Possible implications of the channeling effect in NaI(Tl) crystals
R. Bernabei, P. Belli, F. Montecchia, F. Nozzoli, F. Cappella, A. Incicchitti, D. Prosperi, R. Cerulli, C.J. Dai, H.L. He, H.H. Kuang, J.M. Ma, X.H. Ma, X.D. Sheng, Z.P. Ye, R.G. Wang, Y.J. Zhang
aa r X i v : . [ a s t r o - ph ] O c t ROM2F/2007/15September 2007submitted for publicationPossible implications of the channeling effect inNaI(Tl) crystals
R. Bernabei, P. Belli, F. Montecchia, F. Nozzoli
Dip. di Fisica, Universit`a di Roma “Tor Vergata” and INFN, sez. Roma “Tor Ver-gata”, I-00133 Rome, Italy
F. Cappella, A. Incicchitti, D. Prosperi
Dip. di Fisica, Universit`a di Roma “La Sapienza” and INFN, sez. Roma, I-00185Rome, Italy
R. Cerulli
Laboratori Nazionali del Gran Sasso, INFN, Assergi, Italy
C.J. Dai, H.L. He, H.H. Kuang, J.M. Ma, X.H. Ma, X.D. Sheng, Z.P. Ye ,R.G. Wang,Y.J. Zhang IHEP, Chinese Academy, P.O. Box 918/3, Beijing 100039, China
Abstract
The channeling effect of low energy ions along the crystallographic axes andplanes of NaI(Tl) crystals is discussed in the framework of corollary investigationson WIMP Dark Matter candidates. In fact, the modeling of this existing effectimplies a more complex evaluation of the luminosity yield for low energy recoilingNa and I ions. In the present paper related phenomenological arguments aredeveloped and possible implications are discussed at some extent.
Keywords:
Dark Matter; WIMP; underground Physics
PACS numbers:
It is known that ions (and, thus, also recoiling nuclei) move in a crystal in a differ-ent way than in amorphous materials. In particular, ions moving (quasi-) parallelto crystallographic axes or planes feel the so-called “channeling effect” and show ananomalous deep penetration into the lattice of the crystal [1, 2, 3]; see Fig. 1. also: University of Jing Gangshan, Jiangxi, China c , depicted there (seefor details Sec. 2). Two examples for channeled and unchanneled ions are also shown(dashed lines).For example, already on 1957, a penetration of Cs + ions into a Ge crystal wasobserved to a depth of about 1000 ˚A [4], larger than that expected in the case the ionswould cross amorphous Ge ( ≃
50 ˚A). Afterwards, high intensities of H + ions at 75keV transmitted through thick (3000-4000 ˚A) single-crystal gold films in the < > directions were detected [2]. Other examples for keV range ions have been shown inref. [5] where 3 keV P + ions moving into layers of 500 ˚A of various crystals werestudied.The channeling effect is also exploited in high energy Physics e.g. to extract highenergy ions from a beam by means of bent crystals or to study diffractive Physics byanalysing scattered ions along the beam direction (see e.g. ref. [6]).Recently [7] it has been pointed out the possible role which this effect can playin the evaluation of the detected energy of recoiling nuclei in crystals, such as theNaI(Tl) .In fact, the channeling effect can occur in crystalline materials due to correlatedcollisions of ions with target atoms. In particular, the ions through the open channelshave ranges much larger than the maximum range they would have if their motionwould be either in other directions or in amorphous materials. Moreover, when alow-energy ion goes into a channel, its energy losses are mainly due to the electroniccontributions. This implies that a channeled ion transfers its energy mainly to electronsrather than to the nuclei in the lattice and, thus, its quenching factor (namely the ratiobetween the detected energy in keV electron equivalent [keVee] and the kinetic energyof the recoiling nucleus in keV) approaches the unity.It is worth to note that this fact can have a role in corollary analyses in the Dark For completeness, it is worth to note that luminescent response for channeling in NaI(Tl) wasalready studied in ref. [8] for MeV-range ions. γ sources (in order to avoid induced radioactivity in the materials),the quenching factor is a key quantity to derive the energy of the recoiling nucleusafter an elastic scattering. Generally, for scintillation and ionization detectors thisfactor has been inferred so far by inducing tagged recoil nuclei through neutron elasticscatterings [9]; however, as it will be discussed in Sec. 3, the usual analysis carried outon similar measurements does not allow to account for the channeled events. A list ofsimilar values for various nuclei in different detectors can be found e.g. in ref. [10]. Inparticular, commonly in the interpretation of the dark matter direct detection resultsin terms of WIMP (or WIMP-like) candidates the quenching factors are assumed tobe constant values without considering e.g. their energy dependence, the propertiesof each specific used detector and the experimental uncertainties. An exception wasin the DAMA/NaI corollary model dependent analyses for WIMP (or WIMP-like)candidates [10, 11, 12, 13] where at least some of the existing uncertainties on the q Na and q I values, measured with neutrons, were included.In this paper the possible impact of the channeling effect in NaI(Tl) crystals isdiscussed in a phenomenological framework and comparisons on some of the corollaryanalyses carried out in terms of WIMP (or WIMP-like) candidates [10, 11, 12, 13], onthe basis of the 6.3 σ C.L. DAMA/NaI model independent evidence for particle DarkMatter in the galactic halo , are given. The stopping power of an ion inside an amorphous material is given by the sum of twoeffects: its interaction with the nuclei ( n ) of the material and its interaction with thebinding electrons ( e )[23].If E is the energy of the ion at any point x along the path, its stopping power canbe written as: dE ion dx ( E ) = dE ion − n dx ( E ) + dE ion − e dx ( E ) (1)where dE ion − n dx and dE ion − e dx ( E ) are the nuclear and the electronic stopping powers ofthe ion, respectively. They can be evaluated – following the theory firstly developedin ref. [23] – by using some available packages, as the SRIM code [24].We have to stress that the detectable light produced by a charged particle (eitherelectron or ion) in scintillator detectors mostly arises from the energy loss in theelectronic interactions. Thus, the differential luminosities in scintillators, dL e dx and We remind that various possibilities for some of the many possible astrophysical, nuclear andparticle Physics scenarios have have been analysed by DAMA itself both for some WIMP/WIMP-likecandidates and for light bosons [10, 11, 12, 13, 14], while other corollary analyses are also available inliterature, such as e.g. refs. [15, 16, 17, 18, 19, 20, 21, 22, 7]. Many other scenarios can be consideredas well. L ion dx for electrons and ions, respectively, can be written as: dL e dx = α dE e − e dx for electrons dL ion dx = α dE ion − e dx ( E ) = α × dE ion dx × q ′ ( E ) for ions (recoils) (2)where α is a proportionality constant, dE e − e dx is the stopping power of an electronin the material and q ′ ( E ) = (cid:16) dE ion − e dx ( E ) (cid:17) / (cid:16) dE ion − n dx ( E ) + dE ion − e dx ( E ) (cid:17) is defined as“differential quenching factor”.The total detected luminosities, L = R path dLdx dx , for electrons and ions can bewritten in the form: L e = α Z path dE e − e dx dx = αE e for electrons L ion = α Z path q ′ ( E ) × dE ion dx dx ≡ α × q ( E ion ) × E ion for ions (recoils) ;(3)in addition, the range of an ion is: R ion ( E ) = Z E dE ′ dE ion /dx ≡ q ( E ) × Z E dE ′ dE ion − e /dx = q ( E ) × R e ( E ) . (4)In eq. (3) and (4) q ( E ) = E R E q ′ ( E ′ ) dE ′ is the “light quenching factor” and q ( E ) = R E dE ′ dE ion /dx / R E dE ′ dE ion − e /dx is the “range quenching factor”. In the energy region ofinterest for the dark matter detection q ( E ) ≃ q ( E ) within 10-20%. In particular,the values of the quenching factors for recoiling nuclei in detectors made of amorphousmaterials are well below the unity in the keV energy region.The situation changes when the detector is either a crystal or a multi-crystallinematerial (the size of a single crystal has to be larger than few thousands of ˚A). In thiscase the luminosity depends on whether the recoiling nucleus is (quasi-) parallel to thecrystallographic axes or planes or not. In the first case, since the energy losses of theion are mainly due to the electronic contributions, the penetration (and the range) ofthe ion becomes much larger, of the order of R e , and the quenching factor approachesthe unity.The theory of ion channeling in crystals has been developed e.g. in ref. [25, 3]. Inparticular, this theory deals with channeling of low energy, high mass ions as a separatecase from high energy, low mass ions. Here, we only remind that the condition for alow energy ion and a recoiling nucleus to be axially channeled along a certain stringof atoms in the lattice is linked to a critical angle, Ψ c (see Fig. 1); for details refer to[25, 3]. When the ion (recoiling nucleus) has a moving direction with an angle Ψ withrespect to this string lower than Ψ c , it is axially channeled.The critical angles for axial channeling is given by [25, 3]:Ψ c = s Ca T F d √ (5)4here C ≃ d is the inter-atomic spacing in thecrystal along the channeling direction. The Thomas-Fermi radius, a T F , can be writtenas [25, 3]: a T F = 0 . a (cid:0) √ Z + √ Z (cid:1) / (6)where Z and Z are the atomic numbers of the projectile (recoiling nucleus) andtarget atoms, respectively; a = 0 . A is the Bohr radius.The characteristic angle Ψ is defined as a function of the ion (recoiling nucleus)energy, E , by:Ψ = r Z Z e Ed (7)where e is the electron’s charge. The condition Ψ < Ψ c for axial channeling is valid forΨ > Ψ ,lim = a TF d , that is for E < E lim = Z Z e da TF [25, 3]. Hence, typical values forNaI(Tl) crystal assure that for recoil’s energies less than 170 keV the quoted formulashold. For completeness, we just remind that it has also been suggested that the criticalangles may slightly depend on the temperature [26]. Moreover, the critical angles atlow energy have a weaker dependence on ion energy than those at higher energy. Infact, at higher energy, the critical angle is ≃ C Ψ [25, 3].In the case of planar channeling for low energy ions the critical angle can be writtenas [27] (see also ref. [25]): θ pl = a T F p N d p (cid:18) Z Z e Ea T F (cid:19) / , (8)where N is the atomic number density and d p is the inter-plane spacing. The depen-dence of θ pl on the energy is weaker than that at higher energy, where it can be writtenas [6, 28]: θ pl = a T F p N d p (cid:18) Z Z e CEa
T F (cid:19) / . (9)Taking into account the critical angles for axial and planar channeling in NaI(Tl),we have calculated by Monte Carlo method the solid angle interested by both axialand planar channeling in NaI(Tl) crystals as a function of the energy of the recoilingnuclei, E R ; see Fig. 2. Moreover, just the lower index crystallographic axes and planeshave been considered, for the axial channeling: < > , < > , < > and forthe planar channeling: { } , { } , { } .In this way, the estimated light response of a NaI(Tl) crystal scintillator to Sodiumand Iodine recoils at given energy has been studied taking into account the channelingeffect in the considered modeling. For a given nucleus A with recoil energy E R theresponse of a NaI(Tl) crystal scintillator can be written as dN A dE det ( E det | E R ), where E det is the detected energy. By the definition: R ∞ dN A dE det ( E det | E R ) dE det = 1. Inmost cases of the Dark Matter direct detection field – that is without including the5 R (keV) DW / p Figure 2: Fraction of solid angle interested by both axial and planar channeling inNaI(Tl) crystals as a function of the energy of the recoiling nuclei, calculated accordingto the text. In these calculations just the lower index crystallographic axes and planeshave been considered: for the axial channeling: < > , < > , < > and forthe planar channeling: { } , { } , { } .channeling effect – the light response is assumed equal to a Dirac delta function: dN A dE det ( E det | E R ) = δ ( E det − q A E R ), where q A is the value (assumed constant) of thequenching factor of the unchanneled A nucleus recoils.The evaluation of dN A dE det , when accounting for channeling effect, has been realised bymeans of a Monte Carlo code; the path of a recoiling nucleus, at a given recoil energy E R , has been calculated under the following reasonable and cautious assumptions:i ) isotropic distribution of the recoils;ii ) in the case the recoil would enter in a channel, a de-channeling can occur due tosome interactions with impurities in the lattice, as Tl luminescent dopant centers.The probability density of such a process is assumed to be: p ( x ) = λ e − x/λ , with λ = 1200 ˚A, that is the average distance among the Tl centers;iii ) the energy losses by the recoil nuclei in a channel just depend on the electronicstopping power (see eq. (1));iv ) the energy losses by the recoil nuclei in a channel are converted into scintillationlight with a quenching factor ∼ E det (keVee) a . u . a) IodineE R =4 keV E det (keVee)b) IodineE R =40 keVE det (keVee) a . u . c) SodiumE R =4 keV E det (keVee)d) SodiumE R =40 keV -2 Figure 3: Examples of light responses in terms of keVee, dN A dE det ( E det | E R ), for Iodinerecoils of 4 keV ( a ) and of 40 keV ( b ) and for Sodium recoils of 4 keV ( c ) and of 40keV ( d ) in the modeling given in the text. In this calculation the quenching factorsfor Sodium and Iodine recoils in amorphous or out of channel NaI(Tl) are assumed atthe mean values given in ref. [29]. Just to emphasize the effect of the channeling, thebroadening due to the energy resolution of the detector has not been included here.The peaks corresponding to fully channeled events ( q ∼
1) and to fully quenched events(broadened by the straggling) are well evident; in the middle events, which have beende-channeled at least once, are also visible. It is possible to note that e.g. in the caseof Iodine recoils the fully channeled events are about 25% at 4 keV; this percentagebecomes smaller, about 1% at 40 keV.In Fig. 3 few examples of light responses in terms of keVee for Iodine recoils of 4 keV( a ) and of 40 keV ( b ) and for Sodium recoils of 4 keV ( c ) and of 40 keV ( d ) are given.In these calculations the quenching factors for Sodium and Iodine recoils in amorphousor out of channel NaI(Tl) are assumed at the mean values given in ref. [29]. Just toemphasise the effect of the channeling, the broadening due to the energy resolution ofthe detector has not been included in this figure. The peaks corresponding to fullychanneled events ( q ∼
1) and to fully quenched events (broadened by the straggling)are well evident; in the middle events, which have been de-channeled at least once, arealso visible.Finally, in Fig. 3 it is possible to note that the number of fully channeled ( q ∼ ∼
25% at 4 keVand ∼
1% at 40 keV for Iodine recoils and ∼
18% at 4 keV and ∼ .
3% at 40 keV forSodium recoils. These behaviours are depicted in Fig. 4.7 R (keV) f r a c t i o n Iodine recoilsSodium recoils -3 -2 -1 Figure 4: Fraction of events with quenching factor ≃
1, that is fully channeled events,as a function of the energy of the recoiling nuclei in NaI(Tl) crystals according to themodeling described in the text.
Let us now analyse the phenomenologies connected both with the data on nuclearrecoils induced by neutron scatterings and with the WIMP (or WIMP-like) directdetection in the light of the presence of the channeling effect.In particular, Fig. 5 shows some examples of neutron calibrations of NaI(Tl) de-tectors at relatively low recoil energy. There the energy responses of the used NaI(Tl)detectors to Sodium recoils of 10 keV [30] and of 50 keV [31] are reported as solidhistograms; the peaks corresponding to the quenched events are well clear. The super-imposed continuous curves have been calculated as those of Fig. 3, obviously broaden-ing them by the energy resolution of the corresponding detector. The fully channeledpeaks ( q ∼ det (keV) C o un t s a) Na Recoil Energy: 10 keV02468101214161820 0 1 2 3 4 5 6 7 8 9 10 E det (keV) C o un t s b) Na Recoil Energy: 50 keV0510152025303540 0 5 10 15 20 25 30 35 40 45 50 Figure 5: Examples of neutron calibrations of NaI(Tl) detectors at low recoil energy.In particular, the energy responses of NaI(Tl) detectors to Sodium recoils of 10 keV(left panel) [30] and of 50 keV (right panel) [31] are shown; the peaks correspondingto the quenched events are well clear. The superimposed continuous curves have beencalculated as those of Fig. 3, obviously broadening them by the energy resolution ofthe corresponding detector. The fully channeled peaks ( q ∼ q ≃
1) are probably lost;iii ) no enhancement can be present in liquid noble gas experiments (DAMA/LXe,WARP, XENON, ...);iv ) no enhancement is possible for bolometer experiments; on the contrary someloss of sensitivity is expected since events (those with q ion ≃
1) are lost byapplying some discrimination procedures, based on q ion << Let us now consider the case of WIMP (or WIMP-like) elastic scattering on targetnuclei. In particular, the expected differential counting rate of recoils induced byWIMP-nucleus elastic scatterings has to be evaluated in given astrophysical, nuclearand particle physics scenarios, also requiring assumptions on all the parameters in-volved in the calculations and the proper consideration of the related uncertainties(for some discussions see e.g. [10, 11, 14, 12, 13]). Hence, the proper accounting for9he channeling effects must be considered as an additional uncertainties in the eval-uation of the expected differential counting rate. The usual hypothesis that just onecomponent of the dark halo can produce elastic scatterings on nuclei will be assumedhere. In addition, the presence of the existing Migdal effect and the possible SagDEGcontribution – we discussed in refs. [13] and [12] respectively – will be not includedhere for simplicity. Thus, for every target specie A , the expected distribution of thedetected energy can be written as a convolution between the light response function, dN A dE det , defined in the previous section, and the differential distribution produced in theWIMP-nucleus elastic scattering: dR ( ch ) A dE det ( E det ) = Z dN A dE det ( E det | E R ) dR A dE R ( E R ) dE R . (10)The differential energy distribution of recoils, as function of the recoil energy E R , is: dR A dE R ( E R ) = N T ρ W m W Z v max v min ( E R ) dσdE R ( v, E R ) vf ( v ) dv . (11)In this formula: i) N T is the number of target nuclei of A specie; ii) ρ W = ξρ , where ρ is the local halo density and ξ ≤ m W is the WIMP mass; iv) f ( v ) is the WIMP velocity ( v ) distribution in the Earthframe; v) v min = q m A · E R m WA ( m A and m W A are the nucleus mass and the reduced massof the WIMP-nucleus system, respectively); vi) v max is the maximal WIMP velocityin the halo evaluated in the Earth frame; vii) dσdE R ( v, E R ) = (cid:16) dσdE R (cid:17) SI + (cid:16) dσdE R (cid:17) SD ,with (cid:16) dσdE R (cid:17) SI spin independent (SI) contribution and (cid:16) dσdE R (cid:17) SD spin dependent (SD)contribution.Finally, the expected differential counting rate as a function of the detected energy, E det , for a real multiple-nuclei detector (as e.g. the NaI(Tl)) when taking into accountthe channeling effect can easily be derived by summing the eq. (10) over the nucleispecies and accounting for the detector energy resolution: dR ( ch ) NaI dE det ( E det ) = Z G ( E det , E ′ ) X A = Na,I dR ( ch ) A dE ′ ( E ′ ) dE ′ . (12)The G ( E det , E ′ ) kernel generally has a gaussian behaviour.Few examples of shapes of expected energy distributions with and without account-ing for the channeling effect, calculated in the modeling given above, are shown in Fig.6. For this template purpose – accounting also for the experimental features of thedetectors [32, 33, 10, 11] – we have just adopted the following additional assumptions(among all the many possibilities): i) WIMP mass of m W = 20 GeV; ii) WIMP withdominant Spin Independent coupling and with nuclear cross sections ∝ A ; iii) point-like SI cross section σ SI = 10 − pb; iv) an halo model NFW (identifier A5 in ref. [34],local velocity v = 220 km/s and halo density at the maximum value 0.74 GeV cm − [34]; v) form factors and quenching factors of Na and
I as in case A of ref. [10].These pictures point out the enhancement of the sensitivity due to the channelingeffect according to the given modeling. 10 det (keVee) S ( c pd / k g / k e V ) -6 -5 -4 -3 -2 -1
110 2 4 6 8 10 12 14 16 18 20 E det (keVee) S m ( c pd / k g / k e V ) -6 -5 -4 -3 -2 -1
110 2 4 6 8 10 12 14 16 18 20
Figure 6: An example of the shapes of the expected energy distributions in NaI(Tl)from Sodium and Iodine recoils induced by WIMP interactions with (continuos line)and without (dashed line) including the channeling effect in the crystal for the scenariogiven in the text. Left panel: behaviour of the unmodulated part of the expected signal, S . Right panel: behaviour of the modulated part of the expected signal, S m . Thevertical lines indicate the energy threshold of the DAMA/NaI experiment. The accounting of the channeling effect in corollary quests for WIMPs as Dark Mattercandidate particles can be investigated by exploiting the expected energy distribution,derived above, to some of the previous analyses on the DAMA/NaI annual modulationdata in terms of WIMP-nucleus elastic scattering. For this purpose, the same scalinglaws and astrophysical, nuclear and particles physics frameworks of refs. [10, 11] areadopted. In addition, as already mentioned, for simplicity just to point out the impactof the channeling effect, the possible SagDEG contribution to the galactic halo andthe presence of the existing Migdal effect – whose effects we discussed in refs. [12] and[13], respectively – will not be included here.The results for each kind of interaction are presented in terms of allowed vol-umes/regions, obtained as superposition of the configurations corresponding to likeli-hood function values distant more than 4 σ from the null hypothesis (absence of mod-ulation) in each one of the several (but still a very limited number) of the consideredmodel frameworks. This allows us to account – at some extent – for at least some of theexisting theoretical and experimental uncertainties (see e.g. in ref. [10, 11, 14, 12, 13]and in the related astrophysics, nuclear and particle physics literature). Here only thelow mass volumes/regions, where the channeling effect is dominant, are depicted.Since the Na and
I are fully sensitive both to SI and to SD interactions, themost general case is defined in a four-dimensional space ( m W , ξσ SI , ξσ SD , θ ), where:i) σ SI is the point-like SI WIMP-nucleon cross section and σ SD is the point-like SDWIMP-nucleon cross section, according to the definitions and scaling laws considered11n ref. [10]; ii) tgθ is the ratio between the effective coupling strengths to neutron andproton for the SD couplings ( θ can vary between 0 and π ) [10]. m W (GeV) xs S I ( pb ) a) -7 -6 -5 -4 -3 -2 -1 Figure 7: An example of the effect of the channeling, modelled as in the text, on aDAMA/NaI allowed region for purely SI coupling WIMPs in the given scenario (seetext). The region encloses configurations corresponding to likelihood function values distant more than 4 σ from the null hypothesis (absence of modulation). This examplehas been evaluated according to the assumptions given in the text. In particular, anhalo model Evans’ logarithmic with R c = 5 kpc (identifier A1 in ref. [34]) has beenconsidered for a v value of 170 km/s and halo density at the corresponding maximumvalue [34]; the form factors parameters and the quenching factors of Na and
I areas in case A of ref. [10]. The solid (dashed) curves delimitate the allowed regions whenthe channeling effect is (not) included. For simplicity just to point out the impact ofthe channeling effect, the possible SagDEG contribution to the galactic halo and thepresence of the existing Migdal effect – whose effects we discussed in refs. [12] and[13], respectively – are not included here. Moreover, the same considerations reportedin ref. [10] still hold.Preliminarily, here to offer an example of the impact of accounting for the channel-ing effect as given in the text, Fig. 7 shows a comparison for allowed slices correspond-ing to purely SI coupled WIMPs in some particular given scenario. This example hasbeen evaluated for an halo model Evans’ logarithmic with R c = 5 kpc (identifier A1 inref. [34]) for a v value of 170 km/s and halo density at the corresponding maximumvalue [34]; the form factors parameters and the quenching factors of Na and
I areas in case A of ref. [10]. The solid (dashed) curves delimitate the allowed regions inthe given scenario when the channeling effect is (not) included. As it can be seen,for WIMP masses in the few-20 GeV region the allowed SI region when including thechanneling effect is lower than one order of magnitude in cross section.The subcase of purely SI coupled WIMPs for the scenarios of ref. [10, 11] is shownin Fig. 8, while in Fig. 9 four slices of the 3-dimensional allowed volume ( m W , ξσ SD , θ ) for the purely SD case are given as example; the low mass region of interest for theeffect is just focused here.Finally, in the general case of mixed SI&SD coupling one gets, as mentioned above,12 W (GeV) xs S I ( pb ) -7 -6 -5 -4 -3 -2 -1 Figure 8: Region allowed in the ( ξσ SI , m W ) plane in the same model frameworks of ref.[10,11] for pure SI coupling; just the low mass part of interest for the channeling effectis focused here. The dotted region is obtained in absence of channeling effect [10,11],while the dashed one is obtained when accounting for it as described in the text. Thedark line marks the overal external contour. It is worth to note that the inclusionof other contributions and/or of other uncertainties on parameters and models, suchas e.g. the possible SagDEG contribution [12] and the Migdal effect [13] or morefavourable form factors, different scaling laws, etc., would further extend the regionand increases the sets of the best fit values. For completeness and more see also [10-14].The same considerations reported in the caption of Fig. 7 hold. -3 -2 -1 -3 -2 -1 -1 m W (GeV) xs S D ( pb ) Q = 0 m W (GeV) xs S D ( pb ) Q = p /4 m W (GeV) xs S D ( pb ) Q = p /2 m W (GeV) xs S D ( pb ) Q = 2.43510 -3 -2 -1 Figure 9: Examples of slices of the 3-dimensional allowed volume ( ξσ SD , m W , θ ) in thesame model frameworks of ref. [10,11] for pure SD coupling; just the low mass partof interest for the channeling effect is focused here. Analogous comments and remarksas those in the captions of Figs. 7 and 8 hold.13 4-dimensional allowed volume ( ξσ SI , ξσ SD , m W , θ ). New allowed volume at the givenC.L. is present in the GeV region when accounting for the channeling effect. Fig.10shows few slices of such a volume as examples. -8 -7 -6 -5 -4 -3 -2 xs S I ( pb ) Q = 0 Q = p /4 Q = p /2 Q = 2.435 -8 -7 -6 -5 -4 -3 -2
10 GeV10 -8 -7 -6 -5 -4 -3 -2 -1 -1 -1 -1
40 GeV xs SD (pb) Figure 10: Examples of slices of the 4-dimensional allowed volume ( ξσ SI , ξσ SD , m W , θ )in the model frameworks considered in ref. [10,11] for mixed SI&SD coupling; just thelow mass part of interest for the channeling effect is focused here. Analogous commentsand remarks as those in the captions of Figs. 7 and 8 hold.Note that general comments, extensions, etc. already discussed in ref. [10, 11, 14,12, 13] still hold. In this paper the channeling effect of recoiling nuclei induced by WIMP and WIMP-like elastic scatterings in NaI(Tl) crystals has been discussed. Its possible effect in areasonably cautious modeling has been presented as applied to some given simplifiedscenarios in corollary quests for the candidate particle for the DAMA/NaI model in-dependent evidence. This further shows the role of the existing uncertainties and ofthe correct description and modeling of all the involved processes as well as their pos-sible impact in the investigation of the candidate particle. Some of them have alreadybeen addressed at some extent, such as the halo modeling [34, 10, 11], the possiblepresence of non-thermalized components in the halo (e.g. caustics [35] or SagDEG[12] contributions), the accounting for the electromagnetic contribution to the WIMP(or WIMP-like) expected energy distribution [13], candidates other than WIMPs (e.g.[14] and in literature), etc.. 14bviously, many other arguments can be addressed as well both on DM candidateparticles and on astrophysical, nuclear and particle physics aspects; for more see [10,11, 14, 12, 13] and in literature. In particular, we remind that different astrophysical,nuclear and particle Physics scenarios as well as the experimental and theoreticalassociated uncertainties leave very large space also e.g. for significantly lower crosssections and larger masses.