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Global optical model potential parameters for proton

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Global optical model potential parameters for proton Powered By Docstoc
					Analysis of the elastic scattering of protons on 6,7Li and on 10,11B nuclei has been done in the
framework of the optical model at the beam energies up to 50 MeV. Differential cross sections
for the 6,7Li and 10, 11B were measured over the proton laboratory–energy range from 400 to
1200 KeV, and combined with published differential cross sections for proton elastically
scattering from 6,7Li and 10,11B between 0.5 MeV and 50 MeV are analyzed in terms of the
Optical Model. Depending on the measured data by us and literature data, we could enhance the
potential parameters using Esis88 Code, as well as SPI GENOA Code. Linear relationship between
volume real potential (V0) and proton energy (Ep) have been obtained. Also, surface imaginary
potential WD is proportional to the proton energy (Ep) in the range 0.700 and 14 MeV. Families of
optical model parameters are found characterized volume integral per nucleon pair for the real and
imaginary potentials, JR and Jw (MeV.fm3). Good agreement between theoretical and experimental in
whole range. We attempt to make empirical relations describing the energy dependence of the optical-
model potential.
Introduction

 Optical-model analysis of proton scattering data have been carried out
  for a wide range of incident proton energies, and a few attempts [ 1-3]
  have been made to empirically determine the energy dependence of
  the optical-model potential [4]. The optical model has been used
  extensively in the analysis of elastic scattering data for a wide variety of
  particles and a wide range of energies. In the energy region below 50
  MeV, extensive proton elastic scattering data exist [5]. These have, in
  general been analyzed in terms of an optical model in which the
  interaction is represented as the scattering of a point particle (proton)
  by a potential of form
       Uop(r)=Uc(r) +U(r) + iW(r)+ Uso(r)+ iWso(r)
Where Uc(r) is the coulomb potential due to a uniform distribution
 of appropriate size and total charge. The real term U(r) is almost
 taken to have a volume form –VRfR(r) with fR(r)={1+exp[(r-
 RR)/aR]}-1, the Wood-Saxon form factor.
Peculiarity of measurements

 Measurements of elastic scattering of protons on   10,11B

 and 6,7Li nuclei in low energy region were carried out
 with using the extracted beam from the complex
 recharged UKP-2-1 accelerator of the Institute of
 Nuclear Physics(National Nuclear Center, Republic of
 Kazakhstan) in the angular range 40-170˚. The proton
 energy varied in the range 400 – 1200 KeV. The beam
 intensity was 200 – 300 nA. Scattered particles were
 detected using surface-barrier silicon counters. The
 error of measured differential cross-sections is
 approximately equal to dimensions of presented dots
 and does not exceed 8%.
Table 1 contains the optical parameters for protons scattering on Lithium nuclei. The analysis of
protons data, carried out in wide energy range, had shown that for 6Li nuclei, the most suitable
parameters values are r0=1.05fm, rc=1.3fm, rD=1.923fm, as=0.20fm and rs=1.20 fm.
Table 1 contains the optical parameters for protons scattering on Lithium nuclei.
 Ep MeV    V0 MeV   r0          a0 Fm   WD MeV   rD Fm   aD Fm   vS MeV   rs Fm   aS Fm   JR        Jw
                                                                                          MeV.fm3   MeV.fm3
                    Fm
 0.975    54             1.05   0.52    0.355    1.923   0.57    9.30     1.020   0.200   454       22.19

 3        52             1.05   0.52    0.87     1.923   0.80    9.30     1.020   0.200   437       55.72

 5        50             1.05   0.50    1.18     1.923   0.57    15.6     1.020   0.200   407       75.58

 10       49             1.05   0.65    2.78     1.923   0.49    12.2     1.020   0.770   391       148.3

 14       46.5           1.05   0.50    6.72     1.923   0.42    9.86     1.020   0.200   378       304

 25       38             1.05   0.50    2.80     1.923   0.80    5.57     1.020   0.200   270       309

 29.9     34             1.05   0.67    2.93     1.923   0.80    3.37     1.020   0.200   149       111

 35       34.7           1.05   0.65    2.93     1.923   0.80    3.37     1.020   0.200   142       111

 45       30             1.05   0.65    2.63     1.923   0.80    2.33     1.020   0.200   122       100

 49       26        1.05        0.65    1.69     1.930   0.80    1.69     1.020   0.200   64        106
Results and discussions

 Data on elastic scattering were analyzed within the framework of
  the standard optical model with central potential, having the radial
  dependence in the Woods Saxon’s form. Optical potential
  parameters were selected on the base of achieving the best
  agreement between theoretical and experimental angular
  distributions. The fitting process is carried out using Eciss88 Code
  as well as Spi Genoa Code [14]. A systematic of potentials for
  protons interactions with atomic nuclei was given in the work [15].
  In the analogous approach with the use of measured and literature
  data on the elastic scattering there are determined parameters of
  the potential of protons interactions with 6,7Li and 10,11B – nuclei for
  the wide energy interval from the analysis of these data on the
  optical model.
 It is necessary to note that the selection of the
  potential as the optical one, we follow the physically,
  well- founded value of the volumetric integral of the
  real-valued part of the OP, determined as:
   JR = -(1/ApAli)  V(r)4r2dr ,

 Where Ap – and ALi– mass values of the incident
 particle and the target nucleus. Its value must be close
 to the corresponding value of the nucleon-nucleon
 potential of the interaction.
    We tried to guess the initial parameters depending on the relationV0 = 53.3 – 0.55Ep – 27(N-Z)/A +
    0.4 Z/A1/3[7] and also we depend on another articles to guess the initial parameters used in
    program Eciss88. Fig. 1a, 1b and 1c show the comparison between calculated using Optical Model
    and experimental angular distribution of protons scattered from 6Li.




Fig.1a shows the comparison between calculated and experimental angular distribution of protons scattered
from 6Li at low energies where dots represent experimental data and lines represent the calculated values.
Fig. 2 shows the comparison between calculated and experimental angular
distribution of protons scattered from 6Li where dots represent experimental
data and lines represent the calculated values.
 As expected the relation between WD and Ep is linear.
  The strength parameters in table 1 can be represented
  by:
 V0 = 56.10 - 0.61 Ep
 WD= -0.66 + 0.46Ep,
 The comparison of calculated angular distributions
  with experimental ones for some cases is shown in Fig.
  1. As it is seen there is a good agreement between
  theory and experiment in the whole angular range at
  all energies that give an evidence of pure potential
  character of protons scattering on lithium nuclei.
 Figures 2 and 3 show the relations between V0, WD and
 Ep and the behavior is in a good agreement as
 expected.
     7Li
     In comparison with 7Li we obtain this fig.7 from the work of R. A. Vanestane et al.
     [22].




     It is appears from the Figure 7 that the cross section for the forward scattering for both isotopes of
lithium is almost the same, whereas the cross section for backward scattering for 7Li is considerably larger.
From Figure 7 it is apparent that the cross section for 6Li is much smoother than the cross section for 7Li.
The different in the behavior of differential cross sections for elastic scattering in neighboring isotopes or
isobars in the region of light nuclei is not especially surprising since the small dimensions of nuclei limit the
number of partial waves which participate in the scattering thus the effect of a single partial wave can
become significant. The predominance of a given wave depends on the states available to the system.
Because the number of states is small, the spin of the target nucleus can have an important effect on the
choice of the possible states and consequently, on the nature of elastic scattering [22].
Table 4 contains the optical parameters for protons scattering on 7Li nuclei
This give us normal starting point to deal with light nuclei and their behaviors in spite of
our results are in the simplest form, we tried to put a lot relation in linear and others in
second order. Fig. 8 shows also a comparison between calculated and experimental for
7Li+p.


                                                                                                JR        Jw
    Ep MeV    V0 MeV   r0 fm    a0     WD MeV   rD fm    aD fm    Vs MeV    rs fm     as fm           3         3
                                                                                                MeV.fm    MeV.fm
    0.364       56     1.17    0.65      0.70     1.80    0.504     12.48      1.17      0.50    228.31        11

    0.441       62     1.17    0.60      0.30     1.80    0.504     12.48      1.17      0.50    220.49        4.09

    0.991       55     1.17    1.04      0.93     1.80    0.87      18.86      1.17      0.74    535.89     32.18

     1.03       55     1.17    1.03      0.93     1.80    0.79      18.80      1.17     0.747    535.89     27.25

     3.1      49.67    1.17    0.84     1.012     1.80    0.80      12.86      1.02      0.51    316.03     30.23

     4.0      49.129   1.17    0.913    2.198     1.80    0.346    11.988      1.17     0.769    367.27     19.84

     4.2      48.358   1.17    0.936    2.210     1.80    0.205    12.822      1.17     1.055    379.82     10.99

     5.0      48.956   1.17    0.945    3.798     1.80    0.361    11.689      1.17     0.656    370.82     10.20

    10.3(s)   37.29    1.17    0.527     8.55     1.80    0.545     12.86      1.17      0.8     109.43    140.38

    49.75     32.938   1.17    0.461    4.282     1.80    0.785    11.265      1.17     0.757     80.83    124.08
     (S)      37.249           0.531    5.799             0.593    9.285                0.522
Fig. 9 Contains Li7+p angular distributions at different energies
where dots represent experimental data and lines represent the
calculated values using Optical model
10B
Table 5 contains the optical parameters for protons scattering on 10B nuclei which can be represented by: V0 = 56.68 - 1.15
Ep,
WD= -0.58 + 0.56Ep,     Jw = 8.91+1.3 Ep , and     JR = 724-11.24 Ep
Table 5 contains the optical parameters for protons scattering on 10B nuclei



      Ep MeV    V0 MeV        r0 fm       a0    WD MeV    rD fm    aD fm    Vs MeV    rs fm      as fm      JR MeV.fm3    Jw MeV.fm3
    0.400          62      1.25          0.62   0.104    1.15     0.57      16.46     1.15       0.40      747.97        11


    0.60              59   1.25          0.65   0.65     1.15     0.770     12.5      1.15       0.55      760.87        11


    0.80       55.98       1.25          0.65   0.95     1.15     1.050     10.5      1.15       0.50      721.20        47


    1          51          1.25          0.78   1.54     1.15     0.48      5.50      1.15       0.65      693.64        77


    1.20       54          1.25          0.65   1.50     1.15     0.74      10.0      1.15       0.50      709           44


    5.3        48.5        1.25       0.65      2.00     1.15     0. 54     12.50     1.15       0.84      631.65        38


    8.5        46.5        1.25       0.65      7.20     1.15     0.50      10.50     1.15       0.57      599.67        125


    10         45          1.25       0.65      6.80     1.15     0.54      9.50      1.15       0.50      580.32        118


    13         43          1.25       0.65      7.80     1.15     0.54      12.5      1.15       0.50      554.53        150


    17         46          1.25       0.65      9        1.15     0.54      12        1.15       50        593           173
     As we notice here in 10B a good agreement between experimental and theoretical data
     expected using optical model, but in case of 5.3 MeV a deep minimum is obtained as in
     figure 12b. The resonance is responsible for this deviation and we will deal with this
     phenomenon in other work using different programs.




Fig. 12 shows theoretical (optical model) solid line and experimental as points for angular distribution at different energies for proton
scattering on 10B.
Figure shows theoretical (optical model) solid lines and experimental as points for angular
distribution at different energies for proton scattering on 10B. As we notice here in 10B a good
agreement between experimental and theoretical data expected using optical model, but in case of
5.3 MeV a deep minimum is obtained as in figure 12b. The resonance is responsible for this
deviation and we will deal with this phenomenon in other work using different programs.
B11 As we see for these energies calculated the first minimum is not exactly in reproduced, but the
shape are similar to those of the experimental angular distributions. Table 6 contains optical
parameters calculated for protons scattering on 11B.
Table 6 contains optical parameters calculated for protons scattering on 11B



  Ep MeV    V0 MeV         r0 fm       a0    WD MeV    rD fm    aD fm   Vs MeV   rs fm   as fm    JR MeV.fm3    Jw MeV.fm3
0.60         54.16      1.25          0.64   0.51     1.15     0.75     5.80     1.15    0.58    650.80        11.19


0.80            52.70   1.25          0.75   2.57     1.15     0.66     9.02     1.15    0.50    800.79        16.61


1          47           1.25          0.98   1.82     1.15     0.91     26       1.15    0.50    690.80        21.86


1.20       45.19        1.25          0.92   1.90     1.15     0.61     15.60    1.15    0.52    814.63        33.22


13         43.95        1.25       0.65      8        1.15     0.70     5.50     1.15    0.57    562           139


15.80      44.50        1.25       0.65      8        1.15     0.70     10       1.15    0.57    573           139


17.35      41           1.25       0.65      8        1.15     0.50     10       1.15    0.57    535           139


20         39           1.25       0.65      9        1.15     0.50     10       1.15    0.57    502.95        157.37


30         34           1.25       0.55      5        1.15     0.81     14.43    1.15    0.71    392           164
Fig. 14 shows the relation between beam energy Ep and the volume real potential V0 and imaginary potential WD for
protons scattering on 11B.
Fig. 16 shows the measured values by us of angular distribution 600, 800, 1000 and 1200 KeV for protons scattering on 11B.
Fig. 17 shows comparison between experimental and calculated angular distribution of proton scattering on   11B   at low energies.
Fig. 18 shows comparison between experimental and calculated angular distribution of proton scattering on   11B   between 13
MeV and 20 MeV.
Conclusion
 As we see in 11B+p case the first minimum is shifted from expected
  value at 80° to 70° and the second is shifted in the case of 15.8 MeV ,
  17.35 MeV and 20 MeV to left to the value 135° where in case of 13 MeV
  is shifted to 145° . In fair comparison between 10B and 11B we can see that
  the calculated values obtained for differential cross sections for 11B+p is
  better than for those obtained in case of 10B+p. The energy dependence
  of the strengths of the real potentials determined in present work
 VR= 56.10-0.61Ep+– 27(N-Z)/A + 0.4 Z/A1/3
 The third and fourth term is not examined but it agree with
  experimental results where the fourth parameter contains the
  symmetry parameter α= (N-Z)/A. As I mentioned before we can but
  this relation in simple form as VR= 56.10-0.61Ep. And the energy
  dependence of the strengths of the imaginary potentials WD
  determined in present work especially in 6Li the can be represented as:
 WD= -0.66 + 0.46Ep , for Ep ≤ 14 MeV
 and this for simplicity because our range extend from low
  energies 400 KeV to 50 MeV and this range make the task is
  somewhat difficult because at low energies the processes
  not pure elastic scattering, for higher energies WD is
  inversely proportional with Ep. We used Wv as constant
  value equal zero in spite of as mentioned in [23] that Wv
  values may variables between zero at low energies and
  Wv=1.15(Ec.m-32.7MeV), for 32≤ Ec.m≤39MeV and
  Wv=7.5MeV for 39.3 MeV< Ec.m.
 I’d like to concentrate on the point of obtained parameters
  where we use specially 6Li in our analysis because of the fair
  agreement obtained in 6Li, the fit obtained in these other
  analyses in table 7 are usually better than those of present
  work, where our analysis extracts over wider range.
                                                                                                   Radi
                                                                                                   Para
 Author       VR (Mev)       WD (MeV)                 Wv (MeV)     VSO(Me   aR(F)   aI(F)    aso(f
                                                                                                   (f)
                                                                   V)                        )
erey       53.3-0.55Ep+0.4   13.5±2             None               7.5      0.65    0.47     0.65 rR=rI=
           Z/A1|3+27 (N-                                                                           25
           Z)/A

ricke el   49.9-0.22Ep+0.4   Variable           2-4                6.04     0.75    0.63     0.73 rR=1.
 .         Z/A1/3+26.4 (N-                                                                   8    rI=1.3
           Z)/A                                                                                   rSO=1

 . A.      60.0-0.30Ep+0.4   0.64E For <13.8:   0 for E<32.7:(E-   5.5      0.75    0.50     0.57 rR=rI=
Watson     Z/A1/3+27 (N-                        2.7)X1.15                                         15-0
                             9.6-0.06E For
           Z)/A                                 For32.7≤E≤39
                             E≥13.8
                                                7.5 For E>39.3


resent     56.10 - 0.61     1.05+ 0.738E p-     None               Variable 0.65    variable 0.2   rR=1.
 ork       Ep+0.4 Z/A1|3+27 0.017Ep2 For                                                           rc=1.
           (N-Z)/A          <13.8                                                                  rD=1.

                             2.19811+0.31652
                             E-0.00478 E2

                             For E≥14
 Investigation of elastic scattering oxygen
  ions on carbon at energy near coulomb
                   barrier
 Study of elastic scattering of heavy ions on light nuclei
  at energies near the Coulomb barrier is of interest
  both in terms of establishing reliable values for the
  parameters of interaction potentials of heavy ions at
  low energies, and for studying the mechanism of
  cluster transfer in the scattering.
 The extracted beam of 16O of energy 28 MeV from the
 cyclotron DC-60 was directed to carbon target of
 thickness 20 mg/cm2. The current beam during the
 experiment was nearly equal 30 nA. The differential
 cross section was analyzed in a wide range of angles
 20-165 in center of mass system. In that work in
 addition to our results at energy 28 MeV, That reaction
 was also analyzed in a wide range of energies fro 28-
 608 MeV.
 It was clearly shown that at energy near the coulomb
 barrier , there is a rise in the cross section at backward
 angles, and that phenomenon due to the alpha cluster
 transfer. There are many types of transfer reaction
 A(B,A)B, which could be due to, (a)1 particle transfer
 (proton) such as in the reaction of 11B(12C,11B)12C , (b)
 two particle transfer , (c)or four particle transfer
 (alpha-transfer)as in our studied reaction.

 The optical model code spival and Distorted Wave
 Born Approximation (Dwuck 5)were used in data
 analysis.
 The phenomenon of nuclear rainbow was also
 observed at different energies used in the study.

 The spival code could be used effectively for
 interpreting the forward and scattering.

 DUWCK5 program was used in data analysis at the
 backward angles.

 Good agreement was obtained between the
 experimental and the calculated data , with values of
 the real and imaginary potential depth obey to the
 standard physical trend with energy.
The Cyclotron DC-60, located in Astana, Kazakhstan
Results and analysis
                            5
                       10

                            4
                       10


                       10
                            3                             Spival608MeV_Exp
                                                          Spival608MeV_Cal
    D. Cross section



                            2
                       10

                            1
                       10

                            0
                       10

                        -1
                       10

                        -2
                       10

                        -3
                       10
                                0   5   10   15    20     25    30    35     40

                                                  Angle

Fig 1: The angular Distribution of 16O on 12C at energy 608 MeV using optical potential
                                      code SPIVAL
                        4
                   10

                        3
                   10

                        2                                       Spival260MeV_Exp
                   10
                                                                Spival260MeV_Cal
                        1
D. Cross section




                   10

                        0
                   10

                    -1
                   10

                    -2
                   10

                    -3
                   10

                    -4
                   10

                    -5
                   10
                            0            20           40           60           80           100

                                                           Angle
                            Fig 2: The angular Distribution of 16O on 12C at energy 260 MeV using optical
                                                        potential code SPIVAL
                        5
                   10
                        4
                   10                                           Spival230MeV_Exp
                   10
                        3                                       Spival230MeV_Cal
                        2
                   10
D. Cross section




                        1
                   10
                        0
                   10
                    -1
                   10
                    -2
                   10
                    -3
                   10
                    -4
                   10
                    -5
                   10
                               0         20        40           60      80        100

                                                        Angle
                        Fig 3: The angular Distribution of 16O on 12C at energy 230 MeV using optical
                                                    potential code SPIVAL
                        5
                   10
                        4
                   10
                        3
                   10                                          Spival200MeV_Exp
                   10
                        2                                      Spival200MeV_Cal
D. Cross section



                        1
                   10
                        0
                   10
                    -1
                   10
                    -2
                   10
                    -3
                   10
                    -4
                   10
                    -5
                   10
                            0       20        40        60       80        100      120

                                                     Angle

                   Fig 4: The angular Distribution of 16O on 12C at energy 200 MeV using optical
                                               potential code SPIVAL
                        5
                   10

                        4
                   10
                                                                   Spival80MeV_Exp
                   10
                        3                                          Spival80MeV_Cal
D. Cross section




                        2
                   10

                        1
                   10

                        0
                   10

                    -1
                   10

                    -2
                   10

                    -3
                   10
                            0      20     40     60     80     100    120     140    160    180

                                                         Angle

                            Fig 5: The angular Distribution of 16O on 12C at energy 180 MeV using
                                                optical potential code SPIVAL
                        4
                   10

                        3
                   10
                                                              Spival170MeV_Exp
                        2
                   10                                         Spival170MeV_Cal
D. Cross section



                        1
                   10

                        0
                   10

                     -1
                   10

                     -2
                   10

                     -3
                   10

                     -4
                   10
                            0       20       40       60       80      100      120      140

                                                      Angle
                    Fig 6: The angular Distribution of 16O on 12C at energy 170 MeV using optical
                                                potential code SPIVAL
                        5
                   10

                        4
                   10
                                                         SPIVAL132MeV_Cal
                        3
                   10
                                                         SPIVAL132MeV_Exp
                        2
                   10
D. Cross section




                        1
                   10

                        0
                   10

                     -1
                   10

                     -2
                   10

                     -3
                   10

                     -4
                   10
                             0          20          40           60        80         100

                                                         Angle

                   Fig 7: The angular Distribution of 16O on 12C at energy 132 MeV using optical
                                               potential code SPIVAL
                        5
                   10

                        4
                   10
                                                                 Spival80MeV_Exp
                   10
                        3                                        Spival80MeV_Cal
D. Cross section




                        2
                   10

                        1
                   10

                        0
                   10

                    -1
                   10

                    -2
                   10

                    -3
                   10
                            0     20     40     60     80     100    120    140    160     180

                                                        Angle


                            Fig 8: The angular Distribution of 16O on 12C at energy 80 MeV using
                                                optical potential code SPIVAL
                        5
                   10


                   10
                        4                                              Spival65MeV_Exp
                                                                       Spival65MeV_Cal
                        3
                   10
D. Cross section




                        2
                   10

                        1
                   10

                        0
                   10

                    -1
                   10

                    -2
                   10

                    -3
                   10
                            0      20      40     60      80     100     120     140     160       180

                                                            Angle

                                Fig 9: The angular Distribution of 16O on 12C at energies 65 MeV
                                              using optical potential code SPIVAL
                        5
                   10


                   10
                        4                                           Spival42MeV_Exp
                                                                    Spival42MeV_Cal
                        3
                   10
D. Cross section




                        2
                   10

                        1
                   10

                        0
                   10

                    -1
                   10

                    -2
                   10

                    -3
                   10
                            0     20     40     60     80     100   120    140    160    180

                                                            Angle
                            Fig 10: The angular Distribution of 16O on 12C at energies 42 MeV
                                           using optical potential code SPIVAL
                    4
                   10



                                                             Spival35MeV_Exp
                    3
                   10                                        Spival35MeV_Cal1
D. Cross section




                    2
                   10




                    1
                   10




                    0
                   10

                        20    40      60      80     100     120     140     160    180

                                                   Angle


              Fig 11: The angular Distribution of 16O on 12C at energies 35 MeV using optical
                                           potential code SPIVAL
                        4
                   10                                        Spival28MeV_Exp
                                                             Spival28MeV_Cal
                   10
                        3                                    DWBA_A1
                                                             DWBA_A2
                        2                                    DWBA_A3
D. Cross section




                   10


                        1
                   10


                        0
                   10


                    -1
                   10


                    -2
                   10
                            0    20       40       60       80      100      120      140      160

                                                         Angle

                        Fig 12: The angular Distribution of 16O on 12C at energy 28 MeV using optical
                                                    potential code SPIVAL
          550
                     The relationship between V and E                         30
          500                                                                                The relationship between W and E
                                                                              25
          450

          400                                                                 20
V (MeV)




                                                                    W (MeV)
          350
                                                                              15

          300
                                                                              10
          250

                                                                              5
          200

          150                                                                 0
                                                                                   0   100   200     300    400    500    600   700
                0   50      100     150      200        250   300                                     E (MeV)
                                  E (MeV)


   a) The relationship between the real potential depth V (MeV)and Energy E (MeV)

   b) The relationship between the real potential depth W (MeV)and Energy E (MeV)
E (MeV)    V0 (MeV)   rr (fm)   ar (fm)   W0 (MeV)   ri (fm)   ai (fm)   JV       JW       rc

608        130.2      0.8409    0.215     24.97      1.0629    0.4077    193.16   77.32    0.95*

260        168.29     0.769     0.801     24.863     1.163     0.4542    271.80   101.05   0.95*

230        180.586    0.7630    0.825     22.32      1.162     0.6219    291.98   95.40    0.95*

200        213.218    0.683     0.924     17.838     1.219     0.5612    293.66   85.50    0.95*

170        255.905    0.629     0.970     16.4087    1.245     0.5212    311.65   82.59    0.95*

132        288.19     0.586     0.986     13.617     1.224     0.5608    310.86   66.02    0.95*

80         319.446    0.5460    0.906     8.2505     1.2940    0.5118    274.69   46.27    0.95*

65         334.207    0.518     0.955     7.2634     1.304     0.582     276.53   42.40    0.95*

42         365.066    0.495     0.924     6.80       1.320     0.4073    267.21   39.49    0.95*

35         453.187    0.4850    0.716     5.80       1.34      0.1909    242.26   34.15    0.95*

28         478.19     0.74      0.463     5.30       1.122     5.596     542.99   82.39    0.95*

24         500.39     0.603     0.383     5.20       1.35      1.307     312.40   43.46    0.95*



          Table 1: The optical potential used by optical potential code spival
Conclusions
 As expected, the experimental results of the elastic scattering of
  16O  on 12C at an energy E = 1.75 MeV/ nucleon shows a marked
  rise in cross section of elastic scattering at large angles.

 However, the analysis of experimental data in terms of the
  optical model leads to obtaining a discrete set of parameters of
  the interaction potential for the systems 12C + 16O, 16O + 16O and
  12C + 12C. In order to resolve the ambiguity in determining the

  potential depth, the analysis of angular distributions of elastic
  scattering were made in a wide range of energy. To assess the
  contribution of exchange effects due to clustering phenomena in
  elastic scattering of oxygen on the carbon nucleus for reverse
  angles Born approximation method of distorted waves was used.
  The JV and JW values obtained with the WS1 for all these
  reactions also agree closely with the global systematics found
  for light HI elastic scattering
Thank You

				
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