A new way to explain the 511 keV signal from the center of the Galaxy and some dark matter experiments
J.Va'vra \inst{}
Vavra_small_hydrogen_paper.tex
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\title{A new way to explain the 511 keV signal from the center of the Galaxy and some dark matter experiments}

\author{J.Va'vra
\inst{}
}

\institute{SLAC, Stanford University, CA94309, U.S.A.\\
\email{jjv@slac.stanford.edu}
}

\date{Received April 3, 2013}

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\abstract
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{The first gamma-ray line originating from outside the solar system that was ever detected is the 511 keV emission from the center of our Galaxy. 
The accepted explanation of this signal is the annihilation of electrons and positrons. However, despite 30 years of intense theoretical 
and observational investigation, the main sources of positrons have not been identified up to now. In this paper we propose an alternative 
explanation: the observed signal is due to atomic transitions to "small hydrogen atom," where electron is captured by proton on a small 
tight orbit around proton. This model may also be relevant to some dark matter searching experiments capable of observing a very small signal. 
We propose a detector to improve their detection-reach even further down to smaller signals equivalent to a single electron and a single 
photon of a few eV energy. We describe the status of the experimental search to find the small hydrogen atom, and propose a method how to 
discover it in the lab directly.} 

\keywords{511 keV peak at the galactic center, small hydrogen atom, DDL atom, low mass WIMPs interacting with electron shell, dark matter search experiments
}

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\section{Introduction}

Rutherford suggested already in 1920 that electron-proton could be bound in tight state [Reeves, 2008]. At that point 
neither the Shroedinger equation (1926) nor Dirac equation (1928) was known to him. He asked his team, including Chadwick, to search for 
this atom. After Chadwick's discovery of the neutron in 1932 there was a lot of discussions whether it is an elementary particle 
or a hydrogen-like atom formed from electron and proton [Pais, 1986]. For example, Heisenberg was among those who argued that 
Chadwick's particle is a small hydrogen atom. At the end the Pauli's argument won, that the neutron spin 1/2 follows 
Fermi-Dirac statistics and this decided that the neutron is indeed an elementary particle. 
This is a well-established fact and it is not discussed in this paper.

However, it is a separate question to see if the Schroedinger or Dirac equations would actually allow a solution corresponding to a small hydrogen, which 
would be a completely separate entity to the neutron discovered by Chadwick. It must have been obvious to both 
Schroedinger and Dirac, and certainly to Heisenberg, that there is a peculiar solution to their equations. This particular solution, which 
corresponds to the small hydrogen, was at the end rejected because the wave function is infinite at r = 0 [Schiff, 1968]. The infinity comes 
from the Coulomb potential shape, which has the infinity at r~=~0; it was a consequence of the assumption that the nucleus 
is point-like. In addition nobody has observed it. At that point the idea of small hydrogen died. 
However, its idea was revived again $\sim$~70-years later [Maly and Va'vra, 1993 and 1995], 
where authors argued that the proton has a finite size, being formed from quarks and gluons, and that the electron experiences a 
different non-Coulomb potential at very small radius. In fact, such non-Coulomb potentials are used in relativistic Hartree-Fock 
calculations for very heavy atoms where inner shell electrons are close to nucleus [Smith-Johnson, 1967] or [Bush-Nix, 1993]. 
Maly and Va'vra simply applied a similar idea to the problem of small hydrogen, i.e., they used the Coulomb potential in 
the Schroedinger and Dirac equations to solve the problem outside the nucleus first, then they used the above mentioned non-Coulomb 
potentials in a separate solution for small radius, and then matched the two solutions at a certain radius; one should note that 
probably more sophisticated potentials will have to be used in the future as the proton quark structure is complex. 
Using this method they retained solutions for small hydrogen which were previously rejected; they called these new solutions "Deep Dirac levels" (DDL).
It is interesting to note that the difference between two types of hydrogens, a normal-size and a small-size, is only a sign in one equation.

S. Brodsky pointed out that one should not use the "1920 quantum mechanics" to solve the problem of small hydrogen because the 
electron becomes relativistic; instead one should use the QED theory [Brodsky, 2010]. He also pointed out that there were attempts 
to find a tight electron-proton bound state, called protonium, using the QED theory [Spence, Vary, 1991] with some hints of 
unusual small positronium and hydrogen bound states induced by a short range hyperfine interaction, which includes spin-spin, 
retardation and Coulomb effects; the proton was assumed to be point-like in their calculation. The paper hints that if the 
retardation term is dropped, there is no bound state. In very recent contact with J. Vary, I learned that they checked the 
calculation again, did not find any error, and in fact, he is continuing with this program with new graduate students. 
This paper will not try to resolve this issue theoretically; this has to be done by real theorists. Instead we turn to 
experimental observations to seek any hint of evidence for the existence of such atoms, hoping that if they are found experimentally, 
the real theory can be developed.

One reason why the idea of small hydrogen died is that nobody has found it. Recently we realized that a possible evidence may come 
from the center of our galaxy, which produces a very strong 511 keV signal. The most obvious explanation of this signal 
is the annihilation of electrons and positrons. The problem is that no significant source of positrons have been 
detected so far to explain the measured rate. The model of small hydrogen could explain it, as there is plenty of hydrogen near the 
center of galaxy, which can be ionized, and its plasma may form small hydrogen at certain small rate.

We also question if some Dark matter searching experiments may have some sensitivity to the small hydrogen atom. This type of atom 
would deposit very small dE/dx and a typical shielding may not be thick enough to stop it. It would get to underground experiments via access 
tunnels and elevator shafts. We are in particular interested in those dark matter experiments, which are capable of detecting a very 
small signal and not requiring nuclear recoil. In fact, we propose a new detector to improve the detection sensitivity to even 
smaller signal equivalent to a single electron and a single photon with energy of a few eV.

The paper also discusses the previous laboratory tests, which tried to discover the small hydrogen atom directly, and proposes new searches.

Although we concentrate on a detection of small hydrogen atom, many suggestions of this paper also apply to a search for 
light-mass WIMPs interacting with atom shell-electrons.

\section{The 511 keV gamma signal from the center of galaxy}

One of the most intriguing puzzle of the astrophysics is to explain a 511 keV Gamma signal in the center of the 
Galaxy. Figure~\ref{fig:511keV_signal_a} shows the observation of this signal by the NASA Compton Gamma Ray Observatory 
[CGRO, 1991] with the OSSE instrument aboard [Cheng, 1997; Purcell, 1997]. Figure~\ref{fig:511keV_signal_b} shows the more 
recent observation of this signal by the Integral satellite observatory [Prantzos et al, 2010]. The most obvious explanation of this signal 
is the annihilation of electrons and positrons. Figure 2 shows that the spectrum can be nicely explained using the 
annihilation emission measured with narrow and broad Gaussian lines and an ortho-positronium continuum; 
the power-law shape accounts for the Galactic diffuse continuum emission. The calculation indicates a 
total $e^+$ annihilation rate of more than $\sim 2x10^{43} e^+/s$. The paper points out that the most 
likely sources of positrons are thermonuclear supernovae with a $\beta^+$ radioactive decay 
from $^{26}$Al, $^{44}$Ti or $^{56}$Co. 

However, there is one major problem with the explanation based on the the $e^+e^−$ annihilation model. Citing N. Prantzos's paper 
precisely: "despite 30 years of intense theoretical and observational investigation, the main sources of positrons have not been identified 
up to now [Prantzos, 2010]." 

In the following we offer an alternative explanation of the 511 keV signal using a model of small hydrogen atom. 

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{Osse_511keV_source_signal.pdf}
\caption{The 511 keV signal observed by the NASA Compton Gamma Ray Observatory (CGRO, launched in 1991) with the OSSE instrument 
aboard [Cheng, 1997; Purcell, 1997].}
\label{fig:511keV_signal_a}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{Integral_511keV_peak.pdf}
\caption{The 511 keV signal observed by the ESI instrument aboard the ESA Integral satellite observatory [Prantzos, 2010]. 
Fit of the spectrum of the annihilation emission measured by SPI with narrow and broad Gaussian lines and an ortho-positronium 
continuum. The power-law accounts for the Galactic diffuse continuum emission [Jean, 2006].}
\label{fig:511keV_signal_b}
\end{figure} 


\section{Model of small hydrogen atom and the 511 keV signal from the center of the Galaxy}

\subsection{The small hydrogen atom.}

The mathematics of the small hydrogen atom, was presented in two very detailed papers [Maly and Va'vra, 1993 and 1995]; here 
we provide a summary relevant to the astrophysics problem. Figure~\ref{fig:DDL_model_energy_a} shows energy levels of small 
hydrogen atom as a function of orbital quantum number L (for Schroedinger equation) 
or k (for Dirac equation). One can see that for orbital excitations above k~$\sim$~10 the transition energy 
becomes to be very close to $\sim$~511 keV. Since it is likely that transitions to DDL levels are accompanied 
with large orbital excitations, we can assume that typical single photon will have energy very close to 511keV.

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{DDL_model_a.pdf}
\caption{Energy levels of small hydrogen atom level as a function of orbital quantum number L (for Schroedinger equation) or k (for Dirac equation). 
Terminal energy transition is $\sim$~511 keV for very large L or k.}
\label{fig:DDL_model_energy_a}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{DDL_model_d.pdf}
\caption{Transitions between two levels of the small hydrogen atom as a function of orbital quantum number L or k.}
\label{fig:DDL_model_energy_b}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{DDL_model_c.pdf}
\caption{Bohr radius of small hydrogen atom as a function of orbital quantum number L or k.}
\label{fig:DDL_model_energy_c}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{DDL_model_b.pdf}
\caption{Electron orbit energy of small hydrogen atoms as a function of orbital quantum number L or k.}
\label{fig:DDL_model_energy_d}
\end{figure}

Figure~\ref{fig:DDL_model_energy_b} shows transition energy between two neighboring energy levels as a function of orbital quantum 
number L or k. Notice that the Schroedinger and Dirac equations provide slightly different results. Table~\ref{table:1} shows 
E(k+1)-E(k) transitions; as the quantum number k increases, the transition energy E(k+1)-E(k) decreases. There is a very 
broad range of wavelengths emitted by DDL atoms, all the way from Gamma-rays to infrared wavelengths.  

\begin{table}
\caption{Calculated energy levels and transitions between two levels, k and k+1, of the "small hydrogen atom" in the infrared wavelength region.}
% title of Table
\label{table:1}      % is used to refer this table in the text
\centering                          % used for centering table
\begin{tabular}{c c c}        % centered columns (4 columns)
\hline\hline                 % inserts double horizontal lines
Orbital  & $ Calculated $ &  Calculated  \\    % table heading
quantum number  & energy level & transition \\    % table heading 
k & E(k) [keV] & E(k+1) - E(k) [nm] \\    % table heading 

\hline                        % inserts single horizontal line
1 & 509.135 & 1.330 \\
2 & 510.067 & 3.990 \\
3 & 510.378 & 7.981 \\
4 & 510.533 & 13.301 \\
5 & 510.626 & 19.952 \\
6 & 510.688 & 27.933 \\
7 & 510.733 & 37.244 \\
8 & 510.766 & 47.885 \\   
9 & 510.792 & 59.856 \\
10 & 510.813 & 73.157 \\
11 & 510.830 & 87.789 \\
12 & 510.844 & 103.751 \\
13 & 510.856 & 121.042 \\
14 & 510.866 & 139.664 \\
15 & 510.875 & 159.616 \\
16 & 510.883 & 180.899 \\
17 & 510.889 & 203.511 \\
18 & 510.895 & 227.453 \\
19 & 510.901 & 252.726 \\
20 & 510.906 & 279.329 \\
21 & 510.910 & 307.262 \\
22 & 510.914 & 336.525 \\
23 & 510,918 & 367.118 \\
24 & 510.921 & 399.041 \\   
25 & 510.924 & 432.294 \\
26 & 510.927 & 466.878 \\
27 & 510.930 & 502.792 \\
28 & 510.932 & 540.035 \\
29 & 510.935 & 578.609 \\
30 & 510.937 & 618.513 \\
35 & 510.946 & 885.871 \\
40 & 510.952 & 1145.248 \\
50 & 510.962 & 1765.761 \\
73 & 510.973 & 3592.703 \\
102 & 510.981 & 6987.195 \\
192 & 510.989 & 24644.641 \\
326 & 510.993 & 70896.811 \\
491 & 510.995 & 160660.437 \\
1130 & 510.997 & 855827.765 \\
\hline                                   %inserts single line
\end{tabular}
\end{table}

To estimate electron energy on hydrogen DDL levels approximatelly, we will use a simplification of calculating the Bohr radius (see Fig.~\ref{fig:DDL_model_energy_c}) 
from energy levels (see Table~\ref{table:1}), which then allows an easy estimate of electron equivalent orbit energies (see Fig.~\ref{fig:DDL_model_energy_d}) using 
the De~Broglie formula. This is naive, but it leads to interesting predictions. One can see that at large values of orbital quantum number k, the DDL 
hydrogen atom size is quite large. One can also see that electron needs an energy of $\sim$~100~keV to enter the DDL hydrogen atom for 
k $\sim$~40; that is quite a large energy. This may lead to a difficulty to form the DDL atom artificially, as such energy is not easy to 
obtain in typical laboratory experiments so far. In addition, a transition to the DDL level does not have to go via a single photon as one 
deals with large energy gaps for small k, and the usual perturbation theory of atomic transitions may not apply. If a multiple photon 
transition occurs one would not observe a peak if only one photon is detected, which makes such transition hard to recognize the correct transition. 
All such photons would have lower energy than 511 keV and would appear as low-energy tail. This may explain the assymetric gamma 
energy spectrum from the Galaxy center - see Fig.~\ref{fig:511keV_signal_a}.

It is clear that nobody has observed yet a rapid collapse of normal hydrogen atom into a small hydrogen atom. This is because of three major 
factors: (a) a small wave function overlap, and (b) electron energies are substantially different between normal and DDL atom, 
(c) to latch an electron on the DDL level, it needs a substantial energy, and (d) the transition from a normal level to deep level may 
go via a multi-photon emission.

\subsection{Formation of "small hydrogen atom" close to the black hole at the Galaxy center.}

The vicinity of the black hole at the center of our Galaxy has a high density plasma, including free electrons and protons. 
Energetic electrons can be trapped by protons to form small DDL hydrogen atoms with high orbital quantum numbers; such DDL atoms will emit 
511 keV gammas as discussed before - see Fig.~\ref{fig:DDL_model_energy_a}. Some fraction of DDL hydrogen atoms will leak out 
into the Galaxy halo. We would like to demonstrate this idea on an example of the Sombrero galaxy. Nice thing about this particular 
galaxy is that we see its halo from outside where we would like to search for the small hydrogen. Figure~\ref{fig:Infrared_glow} shows the Sombrero galaxy 
image, recorded by the Spitzer satellite [Bendo, 2006], overlaid over earlier Hubble telescope image in visible. The picture shows 
the very active accretion disk, the dusty ring and the oval shape halo. NASA's explanation of the halo is that it is formed of 
billions of stars circling in all manner of directions. The DDL hydrogen could be part of this halo as well, and its transitions may
contribute to the infrared wavelength region. Figure~\ref{fig:Infrared_spectra} shows Sombrero galaxy images for various wavelength regions. 
If one looks at Table~\ref{table:1}, one sees that in order the DDL hydrogen to radiate in the infrared wavelength region of 850 microns, it 
has to be excited to very high k-values (in the region of $\sim$~1130). There are very specific spectral lines predicted by the DDL hydrogen 
atom model, which one could specifically search for in the Sombrero galaxy halo signal, if clear precise data would exist. We did not find them.

\begin{figure}[tbp]
\includegraphics[width=0.45\textwidth]{Sombrero_Galaxy_Infrared_a.pdf}
\caption{Infrared glow of the Sombrero galaxy (NG4594), recorded by the Spitzer satellite, overlaid on earlier Hubble telescope image in visible [Bendo, 2006].}
\label{fig:Infrared_glow}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.45\textwidth]{Sombrero_infrared_emissions.pdf}
\caption{Infrared emissions of the Sombrero galaxy (NG4594) at 3.6, 8, 24, 70, 160 and 850 microns, recorded by the Spitzer satellite [Bendo, 2006].
The small DDL hydrogen can emit light in this wavelength regime - see Table~\ref{table:1}.}
\label{fig:Infrared_spectra}
\end{figure}
   
\subsection{Other searches for the small hydrogen in astrophysics signals}

First, we checked if there are some optical absorption lines in spectra from the Sun. Unfortunatelly, the situation here is so complicated that we did not find any proof
of the small hydrogen here.

Figure~\ref{fig:Capture_data} shows the analysis of spectra, including the nuclear capture signals, by the Integral satellite, which cannot 
detect neutrons coming from the Sun due to its location. The only possible explanation is that neutron capture peaks are caused by 
cosmic ray proton interactions with the satellite’s structure, producing neutrons, which then capture and produce multi-MeV Gammas. 
The only puzzling conclusion of the paper is this: ”Thermal neutron capture is responsible for numerous and strong lines at several MeV; 
their unexpected presence poses a difficult challenge for our physical understanding of instrumental backgrounds and for Monte Carlo codes” [Weidenspointner, 2003].

Finally, we want to mention an event, which is happening right now. There is a huge hydrogen bubble approaching the Galactic center. This problem was simulated
by [Anninos, 2012], and their perdiction is that the highest proximity to the black hole will be in the middle of 2013 - see Fig.~\ref{fig:Hydrogen_bubble}. 
It would be interesting to see of the 511~keV peak would respond to this effect. One could use the Fermi satellite's gamma burst monitor, for example.

\begin{figure}[tbp]
\includegraphics[width=0.45\textwidth]{Integral_gamma_spectrum_data.pdf}
\caption{Nuclear capture signals detected by the Integral satelite [Weidenspointner, 2003].}
\label{fig:Capture_data}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.45\textwidth]{Gas_near_galaxy_center.pdf}
\caption{Simulation of large hydrogen bubble approaching the black hole at the Galaxy center [Anninos, 2012].}
\label{fig:Hydrogen_bubble}
\end{figure}

\subsection{The galaxy stability question}

Let's assume that the DDL hydrogen is produced at a rate of $\sim~2x10^{43}/s$, i.e., the same rate as observed rate of the 511~keV signal from the galaxy 
center (the rate of production may be higher if multi-photon transitions are eoccuring). For example, if we assume that the small hydrogen is being produced 
at a constant rate since the galaxy formation and that it leaks into the galaxy's halo at a 1$\%$ rate, it would have accumulated a total value 
of $\sim~1.3x10^{33}~kg$ after 13.2 billion years, which turns out to be a negligable fraction of the total weight of all matter in the 
galaxy (the fraction is less than $\sim10^{-10}$, assuming that the mass of the galaxy is $\sim$~1000 billions of sun masses). 
Therefore we do not have an obvious argument that the DDL atom plays a significant role in the Galaxy stability argument, 
although the assumption of the production constancy of the small hydrogen production is likely to be wrong as the amount of the "supply material" must vary.  

\section{Experiments to find the small hydrogen atom directly.}

To discover the small DDL hydrogen atom in the laboratory, one should observe a clear 511 keV signal. 
We tried to find such a transition during controlled sparking experiments in a pure hydrogen gas at low pressure [Va'vra, 1998].
The test searched only for a large and obvious effect, i.e., it was not designed for a long-term search of very rare events. 

\begin{figure}[tbp]
\includegraphics[width=0.3\textwidth]{Spark_gap.pdf}
\caption{The spark gap used in the search for the small hydrogen atoms [Va'vra, 1998].}
\label{fig:Sparking_test_a}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.35\textwidth]{TPC_spark_test.pdf}
\caption{Sparking tests by the author with two back-to-back TPCs. The total energy of all X-rays per event was typically more than 100~keV/spark, 
consisting of many 2-10 keV X-rays, calibrated by the Fe$^{55}$ source.}
\label{fig:Sparking_test_b}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.35\textwidth]{CsI_spark_test.pdf}
\caption{Sparking tests by the author with the CsI crystal with a spark in the middle. Again one sees a hint of large energy depost, 
although the precision was not very high in this test due to the sparking noise. The energy scale was calibrated by the Na$^{22}$ source}
\label{fig:Sparking_test_c}
\end{figure}

A 1mm sparking gap (see Fig.~\ref{fig:Sparking_test_a} operated with peak spark currents of 0.2-0.5~kA at low pressure of $\sim$2~Torr, with 
sparking gap electric gradient of 2.5~kV/mm, the total spark charge more than $\sim$4x10$^{14}$~electrons/spark, and electron densities 
approaching $\sim$10$^{17}$~electrons/cm$^3$ [Va'vra, 1998]. There was a modest gas gain in the sparking gap creating ions. Various detectors were used 
since the original publication: a BF3 counter, a CsI detector with sparking in the middle of it, and two small back-to-back TPCs. No evidence of DDL hydrogen was 
found in terms of observation of a single 511 photon. However, the experiment did detect a very large number of 2-10~keV X-rays for a sparking 
voltage of only $\sim$2.5~kV. X-rays were produced only when positive ions were produced. The total energy of all X-rays per event was typically 
more than 100~keV/spark (see Fig.~\ref{fig:Sparking_test_b} and Fig.~\ref{fig:Sparking_test_c}). It is not clear if X-rays come from a single 
physics event or from many independent events. The experiment did not have a capability to measure X-rays over full solid angle to check if t
he energy integral would be close to 511 keV. A conventional explanation this physics is the pinch effect creating a larger accelerating 
voltage than the electrode voltage.

The next two examples are presented here just to illustrate that one may need to push for higher electron-ion density. First, one should mention that neutrons 
were produced during exploding wire experiments [Stephanankis, 1972]. The experiment reached currents up $\sim$1.2~MA with peak voltages 
up to $\sim$0.6~MV and ion density up to $\sim$10$^{19}$cm$^{-3}$, which is many orders of magnitude higher than what was reached 
in the above mentioned low pressure sparking experiments in pure hydrogen. Next, one may also mention that neutrons were detected 
during lightning strikes [Shah, 1985]. However, these tests are even less clear as one does not control critical parameters at all. 
Just to compare, most of lightning strikes reach currents of less than $\sim$35~kA, charges up to $\sim$20~C and lasting less 
than $\sim$1~ms [Lowke, 1996]; voltages can reach values in excess of $\sim$100~kV. These are again much higher values than in the above 
low pressure sparking tests. 

  Probably the best way to discover the small hydrogen atom in the future is to go back to sparking in the middle of CsI crystal. The transition to small hydrogen 
level may go mostly via a multi-photon effect. One has to catch all photons to get a total energy sum close to 511 keV. One should use smaller electrodes, 
a sub-ns HV pulser, smaller hole in the crystal to catch more photons and hope to get a total sum of 511 keV energy. 

  Another possibility is to take advantage of a possibility that at some depth below the surface the small hydrogen energy will become to be in a thermal equilibrium 
with surrounding atoms. There will be a high concentration of these atoms at this depth. One could simply evacuate a cylinder, and bring it down there. 
The small hydrogen will get through walls and fill up the cylinder. One could then measure absorption lines with an optical spectrometer 
(expected absorption lines in nm: 307.3, 336.5, 367.1, 399.0, 432.3, 466.9,...). This depth has to be determined from the dE/dx calculation.

  If the small hydrogen would make a nuclear capture, one could also check if nuclei at this depth have an "apparent" excess of neutrons. However, 
we should stress that we do not know if the small hydrogen would do a nuclear capture. It does have a small dipole moment, which may prevent it.

  Initially we thought that one should use a powerful laser going through a low pressure hydrogen and produce a high density of electrons-ion pairs, 
and one would look for 511~keV Gammas. For example, SLAC has a 10~TW laser at FACET which can be used to ionize $\sim$~50~Torr hydrogen gas. One could do a test if 
one can generate a 511~keV signal. However, the problem with this scheme is that such a powerful laser, also creates complicated coherent effects, 
causing high electric fields, which can create e$^{+}$ and e$^{-}$ beams, and thus a "legitimate" 511~keV as well; one may not be able to prove anything.

\section{Energy loss of small hydrogen atom}

The DDL hydrogen atom can upset the detector's atomic electron shell, when it is moving very close to the atomic shell-electron. 
It will be an electromagnetic interaction between the shell-electron charge and an electric dipole moment of the small DDL hydrogen atom.
The size d of the DDL atom depends on its orbital excitation, in the ground state its size is small and in the excited state it is 
large - see Fig.~\ref{fig:DDL_model_energy_c}. The dE/dx loss from the DDL hydrogen atom passing through medium will be much smaller 
than from a passing muon. The proper calculation is complicated and will not be presented here, instead we we will make a simple estimate. 
Let's assume that the DDL hydrogen atom is passing at a distance of r from a target atom. A ratio of electric field
from a single charge and a dipole charge is E$_{single~charge}$/E$_{dipole}$ $\sim$~(q/r$^2$)/[(q.d)/r$^3$)] $\sim$~r/d for r~$>>$~d, where 
q is a single charge and d is a distance between two charges in the dipole. This ratio is close to $\sim$~10$^7$ for r = $1~A^\circ$, d = 100 Fermi.
One can assign an effective charge for the dipole atom scaled down from a normal charge by the "E$_{single~charge}$/E$_{dipole}$" ratio, and 
estimate the energy loss of DDL atoms using the Bethe's formula, by scaling it from the muon energy loss, assuming 1.5 MeV/(g/cm$^2$) and 
the medium density of 5.5 g/cm$^3$. Using this recipe one can estimate the expected energy loss for DDL atoms - see Fig.~\ref{fig:Energy_loss_DDL}. 
One can see that the dependence is complex and depends on values of r and d. The dE/dx loss is extremely small for the DDL atom in the ground state, 
corresponding to k = 1, i.e., d close to a few Fermi. It is significant only if the DDL atom is very close to a shell-electron. 
  
\begin{figure}[tbp]
\includegraphics[width=0.45\textwidth]{E_loss_of_DDL_atoms_in_rock.pdf}
\caption{A simple calculation of energy loss of DDL atoms in the typical medium, such as rock, for various values of r (distance to the medium atom) 
and d (size of DDL atom - see Fig.~\ref{fig:DDL_model_energy_c}).}
\label{fig:Energy_loss_DDL}
\end{figure}

Figure~\ref{fig:Annual_modulation} shows annual modulation due to the Earth's motion around the Galaxy and the Sun [Drukier, 1986]. 
Assuming that the Dark Matter is mostly in equilibrium with the baryonic cloud around our Galaxy (see Fig.~\ref{fig:Cloud}), the Sun's 
relative velocity in respect to the Dark Matter is $\sim$~230~km/sec. On Earth we will see a slight modulation of partial pressure of the 
Dark Matter with a phase starting in June due its orbit velocity of $\sim$~30~km/sec around the Sun. This modulation corresponds 
to d(Beta) = d(v/c)~$\sim$~0.0001. This means that the Dark Matter will cross $\sim$~1 meter in about 4 microseconds, with 
a very small modulation due to the $\sim$~30~km/sec effect. If the Dark Matter is the small hydrogen atom, i.e., its mass is close to $\sim$~1~GeV/c$^2$, 
this velocity modulation corresponds to a kinetic energy modulation of less than $\sim$~5keV, again a very small value. 
There would be probably a high energy tail due to collisions with ions and other cosmic rays, but the mean value of the modulation is small. 
The energy loss for such a small value of v/c is on the "Bethe-rise" of the dE/dx-curve at a mean value of Beta = v/c~$\sim$~0.00077 
with a modulation of d(Beta) = v/c~$\sim$~0.0001. 

It is clear that a precise dE/dx calculation is not simple, as one needs the small hydrogen atom size, and it is missing in this paper. 
It is necesary to design the experiment properly.

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{Annual_modulation.pdf}
\caption{Rotation of Earth in the Galaxy and around the Sun. The dark matter signal modulation is expected to be driven by a relative change in kinetic 
energy obtained from relative velocity of 30~km~/~sec of the Earth montion around the Sun [Drukier, 1986].}
\label{fig:Annual_modulation}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.45\textwidth]{Baryonic_cloud_around_Galaxy.pdf}
\caption{Chandra satllite's measurement of the baryonic hot gas halo around our Galaxy. One could probably assume that the dark matter has a similar shape. 
They estimate this distribution from the X-ray attenuation [Chandra, 2012]. It is sufficiently weak that they do not see similar clouds near other galaxies.}
\label{fig:Cloud}
\end{figure}

\section{Search for the light-mass Dark matter}

Most present dark matter experiments rely on the interaction of a weakly interacting heavy-mass dark matter particle (WIMP) with 
a nucleus of Xe, Ar, Ge, Na, etc. The WIMP particle is assumed to be either light-mass (see Fig.~\ref{fig:Sensitivity_a}), or very massive 
(see Fig.~\ref{fig:Sensitivity_b}). Although all these experiments are sensitive to energetic neutrons of a few MeV energy, coming 
from the surrounding radioactive rock, they are not sensitive to a dark matter particle mass close to a "neutron mass" and having a very 
small kinetic energy modulation corresponding to the "30~km/sec modulation" of Earth's orbit around the Sun. 

One could probably visualize the Dark Matter cloud around the Galaxy using the Chandra's measurement of the hot baryonic mass around the Galaxy
using the X-ray attenuation (see Fig.~\ref{fig:Cloud}). It extend well beyond the Galaxy size and it is stationary, i.e., it does not rotate 
with the Galaxy motion. Its density is so low, that we cannot detect similar halos around other galaxies. The estimated mass of the halo 
is comparable to the mass of all the stars in the galaxy [Chandra, 2012].

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{Small_wimp_mass.pdf}
\caption{Sensitivity of various present Dark matter experiments to light-mass WIMP particle [Pyle, 2013].}
\label{fig:Sensitivity_a}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{Dark_matter_search_sensitivity.pdf}
\caption{Sensitivity of various present Dark matter experiments to heavy-mass WIMP particle [Aprile, 2012].}
\label{fig:Sensitivity_b}
\end{figure}

Can one somehow fit the small hydrogen model into the Dark matter search ? What would be its density ? One way to estimate it to take results 
high-resolution numerical simulations by astrophysicist, who estimate that Dark Matter density near Earth is rho $\sim$~0.3~GeV/cm$^3$ [Catena, 2011].
If the Dark Matter mass is equal to mass of the small hydrogen, there is 300 small hydrogen atoms in every liter, i.e., a very large amount. 
And since it is produced all the time, its amount on the Earth would be increasing. The dE/dx deposit from the small hydrogen will be substantially 
smaller than a typical cosmic ray muon, but it will be probably large enough that such atoms will pennetrate a certain depth and will become 
in a thermal equilibrium with the surrounding rock. We do not know how to calculate this depth at present. But probably the only way to reach 
the present dark matter experiments is to get down there through access tunnels or elevator shafts. As we said, the Earth will see a slight modulation 
of the partial pressure of the small hydrogen gas. This includes the Grand Sasso lab, which has an easy highway access. 
Although all above mentioned dark matter searching experiments have local shielding, it may not be thick enough for the DDL atoms. For example, the 
DAMA experiment has a local shielding consisting of $\sim$10~cm of Cu, 15~cm of Pb~+~Cd foils, 10/40~cm Polyethylene/paraffin, and about 1 meter concrete
outside the installation. 

\begin{figure}[tbp]
\includegraphics[width=0.4\textwidth]{DAMA_PH_spectrum.pdf}
\caption{DAMA/LIBRA single-hit scintillation pulse height spectrum in NaI(Tl) crystals. The energy threshold of the experiment is 2 keV 
and corrections for efficiencies are already applied [Bernabei, 2008].}
\label{fig:DAMA_signal}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.4\textwidth]{CoGeNT_PH_spectrum.pdf}
\caption{CoGeNT experiment pulse height spectrum of bulk events, where a contribution from surface and cosmogenic contaminations are removed. 
Overimposed is the expected signal from a WIMP mass of 8.2~GeV [Aalseth, 2012].}
\label{fig:CoGeNT_signal}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.4\textwidth]{DAMIC_PH_spectrum.pdf}
\caption{DAMIC pulse height spectrum. The upper histogram shows the spectrum for all hits, the solid line just below is the result of 
eliminating the single pixel hits, and the hatched histogram corresponds to the events passing the selection cuts, described in the paper [Barreto, 2012].}
\label{fig:DAMIC_signal}
\end{figure}

The small hydrogen atom will cause extremely small atomic excitations, either single electron ionization or single photon excitation.
We would expect to observe the "Landau-like" dE/dx curve with a non-zero peak. This may require a new detector concept (see last chapter), 
but to the extent that existing low mass dark matter experiments are useful for this discussion, we are interested as well. 
For example, experiments such as DAMA, CoGeNT or DAMIC cannot tell if a given excitation comes from the nuclear recoil or 
interaction with the electron shell, and therefore we include them in our consideration. The CDMS experiment can clearly determine a nuclear recoil.
They have 3 events presently using their Si-detectors (no event yet in Ge-detectors), which is not enough to see a modulation. If they will see the 
anual modulation, it will exclude a possibility that the Dark Matter is the small hydrogen. Presently one cannot do it. 

The first experiment to observe a clear annual modulation is the DAMA/LIBRA experiment using single-hit scintillation events 
from a 2-4~keV energy interval [Bernabei, 2008]. Figure~\ref{fig:DAMA_signal} shows the DAMA/LIBRA pulse height spectrum, which 
shows a pulse height bump between 2~keV~$<$~E~$<$~4~keV, and a minimum near the pedestal in the region below $\sim$~2~keV. This shape is not 
expected from either WIMP or DDL hydrogen atom models. There is also a hint of a similar anual modulation signal in the CoGeNT 
experiment and possibly CRESST [Kelso, 2012]. The CoGeNT detects electrons in their Ge crystal, and cannot tell, similarly to DAMA, 
if the signal comes from the electron shell or the nuclear recoil. CoGeNT observes the anual modulation using energy deposits 
from energy intervals 500~eV~$<$~E~$<$~3~keV and 500~eV~$<$~E~$<$~900~eV [Aalseth, 2012]. Figure~\ref{fig:CoGeNT_signal} shows the 
CoGeNT pulse height spectrum, which resembles an exponential, and does not show a bump near 2-4~keV. One possible way forward to 
answer this question is the DAMIC experiment [Barreto, 2012], which is based on CCD technology with extremely low single-electron 
detection thershold [Estrada, 2013]. Figure~\ref{fig:DAMIC_signal} shows the DAMIC pulse height spectrum, which shows an 
exponential spectrum near the threshold, and again does not show DAMA's bump near 2-4~keV. However, at this point, it is 
not yet known if the DAMIC experiment observes the yearly modulation using the signal from these small energy deposits.

\section{Detector proposal to search for small hydrogen atom or light-mass WIMP.}

The best way to detect the small DDL hydrogen atom, and it applies also for a light mass WIMP interacting with electron shell only, is 
to build a large $\sim$~1 meter diammeter spherical TPC [Giomataris, 2004], filled with a high pressure ethane gas with a capability to 
detect both signle electrons. We would add to it a measurement of single photons using PMTs with the Bialkali photocathode, 
placed at an outer radius with as high coverage as practically possible - see Fig.~\ref{fig:New_detector_a}. One would make the 
inner spherical TPC surface reflecting to increase the overall photon detection efficiency. This TPC would be located 
underground, somewhat shielded from cosmic rays, but shallow enough to allow the small hydrogen atoms to penetrate. 
The small hydrogen atoms interacting with atomic-shell electrons would leave a trail of single photon excitations, and an occasional single 
electron deposit. The low mass WIMP, interacting only with a light nucleus, such as hydrogen in ethane, would occasionally create an 
event having a single electron and a single photon (however, for for the WIMP detection, the TPC would have to be located deeper 
under ground to supress the background). A trigger of the experiment would be a single photon. An interesting signal would be a train of 
single photon hits within a $\sim$~8 microsecond window (this would be determined in the on-line DAQ software). With this scheme we might 
even attempt to determine the "Landau-like" dE/dx curve with the most probable value as low as even 10-50~eV. This would represent the 
lowest energy threshold ever achieved in any dark matter detector so far. Of course, the spherical TPC is only an example. One could use 
a normal square TPC at an expense of having more channels. The anual modulation in either the average event duration time or in dE/dx 
will be a proof that we are detecting the Dark Matter, although we would not be sure if it is due to the small hydrogen.

Probably even better way to detect the small DDL hydrogen atom, or the light mass WIMP interacting with electron shell only, is 
simply to build a large $\sim$~1 meter cube TPC, we call it a "Light TPC", with a capability to detect only single photons - see Fig.~\ref{fig:New_detector_b}.
The simplicity would be the main motivation here. One will be looking for a signiture that two or more photons are generated with a $\sim$~8 microsecond window.
The Ligh TPC would have $\sim$~400 DIRC PMTs with a photon reflector to enhance the photon detection efficiency. The radiator would be either (a) a nitrogen boil-off gas at
normal or elevated pressure, or (b) pure water, or (c) the metal-loaded liquid scintillator (WbLS) [Minfang, 2013]. The trigger would be a single photon, and the 
a buffer with TDC values would be readout only if two or more photons are measured within $\sim$~8 microseconds. Again, the anual modulation in either the average 
event duration time or in dE/dx will be a proof that we are detecting the Dark Matter, although we would not be sure if it is due to the small hydrogen.


\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{New_spherical_TPC.pdf}
\caption{Proposed spherical TPC detector to search for DDL atoms or light-mass WIMPs, interacting with electron shell electrons, with the 
smallest possible sensitivity to detect single electrons and single photons of 2.4-4~eV.}
\label{fig:New_detector_a}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=0.5\textwidth]{New_Light_TPC.pdf}
\caption{Proposed Light TPC detector to search for DDL atoms or light-mass WIMPs, interacting with electron shell electrons, with the 
smallest possible sensitivity to detect single photons of 2.4-4~eV.}
\label{fig:New_detector_b}
\end{figure}

\section{Conclusions}

\begin{enumerate}
\item The paper suggest an alternative explanation of the 511~keV gamma signal from the center of our Galaxy. The accepted explanation of this signal is 
the annihilation of electrons and positrons. However, despite 30 years of intense theoretical and observational investigation, the main sources of positrons 
have not been identified up to now. In this paper we propose that the 511~keV signal is due to atomic transitions in the "small DDL hydrogen" atom, 
where an electron is captured by a proton on a small tight orbit around a proton. 
\item The paper suggests that dark matter experiments should search for the smallest possible energy deposit and determine that it shows the anual modulations. 
This include experiments such as DAMA/LIBRA, CRESST, CoGeNT and DAMIT, and perhaps CDMS if it will not require the nuclear recoil. The paper suggests that such 
a signal would be caused by occasional very tiny dE/dx interactions of the "small hydrogen atom" with atomic shell electrons of the detector, and not 
by interactions with the nucleus. If a heavy-mass WIMP does not exist, and all we have is the small hydrogen atom or light-mass WIMP, which interacts 
with shell-electrons only, most of dark matter experiments will not see anything.
\item To observe the anual modulation due to the "small DDL hydrogen" atoms, we propose two detectors: (a) a Spherical TPC, 
equipped with both single electron and single photon sensitivity for photons of 2.5-4~eV energy, and (b) the Light TPC detector 
detecting sinle photons only. Such TPC will also have a chance to observe a "Landau-like" dE/dx distribution with very small most probable energy deposit.
\item Although the paper concentrates on the small hydrogen atom detection, the proposed detector can be used also to a search for a light 
WIMP, interacting with a light nucleus, such as hydrogen in ethane gas, and other dark Matter candidates interacting the atomic-shell electrons.
\item To discover the "small DDL hydrogen" atom directly in the laboratory, we have proposed several practical experiments.
\item It is very important to develop a good dE/dx model for the small hydrogen. This requires to know its size. To do that one 
needs a feedback from J. Vary's QED calculation.
\item If it will be shown that the small hydrogen dE/dx deposit in a typical medium is too small, it may not be possible to do proposed anual modulation experiements. 
However, other tests to discover it, proposed in this paper, would still be possible.
\item Although we have concentrated on the small hydrogen atom only, there are other possible unusual Dark Matter candidates, which 
could interact with atomic-shell electrons [Khlopov, 2008].
\item This paper does not provide a proof that the small hydrogen atom exists. The intention is to provide a motivation for a new search.
\item The original version of this manuscript was updated after author's talk at Brookhaven National Laboratory [Va'vra, 2013].

\section{Acknowledgements}

I would like to thank J. Bjorken who recommended to discuss the DDL hydrogen model with S. Brodsky. I also thank S. Brodsky for treating me very kindly and
for providing several suggestions, including a reference [Spence, Vary, 1991]. I also thank J. Vary for discussing some details of his model.


\end{enumerate}

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\bibitem{Weidenspointner_2003} G. Weidenspointner {\it et al.}, "Astronomy and Astrophysics" 411, L113–L116 (2003).

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\bibitem{Pais_1986} A. Pais, Inward bound, page 397, Clarendon press - Oxford, 1986.

\bibitem{Jean_2006} P. Jean {\it et al.}, Spectral analysis of the Galactic e+e− annihilation emission, A\&A 445, 579–589 (2006).

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\bibitem{Maly_Va'vra_1995} J. Maly and J. Va'vra, Electron Transitions on Deep Dirac Levels II, Fusion Technology, Vol. 27, January 1995. 

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\bibitem{Brodsky_2010} S. Brodsky, SLAC, private communications, 2010.

\bibitem{Spence_1991} J.R. Spence and J.P. Vary, "Electron-proton resonances at low energy from a relativistic two-body wave equation", 
Physics Letters B 271 (1991) 27-31. 

\bibitem{Bendo_2006} G. J. Bendo et al., "SPITZER AND JCMT observations of the active galactic nucleus in the Sombrero galaxy (NGC4594)", 
The Astrophysical Journal, 645:134–147, 2006 July 1. 

\bibitem{Bernabei_2008} R. Bernabei {\it et al.}, "First results from DAMA/LIBRA and the combined results with DAMA/NaI", arXiv:0804.2741 [astro-ph]. 

\bibitem{Drukier_1986} A. Drukier, K. Freese, and D. Spergel, Phys.Rev.D33:3495-3508 (1986).

\bibitem{Catena_2011} R. Catena and P. Ullio, arXiv:1111.3556v1 [astro-ph.CO] 15 Nov 2011.

\bibitem{Chandra_2012} NASA, Chandra sattelite data, 2012, http://www.nasa.gov/.

\bibitem{Kelso_2008} C. Kelso, D. Hooper, M. R. Buckley, "Toward a Consistent Picture for CRESST, CoGeNT and DAMA", arXiv:1110.5338 [astro-ph]. 

\bibitem{Anninos_2012} P. Anninos {\it et al.}, arXiv:1209.1638v1 [astro-ph.GA] 7 Sep 2012).

\bibitem{Aalseth_2012} C.E. Aalseth {\it et al.}, "CoGeNT: A Search for Low-Mass Dark Matter using p-type Point Contact Germanium Detectors", arXiv:1208.5737v2 [astro-ph]. 

\bibitem{Barreto_2012} J. Barreto {\it et al.}, "Direct Search for Low Mass Dark Matter Particles with CCDs", arXiv:1105.5191v4 [astro-ph]. 

\bibitem{Estrada_2013} J. Estrada, "Dark Matter Search using thick CCDs", talk at SLAC cosmic frontier workshop, 2013. 

\bibitem{Nygren_2008} D. Nygren, "A Testable Conventional Hypothesis for the DAMA-LIBRA Annual Modulation Signal", TIPP conference, 2011. 

\bibitem{Pyle_2013} M. Pyle, "Physical Motivation and Detection Techniques for Light Dark Matter", Joint CPAD and Instrumentation Frontier 
Community Meeting, Argonne lab, Jan. 10, 2013.

\bibitem{Aprile_2012} E. Aprile, "Talk at DarkAttack conference", Ascona, July 18, 2012.

\bibitem{Va'vra_1995} J. Va'vra et al., Soft X-ray production in spark discharges in hydrogen, nitrogen, air, argon and xenon gases, 
Nucl. Instr. \& Meth., A 418 (1998) 405 - 419.

\bibitem{Shah_1985} G. N. Shah, H. Razdan, C. L. Bhat and Q. M. Ali, Neutron generation in lightning bolts, Nature, 313, 773-775 (28 February 1985).

\bibitem{Stephanankis_1972} S. J. Stephanankis, L.S. Levine, D. Mosher, I.M. Vitkovitsky, and F. Young, Neutron production during exploding-wire discharges, 
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\bibitem{Giomataris_2004} I. Giomataris and J.D. Vergados, Nucl.Instrum.Meth.A530:330-358,2004, I. Giomataris et al. Nucl.Phys.Proc.Suppl.150:208-213,2006.

\bibitem{Lowke_1996} J. J. Lowke, "A theory of ball lightning as an electric discharge", J. Phys. D: Appl. Phys. 29 (1996) 1237–1244.

\bibitem{Minfang_2013} Minfan Yeh, BNL, private communication, 2013.

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\end{thebibliography}

\end{document}













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The file is : epslatex.pdf 
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\centering
\includegraphics[width=\textwidth]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure}
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\centering
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\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
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\centering
\includegraphics[width=3cm]{empty.eps}
\caption{Vibrational stability equation of state
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$>0$ means vibrational stability.
}
\label{FigVibStab}
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\centering
\includegraphics[bb=10 20 100 300,width=3cm,clip]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
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\begin{figure}
\resizebox{\textwidth}{!}
{\includegraphics[bb=10 20 100 300,clip]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure}
%
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%                                             Simple A&A Table
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\begin{table}
\caption{Nonlinear Model Results}             % title of Table
\label{table:1}      % is used to refer this table in the text
\centering                          % used for centering table
\begin{tabular}{c c c c}        % centered columns (4 columns)
\hline\hline                 % inserts double horizontal lines
HJD & $E$ & Method\#2 & Method\#3 \\    % table heading 
\hline                        % inserts single horizontal line
1 & 50 & $-837$ & 970 \\      % inserting body of the table
2 & 47 & 877    & 230 \\
3 & 31 & 25     & 415 \\
4 & 35 & 144    & 2356 \\
5 & 45 & 300    & 556 \\ 
\hline                                   %inserts single line
\end{tabular}
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\caption{Nonlinear Model Results}             
\label{table:1}      
\centering          
\begin{tabular}{c c c c l l l }     % 7 columns 
\hline\hline       
% To combine 4 columns into a single one 
HJD & $E$ & Method\#2 & \multicolumn{4}{c}{Method\#3}\\ 
\hline                    
1 & 50 & $-837$ & 970 & 65 & 67 & 78\\  
2 & 47 & 877    & 230 & 567& 55 & 78\\
3 & 31 & 25     & 415 & 567& 55 & 78\\
4 & 35 & 144    & 2356& 567& 55 & 78 \\
5 & 45 & 300    & 556 & 567& 55 & 78\\
\hline                  
\end{tabular}
\end{table*}
%
%-------------------------------------------------------------
%                                          Table with notes 
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%
% A single note
\begin{table}[h]
\caption{\label{t7}Spectral types and photometry for stars in the
region.}
\centering
\begin{tabular}{lccc}
\hline\hline
Star&Spectral type&RA(J2000)&Dec(J2000)\\
\hline
69           &B1\,V     &09 15 54.046 & $-$50 00 26.67\\
49           &B0.7\,V   &*09 15 54.570& $-$50 00 03.90\\
LS~1267~(86) &O8\,V     &09 15 52.787&11.07\\
24.6         &7.58      &1.37 &0.20\\
\hline
LS~1262      &B0\,V     &09 15 05.17&11.17\\
MO 2-119     &B0.5\,V   &09 15 33.7 &11.74\\
LS~1269      &O8.5\,V   &09 15 56.60&10.85\\
\hline
\end{tabular}
\tablefoot{ The top panel shows likely members of Pismis~11. The second
panel contains likely members of Alicante~5. The bottom panel
displays stars outside the clusters.}
\end{table}
%
% More notes
%
\begin{table}[h]
\caption{\label{t7}Spectral types and photometry for stars in the
region.}
\centering
\begin{tabular}{lccc}
\hline\hline
Star&Spectral type&RA(J2000)&Dec(J2000)\\
\hline
69           &B1\,V     &09 15 54.046 & $-$50 00 26.67\\
49           &B0.7\,V   &*09 15 54.570& $-$50 00 03.90\\
LS~1267~(86) &O8\,V     &09 15 52.787&11.07\tablefootmark{a}\\
24.6         &7.58\tablefootmark{1}&1.37\tablefootmark{a}   &0.20\tablefootmark{a}\\
\hline
LS~1262      &B0\,V     &09 15 05.17&11.17\tablefootmark{b}\\
MO 2-119     &B0.5\,V   &09 15 33.7 &11.74\tablefootmark{c}\\
LS~1269      &O8.5\,V   &09 15 56.60&10.85\tablefootmark{d}\\
\hline
\end{tabular}
\tablefoot{ The top panel shows likely members of Pismis~11. The second
panel contains likely members of Alicante~5. The bottom panel
displays stars outside the clusters.\\
\tablefoottext{a}{Photometry for MF13, LS~1267 and HD~80077 from
Dupont et al.}
\tablefoottext{b}{Photometry for LS~1262, LS~1269 from
Durand et al.}
\tablefoottext{c}{Photometry for MO2-119 from
Mathieu et al.}
}
\end{table}
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\caption[]{\label{nearbylistaa2}List of nearby SNe used in this work.}
\begin{tabular}{lccc}
\hline \hline
SN name &
Epoch &
Bands &
References \\
&
(with respect to $B$ maximum) &
&
\\ \hline
1981B   & 0 & {\it UBV} & 1\\
1986G   &  $-$3, $-$1, 0, 1, 2 & {\it BV}  & 2\\
1989B   & $-$5, $-$1, 0, 3, 5 & {\it UBVRI}  & 3, 4\\
1990N   & 2, 7 & {\it UBVRI}  & 5\\
1991M   & 3 & {\it VRI}  & 6\\
\hline
\noalign{\smallskip}
\multicolumn{4}{c}{ SNe 91bg-like} \\
\noalign{\smallskip}
\hline
1991bg   & 1, 2 & {\it BVRI}  & 7\\
1999by   & $-$5, $-$4, $-$3, 3, 4, 5 & {\it UBVRI}  & 8\\
\hline
\noalign{\smallskip}
\multicolumn{4}{c}{ SNe 91T-like} \\
\noalign{\smallskip}
\hline
1991T   & $-$3, 0 & {\it UBVRI}  &  9, 10\\
2000cx  & $-$3, $-$2, 0, 1, 5 & {\it UBVRI}  & 11\\ %
\hline
\end{tabular}
\tablebib{(1)~\citet{branch83};
(2) \citet{phillips87}; (3) \citet{barbon90}; (4) \citet{wells94};
(5) \citet{mazzali93}; (6) \citet{gomez98}; (7) \citet{kirshner93};
(8) \citet{patat96}; (9) \citet{salvo01}; (10) \citet{branch03};
(11) \citet{jha99}.
}
\end{table}
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%                                 A rotated Table in landscape  
%  In the preamble, use:   \usepackage{lscape}
%-------------------------------------------------------------
\begin{landscape}
\begin{table*}
\caption{Summary for ISOCAM sources with mid-IR excess 
(YSO candidates).}\label{YSOtable}
\centering
\begin{tabular}{crrlcl} 
\hline\hline             
ISO-L1551 & $F_{6.7}$~[mJy] & $\alpha_{6.7-14.3}$ 
& YSO type$^{d}$ & Status & Comments\\
\hline
\multicolumn{6}{c}{\it New YSO candidates}\\ % To combine 6 columns into a single one
\hline
1 & 1.56 $\pm$ 0.47 & --    & Class II$^{c}$ & New & Mid\\
2 & 0.79:           & 0.97: & Class II ?     & New & \\
3 & 4.95 $\pm$ 0.68 & 3.18  & Class II / III & New & \\
5 & 1.44 $\pm$ 0.33 & 1.88  & Class II       & New & \\
\hline
\multicolumn{6}{c}{\it Previously known YSOs} \\
\hline
61 & 0.89 $\pm$ 0.58 & 1.77 & Class I & \object{HH 30} & Circumstellar disk\\
96 & 38.34 $\pm$ 0.71 & 37.5& Class II& MHO 5          & Spectral type\\
\hline
\end{tabular}
\end{table*}
\end{landscape}
%
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%  In the preamble, use:              \usepackage{longtable}
%-------------------------------------------------------------
%          All long tables have to be placed at the end, after 
%                                        \end{thebibliography}
%
% In the text, at the place where the large table should appear
% add the command:
\addtocounter{table}{1}
% Tables counters will be well numbered.
%
\end{thebibliography}
% If table 2
\longtab{2}{
\begin{longtable}{lllrrr}
\caption{\label{kstars} Sample stars with absolute magnitude}\\
\hline\hline
Catalogue& $M_{V}$ & Spectral & Distance & Mode & Count Rate \\
\hline
\endfirsthead
\caption{continued.}\\
\hline\hline
Catalogue& $M_{V}$ & Spectral & Distance & Mode & Count Rate \\
\hline
\endhead
\hline
\endfoot
%%
Gl 33    & 6.37 & K2 V & 7.46 & S & 0.043170\\
Gl 66AB  & 6.26 & K2 V & 8.15 & S & 0.260478\\
Gl 68    & 5.87 & K1 V & 7.47 & P & 0.026610\\
&      &      &      & H & 0.008686\\
Gl 86 
\footnote{Source not included in the HRI catalog. See Sect.~5.4.2 for details.}
& 5.92 & K0 V & 10.91& S & 0.058230\\
\end{longtable}
}% End \longtab
%
%_____________________________________________________________
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%                                             and in landscape 
%  In the preamble, use:       \usepackage{longtable,lscape}
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%          All long tables have to be placed at the end, after
%                                        \end{thebibliography}
%
% In the text, at the place where the large table should appear
% add the command:                        
\addtocounter{table}{1} 
% Tables counters will be well numbered.
%
\end{thebibliography}
% If table 2
\longtabL{2}{
\begin{landscape}
\begin{longtable}{lllrrr}
\caption{\label{kstars} Sample stars with absolute magnitude}\\
\hline\hline
Catalogue& $M_{V}$ & Spectral & Distance & Mode & Count Rate \\
\hline
\endfirsthead
\caption{continued.}\\
\hline\hline
Catalogue& $M_{V}$ & Spectral & Distance & Mode & Count Rate \\
\hline
\endhead
\hline
\endfoot
%%
Gl 33    & 6.37 & K2 V & 7.46 & S & 0.043170\\
Gl 66AB  & 6.26 & K2 V & 8.15 & S & 0.260478\\
Gl 68    & 5.87 & K1 V & 7.47 & P & 0.026610\\
&      &      &      & H & 0.008686\\
Gl 86
\footnote{Source not included in the HRI catalog. See Sect.~5.4.2 for details.}
& 5.92 & K0 V & 10.91& S & 0.058230\\
\end{longtable}
\end{landscape}
}% End \longtabL
%
% Online Material
%_____________________________________________________________
%        Online appendices have to be placed at the end, after
%                                        \end{thebibliography}
%-------------------------------------------------------------
\end{thebibliography}

\Online

\begin{appendix} %First online appendix
\section{Background galaxy number counts and shear noise-levels}
Because the optical images used in this analysis...

\begin{figure*}
\centering
\includegraphics[width=16.4cm,clip]{1787f24.ps}
\caption{Plotted above...}
\label{appfig}
\end{figure*}

Because the optical images...
\end{appendix}

\begin{appendix} %Second online appendix
These studies, however, have faced...
\end{appendix}

\end{document}
%
%_____________________________________________________________
%        Some tables or figures are in the printed version and
%                      some are only in the electronic version
%-------------------------------------------------------------
%
% Leave all the tables or figures in the text, at their right place 
% and use the commands \onlfig{}{} and \onltab{}{}. These elements
% will be automatically placed at the end, in the section
% Online material.

\documentclass{aa}
...
\begin{document}
text of the paper...
\begin{figure*}%f1
\includegraphics[width=10.9cm]{1787f01.eps}
\caption{Shown in greyscale is a...}
\label{cl12301}}
\end{figure*}
...
from the intrinsic ellipticity distribution.
% Figure 2 available electronically only
\onlfig{2}{
\begin{figure*}%f2
\includegraphics[width=11.6cm]{1787f02.eps}
\caption {Shown in greyscale...}
\label{cl1018}
\end{figure*}
}

% Figure 3 available electronically only
\onlfig{3}{
\begin{figure*}%f3
\includegraphics[width=11.2cm]{1787f03.eps}
\caption{Shown in panels...}
\label{cl1059}
\end{figure*}
}

\begin{figure*}%f4
\includegraphics[width=10.9cm]{1787f04.eps}
\caption{Shown in greyscale is...}
\label{cl1232}}
\end{figure*}

\begin{table}%t1
\caption{Complexes characterisation.}\label{starbursts}
\centering
\begin{tabular}{lccc}
\hline \hline
Complex & $F_{60}$ & 8.6 &  No. of  \\
...
\hline
\end{tabular}
\end{table}
The second method produces...

% Figure 5 available electronically only
\onlfig{5}{
\begin{figure*}%f5
\includegraphics[width=11.2cm]{1787f05.eps}
\caption{Shown in panels...}
\label{cl1238}}
\end{figure*}
}

As can be seen, in general the deeper...
% Table 2 available electronically only
\onltab{2}{
\begin{table*}%t2
\caption{List of the LMC stellar complexes...}\label{Properties}
\centering
\begin{tabular}{lccccccccc}
\hline  \hline
Stellar & RA & Dec & ...
...
\hline
\end{tabular}
\end{table*}
}

% Table 3 available electronically only
\onltab{3}{
\begin{table*}%t3
\caption{List of the derived...}\label{IrasFluxes}
\centering
\begin{tabular}{lcccccccccc}
\hline \hline
Stellar & $f12$ & $L12$ &...
...
\hline
\end{tabular}
\end{table*}
}
%
%-------------------------------------------------------------
%     For the online material, table longer than a single page
%                 In the preamble, use: \usepackage{longtable}
%       or for landscape option: \usepackage{longtable,lscape}
%-------------------------------------------------------------
\documentclass{aa}
\usepackage[varg]{txfonts}
\usepackage{graphicx}
\usepackage{longtable}

\begin{document}
text of the paper
% Table will be print automatically at the end, in the section Online material.
\onllongtab{3}{
\begin{longtable}{lrcrrrrrrrrl}
\caption{Line data and abundances ...}\\
\hline
\hline
Def & mol & Ion & $\lambda$ & $\chi$ & $\log gf$ & N & e &  rad & $\delta$ & $\delta$ 
red & References \\
\hline
\endfirsthead
\caption{Continued.} \\
\hline
Def & mol & Ion & $\lambda$ & $\chi$ & $\log gf$ & B & C &  rad & $\delta$ & $\delta$ 
red & References \\
\hline
\endhead
\hline
\endfoot
\hline
\endlastfoot
A & CH & 1 &3638 & 0.002 & $-$2.551 &  &  &  & $-$150 & 150 &  Jorgensen et al. (1996) \\                    
\end{longtable}
}% End onllongtab

% Or for landscape, large table:

\onllongtabL{3}{
\begin{landscape}
\begin{longtable}{lrcrrrrrrrrl}
...
\end{longtable}
\end{landscape}
}% End onllongtabL

1304.0833.extracted_bib
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