Directory: optical/om-data/ File: om-parameter.readme (Feb.28 2005) ********************************************************** om-parameter-u.dat Optical model parameter library (provided by R. Capote on Feb 28, 2005) **************************************** Content ------- Compilation of the Optical Model Potential parameters. The following extensions of the format were introduced: 1) Energy dependent radius up to E**2 2) Dispersive-like energy dependent radius 3) Soukhovitski et al energy dependence of the real potential See J.Phys.G. Nucl.Part.Phys. 30(2004) 905-920) 4) Buck and Perey energy dependence of the local real potential (as coded and employed by B. Morillon and P. Romain) 5) Wood-Saxon charge distribution is allowed by specifying its difusseness acoul. The following changes were introduced into the processing code: 1) Analytical dispersive integrals are included See Quesada JM et al, Comp. Phys. Comm. 153(2003) 97 Phys. Rev. C67(2003) 067601 2) General numerical solution of the dispersive integral is kept to deal with special Ws(E) and Wd(E) form factors. See Capote et al, J.Phys.G. Nucl.Part.Phys. 27(2001) B15-B19 Numerical integration is used for Nagadi et al dispersive OMP See Nagadi et al, Phys. Rev. C68 (2003) 044610 3) Relativistic kinematics is used to calculate the kinematical conversion factor xkine and reduced mass amu (for irel>0) Kinematical conversion factor for discrete levels is assumed non-relativistic, i.e. energy independent (excellent approximation as discrete level are always below 5 MeV). Format ------ [ALL INPUT PARAMETERS ARE READ IN FREE FORMAT READ STATEMENTS] iref author [1 line of author names] reference [1 line of reference information] summary [4 lines of descriptive information] emin,emax izmin,izmax iamin,iamax imodel,izproj,iaproj,irel,idr *****LOOP: i=1,6 jrange(i) *****LOOP j=1,jrange epot(i,j) (rco(i,j,k), k=1,13) (aco(i,j,k), k=1,13) (pot(i,j,k), k=1,25) *****END i AND j LOOPS jcoul *****LOOP j=1,jcoul ecoul(j),rcoul0(j),rcoul(j),rcoul1(j),rcoul2(j),beta(j),acoul(j) *****END j LOOP (1)*****SKIP TO (2)***** IF IMODEL NOT EQUAL TO 1 nisotopes *****LOOP n=1,nisotopes iz(n),ia(n),ncoll(n),lmax(n),idef(n),bandk(n),[def(j,n), j=2,idef(n),2] *****LOOP k=1,ncoll(n) ex(k,n),spin(k,n),ipar(k,n) *****END k AND n LOOPS (2)*****SKIP TO (3)***** IF IMODEL NOT EQUAL TO 2 nisotopes *****LOOP n=1,nisotopes iz(n),ia(n),nvib(n) *****LOOP k=1,nvib(n) exv(k,n),spinv(k,n),iparv(k,n),nph(k,n),defv(k,n),thetm(k,n) *****END k LOOP *****END n LOOP (3)*****SKIP REMAINING LINES IF IMODEL NOT EQUAL TO 3 nisotopes *****LOOP n=1,nisotopes iz(n),ia(n),beta0(n),gamma0(n),xmubeta(n) *****END n LOOP DEFINITIONS iref = unique fixed point reference number for this potential author = authors for this potential (up to 80 characters, 1 line)) reference = reference for this potential (up to 80 characters, 1 line) summary = short description of the potential (320 characters, 4 lines) emin,emax = minimum and maximum energies for validity of this potential izmin,izmax = minimum and maximum Z values for this potential, where Z is the number of protons in the target nucleus. iamin,iamax = minimum and maximum A values for this potential, where A = Z + N and N is the number of neutrons in the target. imodel = 0 for spherical potential = 1 for coupled-channel, rotational model = 2 for vibrational model = 3 for non-axial deformed model izproj = Z for incident projectile iaproj = A for incident projectile irel = 0 for non-relativistic parameterization = 1 for relativistic parameterization (relat. kinem. + reduced mass calculated from total relativistic energies) idr = 0 dispersion relations not used = 1 dispersion relations with equivalent volume real potential used = 2 exact dispersion relations used. The dispersive integration is carried out analytically for commonly used Ws(E) and Wv(E). The dispersive integration is done in the om-retrieve code. = 3 idr=2 + The dispersive integration is carried out analytically for Wso(E) formfactor contributing to the real Vso. The dispersive integration is done in the om-retrieve code. =-2 exact dispersion relations used. The dispersive integration is carried out numerically for special Ws(E) and Wv(E). The dispersive integration is done in the om-retrieve code. =-3 idr=-2 + The dispersive integration is carried out numerically for Wso(E) formfactor contributing to the real Vso. The dispersive integration is done in the om-retrieve code. index i = 1 real volume potential (Woods-Saxon) = 2 imaginary volume potential (Woods-Saxon) = 3 real surface derivative potential = 4 imaginary surface derivative potential = 5 real spin-orbit potential = 6 imaginary spin-orbit potential jrange = number of energy ranges over which the potential is specified = positive for potential strengths = negative for volume integrals = 0 if potential of type i not used epot(i,j) = upper energy limit for jth energy range for potential i rco(i,j,k)= coefficients for multiplying A**(1/3) for specification of radius R in fm where: if rco(i,j,13) = 0.0 ; default dependence R(i,j) = { abs(rco(i,j,1)) + rco(i,j,3)*eta + rco(i,j,4)/A + rco(i,j,5)/sqrt(A) + rco(i,j,6)*A**(2./3.) + rco(i,j,7)*A + rco(i,j,8)*A**2 + rco(i,j,9)*A**3 + rco(i,j,10)*A**(1./3.) + rco(i,j,11)*A**(-1./3.) + rco(i,j,2)*el + rco(i,j,12)*el*el } * [A**(1/3)] if rco(i,j,13) .ne. 0 ; dispersive like energy dependence R(i,j) = { abs(rco(i,j,1)) + rco(i,j,2)*A ) * ( 1.d0 - ( rco(i,j,3) + rco(i,j,4)*A ) * (E-EF)**nn / ( (E-EF)**nn + ( rco(i,j,5) + rco(i,j,6)*A )**nn ) ) } * [A**(1/3)] where nn = int(rco(i,j,7)) EF = Fermi energy in MeV = pot(i,j,18) + pot(i,j,19)*A If pot(i,j,18) and pot(i,j,19) = 0., then EF = -0.5*[SN(Z,A) + SN(Z,A+1)] (for incident neutrons) = -0.5*[SP(Z,A) + SP(Z+1,A+1)] (for incident protons) where SN(Z,A) = the neutron separation energy for nucleus (Z,A) SP(Z,A) = the proton separation energy for nucleus (Z,A). if rco(4,j,1) >0.0: Woods-Saxon derivative surface potential if rco(4,j,1) <0.0: Gaussian surface potential. [Note that the A dependence of rco(i,j,11) cancels out so that rco(i,j,11) is equivalent to adding a constant of that magnitude to the radius R(i,j)]. aco(i,j,k) = coefficients for specification of diffuseness a in fm where: a(i,j) = abs(aco(i,j,1)) + aco(i,j,2)*E + aco(i,j,3)*eta + aco(i,j,4)/A + aco(i,j,5)/sqrt(A) + aco(i,j,6)*A**(2/3) + aco(i,j,7)*A + aco(i,j,8)*A**2 + aco(i,j,9)*A**3 + aco(i,j,10)*A**(1/3) + aco(i,j,11)*A**(-1/3) pot(i,j,k) = strength parameters in MeV given as follows: if pot(i,j,k>21) .eq. 0, then [standard form] V(i,j) = pot(i,j,1) + pot(i,j,7)*eta + pot(i,j,8)*Ecoul1 + pot(i,j,9)*A + pot(i,j,10)*A**(1/3) + pot(i,j,11)*A**(-2/3) + pot(i,j,12)*Ecoul2 + [pot(i,j,2) + pot(i,j,13)*eta + pot(i,j,14)*A]*E + pot(i,j,3)*E*E + pot(i,j,4)*E*E*E + pot(i,j,6)*sqrt(E) + [pot(i,j,5) + pot(i,j,15)*eta + pot(i,j,16)*E]*ln(E) + pot(i,j,17)*Ecoul1/E**2 if pot(i,j,22) .ne. 0, then [Smith form] V(i,j) = pot(i,j,1) + pot(i,j,2)*eta + pot(i,j,3)*cos[2*pi*(A - pot(i,j,4))/pot(i,j,5)] + pot(i,j,6)*exp[pot(i,j,7)*E + pot(i,j,8)*E*E] + pot(i,j,9)*E*exp[pot(i,j,10)*E**pot(i,j,11)] if pot(i,j,23) .ne. 0, then [Varner form] V(i,j) = [pot(i,j,1) + pot(i,j,2)*eta]/ {1 + exp[(pot(i,j,3) - E + pot(i,j,4)*Ecoul2)/pot(i,j,5)]} + pot(i,j,6)*exp[(pot(i,j,7)*E - pot(i,j,8))/pot(i,j,6)] if pot(i,j,24) = 1, then [extended Koning form] if b(i,j,11) = 0, then V(i,j) = b(i,j,1)*( b(i,j,15) - b(i,j,2)*(E-EF) + b(i,j,3)*(E-EF)**2 - b(i,j,4)*(E-EF)**3 + b(i,j,13)*exp(-b(i,j,14)*(E-EF)) ) + b(i,j,5)*VC + b(i,j,6)*((E-EF)**n(i,j)/((E-EF)**n(i,j) + b(i,j,7)**n(i,j))) + b(i,j,8)*exp(-b(i,j,9)*(E-EF)**b(i,j,12))*((E-EF)**n(i,j)/ ((E-EF)**n(i,j) + b(i,j,10)**n(i,j))) if b(i,j,11) .ne. 0, then V(i,j) = b(i,j,1)*( b(i,j,15) - b(i,j,2)*(E-EF) + b(i,j,3)*(E-EF)**2 - b(i,j,4)*(E-EF)**3 + b(i,j,13)*exp(-b(i,j,14)*(E-EF)) ) + b(i,j,5)*VC + b(i,j,6)*((E-EF)**n(i,j)/((E-EF)**n(i,j) + b(i,j,7)**n(i,j))) + b(i,j,8)*exp(-b(i,j,9)*(E-EF))*((E-EF)**n(i,j)/ ((E-EF)**n(i,j) + b(i,j,10)**n(i,j))) + b(i,j,11)*exp(-b(i,j,12)*(E-EF)) if pot(i,j,24) = 2, then [Morillon-Romain form] if b(i,j,11) = 0, then V(i,j) = Vhf(E) + b(i,j,5)*VC + b(i,j,6)*((E-EF)**n(i,j)/((E-EF)**n(i,j) + b(i,j,7)**n(i,j))) + b(i,j,8)*exp(-b(i,j,9)*(E-EF)**b(i,j,12))*((E-EF)**n(i,j)/ ((E-EF)**n(i,j) + b(i,j,10)**n(i,j))) if b(i,j,11) .ne. 0, then V(i,j) = Vhf(E) + b(i,j,5)*VC + b(i,j,6)*((E-EF)**n(i,j)/((E-EF)**n(i,j) + b(i,j,7)**n(i,j))) + b(i,j,8)*exp(-b(i,j,9)*(E-EF))*((E-EF)**n(i,j)/ ((E-EF)**n(i,j) + b(i,j,10)**n(i,j))) + b(i,j,11)*exp(-b(i,j,12)*(E-EF)) if( (pot(i,j,24).ne.0) and (Ea < 1000) and (E > (EF + EA)) ) then, V(2,j) = V(2,j) + AlphaV*(sqrt(E)+(EF+EA)**1.5/(2.*E)-1.5*sqrt(EF+EA)) where AlphaV = 1.65 constant fixed according to Mahaux 1991 E = projectile laboratory energy in MeV eta = (N-Z)/A Ecoul1 = 0.4Z/A**(1/3) Ecoul2 = 1.73*Z/RC VC = b(i,j,1)*Ecoul2* ( b(i,j,2) - 2.*b(i,j,3)*(E-EF) + 3.*b(i,j,4)*(E-EF)**2 + b(i,j,14)*b(i,j,13)*exp(-b(i,j,14)*elf)) Vhf(E) is the solution of the implicit equation: Vhf(E) = b(i,j,1)*exp( -0.5*miu*(b(i,j,2)*]/hc)**2*[E-Vhf(E)] + 4*(miu*b(i,j,3)*[E-Vhf(E)])**2/hc**4 ) hc = (Plank constant * speed of light constant / (2*pi)) miu is the reduced mass calculated from total energy as: miu = Etarget*Eproj / (Etarget+Eproj) EF = Fermi energy in MeV = pot(i,j,18) + pot(i,j,19)*A If pot(i,j,18) and pot(i,j,19) = 0., then EF = -0.5*[SN(Z,A) + SN(Z,A+1)] (for incident neutrons) = -0.5*[SP(Z,A) + SP(Z+1,A+1)] (for incident protons) where SN(Z,A) = the neutron separation energy for nucleus (Z,A) SP(Z,A) = the proton separation energy for nucleus (Z,A). For cases where abs(idr) .ge. 2 : EP = pot(i,j,20) (for i = 2 or 4) = average energy of particle states. If pot(i,j,20)=0., then use default value of EP=EF. EA = pot(i,j,21) = energy above which nonlocality of the absorptive potential will be assumed. If pot(i,j,21)=0., then use default value of EA=1000. (MeV). For pot(i,j,24).ne.0., the b(i,j,m) are defined as: b(i,j,m) = 0 for i=1,6, j=1,jrange(i), m=1,12, except for the following: if pot(1,j,20) = 0, then [Koning form] b(1,j,1) = pot(1,j,1) + pot(1,j,2)*A + pot(1,j,8)*eta if pot(1,j,20) .ne. 0, then [Soukhovitski form] b(1,j,1) = pot(1,j,1) + pot(1,j,2)*A + pot(1,j,8)*eta + + pot(1,j,20)*eta/(pot(1,j,14) + pot(1,j,15)*A + pot(1,j,16)) b(1,j,2) = pot(1,j,3) + pot(1,j,4)*A b(1,j,3) = pot(1,j,5) + pot(1,j,6)*A b(1,j,4) = pot(1,j,7) b(1,j,5) = pot(1,j,9) b(1,j,11) = pot(1,j,10) + pot(1,j,11)*A b(1,j,12) = pot(1,j,12) b(1,j,13) = pot(1,j,16) b(1,j,14) = pot(1,j,17) b(1,j,15) = pot(1,j,14) + pot(1,j,15)*A if b(1,j,15) = 0 then b(1,j,15) = 1 To preserve compatibility with RIPL-2 Koning database b(2,j,6) = pot(2,j,1) + pot(2,j,2)*A b(2,j,7) = pot(2,j,3) + pot(2,j,4)*A b(4,j,8) = pot(4,j,1) + pot(4,j,8)*eta + pot(4,j,7)*A b(4,j,9) = pot(4,j,2) + pot(4,j,3)/(1. + exp((A-pot(4,j,4))/pot(4,j,5))) b(4,j,10) = pot(4,j,6) b(5,j,11) = pot(5,j,10) + pot(5,j,11)*A b(5,j,12) = pot(5,j,12) b(6,j,6) = pot(6,j,1) b(6,j,7) = pot(6,j,3) n(i,j) = int(pot(i,j,13)) And, continuing the definitions: jcoul = number of energy ranges for specifying coulomb radius and nonlocality range ecoul(j) = maximum energy of coulomb energy range j rcoul0(j),rcoul(j),rcoul1(j),rcoul2(j) = coefficients to determine the coulomb radius, RC, from the expression RC = [rcoul0(j)*A**(-1/3) + rcoul(j) + rcoul1(j)*A**(-2/3) + rcoul2(j)*A**(-5/3)] * A**(1/3) acoul(j) = diffuseness in fm of the Wood-Saxon charge distribution. beta(j) = nonlocality range. Note that when beta(j).ne.0., then the imaginary potential is pure derivative Woods-Saxon for energy range j nisotopes = number of isotopes for which deformation parameters and discrete levels are given iz,ia = Z and A of the target associated with the deformation parameters and discrete levels that follow ncoll = number of collective states in the coupled-channel rotational model for this iz, ia lmax = maximum l value for multipole expansion idef = largest order of deformation bandk = k for the rotational band def = deformation parameters, l=2,4,6,...through lmax ex = rotational level excitation energy (MeV) spin = rotational level spin ipar = rotational level parity (+1 or -1) nvib = number of vibrational states in the model for this iz, ia (first level must be ground state) exv = vibrational level excitation energy (MeV) spinv = vibrational level spin iparv = vibrational level parity (+1 or -1) nph = 1 for pure 1-phonon state = 2 for pure 2-phonon state = 3 for mixture of 1- and 2-phonon states defv = vibrational model deformation parameter thetm = mixing parameter (degrees) for nph=3 beta0 = beta deformability parameter gamma0 = gamma deformability parameter xmubeta = non-axiality parameter