RSICC CODE PACKAGE PSR-612

**1. NAME AND TITLE**

ECIS-12: Coupled Channel, Statistical Model, Schrodinger and Dirac Equation, Dispersion Relation

**2. CONTRIBUTORS**

Service de Physique Theorique, Laboratoire de la Direction des Sciences de la Matiere du Commissariat a l'Energie Atomique, CE-Saclay, F-91190 Gif-sur-Yvette CEDEX, France through the Nuclear Energy Agency Data Bank, Issy-les-Moulineaux, France.

**3. CODING LANGUAGE AND
COMPUTER**

FORTRAN-90 (P612MNYCP00) (NEADB ID: NEA-0850/19).

**4. NATURE OF PROBLEM
SOLVED**

The ECIS code has been developed over a period of more the fifteen years, and several earlier versions exist. The statistical model part is based on ANLECIS, developed by P. Moldauer. There is no new formal report for ECIS06, but there is a “how to use” feature integrated into the program.

**ECIS-95** was
a generalization of ECIS-79: for the rotational model vibrational bands are
included. An option for solving the Dirac equation has been added. It also
contains the statistical model including width fluctuation corrections as
formulated by Peter Moldauer. While ECIS-94 is an update of ECIS-88 and
obsoletes that version, ECIS-79 is still a valid version. Besides the use of
Bessel expansion for form factors, the use of deformation lengths, and the use
of “symmetrized” Woods-Saxon potentials, it includes:

o two bound state transitions for particle-mode excitations with the possibility of the particle in the continuum

o expression of cross sections in terms of Legendre polynomials

o possibility of angular distribution for uncoupled states without giving explicity all the reduced nuclear matrix elements

o for Coulomb excitation, use of the magnetic multipole.

** ECIS03**
differed from previous version in the following features:

o The whole program was converted to double-precision.

o All FORMATS were converted from Hollerith notation into 'quotes' notation.

o In ECIS03 the dispersion relation as described by "C. Mahaux and R. Sartor in Nucl. Phys A528 (1991) 253", is added to the real potencial, (it is a generalisation of the dispersion relation as described in "C. Mahaux and R. Sartor, Nucl. Phys. A458 (1986) 25" already introduced in ECIS96 and 97).

** ECIS06** is primarily ECIS03 modified for the use of a
different relativistic 'reduced mass' in front of 'scalar' potentials,
differing from the one used in front of Coulomb potentials. It is the
application to coupled equations of the principles described in 'DWBA05'
announced in the Workshop 'Perspectives on Nuclear Data in the Next Decade', on
the 26-28/9/2005 at Bruyeres-le-Chatel, France. Some generalizations have been
introduced, in particular for the dispersion relation. ECIS06 contains the
following features:

o The Fortran source was updated to be compatible with current compilers.

o The LOG tables description has been updated.

o The re-start of a search parameter calculation by a different job was not possible. This new version fixes this problem.

o Automatic self-protecting features have been updated: in uninteresting situations, stop for low energy and external potential have been suppressed.

o Automatic self-protecting features have been updated: in uninteresting situations, stop for low energy and external potential have been suppressed.

o Automatic self-protecting features have been updated: in uninteresting situations, stop for low energy and external potential have been suppressed.

** ECIS12** - New version differs from previous version in the following
features:
The possibility to fold the potentials with a Gauss, a Yukawa, or a Woods-Saxon was
not verified in the ECIS codes after ECIS79. The purpose of ECIS12 is to verify it.
However, the concept of folding has been changed. In the previous versions, for the
standard input of potentials, there were three sets of parameters (for real potentials,
imaginary potentials and coulomb potentials), the choice was free for external input of
potentials. For spin-orbit interaction with the Schroedinger equation V(r), two functions
are needed, V1(r)=d/dr(V(r))/r and V2(r)=V(t)/r**2. In the previous versions, V1(r) and V2(r) where folded. In ECIS-12, only V(r) is.
Also, charge distribution and not coulomb potentials can be folded in ECIS-12. Computation of derivatives has been changed from point by point computation to direct derivation.
For standard input of potentials, one or eight sets of folding parameters can be set.
For external input of potentials, two new data are needed when they are given by points:
the line before radii and values

o Indication for spin-orbit potential if d/dr(V(r))/r is given,

o Indication for coulomb interaction if charge distribution or Coulomb potential is given.

**The address of each data is increased by one unit for each form factor read by
points. Only charge densities can be folded. Coulomb potential and interactions related to it should be
read in the same way.
**

**5. METHOD OF SOLUTION**

The ECIS method is designed to solve sets of coupled differential equations when the coupling terms are not too strong. The iteration technique searches for the one required solution among the many which are mathematically possible. The method supposes some ordering of the channels: first the ground state, then the state most strongly coupled to it. All channels must be coupled to some preceding one. The result of each iteration depends on this chosen order. If there is more than one equation related to the ground state the whole calculation must be repeated. The efficiency of the method is proportional to the ratio of the total number of equations to the number of those related to the ground state. The usual methods can also be used, but the iteration method is compulsory for spin-orbit deformation and Dirac formalism.

**6. RESTRICTIONS OR
LIMITATIONS**

None noted.

**7. TYPICAL RUNNING TIME**

CPU time requirements are very problem-dependent.

**8. COMPUTER HARDWARE
REQUIREMENTS**

Linux, Unix and Windows systems.

**9. COMPUTER SOFTWARE
REQUIREMENTS**

Fortran-90 source files included. Must have a functional FORTRAN compiler.

Pentium PC running Windows XP and with Lahey-Fujitsu lf95 v7.1

Pentium PC running Windows VISTA with Compaq Digital Visual Fortran 6.6C

Pentium PC running Ubuntu 7.04 with GNU Fortran 95 (GCC) 4.1.2

Pentium PC running Fedora 7 with 32-bit g77 3.4.6

AMD Opteron running Red Hat Enterprise Linux 4 with pgf95 vers 6.1-6

AMD Athlon running RedHat Linux 7.3(Valhalla) with Lahey-Fujitsu lf95 vL6.10a

**10. REFERENCES**

**10.a included in distribution files and in P227.pdf:**

J. Raynal, “Notes on ECIS94,” CEA-N-2772 (September 1994).

J. Raynal,
“ECIS96”, Proceedings of the Specialists' Meeting on the Nucleon
Nucleus Optical Model up to 200 MeV, 13-15 November 1996, Bruyères-le-Chatel, France

Publication 19 Nuclear Energy Agency, 1997 (p.159-166).

(http://www.nea.fr/html/science/om200/raynal.pdf)

J. Raynal, “DWBA05,” Workshop Perspectives on Nuclear Data in the Next Decade on the 26-28/9/2005 at Bruyeres-le-Chatel, France.

K. Amos, et al. and J. Raynal correspondence (Dec. 2003 to Jan. 2004).

J. Raynal, “Notes on ECIS94,” CEA-N-2772 (September 1994).

**11. CONTENTS OF CODE
PACKAGE**

The package is transmitted on one CD with the references cited above, and a zip file containing the source code and test output for supported systems.

**12. DATE OF ABSTRACT**

May 1986; revised August 1988, April 1995, January 1998, September 2007, April 2015

** KEYWORDS: ** NUCLEAR MODELS; DIFFERENTIAL EQUATIONS SOLVING; WORKSTATION;
MICROCOMPUTER.