Calculation and analysis of p + 40,42,43,44,46,48,natCa reaction cross sections at incident energies from threshold to 250 MeV

Nuclear Instruments and Methods in Physics Research B 269 (2011) 597–611

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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

Calculation and analysis of p + 40,42,43,44,46,48,natCa reaction cross sections at incident energies from threshold to 250 MeV Haiying Liang, Yinlu Han ⇑, Qingbiao Shen Science and Technology on Nuclear Data Laboratory, China Institute of Atomic Energy, P.O. Box 275(41), Beijing 102413, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 21 July 2010 Received in revised form 12 November 2010 Available online 25 January 2011 Keywords: Proton-induced reaction Nuclear models theory Cross section Energy spectra

a b s t r a c t All cross sections, angular distributions and energy spectra of neutron, proton, deuteron, triton, helium, alpha particle emission for p + 40,42,43,44,46,48,natCa reactions have been calculated and analyzed at incident proton energies from threshold to 250 MeV by nuclear theoretical models. The theoretical calculated results are in good agreement with existing experimental data. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction With the rapid development of science and technology, the application field of charged particle nuclear data are becoming promising and expanding, as in accelerator application, astrophysics, space radiation effects, medical radioisotope production, radiation damage of materials, activation analysis, and standard reference nuclear data. The radioisotope yield cross sections can tell us which energy region is more suitable for specific radioisotope production in certain nuclear reaction, and these radioisotopes are used in medicine both for diagnostic studies and therapy. The developments of high-quality nuclear data for natural calcium and its isotopes are particularly important due to calcium is abundant in concrete shielding in accelerator-driven systems (ADS), and is widely used in medical applications for therapy. As the experimental data of charged particle induced reactions at the incident charged particles energies from threshold to 250 MeV are scarce, the theoretical calculation is very important and interesting. Natural calcium is consisted of six isotopes 40 42 43 44 Ca(96.94%), Ca(0.647%), Ca(0.135%), Ca(2.09%), 46 Ca(0.004%) and 48Ca (0.0187%). In this work, the proton optical potential parameters are obtained from experimental data of non-elastic cross sections and elastic scattering distributions for p + 40Ca reaction at incident proton energies from threshold to 250 MeV. All cross sections, angular distributions, energy spectra as well as double differential cross sections for emission neutron, proton, deuteron, triton, helium ⇑ Corresponding author. Tel.: +86 10 69358986; fax: +86 10 69357787. E-mail address: [email protected] (Y. Han). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.01.015

and alpha particle are calculated and analyzed by using the nuclear theoretical models which integrate the optical model, the intra-nuclear cascade model, direct, pre-equilibrium and equilibrium reaction theories. In Section 2, the theoretical models of nuclear reaction are described. Section 3 shows the analysis and comparison of calculated results with existing experimental data. Section 4 gives some simple conclusions.

2. Theoretical models and model parameters The optical model is used to describe non-elastic cross sections, inelastic scattering cross sections, elastic scattering angular distributions and to calculate the transmission coefficients that enter the statistical model of compound nucleus reactions, inverse cross sections of equilibrium reaction theory and pre-equilibrium reaction theory, etc. The phenomenological spherical optical model potentials considered here are Woods–Saxon [1] form for the real part, Woods–Saxon and derivative Woods–Saxon form for the imaginary parts corresponding to the volume and surface absorption, respectively, and the Thomas form for the spin–orbit part. The optimal set of proton optical model potential parameters can be searched automatically by the code APMN [2] to fit the relevant experimental data of non-elastic cross sections and elastic scattering angular distributions. The adjustment of optical potential parameters is performed to minimize a quantity called v2, which represents the deviation of the theoretically calculated results from the experimental values.

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The optical model potential is

Table 1 Optical model potential parameters.

VðrÞ ¼ V r ðrÞ þ i½W s ðrÞ þ W v ðrÞ þ V so ðrÞ þ V c ðrÞ:

ð1Þ

Vr(r) is the real part potential. Ws(r) and Wv(r) are the imaginary part potential of surface absorption and volume absorption. Vso(r) is the spin–orbit potential and Vc(r) is Coulomb potential. The real part potential of optical model potential is

V r ðrÞ ¼ 

V r ðEÞ 

1 þ exp

rRr ar

:

ð2Þ

The imaginary part of surface absorption of optical model potential is

exp W s ðrÞ ¼ 4W s ðEÞ h



rRs as

1 þ exp





rRs as

i2 :

ð3Þ

The imaginary part of volume absorption of optical model potential is

W v ðrÞ ¼ 

W v ðEÞ 

1 þ exp

rRv av

:

ð4Þ

V0 V1 V2 V3 V4 W0 W1 W2 U0 U1 U2 VSO rr rs rv rso rc ar as0 av0 aso as1 av1

54.793 0.362 0.0002 24 0.4 8.7536 0.083 12 2.719 0.2 6E-04 6.2 1.1723 1.1986 1.1815 1.01 1.25 0.6734 0.5112 0.7488 0.75 0.7 0.7

The spin–orbit couple potential is

2V so V so ðrÞ ¼  h aso r

exp



1 þ exp

rRso aso





rRso aso

 i2 :

ð5Þ

The Coulomb potential is

V c ðrÞ ¼

  8 2 > < 0:720448 RZc 3  Rr 2 ; if r < Rc ; c

> : 1:440975Z ; r

ð6Þ

if r 6 Rc :

The potential depth of real part is

V r ðEÞ ¼ V 0 þ V 1 E þ V 2 E2 þ V 3 ðN  ZÞ=A þ V 4 Z=A1=3 :

ð7Þ

The potential depth of imaginary part of surface absorption is

W s ðEÞ ¼ W 0 þ W 1 E þ W 2 ðN  ZÞ=A:

ð8Þ

The potential depth of imaginary part of volume absorption is

W v ðEÞ ¼ U 0 þ U 1 E þ U 2 E2 :

ð9Þ

The diffusive widths of the surface absorption and volume absorption for imaginary part

aj ¼ aj0 þ aj1 ðN  ZÞ=A; j ¼ s; v

ð10Þ

ar and aso are the diffusive widths of the real part and the spin–orbit couple potential.

Ri ¼ r i A1=3 ; i ¼ r; s; v ; so;c;

ð11Þ

rr, rs, rv, rso and rc are the nuclear radii parameters of the real part, the imaginary part of surface absorption, the imaginary part of volume absorption, the spin–orbit couple potential and the Coulomb potential, respectively. A, Z are mass and charge number of the target. E is the incident particle energy in the laboratory system. V0, V1, V2, V3, V4, W0, W1, W2, U0, U1, U2, Vso and Vc are in MeV; rr, rs, rv, rso, rc, ar, as0, as1, av0, av1 and aso are in fermi. Based on experimental data of non-elastic cross sections and elastic scattering distributions for p + 40Ca reaction at incident proton energies below 250 MeV, the set of proton potential parameters for 40Ca is obtained and given in Table 1. While the parameters of the isospin dependent term ((N-Z)/A, Z/A1/3) and the spin–orbit couple potential V3, V4, W2, Vso, rso, as1, av1 and aso

are taken from the global phenomenological spherical optical model potential in Ref. [1], since they are reasonable. Since the set of optical potential parameters are dependent on mass number A and neutrons number N of the target, it is used in p + 42,43,44,46,48Ca reactions. The optical model potential parameters of neutron are taken from fitting experimental data [3–13] of total cross sections, nonelastic cross sections and elastic scattering angular distributions. The optical model potential parameters of deuteron are taken from Ref. [14]. The optical model potential parameters of triton are the same as those of deuteron. The optical model potential parameters of helium and alpha particle are taken from Ref. [15]. The direct inelastic scattering angular distributions to low-lying states are important in nuclear data theoretical calculations. The code DWUCK4 [16] of the distorted wave Born approximation theory is used to calculate the direct inelastic scattering cross sections and angular distributions. The optical model potential parameters obtained are used in DWUCK4 code. The pre-equilibrium statistical theory based on exciton model, evaporation models and Hauser-Feshbach theory with width fluctuation correction [17–19], and intra-nuclear cascade model are used to describe the nuclear reaction pre-equilibrium and equilibrium decay processes. The code MEND [20] included optical model, intra-nuclear cascade model, compound nuclear reaction and pre-equilibrium nuclear reaction theory and treats the direct reaction as input data. It can calculate all kinds of reaction cross sections and energy spectra for six outgoing light particles (n, p, d, t, 3He and a) and various residual nuclei in the energy range up to 250.0 MeV. The equilibrium emissions are calculated by using Hauser-Feshbach theory with width fluctuation correction for the first particle emission process in the low-energy region and the evaporation model for the first and the eighth particle emissions. The pre-equilibrium emissions with exciton model for the first and the fifth particle emissions and the cascade emissions of one to four nucleons with certain fractions before pre-equilibrium and evaporation are considered. The improved Iwamoto-Harada model [21,22] is adopted for composite particles (d, t, 3He, a) emissions and Pauli principle in the calculation of exciton state densities are accommodated, and the pre-equilibrium mechanism of gamma-ray emission are also taken into account. The angular dependent part of the double differential cross sections for emission six outgoing light particles

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599

(n, p, d, t, 3He and a) are obtained from Kalbach phenomenological approach [23–27], which is based on a systematical study of a wide variety of experimental data. The Kalbach systematical parameter K used in the two body residual interaction plays a very important role in nuclear reaction, which determines the contribution of pre-equilibrium and equilibrium decay processes. According to experimental data of various reaction cross sections, K is 1500 MeV3 in this work. The level density adopts Gilbert–Cameron formula in lower energies region, and the Ignatyuk model [28], which includes the washing out of shell effects with increasing excitation energy, is matched continuously onto low-lying experimental discrete level in the higher energies region. The level density parameters a and pair correction parameters D of the back-shifted Fermi gas level density [29] for low-energy are adjusted to more fit with experimental data of cross sections.

3. Theoretical results and analysis The comparison of calculated results of proton non-elastic cross sections with experimental data for 40Ca is shown in Fig. 1. The calculated results are in good agreement with experimental data [30–34]. The calculated results of proton non-elastic cross sections for 42,44,48,natCa are in good agreement with experimental data [35–37]. Figs. 2 and 3 show the comparison between the calculated results and experimental of proton non-elastic cross sections data for 44,natCa. Since there are no experimental data of proton nonelastic cross sections for 43,46Ca, the proton non-elastic cross sections are obtained from model calculations. The calculated results of elastic scattering angular distributions at the incident proton energies from 9.86 to 201.4 MeV and elastic scattering angular distributions in the Rutherford ratio at the incident proton energies from 13.98 to 160.0 MeV are in good agreement with experimental data [38–61] for p + 40Ca reaction. Figs. 4–8 show respectively the comparison of the calculated results with experimental data [38,41,47–61]. The calculated results of elastic scattering angular distributions at the incident proton energies of 9.0, 12.0, 21.0, 25.0, 30.0, 35.0, 40.0, 45.0 and 48.4 MeV, and elastic scattering angular distributions in the Rutherford ratio at the incident proton energies of 22.85, 49.35 and 65.0 MeV are in good agreement with experimental data [47,60,62–64] for p + 42Ca reaction as shown in Figs. 9 and 10. The calculated results of elastic scattering angular distributions

Fig. 1. Calculated proton non-elastic cross sections (solid curve) compared with experimental data (symbols) for p + 40Ca reaction.

Fig. 2. Calculated proton non-elastic cross sections (solid curve) compared with experimental data (symbols) for p + 44Ca reaction.

Fig. 3. Calculated proton non-elastic cross sections (solid curve) compared with experimental data (symbols) for p + natCa reaction.

at the incident proton energies of 9.0, 12.0, 21.0, 25.0, 30.0, 35.0, 40.0, 45.0, 48.4 and 65.0 MeV, and elastic scattering angular distributions in the Rutherford ratio at the incident proton energies of 10.75, 14.15, 15.61, 22.85, 49.35 and 65.0 MeV are in good agreement with experimental data [47,50,58,62–65] for p + 44Ca reaction as shown in Figs. 11 and 12. The calculated results of elastic scattering angular distributions at the incident proton energies of 9.0, 12.0, 21.0, 25.0, 30.0, 35.0, 40.0, 45.0, 48.4 and 201.4 MeV, and elastic scattering angular distributions in the Rutherford ratio at the incident proton energies of 14.03, 15.05, 15.63 and 65 MeV are in agreement with experimental data [47,60,62,65,66] for p + 48Ca reaction as shown in Figs. 13 and 14. Fig. 15 shows good agreement between the calculated results of elastic scattering angular distributions and experimental data [67] at the incident proton energy of 200.0 MeV for p + natCa reaction. The calculated results of elastic scattering angular distributions in the Rutherford ratio are in basically agreement with experimental data [68] at the incident proton energy of 26.3 MeV for p + natCa reaction. The inelastic scattering angular distributions are mainly from contributions of direct reactions and compound nuclear reactions. The contributions of direct reactions are above the incident proton energy of 20.0 MeV, and the contributions of the compound

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Fig. 5. Calculated proton elastic scattering angular distributions (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 10. Fig. 4. Calculated proton elastic scattering angular distributions (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 10.

nuclear reactions are below the incident proton energy of 20.0 MeV. The discrete levels are taken into from ground (3.3526 0+) to the 19th excited (6.9302 6+) state for 40Ca; ground (0 0+) to the 9th excited state (3.4470 3) for 42Ca; ground (0 0+) to the 12th excited state (2.1027 1.5) for 43Ca; ground (0 0+) to the 8th excited state (3.3079 3) for 44Ca; ground (0 0+) to the 7th excited state (3.6389 2+) for 46Ca; ground (0 0+) to the fifth excited state (4.6120 3+) for 48Ca. The calculated results of proton inelastic scattering angular distributions from the second excited state (3.7367 3) for 40Ca at the incident proton energies from 40.0 to 201.4 MeV agree with experimental data [48,54–56,59,69] as shown in Fig. 16. Yagi et al. [48], Ejiri et al. [56] and Seifert et al. [55] respectively measured the proton inelastic scattering angular distributions for different excited states of 40Ca at the incident proton energies of 55.0, 65.0 and 201.4 MeV. Present calculated results are good in agreement with the experimental data [48,55,56]. Fig. 17 shows the comparison of the calculated results with the experimental data [56] at the incident proton energy of 65.0 MeV. Figs. 18 and 19 show the comparison of the calculated results with the experimental data [55] at the incident proton energy of 201.4 MeV. Bane et al. [63] measured the proton inelastic scattering angular distributions of different excited states for 42,44Ca at the incident proton energy of 22.85 MeV. The calculated results are in good agreement with the experimental data [63] as shown in Figs. 20 and 21. The calculated results of proton inelastic scattering angular distributions for different excited states for 48Ca agree with experimental data [56,66] at the incident proton energies of 65.0 and 201.4 MeV. Fig. 22 shows the good agreement between the calculated results of the 1st excited state (3.8317 2+) for 48Ca and experimental data. There are

no experimental data of proton inelastic scattering angular distributions for 43,46Ca up to now. The proton optical potential parameters give a good description of measured elastic and inelastic scattering angular distributions. Direct reactions to low-lying residual nucleus states are precalculated and included as input into the MEND calculations. For (near-)spherical nuclides for which appropriate experimental data exists, the local and global neutron and proton phenomenological optical models potential with incident energies from 1 keV up to 200 MeV and in the mass range 24 6 A 6 209 were given and the dispersion corrections were included in Ref. [70]. The calculated results of proton reaction cross sections and elastic scattering angular distributions from the present optical model potential improve or are similar to those from Koning and Delaroche optical potential [70]. Artun et al. [71] measured reaction cross sections of some reaction channels for p + 40Ca reaction, but every reaction channel only have a experimental datum at the incident proton energy of 110.0 MeV. The calculated results are in agreement with experimental data [71] for 40Ca(p, p0 )40Ca and 40Ca(p, 2p)40Ca reactions as shown in Fig. 23. The other reaction cross sections for 40Ca(p, x)39Ca, 40Ca(p, x)38K, 40Ca(p, 3p)38Ar, 40Ca(p, x)37Ar, 40Ca(p, x)36Ar, 40Ca(p, x)32S and 40Ca(p, x)28Si reactions have been calculated and analyzed. The calculated results are in basically agreement with the experimental data. The Fig. 24 shows the comparison of the calculated results for 40Ca(p, x)39Ca and 40 Ca(p, x)28Si reactions with experimental data [71]. The calculated results are in agreement with experimental data. The calculated results of 42Ca(p, p0 )42Ca reaction cross sections are compared with experimental data taken from [72]. The theoretically calculated results are in good agreement with experimental data. There are no experimental data for other reaction channels.

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Fig. 8. Calculated proton elastic scattering angular distributions in the Rutherford ratio (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 101.

Fig. 6. Calculated proton elastic scattering angular distributions (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 10.

Fig. 9. Calculated proton elastic scattering angular distributions (solid curves) compared with experimental data (symbols) for p + 42Ca reaction. The results are offset by factors of 10.

Fig. 7. Calculated proton elastic scattering angular distributions in the Rutherford ratio (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 102.

The calculated results of 43Ca(p, n)43Sc reaction cross sections are compared with experimental data taken from [73,74]. The calculated results are in good agreement with experimental data as shown in Fig. 25. There are no experimental data for other reaction channels. The calculated results of 44Ca(p, n)44Sc reaction cross sections are compared with experimental data taken from [72,73]. The calculated results are in good agreement with experimental data as shown in Fig. 26. The calculated results of 44Ca(p, 3He)42K reaction

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Fig. 10. Calculated proton elastic scattering angular distributions in the Rutherford ratio (solid curves) compared with experimental data (symbols) for p + 42Ca reaction. The results are offset by factors of 102.

Fig. 12. Calculated proton elastic scattering angular distributions in the Rutherford ratio (solid curves) compared with experimental data (symbols) for p + 44Ca reaction. The results are offset by factors of 102.

Fig. 11. Calculated proton elastic scattering angular distributions (solid curves) compared with experimental data (symbols) for p + 44Ca reaction. The results are offset by factors of 10.

cross sections are in agreement with a experimental datum [75] as shown in Fig. 27. The calculated results of 44Ca(p, 2n)43Sc reaction cross sections are in agreement with the experimental data [73] at the incident proton energies below 25.0 MeV, but smaller than experimental data at the incident proton energies above 25.0 MeV. Fig. 28 shows comparison of calculated results with experimental data. Fig. 29 show that the calculated results are in agreement with experimental data [73,76] for 44Ca(p, 2p)43K reaction cross sections.

Fig. 13. Calculated proton elastic scattering angular distributions (solid curves) compared with experimental data (symbols) for p + 48Ca reaction. The results are offset by factors of 10.

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Fig. 14. Calculated proton elastic scattering angular distributions in the Rutherford ratio (solid curves) compared with experimental data (symbols) for p + 48Ca reaction. The results are offset by factors of 102.

603

Fig. 16. Calculated proton inelastic scattering angular distributions of the second excited state (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 10.

Fig. 15. Calculated proton elastic scattering angular distributions (solid curve) compared with experimental data (symbols) for p + natCa reaction.

Leveberg et al. [77] measured reaction cross sections of 48Ca(p, n)48Sc, 48Ca(p, 2n)47Sc and 48Ca(p, np)47Ca reaction at the incident proton energies above 120.0 MeV, and the calculated results agree well with experimental data [77] for 48Ca(p, n)48Sc and 48Ca(p, 2n)47Sc reactions and are smaller than experimental data for 48 Ca(p, np)47Ca reaction. Fig. 30 shows the comparison of calculated results with experiment data [74,78,79] for 48Ca(p, n)48Sc reaction cross sections. The calculated results are in good agreement with experimental data [78,79], but higher than experimental data [74]. There are no experimental data for other reaction channels. The calculated results of cross sections for p + natCa reaction are from theoretical values of cross sections for p + 40,42,43,44,46,48Ca reactions. The cross sections of natCa(p, x)48Sc, natCa(p, x)47Sc, nat Ca(p, x)46Sc, natCa(p, x)43K, natCa(p, x)42Ar, natCa(p, x)42K reactions are very small and less than 1.5 mb, and natCa(p, x)39Ar reaction cross section are less than 5 mb. The cross sections for natCa(p, x)48Sc reaction are from 48Ca(p, 48 n) Sc reaction. The experimental data [80,81] for natCa(p, x)48Sc

Fig. 17. Calculated proton inelastic scattering angular distributions at the incident proton energy of 65.0 MeV (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 100, 101, 101, 103, 106, 107, 108.

reaction cross sections are above incident proton energies of 20.0 MeV and the calculated results are in good agreement with experimental data [80,81] as shown in Fig. 31. The cross sections for natCa(p, x)47Sc reaction are from 48Ca(p, 2n)47Sc reaction. Leveberg et al. [77] measured experimental data

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Fig. 20. Calculated proton inelastic scattering angular distributions at the incident proton energy of 22.85 MeV (solid curves) compared with experimental data (symbols) for p + 42Ca reaction. The results are offset by factors of 100, 100, 102, 104.

Fig. 18. Calculated proton inelastic scattering angular distributions at the incident proton energy of 201.4 MeV (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 100, 101, 103, 105, 107, 1010.

Fig. 21. Calculated proton inelastic scattering angular distributions at the incident proton energy of 22.85 MeV (solid curves) compared with experimental data (symbols) for p + 44Ca reaction. The results are offset by factors of 100, 101, 103, 106.

Fig. 19. Calculated proton inelastic scattering angular distributions at the incident proton energy of 201.4 MeV (solid curves) compared with experimental data (symbols) for p + 40Ca reaction. The results are offset by factors of 100, 102, 104.

which agree well with the calculated results for 48Ca(p, 2n)47Sc reaction at the incident energies above 120.0 MeV. Walton et al. [82] measured experimental data of natCa(p, x)47Sc reaction cross sections at the incident proton energies between 10.0 and 50.0 MeV, and the value for experimental data [82] of natCa(p, x)47Sc reaction cross sections range from 0.04 to 0.16 b, so the value for experimental data of 48Ca(p, 2n)47Sc reaction cross sections are supposed to range from 20 to 100 b, that is unreasonable. The experimental data [82] of natCa(p, x)47Sc are needed to be checked. The cross sections natCa(p, x)46Sc reaction are from 46Ca(p, n)46Sc and 48Ca(p, 3n)46Sc reactions. Fig. 32 shows that the calculated results are in good agreement with experimental data [80],

Fig. 22. Calculated proton inelastic scattering angular distributions of the first excited state (solid curves) compared with experimental data (symbols) for p + 48Ca reaction. The results are offset by factors of 100, 101.

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Fig. 23. Calculated 40Ca(p, p0 )40Ca and 40Ca(p, 2p)39K reaction cross sections (curves) compared with experimental data (symbols).

Fig. 24. Calculated 40Ca(p, x)39Ca and 40Ca(p, x)28Si reaction cross sections (curves) compared with experimental data (symbols).

Fig. 25. Calculated 43Ca(p, n)43Sc reaction cross section (solid curve) compared with experimental data (symbols).

46

46

and the first peak are contributions from Ca(p, n) Sc reaction and the second peak are contributions from 48Ca(p, 3n)46Sc reaction.

605

Fig. 26. Calculated 44Ca(p, n)44Sc reaction cross section (solid curve) compared with experimental data (symbols).

Fig. 27. Calculated 44Ca(p, 3He)42K reaction cross section (solid curve) compared with experimental datum (symbol).

Fig. 28. Calculated 44Ca(p, 2n)43Sc reaction cross section (solid curve) compared with experimental data (symbols).

The cross sections of natCa(p, x)43K reaction are consisted of Ca(p, 2p)43K, 46Ca(p, a + nt + 2d + 2n2p)43K and 48Ca(p, a2n + 4n2p)46Sc reactions. Fig. 33 shows the comparison of calculated results with experimental data [80,81]. The calculated results 44

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Fig. 29. Calculated 44Ca(p, 2p)43K reaction cross section (solid curve) compared with experimental data (symbols).

Fig. 32. Calculated natCa(p, x)46Sc reaction cross section (solid curve) compared with experimental data (symbols).

Fig. 30. Calculated 48Ca(p, n)48Sc reaction cross section (solid curve) compared with experimental data (symbols).

Fig. 33. Calculated natCa(p, x)43K reaction cross section (solid curve) compared with experimental data (symbols).

Fig. 31. Calculated natCa(p, x)48Sc reaction cross section (solid curve) compared with experimental data (symbols).

Fig. 34. Calculated natCa(p, x)42Ar reaction cross section (solid curve) compared with experimental data (symbols).

are larger than experimental data [80] at the incident proton energy between 25.0 and 65.0 MeV, and smaller than experimental data [81] above 100 MeV.

Fig. 34 shows the comparison of calculated results for natCa(p, x) Ar reaction with experimental data [83]. With the exception of the first experimental datum, the other experimental data are 42

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Fig. 35. Calculated natCa(p, x)42K reaction cross section (solid curve) compared with experimental data (symbols).

good in agreement with the calculated results. The cross sections of nat Ca(p, x)42Ar reaction are consisted of 44Ca(p, 3p)42Ar, 46Ca(p, ap + 2n3p)42Ar and 48Ca(p, pa2n + at + 4n3p)42Ar reactions. Calculated results of natCa(p, x)42K reaction cross sections agree with experimental data [79,80] as shown in Fig. 35. The cross sections of natCa(p, x)42K reaction are consisted of 44Ca(p, 3 He + pd + n2p)42K, 46Ca(p, an + 3n2p)42K and 48Ca(p, a3n + 5n2p)42K reactions. The calculated results of natCa(p, x)39Ar reaction cross section agree with experimental data [83] as shown in Fig. 36. The cross sections for natCa(p, x)39Ar reaction are consisted of 42Ca(p, p3He + p2d + n3p)39Ar, 43Ca(p, ap + 2n3p)39Ar, 44Ca(p, apn + ad + 3n3p)39Ar, 46Ca(p, ap3n + ad2n + 5n3p)39Ar and 48 Ca(p, 7n3p) 39Ar reactions. The comparisons of the calculated results with experimental data [80,83–85] for natCa(p, x)38Ar, natCa(p, x)37Ar, natCa(p, x)36Ar, nat Ca(p, x)36Cl reactions cross sections are shown in Figs. 37–40. The calculated results are in good agreement with experimental data [80,83–85] for natCa(p, x)38Ar, natCa(p, x)36Ar, natCa(p, x)36Cl reactions cross sections. natCa(p, x)38Ar reaction cross sections are mainly from contributions of 40Ca(p, 3p)38Ar reaction; natCa(p, x)36Ar reaction cross sections are mainly from contributions of 40 Ca(p, ap)36Ar reaction; natCa(p, x)36Cl reaction cross sections are mainly from contributions of 40Ca(p, n4p)36Cl reaction.

607

Fig. 37. Calculated natCa(p, x)38Ar reaction cross section (solid curve) compared with experimental data (symbols).

Fig. 38. Calculated natCa(p, x)37Ar and natCa(p, x)37K reaction cross sections (curves) compared with experimental data (symbols).

Fig. 39. Calculated natCa(p, x)36Ar reaction cross section (solid curve) compared with experimental data (symbols).

nat

39

Fig. 36. Calculated Ca(p, x) Ar reaction cross section (solid curve) compared with experimental data (symbols).

The natCa(p, x)37Ar reaction cross sections are mainly from Ca(p, p3He + n3p)37Ar reactions. The calculated results agree with the experimental data [83] at the incident energies above

40

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Fig. 40. Calculated natCa(p, x)36Cl reaction cross section (solid curve) compared with experimental data (symbols).

25.0 MeV and smaller than experimental data at the incident energies below 25.0 MeV where maybe include the contribution of the other reaction channel natCa(p, x)37K reaction. It is mainly from contributions of 40Ca(p, a + 2d + 2n2p)37K reactions, and there are no experimental data for natCa(p, x)37K reaction. Based on agreements of the calculated results with experimental data for all reaction cross sections, the energy spectra and double differential cross sections of emission neutron, proton, deuteron, triton, alpha and helium particle for p + 40,42,43,44,46,48Ca are calculated by means of theoretical models. The energy spectra of emission neutron, proton, deuteron, helium, and alpha particle at energies of 50, 100, 150 and 200 MeV for p + 40Ca are shown in Figs. 41–45. From the figures, it was seen that the increasing importance of pre-equilibrium emission contribution becomes evident as the incident proton energy increases. The structures of emission proton spectra are from contributions of the direct inelastic scattering reaction for higher emission energies. The energy spectra and double differential cross sections of emission neutron, proton, deuteron, triton, alpha and helium for p + 42,43,44,46,48Ca reactions are calculated and analyzed, and their theoretically calculated results are similar to those of p + 40Ca reaction. Fig. 46 shows the overall agreement between experimental data [86] and calculated results of emission neutron for p + 48Ca reaction at the incident proton energies of 25, 35 and 45 MeV.

Fig. 41. Calculated energy spectra of emission neutron (solid curves) for p + 40Ca reaction at the incident proton energies of 50.0, 100.0, 150.0 and 200.0 MeV.

Fig. 42. Calculated energy spectra of emission proton (solid curves) for p + 40Ca reaction at the incident proton energies of 50.0, 100.0, 150.0 and 200.0 MeV.

Fig. 43. Calculated energy spectra of emission deuteron (solid curves) for p + 40Ca reaction at the incident proton energies of 50.0, 100.0, 150.0 and 200.0 MeV.

In overall way, the agreements between our calculated results and existing experimental data for isotopes of calcium are good. But there are some disagreements between calculated results and existing experimental data for natural calcium. It suggests that the discrepancy in the experimental data of proton induced reaction between natural calcium and its isotopes need to be made a check. The evaluated data for p + 40Ca reaction in ENDF/B-VII database [87] were provided over the incident proton energy range from threshold to 150 MeV based on evaluated cross sections from experimental data and calculated results using theoretical model code GNASH [88]. The evaluated data for p + 40,42,43,44,46,48Ca reactions were given in JENDL/HE [89] based on evaluated cross sections from experimental data and calculated results using theoretical model code GNASH. The evaluated data for p + 40,4142,43,44,45,46,47,48Ca reactions were given in TENDL [90] over the incident proton energy range from threshold to 200 MeV using theoretical model code TALYS [91]. The energy–angle-correlations for all outgoing particles (neutrons, protons, deuterons, tritons, alpha particles) are based on Kalbach systematics [25,27].

H. Liang et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 597–611

Fig. 44. Calculated energy spectra of emission helium (solid curves) for p + 40Ca reaction at the incident proton energies of 50.0, 100.0, 150.0 and 200.0 MeV.

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Fig. 46. Calculated energy spectra of emission alpha particle (solid curves) at the incident proton energies of 25.0, 35.0 and 45.0 MeV compared with experimental data (symbols) for p + 48Ca reaction.

clear library and can be used in different applications, such as medicine, concrete shielding in accelerator-driven system. Acknowledgements This work is one of National Basic Research Program of China (973 Program), that is Key Technology Research of Accelerator Driven Sub-critical System for Nuclear waste Transmutation, and supported by the China Ministry of Science and Technology under Contract No. 2007CB209903. References

Fig. 45. Calculated energy spectra of alpha emission particle (solid curves) for p + 40Ca reaction at the incident proton energies of 50.0, 100.0, 150.0 and 200.0 MeV.

The present calculated results in this work improve the evaluated data from Refs. [87,89,90].

4. Conclusions Based on existing experimental data of non-elastic cross sections and elastic scattering angular distributions for p + 40Ca reaction, an optimal set of optical potential parameters for proton induced reaction between natural calcium and its isotopes has been obtained. Proton induced reaction on natural calcium and its isotopes have been studied at incident energies from threshold energy to 250 MeV. All cross sections, angular distributions and energy spectra of emission (n, p, d, t, 3He and a) for p + 40,42,43,44,46,48Ca reactions have been calculated by the theoretical models, which integrate the optical model, the intra-nuclear cascade model, direct, equilibrium and pre-equilibrium reaction theories. The present calculated results are in good agreement with existing experimental data. These evaluated data enriched the nu-

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