International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 2021

ISSN 2229-5518

Systematics of (Gamma-N) Reaction with Light

Nuclei-Part I

Ahmed Abdul-Razzaq Selman

Abstract—Gamma-Nucleon (γ , N ) reactions can provide a wealth of information about nuclear internal structure. Investigation of the

photo-nucleon reaction of the types

(γ , n) and (γ , np) cross-sections was made in the present paper based the theory of Giant Dipole

Resonance (GDR) mechanism. GDR peaks were fitted to obtain the physical quantities related to the well-known Lorentz equation, with results useful in data evaluation of the selected isotopes. The isotopes and reactions selected for the present study are:Li6 (γ , n) Li5, Li6

(γ , n) Li5+Li6 (γ , np) He4, Li

(γ , n) Li6, Li7 (γ , n) Li6+Li7 (γ , np) He5, Be9 (γ , n) Be8, B10 (γ , n) B9, B10 (γ , n) B9+B10 (γ , np) Be8, C12

γ C11

12 γ C11

12 γ B10, C13

(γ , n) C

12+C13

(γ , np) B11

and C14

(γ , n) C

13+C14

(γ , np) B12

reactions examined with energy

( , n)

, C (

, n)

+C (

, np)

range (0-85) MeV. Graphical and numerical comparisons were made. A net result was reached that curve fitting can be safely considered but only for Be9, B10 and C12,13,14 isotopes, while other isotopes might not give acceptable results for data fitting.

Keywords—Gamma reactions, Giant Dipole Resonance, Intermediate energy, Nuclear reactions.

——————————  ——————————

1 INTRODUCTION

HE aim of phenomenological studies is to try to explain complicated physical systems using rather simplified mathematical approach. The yield of such studies was always fundamental in the field of nuclear physics, since solving the
where a regular library was put into use [11]. This mission is currently developing rapidly in the course of the data evalua- tion, which is meant to put the exaggerated reaction data into one standard form evaluated and regularly used in any practi-

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system's equation is still beyond our reach due to the lack of
knowledge about the actual nuclear forces.
Photo-nuclear reactions at intermediate energies character- ize many important nuclear features, thus there were many practical applications for these reactions. These applications span from the experimental investigation of the photo- disintegration reactions of the nuclear constituents, to the in- duced fission reactions [1]. Most significantly, photoneutron nuclear reaction has a unique interest in nuclear waste treat-
ment [2,3,4] and has received special attention. γ -rays reac-
tions has also been the first practical example suggested to explain radiation reaction with the nucleus[5] and is consid- ered as an ideal tool to study the electromagnetic interactions with nuclear matter. Generally, however, the ( γ ,nucleon) re-
action measured from its unique cross-section is explained by two types of reaction models, namely: (a) the low and inter- mediate excitation energy models described by the Giant Di- pole Resonance (GDR) mechanism [6,7] which can be effec- tively used for energies about 30 MeV, and (b) the high excita- tion energy models specified by the Quasi-Deuteron (QD) model [8] which is accepted for applications at energies above
150 MeV. Between these energies lays the intermediate range
which was examined by other mechanisms, such as the exci- ton model [9], or other types of models -see Ref.[10] for de- tails. There have been many experimental measurements to calculate photo-nuclear reaction cross-section. Describing the numerous results by a standard form was one of the achieve- ments of the International Atomic Energy Agency (IAEA),

————————————————

• Dr. Ah med A bd ul-Razza q Selman is cur re ntly a full pr ofes sor a t the Dept. Astrono my & Spa ce, Co lleg e of Scie nce, Baghdad U niv ers ity, Baghdad-Ira q, e mail: aase lma n@s cbaghdad.ed u.iq.

cal calculation that deal with nuclear data. However, this task
was developed further by many attempts to better unify the
standard parameters for this special type of nuclear reactions, i.e., the photo-nuclear reactions aside of other types of reac- tions -for example, see [11-13]. Recent studies of data evalua- tion made for photo-nuclear reaction mostly focused on heavy isotopes found in nuclear fission process, such as U235,238 iso- topes, Pu239, and Th232 [14]. Earlier studies [15] tried to deal with the entire periodic table which provided basic references for nuclear reaction studies in this field.
The scope of present study deals with photo-nuclear reac- tions by means of straightforward evaluation of the reaction parameters for light isotopes, using fitting procedure of the
experimental results to the well-known Lorentz shape of the reaction cross-section. Results are then compared with exper- imentally measured parameters.
However, the present treatment shows a relative inade- quacy for exact interpretation of data based on theoretical
framework, since data fitting was always a method used to correlate data numerically. The examined data were those mainly obtained from online available reaction libraries ac- cessed by JANIS 3.0 program [16], and from the EXFOR li- brary[11]. Details of the examined data and procedure are ex- plained accordingly.

2 GIANT DIPOLE RESONANCE (GDR)

The reason thought to cause GDR phenomena in different nu- clei is that when incident gamma photon (of energy of few tenths of MeV) is absorbed by the nucleus, neutrons and pro- tons will oscillate as individual groups against each other [17]. This oscillation can take two different modes: the isovector and isoscalar modes. Isoscalar mode will correspond to a mo- tion of the center of mass of the entire nucleus, and probably

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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 2022

ISSN 2229-5518

will not cause GDR phenomenon. Isovector mode, on the oth- er hand, corresponds to individual oscillation of the nuclear constituents, thus will lead to energy consumption via dipole

Table (2). The reaction of the type Li7 (γ , n) Li6 could not be

fitted using either of these equations, so a suggested form:

E 2 Γ2

oscillation and GDR will be observed. This is the Goldhaber-
Teller model [18]. Further development of this model was ex-

σ (E DGR γ

) = σ γ E

 2

  +

(4),

2Γ2

plained for hot (excited) nuclei by means of quantum mechan-

 E E E

E  E

 γ γ

ical model -see Ref. [19].
GDR corresponds to a maxima in the reaction cross-
section. This cross-section can be described for spherical nuclei by [15]:

E 2 Γ2

was used, where e is a free fitting parameter.

4 RESULTS

The results of the present fitting are listed in Table (3). A com-

σ (E

DGR γ

) = σ γ E

E  2

(1),

parison with experimental data found in the literature is made

 E 2 − E 2 

+ E 2Γ2

in Table (4). The curves are shown in, respectively: Fig. (1) for

 γ E  γ E

Li6 (γ , n, p) Li5, Fig.(2) for Li6 (γ , n) Li5+Li6 (γ , np) He4, Fig.(3) for

and for deformed nuclei as,

E 2 Γ2

Li (γ , n) Li , Fig.(4) for Li (γ , n) Li +Li (γ , np) He , Fig.(5) for

7 6 7 6 7 5

σ (E ) =

DGR γ

∑ σ

= E, i 

γ E, i

2

(2),

Be9 (γ , n) Be8, Fig.(6) B10 (γ , n) B9, Fig.(7) for B10 (γ , n) B9+B10

(γ , np) Be8, Fig.(8) for C12 (γ , n) C11, Fig.(9) for C12 (γ , n) C11+C12

i 1,2

 E 2 − E 2

 + E 2Γ2

 γ E, i 

γ E, i

10 13 12 13

  (γ , np) B

, Fig.(10) for C

(γ , n) C

, Fig.(11) for C

(γ , n)

Eq.(1) is Lorentzian shape and eq.(2) is the sum of two Lo-

C12+C13 (γ , np) B11 and Fig.(12) for C14 (γ , n) C13+C14 (γ , np) B12

rentzians. In these equations, E1,i ,

σ , and

E1,i

E1,i are the

reactions.
GDR energy position, peak cross section, and width respec-
tively. The deformed nuclear shapes given in general as [17],

In Fig.s (13) and (14), the curve fitting results of C12 (γ , n)

C11 and C12 (γ , n) C11+C12 (γ , np) B10 reactions, respectively, are

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R(θ , φ ) = R 1 +

o

β λ Y (θ , φ )

(3),

plotted with unified data showing the two peaks of these reac-

 λ = 2, 4,6 o o 

tions.
where Y

λo

are spherical harmonics and (θ ,φ ) are angular coordi-

nates in the frame of fixed body, Ro is the (spherical) nuclear radius and β is the deformation parameter. The theory listed

λ o

above can be assumed proper and fair to describe photoneu- tron cross-section in the range below 30 MeV, thus it provides enough theoretical bases for comparison with the results of this work. Further details about photoneutron cross-section calculations are found in Refs. [6,7,10, 15, and 17].

3 DATA

The data used in this research are listed in Table (1). The reac- tions were treated according to eq.(1) or (2), as classified by

5 DISCUSSIONS

It must be mentioned that the present work aimed on fitting available experimental data found in the IAEA standard photonuclear libraries. Therefore curve fitting was made for more than one experimental data set in most cases. Since these sets show some inconsistency amongst themselves some fit- ting results were appropriately made for the average of sets. Data region illustrated in Fig.(1) were selected during fitting, where some of the experimental points (indicated in the fig- ure) were excluded from the

TABLE(1). EXPERIMENTAL DATA SETS USED IN THIS RESEARCH.

Energy

Reaction Type Number of points

Range

(MeV)

Author(s) Reference

J., Vol., p., Yr.

10 5.43-9.00 L.Green and D.J.Donahue Phys. Rev. 135,701,1964

Zhurnal Eksperimental'noi i

Li6 (γ , n) Li5

37 5.40-51.90 E.B.Bazhanov, A.P. Komar, and

A.V.Kulikov

S.Costa, F.Ferrero, C. Manfredotti, L.

Teoret. Fiziki (ZET),46,1479,

1964

40 4.50-85.00

Pasqualini and L. Roasio Nuovo Cimento B,42,382, 1966

S.Karataglidis, D. Zanov, P.D.Harty,

and M.N.Thompson Nucl. Phys. A,501,108,1989

Tot. 123 4.50-85

Li6 (γ , n) Li5+Li6 (γ , np) He4 107 5.68-32.08 B.L.Berman, R.L.Bralett, J.T.Caldwell, R.R.Harvey& S.C.Fultz

Phys. Rev. Lett., 15,727,1965

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ISSN 2229-5518

Li7 (γ , n) Li6 8 7.38-10.83 L.Green and D.J. Donahue Phys. Rev. 135,701,1964

Int. Conf. on Photonucl. Reac-

60 7.05-30.53 R.L.Bralett, B.L.Berman,

M.A.Kelly, J.T.Caldwell, and S.C.Fultz

tions, Pacific Grove (73PACIFI)

1,175, 1973

1 1.56 M.Fujishiro, K.Okamoto,T.Tsujimoto Can. J. Phys., 61,1579,1983

H.Utsunomiya, & Y.Yonezawa,

8 1.79-2.19

58 2.11-6.11

H.Akimune, T.Yamagata, M.Ohta, M.Fujishiro, H.Toyokawa, H.Ohgaki H.Utsunomiya, & Y.Yonezawa, H.Akimune, T.Yamagata, M.Ohta, M. Fujishiro, H.Toyokawa, & H.Ohgaki

Phys. Rev. C 63, 018801,2001

Evaluated from Phys. Rev. C 63,

018801,2001

Li7 (γ , n) Li6+Li7 (γ , np) He5

12 1.68-2.06 K.Sumiyoshi, H.Utsunomiya, S.Goko, and T.Kajino

6 1.67-2.16 M.Fujishiro, T.Tabata, K.Okamoto, & T.Tsujimoto

2 1.68-1.85 J.H.Gibbons, R.L. Maclin, J.B.Marion, and H.W. Schmidt

Nucl.Phys. A,709,467,2002

Can. J. Phys. 60,1672,1982

Phys. Rev.114,1319,1959

3 1.69-1.78 W.John and J.M.Prosser Phys. Rev. 127,231, 1962

4 2.61-8.06 R.D.Edge Nucl.Phys., 2,485,1957

Izv. Rossiiskoi Akademii Nauk,

158 1.67-19.75 A.Goryachev, G.Zalesny &I.V.Pozdnev

Tot.264 1.56-19.75

Ser.Fiz.(IZV),56, 159,1992 and Bull.Russian Academy of Scienc- es – Physics (BAS),56, 762,1992

B10 (γ , n) B9 4 9.00-10.83 L.Green and D.J.Donahue Phys. Rev. 135,701,1964

94 10.52-35.07 U.Kneissl, K.H.Leister, H.O.Neidel, and

A.Weller

B10 (γ , n) B9+B10 (γ , np) Be8

113 8.59-25.26

Tot. 207 8.59-35.07

M.H.Ahsan, S.A.Siddiqui, and

H.H.Thies Nucl. Phys. A, 469,381,1987

C12 (γ , n) C11

26 20.17-21.18 W.E.Del Bianco and W.E.Stephens Phys. Rev.126,709,1962

80 2.15-26.70 W.A.Lochstet and W.E.Stephens Phys. Rev.,141,1002,1966

47 18.7-24.6 J.P.Roalsvig, I.C.Gupta & R.Haslam Can. J. Phys., 39,643,1961

25 20.12-21.04 L.O.Cohen and W.E. Stephens Phys. Rev.Lett.,2,263,1959

96 20.11-26.69 W.A.Lochstet and W.E.Stephens Phys. Rev.,141,1002,1966

S.C.Fultz, J.T. Caldwell,B.Berman,

R.Bralett and R.Harvey Phys. Rev. 143,790,1966

C12 (γ , n) C11+C12 (γ , np) B10

68 19.02-32.06 U.Kneissl,E.A.Koop,G.Kuhl,K.H.Leister,

& A.Weller

34 18-26.25 E.B.Bazhanov, A.P. Komar,A.V. Kuli- kov, and V.I.Ogurtsov

35 18-51.8 E.B.Bazhanov, & A.P.Komar,

Nucl. Inst. Meth. Phys. Res.,

127,1,1975

Yadernaya Fizika (Yad. Fiz.), 3,

711, 1966

A.V.Kulikov,& V.I.Ogurtsov Yad. Fiz,3,711,1966

B.S.Ishkhanov,I.M.Kapitonov

I.M.Piskarev, and V.G. Shevchenko Yad. Fiz.,14,253,1971

J.Miller, C.Schuhl, G.Tamas

and C.Tzara Journal de Physique, 27,8,1969

C13 (γ , n) C12

Tot.594 18-51.8

162 8.09-19.06 R.E.Pywell, B.L.Berman, P.Kean, M.N.Thompson

Nucl.Phys.A,369,141,1981

9 6.61-10.83 L.Green and D.J.Donahue Phys. Rev. 135,701,1964

Tot. 171 6.61-19.06

C13 (γ , n) C12+C13 (γ , np) B11 173 7.59-41.83

J.Jury, B.Berman, D.Faul, P.Meyer, K.

Mcneill, and J.G.Woodworth Phys. Rev.C, 19, 1684, 1979

89 4.87-25.01 R.Koch and H.H.Thies Nucl. Phys. A 272, 296, 1976

Tot.262 4.87-41.83

C14 (γ , n) C13+C14 (γ , np) B12 107 8.24-36.20 R.Pywell,B.Berman,J. Woodworth, J.

Jury, K.G.Mcneill,& N.T.Thompson

Phys. Rev. C,32,384,1985

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TABLE (2). CLASSIFICATION OF THE FITTED REACTIONS.

2

1.8

1.6

1.4

Fit

B.L.Berman et al

1.2

1

0.8

0.6

0.4

0.2

0

0 10 20 30 40 50 60 70 80

Energy, MeV

Fig.(2). Curve fitting results for Li6 (γ , n) Li5 + Li6 (γ , np) He4 reac- tion.

1.2

1

Li-7(,n)Li-6

IJSE0.8 R

0.6

0.4

Fit

S.Karataglidis et al. L.Green and D. J. Donahue

0.2

0

5 7 9 11 13 15

3 Energy, MeV

2.5

Fit

E.B.Bazhanov et al. L.Green and D.J.Donahue S.Costa et al.

Fig.(3). Curve fitting results for Li7 (γ , n) Li6 reaction. Surrounded

points were excluded from fitting.

1

0.9

2

0.8

Li-7(,n)Li-6+Li-7(,n+p)He-5

Fit

R.L.Bralett et al.

1.5

0.7

0.6

1 0.5

0.5

0.4

0.3

0

0 10 20 30 40 50 60 70 80 90 100

Energy, MeV

0.2

0.1

Fig.(1). Curve fitting results for Li6 (γ , n) Li5 reaction. Surrounded points were excluded from the fitting.

0

0 20 40 60 80 100 120

Energy, MeV

Fig.(4). Curve fitting results for Li7 (γ , n) Li6 + Li7 (γ , np) He5 reac-

tion.

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1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

14

Fit

M.Fujishiro et al. 12

H.Utsunomiya et al.

H.Utsunomiya et al. (ev) 10

K.Sumiyoshi et al.

J.H.Gibbons et al.

8

W.John et al.

R.D.Edge

A.M.Goryachev et al. 6

M.Fujishiro et al.

4

W.E.Del Bianco and W.E.Stephens W.A.Lochstet and W.E.Stephens J.P.Roalsvig et al.

L.O.Cohen and W.E.Stephens

W.A.Lochstet and W.E.Stephens L.Katz and A.G.W.Cameron E.B.Bazhanov et al. E.B.Bazhanov et al.

J.Miller et al. B.S.Ishkhanov et al. Fit Peak No.1

Fit Peak No.2

0.2 2

0

0 5 10 15 20 25 30 35 40

Energy, MeV

0

16 21 26 31 36

Energy, MeV

Fig.(5). Curve fitting results for Be9 (γ , n) Be8 reaction. Fitting range

from (2 to 18 MeV).

Fig.(8). Curve fitting results for C12 (γ , n) C11 reaction.

1

0.9

0.8

0.7

0.6

0.5

10

L.Green and D.J.Donahue

9

8

7

6

S.C.Fultz et al. U.Kneissl et al. Fit Peak No.1

Fit Peak No. 2

0.4 5

0.3

4

0.2

3

0.1

2

0

5 7 9 11 13 15

Energy, MeV

1

0

15 17 19 21 23 25 27 29 31 33 35 37 39

Fig.(6). Experimental results for B10

(γ , n) B9

reaction. No proper fit

Energy, MeV

was found anywhere.

7

6

5

Fit U.Kneissl M.H.Ahsan

Fig.(9). Curve fitting results for C12 (γ , n) C11+C12 (γ , np) B10 reac- tion.

7

R.E.Pywell et al.

6

4

3

2

1

0

0 10 20 30 40 50

Energy, MeV

L.Green and D.J.Donahue

5

4

3

2

1

Fig.(7). Curve fitting results for B10 (γ , n) B9 + B10 (γ , np) Be8 reac- tion.

0

0 5 10 15 20

Energy, (MeV)

Fig.(10). Experimental results for C13 (γ , n) C12 reaction. No proper fit was found.

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12 10

Fit Peak No.1

Fit Peak No.2 9

10 J.W.Jury et al.

R.Koch and H.H.Thies 8

Fit Peak No. 1

Fit Peak No. 2

Exp. Data

7

8

6

6 5

4

4

3

2

2

1

0

0 10 20 30 40 50

Energy, (MeV)

0

15 17 19 21 23 25 27 29 31 33 35 37 39

Energy, MeV

Fig.(11). Curve fitting results for C13 (γ , n) C12 + C13 (γ , np) B11

reaction. Data from Jury et al. were fitted only.

Fig.(14). Curve fitting results C12 (γ , n) C11 + C12 (γ , np) B10

plotted with unified data showing the two peaks.

10

Fit

9 R.E.Pywell et al.

8

7

6

fitting to achieve the best results. Some of the points of Ba- zhanov et al. suggest that there are more than one peak in Li6 (γ , n) Li5 reaction, however, the fit assumed only one peak.

Similar remarks are seen for Li6 (γ , n) Li5+Li6 (γ , np) He4

shown in Fig.(2), Be9 (γ , n) Be8 shown in Fig.(5), B10 (γ , n) B9+B10

(γ , np) Be8 as in Fig.(7), C13 (γ , n) C12 as in Fig.(10) and C14 (γ , n)

4

C13+C14 (γ , np) B12 in Fig.(14) where some points suggest more

3

than one cross-section maxima. All these reactions were treat-

2 ed assuming only one peak for simplicity, with acceptable

1 fitting results in general. This choice was made in this work based on the fact that more than one peak in the photonuclear

0

5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Energy, MeV

Fig.(12). Curve fitting results for C14 (γ , n) C13 + C14 (γ , np) B12

reaction.

14

Fit Peak No.1

Fit Peak No.2

12 Exp. Data

10

8

6

4

2

0

16 18 20 22 24 26 28 30

Energy, MeV

Fig.(13). Curve fitting results of C12 (γ , n) C11 plotted with unified data showing the two peaks.

cross-section assumes that there is a certain nuclear defor-
mation [17]. Examining the experimental data for the quadru-
pole moment for Li6, Be9, B10 showed that these nuclei in their
ground states do not possess a detectable quadrupole moment

value [22]. Thus only one peak is assumed during data treat- ment of these nuclei. The experimental data in both Fig.(6) for B10 (γ , n) B9 and Fig. (10) for C13 (γ , n) C12 reactions could not be

fitted by any equation similar to eq.(1) or (2), or the approxi- mate eq.(4). Thus, these data sets were not treated here. Alt- hough the results for Li7 (γ , n) Li6 -Fig.(3)- did not show any

peak, it could be fitted. In Fig.(5) the results for Be9 (γ , n) Be8 reaction may also strongly suggest the presence of another peak at energy above 20 MeV. This was not made since the

peak at energy 8-10 MeV gave excellent results. The results of

C12 (γ , n) C11 shown in Fig.(8) were plotted again in Fig.(13)

after unifying experimental data. It can be perfectly seen that there are two distinguished photonuclear peaks at distant en- ergies. Similar remarks are seen for C12 (γ , n) C11+C12 (γ , np) B10

and for C13 (γ , n) C12+C13 (γ , np) B11 shown in Fig.s(9,11), re- spectively. In Fig.(11), data from Jury et al. were fitted only which gave the best results. These results are acceptable since

the C12 nucleus has experimental quadrupole moment +0.06
mb[22]. Acceptance of the results obtained from these fitting

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procedures suggests that simple fitting can be efficient for da- ta treatment of these isotopes.
Another comparison of the results is indicated in Table (4).
From this table it can be seen that some of the present fitting results encountered percentage error more than 100% which implies their impractical use. However, most these cases with large error actually resulted because the IAEA data were eval- uated for all the peaks of the photonuclear reaction, i.e., there were more

Reaction

σ E Γ e Goodness of the Fit

SSE: 8.598 (1), R-

(1) SSE: Sum of Square Error. (2)R-square: The coefficient of multiple deter-

Li6 (γ , n) Li5 1.89 29.3

8

15.33 –

square: 0.7073(2)AR:

0.7003 (3), RMSE:

0.3199 (4)

mination. (3)AR: Adjusted R-square, the degree of freedom adjusted R- square. (4)RMSE: Root Mean Square Error

Li6 (γ , n) Li5 +

Li6 (γ , np) He4 1.56

17.0

0 12.90 –

SSE: 2.168, R-square:

0.8627AR: 0.8601,

than one peak resolved experimentally while in this work the assumption was to fit for one peak only. This case is seen spe-

RMSE: 0.1437

SSE: 0.01715, R-

cially for Li6 (γ , n) Li5+Li6 (γ , np) He4and Li7 (γ , n) Li6reactions.
This strongly suggests that these types of reactions still need

Li7 (γ , n) Li6 4.17 0.15 4.99 1.3

square: 0.7613 AR:

0.7424, RMSE:

further treatment, where the present treatment might not be efficient. On the other hand, however, most of the remaining

0.02124

results were in a good agreement with the IAEA data..

IJSSE: 0S.4093, R- ER

Li7 (γ , n) Li6+

Li7 (γ , np) He5 0.93 8.56 14.28 –

Be9 (γ , n) Be8 1.43 7.92 7.82 –

square: 0.9011 AR:

0.8976, RMSE:

0.08474

SSE: 0.6516, R- square: 0.931 AR:

0.9289, RMSE:

0.09789

6 CONCLUSIONS

Most photonuclear data found in the IAEA library for the iso- topes Li6,7, Be9, B10, and C12,13,14 were fitted for the photonuclear reactions (γ , n) and (γ , n) + (γ , np) for energies around the GDR

peaks. Careful yet uncomplicated data fitting was made for

B10 (γ , n) B9 – – – – None

these sets of experimental data to obtain the photonuclear data

B10 (γ , n) B9+

B10 (γ , np) Be8 4.69

19.3

1 23.94 –

SSE: 48.27, R-square:

0.8884 AR: 0.8873,

σ , Γ , Γ

o

ically. The results showed acceptable match with earlier eval-

RMSE: 0.4864

uations. It is concluded that, in general, the simple curve fit-

C12 (γ , n) C11

C12 (γ , n) C11

(Peak No.2)

C12 (γ , n) C11

(Both Peaks)

9.16 2.95 22.99 –

5.42 3.42 25.71 –

30.0

9 3.37 23.11 –

SSE: 625.1, R-square:

0.8694 AR: 0.8688,

SSE: 3.475, R-square:

0.6222, AR: 0.6028, RMSE: 0.2985

SSE: 921, R-square:

0.808 AR: 0.8072,

ting for photonuclear data for the selected isotopes can be safely considered but only for Be9, B10 and C12,13,14 isotopes.

(γ , n) + (γ , np) . Other types of re-actions for the selected iso- topes are still needed to be further treated with the same

method specially (γ , n) reaction for O and F isotopes in order

to complete the KL-shell group, and since there are wide in-

RMSE: 1.354

dustrial applications regarding these isotopes.

C12 (γ , n) C11+

C12 (γ , np) B10 7.18 4.52 22.97 –

SSE: 267.8, R-square:

0.7618 AR: 0.7597,

TABLE(4). COMPARISONS OF THE PRESENT RESULTS WITH EXPERIMENTAL AND EVALUATED IAEA PHOTONUCLEAR DATA.

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ISSN 2229-5518

a) Percentage Error (%).

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