AVRIGEANU.readme
Partial Level Densities: Analytical Approach
(M. Avrigeanu et al, Bucharest, Romania, September 1997)
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AVRIGEANU.FOR is the Fortran code (original code name PLD.FOR), providing
a set of subroutines for calculating p-h level densities using analytical
expressions for various equidistant and Fermi-gas single-particle models.
The following text is included also in the comment part of the file
AVRIGEANU.FOR.
C*******************************************************************************
C PROGRAM PLD *
C FORTRAN SUBROUTINES FOR CALCULATION OF PARTIAL LEVEL DENSITIES USED IN *
C PREEQUILIBRIUM NUCLEAR REACTION MODELS, FOR THE DEVELOPMENT OF THE *
C "REFERENCE INPUT PARAMETER LIBRARY" FOR NUCLEAR MODEL CALCULATIONS OF *
C NUCLEAR DATA (NUCLEAR DATA SECTION/IAEA-VIENNA PROJECT , 1994-1997). *
C *
C CARRIED OUT UNDER RESEARCH CONTRACT NO. 8886/R0-R1/RBF BETWEEN *
C INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, AND *
C INSTITUTE FOR NUCLEAR PHYSICS AND ENGINEERING, BUCHAREST, ROMANIA. *
C CHIEF INVESTIGATOR: DR. M. AVRIGEANU, INPE-BUCHAREST. *
C SEPTEMBER 1997. *
C *
C OS/COMPILER: MS-DOS v.5/ MS-FORTRAN77 v.5.0 *
C*******************************************************************************
C
C I.DESCRIPTION OF THE SUBROUTINES/FUNCTIONS (* - 1997 new or major changes)
C ========================================
C
C 1. MAIN. * Reads the input data and organizes the calculation of the
C partial nuclear state densities (PSD) w(p,h,E) by using the specified
C formula [1-8], and partial level densities (PLD) D(p,h,E,J) by
C using the formalism of the spin cutoff factors of Fu [9,10]. It
C calculates (i) the nuclear state density w(E) as the PSD-sum over
C all allowed exciton numbers (p=h) for which PSD is higher than
C WMINACC=0.1 /MeV, and (ii) the total level density D(E) as the
C PLD-sum over the nuclear angular momentum J and allowed particle
C numbers p=h. At the same time are calculated the corresponding
C Wasym(E)- or Dasym(E)-values given by the asymptotical/'closed'
C formulae of the equidistant Fermi gas model (FGM) in order to make
C possible tests of the overall consistency. A two-fermion system
C correction [11] is involved optionally when the one-component
C Fermi gas formulae are used for calculation of PSDs.
C
C 2. PRINTIN. Prints the PSD/PLD formula and parameters used in calculation.
C
C 3. PRINTWN. Tabulates values of the calculated w(p,h,E) or D(p,h,E) (the
C latter being the sum over J of the D(p,h,E,J), i.e. the total
C level density for a given exciton configuration), for either
C (i) some given particle-hole configurations or (ii) all pairs of
C equal numbers of excited particles and holes. In the case (ii)
C there are printed also the w(E) or D(E)-values (within a first
C table including the PSD/PLD for p=h=1 to 7) and the corresponding
C Wasym(E)- or Dasym(E)-values given by the closed FGM formulae
C (within the second table including the PSD/PLD for p=h=8 to 16).
C In the case of the PLD calculation for a particular (p,h)
C configuration it is printed also a table of the D(p,h,E,J)-values
C but only for the last excitation energy E involved in the
C respective calculation; the total level density for this
C configuration is obtained and printed both as the D(p,h,E,J)-sum
C and 'D(p,h,E)-form' based on formula between this quantity and
C w(p,h,E).
C
C 4. WIL1 Calculates the partial nuclear state density w(p,h,E) of a given
C exciton configuration by means of the Williams formula [1] for
C one-component Fermi-gas.
C
C 5. WIL2 As WIL1 but using the two-fermion system formula.
C
C 6. WOB1 Calculates the partial nuclear state density of a given excited
C particle-hole configuration by means of the Betak-Dobes formula
C [2] with the nuclear potential finite-depth correction, for one-
C component Fermi-gas. If a value is specified for the nucleon
C binding energy it is carried out the calculation of the bound-
C state density according to Oblozinsky [3].
C
C 7. WOB2 As WOB1 but using the two-fermion system formula.
C
C 8. WFU1 Calculates the PSD of a given exciton configuration by means of
C the formula including the advanced pairing correction by Fu [4],
C for one-component Fermi-gas.
C
C 9. WFU2 * As WFU1 but using the two-fermion system formula.
C
C 10. WK1 Calculates the PSD of a given exciton configuration by using the
C improved implementation of the pairing correction by Kalbach [5,6]
C for one-component Fermi-gas.
C
C 11. WK2 * As WK1 but using the two-fermion system formula.
C
C 12. WK3 Calculates the PSD of a given exciton configuration by using the
C FGM energy-dependence of the single-excited particle and
C single-hole state densities, and/or the finite-depth correction
C including the nuclear-surface effects introduced by Kalbach [8]
C for one-component Fermi-gas.
C
C 13. WK4 * As WK3 but using the two-fermion system formula.
C
C 14. WM1 Calculates the PSD of a given exciton configuration by using the
C exact calculation of the Pauli-exclusion effect [7] and the
C pairing correction by Kalbach [5,6] for one-component Fermi-gas.
C
C 15. WM2 * As WM1 but using the two-fermion system formula.
C
C 16. WR1 * Calculates the PSD of a given exciton configuration by using
C (i) the improved implementation of the pairing correction by
C Kalbach [5,6], (ii) the FGM energy-dependence of the
C single-excited particle and single-hole state densities, and/or
C (iii) the finite-depth correction including the nuclear-surface
C effects introduced by Kalbach [8], for one-component Fermi-gas.
C
C 17. WR2 * As WR1 but using the two-fermion system formula.
C
C 18. PFU Calculates the advanced pairing correction by Fu [4], for the
C one-component Fermi-gas.
C
C 19. AK * Calculates the advanced pairing correction by Kalbach [5,6],
C for the one-component Fermi-gas.
C
C 20. FDC0 Calculates the nuclear potential finite-depth correction factor
C f(p,h,E,F) [8] for one-component Fermi-gas.
C
C 21. FDC * Calculates the nuclear potential finite-depth correction factor
C f(p+1,h,E,F) [8] in the case of bound states and the
C one-component Fermi-gas.
C
C 22. SUBPLD * Calculates the partial level density D(p,h,E,J) of a given
C 'p'-excited particle and 'h'-hole configuration for the excitation
C energy E and nuclear spin J, and the respective total level
C density D(p,h,E) as the sum over J of these PLDs, by using the
C partial state density w(p,h,E) and the formalism of Fu [9,10].
C
C 23. SIG2FU Calculates the spin cutoff factor for a given excited particle-
C hole configuration [9].
C
C 24. FCTR Calculates the factorial of natural numbers.
C
C
C II. REFERENCES
C ==========
C
C 1. F.C. Williams, Nucl. Phys. A166, 231 (1971)
C 2. E. Betak and J. Dobes, Z. Phys. A279, 319 (1976)
C 3. P.Oblozinsky, Nucl. Phys. A453, 127 (1986)
C 4. C.Y. Fu, Nucl.Sci.Eng. 86, 344 (1984)
C 5. C. Kalbach, Nucl.Sci.Eng. 95, 70 (1987)
C 6. C. Kalbach, Z.Phys. A 332, 157 (1989)
C 7. Mao Ming De and Guo Hua, J. Phys. G: 19, 421 (1993)
C 8. C. Kalbach, Phys. Rev. C 32, 1157 (1985)
C 9. C.Y. Fu, Nucl.Sci.Eng. 92, 440 (1986)
C 10. C.Y. Fu, Nucl.Sci.Eng. 109, 18 (1991)
C 11. J.M.Akkermans and H.Gruppelaar, Z.Phys. A 321, 605 (1985)
C
C
C III. INPUT DATA DESCRIPTION (Formatted read is used for all data in order to
C ====================== be possible the input of only few of them, while
C the rest are receiving zero-values)
C 1. NE,IOPTJ,TITLE
C ************** FORMAT(2I3,74A1)
C NE ..... Number of excitation energies.
C If NE>0 then the calculation is carried out for the energy values
C of E = 1, 2,.., NE MeV (maximum NEN=200), and record No. 2
C should be omitted
C IOPTJ .. Spin distribution (PLD calculation) option
C = 0 Calculate PSD-values, i.e. w(p,h,E) or w(pP,hP,pN,hN,E), and
C the nuclear state densities w(E) (obtained as sum over 'p' with
C the restriction p=h) and Wasym(E) given by the closed
C formulae
C = 1 Calculate the PLDs D(p,h,E,J) or D(pP,hP,pN,hN,E,J), the total
C level density given by the sum over J [ D(p,h,E) ] as well as
C over 'p' with the restriction p=h [ D(E) ], and Dform(E) given
C by the asymptotical/closed formula (Eq. (52) of [9])
C TITLE .. Title of the problem
C
C 2. E(I), I=1,|NE| (only if NE<0!) (it has to be omitted if NE>0!)
C ************** FORMAT(8F10.5)
C ... The excitation energies in MeV at which the PSD/PLDs are calculated
C
C 3. IMOD,ITFC,A,Z,UP
C **************** FORMAT(2I3,7F10.5)
C IMOD .. Select the partial state/level density formula (odd for one-fermion
C system and even for two-fermion system formulas):
C
C =-1, 0 Composite/recommended formula (present work)
C = 1, 2 F.C. Williams, Nucl. Phys. A166, 231 (1971)
C = 3, 4 P.Oblozinsky, Nucl. Phys. A453, 127 (1986), Eqs.(7,9)
C = 5, 6 C.Y. Fu, Nucl.Sci.Eng. 86, 344 (1984)
C = 7, 8 C. Kalbach, Nucl.Sci.Eng.95,70(1987),Z.Phys.A 332,157(1989)
C = 9,10 C. Kalbach, Phys.Rev. C 32, 1157 (1985)
C =11,12 Mao Ming De, J.Phys.G 19,421(1993)
C
C ITFC .. Option for two-fermion system correction
C = 0 No one
C = 1 J.M.Akkermans, H.Gruppelaar, Z.Phys. A 321,605(1985), Eq. (9)
C A ..... Mass number of the excited nucleus (may be omitted if GIN>0.)
C Z ..... Atomic number of the excited nucleus
C UP .... Pairing correction based on the odd-even mass differences
C If UP=-1. and A>0., P-values given by Eq.(9) of Dilg et al., Nucl.
C Phys. A217,269(1973), are adopted
C
C 4. NP0,NH0,GIN,FIN,BIN,F1IN
C ************************ FORMAT(2I3,7F10.5)
C NP0 ... Number 'p' of excited particles within the exciton configuration
C NH0 ... Number 'h' of holes within the exciton configuration
C If NP0=NH0=0 then the calculation is carried out for all pairs
C p=h=1, 2,... for which the PSD/PLD-value at the respective
C excitation energy E is higher than WMINACC=0.1 /MeV, followed by
C their sum to obtain the nuclear state density w(E), respectively
C the total level density D(E), and the values given by the
C asymptotic/closed formulae of the Fermi gas model
C GIN ... Input value of single-particle state density G in 1/MeV
C If GIN<0. the nuclear level density parameter DR(1) is read (record
C No. 6) and it is adopted the value G=(6/3.14**2)*DR(1)
C If GIN=0. and A=0. it is adopted the value G=1.0
C If GIN=0. and A>0. it is adopted the value G=A/13.
C FIN ... Input value of the Fermi energy F in MeV
C If FIN=0. it is adopted the value F=1.E+06
C BIN ... Input value of nucleon binding energy B in MeV
C If BIN=0. it is adopted the value B=1.E+06
C F1IN... Input value of the average effective Fermi energy F1 in MeV [8].
C If FIN=0.0 it is adopted the value F=1.E+06.
C If FIN<0.0 the PSD calculation by means of WR1 and WR2 functions
C is carried out for constant G.
C
C 5. NP0,NH0,NPN0,NHN0,GIN,GN,FIN,FN,BIN,BN,F1IN,F1N
C *********************************************** FORMAT(4I3,6F10.5)
C NP0 ... Number 'pP' of proton excited particles
C NH0 ... Number 'hP' of proton holes
C NPN0 .. Number 'pN' of neutron excited particles
C NHN0 .. Number 'hP' of neutron holes
C If NP0=NH0=NPN0=NHN0=0 the calculation is carried out for all
C configurations (pP=hP,pN=hN) - followed by increasing total exciton
C numbers N=pP+hP+pN+hN=2, 4,.. - for which the sum of PSD/PLDs for a
C given N at the respective excitation energy E is higher than
C WMINACC=0.1/MeV
C GIN ... Input value of single-proton state density G in 1/MeV
C GN .... Input value of single-neutron state density GN in 1/MeV
C If GIN<0 the nuclear level density parameter DR(1) is read (record
C No. 6) and there are adopted the values:
C G=Z/A*(6/3.14**2)*DR(1)
C GN=(A-Z)/A*(6/3.14**2)*DR(1)
C If GIN=0 and A=0. there are adopted the values G=GN=1.0
C If GIN=0 and A>0. are adopted the values G=Z/13 and GN=(A-Z)/13
C FIN ... Input value of the proton Fermi energy F in MeV
C FN .... Input value of the neutron Fermi energy FN in MeV
C If FIN=0. there are adopted the values F=FN=1.E+06
C BIN ... Input value of proton binding energy B in MeV
C BN .... Input value of neutron binding energy BN in MeV
C If BIN=0. there are adopted the values B=BN=1.E+06
C F1IN... Input value of the average effective proton Fermi energy F1 in MeV.
C If F1IN=0 it is adopted the value F1=1.E+06.
C If F1IN<0.0 the PSD calculation by means of the WR2 functions is
C carried out for constant G.
C F1N ... Input value of the average effective neutron Fermi energy F1N (MeV)
C If F1N=0 it is adopted the value F1N=1.E+06.
C If F1N<0.0 the PSD calculation by means of the WR2 functions is
C carried out for constant GN.
C
C 6. DR(K), K=1,3 (if GIN is negative, otherwise it has to be omitted!)
C ************ FORMAT(8F10.5)
C ... Parameters of the Back-Shifted Fermi Gas model for
C nuclear level density (W. Dilg et al., Nucl. Phys. A217,269(1973)]:
C DR(1) .. Nuclear level density parameter 'a'
C DR(2) .. Ratio of effective nuclear moment of inertia to rigid-body value
C calculated by using the reduced nuclear radius r=1.25 fm
C DR(3) .. Shift of the fictive nuclear ground state
C
C 7. ICONT,IEND
C ********** FORMAT(2I3,7F10.5)
C ICONT .. Output and recycle option
C =-1 Print of the first 2 tables only (see PRINTWN description)
C of calculated PSD/PLD, and resumption according to IEND
C = 0 Print of calculated PSD/PLD, and resumption according to IEND
C = 1 New calculation starting with input-data record 1, with the
C results printed together with those of the actual case
C = 2 New calculation starting with input-data record 3 (conserved
C energy grid)
C = 3 Calculation for another exciton configuration given by the
C input-data records either 4 or 5
C = 4 Calculation for another set of the BSFG model parameters given
C by the input-data record 6
C IEND ... Recycle option
C = 0 End
C = 1 New complete case starting with input-data record 1
C = 2 New calculation starting with input-data record 3
C = 3 New calculation for exciton configuration on records 4 or 5
C = 4 New calculation for BSFG model parameters given on record 6
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