The 14N(3He, α)13N reaction

I

2mGI

Nuclear Physics A149 (1970) 323 -336; Not to

@

North-Holland

PubIishing

Co., Amsterdam

be reproduced by photoprint or microfilm without written permission from the publisher

THE “N(3He, a)13N REACTION A. R. KNUDSON US Naval Research Laboratory, Washington, and F. C. YOUNG US Naval Research Laboratory, Washington,

D.C.

D.C.

and Uniwrsity

of Maryland,

Received

College Park, Maryland

10 February

1970

Abstract: Differential cross sections for the 14N(3He, m)13N reaction leading to the ground, 2.37 and (3.51+3.56) MeV states of 13N have been measured for incident energies from 2.5 to 8.5 MeV. Large fluctuations are observed in excitation functions at 50”, 90” and 165”. Angular distributions over the range from 5” to 165” exhibit pronounced forward and backward peaking at 4.5 and 5.5 MeV, but relatively less backward peaking at 7.0 MeV. Differential cross sections for the elastic scattering of 3He from r4N at 4.5 and 7.0 MeV have been measured and used to determine optical potentials. Distorted wave analyses of reaction angular distributions at 7.0 MeV to the ground and 2.37 MeV states have been made. Spectroscopic factors were extracted assuming a direct pickup reaction mechanism. Calculations of the angular distribution to the 2.37 MeV state, assuming a direct knockout reaction mechanism, were made and are compared with the pickup calculations.

E

NUCLEAR REACTIONS 14N(3He, 3He), E = 4.5 and 7.0 MeV; measured a(B). 14NCHe, cc), E = 2.5-8.5 MeV; measured o(E, E,, 0). 13N levels deduced spectroscopic factors. Natural target.

1.Introduction Several investigations lm3) of (3H e, CI) reactions in the light nuclei have been interpreted in terms of a single neutron transfer mechanism and have provided information on single-particle configurations. The 14N(3He, a)13N reaction has been studied previously at 5.2 MeV by Taylor et al. “) and from 17 to 36 Me&r by Artemov et al. “). The measurements at 5.2 MeV suggest the presence of a neutron pickup process. Also 6*7) have been made on the a-particles from magnetic spectrograph measurements this reaction to identify excited states of the residual 13N nucleus. Finally, angular distributions have been measured at 13.9 MeV and interpreted in terms of a knockout process “). The present study was initiated to obtain information about the reaction mechanism for bombarding energies below 10 MeV. Also, it was anticipated that the present measurements would provide additional evidence for the existence of two levels at 3.51 and 3.56 MeV excitation in 13N , The existence of these two overlapping levels is 323

324

A. R. KNUDSON

AND

F. C. YOUNG

inferred from analyses 9*10) of proton elastic scattering measurements on 12C. The 14N(3He, r~) reaction proceeding to these levels of 13N is of interest with regard to nuclear reaction mechanisms. The 3.56 MeV level has J” = 3’ and is believed to correspond to a nearly pure (ls3)4(lp~)8(ld~) shell-model configuration, while the 3.51 MeV level has J” = $- and is believed to correspond to a nearly pure (l~+)~ (1p+)7(lp+)2 shell-model configuration II). If the (3He, a) reaction proceeds by a direct interaction process, then the 3.51 MeV level may be excited by direct processes, such as pickup, or by exchange processes, such as knockout. On the other hand, to the extent that the l4 N ground state can be represented by a (l~~)~(lp~)~(lp+)~ shellmodel configuration, the 3.56 MeV level can only be excited by exchange processes. The Coulomb and nuclear distortions should be similar for both levels because the energies of the outgoing particles corresponding to the excitation of these two levels differ by less than 50 keV. Since the selection rules for exchange processes are considerably less stringent than for pickup processes I’), it was felt that the reaction amplitude from exchange processes for both states should be similar, but that the 3.56 MeY state would be excited only by exchange processes. Unfortunately, these two levels have not been resolved in the present experiment. Measurements lo), which were completed after this work was begun, indicate that the natural widths of these levels are greater than the energy level separation. Therefore, even with very good experimental resolution, it would be impossible to separate the u-particle groups corresponding to these two levels by a direct measurement. The present study gives excitation functions for N-particle groups corresponding to the ground state, first excited state (2.37 MeV), and unresolved second and third excited states (3.51 MeV and 3i56 MeV) for incident 3He particle energies from 2.5 to 8.5 MeV. Complete angular distributions are presented for incident energies of 4.5, 5.5 and 7.0 MeV. In addition, 3He elastic scattering angular distributions on 14N were measured at 4.5 MeV and 7.0 MeV to provide entrance channel optical potentials for a distorted-wave Born approximation (DWBA) analysis of the reaction data. The DWBA calcluations and spectroscopic factors are discussed in some detail in sects. 3 and 4. 2. Experimental

procedure and results

After a substantial effort to develop thin stable nitrogen targets, the most satisfactory experimental results were obtained with targets consisting of adenine evaporated onto thin carbon (20 pg/cm2) or thin nickel (0.05 pm) foils. The nickel backings were used primarily to reduce the carbon content of the targets for 3He elastic scattering measurements. For some of the measurements, the target was rotated at about 1200 rpm so that the beam traced out a circular path approximately 1 cm in diameter on the target to minimize target deterioration. The surface density of the adenine targets was 10 to 20 pg/cm2. The NRL 5 MV Van de Graaff was used to provide beams of 3He ions in the energy range from 2.5 to 8.5 MeV. The beam was magnetically analysed and electrostatically

14N(3He,

focused onto the target. The reaction

325

cc)-N

measurements

at small scattering

angles (B =<30”)

and most of the elastic scattering measurements were performed with a 180” doublefocusing magnetic spectrometer. A position-sensitive solid state detector +, located in the image plane of the spectrometer, was used to detect the analysed particles. A discriminator was used on the energy pulse from the detector to select the particles of interest, and to route the associated spectrum of position pulses into a particular quadrant of a 512-channel analyser. To avoid accepting protons with a-particles, the detector bias was adjusted to make the sensitive region sufficiently thick to stop CIparticles but not protons. Also the position spectrum was examined to ensure that the particle group being measured was focused entirely within the active area of the detector. The remainder of the data was obtained with solid state detectors by using either the target chamber associated with the magnetic spectrometer or a 46 cm diameter I

I----: 600

1

I

I

1(

“N(3He,a)‘3N

+,3 t

t

01.G

I

E ,ob = 5.5MeV

80

40

120

CHANNEL Fig.

1. cc-particle spectrum for the 14N(3He, oz)13N reaction.

scattering chamber. Usually three or four counters were used simultaneously with their pulse-height spectra stored in different quadrants of a 512-channel analyser. Biased amplifiers were used to store energy spectra containing the CI~, aI and CQ,3 groups with optimum dispersion. A typical spectrum obtained with a detector at 90” for 5.5 MeV 3He particles is shown in fig. 1. The background beginning in the neighborhood of CQis believed to be due to the three-body break-up reaction 14N(3He, pa> “CL With the aid of a computer, each spectrum was plotted and the background under CQand CI~,3 was estimated visually and subtracted from the total area under the peak. The magnitude of these background corrections was never more than 20 % of the peak area. t Supplied by Nuclear Diodes, Chicago, Illinois.

326

A. R. KNUDSON

0

;

4

AND

F. C. YOUNG

, 6 5 INCIDENT ENERGY [Mei')

!

7

I

8

2.5-

INCIDENT ENERGY (M&J)

Fig. 2. Excitation functions from 2.5 to 8.5 MeV for the 14N(3He, a)13N reaction to the ground state (CL,,),first excited state (LQ) and second and third excited states unresolved (a%,3) of 13N. The data points are connected by smooth curves for clarity.

30

60

I

90 0cm

I

120

I

150

I 180

'0

30 I

60 I

0cm

90 1

120 \

150 ,

180 I

Fig. 3. Angular distributions for the 14N(3He, a)13N reaction to the ground state (x0), first excited state (Q) and second and third excited states unresolved (dcz 3) of 13N at 4.5, 5.5 and 7.0 MeV incident energy. The curves are a visual fit to the data.

A

0cm

328

A. li

KNUDSON

AND

F. C. YOUNG

Excitation functions for the 14N(3He, a)13N reaction were measured for a,, CI~ and Q, 3 from 2.5 to 8.5 MeV at the laboratory angles of 50”, 90” and 165”. The results are shown in fig. 2. The observed yields at each energy were normalized to the corresponding integrated beam charge. For these measurements a low beam current (< 0.03 PA) and a defocused beam spot on target were used to minimize target deterioration. The target was checked periodically for stability by measuring the reaction yield at 4.5 MeV when using the 3Hef beam and at 6.0 MeV when using the 3He+ ’ beam. These yields indicated that the amount of 14N on the target changed by less than 10 % during the runs. Relative detector solid angles were measured by using a radioactive cI-source placed at the same location as the beam spot on target. The statistical error in the measurements is indicated on a few points in fig. 2. Relative yields at different energies are uncertain to 10 % in these measurements. Angular distributions were measured for CI~,CQand Q, 3 at 4.5, 5.5 and 7.0 MeV over the laboratory angular range from 5” to 165”. The results are given in fig. 3. The distributions were obtained by normalizing the observed yield at each angle to the corresponding yield observed in a fixed monitor detector to eliminate effects of target non-uniformities and deterioration. For angles less than 40”, the particles were analysed with the magnetic spectrometer and position-sensitive detector. For q and Q, 3, measurements were made of the position spectrum above and below the particle group in order to make appropriate background corrections. Uncertainties of 5 % are assigned to these angular distribution measurements as indicated on some points in fig. 3. The angular distribution of elastically scattered 3He particles from 14N was measured at 7.0 MeV and at 4.5 MeV. For the 7.0 MeV measurements, the magnetic spectrometer and position-sensitive detector were used to detect the scattered particles in the angular range from 30” to 90”, and a solid state detector was used for angles from 90” to 130”. The results are given in fig. 4 with the uncertainties (5 “/o)indicated. For the 4.5 MeV measurements, the magnetic spectrometer was used over the angular range from 30” to 110” and a solid state detector was used for the region from 110” to 170”. Only relative cross sections were measured in this case and the uncertainties are about 10 %. The elastic scattering angular distributions are shown in fig. 4. Absolute differential cross sections were obtained by comparing the yields from the 14N(3He, 3He) and the 14N(3He, a) reactions with the yield of protons elastically scattered from 14N at a laboratory angle of 85.9” (90.0” c.m. angle) and 4.0 MeV incident energy. The uncertainty in making this comparison is estimated to be 10 %. The proton elastic scattering cross section at this energy and angle was assumed to be 69&2 mb/sr as measured by Olness, Vorona and Lewis 13). Total cross sections obtained by integrating the measured angular distributions are given in table 1. Normalizing our measurements to the recent proton scattering data of West et al. 14) would reduce our cross sections by less than 10 %. Comparison of the shapes of the angular distributions at 5.5 MeV with previous measurements “) of aO, CQand Q, 3 at 5.2 MeV shows fair agreement for ceoand poor

329

14N(3He, a)-N

agreement for czr and c(~,3. In all cases, the absolute cross section at 5.5 MeV as given in table 1 is 2 to 3 times larger than that of the previous measurements. The excitation curves measured in the present study provide no explanation for this discrepancy. However, cross-section measurements of the l”B ( 3He, a) reaction by Patterson

0.8

I

0”

30

60

90 8cm

120

150

180

Fig. 4. Differential cross sections expressed in terms of the Rutherford cross section for the 14N (3He, 3He)14N reaction at 7.0 and 4.5 MeV incident energy. The curves are optical-model fits using potentials A, B and C of table 2. At 7.00 MeV the dashed curve coTresponds to potential A and the solid curve to potential B. TABLE

1

Total cross sections for the 14N(3He, a)13N reaction E3~e WW

4.5 5.5 7.0

0 (mb) a0

a1

16.0 12.8 15.3

2.87 2.28 3.71

x2.3

21.3 24.3 15.7

et al. 15) disagree with those of ref. “) by a similar factor. The total a, cross section at 7.0 MeV of 15.3 mb z!z10% is in good agreement with the value of 18 mb rf 30% obtained

330

A. R. KNUDSON

AND F.

C. YOUNG

by Hahn and Ricci I6 ). Also the elastic scattering cross section at 7.0 MeV is in reasonable agreement with optical-model predictions at the forward angles where the calculation is relatively insensitive to optical-potential parameters.

3. Distorted-wave analysis 3.1. ELASTIC SCATTERING

The elastic scattering angular distribution measured at 7 MeV incident energy was used to determine an optical potential. Initially, a modified version of the automatic search program ELSA 17) was used in fitting the data. The modifica~on involved replacing a sequential search procedure, in which only one parameter at a time is varied, by the multiparameter variational technique described by Fletcher and Powell ‘*). A six-parameter optical potential of the form U(r) =: -V(l+exp[(r-r,A~)/a]}-‘+4irY,a’

-$ (1fexp[(r-r~A3)/a’])I‘1

was used. Several sets of parameters produced satisfactory fits to the elastic scattering angular distribution. As noted previously I’), these different potentials correspond to well depths for which an additional half-wavele~~h of the wave function of the system is contained inside the well. The most satisfactory fit to the 7 MeV angular distribution was obtained for potential A in table 2. However, despite considerable effort, it was not possible to achieve a satisfactory fit to the 1”N(3He, CQ,)angular distribution at 7 MeV using this potential for the entrance channel and making rcasonable variations in a four-parameter potential (V, W, r,, = r& a = a’> with volume absorption for the exit channel. An optical potential including a spin-orbit term has been used by Kellogg and Zurmuhle ‘) to fit 3He elastic scattering on 13C as well as for DWBA calculations on the 13C(3He, a)‘% and ‘3C(3He, d)14N reactions ‘azo). A good fit was obtained to the elastic scattering of 3He on 14N at 7 MeV by making only shght changes in the optical potential used by Kellogg and ~urmuhle. The search code OPTIC ‘I) was used in making these changes. The calculated angular distrib~ltion is compared with the experimental data in fig. 4 and the parameters used are given by potential B in table 2. This potential was used with some success in subsequent DWBA calculations. The 4.5 MeV elastic scattering angular distribution was also analysed with an optical-model calculation, Since an absolute cross section was not measured in this case, the experimental data were normalized to the optical-model results at the forward angles where the magnitude of the optical-model cross section is relatively insensitive to the well parameters. in fitting this data only the well depths were allowed to vary from those used at 7.0 MeV. The resulting optical-model parameters are given as potential C in table 2 and the fit to the data is shown in fig. 4.

14N(3He,

3.2. DWBA

331

cr)13N

ANALYSIS

The forward peaking of the angular distributions for the CI~and cc1groups at 7.0 MeV suggests that this reaction is proceeding by a direct process. To the extent that the 14N ground state can be represented by a pure (lp&)” configuration, the formation of the 2.37 MeV state of 13N, which is predominantly a (2~~)’ configuration, by a direct pickup process is forbidden. However, the ground state reaction may proceed by such a process and the observation that the yield of the c(~group is approximately 5 times smaller, on the average, than the a, yield favours this interpretation. The TABLE 2 Optical potentials for the 14N(3He, (x)‘~N reaction Potential

Channel (MIV)

EQ~ = 7.0 MeV

63.015

(fiZ)

(fZ)

1.335

0.725

(MZ)

(ZV)

(fz)’

(fi;

(filI”,

10.872

1.254

0.744

1.335

(ZG

A

entrance,

B

entrance,

ESH~= 7.0 MeV

162.3

0.921

0.807

6.114

2.20

0.804

1.20

6.084

C

entrance,

ESH== 4.5MeV

175.8

0.921

0.807

7.563

2.20

0.804

1.20

6.415

D

exit, a0

93

1.00

0.74

10.0

1.00

0.74

1.20

E

exit, CQ (pickup)

93

1.30

0.67

9.2

1.30

0.67

1.20

F

exit, CQ (knockout)

200

1.60

0.67

9.0

1.60

0.67

1.20

shape of the u,, angular distribution is relatively independent of the incident energy except for the large backward peaks at 4.5 and 5.5 MeV. Such backward peaking of the angular distributions may be indicative of a direct exchange process. Also the large fluctuations with widths of the order of 500 kevexhibited by the excitation curves are suggestive of a compound nucleus mechanism involving overlapping levels. However, there is little correlation between the fluctuations in the various curves with the exception of the peak at 4.5 MeV which appears in most of the curves. Excitation functions for the 14N(3He, p)160 reaction from 2.5 to 5.5 MeV incident energy exhibit much less structure ” ). Structure which does occur in that reaction does not appear to be correlated with the structure observed in the present measurements. It may not be possible to interpret these measurements in terms of a single reaction mechanism, but the forward peaking, absence of backward peaking and relative intensity of the angular distributions for the q, and a1 groups at 7.0 MeV suggests that direct pickup is the dominant reaction mechanism, at least for the a0 group at this energy. Accordingly, a DWBA analysis was performed for the ground state reaction at this energy with the code JULIE 23). The distorted waves for the entrance channel were generated with potential B of table 2 which was obtained from the elastic scattering analysis. Since appropriate elastic scattering data were not available for the exit channel, the exit channel optical potential was systematically varied in order to fit the reaction angular distribution. A four-parameter Woods-Saxon form with volume absorption was used. The form factor for the transferred nucleon in the 14N target

332

A. R. KNUDSON

AND

F. C. YOUNG

was calculated from a central Saxon well with r0 = 1.20 fm, a = 0.65 fm and a depth adjusted to give a binding energy equal to the observed neutron separation energy. A spin-orbit potential was not employed for the bound state. Also no radial cutoffs were used in the calculations. Fig. 5 shows the DWBA result for the pickup of a lp neutron using potentials B and D of table 2. Primary concern was given to fitting the angular distribution in the forward hemisphere; the effects of other reaction mechanisms are expected to be more pronounced at backward angles.

Fig. 5. Comparisons of DWBA calculations with measured anguiar distributions for the r4N (3He, GL,#~N and 14N(3He, q)13N reactions at 7.0 MeV. Potential B is used for the entrance channel. In the exit channel, potential D is used for the 14N(3He, c(a) pickup calculation; potential E is used for the 14N(3He, CQ) pickup calculation; and potential F is used for the 14N(3He, CQ) knockout calculation. The parameters of these potentials are given in table 2.

Attempts to fit the ground state angular distribution at 4.5 MeV were less successful. Calculations were carried out using potential C (table 2) in the entrance channel and systematically varying V and W for the exit channel potential away from the values which were used at 7.0 MeV incident energy. The calculated angular distributions invariably resulted in more peaks (4) than the measured distribution (3) and the peak at 100” could not be reproduced. Further calculations were made by adjusting V, Wand Y,.,. for the entrance channel potential in the direction of the values used for 7.0 MeV, but with the requirement that the 4.5 MeV elastic scattering angular distribution be reproduced within experimental uncertainty. No significant improvement in fitting the CI,,angular distribution was achieved with this procedure. It has been suggested ‘“) that the appropriate real potential well depths for (3He, cz) reactions should be related by V, M Vs,,+ Vnucleon. This criterion was used in an attempt to provide an improved fit to the ground state angular distribution at 7.0 MeV. Extensive calculations were carried out for exit channel well depths ranging from 180

14N(3He

> a)-N

333

to220MeV. It was not possible to obtain a satisfactory fit to the angular distribution in the forward direction with these calculations for any reasonable shape parameters or absorptive potential. In general, a separation as large as that observed for the first and second maxima in the angular distribution could not be achieved. If the 14N(3He, a1)13N reaction proceeds by direct pickup, the transferred neutron is expected to arise from sd shell configuration mixing in the 14N ground state because the first excited state of 13N is believed to correspond to a nearly pure (l~+)~(lp~)~(2s+)~ shell-model configuration ‘I). The 14N ground state wave function has been predicted to have small sd shell components ““). Therefore, the 14N (3He, CQ)reaction may proceed by direct pickup with a reduced cross section as observed. A DWBA analysis, similar to that for the ground state, was performed for the first excited state angular distribution at 7.0 MeV. The best fit for the pickup of a 2s neutron is given by the solid curve in fig. 5. Potentials B and E of table 2 were used for this calculation. The exit-channel potential is similar to that used for the ground state angular distribution calculation. Invariably, the first minimum in the theoretical distribution occurs at a smaller angle than the experimental minimum. This reaction may also proceed by the pickup of a Id neutron, but the fit to the measured angular distribution is not improved significantly with the addition of an I = 2 component in the calculation. Even though exchange mechanisms, such as knockout, have been shown to be less significant than direct pickup processes at least for (d, p) reactions 26*27), exchange processes may compete favourably with pickup for a reaction such as 14N( 3He, CX~)’ “N which is inhibited from proceeding by pickup. This reaction for 13.9 MeV incident particles has been analysed with some success in terms of a knockout mechanism “). Therefore, we have made a DWBA analysis of the c(~angular distribution measured at 7.0 MeV in terms of a knockolut mechanism, The zero-range approximation was used as formulated by Bassel et al. ““). Th e t ar get (resi d ua 1) nucleus was assumed to consist of an a-particle (3He particle) bound to a 1‘B core having the same spin, parity and binding energy as the 1OBground state. The form factor for the calculation is expressed as the product of two bound-state wave functions describing the relative motion of the a-particle and the 1°B core in the initial state and the relative motion of the 3He particle and the l”B core in the final state. The bound-state wave function of the initial (final) system is characterized by the relative orbital angular momentum and radial quantum numbers L(L’) and iV(N’) respectively. The values of N and L are restricted by the conservation of harmonic oscillator quanta 2N+ L - 2 for a Talmi transformation from a two-body wave function to a single-particle shellmodel wave function. Both the initial and final systems contain 4 harmonic oscillator quanta. Therefore the allowed values of the bound-state quantum numbers are L = 2, N = 2orL = 4,N = 1andL’ = 2,N’ = 2orL’ = 4,N’ = I.Inprinciple,multipIe values of L and L'are allowed. For the knockout calculation, we have assumed zero angular momentum transfer and L = L' = 2 with N = N’ = 2. A fit to the measured angular distribution was not achieved for the exit-channel optical potential used pre-

334

A. R. KNUDSON

AND F.

C. YOUNG

vjously. A systematic variation of the exit-channel potential parameters was made to obtain the best fit given by the dashed curve in fig. 5. Potential F of table 2, used for this calculation, has a much larger real well depth than is necessary for the pickup calculation for the a, group. Distorted-wave calculations were not carried out for the second and third states because these groups were not resolved in the measurements. However, tropy of the a2, 3 angular distributions relative to the CI~and CI~distributions that both levels are being formed with comparable strengths. This observation sistent with angular correlation measurements for the 14N(3He, a)‘3N*(p)‘2C tion in the vicinity of I%,, = 6 MeV by Bhatia ““). 4. Spectroscopic

excited the isosuggest is conreac-

factors

Spectroscopic factors have been extracted for the pickup calculations on the ground state and first excited state angular distributions. For (3He, E) reactions, the experimental differential cross section may be related to the theoretical (DWBA) cross section by the expression

de) = NC sZ,j uZ,j Ce>2 Lj

where cI, j(0) is the cross section computed by JULIE for the pickup of a particle from the 1,j orbit and S,,j is the corresponding spectroscopic factor including the isospin vector coupling coefficient. The normalization factor, N, depends on the overlap of the internal wave function of 4He with the system of 3He plus a neutron, as well as the strength of the interaction responsible for the transition. A normalization factor of 1.63 has been predicted theoretically under simplifying assumptions ““). More realistic calculations 3 O) have increased the value of the normalization factor to 17. However, it has been found empirically that somewhat larger values of N are generally required. For reactions in the light nuclei, values of N ranging from 7.2 [ref. ‘)I to 148 [ref. ““)I have been reported. These results depend upon theoretical estimates of single-particle strengths. For light nuclei, such estimates are probably more reliable for (3He, a) reactions on the “closed shell” nuclei 160 and 40Ca. A value of N = 41+20 % is consistent with DWBA analyses for these two reactions 32). This value of N is in good agreement with several other DWBA analyses 33-36) of (3He, a) reactions on light nuclei. In the present analysis of the 14N(3He, a,)13N reaction, the value N = 41 gives a spectroscopic factor of 0.83. The sensitivity of the spectroscopic factor to the exit channel optical-potential parameters was determined. Variations of the exit channel potential which reduced the quality of the fit to the measured angular distribution in the forward hemisphere produce changes in the spectroscopic factor of I!Z15 %. This leads to an uncertainty of 25 % in the spectroscopic factor. The present spectroscopic factor determination is in good agreement with results obtained from the 14N(p, d) 13N reaction; a value of 0.8 was obtained by Kozub et al. 37) for Ep = 30.3 MeV and a value of 0.76 was obtained by Bachelier et al. 38) for Ep = 156 MeV. There is also

“N(3He,

agreement

with several theoretical

335

a)13N

predictions:

0.69 by Cohen

and Kurath

3g), 0.93

by True 2s), 0.99 by Nagarajan 40), and 0.823 by Ripka 41). If the same value of N is used for the ’ 4N ( 3He, a1)13N reaction, a spectroscopic factor of 0.037 is obtained. This result may be compared with a value of M 0.02 reported by Kozub et al. 37) using the 14N(p, d)13N reaction and with theoretical predictions of 0.004 [ref. ““)I and 0.010 [ref. ““)I. It should be noted that the first excited state of 13N is unstable to proton decay so the exit channel probably is not adequately described by the optical potential used for rxo. However, since the residual nucleus is unbound by only 424 keV and the width of the first excited state is only 32 keV, it may not be unreasonable to take into account the unbound character of this level by adjusting the exit-channel optical potential to fit the measured x1 angular distribution. This is the procedure that has been used.

5. Conclusion The 14N(3He, ao)r3N reaction at 7 MeV incident energy can be interpreted with success in terms of the pickup of a lp neutron. The spectroscopic factor extracted from a distorted-wave analysis using realistic optical potentials compares favourably with determinations obtained from the 14N(p, d)13N reaction and with theoretical predictions. The largest uncertainty in extracting the spectroscopic factor from the (3He, a) reaction data arises from the normalization factor, iV, which is based on previous empirical determinations. Attempts to interpret the ground state angular distribution at 4.5 MeV in terms of a direct pickup mechanism were unsuccessful. The measured excitation functions and angular distributions suggest that the reaction mechanism does not have a simple interpretation at lower incident energies. The small cross sections observed for the 14N ( 3He , x1)13N reaction are consistent with either a direct pickup process or an exchange reaction mechanism. Calculations of the angular distribution at 7 MeV for these reaction mechanisms provide similar fits to the experimental data, but the exit channel optical potentials required are quite different. The optical potential for the pickup calculation is similar to that used for the analysis of the ground state angular distribution, and the spectroscopic factor is comparable to that determined with the 14N(p, d)13N reaction. For the knockout calculation, a much larger real well depth is required for the exit channel optical potential. On this basis, the interpretation in terms of a pickup mechanism is preferred over the knockout mode. The authors thank Dr. E. A. Wolicki for many useful suggestions. Computer time for this project was supported by National Aeronautics and Space Administration Grant Ns G-398 to the Computer Science Center of the University of Maryland. The financial support of a National Academy of Sciences - National Research Council postdoctoral fellowship by one of theauthors(F. C.Young)isgratefullyacknowledged.

336

A. R. KNUDSON

AND

F. C. YOUNG

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