Systematic extraction of Spectroscopic Factors for Z324 Isotopes Hui Ching Lee, Chinese University o

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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
Spectroscopic Factors Measure the orbital
configuration of the valence nucleons.
Magic number
N20
N10
N2
The National Superconducting Cyclotron
Laboratory _at_Michigan State University
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Measurements of Absolute Spectroscopic Factors
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Rise and Fall of transfer reactions?
Opportunity to do an overview of the
field(especially for outsider)
of papers
Decade
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Spectroscopic Factors from literatures
Example 1p1/2 neutron SF in 13C 12Cn

• Published spectroscopic factors show large
  fluctuations from analysis to analysis
• Consequence of using different optical model
  potentials and parameters for the DWBA reaction
  model.

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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 lt?A?p?fV?B?d?igt
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Extraction of Spectroscopic Factor

• For each angular distribution
• Fit first peak only (emphasize on maximum and
  shape)
• Require more than 1 data point

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Surreys TWOFNR Use global proton optical
potential and standardized parameters Soper-Johnso
n Adiabatic Approximation to take care of
d-break-up effects. n-potential wood-Saxon
shape with depth adjusted to binding energy.
ro1.25 fm ao.65. Include finite range
non-locality corrections
12C(d,p)13Cgs
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Systematic extraction of SFs
Liu et al, PRC 69, 064313 (2004)
Apply the technique to a large data set
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We studied 79 nuclei by digitizing 430 angular
distributions from literaturefor (p,d) (d,p)
reactions on target from Z3-24.
Z3 Li 6, 7, 8 Z4 Be 9, 10, 11 Z5 B 10, 11,
12 Z6 C 12, 13, 14, 15 Z7 N 14, 15,
16 Z8 O 16, 17, 18, 19 Z9 F 19, 20 Z10 Ne 21,
22, 23 Z11 Na 24 Z12 Mg 24, 25, 26,
27 Z13 Al 27, 28 Z14 Si 28, 29, 30,
31 Z15 P 32 Z16 S 32, 33, 34, 35, 36,
37 Z17 Cl 35, 36, 37, 38 Z18 Ar 36, 37, 38, 39,
40 Z19 K 39, 40, 41, 42 Z20 Ca 40, 41, 42, 43,
44, 45, 47, 48, 49 Z21 Sc 45, 46 Z22 Ti 46, 47,
48, 49, 50, 51 Z23 V 51 Z24 Cr 50, 51, 52, 53,
55
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Digitization of 430 angular distributions from
literaturefor (p,d) (d,p) reactions on target
from Z3-24

• No adjustment of input parameters to calculations
• Quality control
• Compare to Endts Best values when available.
• Compare SFs derived from (p,d) and (d,p)
  reactions separately to estimate the
  uncertainties in our method.

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Comparison with Endts results
Endt in 1977 compiled SFs of the s-d shell
nuclei from (p,d), (d,p) 50
uncertainty (p,d), (d,p), (d,t), (3He, a) 25
uncertainty
There are some scattering of the values but there
is a strong correlation between present analysis
and Endt values
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Digitization of 430 angular distributions from
literaturefor (p,d) (d,p) reactions on target
from Z3-24
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
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Comparison of (p,d) and (d,p) reactions
By requiring the chi-square per degree of freedom
is 1, we obtain nominal uncertainty of 20 for
each measurement.
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Textbook Example Spectroscopic factors of Ca
isotopes
Direct Nuclear Reaction Theories by Austern pg
291 l7/2, S1, 2, 0.75, 4, 0.5, 6, 0.25, 8 ACa
40Ca (A-40)n ? Assume 40Ca is a good inert
core.
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40-48Ca isotopes have good single particle states
with spherical cores SF for 49Ca is lower than
IPM and shell model predictions.
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Comparison with Austerns 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
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Compare with Modern Shell Model (Oxbash)
Good agreement with most isotopes Outliners
deformed nuclei and isotopes with small SFs (Ne)
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Measurements of Spectroscopic Factors
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(e,ep) sensitive to interior of the
wave-functions
40Ca
Spectroscopic factor
12C
16O
20
(e,ep) sensitive to interior of the
wave-functions
(d,p), (p,d) sensitive to surface of the
wave-functions Shell model -- long range
correlation effects
40Ca
Spectroscopic factor
12C
16O
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Summary

• We have extracted ground state neutron
  spectroscopic factors for 79 (Z3-24) nuclei
• 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 SFs?
• Most SFs fall short of IPM predictions but agree
  with modern day shell model calculations long
  range correlation.
• Is difference between SFs from (e,ep) and
  transfer reactions the short range correlations?
• Thanks to Hiu Ching Lee