NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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ECIS-12 | NEA-0850/19 | Tested | 17-DEC-2013 |

Machines used:

Package ID | Orig. computer | Test computer |
---|---|---|

NEA-0850/19 | Linux-based PC,PC Windows | PC Windows |

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3. DESCRIPTION OF PROBLEM OR FUNCTION

ECIS-79 uses a sequential iteration method for solving the coupled differential equations arising in nuclear model calculations. It also performs parameter searches to fit calculated results to experimental data. It can be used for a range of models, e.g. first or second order harmonic or anharmonic vibrational model, symmetric or asymmetric rotational model, with a similar range of interaction potentials. It includes spin-orbit deformation.

ECIS-95 is 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. Besides the use of Bessel expansion for form factors, the use of deformation lengths and the use of 'symmetrized' Woods-Saxon potentials, it includes:

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

- expression of cross sections in terms of Legendre polynomials

- possibility of angular distribution for uncoupled states without

giving explicitly all the reduced nuclear matrix elements

- for Coulomb excitation, use of the magnetic multipole.

ECIS-06 - New version differs from previous version in the following features:

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- The whole program was converted to double-precision

- 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 "MAHAUX, C. and SARTOR, R., Nucl. Phys. A458 (1986) 25" already introduced in ECIS96 and 97).

- Conversion of all FORMATS from Hollerith notation into 'quotes' notation.

ECIS-06:

- 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 generalisations have been introduced, in particular for the dispersion relation.

ECIS-12 - 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

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

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.

The constants used in the calculations have been updated according to CODATA 2010. http://physics.nist.gov/cuu/Constants/Table/allascii.txt

- atomic mass constant energy in MeV

CM=931.494061D0 instead of 931.4043D0 MEV/C**2

- Planck constant over 2 pi times c in MeV fm

CHB=197.3269718D0 instead of 197.326968D0 MEV FM

- inverse fine-structure constant

CZ=137.035999074D0 instead of 137.03599911D0 WITHOUT DIMENSION

but this change do not affect the results more than the use of different

compilers.

ECIS-79 uses a sequential iteration method for solving the coupled differential equations arising in nuclear model calculations. It also performs parameter searches to fit calculated results to experimental data. It can be used for a range of models, e.g. first or second order harmonic or anharmonic vibrational model, symmetric or asymmetric rotational model, with a similar range of interaction potentials. It includes spin-orbit deformation.

ECIS-95 is 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. Besides the use of Bessel expansion for form factors, the use of deformation lengths and the use of 'symmetrized' Woods-Saxon potentials, it includes:

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

- expression of cross sections in terms of Legendre polynomials

- possibility of angular distribution for uncoupled states without

giving explicitly all the reduced nuclear matrix elements

- for Coulomb excitation, use of the magnetic multipole.

ECIS-06 - New version differs from previous version in the following features:

-----------------------------------------------------------------------------

- The whole program was converted to double-precision

- 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 "MAHAUX, C. and SARTOR, R., Nucl. Phys. A458 (1986) 25" already introduced in ECIS96 and 97).

- Conversion of all FORMATS from Hollerith notation into 'quotes' notation.

ECIS-06:

- 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 generalisations have been introduced, in particular for the dispersion relation.

ECIS-12 - 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

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

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.

The constants used in the calculations have been updated according to CODATA 2010. http://physics.nist.gov/cuu/Constants/Table/allascii.txt

- atomic mass constant energy in MeV

CM=931.494061D0 instead of 931.4043D0 MEV/C**2

- Planck constant over 2 pi times c in MeV fm

CHB=197.3269718D0 instead of 197.326968D0 MEV FM

- inverse fine-structure constant

CZ=137.035999074D0 instead of 137.03599911D0 WITHOUT DIMENSION

but this change do not affect the results more than the use of different

compilers.

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4. 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.

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.

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10. REFERENCES

- J. Raynal:

'Spin-orbit transition interactions', Physical Review C (Nuclear Physics), Phys. Rev. C 71, 057602 (2005)

- J. Raynal:

Coupled Channel Formalism and ECIS Code.

Specialists'' Meeting on the Use of the Optical Model for the Calculation of Neutron Cross Sections Below 20 MeV, OECD/NEA 1986

(in French).

- J. M. Quesada, R. Capote, A. Molina, M. Lozano and J. Raynal:

"Analytical expressions for the dispersive contributions to the nucleon-nucleus optical potential", Physical Review C (Nuclear Physics), Phys. Rev. C 67, 067601 (2003) (3 pages)

- J. Raynal:

Aspects Geometriques des Reactions. CEA-N-1529 (1972)

- J. Raynal:

Optical-Model and Coupled-Channel Calculations in Nuclear Physics. 'International Atomic Energy Agency Report IAEA-SMR-9/8' pp. 281-322 (IAEA, Vienna, 1972) ICTP International Seminar Course: COMPUTING AS A LANGUAGE OF PHYSICS, Trieste, Italy, August 2-20 1971

- J. Raynal:

Spin-Orbit Interaction in Inelastic Nucleon Scattering. 'THE STRUCTURE OF NUCLEI' 'International Atomic Energy Agency Report IAEA-SMR-9/9' pp. 75-116 (IAEA, Vienna, 1972) International Course on Nuclear Theory: "THE STRUCTURE OF NUCLEI", Trieste, Italy, January 13-March 12 1971

- J. Raynal:

Recurrence Relations for Distorted-Wave Born Approximation Coulomb Exitation Integrals and their Use in Coupled Channel Calculations. Phys. Rev. C., Vol. 23, pp. 2571-2585 (June 1981)

- J. Raynal:

Notes on ECIS-79 (May 25, 1982).

- E. Sartori:

"Report on the International Nuclear Model Code Intercomparison: Coupled-Channel Model Study" January 1984 NEANDC-182A/INDC(NEA)3

- J. Raynal:

'Spin-orbit transition interactions', Physical Review C (Nuclear Physics), Phys. Rev. C 71, 057602 (2005)

- J. Raynal:

Coupled Channel Formalism and ECIS Code.

Specialists'' Meeting on the Use of the Optical Model for the Calculation of Neutron Cross Sections Below 20 MeV, OECD/NEA 1986

(in French).

- J. M. Quesada, R. Capote, A. Molina, M. Lozano and J. Raynal:

"Analytical expressions for the dispersive contributions to the nucleon-nucleus optical potential", Physical Review C (Nuclear Physics), Phys. Rev. C 67, 067601 (2003) (3 pages)

- J. Raynal:

Aspects Geometriques des Reactions. CEA-N-1529 (1972)

- J. Raynal:

Optical-Model and Coupled-Channel Calculations in Nuclear Physics. 'International Atomic Energy Agency Report IAEA-SMR-9/8' pp. 281-322 (IAEA, Vienna, 1972) ICTP International Seminar Course: COMPUTING AS A LANGUAGE OF PHYSICS, Trieste, Italy, August 2-20 1971

- J. Raynal:

Spin-Orbit Interaction in Inelastic Nucleon Scattering. 'THE STRUCTURE OF NUCLEI' 'International Atomic Energy Agency Report IAEA-SMR-9/9' pp. 75-116 (IAEA, Vienna, 1972) International Course on Nuclear Theory: "THE STRUCTURE OF NUCLEI", Trieste, Italy, January 13-March 12 1971

- J. Raynal:

Recurrence Relations for Distorted-Wave Born Approximation Coulomb Exitation Integrals and their Use in Coupled Channel Calculations. Phys. Rev. C., Vol. 23, pp. 2571-2585 (June 1981)

- J. Raynal:

Notes on ECIS-79 (May 25, 1982).

- E. Sartori:

"Report on the International Nuclear Model Code Intercomparison: Coupled-Channel Model Study" January 1984 NEANDC-182A/INDC(NEA)3

NEA-0850/19, included references:

- Jacques Raynal:NOTES ON ECIS94 (Note CEA-N-2772, Septembre 1994)

- Jacques Raynal:

NOTES ON ECIS95

- J. Raynal:

'ECIS96', Proceedings of the Specialists' Meeting on the Nucleon Nucleus

Optical Model up to 200 MeV, 13-15 November 1996, Bruyeres-le-Chatel, France

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

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

- Jacques Raynal:

An aberrant 'spin-orbit interaction' persists in the literature since more than

thirty years (arXiv:nucl-th/0312038 v2 15 Dec. 2003)

- K. Amos et al.:

Raynal's use of the word 'aberrant' appears more appropriate for his ECIS

formulation (arXiv:nucl-th/0401055 v1 27 Jan. 2004)

- Jacques Raynal:

Reply to K. Amos et al nucl-th/0401055 (arXiv:nucl-th/0407060 v2 27 Jul. 2004)

- J. Raynal:

'DWBA05'

Workshop 'Perspectives on Nuclear Data in the Next Decade', on the 26-28/9/2005

at Bruyeres-le-Chatel, France.

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NEA-0850/19

TESTED AT THE NEA DATABANK ON:- COMPUTER : Dell Precision Workstation 670,

Intel Xeon CPU 2.66GHz, 1024Kb

- OPERATING SYSTEM : Microsoft Windows XP Professional (5.1.2600)

- COMPILER : Lahey/Fujitsu Fortran 95 Compiler Release 5.50h

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NEA-0850/19

comment.txt Author's comments\dat\ Input data for sample problems

\doc\ Electronic documentation

\etim\ Source files

Keywords: coupled channel theory, differential equations, nuclear models, statistical models.