Levels of 42Sc from 40Ca(3He, p)42Sc and 40Ca(3He, pγ)42Sc

Nuclear Physics 80 (1966) 259--272; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

L E V E L S O F 42Sc

FROM 4°Ca(SHe, p)42Se AND 4°Ca(3He, pT)42Se R. W. ZURMOHLE, C. M. FOU

Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania and L. W. SWENSON

Bartol Research Foundation of the Franklin Institute Swarthmore, Pennsylvania t Received 6 December 1965 Abstract: Levels of 42Scat 0.62, 1.51, 1.59, 1.88, 2.22, 2.28, 2.40, 2.50, 2.64, 2.82, 3.09, 3.25, 3.33, 3.39 and 3.47 MeV have been studied by means of the ~°Ca(aHe, p)42Sc reaction at 10, 12 and 15 MeV incident energies. Angular distributions have been measured which are consistent with spin assignments of J = 0, 1, 3 and 0 for the ground state, 0.62, 1.51 and 1.88 MeV excited states of 4~Sc, respectively. Spin assignments have been made on the basis of a DWBA analysis of the 12 MeV angular distributions. The assignments are supported by observations of the gamma decays of the 0.62, 1.51 and 2.82 MeV states in coincidence with protons from the '°Ca(SHe, p7)4~Sc reaction at 10 MeV incident energy.

E I

NUCLEAR REACTIONS cr(E;Ep,O),p?-coin. "°Ca(SHe,p?), E= IO, 12,15 MeV;

I

measured er(0). 4~Scdeduced levels, J, l. Natural target.

1. Introduction The 4°Ca(3He, p)42Sc reaction is a useful spectroscopic tool which m a y be employed to obtain information on the states o f 42Sc. This reaction has been the object o f several recent studies 1-3). A n u m b e r o f shell model calculations have recently been reported 4 - 6 ) on f~ shell nuclei following the a p p r o a c h o f Talmi. The quantitative success o f these calculations is based on an empirical knowledge o f the level spacings and spins of the system consisting o f the 4°Ca core plus two nucleons viz. 42Ca, 42Sc and 5°Ti. A description o f the pair o f nucleons outside the 4°Ca core as a pure (f~)2 configuration is further assumed appropriate to these calculations. The 4°Ca(SHe, p)42Sc reaction is particularly well suited for the study o f 42Sc levels in this context because it should strongly excite states corresponding to a (f~)2 configuration. Experimental angular distributions have been measured; comparisons with D W B A calculations will be discussed and spin assignments made for several strongly excited states o f 42Sc.

2. Experimental Method The University o f Pennsylvania T a n d e m Accelerator was used to b o m b a r d natural calcium targets with a 10, 12 and 15 M e V 3He beam. Self-supporting targets of 0.15 to 0.5 m g / c m 2 were prepared by means o f v a c u u m evaporation 7). t Work supported by the National Science Foundation. 259

260

R . W . ZURMUHLE e t al.

The 3He beam entered a 61 cm diam. scattering chamber s) where it was incident upon a target placed in the centre of the chamber. The reaction products were detected by an E - d E / d x solid state detector telescope placed on a rotating table within the chamber. An additional detector was placed at a fixed angle of 45 ° with respect to the incident beam direction to monitor the beam current. For angular distribution measurements the E+ dE/dx sum pulse was stored in the memory, of a 4096-channel Technical Measurement Corporation pulse-height analyser, operating in a oneparameter analyser mode. The dE/dx signal was used to indentify the reaction particle types 9) and to provide a gating pulse for the 4096-channel analyser. The identification of particle types in the (3He, p) reaction study is simplified, by Q-value considerations, to discrimination between proton and helium ion dE/dx pulses for the range of excitation energies studied. Angular distributions of the most prominant proton groups, corresponding to the ground state and the 0.62 and 1.51 MeV excited states of 42Sc, as well as the elastic 3I-Ie group were measured between the angles of 5° and 160 ° at each of the three bombarding energies. In order to locate the energy positions of the 42Sc levels more precisely an exposure with a broad range spectrograph was made at 45 ° and 15 MeV incident energy with a 150 #g/cm 2 target. In a separate investigation the gamma decay of 42Sc levels populated by the 4°Ca(3He, p~)42Sc reaction has also been studied using a 7.6 cm x 10.2 cm NaI(T1) crystal mounted on a RCA-8054 phototube *. The E+dE/dx sum pulses from the solid state detector telescope and the NaI(T1) crystal were analysed by the 4096channel analyser operating in a two-dimensional analyser mode. A coincidence (2z ~ 120 ns) between the charged particle and gamma events was required and used to gate the analyser. In these measurements the particle detector was placed at 50 ° to the right of the incident beam, and the NaI(T1) crystal at 45 ° to the left with its front face 7.6 cm from the target.

3. The 4°Ca(SHe, p) Results A sample solid state counter proton spectrum is shown in fig. 1. The solid points are experimental data points. The open circles represent the energy positions of the proton groups as determined from solid state detector calibrations and from the magnetic spectrograph exposure. The excitation energies indicated in fig. 1 and on the 42Se level diagram of fig. 2 are calculated from the spectrograph exposure. The level diagram obtained for 42Sc is compared with the 42Ca level scheme lo) in fig. 2. The indicated excitation energies carry an estimated experimental error of _+20 keV and are in good agreement with the values 0.618, 1.507, 1.590, 1.895, 2.217, 2.301, 2.400, 2.491, 2.542, 2.638, 2.844, 3.091, 3.232, 3.319 and 3.359 MeV reported by Cline et aL 3). Only the ground state and excited states at 0.62, 1.51, 1.88, 2.82 t Integral line assembly obtained from Harshaw Chemical Co.

9

~1

4°Co (3He,P)4~' Sc 15 MeV

z

l~

OLA B = 52 °

I

>

8

I00 O9 I'--

z

:D

~

rY hi Z

N

LIJ

o (,.)

Z

0

3

_o

50 X

0 28(

i

,

I

290

300

310

|

320

CHANNEL

i

330

340

350

360

370

NUMBER

Fig. 1. Proton spectra for ~°Ca(3He, p)~Sc reaction at 52 ° with ]5 M e V aHe beam. The proton energy calibration is shown. 3.47 3.39 3.191

5.33 5.25

6+

3.09 4-

4

2.751

.....

2.82 2.64 "Z.3-a. . . . .

2+

2.423

___

2_.4_0_ 2.28 2.22

1.836

0+

1.88

1.523

2+

1.59

O+

2+

3 + T:O

1.51

7.+ T:O 0.62

O

O+ 0(:142

O

1

1+ T:O

0 + T=I

S C 42

F i g . 2. L e v e l s c h e m e s o f t = C a a n d 4=Sc c o m p a r e d . E x c i t a t i o n e n e r g i e s are f r o m s p e c t r o g r a p h e x p o s u r e .

'

30

~

60

~CM.

90

120

150

GROUNDSTATE

180

=0Ca(aHc,p)4=Sc reaction leading to the ground state and 0.62 and 1.51 MeV excited states of ~2Sc, for a bombarding energy of 10 MeV. The curves are visual fits to the data and have no theoretical significance.

Fig. 3. Experimental angular distributions of protons from the

O

I.O' ~

1.0:

~=''E nOC~cn

0.1

1.0

E(3He} = IO MeV

O.

0

30

~

O

E

O

120

150

180

*°Ca(SHe, p)¢=Sc reaction leading to the ground state and 0.62 and 1.51 MeV excited states of 4sSc, for a bombarding energy of 12 MoV. See caption fig. 3.

C.M Fig. 4. Experimental angular distributions of protons from the

E

0.1 l.O

1.0

E (3He) =12 MeV

N

ta

~2Sc LEVELS

263

and 3.09 MeV are well resolved in the solid state detector spectra and are indicated by solid lines in the 42Sc level diagram of fig. 2. The broken lines (except for the lowlying 7 + state) indicate the positions of weakly excited states which could only be resolved in the spectrograph exposure. The 1.51 MeV excited state was found to be much more strongly excited in the spectrograph exposure than the 1.59 MeV state. -

E(3Hel : 15 MeV

5

r

"~

n

"

E --~

ev

M

eV

- -

'•

OI

"O

O.I

0.01

-

0

30

60

90

120

150

180

C.M. Fig. 5. Experimental angular distributions of protons from the 4°Ca(SHe,p)4'Sc reaction leading to the ground state and 0.62 and 1.51 MeV excited states of 4~Sc,for a bombarding energy of 15 MeV. See caption fig. 3.

The low-lying isomeric 7 + state could not be seen in our exposure. Its existence is, however, well established from other experiments by Rogers and G o r d o n 11), Harvey et aL 12) and Nelson et aL 13), although the excitation energy is still not well known. This state is either nearly degenerate with the 1 + state at 0.62 MeV, only very weakly excited by the 4°Ca(aHe, p)42Sc reaction or both.

264-

R . W . ZURMUHLE et aL

The experimental angular distributions for the strongly excited ground state and 0.62 and 1.51 MeV excited states are shown in figs. 3-5 for the three bombarding energies. The indicated errors are statistical. The absolute cross sections are believed to be in error b y n o t more than 2070, the principle uncertainty arising from target nonuniformity. The angular distributions depend only slightly upon the incident energy as expected for a direct interaction. 4. DWBA Analysis and Discussion To facilitate our later discussion we begin by summarizing the spectroscopic selection rules as they apply to the (3He, p) reaction. For a reaction initiated on a spin-zero target the spin of the final nuclear state is J = l+s, where l and s are the orbital and spin angular momenta of the transferred nucleons. The assumption of isobaric-spin conservation implies the additional restriction that s = 1 when T = 0 and s = 0 when T = 1, where T is the isobaric spin of the final state. The parity selection rule is An = (-)~, and conservation of parity restricts l to "even" values. Thus even J final-spin states (J = 1) will correspond to angular distributions with unique /-values whereas " o d d " J final-spin states ( J = l+_ 1) will correspond to a mixture of/-values. The experimental angular distributions for 12 MeV bombarding energy are compared in figs. 6-8 with calculated angular distributions using the DWBA method with optical-model potentials of the form

U ( r ) = Uc(r)

V 1+ expxv

iW + 4iWD --d 1 l+expxw dr 1+ expx~,

h sld 1 Vsl. m,c r dr 1 + exp xv'

+--

where Uc(r) is the Coulomb potential for a uniform charge distribution of radius rc A + and xv = (r-rvA~)/av,

xw = (r-rwA÷)/aw.

The numerical values of the parameters which have been used for the various potentials are listed in table 1. The 3He parameters were derived from an opticalmodel fit to the 3He elastic scattering angular distribution at 12 MeV shown in fig. i0. These parameters were kindly supplied by R. H. Bassel 14). The use of the optical potential D results in the best fit to the 3He elastic scattering angular distribution. The SP and SP3 proton potential parameters are quite similar and are derived in the case of SP3 from fits 15) to the angular distribution of elastically scattered 12 MeV p r o t o n s o n ' * 2 C a and from the work of Perey 16) for the set SP. Both SP and SP3 include spin-orbit interaction, but this plays a negligible role in the 12 MeV stripping angular distributions.

0 o

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120 °

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State

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180 °

Fig. 6. C o m p a r i s o n o f experimental angular distribution (solid points) with D W B A calculations at 12 MeV. T h e solid curve represents a calculation using the parameters D]SP3 o f table l a n d W o o d s - S a x o n singleparticle wave functions for the transferred deuteron. T h e broken line represents a calculation using the parameters A/SP a n d oscillator singleparticle wave functions.

b

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with D W B A calculations at 12 M'eV. The calculated 1 = 2 and 1 = 4 stripping curves are compared in the lower portion of the figure and the experimental data are compared with a 66.6~o 1 = 2 plus 3 3 . 3 ~ l = 4 mixture of stripping curves in the upper section of the figure. The D/SP3 parameters of table 1 and a Woods-Saxon single-particle wave function

Fig. 8. Comparison of experimental angular distribution (solid points)

"10

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°.,i

1.0

0o

I

30 °

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I

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i

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s

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3.886

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Fig. 9. Comparison of l = 2 D W B A two-nucleon stripping curves for different choices of the total spin J. The D/SP3 parameters of table 1 and a Woods-Saxon single-particle wave function for the transferred deuteron were used in the D W B A calculations.

"tO

b

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>=

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4t~Sc LEVELS

267

TABLE 1 Optical model parameters for 3He V (MeV)

W (MeV)

WD (MeV)

Vs (MeV)

rv (fm)

rw (fm)

ro (fm)

av (fm)

aw (fm)

A a)

106.3

7.4

0

0.854

1.07

1.81

1.4

0.854

0.592

D b)

181.0

11.5

0

0.854

1.07

1.81

1.4

0.854

0.592

re (fln)

av (fm)

aw (fm)

Optical model parameters for protons V (MeV)

W (MeV)

WD (MeV)

Vs (MeV)

rv (fro)

rw (fm)

Sp e)

52.0

0

11.0

7.5

1.25

1.25

1.25

0.65

0.47

SP3 d)

53.6

0

17.1

8.0

1.217

1.264

1.25

0.60

0.310

• ) Parameters derived from fitting aHe elastic scattering data of Yntema and Zeidman. These parameters also provide a good fit to the 12 MeV elastic scattering data reported here. b) Deep Woods-Saxon well parameters derived from best fit to 12 MeV elastic ZHe scattering angular distribution. These parameters also lead to good fits of other (aHe, c() and (3He, d) data. c) Values from work of Percy. a) Derived from fits to angular distributions of 12 MeV protons elastically scattered from ~2Ca.

I

I

I

I

I

+°Ca (SHeS, He) 12 MeV

1 - ~e'b"-e,ex e~ *ke.

e\e 0.1

0.02o+

I

50 °

I

I

60*

90*

I 120 °

150 °

80*

~C.M. Fig. 10. Ratio of the experimental (solid points) elastic 3He differential scattering cross section to the Rutherford cross section for 4aCa at 12 MeV. Error flags indicate experimental errors larger than the point size. The solid curve is an optical model fit using the parameters D as listed in table 1. The DWBA approximation

calculations were made

by Drisko

a n d R y b i c k i 17) i n z e r o - r a n g e

with no radial cutoff using "best-fit" optical-model parameters

simple shell-model assumptions

f o r t h e 42Sc s t a t e s . I n p a r t i c u l a r , t h e b o u n d

and state

268

R.W.

ZURMI.JHLE et aL

wave-function of the "quasi-deuteron" was obtained by assuming that the neutron and proton are each deposited in a 1 f~ single-particle orbit. We first discuss the transition to the ground state of 42Sc which has been previously established to be 0 + and T = 1, thus restricting the expected stripping pattern to a pure l = 0. Two choices of the single-particle wave-functions for the transferred nucleons are represented by the calculated (with zero lower cut-off) angular distributions of the ground state transition in fig. 6. The broken curve corresponds to the oscillator single-particle wave-function assumption and the solid curve to WoodsSaxon single-particle wave-functions. Both calculated curves exhibit a diffraction structure similar to that of the data, but only the Woods-Saxon choice may be considered to give a quantitative fit. The most striking feature of fig. 6 is the discrepancy of about 15 ° in the location of the maxima and minima of the oscillator diffraction curve. This discrepancy does not seem to be attributable to a particular choice of optical-model parameters. While oscillator wave-functions have been quite successfully employed in a wide range o f single-nucleon transfer reaction calculations, replacement of the oscillator wavefunctions with Woods-Saxon wave-functions dramatically improves the agreement between theory and experiment for the case of the 4°Ca(3He, p) two-nucleon transfer reaction. As Drisko and Rybicki 17) have pointed out, an oscillator wave function has a Gaussian tail which decays too rapidly to approximate the exponential-like tail of a wave function for a finite well, of which the Woods-Saxon shape is an example, and that in general, the approximation of a finite-well single-particle wavefunction by an oscillator single-particle wave-function reduces the effective interaction radius, thereby shifting the diffraction pattern to larger angles. Further, it has been suggested that such an effect is generally characteristic of two-nucleon transfer reactions. Certainly the published 'calculations of Rook and Mitra is) for the 4°Ca(t, p)42Ca reaction offer an additional example of a two-nucleon transfer reaction where the calculated angular distributions are seriously out-of-phase with the experimental angular distributions. The experimental angular distribution for the 0.62 and 1.51 MeV states are compared in figs. 7 and 8 with DWBA calculations using Woods-Saxon singleparticle wave-functions for the transferred nucleons. The optical model parameters D/SP3 of table 1 are the same as those used to fit the ground state angular distribution using these wave functions. Neither the 0.62 nor the 1.51 MeV state angular distribution can be fit with a single/-value stripping curve. The experimental angular distribution for the 0.62 MeV state has a prominant l = 0 feature and is compared with different mixtures of l = 0, 2 diffraction patterns (curves A and B) in the upper section of fig. 7. The calculated l = 0 and l = 2 curves are shown for comparison in the lower portion of the figure. An l = 0, 2 mixture implies J = 1 + for the 0.62 MeV state. No l = 0, 2 mixture, however, produces a quantitative fit to the experimental data of fig. 7 at large angles. If some l = 6 is introduced (curve C) the overall fit is improved. An l = 6 diffraction pattern is the principle

425c LEVELS

269

contribution expected from a 7 + state. The considerable improvement which results in assuming the necessity of an l = 6 contribution might suggest that the 1 ÷ and 7 ÷ states are very nearly degenerate and hence unresolved in the present experiment. In fig. 8 the calculated l = 2 and 1 = 4 stripping curves are shown for comparison and the experimental angular distribution for the 1.51 MeV state is compared with a mixture o f / = 2 and l = 4 stripping curves. The comparison here must be considered quite satisfactory. An l = 2, 4 mixture here implies a 3 + assignment for the 1.51 MeV state. The l = 2 contribution to the experimental angular distribution of fig. 8 f r o m an unresolved state of assumed spin J = 2 at 1.59 MeV is expected to be less than 5 % from the measured yields of these states. The Q-value dependence of the D W B A curves has been found to be small over the range of excitation energy studied. Further, the j-dependence of the calculated curves is not large as indicated in fig. 9, so that the stripping patterns of figs. 7 and 8 may be taken as typical I = 0, 2, 4 curves. The calculated curves of figs. 6-8 have been arbitrarily normalized to the experimental data points at forward angles. For the ground state transition at 45 ° the experimental cross section is 25 times larger (for a spectroscopic factor of unity) than the D W B A predicted cross-section, as calculated for a pure (f~)2 configuration. The theoretically predicted /-value mixture for the 1.51 MeV state does not agree well with what is required to fit the data of fig. 8. The angular distribution is fit quite well with a 66 % l = 2 and 34 ~ l = 4 mixture. However, the corresponding theoretical prediction is 90~o l = 2 and 10% l = 4 for a [(f~)2]J= 3 configuration. The theoretical prediction for the 0.62 MeV state is for 82~o l = 0 and 18% l = 2 assuming a [(f~)2 ]J= i configuration. Possibly the disagreement reflects the neglect of finite range effects, non-locality etc., or perhaps it is due to configuration mixing. In any case it is felt that the D W B A curves are a satisfactory representation of the/-dependence of the angular distribution and that they lead to reliable spin assignments. Since the experimental angular distribution for the transition to the 1.88 MeV state of ~2Sc was not complete it has not been reported here. It, however, strongly suggests an l = 0 pattern, hence it is likely that the 1.88 MeV state is the analog of the 0 + 1.84 MeV state in 42Ca. Further high resolution studies will be necessary to establish the properties of higher excited states in 42Sc.

5. The 4°Ca(SHe, py) Results To obtain additional evidence that the 0.62 MeV state of 42Sc excited by the (3He, p) reaction is not identical with the previously reported isomeric state at about the same excitation energy, p - y coincidence spectra from the 4°Ca(3He, p7)42Sc reaction were measured. For 10 MeV incident 3He energy the number of P--7 coincidences are shown in fig. 11 as a function of the particle and gamma-ray energies. The gamma-ray spectrum represents the sum of all g a m m a rays in coincidence with the proton groups of the same figure. Three peaks in the particle spectrum corre-

270

R . W . ZURM/JHLE et al.

sponding to the levels of 42Sc at 0.62, 1.51 and 2.82 MeV, were intense enough to permit an evaluation of the corresponding individual coincident gamma-ray spectra. These spectra are shown in fig. 12. The observation of the ground state transition from the 0.62 MeV state clearly establishes the state as a low-spin state and confirms the 1 + assignment from the DWBA analysis of the (3He, p) reaction angular dis! '5°?A

I

I

/~ \

"6

|

~ I ° *%,q

5up

,,.j

0/ •

20(

I I0

~EI

Detector o1 5 0 * r

I

l

/

I

I

EHen= IOMeV

,*

~

J

I ~

III ~'O0~-TN 1

1

I

--

~*

~

,~

.~, ,,,

20 50 40 Proton Channel Number

-

-

~.'~.j..4~..t

50

[.l

Co,O(HeZp'r )Sc,, I

I[ l[

EHe'= I0 MeV 7" Spectrum

60 I

yes /

'

o

I0

I 20 30 40 Gommo Chonnel Number

50

60

Fig. l 1. Coincident particle and gamma-ray spectra from the b°Ca(SHe, p7)~2Sc reaction at 10 MeV incident 3He energy. The p r o t o n detector angle was 50 ° to the right o f the incident beam direction and the gamma-ray crystal angle was 45 ° to the left. Energy calibration points o f the NaI(T1) detector with various )'-ray sources are indicated in the ),-spectrum.

tribution. The state at 1.51 MeV cascades through the first excited state to the ground state. This limits the spin of the 1.51 MeV state to < 4 and is, therefore, consistent with a 3 + assignment. The 2.82 MeV state cascades preferentially through the 1.51 and 0.62 MeV states as can be seen from its gamma spectrum. Such a decay mode makes the 2.82 MeV state a possible candidate for the analogue state of the 4 + level

4=Sc

271

LEVELS

in 42Ca at 2.75 MeV. The latter state is strongly excited by the 4°Ca(t, p)42Ca reaction ~o). All observed gamma transitions are indicated in fig. 2. ), - Energy (MeV). I I

2 I 4

I Co ~ (He 3, p r ) S c 4=

EHes= IOMeV 2.8 :> MeV State

2(?

B

.J

•

2_, ,.o

i

eL..

•

LtJ

0.62 MeV State

2oi oo 0 _o

1

o°~ ° Oo oo° o o

o o__.2oo~OoooooOo ooooooooo%ooo9oO~oOogoooOo~oo.

I

1

I

I0

20

30

I 40

I

I

50

60

Channel Number

Fig. 12. Gamma-ray spectra observed in coincidence with protons leading to the 0.62, 1.51 and 2.82 MeV states in 42Sc.

The authors wish to thank R. M. Drisko for carrying out the DWBA calculations of the proton angular distributions and R. H. Bassel for the calculation of the optical-model parameters. We are also indebted to R. Middleton for many valuable discussions. References 1) N. Sarma, MIT Progress Report NYO-10063, (May 1, 1963) (unpublished); A Sperduto, private communication 2) R. W. Zurmiihle, C. M. Fou and L. W. Swenson, Bull. Am. Phys. Sac. 9 (1964) 456, 10 (1965) 478 3) D. Cline, I-I. E. Gave and B. Cuje¢, Bull. Am. Phys. Sac. 10 (1965) 25 and private communication 4) J. D. McCullen, B. F. Bayman and L. Zamick, Phys. Rev. 134 (1964) B515 5) J. N. Ginocchio and J. B. French, Phys. Lett. 7 (1963) 137

272 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

R . w . ZURMUHLEet al. J. N. Ginocchio, Nuclear Physics 63 (1965) 449 S. H. Maxman, Rev. Sci. Instr. 35 (1964) 1572 R. W. Zurmilhle, Nucl. Instr. 36 (1965) 168 L. W. Swenson, Nucl. Instr. 31 (1964) 269 R. Middleton and D. J. Pullen, Nuclear Physics 51 (1964) 77; R. Middleton, private communication P. C. Rogers and G. E. Gordon, Phys. Rev. 129 (1963) 2653 B. G. Harvey et al., Proc. Conf. Nuclear Spectroscopy with Direct Reactions, Chicago (March 1964) Argonne National Laboratory Report 6848, p. 182 J. W. Nelson, J. D. Oberholtzer and H. S. Plendl, Nuclear Physics 62 (1965) 434 R. H. Bassel, private communication G. R. Satchler, private communication F. G. Percy, Phys. Rev. 131 (1963) 745 R. M. Drisko and F. Rybicki, Phys. Rev. Lett. 16 (1966) 275 J. R. Rook and D. Mitra, Nuclear Physics 51 (1964) 96