A study of the 28Si(d, p)29Si reaction

Nuclear Physics A408 (1983) 221-238 0 North-Holland Publishing Company

A STUDY OF THE Z*Si(d,p)29Si REACTION R. J. PETERSON, C. A. FIELDS, R. S. RAYMOND’,

J. R. THIEKE and J. L. ULLMAN

~u~leor Physics Laboratory, Department of Physics, University of Colorado, Boulder, CO 80309, USA ” Received 8 March 1983 (Revised 12 April 1983) Abstract: ‘The Z8Si(d,p)Z9Si reaction has been studied at 17.85 MeV with a very clean silicon target allowing the study of sharp states up to an excitation of 14.8 MeV. Spectroscopic factors for bound states were obtained with: good reliability; these compare well to calculated values for strong low-lying states. A weak-coupling model allowed multistep calculations for several states, resulting in improved tits to the stripping cross-section data. Data for states above the neutron threshold in “Si were compared to DWBA calculations using unbound form factors. The sums of spectroscopic factors show a more complete closure of the d,,, shell at 28Si’than is predicted by Hartree-Fock methods.

E

NUCLEAR REACTIONS ‘sSi(d,p), E = 17.85 MeV; measured o(E,,O). %i deduced spectroscopic factors for bound, unbound states. DWBA, CCBA analyses.

1. Introduction Much progress has been made towards understanding the structure of sd shell nuclei, largely because large-scale shell-model calculations are feasible ‘). Although these predictions have been compared to a wide range of new data, one important experiment has not been treated in the detail it deserves. The (d,p) stripping reaction on “Si examines the distribution of st- and d, strength and is also sensitive to the final tilling of the d, shell. The best previous studies of the 2ESi(d,p)29Si reaction did not examine the highest excitations and were not able to obtain the crucial small-angle data points 2,3). We have repeated this reaction, analyzing sharp final states up to an excitation of 14.8 MeV in 29Si. The structure of 29Si may also be treated in a simpler model appropriate to the study of the (d, p) reaction. The weak-coupling models treat 29Si as a valence formalism, neutron coupled to core states in “Si. With a coupled-channel probabilities for high-spin transitions can be calculated taking the interference + Bldg. 911, AGS Exp. 748, U/M Group, Brookhaven National Laboratory, Upton, NY 11973. ++ Work supported in part by the US Department of Energy. 221

R. J. Peterson ef al. / 28Si(d,p)29Si

222

between

two-step

interference

can

paths be

and the dominant noted

for

some

one-step low-spin

mechanism states

examination of the shapes of the angular distributions. Results of stripping to unbound levels may be used reduced

widths,

and because

of the great difference

into account.

of

29Si

by

to determine

in momenta

between

a

This

detailed neutron the (n, y)

and (d, p) reactions, comparisons of the magnitude of cross sections and widths serve as independent measures of the orbital angular momentum transfer. This comparison has previously been made for levels of 29Si up to 10.477 MeV in excitation 3), particularly looking for a p9 doorway state “). More recent (n, r) data for higher excitation now exist, enabling a more detailed continuation of this comparison5 _ ‘). Since the full di stripping strength is known 2, not to reside in the low-lying states of 29Si, knowledge of the mean separation between the two I = 2 subshells near mass 28 requires a search for many small 3’ components at high excitations. This work locates many new I = 2 states, with total strength more than t,he expected summed shell-model strength.

2. Experimental

and theoretical

methods

An energy-analyzed beam of 17.85 MeV deuterons was University of Colorado AVF cyclotron. The target was composition, 1.48 mg/cm’ thick. This thick target provided a events to those due to surface impurities. Reaction particles with a 50 pm thick front telescope of silicon detectors,

obtained from the of natural isotopic good ratio of silicon were detected in a counter to allow

exploration at high excitations. The overall energy resolution was 50 keV FWHM. The energy calibration was obtained using the (d, p) and (d, d’) reactions on the Si target and on an 0.4 mg/cm2 mylar target, including the energy losses in the targets. This calibration was in good agreement with the known ‘) states of 29Si. The uncertainties in excitations for the sharp peaks are on the order of 30 keV and the errors for the less distinct peaks are about 70 keV. A sample spectrum is shown as fig. 1, which also shows the breakup peak of protons near half the beam energy. These breakup data will be pubhshed separately, together with coincident proton and neutron data 9). Knowledge of the target thickness and detector solid angle allowed the absolute cross sections to be measured. These results agree with the forward-angle elastic scattering predictions. The overall accuracy of the cross sections is estimated to be _+8 %. Distorted-wave Born approximation (DWBA) calculations were used to extract neutron spectroscopic factors, using the parameters listed in table 1. Deuteron parameters were selected which gave good tits to elastic and inelastic scattering data; a well-matching procedure was then. used for the neutron parameters. In fig.

223

28S~ jd,p) IO deg

4.93

838 ! 13 I

0

Fig. I. A sample

spectrum

GS

a27

I

900

Channel for the %i(d , p)‘%i reaction. The prominent is due to the breakup of the deuteron.

bump near 14 MeV of excitation

TABLE 1 Optical

model and other parameters used in the DWBAcalculations (a kite-range was used in the Hulthbn local energy approximation) ‘*Si + d [ref. 1‘)]

V (MeV) rr (fm) a, (fm) W, (MeV) ri (fm) ai

W-4

4W, (MeV) ri (fm) a, (fm) V,.,. (MeV) rr.o. (fm). ap.O.(fm) re (fm) nonlocal (fm) “) b, ‘) “) ‘)

Varied to tit the binding energy. Thomas spin orbit units. - 55.8 +0.32E. Lesser of 0 or 2.7-0.22E. 47.2-E.

- 86.35 1.15 0.81 0 _ _ 14.5 1.34 0.68 0

1.15 0.54

%+n

parameter of 0.65 fm

‘%i fp [ref. “)I

“1

‘)

1.16 0.78 0

1.17 0.75 9 1.32 0.51 ‘) 1.32 0.51 - 24.8 1.01 0.75 1.25 0.85

0

_ 25b) 1.16 0.78 1.16 0.85

224

R. J. Pelerson et al. / z8Si(d,p)29Si

I

I 40

I

I

I

80

120

160

40

II3 80

1 120

I

9 cm

8cm

Fig. 2. Data for elastic and inelastic scattering on *“Si are shown, compared to an optical model prediction and to collective DWBA predictions. The predominance of two-step processes through the 2+ state, rather than the 3- or 4+ states, is expected from the magnitudes shown.

2 are shown

elastic

and

inelastic

deuteron

scattering

data

to strong

low-lying

states, along with the optical model and collective DWBA fits lo, ‘I). Because of the wide range of excitation energies considered, an explicitly energy-dependent proton potential was used for the final states 12). The usual nonlocal and finite-range corrections were used in the DWBA, with stripping assumed to be to the lowest principal quantum number expected to lie above ‘%. Calculations used the binding energy prescription up to states at the neutron separation energy. For a few states just above that excitation a constant binding energy of 0.1 MeV was used to predict the yields. For unbound states, the was used to compute the yields for states of method of Vincent and Fortune 33’ 3, reasonable width. All DWBA calculations used the code DWUCK lo). Bound-state spectroscopic factors were obtained from the expression

normalized at the most forward stripping peak. Only weak j-dependence is noted in the calculations, and we are not able to distinguish between the two j-values for each 1 other than zero. Low-lying states of high spin are not expected to be populated by a direct nucleon transfer. Sequential inelastic scattering and stripping processes for such

R. J. Peterson et al. / 28Si(d,p)29Si

225

states were predicted using the coupled-channel method (CCBA) with the code CHUCK lo). Strong inelastic scattering transitions are shown in fig. 2; these are the basis of two-step calculations to be discussed in detail in sect. 4.

3. Results for bound states In the simplest shell model, the Is, orbit is the lowest above 28Si. Those transitions showing 1 = 0 patterns are compared to DWBA predictions in fig. 3, with their spectroscopic factors listed in table 2. The tits are excellent for the stronger states. The present result for the ground state is somewhat less than that of ref. ‘), where radially mismatched optical model parameters were used for the DWBA computations and the tits were not good. The total 1 = 0 strength and the centroid of this strength are listed in table 3. The next orbital expected above the st is the d,. Data for stripping to known 3’

30

60 9 c.m.

90

Fig. 3. Data and DWBA fits (shown as the solid curves) for I = 0 transitions to bound states of 29Si. The broken curve for the ground state is the result of combined single- and double-step reactions using the weak-coupling model described in the text.

R. J. Peterson et al. / 28Si(d,p/29Si

-.

2ccoc

R. J. Peterson et al.

1 2aSi(d,p)29Si

221

TABLE3 Total stripping spectroscopic factors and centroids of excitation are listed

0.70 0.41

I=0

I=1

1=2

2PW Id 312

Id,,,, I=3

/=4

f,,zf 5,2 &I,,.

0.31 0.72 0.4 1 1.30 0.50 1.80 0.12 0.42 0.36 0.079

3.28 6.31 9.33 1.65 4.93 4.2 1

10.80 6.04 2.31 5.28 11.83 11.06

(bound) (unbound) (total) (bound) (bound) (unbound) (total) (bound) (bound) (unbound) (unbound)

All unknown I = 2 transitions are assigned to the d,,, shell, all bound I = 3 to the fi,2 and all unbound I = 3 to the f,,2 shells. Unknown I = 1 transitions are taken to be to the p,12 shell.

states are compared to DWBA predictions (solid line) in fig. 4. Since most of the higher I = 2 transitions are expected to be d, transfers, all apparent I = 2 data to states of unknown spin are compared to d, predictions in fig. 4. Data for known t’ states, populated by d, transfer, are shown in fig. 5. Data for known z- states are shown in fig. 6, as are all data for I = 3 transfers to bound states of unknown spin. A total angular momentum transfer of $- is assumed for all of these. Although an 1 = 2 transition is claimed ‘) for a state at 7.62 MeV, the present data prefer an I = 3 tit. At higher excitations the DWBA shapes are less distinctive, but for the 7.62 MeV state both 1 = 2 and I = 3 shapes are shown (fig. 6) and are easily distinguished. Data for states showing 1 = 1 transfers are compared to DWBA predictions in fig. 7. Assignments for j for each state are indicated on the figure. The 5.28 MeV state has previously been assigned J” = s’ [ref. “)I. The present data are however clearly inconsistent with 1 = 4 (see below, sect. 4, and the data for the 4.08 MeV 5’ state in fig. 8). There may be two levels at this excitation energy in ?Si. In table 2 we compare the present spectroscopic factors, those of other (d, p) studies *, ’ 5), and those of the mirror (3He, d) reaction 14). Theoretical spectroscopic factors from shell-model calculations are also listed ’ 6*’ ‘), as are those from weak-coupling calculations “5 ’ 9). Projected Hartree-Fock calculations *O) predict the occupation numbers for the sd shell neutrons in **Si. These predict total stripping spectroscopic factors of 0.27 (d*), 0.65 (s+) and 0.77 (d,) out of a maximum of one. The total spectroscopic factors to bound states of 29Si from table 3 are 0.12 (d+), 0.70 (s+) and 1.30 (d,), indicating a crisper closure of the d, shell at *‘Si than expected. The total of I = 2 spectroscopic factors (1.92) indicates that some 2d strength may be present, consistent with the I = 4 strength observed (see below).

228

R. f. Peterson et al, / 2sSi(d,p)29Si

Fig. 4. Data and DWBA fits for d,,, stripping to bound Ievefs of 29Si. DWBA fits are shown as the solid curves and the results of the weak-coupling calculations described in the text provide the broken curves.

4. Second-order calculations

Although for many states the good fits found predictions give reliable spectroscopic factors, there second-order processes are possible. The dominant through the lowest (I.78 MeV) collective 2+ state I/q = 0.39, similar to that found in previous studies

for single-neutron DWBA are transitions for which two-step modes proceed of **Si with a collective *‘); stripping a d, neutron

R. J. Peterson et al. / 28Si(d,p)“9Si 1

I

I

I

1

'*Si(d,p)

-.

I

30

I

60

229

I

5/2+

/

I

9'0

Fig. 5. Data fdr two known i+ 2 states are compared to the solid DWBA curves and to the broken curves for the weak-coupling predictions.

onto this level may result in a final state of spin z+, for instance. Several known high-spin, low-lying states of “Si require this mechanism. In addition, weakcoupling calculations for the levels of 2QSi allow admixtures of the two-step mechanism to states also populated by the single stripping reaction. Since the amplitudes for one- and two-step m~hanisms interfere, a small admixture may have an important role. Weak-coupling models i*, 19) for 29Si have been applied to inelastic electron scattering 22723) and to the 28Si(d, py) reaction 15). Only transitions based on the ‘*Si 2+ state are considered; the other states of 28Si are much weaker in (d, d’). Scattering transitions within 29Si used the same value of & as found for 28Si. This was found to be appropriate for the dominant core excitations of 2QSi by a comparison of (p, p’) [ref. ““)I cross sections on 28Si (l/,Izl= 0.42) and z9Si (l&l = 0.36). A value of I/?[= 0.35 was reported from 3He scattering2s). No evidence for the role of the 28Si 3- excitation (6.28 MeV) has been reported in 29Si. All two-step calculations used /I2 = -0.39 for the ‘*Si inelastic step, to fit the deuteron inelastic scattering [with the phase as given by Clement et al. ‘“)I, The stripping phases were determined within the code CHUCK, but the heavy-particle spectroscopic factors introduce a phase (- l)Jl-Jz for transfer of Jr from the 2+ state to a final state Jz. This same sign enters the weak-coupling inelastic excitation, as seen by invoking time-reversal invariance for the de-excitation phase of de-

R. J. Peterson

230

et al. / 28Si(d,p)29Si

IO

I

I

30

0 cm Fig. 6. Data for I = 3 stripping are compared to DWBA predictions forj = $-. The dashed curves represent the CCBA calculation for the 3.62 MeV state, and the I = 2 DWBA calculation for the 7.62 MeV state.

I

n

,

60

I

I

_

90

“c.m. Fig. 7. Data for I = 1 transfer to bound levels of ‘“Si are compared to DWBA predictions. A total transfer of j = *- is used for the solid curves for the first three states, and j = f- is used for the broken curve for the 5.28 MeV state and the solid curve for the 6.38 and 7.99 MeV states. A spin of i’ is compiled for the 5.28 MeV level.

Shalit 26) while maintaining the symmetry for the two paths available to each state J,. In perfect weak coupling, both paths are equivalent except for the slight difference in strength between (d, d’) and (p, p’). It was found that both paths could be included to a good approximation by multiplying the prediction for the (d, d’)(d, p’) path by 3.3. This is not equivalent to the work of Clement et al. 15) in that they used different values of p for each transition in 29Si, including zero for some steps. The broken lines in figs. 3 through 6 show the CCBA calculations, using the wave functions of Clement et al. Is> in the weak-coupling limit. The strengths and wave functions used are listed in table 4. A good single-step fit for the ground state is found, needing no two-step

R. J. Peterson et al. / 20Si(d,p)29Si

231

TABLE4 Coefficients for the weak-coupling two-step paths used in the predictions shown as broken curves and compared to the data Indirect

Direct State

J

I

j

g.s.

1+

0

f

1.27 2.03

f+ ;+

2 2

3.07 3.62

:+ fz

2 3

DO

I

i

+ +

70 81 30

2 0 2

$ 96 +- 92 $ 110

5 i

15 84

2 1

2 106 3 73

RI

For all transitions a value of p2 = -0.39 was used for ?Si and ?Si (with the appropriate statistical factors). Stripping strengths are given as D,, with D, = + 124.5 for a unit spectroscopic factor. Inclusion of the sequential stripping, scattering process increases the predictions by a factor of 3.3

contribution. The inclusion of the two-step path spoils the fit at the 60” maximum, as seen in fig. 3. The 29Si transition rates of Clement provide a curve indistinguishable from the broken curve shown, which uses the same fi2 in 2sSi and 29Si. The strong 3’ state at 1.27 MeV also needs no two-step strength, as seen in fig. 4. The solid curve is the DWBA prediction normalized to the data. The broken curve for the 2.03 MeV $’ state (fig. 5) shows the prediction including the twostep paths, while the rather different solid curve shows the prediction using zero for the 29Si inelastic transition strength, as used by Clement, The direct spectroscopic factor has been lowered from 0.14 to 0.06 to fit the data. The weak, nondirect yield to the 2.43 MeV $’ state is shown in fig. 4, compared to the DWBA solid curve (which does not fit) and the broken curve for a pure two-step transition due to 2~ stripping (with S = 0.3) onto the 2+ state of 28Si. This reproduces the generally flat shape, but does not agree with the weak&mpling wave function which has an st spectroscopic factor of 0.83. The destructive interference with the weak-coupling wave function was not adequate to lower the prediction. Clement et al. 15) proposed two wave functions for the 3.07 MeV 5’ state. Only the second can reproduce the present data. The 2+ @ 2s, path interferes with the direct path to produce a strong dip at small angles. The broken curve in fig. 5 uses a spectroscopic factor of 0.015, not the 0.04 used by Clement et al. The data for the 3.62 MeV $- state (fig. 6) shows a strong peak, not reproduced by the solid DWBA curves. Again, Clement et al. suggest two wave functions of opposite phase for the two-step path. Only the first, constructive, form reproduces the shape. Little difference is found between the 29Si transitions of Clement et al. and the weak coupling used here, but a spectroscopic factor of 0.47 is needed, not the 0.65 suggested by Clement et al. 15).

232

R. J. Peterson et al. / 28Si(d,p)29Si

stripping mechanism Fig. 8. Data for three states of “Si not accessible to the simplest single-nucleon are shown. The solid curve for the 3’ state represents the expected shape for g,:, stripping. The broken curves show the two-step predictions, as described in the text, for stripping a single neutron onto the first excited state of ‘“Si.

In general, the present comparison is in good accord with the work of Clement rr al., but it is often found that weaker direct spectroscopic factors are required. This may be due to a greater sensitivity to a direct reaction at the higher energy used here. The work of Clement was not able to distinguish the two models for the g- state, as was clearly possible at the higher energy. Of the two choices for the 3.07 MeV 2’ level, the analyzing power data of Clement led them to disagree with the choice preferred at the higher energy, but the structureless low-energy data did not enable a good selection. Second-order processes are necessary

to excite 29Si states of high spin; the data are gathered in fig. 8. The lowest z’ state at 4.08 MeV is expected to be due to a shown as the d, neutron coupled to the 2+ level of ‘%i. The sequential prediction, broken curve, is roughly consistent with the observed shape, with a spectroscopic factor of 0.5. This is notably weaker than the prediction of Caste1 19). The solid curve for a single g, transfer represents the 30” region well but the large-angle behavior indicates but little single-step excitation. The lowest e’ state can be populated by d, stripping onto the 2+ state, but this is weak because of the near filling of the d+ subshell in 28Si. The featureless data are fit by a prediction with a d+ spectroscopic factor of 0.06 for stripping onto the 2 + level.

R. .I. Peterson et al. / 28Si(d,p)29Si

233

The 6.78 MeV y- transition is predicted as an f+ transfer onto the 2+ state 19). The broken curve compared to the data in fig. 8 is computed for a unit spectroscopic factor. Since less than this was found for the lowest i- state and since the forward-angle data are not fit, another process than that computed must also exist. The s- state of the same configuration, presumably the one at 5.25 MeV, is predicted to be populated more weakly by a factor of five. No data could be obtained.

5. Transitions to unbound states The levels of 29Si above 8.47 MeV are not stable to neutron decay, and the DWBA methods used for bound states will not give the proper (d, p) spectroscopic factors. The DWBA predictions will be much too small, resulting in spectroscopic factors which are too large. We have used the code DWUCK4 in its unbound option for (d, p) predictions to unbound states, using the method of Vincent and Fortune 13). The DWBA code provides both the differential cross section and the neutron width of the state for a unit spectroscopic factor. There are two independent constraints to these widths. Our data will determine any total widths greater than about 60 keV. Below 11.13 MeV (the a-decay threshold), these are the same as the neutron widths. Neutron widths for many 29Si states below 10 MeV are known from resonant-neutron reactions on 28Si [refs. 5- ‘)I. Several previous comparisons of these results to (d, p) strengths have been made 3,6) but not to states above 10.5 MeV in excitation. From fig. 1 it is seen that the present work provides data to states up to 14.8 MeV. Since a large photonuclear yield is found at 10.3 MeV [ref. 27)] and ascribed to a pygmy resonance due to the valence neutron in 29Si this region deserves a more thorough study. The dominant photoneutron peak ‘is at 21.2 MeV, with a 5.5 MeV width 27). The data in figs. 9-12 for states above 8.47 MeV are compared to the DWBA predictions for unbound states, shown as the solid curves. Since little distinction is found between the two j-values for each I, only d,,2p, and f+ predictions are used. Excitation energies and spectroscopic results are compiled in table 5. The present results agree with those for the stronger peaks of ref. 3, except for a few cases. The 8.57 MeV state in the present work shows a good I= 3 shape when compared to either bound or unbound DWBA curves. The I= 2 curve suggested by the work of Medsker et al. “) is shown by the dotted curve; the fit is unacceptable. At 9.24 MeV is found a peak agreeing at all but the smallest angles with the I= 1 curve suggested by Medsker. The comparison of 1 = 1 and 1 = 3 predicted widths also confirms the I = 1 fit. The present results do not agree with the previous 1 = 3 assignment for the 9.44 MeV peak. Both I= 1 and 2 shapes are compared to the data in fig. 9. If these were 1 = 1 transitions, the spectroscopic

234

R. J. Peierson el al. 1 28Si(d,p)29Si

R. J. Peterson et al. 1 28Si(d,p)29Si

235

8 cm

Fig. 11. Stripping yields to I = 3 unbound states of 29Si are compared to $- predictions as the solid curves. The prediction for I = 2 (for the 8.56 MeV state) is shown as the dotted curve. The broken curve for the 8.56 MeV state shows the prediction for a bound-state j- form factor,

factors would demand a width of several hundred keV. The peaks are not as broad as predicted for an I = 1 transition, but the best tit is 1 = 1. The poorer I = 2 fit is still superior to that for 1 = 3. A state at 10.35 MeV exhibits a good 1 = 3 fit, shown in fig. 11, in contrast to the I = 2 assignment made previously 3). Above 10.5 MeV excitation no data exist for comparison to the present results. No sharp 1 = 1 transitions are expected, and even I = 2 transitions should exhibit measurable width for the observed spectroscopic factors above about 12 MeV. A state at 12.53 MeV displays a good I = 2 fit, but the spectroscopic factors call for a width of 400 keV. No unusual broadening is seen, indicating that this is an 1 = 3 transition. Fig. 11 shows both the I = 2 (dotted curve) and the 1 = 3 fits. Similarly, for the sharp 12.69 MeV state the 1 = 2 and 1 = 3 fits are of comparable quality, but 1 = 2 is ruled out by the width. The observed 100 keV intrinsic width for the 12.41 MeV state agrees with the width expected for an 1 = 2 transition’ of the observed strength. Since the 1 = 3 and 4 transitions below 15 MeV excitation are weak, no observable width is expected. Indeed, no widths above 150 keV are measured for states of these assignments.

R. J. Peterson et al. / 28Si(d,p)29Si

236

R=4 IO.48 xl0

60

30

90

8

cm

Fig. 12. Yields for

I = 4 unbound

states are shown.

The calculations

assume

a j-transfer

off’.

6. Conclusions Stripping shell-model calculations excitations,

data for the lowest states of 29Si are in good agreement with modern calculations ’ 6,17) and also with the trends shown by weak-coupling 19). Strong components from the fp shell are found at remarkably low but the lack of f% strength precludes’s Nilsson interpretation of the

levels. The lowest The weak-coupling states;

prediction

$- state, at 7.20 MeV [ref. “)I shows no stripping strength. model provides predictions for the excitation of high-spin of the stripping

strengths

on the 2+ state of 28Si presents

a new

test of the shell-model calculations. Consideration of the many weak unbound levels made little difference to the distribution of I = 2 strength, raising the centroid only from 4.21 MeV to 6104 MeV above the ground state. Since the sum of I = 2 spectroscopic factors to bound states exceeds unity, even with individual spectroscopic factors below those reported previously 2), admixtures from the 2d shell may be indicated (see table 5). Since the lowest 1 = 4 strength is found at 10.48 MeV and since only a small sum of 1 = 4 (g+) spectroscopic factors is found, this orbital may be safely disregarded in shell-model calculations. The 10.3 MeV state prominent in the 29Si(y, n) reaction 27) is allowed to have

R. J. Peterson

et al. 1 2aSi(d,p)29Si

231

TABLE 5 Spectroscopic

E, WV) 8.56 9.03 9.24

factors,

I-assignments Orbital f 512 f

h?:, (izf:I:,

9.44 9.67 9.95 10.03 10.24 10.35 10.48 10.88 11.04 11.22 11.48 11.71 11.88 12.14 12.23 12.41 12.53 12.69 12.84 13.05 13.44 13.75 13.94 14.26 14.44 14.57 14.65 14.78

2P,,2 PI,2 f 5/z 2d 312 d 312 2d3,,

d 312 2d’312 d 312 f s/2 g9/2

d 312 2d,,, d 312 W,,

d 312 2d 312 d 312 g9/2 g9/2

f 512 d 312 d 3/z f 512 f s/2 f 5/z f 512 f 512 g9/2

f 512 f 5/z f 5/z f 512 f 512 f 512

and natural

line widths S

0.023 0.045 0.34 0.17 0.027 0.14 0.28 0.033 0.086 0.12 0.023 0.03 1 0.048 0.066 0.024 0.052 0.099 0.028 0.036 0.034 0.043 0.031 0.038 0.015 0.006 0.020 0.030 0.036 0.017 0.019 0.015 0.059 0.034 0.006 0.018 0.013 0.010 0.012 0.010 0.014

are shown

for the unbound

rri, (MeV) (+40

keV)

0.06 1 0.069 0.15 0.15 0.15 0.12 0.12 0.053 0.10 0.10 0.062 0.062 0.059 0.059 0.061 0.057 0.087 0.087 0.087 0.070 0.070 0.070 0.070 0.072 0.074 0.11 0.13 0.12 0.078 0.095 0.095 0.14 0.11 0.12 0.12 0.070 0.070 0.078 0.066 0.13

rr,, is the determined experimental line width and r owucx4 the predicted DWBA possible mixing of the Id,,, and 2d,,z states can be seen from line-width calculations.

states

fDwucn4 (MeV) 2.6 x 1O-5 5.1 x 10-s 0.20 0.21. 3.0 X lo- 5 0.17 0.16 4.4x 1o-5 0.074 0.059 0.020 0.015 0.041 0.033 9.8 x 1O-4 6.9 x 1O-5 0.086 0.10 0.031 0.12 0.037 0.11 0.033 1.7 x 1o-4 3.1 X 1o-4 0.011 0.12 0.14 0.020 0.023 0.018 0.070 0.040 0.002 0.021 0.015 0.012 0.014 0.021 0.029 line width.

A

a spin of $- or $-. No prominent I = 1 stripping is found in this region, although any strong states would also be expected to be broad. The (d, p) reaction finds instead a concentratioai of measurable 1 = 2 strength between 9.9 MeV and 11.5 MeV, consistent with Ml photoabsorption.

238

R. J. Peterson et al. / 28Si(d,p)29Si

While this work was being completed, new measurements by Betz et al. 28) of high-lying levels of 29Si by the 28Si(d, py) reaction appeared. While Betz et al. were able to observe many of the low-spin unbound levels reported in the present study, they are able to assign J” values only to the high-spin unbound states. This work has shown that the strongest, most relevant and interesting features of neutron stripping on 28Si are found at the lower excitations, indicating that the simpler calculations are expected to be very reliable for the A = 29 system. Professor P. D. Kunz provided valuable assistance in implementing the unbound features of his DWBA code DWUCK4.

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