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Applied Radiation and Isotopes 62 (2005) 419–428 www.elsevier.com/locate/apradiso

Measurement and analysis of cross sections for (p,n) reactions in 51V and 113In M.M. Musthafa, Manoj Kumar Sharma, B.P. Singh, R. Prasad Department of Physics, Aligarh Muslim University, Aligarh-202002, India Received 13 January 2002; received in revised form 29 September 2003; accepted 20 October 2003

Abstract Excitation functions (EFs) for the reactions 51V(p,n)51Cr up to 15 MeV and 113In(p,n)113Sn up to 20 MeV from threshold have been measured employing the stacked foil activation technique. To the best of our knowledge EF for the reaction 113In(p,n)113Sn has been reported for the ﬁrst time. The theoretical analysis of the EFs has been done employing both the semi-classical as well as quantum mechanical codes which include compound nucleus and preequilibrium (PE) emission into consideration. In general, theoretical calculations agree well with the experimental data. Effect of various free parameters used in the calculations have also been discussed. A signiﬁcant contribution of preequilibrium component has been observed at these energies. r 2004 Published by Elsevier Ltd.

1. Introduction More and more experimental nuclear reactions crosssection data are needed to determine the optimum irradiation condition for the production yield of various radioisotopes. More recently, these reaction crosssections are also in demand in order to know the transmutation probabilities for the proposed accelerator driven systems (Rubbia et al., 1995) (sub-critical reactors) popularly known as energy ampliﬁers. Though several investigations are available in the literature for the determination of reaction cross-sections related to the production of radio-nuclides, there are large discrepancies in the cross-sections measured for the same reaction by different authors. Further, there are large uncertainties in the measured cross-sections due to the use of low-resolution detectors. Moreover, the details of errors and their evaluation are not discussed Corresponding author. Tel./fax: +91-5-71-401-001.

E-mail address: [email protected] (B.P. Singh). 0969-8043/$ - see front matter r 2004 Published by Elsevier Ltd. doi:10.1016/j.apradiso.2003.10.014

in general. Recent experiments have clearly indicated that in statistical nuclear reactions, at moderate excitation energies, particles are emitted prior to the establishment of thermodynamic equilibrium of the compound nucleus (CN). This process is generally known as pre-equilibrium (PE) emission. Signatures of PE emission are often found in the high energy tails of the excitation functions. The PE emission mechanism has attracted considerable attention from both the experimental and theoretical view points (Gadioli and Hodgson, 1992). Semi-classical models (Blann, 1971; Ernst et al., 1987) have been successfully used to describe the experimental data on PE emission. Recently, quantum mechanical (QM) theories have also been used to analyse the experimental data mostly on nucleon induced reactions (Feshbach et al., 1980; Tamura and Udgawa, 1978; Udgawa and Low, 1983; Gudima et al., 1983; Bonetti et al., 1991). The stress has been, however, laid on the systematic study of input parameters that can describe the large amount of experimental data.

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As part of a programme (Bharadwaj, 1985; Gupta et al., 1989; Singh, 1991; Singh et al., 1933; Musthafa et al., 1995) of measurement and analysis of EFs for a large number of reactions using proton and a-beams, the cross-sections for 51V(p,n)51Cr and 113In(p,n)113Sn reactions have been measured from threshold to 15 and 20 MeV, respectively, using the activation technique. Analysis of EFs has been performed within the framework of both the semi-classical as well as quantum mechanical models using consistently the same set of parameters. The computer codes ALICE-91(Blann, 1991) and ACT (Bharadwaj, 1985) have been used for the semi-classical calculations, while code EXIFON (Kalka, 1991), which uses the multistep compound (MSC) and multistep direct (MSD) formulations (Feshbach et al., 1980), has been employed for the QM calculations. The details of the measurements are presented in Section 2, while analysis of the data is discussed in Section 3. The EF for the reaction 113 In(p,n)113Sn, to the best of our knowledge, has been reported for the ﬁrst time and hence no comparison with literature data is presented.

2. Experimental details In the present measurements the stacked foil activation technique has been used. Natural vanadium and indium materials (99.99% pure) were used for preparing the samples. The samples of vanadium and indium were deposited on aluminium (Al) backing of 6.75 mg/cm2 using vacuum evaporation technique. The thicknesses of vanadium and indium deposition were 0.32 and 4.2 mg/ cm2, respectively. The two stacks, one containing 10 vanadium foils and the other containing 9 indium foils, were separately irradiated by 15 and 20 MeV proton beams respectively, at the Variable Energy Cyclotron Centre (VECC), Kolkata, India. The Al-degraders of suitable thicknesses were used in between the samples in each stack to cover the broad energy range. The energy loss in the samples as well as degrader thickness were calculated employing the stopping power tables (Northcliffe and Shilling, 1970). The beam currents were monitored directly on the Farady cup. The off-line counting of the irradiated samples was carried out using the 100 cm3 HPGe g-ray detector (resolution 2 keV for 1.33 MeV g-ray of 60Co) coupled to the ORTEC’s PC based multichannel analyser. The background spectrum was also recorded and was properly subtracted from the sample counting rates. The detector was pre-calibrated using various standard gamma sources including the 152 Eu point source of known strength, which was also used for the determination of the geometry dependent efﬁciency at various source–detector distances. The residual nuclei were identiﬁed from their characteristic gamma lines as well as from their half-lives. The nuclear

data required for the calculations were taken consistently from the Table of Isotopes (Brown and Firestone, 1986). From the measured intensities of the identiﬁed gamma rays, the cross-sections at different incident energies were computed. If the sample having the initial number of nuclei N0 is irradiated by a beam of ﬂux f for a time t1 and the activity in the sample is recorded for a time t2 after a lapse of time t3, by a detector of geometry dependent efﬁciency G; the reaction cross-section sr is given by the expression: sr ¼

C p l expðlt3 Þ N 0 fyKGf1 expðlt1 Þgf1 expðlt2 Þg

(1)

where Cp being the counts under photopeak, l the decay constant of residual nuclei, y is the branching ratio of the particular radiation. K is the g-ray self-absorption correction for the material of the sample and is given by K ¼ ½f1 expðmdÞg=md ;

(2)

where m is the g-ray absorption coefﬁcient for the sample and d is the thickness of the sample. The experimentally measured cross-sections for the reactions 51V(p,n)51Cr and 113In(p,n)113Sn at different incident proton energies are tabulated in Tables 1 and 2, respectively. In these tables the ﬁrst column lists the incident energy on the foil while the second column lists the corresponding measured cross-section values. The errors mentioned in the cross-section values are the statistical errors of gamma counting. Further, errors in the cross-section may come up mainly due to (a) the uncertainty in the determination of the number of target nuclei in the sample, (b) the current ﬂuctuation of the incident beam, (c) the uncertainty in the determination of geometry dependent detector efﬁciency, (d) the beam intensity loss as the beam traverses the stack thickness, (e) the recoiling of the product nuclei, (f) the dead time of the detector, etc. The average total error due to all these factors is estimated to be o10%. Table 1 Measured cross-sections at different energies for reaction

51

V(p,n)51Cr

Incident energy (MeV)

Cross-section (mb)

3.7070.53 5.2370.53 6.5170.52 7.8970.52 9.3370.51 10.5770.51 11.9770.51 12.9270.50 13.9870.50 15.0070.50

25.2176.57 237.9379.02 275.33711.28 322.47712.86 429.29715.40 432.89712.51 400.9577.86 357.24714.28 309.10710.18 251.0375.25

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Cross-section (mb)

113

(a) For In(p,n) from the reaction 6.1070.54 7.4870.53 9.3170.53 11.3070.52 13.0070.52 14.6570.52 16.5070.51 18.3170.51 20.0070.50

Sn reaction, including the contribution In(p,3n)113Sn 28.0070.77 244.2573.97 441.2575.68 658.1076.81 480.9876.52 390.5972.26 156.9173.74 224.4173.47 1052.06711.03

115

(b) For 113In(p,n)113Sn reaction only 6.1070.54 28.0070.77 7.4870.53 244.2573.97 9.3170.53 441.2575.68 11.3070.52 658.1076.81 13.0070.52 480.9876.52 14.6570.52 390.5972.26 16.5070.51 156.9173.74 18.3170.51 112.1273.47 20.0070.50 86.92711.03

The experimental technique employed in the present work and the data evaluation are described in more detail in some of our earlier publications (Singh et al., 1995; Musthafa et al., 1995).

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In the case of 113In(p,n)113Sn reaction, as may be seen in Fig. 1(b), the measured cross-section in the samples irradiated with energies 18.31 and 20 MeV show a rising trend, which may be due to the contribution from 115 In(p,3n)113Sn reaction (threshold 18:2 MeV), which also produces the same residual nucleus 113Sn. If it is assumed that the total observed counts are only due to the 113In(p,n) reaction, then the cross-section values (given in Table 2(a)) are shown by dark circles in Fig. 1(b). On the other hand if the total activity is attributed to the 115ln(p,3n) reaction, then the crosssection is shown by empty triangles. However, the observed activity has contributions from both the 113 In(p,n) and 115Ir(p,3n) reactions. In order to separate out the contributions due to two reactions at 18.31 and 20 MeV, the ratios of cross-sections sðp;nÞ =sðp;3nÞ are calculated theoretically using the code ALICE-91, with those parameters which give a satisfactory reproduction of the lower energy data for this reaction. The contribution of two reactions has been separated taking into account the relative abundances of 113In and 115In isotopes and the theoretical cross-section ratios. In this way the cross-sections for (p,3n) reaction at 18.31 and 20 MeV are found to be 5:9 mb and 43:3 mb respectively, and are shown by dark triangles. Similarly, the empty circles in this ﬁgure show the contribution of 113 In(p,n) reaction deduced as mentioned above at the two energies. Table 2(b), gives the deduced cross-section values for the 113In(p,n) reaction obtained mentioned above. 3.1. Theoretical interpretation

3. Results and discussion The presently measured excitation functions are presented in Figs. 1–4. In the case of 51V(p,n)5lCr reaction, the presently measured data are compared with the literature data (Wing et al., 1962; Hontzeas and Yaffe, 1963) and are shown in Fig. 1(a). Although, there is reasonable agreement between the presently measured cross-sections and the literature values, the literature values are slightly higher than the present measurements. It may be mentioned that the measurements of Wing and Huizenga (1962) were carried out to study the CN mechanism up to 10.5 MeV only. Further, the measurements of Hontzeas and Yaffe (1963) were done using chemical separation of isotopes with an error of about 17%. Further, they used cross-sections of 63 Cu(p,n)63Zn and 65Cu(p,n)65Zn reactions as standard for monitoring the ﬂux of proton beam. However, it may be pointed out that the cross-section values for these standard reactions reported by different authors differ from each other by large factors (Wing et al, 1962; Ghosal 1950; Hows, 1958).

In the present work the measured EFs for the reactions 51V(p,n)51Cr and 113In(p,n)113Sn have been analysed using both the semi-classical as well as quantum mechanical models with consistent sets of parameters. These parameters for the semi-classical approach were obtained from our earlier analysis of proton, neutron and alpha induced reactions (Bhardwaj et al., 1985; Singh et al., 1933; Singh, 1991; Gupta et al., 1989). The computer codes ALICE-91 (Blann, 1991) and ACT (Bhardwaj, 1985) have been used for the semiclassical analysis while the code EXIFON (Kalka, 1991) has been used for the QM description of the data. Brief details of these codes and the parameters used in the calculations are summarised in the following sections. 3.1.1. Analysis with code ALICE In the code ALICE-91, the compound nucleus (CN) calculations are performed using the Weisskopf-Ewing model (Weisskopf and Ewing, 1940) while the PE component is simulated employing the geometry dependent hybrid (GDH) model (Blann, 1972). In this code the level density parameter ‘a’, mean free path multiplier COST, and the initial exciton number ‘no’ are important

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Fig. 1. (a) Excitation function for the reaction 51V(p,n)51Cr, calculated using different parameters of the code ALICE along with the experimental data. (b) Excitation function for the reaction 113In(p,n)113Sn calculated using different parameters of the code ALICE along with the present measurements.

parameters. The level density parameter ‘a’ is calculated from a ¼ A=K; where, A is the mass number of the compound system and K is a constant, which may be

varied to match the excitation functions. The initial exciton conﬁguration of the compound system deﬁned by its initial exciton number no ¼ ðp þ hÞ is an important

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Fig. 2. (a) Excitation function for the reaction 51V(p,n)51Cr calculated using different parameters of the code ACT along with the present measurements. (b) Excitation function for the reaction 113In(p,n)113Sn calculated using different parameters of the code ACT along with the present measurements.

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Fig. 3. (a) Excitation function for the reaction 51V(p,n)51Cr calculated using different parameters of the code EXIFON along with the present measurements. (b) Excitation function for the reaction 113In(p,n)113Sn calculated using different parameters of the code EXIFON along with the present measurements.

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Fig. 4. (a) Excitation function for the reaction 51V(p,n)51Cr calculated with the best ﬁt values of the parameters of the codes ALICE, ACT and EXIFON along with the present experimental data and other literature values. (b) Excitation function for the reaction 113 In(p,n)113Sn calculated with the best ﬁt values of the codes ALICE, ACT and EXIFON along with the present measurements.

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parameter of PE formalism. It is however, reasonable to assume that an incident proton (particle) in its ﬁrst interaction excites a particle above the Fermi level leaving behind a hole, i.e., in all two particles and one hole, in creating the initial exciton state. Further, the mean free path (MFP) in these calculations is generated using free-nucleon–nucleon scattering cross-sections. The calculated MFP for two-body residual interactions may differ from the actual MFP. To account for that, the parameter COST is provided. In this code the MFP is multiplied by (COST+1). As such, by varying the parameter COST, the nuclear MFP can be adjusted to ﬁt the experimental data. A choice of K ¼ 10; no ¼ 3ð2p þ 1 hÞ and COST ¼ 9; for proton induced reactions gave a satisfactory reproduction of the measured data in our earlier analyses of excitation functions (Musthafa et al., 1995). The same values of these parameters have been used in the present calculations and the calculated EFs for the two reactions 51V(p,n)51Cr and 113 In(p,n)113Sn are shown in Figs. 1(a) and (b), respectively. The calculated EFs with the above parameters reproduce the measured EFs for the reaction 51V(p,n)51Cr satisfactorily. For the reaction 113 In(p,n)113Sn, however, the calculations done with these parameters do not give satisfactory agreement with the experimental data. In order to reproduce the experimental data for this reaction the values of K and mean-free-path multiplier are varied and the corresponding EF’s are shown in Fig. 1(b). As can be seen from this ﬁgure, a value of K ¼ 18; with COST ¼ 9; has been found to satisfactorily reproduce the excitation function for 113In(p,n) reaction. A larger value of K in case of 113In(p,n)113Sn reaction means a relatively smaller value of the level density parameter ‘a’ for the residual nucleus, which is expected in the case of 50Sn113, since it is a closed proton shell nucleus. Further, Weisskopf-Ewing calculations do not include spin effects. 3.1.2. Analysis with code ACT In code ACT, the CN calculations are performed using the Hauser–Feshbach (HF) theory (Hauser and Feshbach, 1952). The PE-component is simulated using the exciton model (Grifﬁn, 1966). The level density parameter ‘a’ and ﬁctive ground state potential ‘D’ initial exciton number ‘no’, and the parameter FM of the two body residual interaction matrix element are the important parameters of this code. Further details of the code are given elsewhere (Bharadwaj, 1985). The level density parameter ‘a’ and the ﬁctive ground state energy ‘D’ used in the calculations are taken consistently from the tables (Dilg et al., 1973). The effective moment of inertia ‘Y’ is taken equal to the rigid body value. The initial exciton number no is taken equal to 3, as in case of calculations done with code ALICE. In the exciton model the intranuclear transition rates depend on the

average of the square of the matrix element for twobody residual interactions |M|2. Its value is generally computed from the expression jMj2 ¼ F M A3 U 1 ; where A and U are the mass number and the excitation energy of the compound system, respectively. In our earlier analysis a value of F M ¼ 140 MeV3 for proton induced reactions was found to give satisfactory reproduction of the experimental data. The calculated EFs for the reactions 51V(p,n)51Cr and 113In(p,n)113Sn using the code ACT are shown in Figs. 2(a) and (b), respectively. The pure CN calculations are also shown in these ﬁgures by dotted lines. For the purpose of comparison, ACT calculations have also been perfonned for different values of the parameter FM. As a typical example, in order to show the variation of EF on the value of the matrix element for two-body residual interaction, the calculated EFs for the reaction 51 V(p,n)51Cr for the values of F M ¼ 140; 230 and 430 MeV3 are also shown in Fig. 2(a). As can be seen the value F M ¼ 430 MeV3 along with no ¼ 3 satisfactorily reproduces the experimental data. The same value F M ¼ 430 MeV3 has been retained for the calculated EF for the reaction 113In(p,n)113Sn and is found to give satisfactory reproduction of the experimental excitation function in this case also. 3.1.3. Analysis with code EXIFON The code EXIFON (Kalka, 1991) is based on an analytical model for statistical multistep direct (SMD) and multistep compound (MSC) reaction model (Feshbach et al., 1980). It predicts the activation crosssections including the equilibrium (CN), pre-equilibrium, and direct (collective and non-collective) processes within a pure statistical multistep reaction model. This approach is based on many-body theory, Green’s function formalism (Ring and Schuck, 1980; Midgal, 1970) and random matrix physics (Agassi et al., 1975; Broady et al., 1981). The pairing correction, Pauli blocking, shell structure effect and the Coulomb effects are taken care of in these calculations. The important parameters of this code are the initial exciton number no, Fermi energy EF, pairing shift ‘D’, and radius parameter ro. The code assumes the value no ¼ 3 for nucleoninduced reactions, as is done in the case of the codes ALICE-91 and ACT. In the standard set of parameters, E F ¼ 33 MeV; D ¼ 12:8A1=2 MeV; and ro=1.214.0A2/315A4/3 (where, A is the mass number of the compound system). Figs. 3(a) and (b), show the calculated EFs for the reactions 51V(p,n)51Cr and 113In(p,n)113Sn, respectively, using the code EXIFON with different sets of parameters including the standard one (Kalka, 1991). As can be seen from Fig. 3(a) the excitation function calculated for 51V(p,n)51Cr reaction with the standard parameters overestimates the measured excitation function at lower energies and underestimates it at higher energies. Calculations done

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by changing only the values of pairing shift D of the standard set to 0.45 as given by Dilg et al. (1973) are shown by a dashed line in Fig. 3(a) and agree reasonably well with the experimental data up to about 12 MeV within the experimental errors. However, beyond 10 MeV, it still underestimates the experimental data. The same calculations are done by changing the Fermi energy EF to 40 MeV and are shown by a dot-dash line. It may be remarked that the change of EF does not very much affect the calculated values. As may be seen from Fig 3(b), the EXIFON calculations using the standard set of parameters underestimate the experimental data for 113In(p,n)113Sn reaction, particularly in the tail portion of the experimental excitation function. In an effort to match the experimental data, calculations are done by changing the values of some of the parameters of the standard set. The values of the pairing correction term D has been changed from 1.12 to 3.0 as suggested by Kalbach-Cline et al. (1974) and Coyrell (1953). The Fermi energy EF is related to the single particle state density ‘g’ and through it to the level density parameter ‘a’. If EF is taken equal to 40 MeV, using the formulations of Kalbach (1971), Oblonzinky (1989) and Avrigeanu et al. (Avrigeanu and Avrigeanu, 1994; Avrigeanu et al., 1990), one gets the value of a ¼ 16 for the nuclei 113In and 113Sn with radius parameter r0 ¼ 1:4 fm; which is in agreement with the value given by Dilg et al. (1973). The EXIFON calculations have also been done using these values of EF(40 MeV) and ro(1.4 fm) with residual interaction of 33 MeV using optical model potentials of Bacchetti and Greenlees (1969). The dashdot curve in Fig. 3(a) shows the result of these calculations, which is in reasonable agreement with the experimental data.

4. Conclusions Results of the present analysis are summarised in Figs. 4(a) and (b), where experimental and theoretical best ﬁt graphs of the excitation functions for 51V(p,n) and 113In(p,n) are given. The effect of varying various parameters of the codes on the calculated EFs is also studied. The high energy tail portion of the EFs can be satisfactorily reproduced if the PE component is included in the calculations. It may be observed that both semi-classical as well as quantum mechanical codes, each with a suitable choice of parameters, may reproduce the experimental data. Further, all these codes give more or less similar descriptions of the data in the peak region, which is of interest from the point of view of CN mechanism. The initial exciton number no ¼ 3 and the value of parameter F M ¼ 430 MeV3 are found to give satisfactory reproduction of the data using the exciton model of the code ACT.

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Acknowledgements The authors acknowledge the VECC personnel and to the IUC-DAEF, Calcutta Centre for all their help and co-operation during the experiments. Authors are also thankful to the Chairman, Department of Physics, AMU for providing the necessary facilities to carry out this work.

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