Direct-semidirect and compound contributions to radiative neutron capture cross sections

Nuclear Physics A339 (1980) 205-218; © North-Holland Publishing Co ., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

DIRECT-SEIIDIRECT AND COMPOUND CONTRIBUTIONS TO RADIATIVE NEUTRON CAPTURE CROSS SECTIONS A. LINDHOLM, L. NILSSON, M. AHMAD t and M. ANWAR t Tandem Accelerator Laboratory, Uppsala, Sweden

I. BERGQVIST Department of Physics, University of Lund, Land, Sweden

and S. JOLY

Service de Physique Neutronique et Nucléaire, Centre d'ENdes de Bruyères-WChßtel, France

Received 6 December 1979 Abstract : Gamma-ray spectra from radiative capture of neutrons in calcium, nickel, yttrium and radiogenic lead have been recorded at neutron energies between 0.5 and 11 MeV. The 7-radiation was detected by a large NaIM scintillation detector using time-of-flight techniques to suppress background radiation. Cross sections for capture to bound final states, mainly ground states, were determined. Measured cross sections and data from previous experiments are compared with predictions of the direct-semidirect and compound-nucleus models . For neutron energies below 4 MeV the compound-nucleus model accounts reasonably well for the observed cross sections . Above 7 MeV the direct-semidirec t model gives a good description of the experimental data . In the energy region from 4 to 7 MeVthe contributions from the two models are of the same order of magnitude and interference between the two capture processes might be important. . E

NUCLEAR REACTIONS 'Ca, "N~ s9Y, 2ospb(n, Y~ E = 0.5-11 MeV; measured a(E) ; compound nucleus, direct-semidirect model analyses

1. Introduction Most of the previous experiments on neutron capture in the giant dipole resonance (GDR) region have been performed to explore reactions of direct type. However, the analysis of the results has indicated that it is important..to know the contribution of other processes, e.g. compound-nuclear (CN) reactions, in this energy region . A strong CN contribution has already been established') for light nuclei ("Si and 32S). It is the purpose of this work to study to what extent CN processes play a role for heavier nuclei. t Permanent address: Pakistan Institute of Nuclear Science and Technology, PO Nilore, Rawalpindi, Pakistan .

205

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The direct-semidirect (DSD) model z . s) has been found to be fairly successful in describing the general features of the experimental capture results in the GDR region a -6). The best description has been obtained with a complex form factor') for the particle-vibration coupling. It appears that a strong imaginary term is required to give an adequate fit to the experimental excitation functions for mediumweight and heavy nuclei It should, however, be noted that a large contribution from CN processes in the low-energy part of the GDR would result in a significant reduction in the strength of the.imaginary part of the interaction function . In the neutron energy region between about 4 and 7 MeV the CN and DSD contributions are of the same magnitude. Therefore this region should be of interest in relation to interference between these two processes. Previous experiments have given little insight into this problem. In this work we have extended earlier measurements of certain y-ray transitions following neutron capture in calcium, nickel, yttrium and radiogenic lead to wider neutron energy regions. The experimental results have been compared to calculations based on the DSD and CN models . 2. Capture cross-section calculations 2.1 . DIRECT AND SEMIDIRECI' CAPTURE

The calculations of direct-semidirect capture cross sections have been done using the formulation in ref.') which has been modified to include direct capture. The combined direct-semidirect (DSD) cross section can be written as unl Deui - COrist I r) t'i'(r

+

unt~r) r r;~(r)~ I2. EY -ER ±Z "'

Here the first term within the brackets represents the direct capture and the second the semidirect capture amplitude; ul.; .(r) and u,,Xr) are the radial wave functions of the scattering and bound states, respectively. The energy and width of the giant dipole resonance state are ER and l', respectively . E7, is the y-ray energy and h(r) the particle-vibration coupling function. In the present calculations we have employed the complex function') h(r) oc r[vlf(r)-iwl4bdf(r)/dr],

(2)

where v l and wl are the strengths of the real and imaginary parts of the symmetry potential and b is the diffuseness parameter in the Woods-Saxon form factor. With this coupling function rather symmetric resonance shapes are obtained with realistic vl values. A somewhat disturbing fact is that the strength of the imaginary term, required to fit the experimental data, is rather large, particularly for heavy nuclei . Wave functions were computed with a version of the ABACUS-2 code') . For the incident wave functions we used optical-potential . parameters according to

RADIATIVE NEUTRON CAPTURE

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TABLE 1

Spectroscopic factors included in the direct-semidirect calculations Final nucleus

E3 (MeV)

n1j

S

Refs.

4 'Ca

0 .00 1 .94 2 .01 2 .46

1f712 2P3n ld 3 /2 2P3/2'

0.86 0.64 0.08 0.22

10)

s9Ni

0 .00 0 .34 0 .47 0.88

2P312 lfs12 2p, /2 2P3n

0.65 0.73 0.61 0.07

11)

90Y

Q.00 0.20

2ds12 2ds12

1 .06 ~) 1 .01 . )

207pb

0.00 0.57 0.90 2 .73

3Pln 2fs/2 3P3/2 289/2

0 .60 0 .12 0 .07 0 .97

12) 13)

1) S = 1.0 in the calculations . TABLE

2

Giant-dipole resonance parameters adopted in the present calculations Nuclei "Ca "Ni 90i

207Pb

El (MeV) 18.0 16.5 16.7 13.5

E2 (MeV) 20.2 19 .1 21 .0

T3 (MeV)

T2 (MeV)

4.0 4.0 4.1 4.0

4.0 4.0 4.1

C1

C2

0 .38 0 .66 0 .92 1 .0

0.62 0.34 0 .08

(mb)

°-'

°' (MeV)

30 48 76 270

75 75 75 75

w' (MeV) .

35 75 110 140

ref. 9 ). The bound-state wave functions were calculated using a real Woods-Saxon potential and a spin-orbit potential of Thomas type with ro = 1.25 fm, a = 0.65 fm and (V..,,.)o = 5.5 MeV. The real potential depth was adjusted by the computer program to give the experimental binding energies of the single-particle states, the spectroscopic strength of which are obtained from the literature to-13) and summarized in table 1 . The parameters ofthe two isospm components of the GDR are given in table 2. The fractional strength distribution among the two components, T, and T, respectively, is given in eq. (8) below. Conservation of isospin in DSD capture of neutrons requires that only the T, component of the GDR of the final nucleus is excited. The integrated bremsstrahlung-weighted photo-nuclear cross sections Q_ 1 given in table 2 . [ref. ta)] have been reduced according to eq. (8).

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2.2 .. COMPOUND-NUCLEUS CAPTURE

Direct and semidirect capture processes take place during the initial period of motion of the incoming nucleon in the nuclear potential. The other extreme is the formation of the compound nucleus in which. the incoming nucleon shares its energy among other nucleons in the nucleus. According to the CN model the neutron radiative capture cross section Q(n, yf) for transitions to a level f can be expressed as

1: Ti, (3) z r where 6x is the cross section for formation of the CN state A at an excitation energy Ex with spin and parity JR, T,xf the transmission coefficient for the y-ray transition from the CN state A to the final state f and Y, T, is the sum of the transmission coefficients for all possible exit channels . We consider in the present calculations neutron, proton and alpha-particle channels. The CN formation cross sections and transmission coefficients for particle emission were calculated with the ABACUS-2 code s) using for nucleons the optical-model parameter set from ref. 9). For the calculation of a transmission coefficients optical-model parameters obtained in ref. 15) were used . The concept of a y-ray strength function 16) was utilized in the estimate of transmission coefficients for radiative transitions. We consider only El transitions for which the formula a(n, Yf)

_ ~. Qa Trzr

TI(E) = 2 n
(5) where g.r is the statistical factor (2J+ 1)/(2Jo + 1) and 6',,(E,) (mb) is the average photoabsorption cross section of a nucleus with ground-state spin Jo for excitation of levels with spin J at energy EY = Ex(MeV). It is generally assumed 16) that aj, is related to the total average absorption cross section by If valid, this implies that f(E) becomes independent of J. The formulae extracted so far apply to ground-state transitions . In the present calculations y-rays to excited states have also been considered These can be taken into account by applying the Brink hypothesis 1 '), postulating that on each excited state is built a giant resonance of the same shape and magnitude as the one based on the ground state. This-implies that y-ray. transmission coefficients can be evaluated also for excited states . Furthermore, it means that the y-ray strength function is a function of E, only, ie. independent of Ez.

RADIATTVE NEUTRON CAPTURE

In the calculation the photoabsorption cross section was assumed to have a lorentzian shape. Considering the splitting of the GDR into two isospin components; indicated by subscripts 1 (T,) and 2 (T,), respectively, the formula for the photoabsorption cross section in rd 'I) becomes

E E 2 Ez+' r 2t E2r (mb~ t=1 ( y- ~)

Z (1+ 0.8y) vrd = 38Á

2

2

(7)

where y specifies the exchange admixture. The fractional strength of the two components is given by ") . 1 C2 1-1 .5To/A4 1 Cl To + 1.5/A} '

where To = -2(N-Z) is equal to T, The strengths are normalized by C 1 +C 2 = 1. The empirical values of the integrated cross section have been utilized and y was used to adjust eq. (7) to these results. For 206 Pb the experimental cross section exceeds the classical sum rule and y ;-- 0.5. For Ca, Ni And Y we have adopted y = 0. In contrast to the case of DSD capture we assume that both isospin components contribute. This assumption is based on the fact that there is no correlation between neutron and y-ray widths in statistical processes. The sum of the transmission coefficients is calculated from t

T=

n s ( f= 1

E,s T1'=+

F. . J1sf[1z J Eoz

l Tf~fs~fx' .

The first term refers to decay by particle x to then individual levels in the residual nucleus with known energy, spin and parity below the excitation energy Eo. and the second term refers to decay to levels above Eos where the density of levels with spin and parity Jfx and nfx is pfx The integration limit E. is equal to E,,-B, where, for particle decay, Bs is the binding energy in the compound nucleus of the emitted particle x and for y-ray decay Bx = 0. .Level densities were treated according to the compilation in ref. 19). 3. Experimental arrangement and procedme The measurements were performed using time-of-flight techniques with pulsed beams from the 6 MV tandem accelerator at Uppsala. The width of the beam pulses for protons and deuterons was 1-2 ns. The 3 H(p, n)3 He and 2H(d, n)3He reactions were utilized to produce monoenergetic neutrons. The first mentioned reaction was used for neutrons with energies below 6 MeV .and the other for neutron energies above 6 MeV, in both cases with gas target systems. The deuterium gas cell, made from one piece of tantalum, was 10 mm in diameter and 24 mm long and had a 6 mg/cm' Ni entrance window. The tritium gas cell, having. the same diameter and a length of.29 mm, was made of brass. Its inside lateral surface was covered with

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A. LINDHOLM et al.

0.3 mm gold and the beam stop was a 0.5 mm "Ni plate.. The entrance window of this cell was a 7 mg/cm' "Ni foil. The gas pressure was normally between 1.4 and 1 .7 atm. The samples, cylindrical in shape, were placed on the axis of the incident . beam at a distance of 16 cm from the target. The target-sample arrangements used in the present work give neutron energy spreads less than f 100 keV. The y-rays from the samples were recorded by means of a NaI(TI) crystal, 22 .6 cm in diameter and 20.8 cm long, placed at an angle of 90" with respect to the incident beam. The crystal was heavily shielded by lithium hydride, lead and borated paraffin except for a front collimator, 10 cm in diameter. To reduce neutron irradiation of the NaI crystal, a 40 cm 11H cylinder was placed in the collimator just in. front of the detector. For y-rays in the energy region 10-20 MeV the resolution ofthe detector was about 9 %. A conventional two-parameter time-of-flight electronic setup including a PDP-15 computer was used for data acquisition. The time resolution ofthe system was about 10 ns implying that a flight path of 90 cm was sufficient for discrimination between neutrons and y-rays. The neutron yield was monitored with a plastic scintillation detector operated in time-of-flight mode and calibrated against a proton-recoil counter. In addition, theflux was. estimated from the target gaspressure, the'ion-beam current and the neutron production cross section. The results of-the two methods were found to agree within 5 % for the 'H(d, n)3He reaction . For the 3H(p, n)3He reaction on the other hand the recoil counter measurements revealed that the tritium content in the target gas decreases with the number ofdesorptions and reabsorptions of the tritium gas by the uranium oven . A tritium content as low as 50 % has been observed. The y-ray spectrum from the sample was obtained by subtracting "background" time groups from "signal" groups in the two-parameter spectrum . The contribution of radiation from the surrounding material was recorded in runs without sample . In the case of yttrium, where the sample consisted of oxide, background runs were performed with a water sample containing the same amount of oxygen atoms. For the energy calibration of the y-ray spectra the 6.86 MeV y-ray line produced by thermal neutron capture in the crystal was used together with the y-ray lines from the radioactive sources '?8Th (E., = 2.614 MeV) and PuBe (E), = 4.44 MeV). Separate short calibration runs were performed between the main runs . The high-energy parts of the y-ray spectra were unfolded using the response functions of the detector. The uncertainties in the cross section measurements originate mainly from the unfolding procedure and include uncertainties in the detection efficiency and the response-line shape, as well as statistical fluctuations in the pulseheight spectra. The overall uncertainty was estimated -to be f 25 %.

RADIATIVE NEUTRON CAPTURE

21 1

4. Experimental results The results of the cross section measurements are shown in figs . 1-5 together with the results of previous experiments 5 " 6.20.21) . The uncertainty in the absolute scale is included in the error bars . The relative errors are normally between 5 and 10 %. 1000

IU w N N N O U W H

a

a

U

10

Fig. 1 . Cross sections for the 'oCa(n, yo)"Ca reaction . The experimental data are from ref. ') (solid circles) and from the present experiment (open circles) . The error bars include the uncertainty in the absolute scale. The extensive data set of ref. 22) in agreement with the present data is not included . The compound-nucleus (CN) and direct-semidirect (DSD) curves are obtained from calculations described in the text . The full curve is the sum of the two others .

In general, the present data are in good agreement with earlier results. There is one notable exception, namely the cross section for "Ni(n, y)S 9Ni. Below E = 4.5 MeV the cross-section values for y-rays to levels below EZ = 0.9. MeV, displayed in 3, are about a factor oftwo larger than theprevious results 20). We have reanalyzed the previous data and found that the cross section determination is based on an erroneous assumption with regard to the neutron flux . The neutrons were produced by the 3H(p, n)3He reaction and the neutron flux was calculated from the proton beam current,, the reaction cross section and the tritium gas pressure. The gas was assumed to be 100 % tritium. As discussed in sect. 3 later experience with tritium

212

A. LINDHOLM et al. 1000 a 3 0

F U W N N N O U w A EL a U

10

5

10 15 NEUTRON ENERGY .MeV

Fig. 2 . Cross sections for neutron capture to levels between 1 .9 and 2 .7 MeV in "Ca. (For further notation see caption to fig. 1 .)

w m N N O K U W K Q U

Fig . 3 . Cross sections for capture to levels below 0.9 in 'Ni. The experimental data are from ref. ")(solid circles) and from the present experiment (open circles). (For further notation see caption to fig . 1 .)

RADIATIVE NEUTRON CAPTURE

213

1000 a

Z O

W100 fn V1 fn U W F-

á 10 U

NEUTRON ENERGY,MeV

Fig. 4. Cross sections for capture to the 2d , ground-state doublet in "Y . The experimental data are from ref. 6) (solid circles) and from the present experiment (Uppsala data-open circles and Bruyères-le Châtel data-filled squares). The data from Bruyères-le -Châtel have been normalized to the Uppsala data as described in the text . (For further notation see caption to fig. 1.) 2 06

F

1

Pb(n,y )~7Pb

1

fsrsu, P3a_u Ef=0.57, 0.90 MeV

Pu2 Ef=0.00M6V

9sn Ef=273MW

Z O

W W

lu

8 10 4 6 8 10 12 10 4 6 NEUTRON ENERGY, MeV Fig. 5. Cross sections for the . ..Pb(n, Y) 2o'Pb transitions to the p,,z ground state (left figure), the f, V and pan (middle figure) and 99,2 (right figure) excited states. The experimental data are from ref. ) (solid circles) and the present experiment (open circles) . The CN and DSD curves are calculated as for the previously reported reactions (figs. 1-4). For the g91, statethe CN curve corresponds to transitions to three levels between 2.62 and 2.73 MeV in 207 Pb. 2

4

6

8

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A. LINDHOLM et

al.

gas systems shows that it is difficult to maintain a high tritium gas purity. As noted earlier, a tritium content as low as 50%, which is required to explain the observed discrepancy, has been found with our present gas system by measuring the neutron flux with theproton recoil counter. It wasconcluded that the earlier values at E = 0.9, 2.5 and 4.0 MeV are incorrect and are therefore not included in fig. 3. The cross sections measured at En Z 4.5 MeV, utilizing the 'H(d, n)'He reaction are still correct, since the purity of the deuterium gas was always found to be higher than 95%. The extensive set ofcross section values for ''°Ca(n, yo)41Ca in the range En = 6-13 MeV obtained in a recent experiment 2Z) has not been included in fig. 1. The relative excitation curve found in this later experiment is in. excellent agreement with the present results but there is a difference in the absolute values. The difference is within the uncertainty in the efficiencies of the y-ray detection systems. For e9Y cross-section measurements have been. performed at Bruyères-le-Chátel at neutron energies between 0.5 and 3.0 MeV. Monoenergetic neutrons were produced by the 'Li(p, n)'Be and 'H(p, n)'He reactions and y-rays were detected by an antiCompton NaI detector arrangement. Further details of the experiment and data analysis have been published elsewhere as). In the overlapping energy region, 2.5-3 .0 MeV, the results are almost 40 % lower than the Uppsala results. This is barely within the absolute experimental uncertainties of the two experiments. To compare the energy dependences of the cross sections from the experiments the data from Bruyères-le-Chdtel have been normalized to the Uppsala results. 5. Discussion The comparison between experimental and theoretical excitation functions, figs . 1-5, indicates three rather distinct neutron energy regions. Below En - 4 MeV, compound-nucleus reactions are . expected to dominate. In several cases, e.g. 40Ca(n, yo) and e9Y(n, yo +yl ), the cross sections fall rather steeply with increasing neutron energy in agreement with predictions ofthe CN model. Above En - 7 MeV, the predominant reactions are direct and semidirect. In this region the predicted CN cross sections are considerably smaller than the experimental data. In the intermediate region, i.e. between 4 and 7 MeV, the model calculations give CN and DSD contributions of about the same magnitude and interference between the two components might play an important role . In the low-energy region, the cross sections calculated from the CN model reproduce the experimental results reasonably well with parameters obtained from the literature. The results of the calculations are sensitive primarily to level density and y-ray strength distributions. The level densities were calculated using parameters given in ref. "). The total decay probability of the .compound state [given by the denominator of eq. (3)] is in general governed by transitions to energy regions in the residual nuclei where

RADIATIVE NEUTRON CAPTURE

21 5

the level scheme is not known in detail. At low incident neutron energies the neutron decay channels are dominant which means that the knowledge of the level schemes in the target nuclei is crucial . For the target nuclei considered in the present work, 4 the spin and parity of levels are known up to E_ ~z- 3 MeV (for °Ca even up to 7 MeV). Hence, for neutron energies below 3 MeV level density expressions do not enter the CN cross section calculations. The level densities needed for the CN calculations of e9Y(n, y)9°Y cross sections must be treated differently because no level density parameters for nuclei around "Y are tabulated in ref. '9). In this case parameter values were obtained from formulae given in ref. '9). These parameter values give level densities in e9Y that are about a factor of three higher than observed. s9Y is the only residual nucleus for which level densities need to be considered, because the neutron width of the compound state accounts for more than 98 % of the total width. The CN cross sections obtained by means of the Gilbert-Cameron level density formulae have thus been corrected by a factor of three. The cross sections calculated in this way are in agreement with those obtained in other. recent calculations 24). The latter work included an extensive investigation of level density parameters in the A = 90 mass region. The y-ray strength distributions [eqs. (5){7)] were assumed to exhibit a lorentzian shape with GDR parameters determined in photonuclear experiments 14,25). Unfortunately, information is scarce about the y-ray strength at energies far from the resonance peak which is of importance in low-energy neutron capture. In general, extrapolation ofthe lorentzian provides a reasonable description ofthe y-ray strength although considerable deviations in magnitude and energy dependence have been observed 16). Such deviations might explain the discrepancies between CN model calculations and the experimental data for' Ca and Y. The DSD model provides a good description of the observed data for neutron energies above about 7 MeV with the particle-vibration coupling strength (v1 and w1) given in table 2. The value adopted for v1 (75 MeV) is in approximate agreement with the results of other types of experiments 26), whereas the w1 values vary considerably over the mass region of the present experiment. The comparison between theory and experiment for the reaction 206Pb(n, y)2 o'Ph is contradictory. The agreement is quite good for capture into the 2gß orbit outside the N = 126 closed shell, but poor for capture to the 3p} ground state and to the 2ft and 3p.. excited states, which are hole states in the N = 126 shell. We find that the DSD model calculations give cross sections a factor of four to five times lower than the experimental values in the energy region where DSD capture is expected to be dominant. These shortcomings of the DSDmodel for the reaction 206pb(n1 Y)207Pb are presently not understood . It is interesting, however, to compare these results with similar data from proton capture experiments in this mass region 27 ). Experimental data and DSD calculations . are presented for the 2°5Tl(p, Y)206 Pb groundstate transition as well as for transitions in 2°8Pb(p, y) 2°9Bi. The calculations agree with the data for the first reaction (3s, fmal state) but overestimate the cross sections

21 6

A . LINDHOLM et at.

to the high angular momentum (lh. ., Ii 4 and 2fj) final states in 2°9Bi considerably. Thus the situations in neutron and proton capture are opposite in the sense that the DSD. model accounts for the transitions to the high-1 particle state in neutron capture but for transitions to the low-1 hole state in proton capture. This situation for nucleon capture in the lead region might imply difficulties with the DSD model in its present formulation and has lead to the suggestion of an alternative model (the pure resonance model 28)) to describe fast nucleon capture data. Theoretical work on this model is in progress. The excitation functions for "'Ca (ground-state transition), "Ni and S9Y exhibit rather well-defined minima in the intermediate-energy region where the estimated CN and DSD contributions become roughly equal. In these cases the experimental minima are significantly deeper than the sum of the predicted cross sections. This might indicate that the energy dependence of the DSD cross section is incorrect due to too high values adopted for the imaginary strength wt ofthe particle-vibration coupling function . We also . note that effects of interference, if present, between CN and DSD capture should be strongest in this intermediate region . Consequently, an alternative explanation to the difference between the observed .and calculated excitation functions might be a destructive interference between the two capture processes. The effect of changing the relative magnitudes of the strength parameters vl and wt in the DSD calculations is illustrated in fig. 6 for 89Y(n, yo +y,) 9°Y. Lower wt

4 8 12 NEUTRON ENERGY, MaV

16

Fig. 6 . Illustration of the effects on the DSD cross section of varying the relative magnitude of the real and imaginary parts of the particle-vibration cowling function.

RADIATIVE NEUTRON CAPTURE

21 7

values result in a faster increase of the cross section on the low-energy side of the GDR and a less steep slope on the high-energy side . From fig. 6 it is clear that in order to obtain a reasonable description of the cross section between 4 and 16 MeV, a complex coupling function is required. The relative strengths ofthe real and imaginary parts cannot be determined very precisely, but vl and wl values ofthe samemagnitude (around 100 MeV) give satisfactory agreement with the experimental data . Angular distribution effects have not been taken into account. Measurements 29) between 7 and 11 MeV show that the angular anisotropy is rather strong and that the angleintegrated cross sections are lower than values given in fig. 6 by about 20 % at 7 MeV and about 25 % at 11 MeV . The angular distribution measurements are in agreement with calculations based on the DSD .model. These calculations show that the angular anisotropy varies slowly in the entire energy range of the data in fig. 6. It appears that the above statement about the coupling function is valid regardless of angular distribution .effects. In the comparison with the .experimental results, effects due to interference between CN reactions and direct and semidirect processes have been ignored. Some years ago a formulation 3°) was derived to modify the traditional Hauser-Feshbach theory to take into account the presence of direct reactions. Numerical estimates s °) for the reaction 2°BPb(n, yo)2°9Pb indicated a rather small correction (of the order of a few percent of the Hauser-Feshbach term) due to the direct processes. It should be noted that the schematic DSD model adopted for the numerical calculations in this study underestimated (by a factor of 3-4) the observed cross sections in the GDR region. However, even if a more realistic DSD model is applied, the interference corrections will probably be rather small. In this work other capture processes, such as capture via single-particle doorway states, were not considered. Theoretical calculations si) indicate that for light nuclei capture through such states contribute significantly to the cross section for neutron energies up to the GDR region. Very . good agreement with the experimental results for 4°Ca(n, y)41Ca has been obtained in this way 32). To summarize, the present work illustrates that CN processes give a good description of capture cross sections below about 4 MeV, within the expected uncertainties in this kind of calculations . It also seems plausible that CN reactions are important in the GDR region in the sense that they affect the relative strengths of the real and imaginary parts of the particle-vibrátion coupling function required to describe the data . The magnitude of this influence cannot be determined accurately until the nature of.the interference between CN processes and reactions of direct type have been investigated more thoroughly.

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