14N(α, d)16O at 30 MeV

Nuclear Physics

A181 (1972) 323-336;

Not to be reproduced

by photoprint

@

North-Holland

or microfilm without

14N(a, d)160

Publishing

written permission

Co., Amsterdam from the publisher

AT 30 MeV

J. LOWE Physics Department,

WilliamsLaboratory

University of Birmingham, England and of Nuclear Physics, University of Minnesota,

USA t

and A. R. BARNETT Williams Laboratory

of Nuclear Physics, Received

tt

University

17 February

of Minnesota,

USA t

1972

Abstract: Data are presented for r4N(a, d)160 at E, = 29.98 MeV, to states of I60 at 6.92, 7.12, 9.85, 10.35, 11.09, 11.52, 14.400, 14.815 and 16.214 MeV. Cross sections cover the range 10” to about 100” (lab). Excitation energies and widths are obtained for the following states: 11.094*0.003 MeV, 14.400&0.003 MeV (r c,m. 5 30 keV), 14.815&0.002 MeV (r,,,. = 60*12 keV) and 16.214*0.015 MeV (I’e,,. = 96+16 keV). Comparison with other data establishes the following states in this energy region: 2p-2h states at 14.400 MeV (5+), 14.815 MeV (6+) and 16.214 MeV (4+), and a collective, 4p-4h state at 16.304 MeV (6+). The existence of two 6+ states and of strong 2p-2h structure in this region is in agreement with recent extensive shell-model calculations. However, the spin sequence of the 2p-2h states, and the structure of the 4+ state, do not seem to be consistent with these calculations.

E

NUCLEAR REACTIONS “N(or, d), 14N(a, a), E = 29.98 MeV; measured u(Ed, f3), ~(0,); widths; deduced optical-model parameters. I60 deduced levels, r. J, x, nuclear structure data.

1. Introduction The two-nucleon transfer reaction, r4N(a, d)160, has been investigated by the Berkeley group in several publications 1- “). An interesting feature is that three states are observed to be strongly excited in the reaction, at excitations of 14.4, 14.8 and 16.2 MeV, in addition to several low-lying states. It is expected that the (a, d) reaction should excite 2p-2h states preferentially, and these three states were identified ’ -“) with the configuration [(14Ng.S.)l+(ldf)S+]J=, J” = 4+, 5+ and 6+. Interest in this suggestion was further aroused by the shell-model calculations of Zuker, Buck and McGrory “) (referred to as ZBM). These calculations included basis states up to 4p-4h in the closed lp shell, but excluded the Id, orbit. Nevertheless, the three 2p-2h states with the configuration [(lp;2)1+(ldi)5+]4+,5+,6+ were predicted to be quite pure (> 98 % by intensity for the 5+ and 6+ states), and to lie in the region of 15 7 Work supported tt Present address:

in part by the US Atomic Energy Commission, contract no. AT(ll-1) 1265. Physics Dept., University of Manchester, Manchester Ml3 9PL, England. 323

324

MeV excitation. It is therefore in 14N(~, d)i60.

J. LOWE et al.

natural

to identify

these states with the triplet observed

Confirmation of this identification would provide a useful test of the ZBM wave functions. Several points in particular suggest experimental investigation: (i) In the ZBM calculations, the spin sequence of the states is 6+, Sf, 4’ (in increasing excitation). This sequence seems to be basic to the model, since not only does it occur in the published wave functions, but is preserved in a wide range of effective interactions tried in the calculations “). (ii) The ZBM model predicts two 6+ states in this region of excitation. One is the remarkably pure 2p-2h state under discussion, and the other is a strongly deformed state, being the fourth member of the well-known rotational band based on the 0’ state at 6.05 MeV. The ZBM calculation is the first to recognise the existence of these two 6’ states lying within a few MeV of each other. (iii) While the 5+ and 6+ 2p-2h states are > 98 y0 pure, the 4’ is predicted to mix somewhat with other configurations. In particular the state contains + about 60 ‘A of the simple 2p-2h configuration. Information on the spins of these states comes from two sources: (a) In DWBA calculations, the angular distributions predicted for the 4+, 5+ and 6+ states are identical, except for kinematic effects depending on the outgoing deuteron energy. However, the absolute cross sections should be proportional to (2J+ 1). Thus, ignoring outgoing-energy-dependent effects, the states can be identified by the magnitudes of their cross sections. (b) Several other states in this region, which have spins assigned by other means, have been identified with these 2p-2h states. Method (a) has not proved very consistent in the past, due in part to resolution difficulties “). For example, in refs. ‘9 “) the states were assigned 4+, 6+, 5 +, while in ref. “) the sequence is 4’, 5+, 6’. Following method (b), the state at 16.2 MeV has been tentatively identified “) as the state at 16.2 MeV observed “) in a-“C scattering, and assigned 6’ from that work. Furthermore, the state at 14.8 MeV may be the same as that observed at 14.81 MeV by Ophel 9slo), and also assigned 6+. The present paper describes a further study of 14N(~, d)160 at E, = 29.98 MeV to this triplet of states. With a view to allowing for kinematic effects in the (2J+ 1) rule, angular distributions to two of the states were measured in more detail than in earlier work, in order to carry out a DWBA analysis. For the same reason, a-14N elastic scattering was measured to derive optical potentials for the analysis. The identification of these states with states observed in other reactions is often frustrated by imprecise knowledge of the excitation energies. Therefore the energies and widths of these states were measured as accurately as possible in the present work. Results are also shown for several lower-lying states. 7 The wave functions used in the present paper were taken from ref. 7). These differ slightly from the published wave functions 5, due to the use of a different interaction. No conclusions are changed by this difference. To conform with the DWBA code used, a phase of i’ was inserted in each single-particle wave function.

14N(a(, d)160 AT 30 MeV

325

2. Experimental method 2.1. CROSS-SECTION

MEASUREMENTS

The source of a-particles was the 30.0 MeV beam from the Williams Laboratory MP tandem accelerator with currents of 50-200 nA. Three experimental arrangements were used. (i) For most of the data collection, the beam was incident on a 150 pg * cm-’ adenine target on a 10 pg * cm-’ carbon backing. Outgoing particles were detected in three detector telescopes, each consisting of a surface-barrier detector (2 30 pm)

300

;

MeV

16

14

EXCITATION

Fig. 1. Spectrum of excitation energy of target contaminants. (tritons from

30MeV

E)lob= 20’

“Nford1’60

12

IO

ENERGY

8

6

IN’*0

deuterons from 14N(cq d)i60 at 20” (lab). The groups are identified by the the excited state in 160, and by the product nucleus when they result from Particle contamination occurs at 7.7 MeV (recoil protons) and 15.6 MeV the 14N(a, t)“Na reaction}. The system energy resolution is 80 keV.

a 3 mm Si(Li) detector. Particle identification was carried out using the CDC 3100 on-line computer’ ‘). Deuteron spectra, an example of which is shown in fig. 1, showed groups corresponding to states in I60 at 6.92, 7.12, 9.85, 10.35, 11.09, 11.52, 14.40, 14.8 1 and 16.21 MeV, and angular distributions were measured +for these, where possible, over the range 10” to 105”(lab). States in I60 were also identified in many spectra at 13.98, 15.17, 15.44, 15.78, 17.18 MeVk0.05 MeV, all with widths s 80 keV, but they were too weakly excited to be analysed. A new state of 160 was observed 80+20 keV lower than the 14.40 MeV member of the (d,)’ triplet, at 14.32kO.02 MeV with r < 30 keV (sect. 3). (ii) Similar counter teIescopes and electronics were used together with a r 4N2 gas target. The target was maintained at a pressure of 300 Torr, and the detectors were collimated so that particles scattered from the organic entrance and exit windows did not enter the detectors. Data were taken for the above states over the range 15”-55” (lab), and also for a- 14N elastic scattering at the same angles; the system resolution

and

+ Data are not presented for the 6.13 and 8.87 MeV states, owing to contamination 6.05 MeV state group and recoil protons, respectively.

from the

J. LOWE et al.

326

was 100 keV. Spectra were obtained free from ’ 4N groups resulting from the l’C(cc, d) 14N reaction, which sometimes obscured the I60 groups when the adenine target was used. In particular, the i 6O 16.21 MeV state was not resolved from the ’ 4N 5.10 MeV state at 30”-50” when the adenine target was used. The use of a gas target also enabled absolute cross sections to be determined. (iii) Particles from the adenine target were also detected in a double-focussing Enge split-pole magnetic spectrometer. Signals from position-sensitive detectors in the focal plane were analysed by the on-line computer ‘I) to yield energy spectra directly. The resolution was limited by the target to about 35 keV (FWHM). Use of the magnetic spectrometer enabled (a) Separation of I60 states from r4N contaminant states mentioned in (ii) above, and (b) Investigation of possible close doublets in 160 , unresolved in the solid-state detector spectra. Measurements were made for the 14.40 and 14.81 MeV states over the range 10”-35”(lab) and c~-‘~N elastic scattering was measured over the range 8”-62.5”Qab). 2.2. ENERGY

AND

WIDTH

DETERMINATIONS

The magnetic spectrometer set-up, described under (iii) above, was used to measure the energies and widths of the 14.81 and 14.40 MeV states, and also the energy of the state observed at 11.09 MeV, since the earlier work could not safely distinguish which of the known doublet 12) at 11.080 and 11.096 MeV is excited here. In each case, a reaction angle was chosen for which the deuteron group corresponding to the 160 state under investigation lay close to that for a known state of 14N, excited in the “C(a 9d)14N reaction. Use of a nominal value for the I60 state excitation enabled the energy calibration of the analyser to be determined. The magnetic spectrometer field was then changed to place the 1 6O deuteron group where the ’ 4N group had been to within a few channels, and the approximate analyser calibration then enabled the ’ 6O state energy to be determined. Iteration of this procedure, using the new I60 state excitation to improve the analyser calibration, proved unnecessary. The measurements were repeated, using a change of reaction angle, rather than spectrometer field strength, to place the 160 deuteron group in the place previously occupied by the 14N group. For the 11.09 MeV state the ’ 4N ground state was used as a calibration, and for the 14.40 and 14.81 MeV states, the 14N state at 13) 3.950+0.002 MeV was used. Measurement of the excitation of the 16.21 MeV state is complicated by its large width. Thus the accuracy of the magnetic spectrometer was not required, and energy determinations were made at three reaction angles, using solid-state detector spectra calibrated using the 14N 5 . 106 and 160 14.40 and 14.81 MeV states. The widths of the 14.81 and 16.21 MeV states were determined from the observed peak widths, by subtracting in quadrature the observed resolution of the system (80 keV for the detector telescopes and 35 keV for the magnetic spectrometer). The

14N(a,

d)160

AT

30 MeV

14.40 MeV state group appeared to be no wider than the system resolution, an upper limit on its width was obtained.

327

so only

3. Results Fig. 1 shows a typical deuteron spectrum taken with a solid-state detector telescope and an adenine target, at 20”(lab). For 160 states below about 12 MeV excitation, there is little background, and errors in the cross sections were usually limited by statistics. For more highly excited states, an additional error arises from estimation of the continuum background under the states. For the a-14N elastic scattering, the ground state a-particle group was always well resolved, and the errors are statistical only. The magnetic spectrometer data, and the counter telescope data taken using solid targets, were each normalised to the gas target data to obtain absolute cross sections. Data for the 14.40 MeV state may be contaminated by a rather weakly excited state observed at 14.32+0.02 MeV. The state, which has not been reported previously, is visible in fig. 1, and was resolved from the 14.40 MeV state in the magnetic spectrometer data and in the solid-target counter data, but not in the spectra from the gas target. The state is also visible in the spectrum of ref. “).

o( _“N

ELASTIC

SCATTERING

3.0 r

Fig. 2. Elastic scattering of 29.98 MeV x-particles as the ratio to the Rutherford by 14N plotted cross section, together with optical-model fits using the potentials of table 2.

Fig. 3. Cross sections for 14N(a, d)r60*(6.92 MeV, 2’) at 29.98 MeV. Finite-range DWBA predictions are also shown using the optical potentials of table 2, and the wave functions of ref. ‘). See the detailed discussion in subsect. 4.3 of the text.

328

J. LOWE

et al.

(M, d)‘%

:,,I0

20

40

60

80

Fig. 4. Cross sections for 14N(a, d)160*(7.12 a+ \\

14N(~.d)15Cl

(7.12 MeV)

100

MeV, l-)

12og

140

cm.

at 29.98 MeV.

(9.95MeV) o.L-

Fig. 5. Cross sections for 14N(a, d)160*(9.85 MeV, 2+); see caption to fig. 3.

14N(ti,d)160

(10.35 MeV)

Fig. 6. Cross sections for 14N(a, d)‘60*(10.35 MeV, 4+); see caption to fig. 3.

The cross-section results, at a mean energy of 29.98 + 0.03 MeV, are shown in figs. 2-11. The errors shown are relative only, and there is an overall normalisation error of + 10 % on all points. The angular error is kO.2”. The angular acceptance was kO.5” for the elastic scattering measurements. For the (~1,d) measurements the finite angular acceptance is of less consequence; values between kO.6” and + 1.5” were used at various times. Results for the excitation energies showed good agreement between the two methods employed, i.e. variation of reaction angle and spectrometer field to place the calibration state close to the “0 state under investigation. The results for both energies

11.094 MeV)

20

40

14N ( ti,df60

(14.400

‘.

’

20 0

’

40 3

8

1

60

I

I

80

I

I

iQll

,

(1

1209

60 ’

8

60 ’

’

MeV)

:

. . . ... 100 L ’ ’

,:.

120,

’

14Q ’

4.m. Fig. 9. Cross sections for ‘*N(a, d)r60*(14.400 MeV, 5+(4+)); see caption to fig. 3. The dotted curve is calculated assuming .J* = l+ for this state, and uses potentials ALPHA l-Dl. “N(cx,~,“~

O.IIJ__-u 0

20

LO

60

80

Fig. 10. Cross sections for l*N(ar, d)r’0*(14.815

(14.815 MeV)

100

120 8

140

c.m.

MeV, 6+); see caption to fig, 3.

1

140

cm. Fig. 8. Cross sections for ‘*N(a, d)i60*(11.52 MeV, 2+); see caption to fig. 3.

Fig. 7. Cross sections for 1*N(a, d)160*(1 1.094 MeV, 4+); see caption to fig. 3.

o.mo

I

330

J. LOWE

v

O.lo

’

20 ’

’

LO :

’

60 ’

et al.

’

60 ’

’

100 ’

’

120 1

If.0 ’

I

0 cm.

Fig. 11. Cross

sections

for 14N(a,

d)160*(16.214

MeV, 4+(5+));

see caption

to fig. 3.

TABLE 1 Energies Excitation energy E. (MeVfkeV)

11.094* 11.096+ 11.094&

14.815+ 2 ‘) 14.82 +30 14.810* 8 14.811& 3 14.8 d,

16.304f20 ‘) s 16.2 16.2 &O.l

“) b, ‘) d, ‘) ‘) ‘) “)

of states observed

in 14N(q

Width (c.m.) r c.m. (keV)

d)r60,

compared

with other

0.3 kO.1

4+

S 30 30+30

5+ b)

360&40 280&90 370*50

this work ‘) Y this work

14N(a, d) 14N(a, d) ‘%+a rzc(a, a) 14N(a, da)

this work ‘) ? ‘) ‘) this work

(-Y

‘.‘N(c(, d) 14N(a, d) r4N(a, da)

6+ 6+

12C(6Li, d) ‘2C(a, a) 12C(6Li, du)

6+ 6+ (-)”

96&16 125+50

14N(3He, p) ‘“C(cc, c() d) d) da)

(_)J+1 60512 69130 67+10 53* 8

data Ref.

Reaction

14N(ct, d)

3 3 6

14.400~ 3 “) 14.40 +30 14.4

16.214*15 16.24 540 16.2

and widths

4+ ‘)

14N(a, r4N(a, 14N(a,

Lowest member of the 2p-2h, (ld*‘) triplet. Deduced from the results of ref. 26), i.e. the state has unnatural parity. The 6+ member of the 2p-2h triplet. The highest member of the 2p-2h triplet. The state has natural parity 26) an d is either 4+ or 5+ (see text). The rotational, 4p-4h, 6+ state. Ref. =). “) Ref. 28). ‘) Ref. I”). ‘) Ref. 4). j) Ref. 26). Ref. l6). “) Ref. *).

‘)

‘1

‘) ‘) “) “) ‘)

I) Ref. 14).

14N(a, d)160 AT 30 MeV

331

and widths are summarised in table 1. The errors in each case result from uncertainty in the centroid of the peaks. Errors due to uncertainty in the beam energy were small. In the analysis, the most recent value 13) for the energy of the ’ 4N second excited state was used, which differs significantly from earlier measurements. The present result can be referred to any other value for this excitation energy using a value for (dE1601/dE1dN*) of 1.0 at EIeO, = 14.4 MeV and 1.2 at EIGol = 14.8 MeV. 4. Analysis and discussion 4.1. ENERGY

AND

WIDTH

MEASUREMENTS

The excitation energy determined for the 11.09 MeV state is 11.094+0.003 MeV in close agreement (table 1) with the established J” = 4+ state at 11.096 + 0.003 MeV. Our value was obtained from the centroid of the peak and it thus seems that any contribution from the 3+ state at 11.080+0.003 MeV must be very small and hence that the latter is not to be identified “) with the ZBM 3+ state at 13 MeV. The widths and energies of the 14.400, 14.815 and 16.214 MeV triplet are given in table 1. The values for the second of these states, 14.815+0.002 MeV and rc.,,. = 60+ 12 keV, agree well with the recent values of Ophel et al. lo) of 14.810+0.008 MeV with T_. = 67& 10 keV. This state was assigned J” = 6+ from their analysis of the i’C(cx, c1), i’C(a, c(‘) and i2C(cr, cc’y) reactions. The same state was observed by Ramirez and Bernstein 14), who also determined J” = 6+, to be at 14.811+0.003 MeV with Tc,,,. = 53 + 8 keV. Thus we are confident that the same ’ 6O state is observed in each of these experiments and hence it is the 6+ member of the (di) triplet. This conclusion is contrary to the predictions of Zuker et al. ’ - ‘) and forms a puzzling discrepancy in their model. It seems unlikely that an explanation can be found in terms of displacement of the 4+ member of the triplet by interaction with other 4+ states since the DWBA analysis presented below suggests that this mixing is if anything less than that calculated by ZBM. A rotational 6+ state of 4p-4h character has long been known “) from a-“C scattering at approximately 16.2 MeV with T_,, = 280+90 keV (see table 1). No phaseshift analysis was carried out in ref. “) so the resonance energy and width were not well determined. A more detailed experimental investigation of a-“C elastic scattering in this region of I60 is in progress i “). The 6+ state was recently observed by Bassani et al. 16) at 16.304+0.020 MeV with T_,. = 36Ok40 keV in the ‘2C(6Li, d) ’ 6O reaction. This width was inconsistent with that of the 14N(a, d)l 6O state of 2p-2h character located in earlier data at “) 16.24kO.04 MeV with T_,. = (125f 50) keV and both groups agreed that the two states did not correspond, on experimental grounds as well as on a consideration of the different reaction mechanisms in the two cases. The present ’ 4N(a, d)’ 6O results, which have improved accuracy, support this conclusion since (table 1) the 2p-2h state is located at 16.214+_0.015 MeV and its width is Tc.,,. = 96k 16 keV. The existence of these two states is predicted by the ZBM wave functions, as discussed in sect. 1; the 16.304 MeV state is the rotational 6+,

J. LOWE

332

et al.

he 14.815 MeV state is the 2p-2h 6+ while the second of these two states near 16.2 MeV is the 16.214 MeV, 2p-2h state with J” = 4+, 5’. 4.2. OPTICAL-MODEL

ANALYSIS

As a preliminary to the DWBA analysis, the tl-14 N elastic scattering data were analysed using the optical-model search program of Hill 17). Starting parameters six-parameter were taken from the work of Weisser et al. la) for 58Ni. A conventional optical model with volume absorption was used, and all six parameters were varied simultaneously. Two of the parameter sets found are given in table 2 and the resulting fits are compared with the data in fig. 2. The set ALPHA 2 gives a better fit to the data, but its volume integral suggests that it belongs to a different family from ALPHA 1. Also, the value of a, seems unrealistically small. Small values for this parameter were found to be characteristic of relatively deep potentials, and probably set ALPHA 1 is the more physically reasonable of the two sets. TABLE 2 Optical-model Set ALPHA ALPHA Dl D2 D3

V 1 130.0 2 187.4 108.2 118.0 118.0

rv

av

WV

f-w

aw

1.369 1.268 1.07 0.970 0.940

0.625 0.625 0.858 0.933 1.000

44.92 28.76 0.0 0.0 0.0

1.364 1.539

0.350 0.145

parameters WD 0.0 0.0 20.8 9.44 10.17

b

1.488 1.827 1.831

al,

0.535 0.468 0.496

VE.O. rs.o.

6.99 7.42 8.92

0.955 0.903 0.967

as.,.

k.4

1.30 1.30 0.500 1.07 0.181 0.97 0.450 0.94

Units are MeV and fm.

In the above searches, the normalisation of the data was not treated as a variable parameter. It was found that any attempt to do so resulted in large changes in parameters, often to unrealistic values, with no improvement in the fit to the data. 4.3. DWBA

ANALYSIS

Since the object of the present analysis was to obtain data on the highly excited states, DWBA analyses were first carried out on the lower states in order to test the applicability of the method and for the selection of suitable optical potentials. For a-particle optical potentials, the sets ALPHA 1 and ALPHA 2 (table 2) were used. Deuteron potentials were taken from published analyses of deuteron scattering by light nuclei. Three for which fits are shown here are given in table 2, and are derived from fits to deuteron scattering + by I’) %i(Dl) and by ““) “C(D2 and D3). Other a-particle and deuteron potentials were tried in the analysis, but were less successful than those of table 2. t A numerical error in the spin-orbit term in ref. 19) was corrected before use.

14N(a, d)160 AT 30 MeV

333

The DWBA analyses were carried out using the two-nucleon transfer program of Nelson and Macefield “I). The program permits the inclusion of finite-range and non-locality corrections in the local WKB approximation. The effect of these corrections on the predictions was found to be quite significant, especially for the higher angular momentum transfers. Values for the relevant parameters were taken from range = 0.2 the work of Nelson et al. ‘L “); range of f orce = 1.6 fm, non-locality fm for m-particles and 0.54 fm for deuterons, cc-particle size parameter = 3.03 fm. In each case the bound-state wave functions were solutions in the real part of the deuteron optical potential, in which the central potential depth was varied to reproduce the total separation energy of the transferred nucleons. The separation energy was divided between the two nucleons in such a way that the proton binding energy was less than the neutron binding energy by the Coulomb energy (3.5 MeV). For the ’ 6O states, the ZBM wave functions were used. The ’ 4N ground state was assumed to be pure (lpi’), +. This assumption may seem inconsistent in view of the highly correlated nature of the 160 ground state in the ZBM wave functions. However, the analysis here is in general confined to states which are strongly excited, and therefore have large components that are reached from the major component of the 14N ground state by the (a, d) reaction. Hence the terms added by the use of a more realistic 14N wave function [e.g. that of ref. ““)I involve transitions between weak components in both initial and final wave functions, and the amplitudes are two orders of magnitude lower than the dominant ones calculated here. Also, the calculations of Weibezahn et al. 24) show that, in a shell-model calculation using the same parameters as ZBM, the r4N ground state remains 98 ‘A pure (lpi’), and in True’s wave functions ‘“) the ground state is 97 % pure (1~;~). Exceptions to this comment are the 6.92 MeV and 7.12 MeV states, for which the largest components in the ZBM wave functions are not excited from the (lpi’) configuration. Therefore predictions for the former must be treated with caution, and no meaningful predictions were obtained for the latter. Predictions using the above procedure and three sets of optical parameters from table 2, are shown in figs. 3 and 5-l 1. Each curve has been normalised to give visually the best fit to the data, especially in the forward angle region. The predictions for the 11.094 MeV state use the wave functions for the second 4+ state of ZBM. For the 6.92, 9.85, 10.35, 11.094 and 11.52 MeV states, at least a qualitative fit is obtained. The 10.35 MeV state is particularly well fitted by the set ALPHA I-D2, but in general there is no strong preference for any of the optical potentials. While the predictions do not give a detailed fit, except perhaps for the 10.35 MeV state, the quality of the fit is as good as that usually obtained to two-nucleon transfer reactions on light nuclei [refs. 22*24925)1* The same procedure was then used to predict cross sections for the 14.400, 14.815 and 16.214 MeV states. Using the ZBM wave functions, the 5+ and 6+ members of this triplet are pure (ldf). The 4+ member (the third 4+ state of ZBM) contains other components; however, the amplitude for the (CI, d) reaction to these is quite

J. LOWE et al.

334

weak +. Hence, the only significant effect of these components is to reduce the predicted cross section by depletion of the (Id:),+ component to an amplitude of -0.77. Thus, apart from the kinematic effects of the different outgoing energy, the predictions for all three states are identical in shape and ‘the relative magnitudes are influenced by the (25+ 1) factor, together with a further factor of ( -0.77) ‘for the 4+ state. Good fits to all three states are given by potentials ALPHA 1-Dl; this quality of fit supports the simple 2p-2h picture for these states ‘). The normalisation factors applied to the DWBA predictions are shown in table 3. Since only relative cross sections are calculated by the program, the overall factor is arbitrary, and the values have been scaled to yield a value of 1.0 for the 14.815 MeV

state. All predictions use the ZBM wave functions, except for the 14.400 and 16.214 MeV states, which were calculated for pure (Id:) coupled to J” = 6+. Thus if the reaction theory and wave functions were exact, all values would be 1.0 except for these two states, of which the Sf member would give (2 x 5+1)/(2x 6+ 1) = 0.85, and the 4+ member, (2 x 4 + 1)/(2 x 6 + 1) x ( -0.77)2 = 0.41. Several points emerge from table 3: TABLE 3

Normalisation State

Transferred J

excitation (MeV)

6.92 9.85 10.35 11.094 11.52 14.400 14.815 16.214

factors for the DWBA predictions

2f 2’ 4f 4+ 2+ 4+, 5+ 6+ 4+, 5+

~2~3 1 3, 5 3 1,3 5 5 5

Normalisation

factor “)

potentials ALPHA l-D1

potentials ALPHA l-D2

potentials ALPHA 2-D3

2.6 0.13 0.41 0.52 0.41 0.71 “) 1.oo 0.86 “)

2.5 0.11 0.38 0.50 0.36 0.70 “) 1.oo 0.73 “)

1.7 0.10 0.32 0.34 0.29 0.62 “) 1.00 0.75 “)

“) These states have Jn = 4+ or 5+, but the normalisation

factors quoted here are calculated

for Jn = 6+. “) The uncertainty (due to matching the curve to the experimental data) is +115 ‘A in general, for the 14.400 and 16.214 MeV states with ALPHA l-D2 and ALPHA 2-D3, where it is 130 %.

except

(i) There is considerable fluctuation in the normalisation factors. As discussed above, the calculation for the 6.92 MeV state is somewhat unreliable since it would be influenced by other components in the 14N wave function. For the remaining states, there seems to be a tendency for the factor to increase but there are too few cases to be conclusive.

with the transferred

+ Note that no other components can be coherent with the dominant (ld+‘) component, latter is the only J = 5 transfer possible within the ZBM basis.

J-value, since the

14N(m, d)160 AT 30 MeV

335

(ii) The triplet of states under study have the largest normalisation, and therefore seem to be well described by the pure 2p-2h configuration, as suggested by ZBM. However, no state appears to be significantly lower than the others, as would be expected for the 4+ state, and thus it seems that the 4+ state must be closer to pure (Id:) than calculated by ZBM. (iii) While the accuracy of the relative normalisations is inadequate to make firm spin assignments for the 14.400, 14.815 and 16.214 MeV states, it is in agreement with the assignment above of 6+ for the 14.815 MeV state. Further information on the states excited in 14N(~, d)’ 60(a)‘2C comes from the work of Artemov et al. 26) who studied their u-decay. States at 14.8 and 16.2 MeV were observed (see table 1) to decay to the i2C ground state while that at 14.4 MeV was not. This establishes that the former have natural parity, so that if the states are 4+, 5’ and 6+, then the 14.400 MeV state is the 5+ member of the triplet. We assume this to be the final link in the chain which establishes the identity of the members of the (Id;) triplet and conclude that the spin sequence is 5+, 6+, 4+ in order of increasing energy. Finally, a prediction is shown in fig. 9 calculated on the assumption that the 14.400 MeV state is the lowest 1’ state. This follows the suggestion of Latorre and Irvine “) that the lowest 1’ state has pure 2p-2h character and should be strongly observed in this region of the spectrum. The ZBM wave function, which is mainly (2sf),+ and (Id;), + was used. The fit is acceptable, although not as good as for the 4+ assumption. Also the normalisation factor required, 2.1, seems unrealistically high. Thus it seems likely that the 1’ state is one of the weaker states in the spectrum (fig. 1).

5. Summary The information obtained from the present investigation is (i) The energies and widths of table 1. These enable detailed comparison with states observed in other reactions to be made. (ii) The angular distribution analysis presented in figs. 3-l 1 and table 3. In general the ZBM wave functions for the 6.92, 9.85, 10.35, 11.094 and 11.52 MeV states are in good agreement with the present results, with a reservation that the absolute magnitude seems to depend on the transferred J-value in a manner that is not understood. From a comparison of the present results with other work, the spins of the following states can now be assigned with reasonable confidence: (a) The 2p-2h states: 5+ at 14.400 MeV, 6’ at 14.815 MeV and 4+ at 16.214 MeV (widths given in table l), (b) The collective 6’ state at I’) 16.304 MeV, Tc.,,. = 360 keV (table 1). Thus the spin sequence is different from that predicted by ZBM, although their predictions of strong 2p-2h structure and of two 6’ states in this region are supported. The 4+ member of the triplet seems to be closer to pure (Id:) than suggested by the ZBM wave functions.

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We would like to thank And&s Zuker, Brian Buck, Sid Kahana and John Nelson for valuable comments on the work. We are also grateful to John Nelson for use of his finite-range DWBA program, and for carrying out some of the calculations shown here. We are grateful to the Atlas Computing Laboratory for provision of computing facilities. One of us (J.L.) wishes to acknowledge the hospitality of the Williams Laboratory during a visit. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28)

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