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DAEMONS AND DAMA: 
THEIR CELESTIAL-MECHANICS INTERRELATIONS 
Edward M. Drobyshevski
 and Mikhail E. Drobyshevski
) Ioffe Physico-Technical Institute, Russian Academy of Sciences, 194021 St.Petersburg, Russia 
) Astronomical Department, Faculty of Mathematics and Mechanics, St.Petersburg State University, Peterhof, 
198504 St-Petersburg, Russia 
Abstract. The assumption of the capture by the Solar System of the electrically charged 
Planckian DM objects (daemons) from the galactic disk is confirmed by the St.Petersburg 
(SPb) experiments detecting particles with V < 30 km/s. Here the daemon approach is 
analyzed considering the positive model independent result of the DAMA/NaI experiment in 
Gran Sasso. The maximum in DAMA signals observed in the May-June period is explained as  
being associated with the formation behind the Sun of a trail of daemons that the Sun captures 
into elongated orbits as it moves to the apex. The range of significant 2-6-keV DAMA signals 
fits well the iodine nuclei elastically knocked out of the NaI(Tl) scintillator by particles falling 
on the Earth with V = 30-50 km/s from strongly elongated heliocentric orbits. The half-year 
periodicity of the slower daemons observed in SPb originates from the transfer of particles, 
that are deflected through ~90°, into near-Earth orbits each time the particles cross the outer 
reaches of the Sun which had captured them. Their multi-loop (cross-like) trajectories traverse 
many times the Earth’s orbit in March and September, which increases the probability for the 
particles to enter near-Earth orbits during this time. Corroboration of celestial mechanics 
calculations with observations yields ~10
 for the cross section of daemon interaction 
with the solar matter. 
Key words: DM detection; DM in Earth-crossing orbits; celestial mechanics; Planckian 
particles 
I. Introduction. Crisis in the Search for DM Candidates 
The origin of dark matter (DM) has intrigued researches for several decades. It has become 
increasingly clear that these are neither neutrinos with m ≥ 10 eV nor massive compact halo 
objects (MACHOs) (Evans and Belokurov, 2005). In the most recent decade, efforts were 
focused primarily on the search for weakly interacting massive particles (WIMPs) and similar 
objects with a mass of ~10-100 GeV, whose existence is predicted by some theories of 
elementary particles beyond the Standard Model. It was believed self-evident from the very 
beginning that the cross section of their interaction with nucleons, s, should be larger than that 
of their mutual annihilation (~3×10-34 cm2) (Primack et al., 1988). The level reached presently 
is s ~ 10
, but still no reliable and universally accepted results have been reported. 
One cannot avoid the impression that the researchers are pursuing an imaginary but 
nonexisting horizon, in other words, that the WIMPs as they were conceived of originally 
simply do not exist. 
The only data that could possibly be treated as evidence for the existence of WIMPs, 
or more generally a DM particle component in the galactic halo, were obtained by the DAMA 
collaboration in their 7-year-long experiment (Bernabei et al., 2003). The  evidence is a yearly 
modulation of the number of 2-6-keV signals accumulated with ~100 kg of NaI(Tl) 
scintillators. The modulation is ~5% and reaches a maximum some time at the beginning of 
June; it could be attributed to a seasonal variation of a ground-level flux of objects from the 
galactic halo caused by the Earth’s orbit being inclined with respect to the direction of motion 
of the Solar system around the galactic centre (Bernabei et al., 2003). The statistical 
significance of the modulation (6.3σ) is high enough to leave no doubt in its existence. The 
experiments being performed on other installations do not, however, support these results. To 
interpret this situation, the scientists running the DAMA have to consider different types of 
WIMPs and different modes of their interaction with matter. Recall, for instance, the recent 
assumption of a light pseudoscalar and scalar DM candidate of ~keV mass (see Bernabei et 
al., 2006, and refs. herein). Another approach was put forward by Foot (2006). He believes 
that the DAMA signals originate from the Earth crossing a stream of micrometeorites of 
mirror matter. 
The purpose of the present paper is to show that the effects observed by DAMA/NaI, 
including the yearly variation of the signal level, allow an interpretation drawn from the 
St.Petersburg  (SPb) experiments on detection of DArk Electric Matter Objects (daemons), 
which presumably are Planckian elementary black holes carrying a negative electric charge 
(md ≈ 3×10
 g, Ze = -10e) (Drobyshevski, 1997a,b). 
Starting from March 2000, we have been reliably detecting by means of thin spaced 
ZnS(Ag) scintillators, both in ground-level and underground experiments, signals whose 
separation corresponds to ~10-15 km/s, i.e., the velocity of objects falling from near Earth, 
almost circular heliocentric orbits (NEACHOs). The flux is ~10
 and it varies with P 
= 0.5 yr, to pass through maxima in March and September (Drobyshevski, 2005a; 
Drobyshevski and Drobyshevski, 2006; Drobyshevski et al., 2003). (Note, that attempts were 
made to treat these results in terms of possible properties of mirror matter also (Foot and 
Mitra, 2003), but observations of a daemon flux directed upward, i.e., from under the ground 
level, are apparently in conflict with this interpretation.) 
II. Specific Features of the Traversal of the Sun by Daemons 
As the Sun moves through the interstellar medium with a velocity V∞, particles of the latter 
(we assume for the sake of simplicity that their velocity is << V∞) become focused by 
gravitation of the Sun, so that its effective cross section becomes Seff = πpmax
[1+(Vesc/V∞)
] (Eddington, 1926). Here R
 is the radius of the Sun, Vesc = 617.7 km/s is 
the escape velocity from its surface, and pmax is the maximum value of the impact parameter 
(the impact parameter is the distance between the continuation of the V∞ vector and the center 
of the Sun). For V∞ = 20 km/s, pmax = 30.9R
In crossing the Sun with a velocity of ~10
 cm/s, daemons are slowed down. One 
cannot calculate at present the associated decelerating force, because a negative daemon 
captures protons and heavy (Zn > Z) nuclei, catalyzes proton fusion reactions, decomposes 
somehow the nucleons in nuclei etc. As a result, the effective charge of the daemon, complete 
with the particles captured and carried by it, varies continuously. Straightforward estimates 
show, however, that daemons of the galactic disk with a velocity dispersion of ~4-30 km/s 
(Bahcall et al., 1992), are slowed down strongly enough to preclude the escape to infinity of 
many of them as they pass through the Sun (Drobyshevski, 1996, 1997a). 
Such objects move along strongly elongated trajectories with perihelia within the Sun. 
Subsequent crossings of the Sun’s material bring about contraction of the orbits and their 
escape under the Sun’s surface. If, however, a daemon moving on such a trajectory passes 
through the Earth’s gravitational sphere of action, it is deflected, which will result in the 
perihelion of its orbit leaving the Sun with a high probability. The daemon will be injected 
into a stable, strongly elongated Earth crossing heliocentric orbit (SEECHO). Straightforward 
estimates made in the gas kinetic approximation and using the concepts of mean free path 
length etc. suggest that daemons build up on SEECHOs to produce an Earth crossing flux of 
~3×10-7 cm-2s-1 (Drobyshevski, 1997a). (These were fairly optimistic calculations performed  
for a rough estimation of the parameters of the daemon detector that was being designed at 
that time, in 1996.) 
In subsequent inevitable crossings by SEECHO daemons of the Earth’s sphere of 
action, their orbits deform to approach that of the Earth; these are near-Earth almost circular 
heliocentric orbits (NEACHOs). And whereas daemons moving in nearly parabolic 
SEECHOs strike the Earth with velocities of up to V⊕√3 = 51.6 km/s (here V⊕ = 29.79 km/s is 
the orbital velocity of the Earth), the NEACHO objects fall on the Earth with a velocity of 
only ~10(11.2)-15 km/s. 
Estimates of the ground-level SEECHO daemon flux made in 1996 were based on 
simple concepts of an isotropic flux of galactic disk daemons incident on the Sun. Our 
subsequent experiments that demonstrated a half-year variation made it clear that the flux is 
not isotropic, probably because of the motion of the Solar system relative to the DM 
population of the disk. We know now also that the daemons detected by us fall, judging from 
their velocity, from NEACHOs (Drobyshevski, 2005b; Drobyshevski et al., 2003). 
III. Calculation of the Passage of Daemons through the Sun 
It appears only natural to assume the flux variations with P = 0.5 yr to be a consequence of 
the composition of the Earth’s orbital motion around the Sun and of the Sun itself relative to 
the galactic disk population. 
The Sun moves relative to the nearest star population with a velocity of 19.7 km/s in 
the direction of the apex with the coordinates A = 271° and D = +30° (equatorial coordinates) 
or L” = 57° and B” = +22° (galactic coordinates) (Allen, 1973). 
Initially, rather than delving into the fundamental essence of the processes underlying 
the celestial mechanics, we invoked a simplified concept of a “shadow”, which is produced by 
daemons captured into SEECHOs from the galactic disk by the moving Sun, and of the 
corresponding “antishadow” created by some daemons crossing the Sun in the opposite 
direction (i.e., in the direction of its motion), an approach that had been reflected in our earlier 
publications (Drobyshevski, 2004; Drobyshevski et al., 2003). 
In a new approach to calculation of the passage of objects through the Sun we made 
use of the celestial mechanics integrator of Everhart (1974). It was adapted to FORTRAN by 
S.Tarasevich (Institute of Theoretical Astronomy of RAS) for use with the BESM-6 
computer. In ITA (and now in the Institute of Applied Astronomy of RAS) it was employed in 
calculation of asteroid ephemeredes and precise prediction of the apparition of comets 
allowing for the action of known planets. We made two important refinements on the code, 
more specifically, we (i) introduced the resistance of the medium in the simplest gas dynamics 
form, F = σρV2 (Drobyshevski, 1996) (where σ is the effective cross section of a particle, and 
ρ is the medium density) and (ii) took into account that the Sun is not a point object but has 
instead a density distributed over the volume (we used the model of the Sun from Allen 
(1973)). 
The very first calculations revealed that the trajectories of particles falling on the Sun 
and crossing it have a non-closed, many-loop pattern (Drobyshevski, 2005b). This should 
certainly have been expected, because inside the Sun particles move in a gravitational field 
not of a point but rather of a radius-dependent mass, so that the trajectories do not close and 
form instead a rosette, whose petals appear successively in the direction opposite to that of a 
body moving around the Sun (see, e.g., Figs.4 and 5 below). 
This prompted us to consider the possibility of combining and explaining the results of 
DAMA/NaI and of our experiments in terms of a common daemon paradigm, all the more so 
because earlier attempts (Drobyshevski, 2005a) had succeeded in proposing an interpretation 
of the so-called “Troitsk anomaly”, i.e., a displacement of the tritium β-spectrum tail 
occurring with a half-year periodicity. 
This approach: 
a) would hopefully provide an answer as to why the results of the DAMA/NaI are not 
confirmed by other WIMP experiments; 
b) would permit us to understand why the intensity of the scintillation signals assigned to 
recoil nuclei lies in the 2-6-keV interval (here 2 keV is the sensitivity threshold of the 
DAMANaI detector) and not higher, whereas elastic interaction of nuclei with WIMPs 
of the galactic halo (V = 200-300 km/s) should seemingly produce signals with 
energies of up to ~200 keV. 
IV. On How to Corroborate the St.Petersburg and DAMA Experiments 
The first question that comes immediately to mind is how could one explain the twofold 
difference in the signal periodicity between the SPb and DAMA experiments? 
Figure 1. Scheme of motion of the Sun and the Earth towards the apex (see text). 
Let us begin with the SPb experiment. 
Figure 1 shows schematically the motion of the Sun together with the Earth in the 
direction of the apex. The angle between the plane of the Earth’s orbit, the ecliptic, and the 
apex direction is approximately α0 = 52°-53° (the direction to the apex, just as the velocity V∞, 
depends on the stars (or interstellar gas clouds etc.) one chooses as references (Allen, 1973); 
we assume in what follows α0 = 52° and V∞ = 20 km/s). We assume also the angle between 
the straight line lying in the ecliptic plane and normal to the apex direction and the equinox 
line to be about 10°; as the Earth moves along its orbit, it crosses first this line, and after that, 
the equinox line. This order of crossing fits our measurements of the positions of the maxima 
in the primary daemon flux (Drobyshevski, 2005a; Drobyshevski and Drobyshevski, 2006), 
which occur some time in the first decade of March or September (and incidentally coincides 
with A = 258° for the Solar apex relative the interstellar gas). 
0 10 20 30 40
p0 (R�)
−  σ = 1.00×10
−  σ = 2.58×10
−  σ = 2.58×10
←|α2|
V∞ = 20 km/s
Figure 2. Angle of deviation for an object having passed through the Sun depending on the impact 
parameter p0 at different cross-sections σ of its interaction with matter (at the object mass 3×10
 g). α1 
is the angle of deviation from the initial velocity V∞ direction after the first passage through the Sun;  
α2 is the angle of deviation from the same direction after the second passage. 
Figure 2 plots the angle of deviation α1 of a material particle from the direction of its 
initial velocity V∞ after emergence from the Sun again to infinity or to the aphelion of the first 
loop (i.e. at R1) of its trajectory vs. the impact parameter p0 (the dependence of R1 on the 
impact parameter p0 is given in Fig.3). We consider subsequently only cases with p0 < pmax. 
Interestingly, in the case of multi-loop trajectories, which is possible for σ ≠ 0, angular 
deflections of subsequent from preceding loops differ little from α1, although they gradually 
decrease. The value of σ can be estimated from a comparison of further calculations with 
experiment. 
Straightforward reasoning suggests that the two maxima observed in March and 
September should be a consequence of passage through the Earth’s orbit of daemons with an 
impact parameter about p0 = ±9.162R
, where they are deflected by the Sun through α1 ≈ 90
0 4 8 12 16
p0 (R�)
−  σ = 1.00×10
−  σ = 3.00×10
(a.u.)
V∞ = 20 km/s
Figure 3. Maximum distance R1 the object reaches after the first passage through the Sun versus σ and 
Figure 4. An example of multi-loop (cross-like) trajectory of an object being braked by the Solar 
matter (the Sun's center is at X = 0, Y = 0) for repeated passages through the Sun's body.  Object of 
3×10-5 g mass and cross-section σ = 0.79×10-19 cm2 falls from infinity (X = -∞; V∞ = 20 km/s) with an 
impact parameter p0 = Y(-∞) = 9.162R
. The figure plane contains the direction to the apex and the 
normal to it lying in the plane of the ecliptic. The figure shows also an ellipse with the major semi-axis 
of 1 AU, i.e., the projection of the Earth’s orbit (the dotted circle of 1 AU radius is given as a scale for 
the reader’s orientation).  
to either side. Moreover, the presence of these maxima suggests also that they originate from 
the daemons that had already been captured by the Sun for σ ≥ 0.78×10-19 cm2 but return 
repeatedly to it and cross its body. Figure 4 (with a table) provides an idea of such trajectories. 
A particle moves along a trajectory making a right cross. First, in traversing the Sun, it 
is deflected through 90° and, in crossing the Earth’s orbit, escapes with σ = 0.78×10-19 cm2 to 
R1 → ∞ (calculations for Fig.4 are made for σ = 0.79×10
to avoid calculations with too 
great a value of R1). Thereafter, returning, now from outside, it crosses for the second time the 
Earth’s orbit and, hitting the Sun on completion of the first loop, it again deflected, leaving it 
through nearly the right angle. Now the daemon moves along the petal oriented in the anti-
apex direction. But here, although R2 > 1 AU, it does not cross the Earth’s orbit because of the 
large inclination of the ecliptic. The subsequent two crossings of the Earth’s orbit (here still 
R3 > 1 AU) from the side opposite to that of the first transit, are completed by the daemon 
after the return and the third crossing of the Sun. In making the fourth passage through the 
Sun after the return, the particle moves toward the apex. Here, depending on the value of σ 
and completing the cross, the daemon can move away from the Sun to a distance R4 > 1 AU 
(but here again, because of the inclination of the ecliptic to the apex direction, it does not 
cross the Earth’s orbit), but may not reach R4 = 1 AU at all. The first value of R4 > 1 AU 
corresponds to σ1 = 0.78×10
 at which the resistance of the solar material in the first 
passage was just high enough to absorb the excess energy ∆E = mdV∞
/2, i.e., the particle was 
captured by the Sun. The second (upper) value σ3 = 1.415×10
 (for the minimum value 
R3 = 1 AU) can be estimated under the assumption that on its third passage the daemon can 
finally reach and crosses slightly the Earth’s orbit (i.e., R3 > 1 AU). The validity of the latter 
assumption is argued for at least by our observation in autumn and spring of two distinct 
maxima; the fourfold (or even six-fold - see below) crossing by daemons of the Earth’s orbit 
increases, accordingly, the probability of their transfer from the loop trajectories into 
SEECHOs and, subsequently, in NEACHOs, whence they fall on the Earth with V ≈ 10-15 
km/s. Thus, we arrive at 0.78×10-19 ≤ σ < 1.415×10-19 cm2 (we point out once more that the 
values of σ thus found depend on the accepted daemon mass; they should be proportional to 
md). For σ = σ3, the Sun does not capture the daemon at p0 > 12.01R
, i.e., when the daemon 
initially passes through more rarefied outer layers of the Sun it moves to infinity again. 
To choose a still more optimistic scenario, assume a daemon that for σ1 = 
0.78(0.79)×10-19 cm2 crosses the Earth’s orbit in the fifth loop as well (with R5 = 1.0919 > 1 
AU). The condition R5 = 1 AU yields σ5 = 0.849 ×10
. With σ1 < σ < σ5, the daemon 
has now crossed the Earth’s orbit six times! In this respect, Jupiter is markedly behind the 
Earth (with only two crossings), while Venus is on the winning side (8 crossings). 
Figure 3 presenting the R1(p0) relation in a graphic form for σ = 1×10
 and 3×10-19 
 facilitates estimation of the energy losses suffered by the daemon in traversing the Sun, 
of the number of such traversals etc. 
Turning now back to the DAMA/NaI experiment, the daemon can obviously cross the 
set-up in June provided it falls after the first traversal of the Sun in the plane of the ecliptic, 
i.e., if it is deflected through α1 = 52°, which occurs at p0 = 4.90R
. The above estimates of σ 
suggest (see Fig. 5a) that R1 > 1 AU, and that the second loop extends up to R2 > 1 AU also, 
while naturally not crossing the Earth’s orbit, because it leaves the ecliptic plane. In June, the 
second loops of the trajectories with p0 = -6.26R
 enter the plane of the ecliptic as well and 
extend in it up to R2 ≈ 2 > 1AU (Figs.5c,d). In December, the second loops of trajectories with 
p0 = 2.215R
 enter the ecliptic plane (Fig.5b). At σ = σ5 = 0.849×10
 they have R2 = 
1.14 AU, i.e. they are able to cause SEECHOs in December, and only at σ ≥ 0.94×10-19 cm2 
R2 becomes ≤ 1 AU. 
Fig. 5. The same as Fig.4, but here the Earth's orbit is projected into the figure plane as a straight line 
segment of 2 AU length with 52° inclination to the apex direction (December is up-left, June is down-
right). 
Thus the calculations performed for σ = σ1 = 0.78×10
, σ = σ5 = 0.849×10
, σ = 1×10-19 cm2, and σ = σ3 = 1.415×10
 suggest that the daemons captured in 
traversing the Sun produce behind it a fairly smeared trail (“shadow”) through which the 
Earth passes in May-June-July, but which, generally speaking, does not reach the part of the 
Earth’s orbit oriented in the direction of the apex and corresponding approximately to the 
November-January period. This is easy to understand, because the second loops of the 
trajectories which fall into the apex hemisphere and could produce an “antishadow” 
correspond to small p0, i.e., to particles passing through the dense central part of the Sun, 
where they suffer the strongest deceleration. This is why, in particular, the second loop of the 
trajectory of the daemon that crossed the Sun at p0 = 2.215R
 and fell into the ecliptic plane 
exactly in December, simply cannot reach the Earth for σ ≥ 1×10-19 cm2 (Fig.5b).  It is thus 
clear that the ground level flux of daemons from SEECHOs should exhibit a distinct 1-year 
periodicity with a minimum some time in December.  
Superimposed on this is the half-year wave of the NEACHO objects, which appear as 
a result of having transferred from numerous SEECHOs just in periods before the equinoxes 
(note these SEECHOs are realizing at both signs of p0 = ±9.162R
). Such transitions are more 
probable in March and September because of the appearance of a noticeably larger number of 
objects in SEECHOs with comparatively short semimajor axes lying close to these ecliptic 
plane zones. The daemons entering these SEECHOs come from the cross-shaped rosette 
trajectories, along which the same object crosses the Earth’s orbit twice (or even thrice) back 
and forth, the second (and all the more so, the third) time doing it with a noticeably below the 
parabolic velocity. Significantly, the projection of the SEECHO object velocity vector on the 
Earth’s orbit reaches its maximum values here, with the correspondingly increasing duration 
(and efficiency) of the Earth’s gravitational perturbations. Note also that the ratio of the minor 
to major semi-axes for the SEECHOs produced in the capture of objects that had crossed the 
outer zones of the Sun (p0 ≈ 10R
) exceeds those for the objects with p0 → 0 (compare Figs.4 
and 5), which, on the whole, also acts so as to increase the velocity vector projection on the 
Earth’s orbit. 
V. The Manifestation of Daemons in the SPb and DAMA/NaI Detectors 
Our SPb detector, made up of thin spaced ZnS(Ag) scintillators, was sensitive to the passage 
of only fairly low-velocity (<30 km/s) daemons. The reason for this, we believe presently, is  
that successive “disintegrations” of daemon-containing nucleons in the Zn (or Fe) nucleus 
captured by the daemon occur with an interval of ~10
 s, whereas the characteristic 
dimension of the set-up is ~20-30 cm. At higher velocities, the complex consisting of the 
captured nucleus (and, possibly, a cluster of atoms) and the daemon traverses the system 
carrying an excessive positive charge, which is readily compensated by electrons captured on 
the way, and, therefore, the daemon does not interact with new nuclei with an attendant 
generation of a noticeable secondary signal. 
The DAMA/NaI experiment with a ~100 kg NaI(Tl) scintillators was designed for 
measurement of the annual modulation signature. In case of WIMPs the measured quantity is 
the energy of the recoil nuclei knocked out by heavy (~10-100 GeV) WIMPs of the galactic 
halo. The set-up is thought to be sensitive to interactions occurring both with I and Na.  
Note that the sensitivity threshold of the system, ~2 keV, corresponds to the velocity 
of an iodine nucleus of 55 km/s if one takes the quenching factor to be about unity (the 
quenching factor is a ratio of efficiencies of producing scintillations by particles under 
consideration and electrons of the same energy). Assuming elastic interaction with a very 
massive particle, the latter, to produce a 2-keV signal, should move with a velocity of ~30 
km/s (in an elastic head-on collision, the velocity of the light particle, a nucleus, should be 
twice that of the heavy projectile particle). If the signals are due to WIMPs of the galactic 
halo (V∞ = 200-300 km/s), the recoil energy of the iodine nucleus could, seemingly, reach as 
high as 110-240 keV. 
Information on the yearly variation of the flux of particles traversing the DAMA/NaI 
is provided primarily by signals in the 2-6-keV range (Bernabei et al., 2003, 2006). The 6-
keV signal corresponds to the velocity of an elastically colliding projectile of ~ 47 km/s. This 
figure is in good agreement with the velocity of 51.6 km/s with which a particle in a quasi-
parabolic orbit hits the Earth (29.78√3 = 51.6 km/s; this velocity would produce a recoil 
nucleus with an energy of 7 keV, but allowing for the statistics of other than head-on 
collisions we would obtain 5-6 keV). But it is with these velocities (when particle energies 
differ exactly by a factor of three; compare, on the other hand, the 6 and 2 keV which one 
measures!) that SEECHO daemons fall on the Earth. A truly remarkable coincidence indeed. 
A number of additional questions, however, immediately arise here, to which one 
cannot yet supply unambiguous answers.  
Indeed, estimates of the velocity with which daemons escape from geocentric Earth-
crossing orbits (GESCO) into the Earth suggest that the resistance offered by a metal-like 
solid to a daemon moving with a velocity of ~10 km/s is ~10
 dyne (Drobyshevski, 2004), 
which entails a release of thermal energy of ~6 MeV/cm. It is unclear what energy would be 
liberated in a dielectric (without conductive electrons) scintillator. If it is heat, the scintillator 
will not detect it. (On the other hand, it is too high for the cryogenic systems of the type 
CDMS-I and Edelweiss-I designed for the detection of WIMPs either; see refs. in Bernabei et 
al. (2003).)  
The situation is not yet clear with regard to the quenching factor, which we considered 
above to be about unity for the low-energy iodine nuclei. Neutron elastic scattering 
experiments give a value of about 0.09 for I and 0.30 for Na (see Bernabei et al., 2003, and 
refs. therein). We will not give details of such calibrations, nor discuss the different 
possibilities here (see, however, arXiv:0706.3095). 
Also, one should not forget that the DAMA/NaI system, by the multiple hit rejection 
criterion by Bernabei et al. (2003, see Sec.3.3), rejects events with signals appearing 
simultaneously in two or more scintillators (nine scintillators altogether). But then how (and 
with what efficiency) do recoil nuclei form in one detector piece only? 
One may recall that immediately after leaving a solid, the daemon moves in vacuum 
(or in air) together with a cluster of atoms, in one of whose nuclei it resides (Drobyshevski, 
2005a). When it enters a solid object again, the daemon leaves a larger part of this cluster 
close to the surface of the object, and moves inside it only with a small part of the cluster, or 
even only with the remainder of the nucleus in which it rests. It is unclear how efficiently 
such a complex can initiate scintillations. It is conceivable that as long as it carries an excess 
positive charge, it is surrounded by electrons, and, in moving as a conventional heavy atom 
(or ion with Zi = 1) with a relatively low velocity (<50 km/s; recall that this corresponds to 
less than ~2 keV energy of an iodine nucleus), but in a rectilinear trajectory and without 
noticeable deceleration, through the dielectric and only moving atoms apart rather than 
penetrating into them, it will excite only phonons but not scintillations. The daemon resides in 
this state for tens of microseconds, “digesting” gradually the nucleons of the nucleus it is 
carrying and traveling tens of cm in this time. (We are not discussing here the points bearing 
on possible modes of “digestion” by the daemon, an elementary black hole, of nucleons that 
could leave no trace in a scintillation detector.) Eventually, however, the daemon/nuclear-
remainder complex acquires zero charge to become a particle of the neutron type. This state 
lasts until the next proton in the nucleus disintegrates and the system then acquires a negative 
charge, ~10
 s (with the distance traveled ~5 cm). It is in this state that this neutral (but 
supermassive, ~3×10-5 g) complex, 1-3 fermi in size, passes through electronic shells of atoms 
and is capable, in a path length of ~5 cm, to produce a recoil nucleus with a double velocity of 
up to ~100 km/s. It is such SEECHO-daemon-caused events that satisfy the multiple hit 
rejection criterion (Bernabei et al., 2003) that are possibly detected by the DAMA/NaI. The 
processes involved here certainly need a deeper analysis. 
VI. Conclusions 
The daemon approach had offered an explanation for the ~5-eV drift of the tritium β-spectrum 
tail with a half-year period, the so-called “Troitsk anomaly”, and some predictions regarding 
the KATRIN experiment on direct measurement of the neutrino mass (Drobyshevski, 2005a). 
It now appears that one can corroborate within the daemon paradigm the results of the 
DAMA/NaI experiment with the inferences drawn from the SPb study, which, in addition to 
detecting daemon populations of different velocities captured by the Solar system and moving 
within it in orbits of different, including geocentric, populations, established also a half-year 
variation in the NEACHO flux, demonstrating the advantages of vacuum systems in daemon 
detection, and revealing some of their remarkable properties and specific features of their 
interaction with matter. 
We find it particularly impressive that the range (2-6 keV) of the recorded signals in 
which the DAMA/NaI exhibits a yearly periodicity coincides with exactly the same level (2-7 
keV) that follows from the celestial mechanics scenario. On the other hand, a more careful 
analysis of the evolution of daemons captured by the Sun from the galactic disk and governed 
by celestial mechanics sheds light on reasons underlying the detection of the yearly 
periodicity of the high-velocity population (30-50 km/s) measured by DAMA, and of the half-
year periodicity of the low-velocity population (5-10-30 km/s) in the SPb experiment (in the 
latter case, the part played by the cross-like multi-loop trajectories of daemons traversing the 
Sun and captured by it appears significant). If performed with good statistics, the more 
advanced measurements on DAMA/LIBRA will hopefully also reveal the half-year harmonic 
in low signal level events (~2-3 keV). Such events originate from the fall of daemons from 
“short” SEECHOs in March and September. 
An analysis of the conditions favouring capture of daemons by the Sun and 
corroboration of their subsequent possible celestial mechanics evolution with the results 
gained in the SPb and DAMA/NaI experiments permits one to impose fairly strong constraints 
(one would almost say, to measure) on the effective cross section σ of daemon interaction 
with the Solar material. It was found to be 0.78×10-19 ≤ σ < 1.4×10-19 cm2. This is ~500 times 
the cross section of the neutral “antineon” atom formed by a daemon (Ze = -10e) and ten 
protons it captured, while being 3000-5000 times smaller than the cross section for a 
daemon/heavy-nucleus complex with electrons surrounding it. On the other hand, σ can be 
governed also by the Coulomb interaction of the daemon changing continuously its effective 
charge with particles of the solar plasma (Drobyshevski, 1996), which, in turn, may be helpful 
in refining our knowledge of the characteristics of the solar material. 
Obviously enough, the problems addressed in the paper (interaction of daemons both 
with the solar matter and with the scintillator material, the celestial mechanics and statistical 
evolution of their ensemble after capture by the Solar system, the part played by the initial 
conditions and the starting velocity dispersion in the daemon population of the galactic disk, 
refinement of the apex relative to this population, - it seems it is closer to the apex relative the 
interstellar gas, not stars (see. Fig.1), transfer to SEECHOs and, subsequently, to NEACHOs 
and GESCOs etc.) would require a much more careful and comprehensive analysis. This 
would permit a quantitative comparison of theoretical predictions with future experimental 
results.  
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  The assumption of the capture by the Solar System of the electrically charged
Planckian DM objects (daemons) from the galactic disk is confirmed not only by
the St.Petersburg (SPb) experiments detecting particles with V<30 km/s. Here
the daemon approach is analyzed considering the positive model independent
result of the DAMA/NaI experiment. We explain the maximum in DAMA signals
observed in the May-June period to be associated with the formation behind the
Sun of a trail of daemons that the Sun captures into elongated orbits as it
moves to the apex. The range of significant 2-6-keV DAMA signals fits well the
iodine nuclei elastically knocked out of the NaI(Tl) scintillator by particles
falling on the Earth with V=30-50 km/s from strongly elongated heliocentric
orbits. The half-year periodicity of the slower daemons observed in SPb
originates from the transfer of particles that are deflected through ~90 deg
into near-Earth orbits each time the particles cross the outer reaches of the
Sun which had captured them. Their multi-loop (cross-like) trajectories
traverse many times the Earth's orbit in March and September, which increases
the probability for the particles to enter near-Earth orbits during this time.
Corroboration of celestial mechanics calculations with observations yields
~1e-19 cm2 for the cross section of daemon interaction with the solar matter.

Introduction. Crisis in the Search for DM Candidates 
The origin of dark matter (DM) has intrigued researches for several decades. It has become 
increasingly clear that these are neither neutrinos with m ≥ 10 eV nor massive compact halo 
objects (MACHOs) (Evans and Belokurov, 2005). In the most recent decade, efforts were 
focused primarily on the search for weakly interacting massive particles (WIMPs) and similar 
objects with a mass of ~10-100 GeV, whose existence is predicted by some theories of 
elementary particles beyond the Standard Model. It was believed self-evident from the very 
beginning that the cross section of their interaction with nucleons, s, should be larger than that 
of their mutual annihilation (~3×10-34 cm2) (Primack et al., 1988). The level reached presently 
is s ~ 10
, but still no reliable and universally accepted results have been reported. 
One cannot avoid the impression that the researchers are pursuing an imaginary but 
nonexisting horizon, in other words, that the WIMPs as they were conceived of originally 
simply do not exist. 
The only data that could possibly be treated as evidence for the existence of WIMPs, 
or more generally a DM particle component in the galactic halo, were obtained by the DAMA 
collaboration in their 7-year-long experiment (Bernabei et al., 2003). The  evidence is a yearly 
modulation of the number of 2-6-keV signals accumulated with ~100 kg of NaI(Tl) 
scintillators. The modulation is ~5% and reaches a maximum some time at the beginning of 
June; it could be attributed to a seasonal variation of a ground-level flux of objects from the 
galactic halo caused by the Earth’s orbit being inclined with respect to the direction of motion 
of the Solar system around the galactic centre (Bernabei et al., 2003). The statistical 
significance of the modulation (6.3σ) is high enough to leave no doubt in its existence. The 
experiments being performed on other installations do not, however, support these results. To 
interpret this situation, the scientists running the DAMA have to consider different types of 
WIMPs and different modes of their interaction with matter. Recall, for instance, the recent 
assumption of a light pseudoscalar and scalar DM candidate of ~keV mass (see Bernabei et 
al., 2006, and refs. herein). Another approach was put forward by Foot (2006). He believes 
that the DAMA signals originate from the Earth crossing a stream of micrometeorites of 
mirror matter. 
The purpose of the present paper is to show that the effects observed by DAMA/NaI, 
including the yearly variation of the signal level, allow an interpretation drawn from the 
St.Petersburg  (SPb) experiments on detection of DArk Electric Matter Objects (daemons), 
which presumably are Planckian elementary black holes carrying a negative electric charge 
(md ≈ 3×10
 g, Ze = -10e) (Drobyshevski, 1997a,b). 
Starting from March 2000, we have been reliably detecting by means of thin spaced 
ZnS(Ag) scintillators, both in ground-level and underground experiments, signals whose 
separation corresponds to ~10-15 km/s, i.e., the velocity of objects falling from near Earth, 
almost circular heliocentric orbits (NEACHOs). The flux is ~10
 and it varies with P 
= 0.5 yr, to pass through maxima in March and September (Drobyshevski, 2005a; 
Drobyshevski and Drobyshevski, 2006; Drobyshevski et al., 2003). (Note, that attempts were 
made to treat these results in terms of possible properties of mirror matter also (Foot and 
Mitra, 2003), but observations of a daemon flux directed upward, i.e., from under the ground 
level, are apparently in conflict with this interpretation.) 
II. Specific Features of the Traversal of the Sun by Daemons 
As the Sun moves through the interstellar medium with a velocity V∞, particles of the latter 
(we assume for the sake of simplicity that their velocity is << V∞) become focused by 
gravitation of the Sun, so that its effective cross section becomes Seff = πpmax
[1+(Vesc/V∞)
] (Eddington, 1926). Here R
 is the radius of the Sun, Vesc = 617.7 km/s is 
the escape velocity from its surface, and pmax is the maximum value of the impact parameter 
(the impact parameter is the distance between the continuation of the V∞ vector and the center 
of the Sun). For V∞ = 20 km/s, pmax = 30.9R
In crossing the Sun with a velocity of ~10
 cm/s, daemons are slowed down. One 
cannot calculate at present the associated decelerating force, because a negative daemon 
captures protons and heavy (Zn > Z) nuclei, catalyzes proton fusion reactions, decomposes 
somehow the nucleons in nuclei etc. As a result, the effective charge of the daemon, complete 
with the particles captured and carried by it, varies continuously. Straightforward estimates 
show, however, that daemons of the galactic disk with a velocity dispersion of ~4-30 km/s 
(Bahcall et al., 1992), are slowed down strongly enough to preclude the escape to infinity of 
many of them as they pass through the Sun (Drobyshevski, 1996, 1997a). 
Such objects move along strongly elongated trajectories with perihelia within the Sun. 
Subsequent crossings of the Sun’s material bring about contraction of the orbits and their 
escape under the Sun’s surface. If, however, a daemon moving on such a trajectory passes 
through the Earth’s gravitational sphere of action, it is deflected, which will result in the 
perihelion of its orbit leaving the Sun with a high probability. The daemon will be injected 
into a stable, strongly elongated Earth crossing heliocentric orbit (SEECHO). Straightforward 
estimates made in the gas kinetic approximation and using the concepts of mean free path 
length etc. suggest that daemons build up on SEECHOs to produce an Earth crossing flux of 
~3×10-7 cm-2s-1 (Drobyshevski, 1997a). (These were fairly optimistic calculations performed  
for a rough estimation of the parameters of the daemon detector that was being designed at 
that time, in 1996.) 
In subsequent inevitable crossings by SEECHO daemons of the Earth’s sphere of 
action, their orbits deform to approach that of the Earth; these are near-Earth almost circular 
heliocentric orbits (NEACHOs). And whereas daemons moving in nearly parabolic 
SEECHOs strike the Earth with velocities of up to V⊕√3 = 51.6 km/s (here V⊕ = 29.79 km/s is 
the orbital velocity of the Earth), the NEACHO objects fall on the Earth with a velocity of 
only ~10(11.2)-15 km/s. 
Estimates of the ground-level SEECHO daemon flux made in 1996 were based on 
simple concepts of an isotropic flux of galactic disk daemons incident on the Sun. Our 
subsequent experiments that demonstrated a half-year variation made it clear that the flux is 
not isotropic, probably because of the motion of the Solar system relative to the DM 
population of the disk. We know now also that the daemons detected by us fall, judging from 
their velocity, from NEACHOs (Drobyshevski, 2005b; Drobyshevski et al., 2003). 
III. Calculation of the Passage of Daemons through the Sun 
It appears only natural to assume the flux variations with P = 0.5 yr to be a consequence of 
the composition of the Earth’s orbital motion around the Sun and of the Sun itself relative to 
the galactic disk population. 
The Sun moves relative to the nearest star population with a velocity of 19.7 km/s in 
the direction of the apex with the coordinates A = 271° and D = +30° (equatorial coordinates) 
or L” = 57° and B” = +22° (galactic coordinates) (Allen, 1973). 
Initially, rather than delving into the fundamental essence of the processes underlying 
the celestial mechanics, we invoked a simplified concept of a “shadow”, which is produced by 
daemons captured into SEECHOs from the galactic disk by the moving Sun, and of the 
corresponding “antishadow” created by some daemons crossing the Sun in the opposite 
direction (i.e., in the direction of its motion), an approach that had been reflected in our earlier 
publications (Drobyshevski, 2004; Drobyshevski et al., 2003). 
In a new approach to calculation of the passage of objects through the Sun we made 
use of the celestial mechanics integrator of Everhart (1974). It was adapted to FORTRAN by 
S.Tarasevich (Institute of Theoretical Astronomy of RAS) for use with the BESM-6 
computer. In ITA (and now in the Institute of Applied Astronomy of RAS) it was employed in 
calculation of asteroid ephemeredes and precise prediction of the apparition of comets 
allowing for the action of known planets. We made two important refinements on the code, 
more specifically, we (i) introduced the resistance of the medium in the simplest gas dynamics 
form, F = σρV2 (Drobyshevski, 1996) (where σ is the effective cross section of a particle, and 
ρ is the medium density) and (ii) took into account that the Sun is not a point object but has 
instead a density distributed over the volume (we used the model of the Sun from Allen 
(1973)). 
The very first calculations revealed that the trajectories of particles falling on the Sun 
and crossing it have a non-closed, many-loop pattern (Drobyshevski, 2005b). This should 
certainly have been expected, because inside the Sun particles move in a gravitational field 
not of a point but rather of a radius-dependent mass, so that the trajectories do not close and 
form instead a rosette, whose petals appear successively in the direction opposite to that of a 
body moving around the Sun (see, e.g., Figs.4 and 5 below). 
This prompted us to consider the possibility of combining and explaining the results of 
DAMA/NaI and of our experiments in terms of a common daemon paradigm, all the more so 
because earlier attempts (Drobyshevski, 2005a) had succeeded in proposing an interpretation 
of the so-called “Troitsk anomaly”, i.e., a displacement of the tritium β-spectrum tail 
occurring with a half-year periodicity. 
This approach: 
a) would hopefully provide an answer as to why the results of the DAMA/NaI are not 
confirmed by other WIMP experiments; 
b) would permit us to understand why the intensity of the scintillation signals assigned to 
recoil nuclei lies in the 2-6-keV interval (here 2 keV is the sensitivity threshold of the 
DAMANaI detector) and not higher, whereas elastic interaction of nuclei with WIMPs 
of the galactic halo (V = 200-300 km/s) should seemingly produce signals with 
energies of up to ~200 keV. 
IV. On How to Corroborate the St.Petersburg and DAMA Experiments 
The first question that comes immediately to mind is how could one explain the twofold 
difference in the signal periodicity between the SPb and DAMA experiments? 
Figure 1. Scheme of motion of the Sun and the Earth towards the apex (see text). 
Let us begin with the SPb experiment. 
Figure 1 shows schematically the motion of the Sun together with the Earth in the 
direction of the apex. The angle between the plane of the Earth’s orbit, the ecliptic, and the 
apex direction is approximately α0 = 52°-53° (the direction to the apex, just as the velocity V∞, 
depends on the stars (or interstellar gas clouds etc.) one chooses as references (Allen, 1973); 
we assume in what follows α0 = 52° and V∞ = 20 km/s). We assume also the angle between 
the straight line lying in the ecliptic plane and normal to the apex direction and the equinox 
line to be about 10°; as the Earth moves along its orbit, it crosses first this line, and after that, 
the equinox line. This order of crossing fits our measurements of the positions of the maxima 
in the primary daemon flux (Drobyshevski, 2005a; Drobyshevski and Drobyshevski, 2006), 
which occur some time in the first decade of March or September (and incidentally coincides 
with A = 258° for the Solar apex relative the interstellar gas). 
0 10 20 30 40
p0 (R�)
−  σ = 1.00×10
−  σ = 2.58×10
−  σ = 2.58×10
←|α2|
V∞ = 20 km/s
Figure 2. Angle of deviation for an object having passed through the Sun depending on the impact 
parameter p0 at different cross-sections σ of its interaction with matter (at the object mass 3×10
 g). α1 
is the angle of deviation from the initial velocity V∞ direction after the first passage through the Sun;  
α2 is the angle of deviation from the same direction after the second passage. 
Figure 2 plots the angle of deviation α1 of a material particle from the direction of its 
initial velocity V∞ after emergence from the Sun again to infinity or to the aphelion of the first 
loop (i.e. at R1) of its trajectory vs. the impact parameter p0 (the dependence of R1 on the 
impact parameter p0 is given in Fig.3). We consider subsequently only cases with p0 < pmax. 
Interestingly, in the case of multi-loop trajectories, which is possible for σ ≠ 0, angular 
deflections of subsequent from preceding loops differ little from α1, although they gradually 
decrease. The value of σ can be estimated from a comparison of further calculations with 
experiment. 
Straightforward reasoning suggests that the two maxima observed in March and 
September should be a consequence of passage through the Earth’s orbit of daemons with an 
impact parameter about p0 = ±9.162R
, where they are deflected by the Sun through α1 ≈ 90
0 4 8 12 16
p0 (R�)
−  σ = 1.00×10
−  σ = 3.00×10
(a.u.)
V∞ = 20 km/s
Figure 3. Maximum distance R1 the object reaches after the first passage through the Sun versus σ and 
Figure 4. An example of multi-loop (cross-like) trajectory of an object being braked by the Solar 
matter (the Sun's center is at X = 0, Y = 0) for repeated passages through the Sun's body.  Object of 
3×10-5 g mass and cross-section σ = 0.79×10-19 cm2 falls from infinity (X = -∞; V∞ = 20 km/s) with an 
impact parameter p0 = Y(-∞) = 9.162R
. The figure plane contains the direction to the apex and the 
normal to it lying in the plane of the ecliptic. The figure shows also an ellipse with the major semi-axis 
of 1 AU, i.e., the projection of the Earth’s orbit (the dotted circle of 1 AU radius is given as a scale for 
the reader’s orientation).  
to either side. Moreover, the presence of these maxima suggests also that they originate from 
the daemons that had already been captured by the Sun for σ ≥ 0.78×10-19 cm2 but return 
repeatedly to it and cross its body. Figure 4 (with a table) provides an idea of such trajectories. 
A particle moves along a trajectory making a right cross. First, in traversing the Sun, it 
is deflected through 90° and, in crossing the Earth’s orbit, escapes with σ = 0.78×10-19 cm2 to 
R1 → ∞ (calculations for Fig.4 are made for σ = 0.79×10
to avoid calculations with too 
great a value of R1). Thereafter, returning, now from outside, it crosses for the second time the 
Earth’s orbit and, hitting the Sun on completion of the first loop, it again deflected, leaving it 
through nearly the right angle. Now the daemon moves along the petal oriented in the anti-
apex direction. But here, although R2 > 1 AU, it does not cross the Earth’s orbit because of the 
large inclination of the ecliptic. The subsequent two crossings of the Earth’s orbit (here still 
R3 > 1 AU) from the side opposite to that of the first transit, are completed by the daemon 
after the return and the third crossing of the Sun. In making the fourth passage through the 
Sun after the return, the particle moves toward the apex. Here, depending on the value of σ 
and completing the cross, the daemon can move away from the Sun to a distance R4 > 1 AU 
(but here again, because of the inclination of the ecliptic to the apex direction, it does not 
cross the Earth’s orbit), but may not reach R4 = 1 AU at all. The first value of R4 > 1 AU 
corresponds to σ1 = 0.78×10
 at which the resistance of the solar material in the first 
passage was just high enough to absorb the excess energy ∆E = mdV∞
/2, i.e., the particle was 
captured by the Sun. The second (upper) value σ3 = 1.415×10
 (for the minimum value 
R3 = 1 AU) can be estimated under the assumption that on its third passage the daemon can 
finally reach and crosses slightly the Earth’s orbit (i.e., R3 > 1 AU). The validity of the latter 
assumption is argued for at least by our observation in autumn and spring of two distinct 
maxima; the fourfold (or even six-fold - see below) crossing by daemons of the Earth’s orbit 
increases, accordingly, the probability of their transfer from the loop trajectories into 
SEECHOs and, subsequently, in NEACHOs, whence they fall on the Earth with V ≈ 10-15 
km/s. Thus, we arrive at 0.78×10-19 ≤ σ < 1.415×10-19 cm2 (we point out once more that the 
values of σ thus found depend on the accepted daemon mass; they should be proportional to 
md). For σ = σ3, the Sun does not capture the daemon at p0 > 12.01R
, i.e., when the daemon 
initially passes through more rarefied outer layers of the Sun it moves to infinity again. 
To choose a still more optimistic scenario, assume a daemon that for σ1 = 
0.78(0.79)×10-19 cm2 crosses the Earth’s orbit in the fifth loop as well (with R5 = 1.0919 > 1 
AU). The condition R5 = 1 AU yields σ5 = 0.849 ×10
. With σ1 < σ < σ5, the daemon 
has now crossed the Earth’s orbit six times! In this respect, Jupiter is markedly behind the 
Earth (with only two crossings), while Venus is on the winning side (8 crossings). 
Figure 3 presenting the R1(p0) relation in a graphic form for σ = 1×10
 and 3×10-19 
 facilitates estimation of the energy losses suffered by the daemon in traversing the Sun, 
of the number of such traversals etc. 
Turning now back to the DAMA/NaI experiment, the daemon can obviously cross the 
set-up in June provided it falls after the first traversal of the Sun in the plane of the ecliptic, 
i.e., if it is deflected through α1 = 52°, which occurs at p0 = 4.90R
. The above estimates of σ 
suggest (see Fig. 5a) that R1 > 1 AU, and that the second loop extends up to R2 > 1 AU also, 
while naturally not crossing the Earth’s orbit, because it leaves the ecliptic plane. In June, the 
second loops of the trajectories with p0 = -6.26R
 enter the plane of the ecliptic as well and 
extend in it up to R2 ≈ 2 > 1AU (Figs.5c,d). In December, the second loops of trajectories with 
p0 = 2.215R
 enter the ecliptic plane (Fig.5b). At σ = σ5 = 0.849×10
 they have R2 = 
1.14 AU, i.e. they are able to cause SEECHOs in December, and only at σ ≥ 0.94×10-19 cm2 
R2 becomes ≤ 1 AU. 
Fig. 5. The same as Fig.4, but here the Earth's orbit is projected into the figure plane as a straight line 
segment of 2 AU length with 52° inclination to the apex direction (December is up-left, June is down-
right). 
Thus the calculations performed for σ = σ1 = 0.78×10
, σ = σ5 = 0.849×10
, σ = 1×10-19 cm2, and σ = σ3 = 1.415×10
 suggest that the daemons captured in 
traversing the Sun produce behind it a fairly smeared trail (“shadow”) through which the 
Earth passes in May-June-July, but which, generally speaking, does not reach the part of the 
Earth’s orbit oriented in the direction of the apex and corresponding approximately to the 
November-January period. This is easy to understand, because the second loops of the 
trajectories which fall into the apex hemisphere and could produce an “antishadow” 
correspond to small p0, i.e., to particles passing through the dense central part of the Sun, 
where they suffer the strongest deceleration. This is why, in particular, the second loop of the 
trajectory of the daemon that crossed the Sun at p0 = 2.215R
 and fell into the ecliptic plane 
exactly in December, simply cannot reach the Earth for σ ≥ 1×10-19 cm2 (Fig.5b).  It is thus 
clear that the ground level flux of daemons from SEECHOs should exhibit a distinct 1-year 
periodicity with a minimum some time in December.  
Superimposed on this is the half-year wave of the NEACHO objects, which appear as 
a result of having transferred from numerous SEECHOs just in periods before the equinoxes 
(note these SEECHOs are realizing at both signs of p0 = ±9.162R
). Such transitions are more 
probable in March and September because of the appearance of a noticeably larger number of 
objects in SEECHOs with comparatively short semimajor axes lying close to these ecliptic 
plane zones. The daemons entering these SEECHOs come from the cross-shaped rosette 
trajectories, along which the same object crosses the Earth’s orbit twice (or even thrice) back 
and forth, the second (and all the more so, the third) time doing it with a noticeably below the 
parabolic velocity. Significantly, the projection of the SEECHO object velocity vector on the 
Earth’s orbit reaches its maximum values here, with the correspondingly increasing duration 
(and efficiency) of the Earth’s gravitational perturbations. Note also that the ratio of the minor 
to major semi-axes for the SEECHOs produced in the capture of objects that had crossed the 
outer zones of the Sun (p0 ≈ 10R
) exceeds those for the objects with p0 → 0 (compare Figs.4 
and 5), which, on the whole, also acts so as to increase the velocity vector projection on the 
Earth’s orbit. 
V. The Manifestation of Daemons in the SPb and DAMA/NaI Detectors 
Our SPb detector, made up of thin spaced ZnS(Ag) scintillators, was sensitive to the passage 
of only fairly low-velocity (<30 km/s) daemons. The reason for this, we believe presently, is  
that successive “disintegrations” of daemon-containing nucleons in the Zn (or Fe) nucleus 
captured by the daemon occur with an interval of ~10
 s, whereas the characteristic 
dimension of the set-up is ~20-30 cm. At higher velocities, the complex consisting of the 
captured nucleus (and, possibly, a cluster of atoms) and the daemon traverses the system 
carrying an excessive positive charge, which is readily compensated by electrons captured on 
the way, and, therefore, the daemon does not interact with new nuclei with an attendant 
generation of a noticeable secondary signal. 
The DAMA/NaI experiment with a ~100 kg NaI(Tl) scintillators was designed for 
measurement of the annual modulation signature. In case of WIMPs the measured quantity is 
the energy of the recoil nuclei knocked out by heavy (~10-100 GeV) WIMPs of the galactic 
halo. The set-up is thought to be sensitive to interactions occurring both with I and Na.  
Note that the sensitivity threshold of the system, ~2 keV, corresponds to the velocity 
of an iodine nucleus of 55 km/s if one takes the quenching factor to be about unity (the 
quenching factor is a ratio of efficiencies of producing scintillations by particles under 
consideration and electrons of the same energy). Assuming elastic interaction with a very 
massive particle, the latter, to produce a 2-keV signal, should move with a velocity of ~30 
km/s (in an elastic head-on collision, the velocity of the light particle, a nucleus, should be 
twice that of the heavy projectile particle). If the signals are due to WIMPs of the galactic 
halo (V∞ = 200-300 km/s), the recoil energy of the iodine nucleus could, seemingly, reach as 
high as 110-240 keV. 
Information on the yearly variation of the flux of particles traversing the DAMA/NaI 
is provided primarily by signals in the 2-6-keV range (Bernabei et al., 2003, 2006). The 6-
keV signal corresponds to the velocity of an elastically colliding projectile of ~ 47 km/s. This 
figure is in good agreement with the velocity of 51.6 km/s with which a particle in a quasi-
parabolic orbit hits the Earth (29.78√3 = 51.6 km/s; this velocity would produce a recoil 
nucleus with an energy of 7 keV, but allowing for the statistics of other than head-on 
collisions we would obtain 5-6 keV). But it is with these velocities (when particle energies 
differ exactly by a factor of three; compare, on the other hand, the 6 and 2 keV which one 
measures!) that SEECHO daemons fall on the Earth. A truly remarkable coincidence indeed. 
A number of additional questions, however, immediately arise here, to which one 
cannot yet supply unambiguous answers.  
Indeed, estimates of the velocity with which daemons escape from geocentric Earth-
crossing orbits (GESCO) into the Earth suggest that the resistance offered by a metal-like 
solid to a daemon moving with a velocity of ~10 km/s is ~10
 dyne (Drobyshevski, 2004), 
which entails a release of thermal energy of ~6 MeV/cm. It is unclear what energy would be 
liberated in a dielectric (without conductive electrons) scintillator. If it is heat, the scintillator 
will not detect it. (On the other hand, it is too high for the cryogenic systems of the type 
CDMS-I and Edelweiss-I designed for the detection of WIMPs either; see refs. in Bernabei et 
al. (2003).)  
The situation is not yet clear with regard to the quenching factor, which we considered 
above to be about unity for the low-energy iodine nuclei. Neutron elastic scattering 
experiments give a value of about 0.09 for I and 0.30 for Na (see Bernabei et al., 2003, and 
refs. therein). We will not give details of such calibrations, nor discuss the different 
possibilities here (see, however, arXiv:0706.3095). 
Also, one should not forget that the DAMA/NaI system, by the multiple hit rejection 
criterion by Bernabei et al. (2003, see Sec.3.3), rejects events with signals appearing 
simultaneously in two or more scintillators (nine scintillators altogether). But then how (and 
with what efficiency) do recoil nuclei form in one detector piece only? 
One may recall that immediately after leaving a solid, the daemon moves in vacuum 
(or in air) together with a cluster of atoms, in one of whose nuclei it resides (Drobyshevski, 
2005a). When it enters a solid object again, the daemon leaves a larger part of this cluster 
close to the surface of the object, and moves inside it only with a small part of the cluster, or 
even only with the remainder of the nucleus in which it rests. It is unclear how efficiently 
such a complex can initiate scintillations. It is conceivable that as long as it carries an excess 
positive charge, it is surrounded by electrons, and, in moving as a conventional heavy atom 
(or ion with Zi = 1) with a relatively low velocity (<50 km/s; recall that this corresponds to 
less than ~2 keV energy of an iodine nucleus), but in a rectilinear trajectory and without 
noticeable deceleration, through the dielectric and only moving atoms apart rather than 
penetrating into them, it will excite only phonons but not scintillations. The daemon resides in 
this state for tens of microseconds, “digesting” gradually the nucleons of the nucleus it is 
carrying and traveling tens of cm in this time. (We are not discussing here the points bearing 
on possible modes of “digestion” by the daemon, an elementary black hole, of nucleons that 
could leave no trace in a scintillation detector.) Eventually, however, the daemon/nuclear-
remainder complex acquires zero charge to become a particle of the neutron type. This state 
lasts until the next proton in the nucleus disintegrates and the system then acquires a negative 
charge, ~10
 s (with the distance traveled ~5 cm). It is in this state that this neutral (but 
supermassive, ~3×10-5 g) complex, 1-3 fermi in size, passes through electronic shells of atoms 
and is capable, in a path length of ~5 cm, to produce a recoil nucleus with a double velocity of 
up to ~100 km/s. It is such SEECHO-daemon-caused events that satisfy the multiple hit 
rejection criterion (Bernabei et al., 2003) that are possibly detected by the DAMA/NaI. The 
processes involved here certainly need a deeper analysis. 
VI. Conclusions 
The daemon approach had offered an explanation for the ~5-eV drift of the tritium β-spectrum 
tail with a half-year period, the so-called “Troitsk anomaly”, and some predictions regarding 
the KATRIN experiment on direct measurement of the neutrino mass (Drobyshevski, 2005a). 
It now appears that one can corroborate within the daemon paradigm the results of the 
DAMA/NaI experiment with the inferences drawn from the SPb study, which, in addition to 
detecting daemon populations of different velocities captured by the Solar system and moving 
within it in orbits of different, including geocentric, populations, established also a half-year 
variation in the NEACHO flux, demonstrating the advantages of vacuum systems in daemon 
detection, and revealing some of their remarkable properties and specific features of their 
interaction with matter. 
We find it particularly impressive that the range (2-6 keV) of the recorded signals in 
which the DAMA/NaI exhibits a yearly periodicity coincides with exactly the same level (2-7 
keV) that follows from the celestial mechanics scenario. On the other hand, a more careful 
analysis of the evolution of daemons captured by the Sun from the galactic disk and governed 
by celestial mechanics sheds light on reasons underlying the detection of the yearly 
periodicity of the high-velocity population (30-50 km/s) measured by DAMA, and of the half-
year periodicity of the low-velocity population (5-10-30 km/s) in the SPb experiment (in the 
latter case, the part played by the cross-like multi-loop trajectories of daemons traversing the 
Sun and captured by it appears significant). If performed with good statistics, the more 
advanced measurements on DAMA/LIBRA will hopefully also reveal the half-year harmonic 
in low signal level events (~2-3 keV). Such events originate from the fall of daemons from 
“short” SEECHOs in March and September. 
An analysis of the conditions favouring capture of daemons by the Sun and 
corroboration of their subsequent possible celestial mechanics evolution with the results 
gained in the SPb and DAMA/NaI experiments permits one to impose fairly strong constraints 
(one would almost say, to measure) on the effective cross section σ of daemon interaction 
with the Solar material. It was found to be 0.78×10-19 ≤ σ < 1.4×10-19 cm2. This is ~500 times 
the cross section of the neutral “antineon” atom formed by a daemon (Ze = -10e) and ten 
protons it captured, while being 3000-5000 times smaller than the cross section for a 
daemon/heavy-nucleus complex with electrons surrounding it. On the other hand, σ can be 
governed also by the Coulomb interaction of the daemon changing continuously its effective 
charge with particles of the solar plasma (Drobyshevski, 1996), which, in turn, may be helpful 
in refining our knowledge of the characteristics of the solar material. 
Obviously enough, the problems addressed in the paper (interaction of daemons both 
with the solar matter and with the scintillator material, the celestial mechanics and statistical 
evolution of their ensemble after capture by the Solar system, the part played by the initial 
conditions and the starting velocity dispersion in the daemon population of the galactic disk, 
refinement of the apex relative to this population, - it seems it is closer to the apex relative the 
interstellar gas, not stars (see. Fig.1), transfer to SEECHOs and, subsequently, to NEACHOs 
and GESCOs etc.) would require a much more careful and comprehensive analysis. This 
would permit a quantitative comparison of theoretical predictions with future experimental 
results.  
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