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Nuclear Instruments and Methods in Physics Research B 239 (2005) 314–330

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Calculation and analysis of 63,65,natCu(p,x) reactioncross sections in the Ep 6 250 MeV energy range

Yinlu Han a,*, Zhengjun Zhang b, Jonghwa Chang c,Sooyoul Oh c, Chonghai Cai d

a China Institute of Atomic Energy, P.O. Box 275(41), Beijing 102413, People�s Republic of Chinab Department of Physics, Northwest University, Xi�an 710069, People�s Republic of Chinac Korea Atomic Energy Research Institute, P.O. Box 105, Yusong, Taejon, 305-600, Koread Department of Physics, Nankai University, Tianjin 300071, People�s Republic of China

Received 21 January 2005; received in revised form 21 March 2005Available online 6 July 2005

Abstract

According to advanced nuclear models that account for details of nuclear structure and the quantum nature ofnuclear reactions, and the experimental data of reaction cross sections and elastic scattering angular distributions ofnatural copper and its isotopes, all cross sections of proton induced reaction, energy spectra, and the double differentialcross sections for neutrons, protons, deuterons, tritons, helium and alpha emissions are calculated and analyzed forp+63,65,natCu at incident proton energies below 250 MeV by using nuclear theoretical models. Theoretical calculatedresults are compared with existing experimental data.� 2005 Elsevier B.V. All rights reserved.

PACS: 25.40.Cm; 25.55.�e; 25.60; 24.10.Ht; 29.27.�a; 29.30.Kv

Keywords: Proton induced reaction cross section; Copper target; Radioisotope production; Nuclear models theory; Model calculat-ions

0168-583X/$ - see front matter � 2005 Elsevier B.V. All rights reservdoi:10.1016/j.nimb.2005.05.045

* Corresponding author. Tel.: +86 10 69357275; fax: +86 1069357008.

E-mail address: [email protected] (Y. Han).

1. Introduction

With the development of nuclear science andtechnology, the accelerator-driven clean nuclearpower system (ADS) has been an interesting focusin nuclear physics. They require accurate nuclearreaction data of common cross sections and

ed.

mailto:[email protected]

Y. Han et al. / Nucl. Instr. and Meth. in Phys. Res. B 239 (2005) 314–330 315

especially need the data of neutron and protoninduced energy-angle correlated spectra of second-ary light particles as well as double differentialcross sections, c-ray production cross sectionsand c-ray production energy spectra. The develop-ment of high-quality nuclear data for copper isparticularly important due to copper�s role as animportant structural material in many accelera-tor-driven system designs. The application fieldof charged particle nuclear data is becoming prom-ising and expanding, as in space radiation effects,medical radioisotope production, radiation dam-age of materials, activation analysis, and standardreference nuclear data. The radioisotope yieldcross sections can tell us which energy region ismore suitable for specific radioisotope productionin certain nuclear reactions. These radioisotopesare used in medicine both for diagnostic studiesand therapy. Natural Cu consists of two isotopes,that is 63Cu (69.345%) and 65Cu (30.365%).

Since the experimental data of charged particleinduced reactions are scarce and there are signifi-cant discrepancies among experimental data ofdifferent laboratories, self-consistent calculationand analysis using nuclear theoretical models arevery important and interesting. Better nucleardata libraries for the p+63,65,natCu reactions arealso required for applications over the incidentproton energy range from threshold energy to250 MeV.

In this work, the double differential cross sec-tions for emission neutrons, protons, deuterons,tritons, helium and alpha, angle-integrated spectraand proton induced cross sections are calculatedusing the nuclear theoretical models code MENDwhich integrates the optical model, the intra-nucle-ar cascade model and the direct, pre-equilibriumand equilibrium reaction theories. The opticalmodel potential parameters are obtained fromexperimental data of reaction cross sections andelastic scattering angular distributions forp+63,65,natCu reactions, and elastic scatteringangular distribution for p+58Ni and p+68Zn.The double differential cross sections for emissionneutrons and protons are obtained from Kalbachsystematics.

Section 2 provides a description of the theoret-ical models used in this work. Section 3 gives anal-

ysis and comparisons of calculated results withexperimental data. Section 4 gives simpleconclusion.

2. Theoretical models and model parameters

2.1. Optical model and optical potential parameters

The optical model is used to describe measuredreaction cross sections and elastic scattering angu-lar distributions, and calculate the transmissioncoefficient of the compound nucleus and the pre-equilibrium emission process. The optical poten-tials considered here are Woods–Saxon [1] formfor the real part, Woods–Saxon and derivativeWoods–Saxon form for the imaginary parts corre-sponding to the volume and surface absorptions,respectively, and the Thomas form for the spin–or-bit part. In order to obtain a set of proton opticalpotential parameters for 63,65,natCu, the codeAPMN [2] is used in this work. By this code, thebest proton optical potential parameters can besearched automatically to fit with the relevantexperimental data of reaction cross sections andelastic scattering angular distributions.

The experimental data of proton reaction crosssections given by different laboratories, and theexperimental data of natural Cu are basically inagreement for energies below 300 MeV. The exper-imental data for 63,65,natCu were collected in [3]and are used to guide the theoretical calculation.Since there are no experimental data of elasticscattering angular distributions for p+Cu reactionabove energies of Ep > 35 MeV, the experimentaldata of elastic scattering angular distributions forp+Ni and p+Zn reactions are used. The experi-mental data of elastic scattering angular distribu-tions taken from EXFOR Library for 63Cu, 58Niand 68Zn are used in the theoretical calculation.The optical potential parameters for neutron areobtained from the experimental data of n+63Cureaction. The optical potential parameters forother charged particles are taken from [4].

The adjustment of optical potential parametersis performed to minimize a quantity called v2,which represents the deviation of the theoreticalcalculated results from the experimental values.

316 Y. Han et al. / Nucl. Instr. and Meth. in Phys. Res. B 239 (2005) 314–330

The energy dependencies of potential depthsand optimum proton optical potential parametersfor 63Cu are expressed as follows:

The real part of the optical potential:

V ¼ V 0 þ V 1E þ V 2E2 þ V 3ðN � ZÞ=Aþ V 4Z=A1=3.

ð1ÞThe imaginary part of the surface absorption:

W s ¼ W 0 þ W 1E þ W 2ðN � ZÞ=A. ð2ÞThe imaginary part of the volume absorption:

W v ¼ U 0 þ U 1E þ U 2E2. ð3ÞThe diffusive width of the surface absorption

and the volume absorption potential:

as ¼ as0 þ as1ðN � ZÞ=A;av ¼ av0 þ av1ðN � ZÞ=A; ð4Þ

where Z, N and A are charge, neutron and massnumbers of the target, respectively, E is the inci-dent proton energy in the center of the masssystem.

The spin–orbit couple potential: Uso.The radii of the real part, the surface absorp-

tion, the volume absorption and the spin–orbitcouple potential are rr, rs, rv and rso.

The diffusive widths of the real part, the surfaceabsorption, the volume absorption and the spin–orbit couple potential are ar, as, av and aso.

The units of the potential V, Ws, Wv, Uso are inMeV, the lengths rr, rs, rv, rso, ar, as, av, aso are infermis, the energy E is in MeV.

The optical model potential parameter obtainedfor 63Cu is given in Table 1.

Table 1Optical model potential parameters

V0 56.8982 Uso 6.2V1 �0.3173 rr 1.1149V2 �0.0006848 rs 1.2923V3 30.0 rv 1.2671V4 0.6169 rso 1.01W0 13.7379 ar 0.7074W1 �0.2090 as0 0.4501W2 10.9164 av0 0.4608U0 �2.7390 aso 0.75U1 0.1956 as1 0.7U2 �0.0004210 av1 0.7

Since the set of optical model potential param-eters of 63Cu is obtained to fit the experimentaldata of reaction cross sections and elastic scatter-ing angular distributions for natural Cu and63,65Cu, and the optical model potential depthsare dependent on mass number A and neutronnumber N of the target, this set of optical modelpotential parameters is used in p+63,65Cu reac-tions, and the calculated results of proton reactioncross sections and elastic scattering angular distri-butions are compared with existing experimentaldata. The calculated results of the reaction crosssections and elastic scattering angular distributionsare in very good agreement with the experimentaldata.

The comparison of calculated results of protonreaction cross sections with the experimental data[5–23] for 63Cu is given in Fig. 1. The calculatedresults of proton reaction cross sections for 63Cuare in good agreement with experimental data ofnatural Cu above energies Ep > 80 MeV, and thecalculated results of elastic scattering angulardistributions are in good agreement with theexperimental data [24,25] as shown in Fig. 2. Thecalculated results of elastic scattering angular dis-tributions from this set of proton optical potentialparameters are in good agreement with the exper-imental data for p+58Ni and p+68Zn reactions.

Fig. 1. Calculated proton reaction cross sections (solid line)compared with experimental data (symbol) for p+63Cureaction.

Fig. 2. Calculated proton elastic scattering angular distribution(solid line) compared with experimental data (symbols) forp+63Cu reaction.


Based on the above fitting, this set of protonoptical potential parameters is determined forp+63,65,natCu reactions.

For (near-)spherical nuclides for which ap-propriate experimental data exists, the local andglobal neutron and proton phenomenologicaloptical model potentials with incident energiesfrom 1 keV up to 200 MeV and in the mass range24 6 A 6 209 were given, and the dispersion cor-rections are included in [26]. The calculated resultsof proton reaction cross sections and elastic scat-tering angular distributions from the present opti-cal potential are similar to those from Koning andDelaroche optical potential [26].

2.2. The pre-equilibrium and equilibrium processes

The pre-equilibrium statistical theory based onexciton model, evaporation model and Hauser–Feshbach theory with width fluctuation correction[27,28], and intranuclear cascade model is used todescribe the nuclear reaction pre-equilibrium andequilibrium decay processes for incident nucleonenergies below 250 MeV.

The new nuclear reaction models code MEND,which can give all kinds of reaction cross sectionsand energy spectra for six outgoing light particles

(neutron, proton, alpha, deuteron, triton and he-lium) and various residual nuclei in the energyrange up to 250 MeV, is being developed in China.It includes optical model, intranuclear cascademodel, equilibrium and pre-equilibrium reactiontheories, and treats the direct reaction as inputdata calculated by the distorted wave Bornapproximation theory. There are a few differencesin theoretical treatments between GNASH [29]and MEND. In the MEND code, the equilibriumemissions are calculated by using Hauser–Fesh-bach theory with the width fluctuation correctionfor the first particle emission in the low-energy re-gion and the evaporation model for the first to theeighteenth particle emissions. The pre-equilibriumemissions with the exciton model for first to thefifth particle emissions and one to four cascadenucleon emission with some fraction are consid-ered with the empirical formula, so it can be usedin higher energy range. Furthermore, the improvedpickup mechanism [30] for composite particle(a,d, t, 3He) emissions and Pauli principle in thecalculation of exciton state densities [31] areaccommodated, and the pre-equilibrium mecha-nism of gamma-ray emission are also taken intoaccount in the program. The double differentialcross sections for emission neutrons and protonsare obtained from Kalbach systematics [32] inMEND. The Kalbach systematics is based on pureexperimental information and the insight is that ingeneral, a pre-equilibrium process consists of a for-ward peaked part (multi-step direct) and an isotro-pic part (multi-step compound), and the angulardistributions are fairly structureless and look alike.

Using the proton optical potential parametersshown above, adjusting other charged particleoptical potential parameters and level densityparameters, all reaction cross sections, angular dis-tributions, double differential cross sections andenergy spectrum are calculated for p+63,65,natCuat incident proton energies below 250 MeV bycode MEND. The Kalbach systematical parameterK used in the two-body residual interaction playsan important part in nuclear reactions, whichdetermine the contribution of pre-equilibriumand equilibrium decay processes. According tothe experimental data of reaction cross sections,K is equal to 950 MeV3 in this work. The level


density parameter a and pair correction parameterD of the Back-Shifted Fermi gas level density [33]for low energy are used. The Ignatyuk et al. nucle-ar level densities are used, which include the wash-ing out of shell effects with increasing excitationenergy, collective as well as single particle excita-tions, depart from the more traditional ones, andare matched continuously onto low-lying experi-mental discrete levels. The Ignatyuk model [34]for describing the statistical level density proper-ties of excited nuclei is particularly appropriatefor the relatively high energies and used in MENDcode. The expression of Ignatyuk model is semi-empirical since its functional form has not beenderived theoretically but is fitted to theoretical cal-culations of level densities. It reads

aðExÞ ¼ �a½1þ dW ð1� expð�cUÞÞ=U �; ð5ÞU ¼ Ex � D. ð6Þ

Here, �a is the asymptotic level density value whichresults from a simultaneous fit to a large set ofaverage resonance parameters, c is called the shelldamping parameter, dW is the shell correction en-ergy which is defined as the difference between thereal mass of the nucleus and its spherical liquid

Fig. 3. Calculated (p,n) reaction cross section (solid line) compa

drop model mass, D is the pairing energy and Ex

is the excitation energy. The expressions of �a, cand dW can be obtained in [34]. The level densityparameter a(Ex) can be completely computed atany excitation energy from the Ignatyuk model.

3. Theoretical results and analysis

3.1. For p+63Cu reaction

The calculated results of (p,n) reaction crosssections are compared with experimental data[20,35–52] taken from different laboratories. Thecalculated results for 63Cu(p,n) reaction cross sec-tions are in good agreement with the experimentaldata taken from EXFOR as shown in Fig. 3. Thecalculated curves pass through the experimentaldata [53] within error bars for 63Cu(p,a) reactionas shown in Fig. 4. The experimental data[37,38,41,53–57] for 63Cu(p,2n) reaction given bydifferent laboratories are inconsistent with eachother (Fig. 5). The present theoretically calculatedresults are in good agreement with experimentaldata taken from [37]. The cross sections for

red with experimental data (symbols) for p+63Cu reaction.

Fig. 4. Calculated (p,a) reaction cross section (solid line)compared with experimental data (symbol) for p+63Cureaction.

Fig. 5. Calculated (p,2n) reaction cross section (solid line)compared with experimental data (symbols) for p+63Cureaction.

Fig. 6. Calculated (p,3n) reaction cross section (solid line)compared with experimental data (symbol) for p+63Cureaction.

Fig. 7. Calculated (p,np) reaction cross section (solid line)compared with experimental data (symbols) for p+63Cureaction.


63Cu(p,3n) reaction are small, the theoretical re-sults are consistent with the experimental data[58] (Fig. 6). The experimental data for 63Cu(p,np)reaction cross sections are given in [38,55,41], andthere is a discrepancy between them. The presenttheoretical results are in agreement with experi-mental data taken from [38] as shown in Fig. 7.There are no new experimental data until now.The experimental data for 63Cu(p, p2n) reaction

cross sections are also given in [37,41], and arebasically in agreement with Greenwood et al. [56]measurements. The calculated curves pass throughthe experimental data within error bars. The theo-retically calculated results for 63Cu(p, p3n) reac-tion cross sections are in good agreement withthe experimental data taken from [58] and areshown in Fig. 8. Due to the lack of experimentaldata for other reaction channels, the evaluateddata are heavily based on model calculations.

Fig. 8. Calculated (p,p2n) and (p,p3n) reactions cross sections(solid and dashed lines) compared with experimental data(symbols) for p+63Cu reaction.

Fig. 10. Calculated (p,n) reaction cross section (solid line)compared with experimental data (symbols) for p+65Cureaction.


3.2. For p+65 Cu reaction

The comparison of the calculated results withthe experimental data for proton reaction crosssections of 65Cu is given in Fig. 9. The calculatedresults of proton reaction cross sections are ingood agreement with the experimental data [5–23] of natural Cu. The experimental data [20,35–37,39,42,44–49,51,52,54,56,57,59–65] of 65Cu(p,n)

Fig. 9. Calculated proton reaction cross sections (solid line)compared with experimental data (symbols) for p+65Cureaction.

reaction cross sections were given by different lab-oratories for energy levels below 150.0 MeV. Thecalculated results are in good agreement with theexperimental data as shown in Fig. 10. The exper-imental data [53] of 65Cu(p,a) reaction crosssections are given from 4.0 to 10 MeV. The cal-culated curves reasonably pass through the exper-imental data as shown in Fig. 11. The experimentaldata [41] for 65Cu(p,3n) and 65Cu(p,4n) reaction

Fig. 11. Calculated (p,a) reaction cross section (solid line)compared with experimental data (symbol) for p+65Cureaction.


cross sections are given for energy levels below100.0 MeV, and the errors of the experimentaldata are not given. The calculated results are basi-cally in agreement with the experimental data, asshown in Figs. 12 and 13. The experimental datafor 65Cu(p,np) reaction cross sections are givenin [37,55,41,56,66–71]. The present results are ingood agreement with the experimental data below30.0 MeV, while above 30 MeV, the calculated re-



sults are lower than the experimental data. Fig. 14is the comparisons of calculated results with exper-imental data for 65Cu(p,np) reaction and the cal-culated results for 65Cu(p,p2n) reaction are alsogiven in the figure. The experimental data for65Cu(p,np) reaction may include the contributionof 65Cu(p,p2n) reaction. The experimental datafor 65Cu(p,p3n) and 65Cu(p,p4n) reaction crosssections are also given in [41] for energy levels be-low 100.0 MeV. The calculated results are basi-cally in agreement with the experimental data asshown in Figs. 15 and 16. There are no experimen-tal data for other reaction channels until now. Thecross sections are predicted by the theoreticalmodel.

We also notice that the cross sections for63Cu(p,xn) reaction are smaller than thosefor 65Cu(p,xn) reaction, and cross sections for63Cu(p,pn) and 63Cu(p,p2n) reactions are largerthan those for 65Cu(p,pn) and 65Cu(p,p2n) reac-tions. For 63Cu(p,p3n) and 63Cu(p,p4n) reactions,cross sections are smaller than those for65Cu(p,p3n) and 65Cu(p,p4n) reactions. The crosssections for 63Cu(p,a) reaction are larger thanthose for 65Cu(p,a) reaction. Since the above reac-tion cross sections show the properties of nuclearstructure, the present calculated results arereasonable.

Based on the agreements of the calculated re-sults with the experimental data for all reactioncross sections, the energy spectrum and doubledifferential cross sections of neutron, proton,deuteron, triton, helium and alpha emission forp+63,65,natCu reactions are calculated by theoreti-cal models.

Due to the lack of experimental data for pro-ton-induced reaction cross sections, the evaluateddata are heavily based on model calculations.The energy spectra of neutron, proton, deuteron,triton, helium and alpha emission are calculated,and the emitted neutron, proton, deuteron andhelium energy spectra at incident energies of 50,100, 150, 200 and 250 MeV are given in Fig. 17.The increasing importance of pre-equilibriumemission with incident energy is evident in Fig. 17,as can be seen from the significant contributionof high-energy ejectiles for the higher incidentenergy reactions. In addition, those figures also

Fig. 14. Calculated (p,np) and (p,p2n) reactions cross sections (solid and dashed lines) compared with experimental data (symbols) forp+65Cu reaction.

Fig. 15. Calculated (p,p3n) reaction cross section (solid line)compared with experimental data (symbol) for p+65Cureaction.

Fig. 16. Calculated (p,p4n) reaction cross section (solid line)compared with experimental data (symbol) for p+65Cureaction.


show the decreased particle emissions in the evap-oration regime with increasing incident energy dueto energy conservation. The cluster formationfactor for composite particle emission in thepick-up mechanism is included in pre-equilibriumemission processes, the energy spectra of the

composite particles deuteron, triton, helium andalpha are improved. The yield cross sections oflong-lived radioactive residual nuclei are calcu-lated for p+63Cu reaction.

The cross sections, energy spectra and doubledifferential cross sections for p+65Cu reaction

Fig. 17. (a) Calculated energy spectra of neutron emission for p+63Cu reaction at incident energies 50, 100, 150, 200 and 250 MeV. (b)Calculated energy spectra of proton emission for p+63Cu reaction at incident energies 50, 100, 150, 200 and 250 MeV. (c) Calculatedenergy spectra of deuteron emission for p+63Cu reaction at incident energies 50, 100, 150, 200 and 250 MeV. (d) Calculated energyspectra of helium emission for p+63Cu reaction at incident energies 50, 100, 150, 200 and 250 MeV.


are also calculated and analyzed, respectively. Theresults show theoretical calculations are similar tothose for n+63Cu reaction.

3.3. For p+natCu reaction

The calculated results for p+natCu reaction arefrom isotopic theoretical values. The comparison

of calculated results with the experimental data[5–19] for p+natCu reaction cross sections is givenin Fig. 18. The calculated results of proton reac-tion cross sections are in good agreement withthe experimental data. The cross sections fornatCu(p,x)65Zn reaction are from 65Cu(p,n)65Znreaction, the calculated results are in good agree-ment with experimental data [65,72–75] as shown

Fig. 20. Calculated natCu(p,x)63Zn reaction cross section (solidline) compared with experimental data (symbols).

Fig. 18. Calculated proton reaction cross sections (solid line)compared with experimental data (symbols) for p+natCureaction.


in Fig. 19. The comparison of the calculatedresults with the experimental data fornatCu(p,x)63Zn reaction cross sections is given inFig. 20. The calculated results are in good agree-ment with the experimental data [72–74,76] forincident proton energy levels below 20 MeV, andare larger than experimental data for incident pro-ton energy levels above 20 MeV. The cross sectionsfor natCu(p,x)62Zn reaction are given in Fig. 21.

Fig. 19. Calculated natCu(p,x)65Zn reaction cross section (solidline) compared with experimental data (symbols).

The calculated results are larger than the experi-mental data [72,73,75–77], and smaller than theexperimental data taken from [78]. The crosssections for natCu(p,x)64Cu and natCu(p,x)63Cureactions are given in Fig. 22. Since there are noexperimental data for natCu(p,x)63Cu reaction, theexperimental data [72,73,75] for natCu(p,x)64Cureaction cross sections are given in the figure.The calculated results for natCu(p,x)64Cu reactioncross sections are larger than the experimentaldata for incident proton energy levels below40 MeV, and larger than experimental data forincident proton energy levels above 40 MeV wherethe cross section of natCu(p,x)63Cu reaction maybe included. The comparison of the calculated re-sults with the experimental data [72,73,75,76,78]for natCu(p,x)61Cu reaction cross sections is givenin Fig. 23. The calculated results are in agreementwith the experimental data, except for the incidentproton energies 30 6 Ep 6 40 MeV. The compari-son of the calculated results with the experimentaldata [72,73,76] for natCu(p,x)60Cu reaction crosssections is given in Fig. 24. The calculated resultsare in agreement with the experimental data.The experimental data [54,56,72,73,75,76,78] fornatCu(p,x)60Co, natCu(p,x)58Co, natCu(p,x)57Co,natCu(p,x)56Co and natCu(p,x)55Co reaction crosssections were given from different laboratories.The comparison of the calculated results with

Fig. 21. Calculated natCu(p, x)62Zn reaction cross section (solid line) compared with experimental data (symbols).

Fig. 22. Calculated natCu(p,x)64Cu and natCu(p,x)63Cu reactions cross sections (solid line) compared with experimental data(symbols).


the experimental data for natCu(p,x)58Co,natCu(p,x)57Co, natCu(p,x)56Co reaction cross sec-

tions is given in Figs. 25–27. The calculated resultsare in agreement with the experimental data. The

Fig. 23. Calculated natCu(p, x)61Cu reactions cross sections (solid line) compared with experimental data (symbols).

Fig. 24. Calculated natCu(p, x)60Cu reactions cross sections (solid line) compared with experimental data (symbols).


natCu(p,x)55Co reaction cross sections are less than2.0 mb. The calculated results are in agreementwith the experimental data.

The calculated results for natCu(p,x)65Zn,natCu(p,x)63Zn and natCu(p,x)60Cu reaction crosssections are in good agreement with the experi-

Fig. 25. Calculated natCu(p, x)58Co reactions cross sections(solid line) compared with experimental data (symbols).


mental data and show that the experimental datafor 65Cu(p,n)65Zn, 63Cu(p,n)63Zn, 63Cu(p,p3n +d2n + nt)60Cu and 65Cu(p,p5n + d4n + t3n)60Cureaction cross sections are consistent with thoseof natCu(p,x) reaction. The discrepancy betweenthe calculated results and the experimental data for

Fig. 26. Calculated natCu(p,x)57Co reactions cross sections (

natCu(p,x)62Zn, natCu(p,x)64Cu and natCu(p,x)61Cureaction cross sections shows that the experi-mental data for 63Cu(p,2n)62Zn, 65Cu(p,4n)62Zn,65Cu(p,pn + np)64Cu, 63Cu(p,p2n + nd + t)61Cuand 65Cu(p,p4n + d3n + t2n)61Cu reaction crosssections are inconsistent with those of natCu(p,x)reaction. The agreement between the calculated re-sults and the experimental data for natCu(p,x)60Co,natCu(p,x)58Co, natCu(p,x)57Co, natCu(p,x)56Coand natCu(p,x)55Co reaction cross sections showsthat the calculated results are reasonable for63Cu(p,x)60Co, 65Cu(p,x)60Co, 63Cu(p,x)58Co,65Cu(p,x)58Co, 63Cu(p,x)57Co, 65Cu(p,x)57Co,63Cu(p,x)56Co, 65Cu(p,x)56Co, 63Cu(p,x)55Coand 65Cu(p,x)55Co reaction cross sections.

The discrepancy in the experimental data ofproton induced reaction between isotopes and nat-ural copper need to be checked in the experimentalmethod.

The well-known ALICE-91 [79] code uses theWeisskopf–Ewing evaporation theory for the equi-librium part and a geometry-dependent hybridpre-compound model. The ALICE-HMS code[80] is based on a new pre-compound model. This

solid line) compared with experimental data (symbols).

Fig. 27. Calculated natCu(p, x)56Co reactions cross sections (solid line) compared with experimental data (symbols).


hybrid Monte-Carlo simulation (HMS) modeldoes not rely on exciton state densities beyondthree excitations, permits unlimited multiple pre-compound emission for each interaction and couldbe employed to calculate the exclusive particlespectra and yields. The evaporation part of the cal-culation is based on the usual Weisskopf–Ewingformalism. The ALICE-IPPE code [81] includesthe generalized super-fluid level density modeland pre-equilibrium cluster emission. For thepre-equilibrium nucleon emission, the geometry-dependent hybrid model is used. Two differentversions of the model code ALICE-91 were usedto calculate the cross sections of processes leadingto the formation of 48V below 50 MeV in [74].There is a big discrepancy between the experimen-tal results and the value of the ALICE-IPPE calcu-lation concerning the position of maximum valueof the excitation function curve. Although theshape of the curve of the ALICE-HMS calculationseems to be acceptable, its values are systemati-cally higher over the whole energy region.

The calculated results of MEND code overcomethe shortage of calculated results of ALICE-91code, though the present calculated results andthe results taken from [74] are for different targets.

4. Conclusions

According to the experimental data of reactioncross section and elastic scattering angular distri-bution of p+63,65,natCu reactions, and experimen-tal data of elastic scattering angular distributionfor p+58Ni and p+68Zn reactions, a set of opti-mal proton optical potential parameters is ob-tained up to 250 MeV by code APMN. All crosssections of proton induced reactions, angular dis-tributions, and double differential cross sectionsfor 63,65,natCu are calculated using nuclear theorymodels that integrate the optical model, the in-tra-nuclear cascade model and the direct, pre-equi-librium and equilibrium reaction theories atincident proton energies from threshold energy to250 MeV. Since the recoil effect in MEND codeis taken into account, the energy for the wholereaction processes is in balance. Good agreementis generally observed between the calculated resultsand the experimental data. The evaluated data aregiven in the format of LA150 library.

These data can be used in radiation transportcalculations for simulations of accelerator-drivensystems, and for calculations of energy deposition,material damages and activation.


Acknowledgements

This work is one of the Major State BasicResearch Development Program of China, thatis the physical and technological researches ofaccelerator-driven clean nuclear power system(ADS) and supported by the Chinese Ministry ofScience and Technology under Contract No.G1999022603. A part of this work was supportedby the Korean Ministry of Science and Technologyas one of its long-term nuclear R&D programs.

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