1 gaskelld 1.1 From Omar.Benhar@roma1.infn.it Mon May  7 19:17:44 2001
  2              Date: Fri, 20 Apr 2001 09:47:27 +0200 (MET DST)
  3              From: "Omar Benhar - INFN, Roma - ++39-06-49914298"
  4                  <Omar.Benhar@roma1.infn.it>
  5              To: John R. Arrington <johna@cedar.phy.anl.gov>
  6              Cc: Omar Benhar <benhar@roma1.infn.it>
  7              Subject: Spectral Functions
  8              
  9              
 10              Hallo John, 
 11              
 12              sorry for being somewhat late in getting back to you with the promised sftuff.
 13              Attached to this message are five files, containing the spectral functions
 14              of Carbon, Iron, Gold, Nuclear matter and 4He.
 15              
 16              As for 3He, we never did a calculation of the full spectral function. To 
 17              obtain inclusive cross sections and EMC ratios I have been using the 
 18              spectral function of the Hannover group. However, I also have a 3He spectral function 
 19              obtained using the approximation scheme developed for 4He. Just let me know
 20              which one you want.
 21              
 22 gaskelld 1.1 The relevant references are
 23              
 24              LDA spectral functions (Carbon, Iron and Gold)
 25              O. Benhar, A. Fabrocini, S. Fantoni and I. Sick, Nucl. Phys. A579(1994)493  
 26              
 27              Nuclear matter
 28              O. Benhar, A. Fabrocini and S. Fantoni, Nucl. Phys. A505(1989)267 
 29              
 30              4He
 31              O. Benhar and V.R. Pandharipande, Phys. Rev. C  47(1993)2218
 32              
 33              Below is a short explanantion of the way the files are arranged.
 34              
 35              That's all for now
 36              
 37              Best
 38              
 39              		Omar
 40              
 41              
 42              *************************************************************************************
 43 gaskelld 1.1 
 44              The files are organized as follows
 45              
 46               *** Gold: file 'pke197_tot.data' ***
 47              
 48              - P(k,E) is given on a 40*80 grid. The binsizes are 20 MeV/c for K and 5 MeV
 49                for E. The E-range starts at E_min = 0. The p-range starts at p_min = 0.
 50              
 51              - there are 40 bloks (one for each value of k), each of them containing 21 lines.
 52              
 53              - the first line of each block gives the value of k in MeV/c. Then follow 20
 54                lines containing four pairs of (E,P(k,E)) values each.
 55              
 56              - the spectral function is normalized to Z=79.  
 57              
 58               *** Iron: file 'pke56_tot.data' ***
 59              
 60              - P(k,E) is given on a 40*80 grid. The binsizes are 20 MeV/c for K and 5 MeV
 61                for E. The E-range starts at E_min = 2.5 MeV. The p-range starts at p_min = 0.
 62              
 63              - there are 40 bloks (one for each value of k), each of them containing 21 lines.
 64 gaskelld 1.1 
 65              - the first line of each block gives the value of k in MeV/c. Then follow 20
 66                lines containing four pairs of (E,P(k,E)) values each.
 67              
 68              - the spectral function is normalized to Z=26.    
 69              
 70               *** Carbon: file 'pke12_tot.data' ***
 71              
 72              - P(k,E) is given on a 40*80 grid. The binsizes are 20 MeV/c for K and 5 MeV
 73                for E. The E-range starts at E_min = 0. The p-range starts at p_min = 0.
 74              
 75              - there are 40 bloks (one for each value of k), each of them containing 21 lines.
 76              
 77              - the first line of each block gives the value of k in MeV/c. Then follow 20
 78                lines containing four pairs of (E,P(k,E)) values each.
 79              
 80              - the spectral function is normalized to Z=6.         
 81              
 82               *** Nuclear matter: file 'ompkeb4.dat' ***
 83              
 84              The spectral function P(k,E) (in units of fm^3*MeV^-1) is tabulated
 85 gaskelld 1.1 as a function of k (in units of fm) and E (in units of MeV).
 86              The k grid consists of 24 points, 13 at k less than the Fermi momentum k_F
 87              (for symmetric nuclear matter at equilibrium density k_F = 1.33 fm^-1)
 88              (steplength .1 fm) and 11 at k>k_F (steplength .266 fm). For any value
 89              of k the table gives the spectral function integrated over a missing energy
 90              bin, whose central value is also tabulated.    
 91              
 92              The file is organzed as follows:
 93              
 94               - the first line contains the step lengths and the number of steps for the
 95                  k grid (.1 .266 13 11 24).
 96              
 97               - then come 24 similar bloks, one for each value of k. The first line in each
 98                 block gives the value of k, the width of the bin in E and the number of
 99                 bins. The following lines contain the central energies of the bins and the
100                 integrals of the spectral function over the energy bins.     
101              
102              For example, the first two entries in the fourth line of the file say that
103              at k=.1 fm^-1 the spectral function integrated over the energy range 32-36 MeV
104              is .618e-3 fm^3*MeV^-1.
105              
106 gaskelld 1.1 The overall normalization is such that:
107              
108                  (3/k_F^3) \int dE dk k^2*P(k,E) = 1         
109              
110               *** 4 Helium: file 'spec4he.dat'
111              
112               - the first line gives the number of momentum and energy bins (50 and 35, respectively)
113              
114               - the central values of momentum bins are given in lines 2-51
115              
116               - lines 52-86 give central values and size of the energy bins
117              
118               - then follows 35 blocks of 13 lines each, giving the spectral function as a function 
119                 of momentum for each energy. For example, line 87 gives the spectral function for the 
120                 first energy bin nad the first four momentum bins.
121              
122               - the normalization is 
123              
124                  4 \pi \int dE dk k^2*P(k,E) = 1
125              
126              ********************************************************************************************
127 gaskelld 1.1 
128              ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
129              Omar Benhar                      phone  ++39-06-49914298
130              INFN, Sezione Roma 1             fax    ++39-06-4454749
131              Piazzale Aldo Moro, 2            e-mail benhar@roma1.infn.it
132              I-00185 Rome, Italy
133              ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
134              
135                  [ Part 2, ""  Text/PLAIN (Name: "pke12_tot.data")  1,328 lines. ]
136                  [ Unable to print this part. ]
137              
138              
139                  [ Part 3, ""  Text/PLAIN (Name: "pke56_tot.data")  1,328 lines. ]
140                  [ Unable to print this part. ]
141              
142              
143                  [ Part 4, ""  Text/PLAIN (Name: "pke197_tot.data")  1,328 lines. ]
144                  [ Unable to print this part. ]
145              
146              
147                  [ Part 5, ""  Text/PLAIN (Name: "ompkeb4.dat")  1,465 lines. ]
148 gaskelld 1.1     [ Unable to print this part. ]
149              
150              
151                  [ Part 6, ""  Text/PLAIN (Name: "spec4he.dat")  644 lines. ]
152                  [ Unable to print this part. ]
153