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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Title page
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\bc
{V o l k s w a g e n \ \ F o u n d a t i o n}
\vspace{3.5cm}

{\Large          Annual report on the cooperation project}\\[1.5cm]

{\Large\bf         Light scattering by small particles:\\[1cm]

                   new methods and techniques}\\[2cm]
\ec

\bc{\it August 1, 1998}\ec
\vspace{3cm}

\noi{{\bf Project head:}\\
Prof. Dr. Th. Henning (Jena)
}\\ \\ \\

\noi{{\bf Participants:}\\
Astrophysical Institute and University Observatory, Jena, Germany \\
Astronomical Institute of St.~Petersburg University, St.~Petersburg, Russia \\
Physical Institute of St.~Petersburg University, St.~Petersburg, Russia \\
St.~Petersburg University of Aerocosmic Instrumentation, St.~Petersburg, Russia
 }


\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TOC page
\bigskip
\bc{\large\bf         Table of content} \ec

\bigskip
\begin{itemize}
\item Research activity \dotfill ~3
\begin{itemize}
\item[ ] A. Light scattering theory \dotfill ~3
\begin{enumerate}
\item[\ ]  1. New numerical code for separation of variables method \dotfill ~3
\item[\ ]  2. New method and  numerical code for axisymmetric particles \dotfill ~3
\item[\ ]  3. Comparison of different methods \dotfill ~4
\end{enumerate}
\item[ ] B. Database of optical constants \dotfill ~5
\item[ ] C. Astrophysical applications \dotfill ~6
\item[ ] D. Conclusions \dotfill ~8
\end{itemize}
\item Visit activity \dotfill ~9
\item Literature and hardware purchasing \dotfill 10
\item Software development contracts \dotfill 11
\item List of the Attached Documents \dotfill 13
\end{itemize}

\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Research Activities
\bc {\large\bf Research activity }\ec

\bigskip
The project includes research activity in three directions:
{\bf light scattering theory, laboratory data analysis}, and
{\bf scientific applications} of the theory.
 Below, we briefly outline the work done in each direction
during the first year (the text is given by italics).
 After that the main results obtained are described in more detail.

\bigskip
%========================================
{\underline{\sf A. Light scattering theory}}

\smallskip
{\it
A sophisticated approach to calculate the spheroidal wave functions was
developed. It has revived the basic method of the light scattering theory --
the separation of variables method. The computer code written allows to
treat the light scattering by very large layered
and highly absorbing spheroidal particles.

An advanced method for axisymmetric particles was created. It involves
the ideas of the separation of variables and T-matrix methods and is based
on a superposition of special scalar potentials: those for spheres and
those for cylinders. The method is most efficient for
particles whose shape essentially deviates from the spherical one.

A comparative analysis of different approaches to calculations of the
scattering properties of spheroids was performed.
 We have also determined the area of the
exact and approximate approaches' applicability and
discussed the main features of the light scattering by absorbing spheroids.
}

\medskip
%----------------------------------------
{\bf 1. New  numerical code for separation of variables method}

\smallskip
A computer code basing on the separation of variables method (SVM) for
spheroids and involving different approaches to calculate the spheroidal
prolate and oblate wave functions was developed.
 The approaches include the expansions of the functions
in terms of the Legendre functions or the Bessel functions, and
numerical solution of the specific differential equation.
 An advanced method for calculation of the eigenvalues of the spheroidal
functions was also numerically realized.

 The results were the subroutines to derive the
eigenvalues and the expansion coefficients of the spheroidal wave functions
and the radial spheroidal prolate and oblate functions of the first
and second kinds and their first derivatives.
 Test calculations were performed for the
functions with the complex size parameter $|c| \leq$~100 and various shape
parameters corresponding to particles close to spheres or to
needles and disks.

 Different criteria to control the accuracy of the calculations were
developed and applied during the work.
 The best approach for given parameter values was determined.

 More details can be found in the Final Report on
the software contract ``Numerical Treatment of Spheroidal Wave Functions"
(see the Attached Document \#1).

%\newpage
\medskip
%----------------------------------------
{\bf 2. New method and numerical code for axisymmetric particles}

\smallskip
A new solution to the light
scattering problem for homogeneous axisymmetric particles
was developed.
 It is as efficient as the standard T-matrix method (TMM) but does not
have its main defect which is the inability to treat the
particles with a relatively strong non-sphericity.

 We formulated the diffraction problem in the
form of the surface integral equations and spherical
wave function were used as the basic ones. However, unlike in the
conventional TMM, the incident, scattered and internal electromagnetic
fields were divided in two parts: the axisymmetric part (no dependence
on the azimuthal angle) and the non-axisymmetric part. The diffraction
problem was solved independently for each of the parts. Specific
scalar potentials were selected: a superposition of the Debye and
Hertz potentials for the non-axisymmetric part and the Abraham
potentials for the axisymmetric one.

 The new method allows to consider layered particles with
a non-trivial structure (e.g., particles with an oblate spheroid
as a core and a prolate spheroid as a mantle, which is impossible
in the SVM).

 We have created a computer code in Fortran realizing this
new theoretical approach.
 Test calculations have been made for dielectric and absorbing
spheres of various sizes and prolate and oblate spheroids of different
aspect ratios and sizes. The computations showed the high accuracy
and a wide range of applicability of the code.

 A comparison with the standard TMM codes of Barber \& Hill
(Light Scattering by Particles: Computational Methods,
World Science, Singapore 1990)
and Mishchenko (Appl. Optics, 32, 4652, 1993) has shown that our code is
only slightly slower than these codes but can treat
much larger particles in the case of spheroids of large
aspect ratios. All the problems of our code
revealed during this testing were found to be common to
all the codes based on the T-matrix method.

 Some original improvements of our code have been made
to increase its speed, and
the code has been used in the calculations described below in Sect.~4.

 A part of the code was written in the special program language
C++ for calculating with high or even arbitrary precision
(the loss of accuracy in computer operations basically restricts
the applicability of the TMM method).
 The subroutines calculating the spherical functions with about
100 significant digits have been carefully tested.
 They were found to be fast enough to be involved
in extensive calculations. Other program blocks
(inversion of matrix, surface integrals, etc.) are on the stage of
testing and improvement.

The complete formalism
of the new method %(and a brief description of the codes)
is presented in the Attached Document \#2
-- the paper prepared for publication in
``Optics and Spectroscopy'' (the paper is in Russian since
this international journal is
printed in Russia; English version of journal is printed in USA).

\medskip
%----------------------------------------
{\bf 3. Comparison of different methods}

\smallskip
 We have performed extensive calculations of the optical properties
of prolate and oblate spheroids of different sizes, aspect ratios,
chemical compositions. Various codes including those
developed within the project were utilized.
 The final results of the calculations are presented
in the form of three-dimensional graphics: maximum diffraction parameter
reachable vs aspect ratio vs refractive index.
 They will be presented in a paper prepared for publication.
 A part of the results obtained were interesting enough to be published
in separate papers.
 These papers have been completed
and their content is briefly described below.

1). We studied in detail the optical properties of
absorbing spheroids of soot, graphite, iron (their consideration was absent
in the literature).
 The shape/size effects in extinction and polarization of radiation
by such particles were revealed.
 Namely, we found that extinction by spheroids is normally about 2
times larger than that by spheres of the equal volume. The albedo of
non-spherical particles rather slightly depends on their shape.
Large spheroidal particles independent of their aspect ratio
do not polarize the transmitted radiation.

The results of the work are presented in the paper to be submitted
to the Journal of Quantitative Spectroscopy \& Radiative Transfer
(see the Attached Document \#3).
Some cross-sections obtained with high accuracy (7 significant digits)
by different methods
are given in the paper in tabular form to serve as benchmarks.

2). We have considered different approximations for light scattering by
small spheroids.
 Formulae for the quasistatic approximation for such particles were
obtained.
 The range of the formulae applicability was estimated
on the base of special calculations.
 The approximate approach was also compared with the
well-know Rayleigh approximation.
 All the results are described in the paper submitted
to ``Optics and Spectroscopy''.

\bigskip
%========================================
{\underline{\sf B. Database of optical constants}}

\smallskip
{\it
The database created contains references to the papers,
data files and links to the Internet resources related to
measurements and calculations of the optical constants
of different silicates, ices, oxides, sulfides, carbides,
carbonaceous species from amorphous carbon to graphite and diamonds,
etc.
 The database has free access via Internet
{\it http://www.astro.uni-jena.de/Users/database/entry.html}.
}

\medskip
The main topics of the database are the optical constants
of materials involved in calculations in astronomy and optics of
the Earth atmosphere.
 These materials are:
different kinds of amorphous/glassy/crystalline
terrestrial/solar-system/artificial silicates;
crystalline/fused quartz; % (SiO, SiO$_2$)
metals (Fe, Mg, etc.);
oxides (FeO, Fe$_2$O$_3$, Fe$_3$O$_4$, MgO, Al$_2$O$_3$, SiO);
sulfides (FeS, MgS, SiS$_2$);
carbides (SiC, TiC);
carbonaceous species (amorphous carbon, glassy carbon,
 hydrogenated amorphous carbon,
   coals, graphite, diamonds);
organics (tholin, kerogen, ``organic refractory");
H$_2$O, CO, CO$_2$, NH$_3$, CH$_3$OH and other ices.
 The database includes the references to the papers,
data files and links to the Internet resources.

 The database gives more than 300
(as many as we could find in the literature from the 50s till 1998)
references to the papers, books, dissertations
where the refractive index,
reflectance, transmittance, mass absorption coefficient, and so on
were derived.
 All together we have comprised about 80\% of such papers.
For many of them we have now hard copies.

 The data we included are in both tabular and graphic forms
and used to be supplied with an information on
how the data were obtained,
what equipment was used and
what samples were considered.
 The data are given in their initial format (table or figure)
and in our standard format (table) and supplied with the plots:
refractive index vs wavelength and dielectric permittivity vs energy.
 The service codes in the database allow
to transfer the data from our standard format to a desirable form
(refractive index or dielectric permittivity vs wavelength, wavenumber
or energy).
 Our scattering codes (Mie theory code, SVM code, etc.) give possibility
quickly to transform the data into the cross-sections, emissivity, and
so on.

 We included in the database
references to some general books and reviews on the subject
and links to Internet collections of optical data files and
the personal WWW pages with related software.
 Among these resources one should mention
the WWW database of the optical constants in the X-ray domain and
the collections of the original data files for
ices, carbonaceous species, and water.
 There are also useful tools of the Kramers-Kronig analysis
and the Effective Medium Theory.
 Two general lists of light scattering codes are available in WWW.
Besides their addresses,
we also give direct links to personal WWW pages where one can find
most popular codes to simulate the electromagnetic radiation scattering
by spheres (Mie theory), spheroids (Separation of Variables Method),
axisymmetric particles (T-matrix Method),
irregular-shaped particles (Discrete Dipole Approximation) and others.
%as well as some useful approximate formula.

In more detail the database is described in the paper to be
submitted to Astronomy \& Astrophysics Supplement
(the Attached Document \#6) and the Final Report on
the software contract ``Database of Optical Constants"
(the Attached Document \#5).
 One can also freely
access the database via anonymous FTP or World Wide Web.

\bigskip
%========================================
{\underline{\sf C. Astrophysical applications}}

\smallskip
{\it
The codes created within the project
have been used to obtain new knowledge
on the properties of interstellar dust grains
from the analysis of recent polarimetric and photometric
observations.
 Namely, we have developed a new spheroidal model to interpret
the interstellar polarization observed in the optical and infrared
spectral regions.
 The effects of the chemical composition of interstellar dust grains
were considered and the composition was constrained.
 Former estimates of the size
distribution of the grains were strongly criticized.
 The ratio of the starlight polarization degrees
in the visual and the infrared silicate band if observed
was shown to be a good possible test of existing models of
interstellar grains.

 Besides that, we have also considered the accuracy of
the commonly used Rayleigh approximation for coated spheroids
in the interpretation of the interstellar
extinction and polarization observed
in the infrared ($\lambda =$ 2.5--25 \mkm).
}

\medskip
1). In contrast to calculations of interstellar polarization
by other authors, we used a more realistic shape of the
particles, namely a distribution of spheroids.
 As a reference model, we started with the well-known
 model of Mathis et al. (Astrophys. J., 217, 425, 1977).
 The irregular shape of interstellar grains
and their possible shape distribution were simulated by a
semiaxes ratio distribution of both prolate and oblate spheroids.

 The interstellar extinction and polarization curves
in the visual and infrared wavelength regions were calculated and
compared with observations.
 It was found that the shape distribution rather weakly affected
the polarization curve in
comparison with possible variations of other model parameters
(e.g. the size of the grains).
 The shape of the polarization curve is mainly determined by the
oblate spheroids.
 This curve is always narrower than the observed curve.
Adding a fraction of prolate spheroids only
broadens the polarization curves at their blue wings.
 The larger the fraction is, the wider the curve is.
 Prolate spheroids alone can produce the polarization curve
nearly as wide as observed.
 However, we cannot adopt this as an argument in favour of
a prolate (on average) shape of interstellar grains
because the polarization curves for these particles are  blueshifted
compared with observed curves.

In the near infrared, spheroids produce a decrease
of the polarization with wavelength ($P_\lambda \sim \lambda^{-\beta}$,
where $\beta \approx$ 3--4) which is too steep compared
with observations ($\beta \approx$ 1.8--2).
 We discuss how ``dirtiness'' of silicates (different iron content
and/or absorbing inclusions) can affect the polarization
in this spectral region.
 It is found that only a very large (12--15\% by volume)
admixture of magnetite (Fe$_3$O$_4$)
can explain the observed  $P_\lambda$ law without
contradicting other observational constraints.

We also model the interstellar polarization in the infrared silicate bands
and show that the ratio of the polarization strength in the bands to that
in the visual could be used to constrain interstellar dust models.

For more details of this research, we refer to our paper submitted
to the Astronomy \& Astrophysics (see the Attached Document \#7).

\medskip
2). Calculations of the extinction and polarization in the
wavelength range from 2.5 to 25 \mkm \, were performed
for silicate core/icy mantle spheroidal particles using
the SVM code and the Rayleigh approximation.
 It was found that the approximation
gave wrong results (errors strongly exceed 10\%) for
the particles whose size was larger than 0.1 \mkm.
 Thus, as the size of interstellar dust grains is much larger
than 0.1 \mkm,
 the common use of the approximation to  interpret
 the observations of the infrared bands must lead to
inappropriate conclusions concerning the properties of
dust grains in the interstellar medium.

In more details the results are given in the paper
submitted to the Astronomy \& Astrophysics
(see the Attached Document \#8).

\bigskip
\bigskip
%========================================
{\underline{\sf D. Conclusions}}

\medskip
The main results of the work on the project during the first year
are as follows:
\begin{itemize}

\item an efficient numerical code based on the separation of variables method;

\item a new method and computer code for the calculation of the optical
properties of axisymmetric particles;

\item a comparative review of the current approaches to treat the light
scattering by non-spherical particles;

\item a database with optical constants of various materials that is available
via Internet (anonymous FTP, World Wide Web);

\item new knowledge on the properties of interstellar dust grains from the
analysis of recent observations.

\end{itemize}
Thus, nearly a half of the planned results declared in our
proposal have been obtained during the first year.

\medskip
There were only small changes in the initial work plan,
and the work in all 6 planned directions is in progress.
 The work on the project in general follows the initial timetable.
 An exception is the writing of a few papers proposed for the first year
and shifted to the second year.
 On the other hand, the creation
of the codes realizing the new approach for axisymmetric particles and
the code for the new statistical method planned for the second year
has been nearly finished in the first year.

\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Visit Activities
\bc {\large\bf Visit activity }\ec

\bigskip
There were 4 visits during the first year of the project.

\medskip
{\bf Prof. Th.~Henning, the head of the project,
visited St.~Petersburg for 1 week in October, 1997.}
 He met all project participants from the Russian side and
had extensive discussions with them. As a result the tasks
to be solved were outlined and intermediate steps in their solution were
stated.
 Prof. Th.~Henning also gave a talk at the Astronomical Institute of the
St.~Petersburg University. A joint paper (together Dr. V.B.~Il'in)
within the project topics was completed and sent to
the Astronomy \& Astrophysics journal.

\medskip
{\bf Prof. N.V.~Voshchinnikov visited Jena twice
for a week in October, 1997 and for 1.5 month in January--February, 1998.}
 He had discussions with German participants of the project as well as
with some experts at the Jena University, namely
Dr.~B.~Michel (light scattering),
Dr.~O.~Fischer (astronomical polarimetry),
Dr.~Ch.~Friedemann (circumstellar dust),
and others.
 Prof. N.V.~Voshchinnikov gave a talk at the Jena University on the
light scattering methods.  He also performed extensive calculations
which became a basis
of the joint paper (see the Attached Document \#3) and discussed
the results with the coauthors in Jena.

\medskip
{\bf Dr. N.A.~Krivova visited Jena for 1 month in January--February, 1998.}
 She installed the Database of Optical Constants
created by the Russian side on the server of the Astronomical
Institute of the Jena University.
 After the installation, the content and design of the Database were discussed
with different experts at the Jena University
and suggested improvements were made.
 She was also searching in the scientific libraries in Jena
for more papers and data to be included in the Database and
coping the papers
published in the journals currently not available in St.~Petersburg.
Data in some selected papers (tables and figures with data)
were scanned.
% Some time was devoted to a consideration of astrophysical applications.

\medskip
It should be mentioned that for valid causes
some planned visits of the Russian scientists
(Prof. V.G.~Farafonov, Dr. V.B.~Il'in, Prof. L.S.~Ivlev)
to Jena did not occur during the first year, and
these visits were shifted to the second year.

\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Literature and Software Purch.
\bc {\large\bf Literature and hardware purchasing }\ec

\bigskip
The following books have been purchased for
the Russian side:

\medskip
\noi Polarimetry of the Interstellar Medium,  Whittet D.C.B., Roberge W.G. (eds.),

ASP Conf. Ser., Vol. 96, 1996 \dotfill \$59\\
Annual Review of Astronomy and Astrophysics, Vol. 34, 1996 \dotfill \$70\\
Annual Review of Astronomy and Astrophysics, Vol. 33, 1995 \dotfill \$65\\
Annual Review of Astronomy and Astrophysics, Vol. 32, 1994 \dotfill \$65\\
Annual Review of Astronomy and Astrophysics, Vol. 31, 1993 \dotfill \$62\\
Annual Review of Astronomy and Astrophysics, Vol. 30, 1992 \dotfill \$62\\
Annual Review of Astronomy and Astrophysics, Vol. 29, 1991 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 28, 1990 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 27, 1989 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 25, 1987 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 24, 1986 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 23, 1985 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 22, 1984 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 21, 1983 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 20, 1982 \dotfill \$58\\
Annual Review of Astronomy and Astrophysics, Vol. 19, 1981 \dotfill \$58\\
TOTAL SUM \dotfill 2112,34 DM

\medskip
\bigskip
The following hardware has been purchased for
the Russian side and delivered to St.~Petersburg:

\medskip
\noi
Mainboard ChainTech 5TDM2 PCI 512KB Pipelined Burst Cache (in duplicate) \\
Intel Pentium Processor 166 MHz MMX (in duplicate)\\
Memory 32 MB SIMM EDO (in duplicate)\\
Graphic Card S3 Trio 64 V2/DX PCI 2 MB (in duplicate)\\
TOTAL SUM \dotfill  1981,45 DM

\bigskip
It should be noted that these blocks of personal computers
were necessary to upgrade two old computers at the
Russian Institutes that were required for efficient work on the project.
 The planned purchase of a big personal computer was postponed
(shifted to the second year).
 The reason is that the Russian dealer of the IBM corporation
selected for this operation had become a bankrupt
in the beginning of 1998 and an extra time was spent
to find a new partner.

\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Software Contracts
\bc {\large\bf Software development contracts }\ec

\bigskip
There were three contracts for developing special
software by Russian programers.
 These contracts have the titles:
{\bf ``Numerical Treatment of Spheroidal Wave Functions",
      ``WWW Database of Optical Constants"}, and
{\bf  ``Computer Codes for Separation of Variables Method and
      TMM-method"}.
 The work within the first two contracts has been completed, while
the activity within the third contract is in progress.
 Here we summarize the main results obtained.

\medskip
{\bf 1. Numerical Treatment of Spheroidal Wave Functions}

 The subroutines to calculate the spheroidal
prolate and oblate wave functions using different approaches
were created.
 The approaches are the standard expansions of spheroidal functions
in terms of Legendre functions, or Bessel functions, and
numerical solution of the specific differential equation.
 An automatic choice of the best approach for given values of the
parameters is incorporated.
 The procedures developed allow to compute the
eigenvalues and the expansion coefficients of the spheroidal wave functions
and the radial spheroidal prolate and oblate functions of the first
and second kinds and their first derivatives.

 The work within the contract was completed and the Final Report
is enclosed (see Attached Document \#1).
 The complete procedures in Fortran 77 with extensive documentation and
test cases both as hard copies and in computer readable form
were delivered from the group of Russian programers to the head
of the project on October 30, 1997.

\medskip
{\bf 2. WWW Database of Optical Constants}

Efficient WWW database with presentation of the data in graphical and
tabular forms, additional tools for data conversion in different
wavelength/frequency/wavenumber scales, and Mie and SVM light scattering
codes for calculations of absorption and scattering efficiencies
was developed.
 The database contains about 150 files with the optical constants
of different materials and about 40 HTML pages to allow the access to
the database via Internet.

 The work within the contract was completed and the Final Report
is enclosed (see Attached Document \#5).
 The database has been installed at the server of the Astronomical
Institute of the Jena University and carefully tested.

\medskip
{\bf 3. Computer Codes for Separation of Variables Method and TMM-method}

New version of numerical codes based on the Separation of Variables Method (SVM)
for homogeneous and core-mantle spheroids was written
using the methods of calculations of spheroidal functions developed
in the project.
 These codes include switching on an optimal approach for given
parameter values and allow to calculate the optical properties
(scattering matrix and different cross-sections) for large non-spherical
inhomogeneous particles.

 Numerical code realizing the new approach for axisymmetric particles
based on the T-Matrix Method was written and tested for spherical
particles and prolate and oblate spheroids. It includes the
calculations of the  spherical wave functions of very large orders and
size parameters, the calculations of integrals of products of spherical
functions and the iterative method of the solution of the algebraic
systems with the corresponding tests.

Parts of the codes were written
using the special programming language C++ and
involving a non-standard (very high or arbitrary) length of numbers.

The work on this contract is in progress.
The created codes are testing and improving in their speed and efficiency.
%Complete computer codes in C++ with extensive documentation and test
%cases both as hard copies and in computer readable form.
The contract finishes on September 30, 1998.


\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% List of Attached Documents
\bc {\large\bf List of the Attached Documents }\ec

\bigskip
%...

\begin{enumerate}

\item[\#1] Final report on the software contract
      ``Numerical Treatment of Spheroidal Wave Functions".

\item[\#2] Paper of V.G.~Farafonov
       ``New method of calculations of light scattering by
       dielectric axisymmetric particles"
       prepared for publication in
       ``Optics and Spectroscopy'' which is the international journal edited
       in Russia.

\item[\#3] Paper of
      N.V.~Voshchinnikov, V.B.~Il'in, Th.~Henning, B.~Michel, V.G.~Farafonov
      ``Extinction and Polarization of Radiation by Absorbing
      Spheroids: Shape/Size Effects and Some Benchmarks"
      submitted to the Journal of Quantitative Spectroscopy \&
      Radiative Transfer.

\item[\#4] Paper of
      N.V.~Voshchinnikov, V.G.~Farafonov
      ``On Applicability of Quasistatic and Ray\-leigh Approximations
      for Spheroidal Particles" (in Russian)
      submitted to ``Optics and Spectroscopy''.

\item[\#5] Final report on the software contract
      ``WWW Database of Optical Constants".

\item[\#6] Paper of
      Th.~Henning, V.B.~Il'in, N.A.~Krivova, B.~Michel, N.V.~Voshchinnikov
      ``WWW Database on Optical Constants for Astronomy"
      submitted to Astronomy \& Astrophysics Supplement.

\item[\#7] Paper of
      V.B.~Il'in, Th.~Henning
      ``Modeling of Optical and Infrared Interstellar Polarization with
      Spheroidal Particles"
      submitted to Astronomy \& Astrophysics.

\item[\#8] Paper of
      V.V.~Somsikov, N.V.~Voshchinnikov
      ``On the Applicability of the Rayleigh Approximation for
      Coated Spheroids in the Near-Infrared"
      submitted to Astronomy \& Astrophysics.

\end{enumerate}

\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

