(ftp://nt1.c.u-tokyo.ac.jp/hfs3/program/mom2alm.txt, 17/apr/96)
(history  17/nov/94,20/sep,22/dec/95,10/jan,17/apr/96)

Dear Users,

This document explains the usage of a fortran source code included in
a file named "mom2alm.for".  We request those who utilize the results
calculated with this code in their papers to cite our paper as:

    N. Tajima, S. Takahara, and N. Onishi, preprint UT-Komaba 96-9, 
    to be published in Nuclear Physics A.

This code computes the deformation parameters of a sharp-surface
uniform-density liquid drop which has the given multipole moments.
See the comments in the program for the explanation of the inputs and
the outputs.

The program has been made using the Mathematica.  As we have very
thoroughly checked the formulation, the coding, and the accuracy, we
think that the code is totally reliable within the scope of our
formulation.

          *          *          *          *          *          *

In the main program, the input values of q(1..7) are calculated from

      mass=138
      r.m.s. radius=5.0225d0
      q20  =  460.399775991802
      q22  = -2.57516134682126
      q40=1056.09d0
      q42=20.00d0
      q44=-156.81d0

For those who utilize a Cartesian-mesh Hartree-Fock+BCS code EV8
(Bonche et al, Nucl. Phys. A443 (1985) 39), we indicate in the
following in which part of the output file these input numbers can be
found:
--------------------------------------------------------------------(begin)---
 MASS   138.000000  CHARGE    66.000000  N    72.000000
 RT=  5.0225FM   RP=  5.0495FM   RN=  4.9976FM
    Q         X(FM2)      Y(FM2)      Z(FM2)     Q0(FM2)     GAMMA(DG)
 TOTAL       -739.886    -719.886    1459.772    1459.772      -0.000

         Y40          Y42          Y44    (QUANT. AXIS ALONG Z)
 T    1056.09        20.00      -156.81
----------------------------------------------------------------------(end)---
q20 and q22 can be calculated from
      qx=-739.886d0
      qy=-719.886d0
      qz=1459.772d0
using the relations of
      q20=qz*sqrt(5/(16*pi))
      q22=sqrt(5/(96*pi))*(qx-qy)


The output of the code will look like:
(with NeXT station turbo and absoft-f77)
----------------------------------------------------------------------(begin)-
q20  =  460.399775991802
q22  = -2.57516134682126
q40  =  1056.09000000000
q42  =  20.0000000000000
q44  = -156.810000000000
r^2  =  3481.11986250000
mass =  138.000000000000
a20  =  .328092024459405
a22  = -2.866740980512811E-003
a40  = -4.914769563969730E-002
a42  =  1.060330650216800E-003
a44  = -4.977246432709680E-003
rho0 =  .128921272507230
R0   =  6.29070625988450
------------------------------------------------------------------------(end)-

The above example is for the MASS deformation, but the deformation
parameters for only protons (neutrons) can be calculated by using the
moments of protons (neutrons). The mass number, too, has to be changed
to Z (N).

There is two additional comments on this program:

(1) This code does not fit to the standard fortran-77 grammer in the
sense that the number of continuation lines is greater than 20.  If
this code is not accepted by the fortran compiler which one uses, one
has to separate the lines so that each statement contains less than
twenty lines as follows:

From:
      Q(1)=a(1) + 0.3604475031457372*a(1)**2 +
     -  0.34104630662549*a(1)**3 +
     -  0.06518977483042678*a(1)**4 +
     -  0.00838227824213896*a(1)**5 -
     -  0.7208950062914744*a(2)**2

To:
      Q(1)=a(1) + 0.3604475031457372*a(1)**2 +
     -  0.34104630662549*a(1)**3 +
     -  0.06518977483042678*a(1)**4
      Q(1)=Q(1)+
     -  0.00838227824213896*a(1)**5 -
     -  0.7208950062914744*a(2)**2

(2) Real constants are not explicitly declared as double-precision.
If the compiler interprets "0.3604475031457372" as "0.3604475E+00",
one has to change all the real constants like
"0.3604475031457372" --> "0.3604475031457372D0".

(3) Q_{4,m} moments may be not-negligibly influenced by the shape of
the cavity (a rectangular box in the case of EV8).  If one encounters
this problem, one should use <r^2 Y_{4,m} > moments instead of
<r^4 Y_{4,m}> moments to calculate a_{l,m} parameters.  Although we
have also made a code for such calculations, the code has not been
completely tested and therefore cannot be transferred to other peolpe.

Inquiries:
------------------------------------------------------------------------
Institute of Physics,          |Naoki TAJIMA, Research Associate
College of Arts and Sciences,  |e-mail : tajima@nt1.c.u-tokyo.ac.jp
University of Tokyo, Komaba,   | phone : Japan-3-5454-6544
Meguro-ku, Tokyo, 153, Japan   | FAX   : Japan-3-3467-1281
------------------------------------------------------------------------

(end of ftp://nt1.c.u-tokyo.ac.jp/hfs3/program/mom2alm.txt)