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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CERBERO | NEA-0648/01 | Tested | 22-SEP-1981 |

Machines used:

Package ID | Orig. computer | Test computer |
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NEA-0648/01 | IBM 3033 | IBM 3033 |

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3. DESCRIPTION OF PROBLEM OR FUNCTION

The CERBERO-3 code calculates a complete consistent set of binary cross sections, on the basis of the nuclear optical model and of the nuclear statistical model, for incident particles with spin 0 and 1/2. Neutron, proton, alpha particle and gamma-ray competitions can be considered. The present program is designed for use in the incident particle energy region where it may be assumed that shape elastic scattering and compound nucleus absorption are predominant, so that compound nucleus trans- mission coefficients are those of the optical model and the absorp- tion cross section is equivalent to the compound nucleus cross section. The program outputs are the total and compound nucleus cross sections, the shape elastic differential and integrated cross sections, the differential and integrated fluctuation cross sections for the excitation of discrete levels, the differential and inte- grated elastic cross sections, the continuum level excitation func- tions, the total inelastic scattering cross section and the capture cross section.

The CERBERO-3 code calculates a complete consistent set of binary cross sections, on the basis of the nuclear optical model and of the nuclear statistical model, for incident particles with spin 0 and 1/2. Neutron, proton, alpha particle and gamma-ray competitions can be considered. The present program is designed for use in the incident particle energy region where it may be assumed that shape elastic scattering and compound nucleus absorption are predominant, so that compound nucleus trans- mission coefficients are those of the optical model and the absorp- tion cross section is equivalent to the compound nucleus cross section. The program outputs are the total and compound nucleus cross sections, the shape elastic differential and integrated cross sections, the differential and integrated fluctuation cross sections for the excitation of discrete levels, the differential and inte- grated elastic cross sections, the continuum level excitation func- tions, the total inelastic scattering cross section and the capture cross section.

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4. METHOD OF SOLUTION

Only spherical local potentials are allowed.

The scattering amplitudes and the other optical model quantities as well as the shape elastic and compound nucleus cross sections are calculated in accordance with the above described optical model potentials, by the usual methods.

The total cross section is given as the sum of the shape elastic and compound nucleus cross sections.

The integrated and differential cross sections for compound nucleus processes may be given according to the three following approxi- mations:

1. The Hauser-Feshbach theory.

2. The Hauser-Feshbach theory corrected by the width fluctuation effect.

3. The Moldauer theory.

Integrated capture cross sections are given according to the various approximations 1, 2, 3 as a difference between the total compound nucleus cross section and the sum of the cross sections for compound elastic and all possible inelastic processes. Therefore for the purpose of capture cross section calculations, the program should be used only as long as the ratio of the total radiative width to the capture width is roughly unity.

Whenever direct processes may be considered unimportant, the CERBERO program can work up to the threshold for the second particle emis- sion.

All cross sections are calculated in the c.m.s. and are given in barns.

Only spherical local potentials are allowed.

The scattering amplitudes and the other optical model quantities as well as the shape elastic and compound nucleus cross sections are calculated in accordance with the above described optical model potentials, by the usual methods.

The total cross section is given as the sum of the shape elastic and compound nucleus cross sections.

The integrated and differential cross sections for compound nucleus processes may be given according to the three following approxi- mations:

1. The Hauser-Feshbach theory.

2. The Hauser-Feshbach theory corrected by the width fluctuation effect.

3. The Moldauer theory.

Integrated capture cross sections are given according to the various approximations 1, 2, 3 as a difference between the total compound nucleus cross section and the sum of the cross sections for compound elastic and all possible inelastic processes. Therefore for the purpose of capture cross section calculations, the program should be used only as long as the ratio of the total radiative width to the capture width is roughly unity.

Whenever direct processes may be considered unimportant, the CERBERO program can work up to the threshold for the second particle emis- sion.

All cross sections are calculated in the c.m.s. and are given in barns.

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7. UNUSUAL FEATURES OF THE PROGRAM

a. Optical model particle transmission coefficients are calculated according to a spherical optical model.

Optical model parameter sets can be given in input or selected by means of acronyms out of a library available internally to the code.

b. The correction for the width fluctuations has been introduced into channels leading both to discrete and to continuum level excitation.

c. Composite level density like Gilbert-Cameron is used but with constant in spin distribution K = .146, when not given in input. For low lying levels between Ecut and U(x), sigma(E)**2 is auto- matically interpolated between sigma(LEVELS)**2 and sigma(U(x))**2 = K.SQRT(aU(x)).exp(A,2/3). The value

sigma(LEVELS)**2 is obtained by maximum likelihood method to fit known discrete levels distribution.

Sigma(LEVELS)**2 is calculated by the code on the basis of adop- ted level for each nucleus involved. Alternatively sigma(LEVELS)**2 can also be given in input, in those particu- lar nuclei where additional information is known above Ecut, as far as spin attribution is concerned.

d. Optionally a parity distribution p(pi)=exp(AE+B) according to ref. 1 can also be assumed provided A and B are given in input.

e. Gamma-ray transmission coefficients are calculated according to one or two Lorentzian curves for the E1 photoabsorption cross sections. Peak energy, half maximum width, peak cross section must be given in input for the E1 giant resonance.

The resulting total radiative width is spin and parity depen- dent. In principle it should not be normalized because the model proved to work satisfactorily. For the purpose of evalua- tion a normalization constant N (J and pi independent) can be given in input.

f. Q values are calculated from recent mass excess tables (internal to the code) provided by Wapstra in 1978 as a private communica- tion.

g. i) The output are average resonance parameters like strength functions (from adopted optical model), radiative width and mean observed level spacing.

ii) Angular distributions are given for compound, shape and total elastic. Total cross section and primary spectra are given for all involved particle and gamma-ray emis- sions.

Compound nucleus and total cross section from optical model are given at the end together with the percentual differ- ence between compound nucleus cross section and the sum of the contribution of all channels via compound nucleus re- action mechanism.

a. Optical model particle transmission coefficients are calculated according to a spherical optical model.

Optical model parameter sets can be given in input or selected by means of acronyms out of a library available internally to the code.

b. The correction for the width fluctuations has been introduced into channels leading both to discrete and to continuum level excitation.

c. Composite level density like Gilbert-Cameron is used but with constant in spin distribution K = .146, when not given in input. For low lying levels between Ecut and U(x), sigma(E)**2 is auto- matically interpolated between sigma(LEVELS)**2 and sigma(U(x))**2 = K.SQRT(aU(x)).exp(A,2/3). The value

sigma(LEVELS)**2 is obtained by maximum likelihood method to fit known discrete levels distribution.

Sigma(LEVELS)**2 is calculated by the code on the basis of adop- ted level for each nucleus involved. Alternatively sigma(LEVELS)**2 can also be given in input, in those particu- lar nuclei where additional information is known above Ecut, as far as spin attribution is concerned.

d. Optionally a parity distribution p(pi)=exp(AE+B) according to ref. 1 can also be assumed provided A and B are given in input.

e. Gamma-ray transmission coefficients are calculated according to one or two Lorentzian curves for the E1 photoabsorption cross sections. Peak energy, half maximum width, peak cross section must be given in input for the E1 giant resonance.

The resulting total radiative width is spin and parity depen- dent. In principle it should not be normalized because the model proved to work satisfactorily. For the purpose of evalua- tion a normalization constant N (J and pi independent) can be given in input.

f. Q values are calculated from recent mass excess tables (internal to the code) provided by Wapstra in 1978 as a private communica- tion.

g. i) The output are average resonance parameters like strength functions (from adopted optical model), radiative width and mean observed level spacing.

ii) Angular distributions are given for compound, shape and total elastic. Total cross section and primary spectra are given for all involved particle and gamma-ray emis- sions.

Compound nucleus and total cross section from optical model are given at the end together with the percentual differ- ence between compound nucleus cross section and the sum of the contribution of all channels via compound nucleus re- action mechanism.

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10. REFERENCES

- G. Reffo:

"Theory and Application of Moment Methods in Many Fermion Systems" p. 167, edited by B.J. Dalton, S.M. Grimes, J.P. Vary, S.A.

Williams - Plenum 1980.

- G. Reffo, F. Fabbri:

N.S.E. 66, 251 (1978).

- For Optical Model Potential Calculations see for example D.T.

Goldmann and C. L. Lubitz

KAPL-2163 (1961).

- G. Reffo:

"Theory and Application of Moment Methods in Many Fermion Systems" p. 167, edited by B.J. Dalton, S.M. Grimes, J.P. Vary, S.A.

Williams - Plenum 1980.

- G. Reffo, F. Fabbri:

N.S.E. 66, 251 (1978).

- For Optical Model Potential Calculations see for example D.T.

Goldmann and C. L. Lubitz

KAPL-2163 (1961).

NEA-0648/01, included references:

- A. Prince, G. Reffo, E. Sartori:"Report on the International Nuclear Model Code Intercomparison,

Spherical Optical and Statistical Model Study", October 1983

NEANDC/INDC(NEA)4

- F. Fabbri, G. Fratamico, G. Reffo:

CERBERO 2: Improved version of the CERBERO computer code for

calculation of nuclear reaction cross sections

CNEN - RT/FI(77)6 (April 1977)

- F. Fabbri, G. Reffo:

CERBERO - A FORTRAN programme for the calculation of nuclear

reaction cross sections

CNEN - RT/FI(74)36 (August 1974)

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NEA-0648/01

File name | File description | Records |
---|---|---|

NEA0648_01.001 | CERBERO SOURCE F4 | 3375 |

NEA0648_01.002 | TODAY DUMMY ROUTINE | 9 |

NEA0648_01.003 | CERBERO SAMPLE PROBLEM INPUT | 53 |

NEA0648_01.004 | CERBERO SAMPLE PROBLEM OUTPUT | 795 |

NEA0648_01.005 | JCL AND INFORMATION | 56 |

Keywords: Hauser-Feshbach theory, absorption, capture, cross sections, elastic scattering, fluctuations, optical models, statistical models.