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					Survey of the neutron spectroscopic factors from Li to Cr
                    Betty Tsang, 2/24-26/2005
     INFN Workshop on Reactions and Structure with Exotic Nuclei


                        Magic number        Spectroscopic Factors:
                             N=20           Measure the orbital
                                            configuration of the
                                            valence nucleons.
                             N=10
                                                        d
                                                      (     ) EX
                                            Sl , j     d
                             N=2                       d
                                                     (     ) DWBA
                                                       d

               The National Superconducting
                   Cyclotron Laboratory
                           @Michigan State University
Measurements of Absolute Spectroscopic Factors




              Transfer Reactions
                       Rise and Fall of transfer reactions?
                    Opportunity to do an overview of the field
                            (especially for outsider)
              600
                                            (p,d) & (d,p) reactions
# of papers




              400


              200


               0
                    50's    60's    70's     80's      90's     2000-
                                       Decade
          Spectroscopic Factors from literatures
                  Example: 1p1/2 neutron SF in 13C = 12C+n




• Published spectroscopic factors show large fluctuations from analysis to analysis
• Consequence of using different optical model potentials and parameters for the
DWBA reaction model.
              d
            (    ) EX
Sl , j       d
             d                     A(d,p)B  B(p,d)A
           (    ) DWBA
             d




 Basic assumptions
     of DWBA
   The reaction is dominated by 1-step direct transfer.
   Elastic Scattering is the main process in the entrance and
   exit channels.
                   TDWBA = <Apf|V|Bdi>
                                                                14.3 MeV Ca40(d,p)Ca41
   Extraction of
Spectroscopic Factor                         10                                          CH
                                                                                         DWBA
                                                                                         Hjorth




                             d.c.s (mb/sr)
             d                               1
           (    ) EX
Sl , j    d
             d
           (    ) RM                          0
             d                                   0   20   40      60    80 100 120 140 160 180
                                                                        angle (deg)



For each angular distribution:
1. Fit first peak only (emphasize on maximum and shape)
2. Require more than 1 data point
Surrey’s TWOFNR
Use global proton          12C(d,p)13C
                                      gs
optical potential and
standardized parameters
Soper-Johnson
Adiabatic
Approximation to take
care of d-break-up
effects.
n-potential – wood-
Saxon shape with depth
adjusted to binding
energy. ro=1.25 fm &
ao=.65.
Include finite range &
non-locality corrections
Systematic extraction of SF’s
                                          Liu et al, PRC 69, 064313 (2004)




The spectroscopic factors deduced in a systematic and
consistent way show that we can extract spectroscopic
factors within the measurement uncertainties.

        Apply the technique to a large data set
                       Z=3    Li   6, 7, 8
                       Z=4    Be   9, 10, 11
                       Z=5    B    10, 11, 12
                       Z=6    C    12, 13, 14, 15
We studied 79          Z=7    N    14, 15, 16
nuclei by digitizing   Z=8    O    16, 17, 18, 19
                       Z=9    F    19, 20
~ 430 angular          Z=10   Ne   21, 22, 23
distributions from     Z=11   Na   24
literature             Z=12   Mg   24, 25, 26, 27
                       Z=13   Al   27, 28
for (p,d) & (d,p)      Z=14   Si   28, 29, 30, 31
reactions on target    Z=15   P    32
                       Z=16   S    32, 33, 34, 35, 36, 37
from Z=3-24.           Z=17   Cl   35, 36, 37, 38
                       Z=18   Ar   36, 37, 38, 39, 40
                       Z=19   K    39, 40, 41, 42
                       Z=20   Ca   40, 41, 42, 43, 44, 45, 47, 48, 49
                       Z=21   Sc   45, 46
                       Z=22   Ti   46, 47, 48, 49, 50, 51
                       Z=23   V    51
                       Z=24   Cr   50, 51, 52, 53, 55
Digitization of ~430 angular distributions from literature
   for (p,d) & (d,p) reactions on target from Z=3-24


   No adjustment of input parameters to calculations
   Quality control:
   1. Compare to Endt’s “Best” values when available.
   2. Compare SF’s derived from (p,d) and (d,p)
      reactions separately to estimate the uncertainties
      in our method.
                   Comparison with Endt’s results
       Endt in 1977 compiled SF’s of the s-d shell nuclei from
       (p,d), (d,p) – 50% uncertainty
       (p,d), (d,p), (d,t), (3He, a) – 25% uncertainty
                 10
                             line
                             Endt vs. Data

          Data


                  1




                 0.1
                       0.1                   1            10

                                       Endt's best SF

There are some scattering of the values but there is a strong
  correlation between present analysis and Endt values
Digitization of ~430 angular distributions from literature
   for (p,d) & (d,p) reactions on target from Z=3-24

   Data come from many groups over 40 years.
          -- Require quality control
   How to assess the uncertainties of the procedure?
               Self Consistency Checks
         Sn                79 nuclei from Li to Cr
         (p,d) : S+        47 nuclei
         (d,p) : S-        55 nuclei
         (p,d) & (d,p)     18 nuclei


   A+pB+d            S+
                           Equivalent processes S+ = S-
   B+dA+p            S-
                Comparison of (p,d) and (d,p) reactions

                10
                            pd vs. dp
                            line
      SF(d,p)


                 1




                0.1
                      0.1                 1               10
                                        SF(p,d)
By requiring the chi-square per degree of freedom is 1, we
obtain nominal uncertainty of 20% for each measurement.
  Textbook Example: Spectroscopic factors of Ca isotopes
         Direct Nuclear Reaction Theories by Austern; pg 291
                                                                       n 1
S    nA         l=7/2, S=1, 2, 0.75, 4, 0.5, 6, 0.25, 8       S  1
                                                                      2 j 1
        Ca = 40Ca +(A-40)n  Assume 40Ca is a good inert core.

       S_n
 Isotope           s              IPM
                            valence-n Endt shell Expt

 Ca40     15.51    1d3/2         4    4          4            4.31
 Ca41     9.367    1f7/2         1    1 0.85     1            1.03
 Ca42     11.12    1f7/2         2    2 1.6 1.81              1.82
 Ca43      8.04    1f7/2         3 0.75 0.58 0.75             0.63
 Ca44     11.27    1f7/2         4    4 3.1 3.64              3.82
 Ca45     7.761    1f7/2         5 0.5         0.5            0.41
 Ca47     6.546    1f7/2         7 0.25      0.256            0.25
 Ca48     8.846    1f7/2         8    8       7.38            7.06
 Ca49      4.43    2p3/2         1    1      0.918            0.66
 Sc45     12.27    1f7/2         4    4 0.6 0.35              0.32
                            IPM (Austern, pg 291)                       For n odd
                            For n even                                     n 1
                            S n                                   S  1
                                                                          2 j 1
   spectroscopic factor

                          10




                           1

                                     Data
                                     Austern IPM model
                                     Shell model
                          0.1                                 Ca
                                39           41          43            45     47    49

                                                                   A
40-48Ca     isotopes have good single particle states with spherical cores
          SF for 49Ca is lower than IPM and shell model predictions.
                      Comparison with Austern’s IP Model
            Most experimental SF values are less than predictions.
            There are no constant quenching even for close shell nuclei.
            Discrepancies may be explained by including interaction
            between nucleons and core
                                                                   Be
          10                                                       line
                                                                   B
                                                                   C
                                                                   N
                                                                   O
                                                                   Na
Expt SF




                                                                   Mg
                                                                   Al
           1                                                       Si
                                                                   P
                                                                   S
                                                                   Cl
                                                                   Ar
                                                                   K
                                                                   Ca
                                                                   Sc
          0.1                                                      Ti
                                                                   V
                0.1                 1                    10        Cr
                                                                   20% line
                                IPM SF                             -20% line
                                                                   Li
            Compare with Modern Shell Model (Oxbash)
                     Good agreement with most isotopes
           Outliners: deformed nuclei and isotopes with small SF’s
                                   (Ne)                         Be
          10                                                   line
                                                               B
                                                               C
                                                               N
                                                               O
Expt SF




                                                               Na
                                                               Mg
           1                                                   Al
                                                               Si
                                                               P
                                                               S
                                                               Cl
                                                               Ar
                                                               K
          0.1                                                  Ca
                                                               Sc
                0.1              1                   10        Ti
                                                               20% line
                        Shell Model SF                         -20% line
 Measurements of Spectroscopic Factors




                                                Be
          10                                    line
                                                B
                                                C
                                                N
                                                O
Expt SF




                                                Na
                                                Mg
           1                                    Al
                                                Si
                                                P
                                                S
                                                Cl
                                                Ar
                                                K
          0.1                                   Ca
                                                Sc
                0.1          1             10   Ti
                                                20% line
                        Shell Model SF
                      Transfer Reactions        -20% line
                                                Li
                                                F
                       (e,e’p) – sensitive to interior of the wave-functions




                        4
                                                                40Ca
Spectroscopic factor




                        2

                                                                       IPM

                             12C                                       e,e'p
                                                  16O

                        0
                                        Speculations:
                       (e,e’p) – sensitive to interior of the wave-functions
                       (d,p), (p,d) – sensitive to surface of the wave-functions
                                Shell model -- long range correlation effects
                       SF(p/d) – SF(e,e’p) -- short range correlation effects!


                        4
                                                                40Ca
Spectroscopic factor




                        2
                                                                   IPM
                                                                   Shell Model
                             12C                  16O              p,d
                                                                   e,e'p
                        0
                  Summary
1. We have extracted ground state neutron
   spectroscopic factors for 79 (Z=3-24) nuclei
2. 40Ca to 48Ca isotopes follow the simple IPM
   predictions
    Good valence nucleons around spherical cores
    No quenching for gs n-orbital for the closed shell
     nuclei of 40Ca?
   • Are we measuring absolutely SF’s?
3. Most SF’s fall short of IPM predictions but
   agree with modern day shell model
   calculations – long range correlation.
4. Is difference between SF’s from (e,e’p) and
   transfer reactions the short range
   correlations?

5. Thanks to Hiu Ching Lee

				
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