AVRIGEANU.readme Partial Level Densities: Analytical Approach (M. Avrigeanu et al, Bucharest, Romania, September 1997) ********************************************************
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 C*******************************************************************************