Guillaume Andéol
email: guillaume.andeol@defense.gouv.fr

Clara Suied

Sébastien Scannella

Frédéric Dehais

The Spatial Release of Cognitive Load in Cocktail Party Is Determined by the Relative Levels of the Talkers

Keywords: cocktail party, cognitive load, spatial cues, near infrared spectroscopy, prefrontal cortex

In a multi-talker situation, spatial separation between talkers reduces cognitive processing load: this is the Bspatial release of cognitive load^. The present study investigated the role played by the relative levels of the talkers on this spatial release of cognitive load. During the experiment, participants had to report the speech emitted by a target talker in the presence of a concurrent masker talker. The spatial separation (0°and 120°angular distance in azimuth) and the relative levels of the talkers (adverse, intermediate, and favorable target-tomasker ratio) were manipulated. The cognitive load was assessed with a prefrontal functional nearinfrared spectroscopy. Data from 14 young normalhearing listeners revealed that the target-to-masker ratio had a direct impact on the spatial release of cognitive load. Spatial separation significantly reduced the prefrontal activity only for the intermediate target-to-masker ratio and had no effect on prefrontal activity for the favorable and the adverse target-to-masker ratios. Therefore, the relative levels of the talkers might be a key point to determine the spatial release of cognitive load and more specifically the prefrontal activity induced by spatial cues in multi-talker situations.

INTRODUCTION

In a multi-talker situation, the auditory system uses a variety of cues to attribute among stream of speeches one to a unique target talker, among the other masker(s) talker(s). Previous studies (reviewed in [START_REF] Bronkhorst Aw | The cocktail-party problem revisited: early processing and selection of multi-talker speech[END_REF] have found that two cues are particularly important: the voice frequency characteristics and the spatial separation between talkers. The most favorable voice characteristic condition is reached when the target and the masker have different genders. Likewise, higher intelligibility can be attained when the target and the masker are spatially separate. It seems that large spatial separation led to greater improvement in speech reception threshold 50 (SRT 50 , level differences between the target and the masker to obtain 50 % intelligibility) than did gender differences (Zekveld et al. 2014b).

Hence, one important question is to know whether this improvement of speech intelligibility due to spatial separation is achieved at the expense of a cognitive cost. Indeed, probably due to cognitive decline, older listeners seemed to be less able to take advantage of spatial separation between talkers [START_REF] Glyde | Problems hearing in noise in older adults: a review of spatial processing disorder[END_REF]. Similarly, working memory span size seems to limit the ability to use spatial cues in hearing impaired listeners [START_REF] Neher | Benefit from spatial separation of multiple talkers in bilateral hearing-aid users: effects of hearing loss, age, and cognition[END_REF]). Nevertheless, those results are questioned when audiometric sensitivity is considered [START_REF] Füllgrabe | Age-group differences in speech identification despite matched audiometrically normal hearing: contributions from auditory temporal processing and cognition[END_REF]. In normal hearing listeners, there is no consistent result about the relationship between cognitive resources and the use of spatial cues (Zekveld et al. 2014b).

Recently, the relationship between cognitive resources and spatial release from masking was addressed by measuring the cognitive load in multitalker situations. Zekveld and colleagues (Zekveld et al. 2014b) assessed the cognitive load of listeners by pupil dilation while measuring the SRT 50 . The authors found that the spatial separation between talkers improved performance but had no effect on the cognitive load, whereas gender differences between talkers improved performance and reduced cognitive load. However, the null effect of spatial separation on cognitive load was questioned by [START_REF] Xia | Spatial release of cognitive load measured in a dual-task paradigm in normalhearing and hearing-impaired listeners[END_REF]. In this latter study, listeners had to perform the speech task while performing a secondary task (visual tracking), the score of which was used as an indicator of the cognitive load. Unlike Zekveld and colleagues, Xia and colleagues found that spatial separation yielded lower cognitive load than gender differences.

Interestingly, those two recent studies differ in the relative levels of the target and masker talkers (Targetto-Masker Ratio, TMR). Xia and colleagues presented the target and the maskers at the same level (approximately 0 dB TMR). Zekveld and colleagues used a louder masker level (approximately -8 dB TMR) in order to decrease the intelligibility score (SRT 50 ) down to 50 % with spatial separation. Such experimental differences can explain the contradictory results between these two studies, as the impact of TMR on speech intelligibility has been shown in many previous studies [START_REF] Brungart Ds | Informational and energetic masking effects in the perception of two simultaneous talkers[END_REF][START_REF] Eddins Da | Psychometric properties of the coordinate response measure corpus with various types of background interference[END_REF][START_REF] Bronkhorst Aw | The cocktail-party problem revisited: early processing and selection of multi-talker speech[END_REF]. The speech intelligibility generally decreases as the TMR decreases, i.e., when the masker gets louder. There was an 8-dB TMR difference between the Zekveld and colleagues and the Xia and colleagues' study. In a given experiment, an 8-dB TMR decrease could greatly reduce the performance (for instance see [START_REF] Eddins Da | Psychometric properties of the coordinate response measure corpus with various types of background interference[END_REF]. In addition, we could also expect an impact of this large TMR difference on the cognitive load.

Moreover, for adverse TMR, a different pattern could emerge: because of the large level difference between the target and the masker, the listeners could specifically attend to the softest voice [START_REF] Brungart Ds | Informational and energetic masking effects in the perception of two simultaneous talkers[END_REF]. Therefore, various TMRs can produce different effects on speech intelligibility. This suggests complex interactions between the TMR and the spatial separation which could explain a part of the inconsistency in the cognitive load results of the two previous studies.

The current work aims to investigate the role played by the TMR in the spatial release of cognitive load in a classic cocktail-party paradigm. The cognitive load was assessed by the activity of the prefrontal cortex recorded with a functional near-infrared spectroscopy (fNIRS) device. fNIRS is a brain imaging device that takes advantage of the optical properties of the human tissues that are transparent to near infrared light. Interestingly enough, oxygenated (HbO2) and deoxygenated (HHb) hemoglobin are two chromophores that absorb near-infrared light at two different wavelengths and their changes in concentration are associated with cortical activity [START_REF] Ayaz | Optical brain monitoring for operator training and mental workload assessment[END_REF]. Using the modified Beer-Lambert Law [START_REF] Villringer | Near infrared spectroscopy and imaging[END_REF], relative and local concentrations of Hb02 and HHb can be estimated from the near-infrared light transmittance of the brain measured by placing a light emitter and a light sensor around the area of interest. This affordable, field deployable, and easy-to-use technique [START_REF] Ayaz | Continuous monitoring of brain dynamics with functional near infrared spectroscopy as a tool for neuroergonomic research: empirical examples and a technological development[END_REF][START_REF] Mckendrick R | Wearable functional near infrared spectroscopy (fNIRS) and transcranial direct current stimulation (tDCS): expanding vistas for neurocognitive augmentation[END_REF] has been used to measure hemodynamics in response to stimuli [START_REF] Strait | What we can and cannot (yet) do with functional near infrared spectroscopy[END_REF] in a variety of experimental paradigms such as speech processing-related task [START_REF] Dieler Ac | Functional near-infrared spectroscopy for the assessment of speech related tasks[END_REF]. fNIRS has gained momentum to investigate cognitive load [START_REF] Bunce Sc | Implementation of fNIRS for monitoring levels of expertise and mental workload[END_REF][START_REF] Gagnon J-F | Anticipating human error before it happens: towards a psychophysiological model for online prediction of mental workload[END_REF][START_REF] Ayaz | Optical brain monitoring for operator training and mental workload assessment[END_REF][START_REF] Durantin | Processing functional near infrared spectroscopy signal with a Kalman filter to assess working memory during simulated flight[END_REF][START_REF] Gateau T | Real-time state estimation in a flight simulator using fNIRS[END_REF][START_REF] Mandrick | Why a comprehensive understanding of mental workload through the measurement of neurovascular coupling is a key issue for neuroergonomics?[END_REF] as it gives a more direct insight on the cortical activity than do other psychophysiological techniques [START_REF] Durantin | Using near infrared spectroscopy and heart rate variability to detect mental overload[END_REF].

MATERIALS AND METHODS

Participants

Fourteen young (8 men and 6 women; mean age, 21.9 ± 2.1 years) normal-hearing listeners took part in the present study. All had audiometric thresholds below 20 dB HL for all octave frequencies from 125 to 8 kHz evaluated using AudioConsole software and Silento Supermax headphone. All listeners were undergraduate engineer students at Institut Supérieur de l'Aéronautique et de l'Espace (ISAE), and all have perfect understanding of English number and color words. This study was approved by the Institutional Review Board, IRB00003888. Written informed consent was obtained.

Multi-Talker Task

The performance in a multi-talker situation was assessed by using the coordinate response measures (CRM) corpus [START_REF] Bolia Rs | A speech corpus for multitalker communications research[END_REF]. In that corpus, all sentences had the same pattern: BReady call sign go to color number Now.^The call signs could be the following words: Baron, Charlie, Ringo, Eagle, Arrow, Hopper, Tiger, Laker. The colors can be red, blue, green, and white, and the numbers one to eight. Only male voices (four talkers) were used for the target and the masker.

Experimental conditions varied according to two factors: the TMR and the spatial separation between the target and the masker. Three TMRs were used (-12, -4, and +4 dB). We chose 8-dB steps to get strong contrasts between the levels of the TMR factor: adverse (-12 dB), intermediate (-4 dB), and favorable (+4 dB) TMR. The spatial locations of the talkers were manipulated by filtering voice signals with head related transfer functions (HRTFs). Two conditions were tested: in the separate talker condition, the target talker was presented at 60 degrees right and the masker at 60 degrees left; in the collocated condition, the two talkers were presented straight ahead (0 degree).

The experiment consisted in six homogenous blocks. Each block was the combination of one TMR and one spatial separation: TMR-12 collocated, TMR-12 separate, TMR-4 collocated, TMR-4 separate, TMR + 4 collocated, TMR + 4 separate. The block order was randomized for each participant using a Latin square design. Each block contained 32 trials, i.e., 32 repetitions for each experimental condition. In each trial, two sentences were simultaneously presented: one by the target (call sign Baron) and the other one by the masker (all the seven others call signs except Baron). The listener had to report the color and the number of the sentence corresponding to the target call sign. The color and number in each sentence was chosen randomly. In a given sentence, the color and number of the masker talker were different from the color and number of the target talker. Each block lasted approximately 5 min. Before data acquisition, all listeners performed two short training blocks of 16 trials at 0 dB TMR. Half of the listeners began the training with the spatially separate talkers and the other half with the collocated talkers. The experiment lasted approximately 40 min.

Stimuli were generated using custom software written in Mathworks Matlab®. The audio files (.wav) were transmitted from the computer (Dell Optiflex 990) to a digital signal processor (RX8; Tucker Davis Technologies) to be filtered in real time with HRTFs measured with an artificial head (Neuman KU-100). The signal was amplified through a headphone buffer (HB7, TDT) and presented using headphones (Beyer Dynamics DT770) at an overall level around 70 dB SPL (rms power) at both ears. The combined signal (target speech and masker speech) was roved over a 6-dB range (from 67 dB SPL to 73 dB SPL, in 1-dB step).

Behavioral responses were recorded using a homemade response box with three button rows (the first row was dedicated to the colors, the second row to the numbers one to four, and the third row to the numbers five to eight). The response box was linked to the real-time processor and the responses were recorded with the custom software.

fNIRS Measurements

In the current study, during each session, hemodynamics of the prefrontal cortex was recorded with the functional near-infrared spectrometer fNIR100 (Biopac®) equipped with 16 prefrontal optodes (Fig. 1). Each optode recorded hemodynamics at a frequency of 2 Hz in terms of light level variations in comparison to a 10-s baseline. The baseline was acquired at the beginning of the recording and consisted of a 20-sample recording at rest. The data was then referenced to the averaged baseline value. fNIRSoftPro® was used for preprocessing and to calculate changes in oxygenated hemoglobin (HbO2) and deoxygenated hemoglobin (HHb) concentrations with the modified Beer-Lambert Law [START_REF] Delpy Dt | Estimation of optical pathlength through tissue from direct time of flight measurement[END_REF]). Statistical differences between condition-related HbO2 and HHb would ensure cortical-related activations whereas coevolution of both chromophores would stand for a blood volume effect. Concentration measurements were band pass filtered (0.012 Hz to 0.33 Hz) with a finite impulse response linear filter (order of 20) to remove signal noise components (thermoregulation, vasomotion, respiration, heart pulse) and slow signal drift [START_REF] Zaaimi | NIRS-measured oxy-and deoxyhemoglobin changes associated with EEG spikeand-wave discharges in children[END_REF]). HbO2 and HHb concentrations were then normalized using a signal detrending and an offset subtraction, and mean concentrations for each experimental condition (TMR × spatial separation) were calculated.

Due to artifacts induced by frontal sinus, the data from optodes 8 and 10 were excluded from the analyses.

Statistical Analysis

For each block and each listener, the CRM scores and the fNIRS measures were recorded. The CRM score corresponded to the percent of trials where the number and the color were both correctly reported. Before statistical analysis, the CRM scores were transformed from percent correct to rationalized arcsine unit (RAU, Studebaker, 1985) to control for ceiling effect. The effect of spatial separation and TMR on speech intelligibility were assessed using a repeated measures analysis of variance (ANOVA) with spatial separation (collocated vs. separate) and TMR (-12 dB vs. -4 dB vs. +4 dB) as factors. The same analysis was performed to analyze the prefrontal activity with optodes (14 optodes) as a supplementary factor. In case of violation of sphericity, a Greenhouse-Geisser correction was applied. The relationship between speech intelligibility and prefrontal activity according to the combinations of the spatial separation and TMR factors was explored using a linear mixed-effect model. All analyses were performed using the software R and the packages Bezf or repeated measures ANOVA and BlmerTest^for linear mixed-effect model. Pairwise post hoc comparisons were carried out with the Tukey's honestly significant difference (HSD) with a P value threshold of 0.05. No P value was reported for F ratio below 1 (withinsample variability greater than between-sample variability).

RESULTS

Speech Intelligibility

As shown in previous studies [START_REF] Brungart Ds | Informational and energetic masking effects in the perception of two simultaneous talkers[END_REF][START_REF] Xia | Spatial release of cognitive load measured in a dual-task paradigm in normalhearing and hearing-impaired listeners[END_REF], higher scores of speech intelligibility were provided by favorable TMR (F (1.4, 18.18) = 21.67, P = 0.00006, η 2 G = 0.30) and separate talkers (F (1, 13) = 133.96, P = 0.00000008, η 2 G = 0.73). The interaction between TMR and spatial separation [F (1.82, 23.64) = 12.86, P = 0.0002, η 2 G = 0.14) revealed that the effect of spatial separation was more pronounced for intermediate TMR (Fig. 2, upper panel). Moreover, in the collocated condition, post hoc tests showed that the decrease in TMR from intermediate to adverse did not give lower averaged speech intelligibility but rather increased the scattering of listeners. We thus explored in more details the pattern of results according to the listeners (Fig. 3, upper panel). Half of the listeners (three females, four males) had a U-shape performance, defined as similar performances between the adverse and the favorable TMR despite the 16-dB gap. The other listeners (three females, four males) had a more monotonous decrease in performance following the decrease of TMR in the collocated conditions. The comparison between the performances of the adverse and favorable TMR was performed for each listener with a Chi 2 : U-shape performers were defined as listeners who showed no significant difference (i.e., each P 9 0.2), whereas non U-shape performers were defined as the listeners who showed lower performance with the adverse than with the favorable TMR (each P G 0.05) in the collocated conditions.

Prefrontal Activity

A repeated measures ANOVA was conducted on HBO2 changes with TMR, spatial separation, and optode number as within-listener variables. A main effect of spatial separation was observed (F (1, 13) = 7.05, P = 0.02, η 2 G = 0.08) with higher HbO2 concentrations ([HbO2]) for the collocated condition. No significant main effect of TMR [F (2, 26) = 3.10, P = 0.06] nor optode number [F (13, 169) = 0.98] was found. However, the effect of spatial separation on prefrontal activity varied with the TMR as shown by a significant interaction between the two factors (F (2, 26) = 3.9, P = 0.03, η 2 G = 0.03). The post hoc tests revealed that spatial separation provided lower prefrontal activity only for the intermediate TMR. No significant difference was observed for the adverse and favorable TMR (Fig. 2, lower panel).

Moreover, no interaction involving the factor optode number (spatial separation × optode number: F (13, 69) = 0.95; TMR × optode number: F (26, 338) = 1.21, P = 0.23; spatial separation × TMR × optode number: F (26, 338) = 1.38, P = 0.10) was observed.

No effect of spatial separation nor TMR was observed on HHb (spatial separation: F (1, 13) = 0.1; TMR: F (2, 26) = 0.63, spatial separation × TMR: F (2, 26) = 0.38).

Following the speech intelligibility results, we compared the patterns of [HbO2] across the TMR for the groups of U-shape and non-U-shape performers in the collocated condition (Fig. 3, lower panel). We found that the group of U-shape performers showed higher [HbO2] with the adverse and intermediate TMRs than with the favorable TMR in the collocated condition (Kruskal-Wallis test, Chi 2 = 7.4; P = 0.025). On the contrary, the group of non-U-shape performers showed similar [HbO2] across the TMRs in the collocated condition (Chi 2 = 0.20; P = 0.90).

Relationship between Speech Intelligibility Performance and Prefrontal Activity

Previous results revealed that the effects of the spatial separation and TMR played a role in both performance level and prefrontal activity. Further analyses were conducted to explore the relationship between performance and prefrontal activity (mean [HbO2]) according to spatial separation and TMR.

Given the absence of voxel number effect, the [HbO2] changes were averaged across the optodes for each listener. Then, a linear mixed-effect model was computed: the dependent variable was the speech intelligibility scores transformed in RAU, and the predictors were the [HbO2] changes, the spatial separation, and the TMR. The listeners were considered as a random effect. The model revealed a significant interaction between the three predictors (F (2, 75.4) = 4.64, P = 0.013). To decompose that interaction, the correlation between speech intelligibility scores and [HbO2] changes was computed for each combination of the factors spatial separation and TMR.

A significant positive correlation was observed with the adverse TMR in the collocated condition (r 2 (12) = 0.38, P = 0.018) (Fig. 4, upper-left panel). With the adverse TMR, higher performance is related with higher prefrontal activity in the collocated condition. It appeared that U-shape performers exhibited both high performance and high prefrontal activity in that condition.

No correlation was observed in the separate conditions.

DISCUSSION

The motivation of our study was to examine how the relative levels of the talkers influenced the spatial release of the cognitive load in a cocktail party paradigm. The cognitive load was assessed by the [Hb02] changes reflecting prefrontal activity measured by fNIRS. We observed that the cognitive load was reduced by the spatial separation of talkers only for the intermediate TMR. The prefrontal activity did not seem to vary significantly across the optodes as we found no effect of optode number in our analyses. It was consistent with neuroimaging studies, revealing that not a specific area but rather a broad network of cortical areas including several frontal areas are recruited during a multi-talker listening situation (Zekveld et al. 2014a).

Our results at intermediate TMR are consistent with [START_REF] Xia | Spatial release of cognitive load measured in a dual-task paradigm in normalhearing and hearing-impaired listeners[END_REF] who found that the spatial separation of different gender talkers presented at the same voice level reduced the cognitive load. However, Xia and colleagues found no spatial release of cognitive load for same-gender talkers. The authors explained this counter-intuitive result by a tradeoff in favor of the secondary task for too difficult listening condition. Our results support this hypothesis: in the absence of any segregating cue (nor spatial nor gender cue), their primary auditory task was too difficult. The absence of spatial release of cognitive load for same-gender talkers in Xia and colleagues could then be due to the dual-task paradigm.

In line with Zekveld and colleagues (Zekveld et al. 2014b), no spatial release of the cognitive load at adverse TMR was found in our study. Zekveld and colleagues compared the cognitive load at two TMRs, one for the separate talkers and one for the collocated For each TMR, the results of the non U-shape performers are plotted in green (left boxplots), and the results of the U-shape performers are plotted in red (right boxplots). The boxplots show the median (horizontal bar) and the interquartile range (boxes) and the whiskers show the 5-95 percentile interval. By definition, for the Ushape performers, the intelligibility score was similar for adverse and favorable TMR. For the non-U-shape performers, the intelligibility scores decreased with the TMR. For the U-shape performers, [HbO2] increased with the TMR. For the non-U-shape performers, [HbO2] was similar across the TMRs.

talkers. The two TMRs were adapted to give the same performance in terms of SRT 50 . The point is that SRT 50 was obtained at an adverse TMR with separate talkers whereas it required favorable TMR with collocated talkers. Therefore, Zekveld and colleagues compared the cognitive load between those two combined conditions: adverse TMR/separate talkers vs. favorable TMR/collocated talkers. We also found no difference in our data for those specific conditions. Thus, the studies of Xia and colleagues and Zekveld and colleagues could be conciliated by taking into account the role of TMR in the spatial release of cognitive load. Interestingly, those results are consistent despite the differences in terms of paradigm and measure to assess the cognitive load: Xia and colleagues used a CRM paradigm with a dual task, Zekveld and colleagues an SRT paradigm with pupil dilation, and our study a CRM paradigm with fNIRS.

Our findings also confirm that the level difference between the masker and the target can paradoxically be used as a cue to distinguish the talkers in the adverse TMR condition [START_REF] Brungart Ds | Informational and energetic masking effects in the perception of two simultaneous talkers[END_REF][START_REF] Ihlefeld | Spatial release from energetic and informational masking in a selective speech identification task[END_REF]. Actually, individual analysis disclosed that half of the listeners (U-shape performers) had similar performance in the adverse and the favorable TMRs of the collocated condition, probably because they were able to use the level difference between the target and the masker to segregate them (the condition blocks were randomized across listeners). In other words, with the adverse TMR, i.e., the most difficult condition, the U-shape performers reached similar scores to those achieved with the positive TMR, a much easier condition (16-dB gap in favor of the target). The U-shape performers have probably used the level difference between the two voices to focus on the softest one. Their performance was achieved at a cognitive cost as supported by higher prefrontal activity in the adverse TMR than with the favorable TMR (Fig. 3) in the collocated condition. This increase in prefrontal activity as a function of the TMR may reflect the activation of attentional systems. However, as the attentional systems are not restricted to prefrontal cortex, the measures of other cortical areas (parietal cortex) are required to confirm that hypothesis. The non-U-shape performers showed similar prefrontal activity across the TMRs in the collocated condition which could suggest a lack of attentional engagement [START_REF] Durantin | Using near infrared spectroscopy and heart rate variability to detect mental overload[END_REF]). More generally, for challenging conditions, the differences in speech intelligibility and prefrontal activity could be related as evidenced by the positive correlation: the higher the prefrontal activity, the higher the speech intelligibility (Fig. 4).

In normal-hearing listeners, our results provide evidence that the measure of prefrontal activity with fNIRS could help undercover the relationship between speech intelligibility, spatial separation, and cognitive load. For instance, spatial separation can dramatically improve speech intelligibility without increasing the cognitive load. In fact, the spatial separation can even decrease the cognitive load for intermediate TMR, as For collocated talkers, at adverse TMR, the higher the prefrontal activity, the higher the performance was.

shown by our data. The cognitive resources of listeners can often be limited in everyday life situations, either by age or pathology or when task demands exceed listener's mental capacity-for instance, in multitasking environment. Moreover, those same people can also suffer from low speech intelligibility because of weak or no access to spatial cues, such as hearing-impaired listeners wearing hearing aids [START_REF] Neher | Benefit from spatial separation of multiple talkers in bilateral hearing-aid users: effects of hearing loss, age, and cognition[END_REF] or the operators of complex systems dealing with multi-channel communications (Brungart et al. 2001). Binaural techniques are therefore a promising way to improve speech intelligibility (Brungart and Simpson 2005) in a cognitively efficient way.

FIG. 1 .

 1 FIG. 1. fNIRS device optode location. The device is composed of four light sources and ten light detectors. The association of one light source and one light detector composes the optodes. The disposition of the sources and detectors leads to 16 optodes over the prefrontal cortex. The emitter-detector distance is 25 mm. The original image comes from the fNIRSOFT® manual and has been slightly modified.

FIG. 2 .

 2 FIG. 2. Correct response scores (upper panel) and oxygenation change (lower panel) plotted against TMR. For each TMR, the results with collocated talkers are plotted in black (left boxplots), and the results with separate talkers are plotted in orange (right boxplots). The boxplots show the median (horizontal bar) and the interquartile

FIG. 3 .

 3 FIG. 3. Correct response scores (upper panel) and oxygenation change (lower panel) plotted against TMR in the collocated condition. For each TMR, the results of the non U-shape performers are plotted in green (left boxplots), and the results of the U-shape performers are plotted in red (right boxplots). The boxplots show the median (horizontal bar) and the interquartile range (boxes) and the

FIG. 4 .

 4 FIG. 4. Intelligibility scores plotted against [HbO2] changes foreach combination of TMR and spatial separation conditions. The letter BU^indicates the U-shape performers and the letter BNî ndicates the non-U-shape performers. The Pearson's coefficient of correlation and its degree of significance is indicated in each panel. For collocated talkers, at adverse TMR, the higher the prefrontal activity, the higher the performance was.

ACKNOWLEDGMENTS

This work was supported in part by the French Procurement Agency (Direction Générale de l'Armement, DGA). The authors warmly thank Jean Christophe Bouy for software development and Patrick M.B. Sandor for his helpful comments on a previous version of this manuscript.

COMPLIANCE WITH ETHICAL STANDARDS

Conflict of Interest

The authors declare that they have no conflict of interest.


Nicolae Bogdan Mandache
email: mandache@infim.ro

Dragos Iustin Palade

The physical origin of the nucleon-nucleon attraction by pion exchange

Keywords: pion exchange, dynamical mass, central nucleon-nucleon potential, bound state

A formula is derived for the central nucleon-nucleon potential, based on an analysis of the physical origin of the nucleon-nucleon attraction by pion exchange. The decrease of the dynamical mass of the interaction field, exchanged pion in this case, is the principal mechanism responsible for the nuclear attraction in a similar way the decrease of the kinetic energy of the exchange electron in the diatomic molecule is directly responsible for the covalent molecular attraction. The minimum value of this central nucleon-nucleon potential and the position of the minimum are similar with the values reported in literature for a potential calculated by lattice QCD, which shares the features of the phenomenological nucleon-nucleon potentials. The Schrodinger equation with this potential was solved numerically for different values of the pion mass. It results that the nucleon-nucleon binding energy increases with the decrease of the pion mass. A very small binding energy (0.05 MeV) was obtained for the real pion mass. We discuss on the two pion exchange and hard core repulsion. The minimum value of the potential for two pion exchange is comparable with the minimum value of the CD Bonn potential.

Introduction

The effective degrees of freedom in the nuclear interaction at low energy, in particular in the nuclear bound state, are the nucleons and the pions. The pion exchange is the basic mechanism of nucleon-nucleon (NN) attraction at low energy [START_REF] Ericson | and Nuclei[END_REF][START_REF] Machleidt | [END_REF][START_REF] Lacroix | [END_REF][START_REF] Epelbaum | [END_REF][START_REF] Machleidt | [END_REF][START_REF] Muhin | Fizica Nucleara Experimentala[END_REF].

As it is well known the current masses of quarks (antiquarks) u (ū) and d (đ) are very small; the nucleon and pion masses are mainly of dynamical origin ("kinetic" energy). The confinement of the quarks into nucleon and pion associate an energy, given by the Heisenberg uncertainty relation, which is just the dynamical mass.

The long range structure of the nucleon is given roughly by the pion [7,8], which also gives the range of nuclear forces. In particular, the Compton wavelength of the pion

c m   /   
, which has a value of 1.41 fm for the charged pion, gives the range N r of the nucleon extension. The pion in nucleon can be represented by a degree of freedom of current mass 0, localized into a region of radius

   N r .
This localization into the nucleon associates an energy (dynamical mass)

2 / c m c pc E       
, given by the uncertainty relation, which is just the mass of the pion. At the formation of a nuclear bound state this dynamical mass decreases, wich means a mass defect and consequently a binding energy for the nucleon-nucleon state [9]. Indeed, when two nucleons approach each other to form a bound state, in particular the deuteron, they put in common their pion degrees of freedom (pion exchange). This is equivalent with a slight de-localization of the pion degree of freedom from a region of radius

   N r to a region of radius ) ( ) ( R R r N       
, where ) (R  is direct proportional to the distance R between the two bound nucleons and is strongly dependent on the probability of the pion to penetrate the potential barrier between the two nucleons . The dynamical mass gets:

) (R c E       
and is lower than the initial one (that in the free nucleon). To form a bound state, the decrease of the dynamical mass of the pion degree of freedom:

) (R c c E            (1)
must be larger than the kinetic energy acquired by the system of two nucleons due to their localization at a distance R each other: This mechanism of nuclear binding has similarities with the mechanism of molecular binding of diatomic molecules [START_REF] Feynman | Feynman Lectures on Physics[END_REF]. In fact Heisenberg was the first who presented the attractive force between proton and neutron in analogy to that in the hydrogen molecular ion  2 H , where the electron is the particle exchanged between the two protons [START_REF] Machleidt | [END_REF].

Feynman approach to the molecular and nuclear exchange interactions

Let's start with the physical interpretation of the mechanism of H 2 + ion binding presented by Feynman in [START_REF] Feynman | Feynman Lectures on Physics[END_REF].

In the 

2

H ion, since there are two protons, there is more space where the electron can have a low potential energy than in the case of hydrogen atom. The electron spreads out lowering its kinetic energy, in accord with uncertainty relation, without increasing its potential energy. This energy decrease is at the origin of the binding energy of  2 H ion. The attractive force comes from the reduced energy of the system due to the possibility of the electron jumping from one proton to the other [START_REF] Feynman | Feynman Lectures on Physics[END_REF][START_REF] Ruedenberg | [END_REF]12,13].

For large distances between the two protons of the 

2

H ion the electrostatic potential energy of the electron is nearly zero over most of the space it must go when it makes its jump. In this space, then, the electron moves nearly like a free particle in empty space but with a negative energy [START_REF] Feynman | Feynman Lectures on Physics[END_REF]:

H e W m p   2 2 ,
where H W is the binding energy (+13.6 eV) of the hydrogen atom. This means that p is an imaginary number:

H e W m i p 2  .
The amplitude A for a particle of definite energy to get from one place to another a distance R away is proportional to: R e A pR i ) / ( ~ where p is the momentum corresponding to the definite energy. Replacing p one obtains that the amplitude of jumping of electron from one proton to the other, for large separation R between the two protons, will vary as [START_REF] Feynman | Feynman Lectures on Physics[END_REF]:

R e R e A a R R W m H e 0 / ) / 2 ( ~   
where 0 a is the Bohr radius.

If the particle goes in one direction the amplitude is [START_REF] Feynman | Feynman Lectures on Physics[END_REF]:

0 / ~a R e A 
One can note that the exponential factor limits drastically the amplitude of electron exchange for large separation.

The nuclear interaction which takes place between a neutron and a proton by pion exchange is described by Feyman, for large R, with similar arguments in the same chapter [START_REF] Feynman | Feynman Lectures on Physics[END_REF].

Since in the nuclear process the proton and the neutron have almost equal masses, the exchanged pion will have zero total energy. But the relation between the total energy E and the momentum p for a pion of mass  m is:

2 2 2 2 2 c m c p E    .
Since E is practically zero the momentum is again imaginary:

c im p  
This means the amplitude for the pion to jump from one nucleon to another is for large R:

    / ) / ( ~R R c m e e A    (2)
The exponential factor is typical for a Yukawa potential or exponential potential, and again it limits drastically the exchange for large R.

The central nucleon-nucleon potential due to pion exchange

In fact, the exponential factor is well known from the tunneling of a potential barrier of width R by a particle with an energy much lower than the barrier height. The probability of transmission is proportional to the square of the amplitude, this means in our case:

  / 2 ~R e P  (3) The increase ) (R 
of the radius of localization region of the pion degree of freedom, which appears in formula [START_REF] Ericson | and Nuclei[END_REF], is strongly limited by this exponential factor (3), i.e. the probability for the pion to penetrate the potential barrier between the two nucleons. Therefore ) (R  , which is direct proportional to the distance R between the nucleons, is taken equal to:

  / 2 Re ) ( R R    (4)
By replacing (4) in formula (1), we obtain the decrease of the dynamical mass of the pion degree of freedom, which is at the origin of nuclear attraction. In fact with sign minus this decrease is just the NN potential due to pion exchange:

                 / 2 / 2 / 2 Re Re * Re ) ( R R R c c c E R V             (5)
where

2 / c m c      .
The NN potential V(R) as a function of inter-nucleon distance R is shown in Fig. 1 for a charged pion exchange between the two nucleons

) 41 . 1 ( fm   
. This potential has some similarities with that obtained by lattice QCD [14], which shares the features of the phenomenological NN potentials: an attractive well at intermediate and larger distances and a hard core repulsion at small range, with the maximum depth of the potential in the intermediate range [START_REF] Ericson | and Nuclei[END_REF][START_REF] Machleidt | [END_REF][START_REF] Lacroix | [END_REF][START_REF] Epelbaum | [END_REF][START_REF] Machleidt | [END_REF]. The minimum value of the potential (-22 MeV) and the position of the minimum (0.7 fm) in Fig. 1, are comparable with the values shown in Fig 3 from [14]: about -25 MeV and 0.7 fm. The fall of the potential towards zero value in Fig. 1 for small R (R<0.6 fm) is compatible with the beginning of the hard core repulsion region [START_REF] Ericson | and Nuclei[END_REF][START_REF] Machleidt | [END_REF][START_REF] Lacroix | [END_REF][START_REF] Epelbaum | [END_REF][START_REF] Machleidt | [END_REF]14] which gets dominant at short range.

The potential in Fig 1 is a little larger, in particular the fall towards higher values of R is slower than in the case of potential obtained in [14]. On the other hand the results in [14] were obtained with a pion mass (530 MeV) higher than the real pion mass. For a lower pion mass (360 MeV) the range of the potential gets wider also [14]. Fig. 1 The NN potential in the case of charged pion exchange.

We solved numerically the Schrodinger equation for the potential V(R) given in relation [START_REF] Machleidt | [END_REF], for different values of the pion mass  m :

) ( ) ( ) ( ) ( 2 2 R E R R V R          ( 6
)
where  is the reduced mass of the two nucleons. From a numerical point of view, the Schrodinger equation in central potential has been solved using the substitution:

R R R / ) ( ) (   
which, in turn, gives a standard Sturm-Liouville eigenvalue problem with a constant coefficient for the second order derivative:

) ( ) ( ) ( ) ( 2 2 2 2 R E R R V dR R d         (7)
We look for the ground state, this means zero centrifugal energy (l=0).

The spatial dimension has been truncated as The total energy of the two nucleons decreases, this means the binding energy increases with the decrease of the pion mass, a result obtained in [START_REF] Epelbaum | [END_REF] for the binding energy of deuteron in function of pion mass. In the same time the range of the potential gets wider. For masses higher than the real pion mass the total energy gets positive. This highlights the role of the pion as main player in the production of nuclear attraction. To underline this conclusion we mention that for a mass of exchanged meson equal to 770 MeV (the ρ meson mass) the potential energy given by relation ( 5) has significant values only for R lower than about 0.8 fm. This means a very low contribution to the nuclear potential in the intermediate range attraction region.

The two pion exchange and the hard core repulsion.

The maximum molecular attraction is realized in the diatomic molecular bound by exchange of two electrons [START_REF] Feynman | Feynman Lectures on Physics[END_REF]. This is the case of the hydrogen molecule 2 H in which the two hydrogen atoms put in common (exchange) their electrons.

Similar the maximum of NN attraction is given by the exchange of two pions [START_REF] Ericson | and Nuclei[END_REF][START_REF] Machleidt | [END_REF][START_REF] Lacroix | [END_REF][START_REF] Epelbaum | [END_REF][START_REF] Machleidt | [END_REF]. When the two nucleons approach each other to form a bound state, in particular the deuteron, they put in common (exchange) their pion degrees of freedom. The attractive potential in this case is practically two times the potential given by relation [START_REF] Machleidt | [END_REF]. The minimum value of the potential gets -44 MeV, which is comparable with the minimum value (-50 MeV) of the CD Bonn potential [START_REF] Machleidt | [END_REF]. For a value of the hard core repulsion radius equal to 0.6 fm (Fig. 3), a typical value for phenomenological nucleon-nucleon potentials [START_REF] Ericson | and Nuclei[END_REF][START_REF] Machleidt | [END_REF][START_REF] Lacroix | [END_REF][START_REF] Epelbaum | [END_REF][START_REF] Machleidt | [END_REF], the binding energy is 0.7 MeV.

Discussion and conclusions

The pion exchange is at the origin of the nuclear attraction, in a similar way the electron exchange is at the origin of attraction in the molecular covalent bound. The decrease of the kinetic energy (in fact dynamical mass decrease from a relativistic point of view) of the exchange electron in the  2 H ion, directly responsible for the formation of the molecular bound state, is replaced by the decrease of the dynamical mass of the pion degree of freedom in the case of the nuclear bound by pion exchange. The slight de-localization of the pion degree of freedom, which is at the origin of this dynamical mass decrease, is drastically limited by an exponential factor, which represents the probability for the pion to penetrate the potential barrier between the two nucleons. A similar exponential factor exists in the case of molecular bound.

The analytical formula of the central nuclear potential [START_REF] Machleidt | [END_REF] derived for the NN interaction by pion exchange does not contain any unknown parameter. The minimum value of the NN potential and the position of the minimum are similar with the values reported in literature for the central NN potential obtained by lattice QCD, which shares the features of the phenomenological NN potentials. A very small binding energy (0.05 MeV) was obtained by solving numerically the Schrodinger equation. The binding energy increases for pion masses lower than the real pion mass.

The fall of the potential (5) towards zero value for small R (Fig. 1) is compatible with the beginning of the well known hard core repulsion region which is dominant at short range. The Yukawa potential, which was derived in analogy with the coulomb attraction which originates in photon exchange, gets infinite attractive for 0

 R due to factor R / 1  [1, 2]. Since the maximum value of   / 2 Re R  is 0.26 fm (for 2 /    R
), this means substantially smaller than fm 41 . 1   

, relation (5) can be written in a good approximation as:

     / 2 2 ) ( R e R c m R V    (8)
The NN nuclear potential is proportional to the mass of the interaction field. It is also proportional to the ratio

  / R
, which is directly related to the slight de-localization of the pion degree of freedom and its (dynamical) mass decrease. This de-localization is drastically limited by the exponential function, which is similar to an exponential potential except the factor 2.

In the case of two pion exchange the minimum of the potential gets comparable with the minimum value of the CD Bonn potential. The potential in this case is in a good aproximation:

      / 2 2 2 2 ) ( R e R c m R V    ( 9
)
The dependence of the type x xe  of the nuclear potential, where

  / 2R x 
is similar with the attractive part of the Rydberg potential used to describe the molecular covalent bonding [15].

A hard core repulsion was added to the two pion exchange potential and the Scrodinger equation was solved numerically for different values of hard core repulsion radius. For a radius of 0.6 fm the binding energy is about 0.7 MeV.

Let's compare the strength of the nuclear potential ) ( 2 R V  from relation (9) with the coulombian

potential R q V C 2 
. The ratio of the two potentials for

   R is: 2 2 2 2 1 2 2 ) ( / ) (     e e q c V V C        ( 10
)
where  is the e.m coupling constant, a typical result for the relative strength of the nuclear interaction to the e.m. interaction.

If we analyze the mechanism of NN interaction at quark level, we could say that by pion exchange between two nucleons some quark degrees of freedom are implicitly exchanged and in consequence are slightly de-localized. The confinement region of a quark slightly increases and accordingly its dynamical mass decreases. This suggests to interpret the nuclear interaction as a residual strong interaction.

.

  Such large radial extension is needed in order to resolve properly the states lying closely to the continuum ( 0  E ). The eigenvalue problem is solved by means of a finite difference method with the boundary values 0 exponential decay at large radius. The resulting Hamiltonian is diagonalized and the eigenvalues (energy) are obtained. In Fig. 2 is given the dependence of the total energy of the two nucleons in function of the ratio of pion mass  m to the real pion mass 0  m . For the real pion mass ( 1 small binding energy, about 0.05 MeV, was obtained.

Fig. 2

 2 Fig. 2 The total energy of the two nucleons as a function of the ratio of pion mass  m to the real pion mass 0  m

Fig. 3

 3 Fig.3The NN potential in the case of two pion exchange and hard core repulsion at 0.6 fm

Fig. 4

 4 Fig.[START_REF] Epelbaum | [END_REF] The total energy of the two nucleons as a function of hard core repulsion radius 0 r for the two pion exchange potential

Acknowledgments. We thank E. Dudas for helpful discussions and suggestions.