at least reducing pain so that it becomes endurable is a lasting endeavour for people living in chronic pain. As aforementioned, they do not experience that they are but that they have a body [START_REF] Zeiler | A Phenomenological Analysis of Bodily Self-awareness in the Experience of Pain and Pleasure: On Dys-appearance and Eu-appearance[END_REF]. In pain, there is a fracture between the body as object, i.e.

Körper [START_REF] Husserl | Ideas Pertaining to a Pure Phenomenology and to Phenomenological Philosophy[END_REF], and the body as subject, i.e. Leib (Ibid.) or corps propre [START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF]. Chronic pain not only amounts to an 'I cannot,' but also corresponds to the impossibility to be the body one has (see also [START_REF] Slatman | Is It Possible to "Incorporate" a Scar? Revisiting a Basic Concept in Phenomenology[END_REF][START_REF] Slatman | Hand Transplants and Bodily Integrity[END_REF]. Such inability is however not limited to the experience of chronic pain. Rather, it extends to life with chronic pain as it is managed by medication.

When Chronic neuropathic pain and its management with pain medication unmakes Mr Meijer and his wife's world -their world. It prevents them from living a 'normal life,' one that entails leaving the house and having social connections and activities, hence living like 'everybody else' [START_REF] Winance | Histoires de normes. Articuler récits biographiques et analyses des processus de normalisation par les sciences sociales[END_REF]. It is not just the intentionality of the pain sufferer that is disrupted but that of his or her loved ones too. 'I cannot' becomes 'we cannot.'

In all three accounts, pain medication is associated with unpleasant experiences and memories. Not only is their body-in-pain experienced as other, but with medication they also feel that they are not themselves. This resonates with Jean-Luc Nancy's account of his experience with heart transplantation and immunosuppressants. 'An intruder is in me, and I am becoming a stranger to myself,' writes Nancy (2008, p. 167), before explaining that '[y]ou no longer recognize yourself: but "recognize" no longer means anything. Very soon, you are just a wavering, a strangeness suspended between poorly identified states, between pains, between impotences, between failings. Relating to the self has become a problem, a difficulty or an opacity: it happens through evil or fear, no longer anything immediate -and the mediations are tiring.

[…] I end/s up being nothing more than a fine wire stretched from pain to pain and strangeness to strangeness' (Ibid., p. 169). The rift that takes place within the body-in-pain, with the impossibility to be the body one has, seems to be exacerbated with pain medication, with one's sense of self being jeopardised or dis-articulated (Charmaz, 1999, p. 364). Such an experience strongly colours the way spinal cord stimulation is perceived by people living with chronic neuropathic pain, especially as the technology is implanted in case of refractory chronic pain. People living with spinal cord stimulation have, therefore, experienced the disabling effects of pain medication without the promised pain relief.

If chronic pain and analgesic medication can be apprehended as biographically disruptive, being implanted with spinal cord stimulation appears as a rebirth or a reconstruction.

Reconstruction happens in at least two respects. First, through the implantation of the SCS system, one's subjective experience of chronic pain is objectivised and legitimised. In this respect, Baszanger points out that in each medical encounter, 'the evaluation and legitimation of pain -the question of credibility -arises because pain is a sensation that can be directly perceived only by the person who feels it ' (1989, p. 427). That is, others, including physicians, have to rely on the person's subjective experience and the way s/he expresses it to appreciate the presence and intensity of pain. As the neurosurgeon implanting the neuromodulation device expressed it during one of our discussions, 'there is no person in the world who can objectively measure if somebody has pain: we have to believe that somebody has pain.' In this context, the existence of pain is rendered questionable (see also Jackson, 1994, p. 213). Screening tools, such as the DN4, and rating scales contribute to objectivise pain by turning it into an operational medical object (Baszanger, op.cit.). Yet, to the extent that there might not be an identifiable lesion, doubt can still be cast on its reality. As the electrode array is positioned on the spine, as the electrical field of stimulation is mapped, and as the burning and shooting pain felt in one's lower back, legs and/or feet is replaced by a tingling sensation, pain is objectivised. Maes, the specialised nurse at the regional hospital where fieldwork was realised)

Paradoxically, neuropathic pain materialises through its disappearance, or rather, replacement by paraesthesia. The (technologically-induced) validation of chronic neuropathic pain can be experienced as a recognition of the credibility of the sufferer's claims, hence as a reparation.

Second, SCS is experienced as a 'reworlding' [START_REF] Besmer | Embodying a Translation Technology: The Cochlear Implant and Cyborg Intentionality[END_REF]. With her body-in-pain significantly less, if not no longer, at the forefront of her attention and awareness, that is, no longer an absent absence [START_REF] Leder | The Absent Body[END_REF], Mrs Bloemen is able to undertake previously unimaginable actions, such as climbing a mountain. It is, for her, a victory. It is, in fact, a hard-won one. Bodily intentionality and agency have been regained

after a prolonged and straining journey as well as through much efforts. Indeed, as I shall describe shortly, 'I can' is not a straightforward result of implantation. Rather, it demands work.

Life with chronic pain managed with (strong) analgesic medication is associated with 'I cannot.' As in pain, one cannot be the body one has, and one's sense of self is severely disrupted. Implantation with spinal cord stimulation gives way to a reworlding. That is, one is able to project oneself in the world. The latter is again marked by 'I can.' As we will see, such outcome is however neither effortless nor absolute.

Living well with spinal cord stimulation: A hard-won achievement

Spinal cord stimulation replaces pain perception with a 'more pleasant' sensation, namely tingling or pins and needles . Although the technology is implanted, its disappearance under 6 the skin does not mean that it disappears from one's awareness. For the SCS system to become 'transparent' [START_REF] Ihde | Technics and Praxis: A Philosophy of Technology[END_REF], that is for the technology and its effects not to be brought to the forefront of one's attention and experienced as bothersome or disabling, living with SCS, and even more so living well with such technology, demands long-term work and a particular attentiveness to one's sociomaterial environment. If SCS enacts a lifeworld of 'I can,' the latter results from training and sustaining activities and efforts, all the while it remains quite precarious.

SCS creates new sensations which can be quite disorientating for its users. After implantation, the sensations elicited by SCS are unfamiliar and awkward, and one is highly aware of them.

As developed elsewhere [START_REF] Dalibert | Posthumanism and Somatechnologies: Exploring the Intimate Relations between Humans and Technologies[END_REF][START_REF] Dalibert | Living with Spinal Cord Stimulation: Doing Embodiment and Incorporation[END_REF], making these sensations one's own is the result of a reflexive exploration process, through which one (playfully) experiments with the technology. It is by varying the intensity of the stimulation, performing bodily movements and assessing the resulting sensations that progressively SCS becomes embodied, that is, rendered (quasi-) transparent at the sensory-kinetic level [START_REF] Ihde | Technics and Praxis: A Philosophy of Technology[END_REF][START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF].

As such, embodiment demands a renewed and sustained attentiveness to one's body. Over

Stimulation with frequencies below 30Hz evokes distinct tingling sensations. New stimulation paradigms, time however, such process of 'adjustment' (Winance, 2015) no longer requires reflexion: rather, people living with SCS have acquired know-how and become habituated to the technology. Yet, to live well with SCS, the latter must not only be embodied (in one's body schema) but also incorporated (in one's body image): besides no longer drawing attention to itself, it must be seen and experienced as a part of one's body. To achieve that, one must be able to identify with one's technologically transformed body, that is, 'to appreciate and accept both the strange body part's visual features […] and its haptic, affective aspects' (Slatman & Widdershoven, 2010. p. 75). Doing so, or in other words, being the body one has, is hardly accomplished alone. Loved ones as well as social norms play a key role here, insofar as they can hinder or, on the contrary, facilitate identification and incorporation (see [START_REF] Dalibert | Posthumanism and Somatechnologies: Exploring the Intimate Relations between Humans and Technologies[END_REF][START_REF] Dalibert | Living with Spinal Cord Stimulation: Doing Embodiment and Incorporation[END_REF].

Embodiment and incorporation, two processes that enable people to regain bodily intentionality and agency, and live well with spinal cord stimulation, are not realised once and for all in the weeks and months following implantation. Bodies implanted with technology must be 'sustained' in the long term [START_REF] Oudshoorn | Sustaining Cyborgs: Sensing and Tuning Agencies of Pacemakers and Implantable Cardioverter Defibrillators[END_REF][START_REF] Oudshoorn | Resilient Cyborgs: Living and Dying with Pacemakers and Defibrillators[END_REF]. While sustaining bodies in chronic neuropathic pain is generally realised by humans, i.e. family, friends, (health-) care professionals, in the case of SCS, it also entails a distinctive technological care. For SCS to optimally replace pain perception with paraesthesia, the pulse generator has to be properly programmed. After implantation, people have one or two programmes set by the nurse or the physician in charge. With time, however, they require new adjustments of the device.

Throughout time and depending on one's activities, postures and tiredness, pain's intensity and one's sensitivity to it and to paraesthesia might change, as well as the way one's feet, legs and lower back are affected during the day and at night. Therefore, regular control visits are organised at the hospital to check whether the technology is working correctly and whether people experience appropriate stimulation for their pain. Yet, fine-tuning the device so that the electrode's 8 contact points create the right electrical field to interrupt pain signals and induce paraesthesia in the desired body parts is a complex endeavour. Fine-tuning requires the collaborative and coordinated actions of the person living with SCS and the programming nurse or physician.

I was able to assist to such a 'dance of agency' [START_REF] Pickering | The Mangle of Practice: Time, Agency, and Science[END_REF] between SCS and its human users (the person implanted and the person programming the device) during the control visit that I observed. There, Judith Hart, who connected a programmer (a small PDA) to the patient's pulse generator in order to fine-tune it, explained:

-Judith Hart: On one lead, there are 8 points.

[…] They can all be positive, or negative, or neutral. So I have lots of possibilities and we have tried almost everything with Mr. Koopman.

-Mr Koopman: Yes and we have, ehm, since I experience pain especially under my feet, you must also try to stop that tingling right there, but we haven't achieved that yet.

-LD: It is hard to reach?

-Judith: Yes and maybe not even possible…

[…]
-Judith [starts recording values for each contact point on the lead] The first is 500.

[To Mr

Koopman] You can tell when something… -Mr Koopman: Yes, is there something coming now?

-Judith: Yes.

-Mr Koopman: Yes… I feel something.

-Judith: Where?

-Mr Koopman: Ehm… in… at the top of my lower back and in my buttocks.

-Judith: So, and at the end?

-Mr Koopman: Yes… because it reaches… it is going to the left… The concentration is particularly at my calves.

-Judith: Ok, that's good.

[…]

-Judith: I can give you this program for now… Do you feel it now?

-Mr Koopman: Yes.

-Judith: Yes? Gently? And now? Now if I increase it? Then it becomes a pleasant tingling?

-Mr Koopman: Yes… Yes, I think I like this.

-Judith: Then I am at least increasing this one, so that the right side is added a bit.

-Mr Koopman: Did you decrease it now?

-Judith: I adjusted it now like you said, I think that makes a good baseline.

-Mr Koopman: Put it lightly higher.

-Judith: Higher? -Mr Koopman: Yes.

-Judith: Umm… like this… It's back up again now.

-Mr Koopman: Yes, it is ok now.

-Judith: Like this? Then I'll save it like it is now.

-Mr Koopman: Yes… It's good like this. That is the neutral program, right?

-Judith: Yes.

-LD: So that is the baseline, in a way?

-Mr Koopman: Yes, that's like the ideal position.

[PDA makes a beeping sound] -Judith: And now you can go in any direction [increase or decrease].

The stimulation creates new sensations. Similar to what is demanded of them during implantation, during control visits, people living with SCS have to assess the new sensations that are created by the device. They have to be attentive to their bodily feel as the physician is acting on the stimulation parameters, so as to report the paraesthesia's location, type and intensity to her. While their sensory experiences guide the physician's actions, she reciprocally directs them with her questions, e.g., 'do you feel it now?', 'like this?'

Challenging for people living with SCS, fine-tuning is also difficult for the physician, whose

understanding of what constitutes the right settings might be even so slightly at odds with what her patients experience. Although essential, the adjustment process is also highly precarious -and not only because stimulation might not be able to induce paraesthesia in all painful areas. Anna Maes explains that after fine-tuning and stimulating for 30 to 45 minutes, that's enough. People tend to not feel at all or feel everything… tingly. And that's not because they feel the tingly feeling everywhere, but they don't know where to feel what, where the tingly feeling is at. So you can't have it located. That's the experience I have. Yeah, most of the patients say, I don't know, I don't know

where that is: it seems to be here, but then again it seems to be there, [Anna points at different parts of her legs and feet] and that's difficult, yeah, to explain.

Fine-tuning, due to the intense self-awareness it requires, can be overwhelming for patients.

Eventually, they cannot make sense of their sensations, which jeopardises the adjustment procedure. In her illuminating account of fine-tuning pacemakers and implantable cardioverter defibrillators, Nelly [START_REF] Oudshoorn | Sustaining Cyborgs: Sensing and Tuning Agencies of Pacemakers and Implantable Cardioverter Defibrillators[END_REF][START_REF] Oudshoorn | Resilient Cyborgs: Living and Dying with Pacemakers and Defibrillators[END_REF] writes about the importance of these regular adjustments to create a 'body-technology alliance.' Such a process is not only essential for the technology to be experienced as transparent, hence embodied at the sensorykinetic level, but it is also key in fostering 'resilient cyborgs' (Ibid.), that is people who can cope with the challenges entailed by being and having a technologically transformed body.

Such body-technology alliance is fragile. Fine-tuning enables the technology to remain transparent and to maintain bodily intentionality. However, despite optimal settings, embodiment, incorporation and bodily intentionality can be disrupted. Paradoxically, while living well with SCS necessitates that one becomes attentive to his or her technologically transformed body in order to create a body-technology alliance, it also demands a particular 'disentanglement work' (Oudshoorn, 2020: 118)

Conclusion

In this article, I have explored life with chronic neuropathic pain as it is managed by spinal cord stimulation. Relying on a phenomenological framework, I have addressed how chronic neuropathic pain unmakes one's world, as well as the world of one's loved ones. As it ties its sufferer to his or her here-and-now body and fills him or her with bodily doubt, one's projection towards the world and ability to act and make projects is hindered. One's lifeworld is marked by 'I cannot.' In this context, people look for remedies against their pain. Before being implanted with SCS, people living in and with chronic pain have taken strong analgesic medication, be it opioids, anticonvulsants, antidepressants or more. If their life with chronic pain managed by medicine was no longer saturated with pain, not only was their intentionality still disrupted but their sense of self was also severely compromised. In chronic pain as well as with chronic pain managed by medication, it is not just one's lifeworld that is affected but also the lifeworld that is shared with loved ones. 'I cannot,' which characterises these two experiences, extends into a 'we cannot.' An account of what it means to be living with spinal cord stimulation cannot dispense with these previous experiences. This is so for at least two reasons. First, they form the backdrop against which SCS is experienced as a reparation and a reworlding. The intensity with which one feels that s/he is now part of the world, or of life as Mr van Houten would have it, is intrinsically linked to the extensive disabling effects of chronic neuropathic pain and its management with medication. Second, although they are in the past, life with chronic neuropathic pain and life with chronic neuropathic pain managed with analgesic drugs are however not distant memories but inform present and future considerations -and fears. This is an aspect that was not developed in the body of the article but that deserves to be touched upon in this conclusion.

Even when chronic pain is satisfactorily taken care of by SCS, chronic pain is still there in one's present and one's future. More precisely, the technology keeps pain perception at bay by replacing it with paraesthesia, but it is not a cure, while the future holds the possibility that SCS will eventually stop working. The frailty of one's body is matched with the frailty of the technology: electrodes are fragile and can break -one of the contact points on the electrode implanted in Mr Koopman's body actually broke a few days before his control visit -with little if no option to change or repair them. This colours the horizon of people living with chronic pain managed by SCS. Likewise, the 'repair' that people experience with SCS should not be conceived as the restoration of a former, pain-free existence. As Havi Carel explains in the context of chronic illness, 'it is impossible to return to the naïve (and, in retrospect, gullible) state of confidence once was in before. There is no turning back once genuine bodily doubt has been experienced; one's basic orientation in the world has changed and the possibility of catastrophic bodily failure is now part of one's experiential horizons ' (2016, p. 95). This 'loss of innocence' is shared by people living with SCS.

In this article, I also showed that while people experiencing chronic neuropathic pain strive to live a 'normal life,' to live well with spinal cord stimulation demands particular and constant efforts. A well-programmed pulse generator, hence fine-tuning, is essential not only to be able to get habituated to the technology but also to be able to identify with one's technologically transformed body. Yet fine-tuning is a delicate and demanding exercice, for both the physician and the person living with SCS. Furthermore, people living with SCS have to navigate their intimate entanglement with other devices, which might result in misfits. The 'I can' enabled by SCS is therefore not absolute, but can give way to 'I cannot.' Importantly, what these disabling sociomaterial encounters reveal is that one's 'I can' and 'I cannot' should not be seen as resting with one's body, abilities and impairments. Rather, they are also dependent on one's embeddedness in power relations and socio-cultural norms [START_REF] Dalibert | Living with Spinal Cord Stimulation: Doing Embodiment and Incorporation[END_REF]. With chronic neuropathic pain and SCS, 'I can' and 'I cannot' are particularly linked to 'compulsory able-bodiedness,' [START_REF] Mcruer | Compulsory Able-Bodiedness and Queer/Disabled Existence[END_REF], which values and posits able-bodies as the norm and unavoidable injunction. The latter affects how one can live, and all the more so live well, with chronic neuropathic pain managed by spinal cord stimulation.

Finally, the people living with SCS that I interviewed were relatively young, being between 45 and 63 years old. Therefore, it is to be expected that they will age with the device. This raises questions about the vulnerabilities they will face as the technology will also also grow older with them and might malfunction or be damaged. They invite researchers to investigate what it means to be ageing with chronic neuropathic pain and an ageing technology.

  The pain that I have in my feet is constant. I'm always in the South of France along the river, on pebbles with my bare feet. So you should imagine walking on that. But, well, I also have a lot of flashy shooting pain. In my feet and toes. And often I have cold feet (Mr Koopman, 53 years old).A burning pain on the feet, like you're stepping on a rope constantly, constantly. I didn't sleep at night: 4 times a night, I had to go out of bed because of so much pain (Mr Mulder, 57 years old).It's like walking on glass, on broken glass. It's ouh. So walking is full of pain. I can't walk on sand, on the beach: it doesn't work. When I go under the shower or go swim, the water hurts. […] The pain is inside, all the time. […] At home, I am always walking on slippers, shoes are not possible anymore. When I am in bed, the blanket is not on my feet, otherwise I can't sleep. I can't handle anything at my feet, everything hurts: socks, shoes, everything (Mr Meijer, 56 years old).

Figure 1 :

 1 Figure 1: Two ways of mapping the electrical field on the dorsal column of the spinal cord and interrupting pain signals with the electrode (photo taken from textbook belonging to Anna

  It [SCS] changed my life. What I can do and how I feel […] Now I can go outside, I can go shopping, I can take care of my husband. And when I don't have this, [sigh] yeah, then I can do nothing. […] I can say now I ehm, I belong somewhere again. I'm now part of the life (Mr van Houten). I have been very active after [the implantation]! [Both he and his wife laugh] I went swimming again, I went working again, at 100%. I became a board member of [a patient association]. It changed my life 100% (Mr Meijer).SCS enables both men to engage in activities and make (new) projects. As it allows them to project themselves in the present and the future, it enables them to be part of the world -of life -again. As such, the neuromodulation technology 'rebuilds' their bodily intentionality and projection towards the world. Their lifeworld is characterised by 'I can.' After years with disabling chronic pain and pain medication, this regained agency is lived as a relief and an achievement. In this respect, when asked whether SCS improved her daily life, Mrs Bloemen answers that Yes. Yes. A lot. I can walk better, longer. Ehm… Vier [four], vijf [five]… Four, five years ago, we did go back to France: we've been there 25 years ago, with my parents, and the first time there we climbed the mountain that we could see from the camping. Five years ago, we did it again! We didn't make it quite to the top [her voice fills up with emotion] but it was ehm, yeah overwinning [Dutch]. Mr Bloemen: A victory. Mrs Bloemen: A victory. Yeah, that I could do that. And ehm… yeah… it felt all right.

  asked if he was taking some forms of medication before being implanted with spinal If medication reduces pain perception, it does not restore one's bodily intentionality and projection towards the world. The opacity with which the world is experienced when chronic pain is managed with medicine is not the exclusive preserve of opioids. Indeed, Mr Koopman recalls that I used some medicines, […] a type of antidepressant [that], as a side effect,[…] can fight the pain. […] But my mind was flat, so to speak. And I did not noticed that so well, but my wife and the people around me who noticed said it, and that is an unpleasant experience to hear afterwards… So then I said resolutely: I quit. Before the technology, I was taking 21 pills to reduce the pain and was getting a little bit mad because of the medicine. […] The medicine has such an influence on your brain that… I can't work. I could be there but no thinking. I have a financial job so I have to make a lot of calculations. But my colleagues said 'don't do that.' You don't know if you're doing it right. That was a hard period.Mrs Meijer: We didn't go out then, because he was tired. He was always lying on the couch or in his bed because of the pills, and because of the pain of course. It was not a normal life then.

	And that is what we did.
	cord stimulation, Mr van Houten indicates that
	Yes, very much. Morphine, yes.
	LD: And how did you feel about it?
	Mr van Houten: Oh… Like [he laughs] I don't know where I was: I couldn't drive
	a car, nothing. [Silence] […] The medications you take, you're gevoel [Dutch:
	feeling] […] Your mind is not clear with the medication.

The hazy, disabling effects of pain medication are perceived by oneself as well as others. It is Mr Koopman's wife and loved ones who became first aware of the behavioural changes that were occurring with him when he was taking antidepressants, and who told him about it. As he is not the only one being affected by medicine, it is in fact not just 'I' but 'we' who quit taking it. The way analgesic drugs impact others and upset loved ones all the while it does not restore intentionality ('I can') is quite salient in Mr and Mrs Meijer's exchange: Mr Meijer: My former neurologist told me 'I will give you a morphine pump.' I didn't like it. Because today it's 10 CC, tomorrow 20, 40, 50, you know. Lying on the couch all day, I don't like that. I have been looking for such a long time [to find a solution for the pain].

[…]

  If in high-income countries, we live in environments filled with technological devices, the density and 'the texture of [the] "technosphere" within which we undertake our daily affairs'(Ihde, 1979, p. 7) is more intensely felt by people living with neuromodulation (as well as, in general, implanted and prosthetic) technologies[START_REF] Dalibert | Posthumanism and Somatechnologies: Exploring the Intimate Relations between Humans and Technologies[END_REF]. Whether it is when one's entrance or exit from a shop triggers (metal) detection gates to beep -Action and Kruitvat have become infamous shops for people living with SCS in the Netherlands (interview with Judith Hart) -or when one has to go through airport security, one is reminded not only of the technological nature of his or her lifeworld, but also of his or her intimate entanglement in it. As I could hear it during a conversation that I witnessed between Anna Maes and Mr Smit (one of her patients), despite the fact that people living with SCS are advised to turn off their neuromodulation device before going though airport security and are provided with a card that they can show when passing through detection technologies, 'passing,' as able-bodied, is precisely what is precluded here.SCS enacts a lifeworld marked with 'I can,' but the latter is not without particular limitations or specific contraints. Embodying and incorporating the neuromodulation technology and the distinct sensations it creates demand work. They also require regular fine-tuning, which

	necessitates finding a delicate balance between different agencies. Fine-tuning can also be
	experienced as overwhelming for the person living with SCS who has to be extremely
	attentive to one's bodily feel. Finally, with SCS implanted in one's bodies, one is intimately
	entangled with his or her sociomaterial environment, which renders him or her subject to
	disabling misfits where 'I can' risks collapsing in 'I cannot.' Living well with chronic pain
	managed by SCS requires being able to create resilience in navigating these hurdles. It is a
	hard-won achievement.
	from other devices and people that can be
	potentially disruptive, if not harmful. People living with the neuromodulation device have to be attentive to the actions of others, be they human or nonhuman, especially how they might interact and interfere with the proper functioning of the technology as well as with their bodily agency. Speaking about the remote control that enables her to modulate the stimulation, Mrs Bos, 61 years old, explains that I always keep it in this [she points to a small leather case]. I always put it back in here as well because the grandchildren are walking around and if they see something with buttons… They are crazy with buttons [she laughs] So no, the remote goes behind bars [Dutch expression which means that it is properly tucked away]! Disentanglement work does not only mean being watchful of others' interactions with the remote control but also anticipating the interferences between one's technologically of misfit to account for such disabling practices. When bodies are sustained and enabled by their sociomaterial environment -largely construed by Garland-Thomson as comprising not only of buildings (and the accessibility thereof) as well as natural surroundings, but also of technological artefacts and other humans -one can speak of a fit. Conversely, when the interaction between a particular body and the sociomaterial environment is not harmonious, a misfit happens. In Garland-Thomson's words, '[a] misfit occurs when world fails flesh in the environment one encounters -whether it is a flight of stairs, a boardroom full of misogynists, an illness or injury, a whites-only country club, subzero temperatures, or a natural disaster' (Ibid., p. 600). Misfits call into question the possibility of being the body one has: one's body is no longer an absent presence but rather dys-appears while one's bodily transformed body and other devices. of the world (Winance, 2010). Rosemarie Garland-Thomson (2011) has proposed the concept intentionality is disrupted. 'I can' fades into 'I cannot.'

Screening devices become 'outing' and disabling technologies, whose beeping attracts others' gaze on oneself. Interfering with SCS, they expose one's bodily difference to public view.

One is interpellated as different, disable, other than normal. In this context, the technology that, a minute ago, was experienced as being part of oneself is now experienced as an object Living well with spinal cord stimulation is an intricate matter. If it is experienced as a reparation and a rewording, this state of affairs is neither effortless nor absolute. Assuredly,

Temple University Press

however, with intermittent or continuous stimulation frequencies of 500Hz and above are believed not to cause any paraesthesia at all and to achieve good results as well[START_REF] De Ridder | Burst Spinal Cord Stimulation: Toward Paraesthesia-free Pain Suppression[END_REF][START_REF] Van Buyten | High-Frequency Spinal Cord Stimulation for the Treatment of Chronic Back Pain Patients: Results of a Prospective Multicenter European Clinical Study[END_REF]).

Fieldwork for this research has been funded by a grant from the Dutch Research Council (NWO) awarded to P.-P. Verbeek . I would like to thank the people living with spinal cord stimulation for sharing their experiences with chronic neuropathic pain. I am also grateful to Cecile De Vos and the healthcare professionals who have granted me access to the hospital to conduct fieldwork, allowed me to conduct observations, and given some Gaille and Mathilde Lancelot for their invitation to participate in the workshop 'Soin technologique et éducation


Marie Gueguen

François Lique

Collisional excitation of N + ( 3 𝑃) in interstellar clouds

Keywords:

The detection of the N + ion in ionized interstellar regions, as well as its use as a tracer for atomic nitrogen (N) in interstellar media, make it an interesting ion from the astrophysical point of view. Accurate determination of the N + abundance in the interstellar clouds requires detailed modeling of its excitation conditions. Hence, collisional excitation induced by the dominant interstellar species has to be studied. In this paper, we study the collisional excitation of N + by He and H 2 . We provide new potential energy surfaces describing the interactions between N + and He and between N + and H 2 considered as a structureless collider. Quantum calculations of the excitation cross sections for collisions of N + with He and H 2 are provided, as well as the first excitation rate coefficients for N + induced by these two species. The results are compared to collisional data for the excitation induced by electrons. It is shown that the excitation of N + by a neutral collider can play a significant role in weakly ionized regions as well as in warm molecular clouds.

INTRODUCTION

N and N 2 , the dominant nitrogen-bearing elements (Le Gal et al. 2014;Maret et al. 2006) in the interstellar medium (ISM), are respectively impossible and difficult to detect spectroscopically through infrared or millimeter-wavelength transitions. This is due to the fact that N and N 2 do not have fine structure levels and dipole moment, respectively. Proxy are thus used to infer their abundance in interstellar clouds (Le Gal et al. 2014). The N + ion is detected in the warm and ionized interstellar medium (Langer et al. 2017;Doherty et al. 2020;Goldsmith et al. 2015) and could qualify as such a proxy. Indeed, N + is considered as an important tracer for N in (fully) ionized regions. It can also be used for discriminating between fully and weakly ionized regions. Despite not (yet) detected in cold molecular clouds, N+ is also expected to be important constituant of such region that initiates the nitrogen chemistry and particularly the formation of ubiquitous ammonia (Dislaire et al. 2012).

The spin-orbit interaction in ionized nitrogen N + splits its ground electronic state into a triplet of fine-structure levels 3 𝑃 𝑗 with 𝑗 = 0, 1, 2. The 3 𝑃 1 and 3 𝑃 2 levels are at 48.738 cm -1 and 130.8 cm -1 above 3 𝑃 0 (Shen et al. 2022), respectively. Transitions with Δ 𝑗 = 1 are allowed and thus make the detection of N + possible.

Collisional data are needed for interpreting N + observations and estimating physical conditions. Indeed, in environments that do not reach local thermodynamic equilibrium (LTE), the population of N + levels has to be modeled through the competition between radiative and collisional processes (Roueff & Lique 2013). Collisional data for N + , although known for the excitation induced by electrons (Tayal 2011), are still missing for the excitation induced by heavier species ★ E-mail: marie.gueguen@univ-rennes.fr † E-mail: francois.lique@univ-rennes.fr such as He or H 2 . Without them, astrophysical observations must be interpreted on the basis of the LTE assumption, which does not allow to make the most of the highly resolved molecular spectra that recently developed facilities do offer. Due to the lack of collisional data available for N + with the main neutral colliders (He, H and H 2 1 ), [START_REF] Persson | [END_REF] had to model spectral observations based on scaled C-H rate coefficients. Such approximation may lead to significant errors in the observations interpretation and exploitation.

Calculation of these data requires first to compute an interaction potential between N + and the projectile (H 2 or He in the present study). He and H2 are the dominant colliders in cold molecular clouds where N+ is expected to play a significant role in nitrogen chemistry. In warm (ionized) clouds where N+ has been detected, H is the dominant neutral projectile. Calculations with H projectile are difficult to perform and we estimate that calculations with He and H2 projectiles can serve as template for the modelling the impact of neutral colliders (Roueff & Lique 2013). Two studies (Aïssaoui et al. 2020;[START_REF] Soldán | [END_REF] have provided potential energy curves (henceforth PECs) for N + -He in the last two decades. However, their PECs are based on coupled-cluster methods with an incomplete basis. Nowadays, computing facilities should allow to improve the description of the N + -He interaction. At the opposite, the determination of global N + -H 2 potential energy surfaces (henceforth PESs) involved in the collisional process as well as the non adiabatic and spin orbit couplings between them is a very challenging task because of the reactive nature of the system. In order to overcome this difficulty, Gómez-Carrasco et al. (2022) have recently provided PESs for the reactant and product channels separately without considering the intermediate region and have simulated the dynamics of the N + + H 2 → NH + + H reaction using statistical theories.

Full dimension quantum time-independent close-coupling calculations is the method of choice to obtain accurate collisional rate coefficients. Such an approach can be easily used for non-reactive collisional systems such as N + -He. However, in the case of reactive systems such as N + -H 2 (Gómez-Carrasco et al. 2022), this approach is impractical due to its memory and CPU requirements and approximate treatments have to be considered.

In this paper, we provide new highly accurate PECs for studying the collisional excitation of N + by He. We also provide PECs averaged over H 2 rotations for N + -H 2 interaction. This later potential relies on important approximations, as it treats this system as a non-reactive system. Then, we report inelastic cross sections of the collisional systems from quantum close-coupling (CC) calculations, and we derive collisional data for both systems. This paper is organized as follows: in section 2, we present the new N + -He PECs, as well as the spherically averaged PECs for the N + -H 2 interaction. Section 3 presents the inelastic cross sections and the rate coefficients obtained from our new PECs. Finally, in section 4, we discuss our results and their astrophysical implications.

N + -HE AND N + -H INTERACTION POTENTIALS

N + -He potential energy curves

The interaction of a closed-shell rare-gas atom with a 3 𝑃-state atom gives rise to two electronic states: a 3 Σ state and a doubly degenerate 3 Π state. Ab initio calculations were performed for internuclear distances in the range 1.8 < 𝑅 < 100 𝑎 0 for the 3 Σ electronic state and 2.5 < 𝑅 <100 𝑎 0 for the 3 Π electronic state, using the spin restricted coupled cluster method with single and double excitation and a perturbative treatment of triple excitation [RCCSD(T)] ( Knowles et al. 1993Knowles et al. , 2000) ) and the MOLPRO package (Werner et al. 2020).

As is usually the case in standard ab initio calculations, the spinorbit coupling was neglected, but taken into account in the scattering calculations. Calculations were performed with the augmented correlation consistent [aug-cc-pVXZ (X=T, Q, 5)] basis set and extrapolated to the complete basis set (CBS) using the procedure of Peterson et al. (1994). Standard corrections were applied to account for the basis set superposition error (BSSE), using Boys & Bernardi (1970)'s procedure.

In order to obtain an analytical representation, suitable for scattering calculations, we have used the following procedure. For shortrange (SR) 𝑅-distances, we have used the Born-Mayer formula that traditionally describes the ion-atom curves such as:

𝑉 (𝑆𝑅) (𝑅) = 𝛼 exp (-𝛽𝑅) (1)
with 𝛼 and 𝛽 being constants parameters [START_REF] Pauly | Atom-Molecule Collision Theory[END_REF]. Three coefficients (𝐶 4 , 𝐶 6 , 𝐶 8 ) adjusted from the 𝑎𝑏 𝑖𝑛𝑖𝑡𝑖𝑜 energy values at 15, 20 and 25 𝑎 0 were used to describe the PES at long-range (LR) 𝑅-distances using the following analytic formula:

𝑉 𝐿𝑅 (𝑅) = 𝐶 4 𝑅 4 + 𝐶 6 𝑅 6 + 𝐶 8 𝑅 8
(2)

Table 1 shows the value calculated for the short-range and longrange parameters.

𝐶 4 , 𝐶 6 and 𝐶 8 correspond to the leading terms in the long range expansion of the N + -He interaction: dipole-dipole induction coefficient, dispersion and induction coefficients, respectively ( Finally, we used a cubic spline for interpolating smoothly our ab initio data points.

Figure 1 presents the N + -He PECs obtained. The PECs are characterized by a minimum at 2.9 𝑎 0 of -2037 cm -1 for the 3 Σ state and at 5.0 𝑎 0 of -204.05 cm -1 for the 3 Π state. The well is thus much deeper for 3 Σ than for 3 Π, which can easily be explained since the 3 Σ state corresponds to approaches of He along the unoccupied 𝑝 orbital. In that case, He can get much closer to the ion and the well will thus be much deeper. Note that our results, although improving upon former PECs published by [START_REF] Soldán | [END_REF] and Aïssaoui et al. (2020) as relying on an extrapolation to the complete basis set, are in good agreement with them, with a difference of less than 0.2 % and 4.5% for the 3 Σ and 3 Π minima, respectively. Table 2 shows and compares the main characteristics of the PECs obtained by [START_REF] Soldán | [END_REF] . N + -H 2 collisional system in Jacobi coordinates. On the left, the linear approach corresponding to 𝜃 = 0 degree. On the right, the perpendicular approach, where 𝜃 = 90 degree.

N + -H 2 spherically averaged potential energy curves

As mentioned in the introduction, obtaining global PESs for the H 2 N + system is highly challenging because of the reactive nature of this system, as exemplified by the work done by Gómez-Carrasco et al. (2022). Indeed, these authors only computed a PES for the entrance (N + + H 2 ) and exit (NH + + H) channel, neglecting the intermediate (NH 2 + ) region. Here, we used a different strategy and we selected a reduced dimensional approach, where the H 2 molecule is described as a structureless sphere. This approach requires to keep the intermolecular distance between the two H atoms fixed, which amounts to treating the complex as non-reactive. Then, we averaged the PECs thus obtained for limited H 2 orientations which means that we treat H 2 as a pseudo-atom rather than as a molecule. Hence, as shown in Figure 2, the N + -H 2 PECs are described by the two Jacobi coordinates 𝑅, the distance from the center of mass of H 2 molecules to the N + atom, and 𝜃, the angle between 𝑅 and the H 2 bond axis 𝑟. We considered that the H 2 molecule only approaches the ion linearly (𝜃 = 0 degree) or perpendicularly (𝜃 = 90 degree).

𝐴𝑏 𝑖𝑛𝑖𝑡𝑖𝑜 calculations were performed using the RCCSD(T) approach with the augmented correlation consistent triple zeta (augcc-pVTZ) basis set. We chose to stay at this level of precision given the level of approximations involved in the spherically-averaged approach that we adopted. Calculations were performed in the range 1.3 < 𝑅 < 100 𝑎 0 for all electronic states considered here. Interactions between the ion N + and H 2 along the linear approach give rise to three electronic states: a 3 Σ state and two degenerate 3 Π states. Regarding the perpendicular approach, the degeneracy disappears and the 3 Σ and 3 Π state split into 3 𝐴 2 (for 3 Σ), 3 𝐵 1 and 3 𝐵 2 (for 3 Π) electronic states in the C 2𝑣 symmetry group respectively. Thus, we calculated a total of five PECs, two for the linear approach ( 3 Σ and 3 Π) and three for the perpendicular approach ( 3 𝐴 2 , 3 𝐵 1 and 3 𝐵 2 ). Figure 3 presents the five PECs obtained.

N + -H 2 spherically averaged PECs (𝑉 𝑖 𝑎𝑣 (𝑅)) are obtained by averaging over the linear and perpendicular approaches using the following formula, with 𝑉 𝑖 the interaction potential at a given distance 𝑅:

𝑉 𝑖 𝑎𝑣 (𝑅) = 1 5 [2𝑉 𝑖 (𝑅, 𝜃 = 0 • ) + 3𝑉 𝑖 (𝑅, 𝜃 = 90 • )] (3)
Note that we tested three different ways of proceeding to this average to get the N + -H 2 PECs for 3 Σ and 3 Π pseudo states. First, the average was done over the linear potential and the perpendicular potential using only the 3 𝐵 1 state and the 3 𝐴 2 state for the latter; only the 3 𝐵 2 state and the 3 𝐴 2 state; and finally an average over the 3 𝐵 1 and the 3 𝐵 2 state and the 3 𝐴 2 state. Given that we did not observe significant differences between the final PECs thus obtained, we adopted the averaged curve over 3 𝐵 1 and 3 𝐵 2 for the scattering calculations, as displayed in Figure 4, albeit physically meaningless. Such a weak influence of the use of 3 𝐵 1 or 3 𝐵 2 states for the gener- ation of the N + -H 2 spherically averaged PECs can be explained by the fact that the two 3 𝐵 1 or 3 𝐵 2 states are almost degenerate up to 𝑅-distances of 2.4 𝑎 0 .

Similarly to what has been done for the analytical representation of the N + -He PECs, the extrapolation to short-range distances is based on the Born-Mayer formula, with 𝛼 = 1223.76 and 𝛽 = 3.05 a.u. for the 3 Σ state and 𝛼 = 9328.61 and 𝛽 = 8.42 a.u. for 3 Π state. The extrapolation for long-range distances relies on multipolar expansion (𝑅 -𝑛 terms) through the C 3 , C 4 and C 5 coefficients, whose value is determined from long range ab initio points and correspond respectively to 0.0514, -2.7823 and 1.0847 a.u. for the Σ state; and 0.0619, -3.2309 and 3.2563 a.u. for the Π state. Finally, ab initio points were smoothly connected on the basis of a cubic spline interpolation.

Figure 4 presents the PECs obtained for the 3 Σ and the 3 Π states through this spherically averaged approach. Compared to the PECs of N + -He, we observe an inversion of the states's hierarchy: the potential well is deeper for the 3 Π state than for 3 Σ one, and the minima are much deeper than for He (see Table 3 for PECs characteristics).

QUANTUM SCATTERING CALCULATIONS

State-to-state cross sections

Scattering calculations for N + -He and N + -H 2 were performed with the close-coupling approach (Arthurs & Dalgarno 1960), following the method described by Alexander et al. (1983); Orlikowski & Alexander (1984) for 3 𝑃-atom -structureless projectile collisions and implemented in the HIBRIDON code [START_REF] Alexander | HIBRIDON is a package of programs for the time-independent quantum treatment of inelastic collisions and photodissociation Arthurs A[END_REF]). The spin-orbit couplings dependence on R was neglected. As is usually done, we use the asymptotic experimental spin-orbit splittings of N + ( 3 𝑃), Δ 𝑗=1 = 48.738 cm -1 and Δ 𝑗=2 = 130.8 cm -1 respectively, to determine spin-orbit corrected potential energy curves (PECs). The hybrid log-derivative/airy propagator implemented in the HIBRIDON code has been used, starting from R 𝑚𝑖𝑛 = 1.5 𝑎 0 to R 𝑚𝑖𝑑 = 25 𝑎 0 for the log-derivative method, and from R 𝑚𝑖𝑑 = 25 𝑎 0 to R 𝑚𝑎𝑥 = 250 𝑎 0 for the Airy propagator for N + -He collisions and from R 𝑚𝑖𝑛 = 1.2 𝑎 0 to R 𝑚𝑖𝑑 = 40 𝑎 0 for the log-derivative method, and from R 𝑚𝑖𝑑 = 40 𝑎 0 to R 𝑚𝑎𝑥 = 200 𝑎 0 for the Airy propagator for N + -H 2 collisions. All these parameters were adequate to ensure a convergence of cross sections to better than 1%. These calculations have been performed for total energies up to 10000 cm -1 . For the energy grid, we have used a variable step. For energies smaller than 100 cm -1 , the step is 0.2 cm -1 . Then, between 100 and 200 cm -1 , the step is increased to 0.5 cm -1 , between 200 and 400 cm -1 to 2, between 400 and 600 cm -1 to 10. Finally, between 600 and 1000 cm -1 , the step is increased to 20 cm -1 and to 100 cm -1 above that limit. The reduced mass of the complexes were 𝜇 = 3.11 u for N + -He and 𝜇 = 1.76 u for N + -H 2 . For the former, the maximum total angular momentum considered was 𝐽 = 20 for energies lower than 300 cm -1 , 𝐽 = 30 for energies between 300 and 1000, 𝐽 = 50 for energies between 1000 and 2500, and 𝐽 = 80 for energies greater than 2500 cm -1 . For the latter, the maximum total angular momentum considered was 𝐽 = 30 for energies lower than 300 cm -1 , 𝐽 = 50 for energies between 300 and 1000 and 𝐽 = 80 for energies superior to 1000 cm -1 .

Figure 5 shows the state-to-state cross-sections for the deexcitation transitions of N + induced by collisions with He. We can see that the transition from 3 𝑃 2 to 3 𝑃 1 dominates the de-excitation process and that the 3 𝑃 1 to 3 𝑃 0 transition is weak, which is not surprising as this transition is classically forbidden (Monteiro & Flower 1987). This behavior has been noticed for others atoms with a 3 𝑃 electronic ground state in collision with He (Alexander et al. 1983;Monteiro & Flower 1987;Lique et al. 2018).

Figure 6 presents the state-to-state cross-sections of N + with H 2 . Cross-sections at low collision energy (𝐸 𝑐 ) exhibit strong Feshbach and shape resonances due to the attractive potential wells (Costes & Naulin 2016). These resonances disappear when 𝐸 𝑐 is large compared to the well depth. The transition from 3 𝑃 2 to 3 𝑃 1 is the most efficient; and the transition from 3 𝑃 1 to 3 𝑃 0 dominates over the 3 𝑃 2 to 3 𝑃 0 at low energy, thanks to a coupling through 3 𝑃 2 that is stronger at low energy, as noted in Alexander et al. (1983).

Rate coefficients

From the inelastic cross sections 𝜎(𝐸 𝑐 ), one can derive the corresponding rate coefficients at temperature 𝑇 by an averaging over the collision energy (𝐸 𝑐 ):

𝑘 𝑖→ 𝑗 (𝑇) = ( 8
𝜋𝜇𝑘 3 𝐵 𝑇 3 ) 1 2 ∫ +∞ 0 𝜎 𝑖→ 𝑗 𝐸 𝑐 exp ( -𝐸 𝑐 𝑘 𝐵 𝑇 )𝑑𝐸 𝑐 (4)
where 𝑘 𝐵 is the Boltzmann constant, and 𝑖 and 𝑗 denote the initial and final levels of the target, respectively. Calculations of the cross sections at total energies up to 10000 cm -1 allow the determination of rates up to 2000 K without loss of accuracy. Unsurprisingly, the rate coefficients derived from the N + -He crosssections reflects the hierarchy of transitions observed for the latter, as shown in Figure 7. The transition from the 3 𝑃 2 state to the 3 𝑃 1 one largely dominates the other transitions and the 3 𝑃 1 to 3 𝑃 0 remains negligible. Likewise, in the case of N + -H 2 , the same behavior is observed for the transitions's hierarchy with respect to rate coefficients than for the cross-sections, with the transition from 3𝑃 1 to 3𝑃 0 dominating over the 3𝑃 2 to 3𝑃 0 up to ∼500 K.

Discussion and comparison with electronic excitation rate coefficients

As mentioned in the introduction, H 2 is the most abundant partner in interstellar molecular clouds and thus the dominant collisional partner in such media. Despite significant update for many interstellar atoms and molecules (Roueff & Lique 2013;van der Tak et al. 2020), collisional data are still difficult to produce for collisions with H 2 , especially for reactive molecules and ions. When data for collisions with He are available, it has often been proposed to derive H 2rate coefficients from He-rate coefficients calculated for the same molecule. Such an approach (Lique et al. 2008;Schöier et al. 2005) consists in assuming that the excitation cross-sections are similar for both colliding systems and that the rate coefficients would only differ by a scaling factor, that corresponds to the square root of the ratio between the reduced masses appearing in the conversion of the cross sections into rate coefficients [Eq. 4]. Hence, the following scaling relationship could be used in our case:

𝑘 He ≃ 1.4 × 𝑘 H 2 . ( 5
)
Note that this approximation is only supposed to be used for H 2 at low temperatures (e.g., when most H 2 is in its ground state), but has already been challenged for many species; for a general criticism of this assumption see Roueff & Lique (2013).

Here, we discuss the validity of estimating H 2 -rate coefficients from He ones when it comes to our system, i.e, to determine whether He can be a good template model for understanding and quantifying the collisional excitation of N + by H 2 . One caveat that must be addressed in order to answer this question is the following: we do not have state-of-the-art results for H 2 , but only quantum scattering calculations performed on the basis of interaction potentials contain-ing important approximations. N + -H 2 was treated as a non-reactive system given that the intermolecular distance between the two H was fixed, and H 2 was treated as a pseudo-atom given that we averaged the PESs over H 2 rotations. There is no way to determine how these approximations impact the collisional rate coefficients obtained for N + -H 2 . We have reasons however to believe that, albeit these approximations, our calculations may provide the right order of magnitude of the fine structure resolved rate coefficients. Thus, we may be allowed to use them at least to interpret the exact results obtained for He and to determine on this basis whether the 1.4 scaling factor assumption is valid for this system.

We see in Figs. 5 and 6 that, as expected, given the deeper potential well in the N + -H 2 interaction as compared to N + -He one, H 2 -crosssections are much larger for the He ones. A difference of one order of magnitude can be observed between the corresponding crosssections. The order of magnitude of the cross sections is not the only difference between the two collisional complexes. The behavior of the state-to-state cross sections observed for the N + -H 2 system is very different from the one observed for N + -He one. Whereas the 3𝑃 1 to 3𝑃 0 transition induced by He collisions was negligible, for N + -H 2 collisions, it is not only much more important proportionally, and it actually dominates over the the 3 𝑃 2 to 3 𝑃 0 transition thanks to an efficient coupling of the 3 𝑃 0 and 3 𝑃 1 states with the 3 𝑃 2 one. Our results show that He is not a correct model to describe the excitation of N + induced by H 2 .

In astrophysical media where N + is found, electronic collisions are also supposed to play a significant role for the excitation of N + . Thus, it is important to compare the efficiency of electron and neutral collisional partners (He and H 2 ) for the excitation of N + . In Fig. 7, we compare rate coefficients for the de-excitation of N + induced by electron impact (Tayal 2011) to the de-excitation rate coefficients induced by He and H 2 collisions computed in this work. Rate coefficients for the (de-)excitation of N + by electrons are ∼ 2-3 orders of magnitude higher than that of the collisional (de-)excitation induced by H 2 . Such a difference suggests that in astrophysical environments where the electronic fraction is low (𝑛 𝑒-≤ 10 -4 ), collisions with H 2 will compete or even dominate the excitation of N + , and indicates that N + -H 2 collisional data should be used in order to accurately model N + excitation in interstellar clouds. At the opposite, in highly ionized media, the electronic excitation will dominate.

THE EXCITATION OF N + IN INTERSTELLAR MEDIA

Calculations of critical densities can help to identify more precisely when such N + rate coefficients would need to be considered in radiative transfer models. The concept of critical density refers to the ratio between the Einstein coefficients, expressed in s -1 and the collisional de-excitation rate coefficients for a given transition (in cm -3 s -1 ). Put differently, the ratio of the Einstein coefficients A 𝑖→ 𝑗 to the collisional de-excitation rate coefficients 𝑘 𝑖→ 𝑗 defines the critical density 𝑛 * of a given line, i.e, the density at which photon de-excitation and collisional de-excitation are equal.

𝑛 * (𝑇) = 𝐴 𝑖→ 𝑗 𝑘 𝑖→ 𝑗 (6)
Above such density, LTE conditions can generally be safely assumed. Critical densities for electrons had already been calculated by Goldsmith et al. (2015), on the basis of Tayal's collisional rates. Figure 8 displays the critical densities for He, H 2 and electrons for the two allowed radiative transitions as a function of temperature.

It can be seen that for ionized warm media where N + has been detected (with densities lower than 10 2 cm -3 ), LTE conditions are not met and that rate coefficients are required to model the N + emissions, although most often ignored to this day. Then, we decided to test the impact of our rate coefficients on the excitation of N + in astrophysical media, by performing radiative transfer calculations for physical conditions corresponding to media where N + is detected. Non-LTE calculations were performed with the RADEX code (Van der Tak et al. 2007). Both collisional and radiative processes are taken into account. We focus on the calculation of the excitation temperature for N + transitions, with a background temperature of 2.73 K and a N + column density of 10 14 cm -2 . H 2 is used as the only representative of neutral colliders. 2 Figure 9 shows the excitation temperature of 3 𝑃 1 to 3 𝑃 0 and 3 𝑃 2 to 3 𝑃 1 transitions as a function of the density of neutral species, with the electronic density kept fixed at 𝑛 𝑒-= 10 -2 cm -3 and 𝑛 𝑒-= 1 cm -3 , respectively. A kinetic temperature of 2000 K 3 was adopted. One observes that at low densities of neutral species, even with a neutral to electron abundance ratio greater than 10 2 , the excitation temperature remains weakly sensitive to the density of neutral species. It is only above a critical threshold of 𝑛(H 2 ) ≥ 10 3 -10 4 cm -3 that the excitation temperature increases and that the media starts to thermalize very fast as the density increases, with an excitation temperature equal to the kinetic temperature around 𝑛(H 2 ) ≥ 10 5 cm -3 . Below this threshold, collisions are inefficient and do not contribute significantly to the excitation of the N + ion, regardless of the ratio neutral species to electrons and of the density of electrons. Note that this neutral density value is much higher than the one typically observed in warm ionized clouds, i.e., 0.1 to 100 cm -3 . Thus, environments where N + is detected do not satisfy the local thermodynamic equilibrium, 2 In such media, H is expected to be the dominant neutral collider and our results should be consider with cautious despite the fact the H 2 and H-rate coefficients are usually of similar magnitude (Schöier et al. 2005). 3 N + has been detected in interstellar clouds with a typical temperature of ∼ 8000 K but we restrict our models at 2000 K in agreement with the temperature range of our new data. We anticipate that because of the weak dependence of the rate coefficients, the results obtained at 2000 K will not vary significantly at 8000 K. The electronic density is kept fixed at 𝑛 𝑒 -= 10 -1 cm -3 (upper panel) and 𝑛 𝑒 -= 1 cm -3 (bottom panel).

and collisional rate coefficients are needed to appropriately model observations. As a second application of our rate coefficients, we decided to verify assumptions made about N + in modeling the nitrogen chemistry in cold environments such as dark clouds. As emphasized in Dislaire et al. (2012), N + + H 2 → NH + + H is identified as a key reaction for the formation of nitrogen hydrides in dark clouds (Le Gal et al. 2014;Agúndez & Wakelam 2013;Hily-Blant et al. 2013). Whether the reaction N + + H 2 → NH + is efficient enough to reproduce the observed amount of ammonia in dark clouds has actually been debated since the original claim made by Le Bourlot (1991), a claim later challenged by updated calculations of the rate coefficients for N + + H 2 → NH + + H (Dislaire et al. 2012), which felt below the critical value that had been inferred to explain the observed abundance of ammonia. However, due to the fact that in such cold environments, N + cannot be detected, assumptions have to be made about the distribution of its fine structure population. It is thus interesting to check the assumption according to which its population follows a LTE distribution in cold molecular clouds.

In such environments, the exact population of N + fine structure levels is not known and can influence the reactivity of N + . LTE conditions are usually assumed but not checked because of the lack of collisional data (Gómez-Carrasco et al. 2022). Thus, we decided to perform radiative transfer calculations to determine the population levels of the fine structure levels of N + as a function of the density of neutral species (𝑛(H 2 )), where 'neutral species' refer to 90% of H 2 and 10 % of He, at 10, 20 and 50 K respectively (see Fig. 10). At 10K, as could have been anticipated, almost 100% of N + is in its ground state (not shown here), even at high densities according to the LTE distribution. But the level population changes as the temperature increases: at 20 K already, one observes 2 to 5% of N + in level 3 𝑃 1 at densities of 10 4 -10 5 cm -3 . At 50 K, 20 to 30% of the whole N + is in the 3 𝑃 1 level for a density of neutral species of 10 4 -10 5 cm -3 . Such values are below the LTE conditions that predict ∼ 10 % and ∼ 40% of N + is in 3 𝑃 1 level, respectively. Given that the N + + H 2 → NH + + H rate coefficients depends on the N + energy level population, this means that the reaction will not happen as predicted by the model. This could possibly have an important impact on the determination of the age of the clouds when the abundance of NH 3 is taken as the main tracer of it.

CONCLUSION

We have calculated new PECs for N + -He at the RCCSD(T) level of theory with an extrapolation to the complete basis set. The calculations was found to be in good agreement with former theoretical studies. Using these new PECs, we have performed close-coupling calculations in order to determine collisional excitation cross sections for N + -He and derive collisional rate coefficients.

N + -H 2 have also been studied. These data have been computed also using RCCSD(T) approach on the basis of a spherically averaged approach to the potential energy curves for N + -H 2 , relying on important approximations. The comparison of the N + -H 2 rate coefficients with the N + -He one shows that significant differences exist. The differences are of such nature, e.g. differences in the hierarchy of different de-excitation transitions, that even scaled by the square root of the collision reduced mass, the He rate coefficients cannot be reasonable approximation to the N + -H 2 rate coefficients.

Then, we considered the astrophysical consequences of our calculations. First, we have shown that media where N + is typically observed are not at LTE, and that LTE conditions are reached only for densities much higher than the typical conditions of warm ionized clouds. This illustrates the importance of taking into account the collisional rates coefficients. Furthermore, we have tested some important assumptions that are traditionally part of the modelling of nitrogen and ammonia. Our results show that the assumption of LTE distribution of the N + energy levels at temperatures below 50 K is not verified above 10 K. This could have an important impact on the modeling of ammonia, especially on the determination of the age of the clouds where N + is detected. Finally, we emphasize that the present study should be completed by the theoretical study of the collisional excitation of N+ by H and H+, the dominant heavy projectiles in warm (ionized) clouds in order to fully interpret and exploit the N+ observations recently performed.

Figure 1 .

 1 Figure 1. Potential energy curves for the HeN + complex.

  (SH02), Aïssaoui et al. (2020) (A20) and this work.

  Figure2. N + -H 2 collisional system in Jacobi coordinates. On the left, the linear approach corresponding to 𝜃 = 0 degree. On the right, the perpendicular approach, where 𝜃 = 90 degree.

Figure 3 .Figure 4 .

 34 Figure 3. Potential energy curves for the five orientations of N + -H 2 . Black lines correspond to the linear approaches, and the red lines to the perpendicular ones.

Figure 5 .Figure 6 .

 56 Figure 5. State-to-state cross-sections of N + with He as a function of energy.

Figure 7 .

 7 Figure7. Comparison between collisional rate coefficients for N + -He (dashed lines), for N + -H 2 (solid lines) and for N + -e (dashed dotted lines)(Tayal 2011) as a function of temperature.

Figure 8 .

 8 Figure8. Critical densities for He, H 2 and electrons as a function of temperature. Red lines correspond to the 3 𝑃 1 to 3 𝑃 0 transition and black lines to the 3 𝑃 2 to 3 𝑃 1 transition.

Figure 9 .

 9 Figure 9. Excitation temperature of the 3 𝑃 1 to 3 𝑃 0 (black) and 3 𝑃 2 to 3 𝑃 1 (red) transitions as a function of the density of neutral species at 2000 K. The electronic density is kept fixed at 𝑛 𝑒 -= 10 -1 cm -3 (upper panel) and 𝑛 𝑒 -= 1 cm -3 (bottom panel).

Table 1 .

 1 Côté & Dalgarno 2000;Bouchelaghem & Bouledroua 2014). The values adopted for the short-range and long-range parameters.All units are in a.u.

	Parameters	3 Σ	3 Π
	𝛼	95.65 19.38
	𝛽	4.09	2.12
	𝐶 4	0.69	-0.69
	𝐶 6	7.54	-3.50
	𝐶 8	78.67	-6.69

Table 2 .

 2 Characterization of the HeN + PECs obtained by SH02, A20 and in this work.

			3 Σ	3 Π
		𝑅 (𝑎 0 ) 𝑉 (cm -1 )	𝑅 (𝑎 0 ) 𝑉 (cm -1 )
	SH02	2.9	-2004.85	5.0	-202.49
	A20	3.0	-2041.03	5.0	-213.15
	This work	2.9	-2037.33	5.0	-204.05

Table 3 .

 3 Characterization of the N + -H 2 PECs according to this work.

		3 Σ			3 Π
		𝑅 (𝑎 0 ) 𝑉 (cm -1 )	𝑅 (𝑎 0 )	𝑉 (cm -1 )
	This work	4.5	-968.32	2.7	-17121.22

H

is usually by far the dominant collider in molecular clouds.© 2022 The Authors

MNRAS 000, 1-7 (2022)

This paper has been typeset from a T E X/L A T E X file prepared by the author.MNRAS 000, 1-7 (2022)

ACKNOWLEDGEMENTS

This project received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program (Grant Agreement No. 811363) and from the European Union Horizon 2020 research and innovation program under the Marie Slodowska-Curie grant agreement No.101026214.

DATA AVAILABILITY

The data underlying this article will be made available through the EMAA 4 , LAMDA (Schöier et al. 2005;van der Tak et al. 2020) and BASECOL (Dubernet, M.-L. et al. 2013) data bases. The PECs computed in this work are available fron the authors upon request.


The HIV care cascade

›

  Low transcontinental migration › Intra-sub-Saharan African migration is the largest south-to-south movement › High level of internal mobility › Rural to urban, between rural, rural to semi-urban… › "Household fluidity" (PopART HPTN 071) (Hoddinot et al. JIAS 2018)

-1.6% -21.0% Population dynamics & the HIV care cascade

	› Population-based and Mobility and HIV acquisition Population dynamics & the HIV care cascade	+17.3%	+0.2%	+4.8%
	cross-sectional concept › Increased sexual risk behaviour and › Data from ANRS 12249 TasP trial	In-migration	16 th birthday	HIV sero-conversion
	› Proportion of HIV+ being HIV prevalence among migrants › rural KwaZulu Natal
	› diagnosed, › 2012-2016
	› in care, › on ART, › virally suppressed › Individual longitudinal trajectories		Resident adult population living with HIV
	› Computed
	› among resident PLWHIV › within a geographical area	Out-migration		Death
	› at a specific time point

› in Kenya and Uganda (SEARCH) (Camlin et al. JIAS 2018) › in rural KwaZulu Natal (South Africa) (McGrath et al. Lancet HIV 2015) › Relation between distance of migration and HIV acquisition (Dobra et al. AIDS 2017) › residency › HIV status › engagement with HIV care (Larmarange et al. JIAS 2018) › Data from ANRS 12249 TasP trial › rural KwaZulu Natal › 2012-2016 › Individual longitudinal trajectories › residency › HIV status › engagement with HIV care (Larmarange et al. JIAS 2018)

Annual rates Entries Exits Cascade status at entry/exit

ANRS 1229 TasP (Larmarange et al. JIAS 2018) Deaths Relative

position in the HIV care cascade

	Mobility, access to and African migrants Key Populations (re)Setting the policy
	retention into care in Europe › aMASE study (Fakoya et al. JIAS 2018) and mobility agenda on migration
	› 9 European countries / 57 HIV clinics
	› Optimal lifelong engagement with HIV care could be threatened by mobility › Median time to diagnosis › Missed opportunities in terms of › It is crucial to integrate the dimension of › Overrepresented in European epidemic › 5 years (women) prevention among gay and bisexual mobility and migrations into our responses › ANRS Parcours study › 8 years (heterosexual men) migrants in Europe (Fakoya et al. JIAS 2018) to the HIV epidemics
	› ~ half of African migrants acquired HIV › 7 years (gay and bisexual men)
	› Will be detailed in the following presentations, in particular with results from PopART HPTN 071 and MaxART › Migrants face specific vulnerabilities that limit their retention at each step of the after migration (Desgrées du Lou et al. Eurosurveillance 2015) › Increased exposure to HIV acquisition due to social hardships, including lack of a residence permit (Pannetier et al. Lancet Public Health 2017) › Sex workers and men who have sex with › Access to prevention and care is also a › Late diagnosis men very mobile in southern Africa fundamental right for mobile populations › Despite utilization of health services (Vearey JIAS 2018) › Missed opportunities for testing › "There is an urgent need to develop › Migration-specific barriers, including › Mobility of female sex workers in Côte migration-aware and mobility-competent difficulties understanding the legal rights prevention and care to accessing health care d'Ivoire: a challenge for continuity of responses to health globally."	Deaths
	cascade

ANRS 1229 TasP (Larmarange et al. JIAS 2018) › Timing and determinants: tomorrow at 11:00 in Elicium 1 (Gosselin #WEAC0104) Migrants in Europe (2) (Becquet et al. ICASA 2017) (Vearey JIAS 2018)

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