Spectroscopic information on 13,14C, 15N, 17O, 29–31Si, 33S, 28Cl and 111,113,115,117Cd from the (d,p) reaction

Nuclear Physics A510 (1990) 301-321 Nosh-~oliand

SPE~ROSCOPIC INFORMATION ON ‘3v’4C, 15N, “0, 29-3’Si, 33S, 3sCI AND “171’3*1’5**‘7Cd FROM THE (d, p) REACTION S. PlSKOR and W. SCHAFERLINGOVA Nuclear

Physics Institute, 250 68 gef,

Czechoslovakia

Received 31 March 1989 (Revised 30 October 1989) Abstract: The accurate and precise (d, pf reaction Q-values and excitation energies corresponding to 98 states of final nuclei ‘3%, “N, r70v z9-3’Si, 33S -‘%I and it’*“3~1’S*“7Cdare presented as a result of high resolution experiments performed with 12.3 MeV deuterons. The protons were analysed by multi-angle magnetic spectrograph. The resolving power E/AE of about 2000 and accurate calibration of spectra allowed to get the energies of most states with higher precision than is presently known. Angular distributions of protons from the reaction 37Cl(d, ~)~sCl were analysed using DWBA calculations. Revised values of transferred orbitai angular momenta and spectroscopic factors for 25 states of 38C1are given. Single-panicle strengths for If and 2p orbitals are compared with respective single-particle strengths from the reaction 36S(d,p)3’S, Sum rules indicate that substantial parts of ff and 2p single-particle strengths are exhausted by states observed in present experiment.

E

1, Introduction For many years, nuclear reactions have been used as an effective and powerful tool in studying properties and fundamental characteristics of nuclei. The ground-state transition Q-values relate directly the rest masses of nuclides in entrance and exit channels. The nu&dic masses are periodically readjusted ‘) in a coherent manner using results of all the recent accurate and precise measurements and there is an urgent need of collecting such data. The well-known fact that different nuclear reactions are quite selective with respect to the structure or character of nuclear states is widely used in revealing the nature of the states. Nevertheless, in performing comparison to what degree the state is populated in different reactions, we must be sure that we are dealing with the same state. Unfortunately, not many of the presently gathered reaction data possess the necessary accuracy and precision. More high resolution, high accuracy and high precision measurements are very much required. 0375~9474/90/$03.50 @ Elsevier Science Publishers B.V. (North-Holland)

3. Piskoi,

302

W. Schliferlingovd

/ Spectroscopic

information

most recent precise data on excitation energies of nuclei and on their neutron binding energies are derived from (n, y) experiments, though, as was pointed out earlier ‘), difficulties with interpretation of gamma transitions might occur in nuclei with complex level schemes, e.g. in the case of odd-odd nuclei, when several hundreds of transitions are observed. The binary reactions with light particles which left the final nucleus in a definite bound or unbound state if studied with high resolution are usually unambiguously interpreted, i.e. that each spectral line corresponds to a definite state of the final nucleus. Employing as calibration standards the accurate and precise excitation energies derived mainly from (n, r) experiments, the high resolution of the present experiment gives us scope to perform the desired high-accuracy and high-precision energy determinations. The achieved precision is quite comparable with (n, y) results, which is important especially for states which are not populated in (n, y) reactions. This paper follows up logically our recent results concerning 35Cl(d, P)~~CI reaction *) and 34,36S(d,p)35*37 S reactions 3, with accurate and precise ground-state transition Q-values for the reactions 12z’3C(d,p)13*r4C, 14N(d, p)“N, 160(d, p)r70, Z8_3OSi(d, p)“9-3’Si, p) 111,1’3,115,117Cdl with the 37Cl(d, p)38Cl and ~1~,~~2,~~4,116~d(d, excitation energies of states populated through (d, p) reaction in 13,r4C 15N 170, 29-31Si33S,and 38Cl nuclei, and with revised l-value assignments and sp&rosLopic factors for the reaction 37Cl(d, P)~~C~. Previously, the bulk of spectroscopic info~ation on the nucleus 38Cl had been obtained by means of the 37Cl(d, P)~‘C~ reaction by Rapaport and Buechner 4, at 7 MeV incident energy, and by Fink and Schiffer ‘) at 12 MeV deuteron energy, by Spits and Akkermans 6, using the 37Cl(n, Y)~*CI reaction, and by means of some other reactions, as reviewed in the article by Endt and Van der Leun ‘). We have found a lack of agreement between the results given in ref. “) and those in ref. ‘) and some hidden discrepancy between the experimental data and deduced quantities in ref. “). Though the cross sections for different states of 38C1given by Rapaport and Buechner can be we11reproduced by the DWBA calculations employing their optical-model parameters and their derived spectroscopic strengths, it is not the case with ref. ‘). For this reason the repeated measurement of the 37Cl(d, P)~‘C~ reaction seems worthwhile. The

2. Experimental procures 2.1. EXPERIMENTAL

SET-UP

aad methods of data analysis

AND DATA ACQUISITION

The experiments were performed with the 12.3 MeV momentum-separated beam of deuterons from the cyclotron U120 of the Nuclear Physics Institute of the Czechoslovak Academy of Sciences at Rei. Protons from the (d, p) reaction were

3. Piskoi, W. Schiiferlingova’/ Spectroscopic information

303

analysed by a multi-angle magnetic spectrograph “) giving in a single run eleven spectra in the range from 0” to 90” reaction angle, and registered by 700 mm long nuclear emulsion plates Ilford L4 located in the focal planes of the spectrograph channels and covered by the Teflon-coated aluminium absorbers to remove the heavier products of competing reactions. The plates were scanned with the automatic plate scanner ‘). The computer code I*) was used to decompose the spectra in an interactive mode, part-by-part, determining the peak positions, peak areas and corresponding error estimates. Two natural chlorine targets of approximately 50 Fg/cm2 thickness were made by evaporation of CdCl, on 10 pg/cm’ carbon backings. Targets were made from compounds of different origin and contained therefore different amounts of admixtures. Silicon target of about 100 @g/cm2 thickness was made by evaporation of silicon oxide on 10 &g/cm2 carbon backing. With each of the CdC& targets were made two 1500 uC exposures having different orientations of the spectrograph with respect to the beam direction. The overall resolving power E/AE achieved with these targets amounts to about 2000. A portion of the proton spectrum is shown for illustration in fig. 1. One run was made with the silicon target as we have expected non-negligible build-up of silicon on the target during the experiment due to the silicone oil used in our diffusion pumps. The resolving power achieved in this case was about 1500. Elastically scattered deuterons were measured with the same experimental set-up at C)lab = 10” and 0 lab= 20” reaction angles. 2.2. IDENTIFICATION.

CALIBRATION

AND

ENERGY

EVALUATION

Data processing procedures concerning experimental spectra, i.e. identification of spectral lines, calibration, Q and excitation-energy evaluation and subsequent data reduction are described in full elsewhere *I); only a brief synopsis will be given here. To prepare the desirable set of data for calibration we used the procedure as follows: (i) A few unambiguously identified spectral lines corresponding to the studied nucleus and to some well-known impurities, and to which fairly well-known Q-values can be ascribed, are used in calibration of the spectra. {ii) On the basis of the calibration more spectral lines with known Q-values are identified and together with the previous ones used in a new calibration run until the final calibration set is acquired. By identification it is understood that to a particular spectral line a particular target nucleus is ascribed. The spectral lines were identified by their kinematical shifts with the reaction angle and by the visual examination of intensity relations between the same lines in spectra taken at the same reaction angle but with targets containing different amounts of constituents. The calibration points having the

304

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NSL

8O’ZbPi Pd“s*dl

13 9E 13 SE 138E

1396

!36t

3. Pisko?, W Schiiferlingova’ / Spectroscopic information

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LL’EESE 3

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l, -

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139F

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139f SfF

EI’OILS OL’fSZf

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3. Pisko?, W. Schiiferlingovb

306

greatest

weights

it was possible,

in the calibration

/ Spectroscopic

information

set were cross-checked

as many as 80 calibration

with extreme

points were used to calibrate

care. When

each individual

spectrum. The (d, p) reaction

Q-values

used for calibration

were derived

from the following

sources: (i) The neutron

binding

energies

for all nuclei

in question

from ref. ‘).

(ii) The excitation energies of 13*14Cand “N from ref. 12), of “0 from ref. r3), of 29*30Sifrom refs. ‘,I4 ), of 31Si and 38C1 from ref. ‘), and of 36C1, using the averaged values from refs. r5-“). Calibration procedure ‘l) resulted in sets of calibration parameters and correlation matrices for each individual spectrum. These allowed us to calculate Q-value and random error estimates Q-values and their error Appropriate statistical the presence of possible

2.3. ABSOLUTE MODEL

for each identified spectral line and to use the particular estimates from different spectra in further averaging. tests ‘l) were applied to residuals with the aim to estimate systematic errors in our energy determinations.

DIFFERENTIAL

CROSS

SECTIONS

AND

OPTICAL

PARAMETERS

We used chlorine targets of natural abundance, i.e. containing 75.77% of 35C1 and 24.23% of 37C1. The target thicknesses and therefore the absolute cross sections were calibrated at &,. = 21” by putting the ratio of the deuteron elastic scattering cross is believed section to the Rutherford one, i.e. a/a R, equal to 0.78. Such normalization to be accurate within about 10%. The parameters of optical potentials which the elastic scattering of particles in entrance

are expected to describe reasonably and exit channels are presented in

table 1.

2.4. DWBA

ANALYSIS

We performed standard one-step neutron transfer DWBA calculations by means of the code DWUCK 2’) to obtain I-assignments and to deduce spectroscopic factors for the states of 38C1 populated in the (d, p) reaction. The distorted waves were generated by the optical-model potentials with parameters given in table 1. The potential binding a neutron to the core was assumed to be of Woods-Saxon shape with the commonly accepted geometrical parameters: R = 1.25A1’3 fm, a = 0.65 fm. The usual factor A = 25 was used in the spin-orbit term having the same geometry. The depth of the central part of the potential, V,, was adjusted to obtain the appropriate neutron binding energy. The finite-range and non-locality corrections were included in the calculations. The finite-range parameter was taken to be equal

3. Piskoi, W. Schtiferlingova’ / Spectroscopic information

307

TABLE 1 Optical

potential

parameters

deu terons “) :

106.03 protons y: 53.38

0.855

“) Parameters ref. 19), i.e.

derived

11.24

7.43

0.842

0.633

0.583

1.051

1.548

0.894

9.02

6.20

0.750

0.584

0.750

1.170

1.320

1.010

from those

given by Abegg

and Datta

I’), set 1, employing

the formulae

of

V, = V,+0.25(E,-E,)-2.3(Z,/A;‘3-Z,/A;’3), r,, = r,,,q

0.9(A,“3

- A;“‘),

= ~,,-0.082(A;‘~

- A;“).

The subscript 0 refers to the parameters given by Abegg and Datta, whereas the subscript 1 refers to those corrected. Non-local correction factor p = 0.54; r, = 1.3 fm. b, Systematics by Becchetti and Greenlees ‘O). Non-local correction factor p = 0.85; r, = 1.3 fm.

to 0.621. The non-locality

correction

factors

for the deuteron

and proton

optical

potentials were taken to be 0.54 and 0.85, respectively. The spectroscopic factors S, normalizing the calculated transfer cross sections were determined by least square fitting of the theoretical cross sections to the experimental ones in the vicinity of the main maxima, where the cross section is presumably dominated by the direct transfer process. With this purpose the following formula relating the experimental and theoretical cross sections was employed:

[_-I da

dR

Here

Ji and

respectively,

Jr are the total

j (or 1) stands

angular

momenta

for the total (or orbital)

of the initial angular

and

momentum

final

states,

transferred

by the neutron, S, are spectroscopic factors (fitting parameters), and cti( 0) are the cross sections calculated by DWUCK. Because of non-zero spin of the target nucleus (J: = i’), different orbitals allowed by angular momentum coupling rules can contribute. Shapes of angular distributions in single-nucleon transfers are practically dependent on the l-value only, therefore experimentally no distinction can be made between transfers with different spin orientations. For that reason in our calculations only the most probable final single-neutron states were considered, i.e. the 2p,,,, Id,,, and If,,, states for I= 1, I= 2 and 1= 3 transfers, respectively, and therefore only the corresponding spectroscopic factors are given. Experimental angular distributions (dots) fitted with DWBA curves are presented in fig. 2. Indicated errors of the individual points include the statistical uncertainty

3. Pi&i,

308

W. Schiiferlingova’ / Speciroscopic information

~~,~~~~

20

QO

60

0

20

:I,_, ,Yo.I 20 d

0

40

60

0

20

80

40

.\d”t

20

40

60

0

20

00

60

0

20

20

r10

60

0

20

a0

60

0

20

r10

60

0

20

40

60

0

,Y,,j , .A i

20

40

30

60

0

20

40

60

0

20

60

0

20

40

60

0

20

60

.u 60

60 30 Oc.n.[d.gI

reaction at E,, = 12.3 MeV. The curves Fig. 2. Angular distribution of protons from the 37Cl(d, p)%I are the results of DWBA analysis with finite-range and non-locality corrections included.

as well as some estimated background subtraction.

non-statistical

contributions

due to inaccuracies

in the

3. Results and discussion 3.1. GROUND-STATE

TRANSITION

Q-VALUES

Table 2 summarizes the ground-state transition Q-values as determined from the present experiment in comparison with values derived from the recent atomic masses

3. Piskof, W. Sch-f a er I’mgova’ / Spectroscopic information

309

TABLET The ground-state

transition

Q-values

Q (kev) Reaction present “C(d, %(d, 14N(d, 160(d, %(d, %i(d, %i(d, “Cl(d, ““Cd(d, “‘Cd(d, ‘%d(d, ‘%d(d,

p)“C p)% p) “N p)“O p)%i p)%Si p)3’Si P)~*CI p)“‘Cd p)‘13Cd p)“‘Cd p)“‘Cd

“)

2721.803 * 0.038 595 1.85 + 0.20 8608.828 *0.061 b, 1918.737 kO.062 ‘) 6249.350 * 0.037 8384.92+0.16 b, 4364.18 * 0.23 d, 3883.282 * 0.064 ‘) 4750.68 f 0.73 4315.56*0.40 3916.30* 0.32 3552.66 * 0.85

Wapstra

and Audi ‘)

2721.770~0.014 5951.91*0.02 8608.73 * 0.02 1919.0*0.4 6249.366 * 0.012 8384.96 f 0.03 4363.8*0.3 3883.28 * 0.10 4750.63 f 2.4 4315.7*0.5 ‘) 3916.3 *0.5 ‘) 3543.0* 13

“) Quoted errors are purely statistical ones. True estimation of possible systematic uncertainties can be made on the basis of the external consistency only. For more discussion of this question see text, especially the end of the subsect. 3.1. b, Weighted average of values derived from present excited-state transition Q-values and corresponding excitation energies from (n, y) experiment 14). ‘) Value 1918.878*0.303 keV can be derived from ref. *a). d, Weighted average of values derived from present excited-state transition Q-values and excitation energies from ref. ‘). ‘) Weighted average of present directly measured ground-state transition Q-values and those derived from present excited-state transition Q-values and excitation energies from ref. ‘). ‘) Based on our preliminary results.

evaluated by Wapstra and Audi I). The first eight items in second column of table 2 are in fact the readjusted values of those in the third column which were used in deriving the calibration set. For some considered reactions corresponding to the ground-state

we were not able to measure the proton transitions. In these cases the ground-state

groups transi-

tion Q-values were derived employing the measured excited-state transition Q-values and the corresponding current best values of excitation energies. All such cases in table 2 are commented in footnotes below the table. The direct measurement of the ground-state transition Q-value for the reaction 37Cl(d, P)~‘CI was possible only at the reaction angles beyond about 40” as the proton group from the reaction 35Cl(d, ~)~‘%l corresponding to 2468 keV excitation in 36C1 interfered at forward angles. The ground-state transition Q-value for this reaction given in table 2 is the average of our directly measured Q0 values and those derived from our Q-values to excited states and corresponding excitation energies from the literature ‘).

3, Piskof,

310

The proton

groups

related

set, as the corresponding tion Q-values

relating

around

to cadmium

isotopes

data lack the necessary these nuclei

tions in the framework which

W. Schiiferlingova’ / Spectroscopic

information

were not used in our calibration precision.

The ground-state

(the last four items in table 2) are our determina-

of the used calibration

sets consisting

40% were states of 36C1 with well-established

of about 6.5 MeV. The high precision

attained

transi-

in some cases is a result

of up to 80 items of Q-values

in the range

of inclusion

in the final

averaging of more than forty determinations of a particular Q-value from accurately calibrated spectra obtained with different targets and at different reaction angles. With the intention to estimate the presence of some systematic errors connected with our energy measurements the residuals corresponding to calibration Q-values were carefully analysed. From the analysis follows: (i) For all calibrated spectra, irrespective of target or reaction angle, the residuals corresponding to a particular nucleus fluctuate within the random errors (the reduced chi-square not exceeding 1) around the mean of residuals related with the respective ground-state transition Q-value. (ii) All residuals as a function of the coordinate (along the spectra) fluctuate randomly around zero. This indicates that the systematic

errors

due to the “sandwich

structure”

of the

target or due to improper parametrization of the calibration curve have rather low probabilities to be present in our energy determinations. The final averaging of all measurements with different targets and at different reaction angles further reduces the systematic errors of this type. In spite of this we must have in mind that the systematic errors never could be found or fully excluded by checking on internal consistency

only. The check on an external

consistency

is always necessary

for this

purpose.

3.2. EXCITED-STATE

The reaction

TRANSITION

energies,

Q-VALUES

excitation

energies

AND EXCITATION

and corresponding

ENERGIES

error estimates

as

resulting from the present experiment, together with the adopted up-to-date values for excitation energies are displayed in tables 3-8. In deriving the excitation energies the ground-state transition Q-values were taken from the present experiment or from ref. I), whichever was quoted with higher precision. 13C nucleus, with the exception of the The ‘-‘C nucleus. Our data concerning fourth excited state at 6864.07 keV excitation, have relatively lower precision in comparison with the most recent best values adopted in ref. 12), and are therefore bringing little new information. They are presented in table 3 mainly to demonstrate the reliability of the method as the comparison exhibits very good compatibility indeed. The third excited state of 13C is the one most strongly populated in the (d, p) reaction. Due to this fact we were not able to hold properly the corresponding

3. Piskoi, W. Schiiferlingovi / Spectroscopic information

311

TABLE 3 Energy levels of 13C and (d, p) reaction

Q-values

“)

E, WV

Q OW present

Ajzenberg-Selove

present ‘)

-367.65

f 0.07

3089.42*0.07

3089.443 + 0.020

-962.73

* 0.06

3684.50 * 0.06

3684.507 + 0.019

-1131.90*0.20

3853.67 + 0.20

3853.807 f 0.019

-4142.30

6864.07 * 0.46

6864+ 3

* 0.46

“) See comment

“) below

b, Q0 = 2721.770*

“)

table 2.

0.014 keV [ref. ‘)I.

extremely intense spectral line in spectra taken at forward angles where tion is more precise. This circumstance results in relatively low precision in low accuracy of the Q-value and excitation energy for this state. The 14C nucleus. The 14C nucleus has been studied in many ways in averaged results presented in the compilation in ref. I’) are displayed well as the data derived from this experiment. Except for the second at 6589.58 keV, which is weakly

populated

in the (d, p) reaction,

the calibraand, maybe, the past and in table 4 as excited state

our data are more

precise. For all but one state the consistency of both sets is very good. For the third excited state we have found the excitation energy 673 1.58 f 0.11 keV, which is significantly different from the value adopted in ref. I*), but compatible with 6733 f 4 keV from ref. 23). The energy difference between the third and the fourth excited states from our measurements is 170.66kO.21 keV, in good agreement with 171*3 keV from ref. 24). The excitation energy of the third excited state of 14C adopted in ref. 12) is based on the value 6728.1 f 1.4 keV given by Throop 25) who measured the ground-state TABLE 4 Energy

levels of 14C and (d, p) reaction

Q &eV)

Q-values

“)

E, GeV)

present

present b,

Ajzenberg-Selove

-142.14+0.11

6094.05 + 0.11

-637.67

6589.58 f 0.39

6589.4 + 0.2

-779.67+0.11

6731.58*0.11

6728.2 f 1.3

-950.33

6902.24*0.18

6902.6 zt 0.2

7011.4+0.8

7012.0 f 4.2

* 0.39 *0.18

-1059.5*0.8 -1390.74*0.32 “) See comment

7342.65 * 0.32 “) below

table 2.

b, Q,, = 5951.91 kO.02 keV [ref. ‘)I.

6093.8 f 0.2

7341.4*3.1

‘*)

3. Pisko?, W. Schiiferlingova’ / Spectroscopic information

312

transition

gamma

inspection

of the paper

from

peaks corresponding the double

escape

this

state

populated

in the

reaction

we can see that in the given spectra

to ground-state peaks

transition

corresponding

6443.7 f 1.8 keV in i4N have reasonably

9Be(7Li, d)14C. By

only the double-escape

from the state in question

to ground-state good statistics.

transition

in i4C and

from the state

A more accurate

recent value

of excitation energy of the state in 14N nucleus adopted by Ajzenberg-Selove ‘*) is 6446.17 f 0.10 keV, i.e. almost 2.5 keV higher than the value obtained by Throop. It is therefore not surprising that in the case of the 14C nucleus the true excitation energy of the state is significantly higher than the value given by this author. 7’he “N nucleus. In table 5 are listed Q-values and excitation energies for ten states of i5N, derived from the present (d, p) experiment, together with the earlier results as presented in the compilation by Ajzenberg-Selove 12). In evaluation of the excitation energies the ground-state transition Q-value 8608.73 f 0.02 keV [ref. ‘)I was used. Our (d, p) data agree well with those obtained in (n, y) experiments, i.e. the first through fourth and the sixth items in the third column of table 5. The state at 11235.5bO.5 keV excitation is nucleon unstable. The remaining four states are not populated in the thermal neutron capture. In two cases we found excitation energies significantly different from those in ref. ‘*). In the first case (the fifth item in table 5) we found 7563.25+0.19 keV excitation energy, which is almost 4 keV lower than the value adopted by AjzenbergSelove ‘*), but in agreement with the earlier value 7563.0* 1.8 keV given in ref. 26).

TABLE

Energy

present 3338.5 + 1.3 2284.7 f 1.0 1453.88kO.17 1307.93 f 0.09 1045.48*0.19 295.94kO.12 37.20* 0.25 -441.51* 0.33 -1455.61+0.31 -2626.8 f 0.5

5

levels of 15N and (d, p) reaction

present

b,

5270.2 f 1.3 6324.0 f 1.O 7154.85kO.17 7300.80 f 0.09 7563.25 f 0.19 8312.79kO.12 8571.53*0.25 9050.24 * 0.33 10064.34 * 0.31 11235.5*0.5

Q-values

“)

Ajzenberg-Selove

12)

5270.15 f 0.02 6323.89 f 0.02 7155.11*0.02 7300.86 * 0.02 7567.1~ 1.0 8312.6OiO.02 8571.4+ 1.0 9050.0 * 0.7 10070*3 ‘) 11235*5

“) See comment “) below table 2. b, Q,=8608.73+0.02 keV [ref. I)]. From the present Q-values and excitation energies from (n, y) [ref. “‘)I the derived Q0 is 8608.83 f 0.06 keV, being in satisfactory agreement with the value of ref. ‘). ‘) The excitation energy 10064* 1 keV was observed in the reaction ‘sN( ‘y, y’)15N [ref. “)I for this state (not included in the averaging in ref. “)).

3. Piskoi,

For the second

state in question

0.31 keV, differing value 10064* account

W. Schiiferlingova’ / Spectroscopic

by almost

(the ninth

313

item in table 5) our result is 10064.34*

6 keV from the value in ref. ‘*), but supported

1 keV from the 15N( -y, y’)“N

in ref. 12). Generally

information

speaking,

experiment

the results of (7, 7’) measurement

with ours but are less precise. The “0 nucleus. In table 6 are presented

by the

27), which was not taken into

(d, p) reaction

Q-values

agree well

and excitation

energies for ten levels of I70 nucleus, as derived from the present experiment, together with excitation energies from compilation by Ajzenberg-Selove 13). The first three are the bound states, the other seven are nucleon unstable. Both sets of data are quite compatible with each other, but with the exception of the second excited state we attained higher precision. The 29Si nucleus. The set of eighteen levels of 29Si nucleus for which we present Q-values and excitation energies in table 7 exhibits good compatibility with the excitation energies obtained by averaging of those from some earlier experiments ‘) and with values of excitation energies of few states measured in (n, y) [ref. ‘“)I. As a whc’e the excitation energies derived from the present experiment for states which are nit populated in (n, y) are much more precise than the earlier ones. We point out one level for which we found the excitation energy significantly different from the value presently adopted, namely, we have 6194.14*0.12 keV, which is 2.74 keV higher and almost one order more precise than the value in ref. ‘). The 3or3’Si nuclei. In our experiment we observed only few most strongly populated states of these nuclei. We included them in table 7 mainly for completeness as they do not reveal significantly higher precision nor higher accuracy in comparison with data from the literature 7z14). Nevertheless, they may be of interest as more or less independent measurements. TABLE 6 Energy

levels of “0

and (d, p) reaction

Q (kev)

Q-values

“)

E, (kev)

present

present b,

1048.01 ztO.08

870.73 20.10

Ajzenberg-Selove 870.81 k-o.12

-1136.24*0.19

3054.98 * 0.20

- 1924.02 f 0.42

3842.76 * 0.42

3841+ 3

-2635.1~~~ 1.6

4553.8 f 1.6

4552 * 2

5084.8 f 0.9

5085*2

-3166.1 -3297.03 -3460.5

iO.9 f 0.45

3055.3650.16

5215.77ztO.45

5218

f 1.4

5379.2 f 1.4

-3778.52

* 0.33

5697.26 * 0.33

5697 * 2

-3814.05

* 0.52

5732.79 * 0.52

5733 f 2

-3950.33

* 0.55

5869.07 f 0.55

5868 * 2

“) See comment

“) below

b, Q0 = 1918.737*0.062

5378*2

table 2. keV from the present

work was used.

13)

314

L? Piskoi,

W. Schii,ferlingovd

/ Spectroscopic

information

TABLE 7 Energy levels of 29-3’Si and (d, p) reaction Q-values “)

Q WV) present

E, (kev) present b,

ref. ‘)

(n, Y), ref. “?

1273.31 *to.17 2028.72 f 0.25 3066.94 f 0.50 3624.15*0.15 4840.15kO.45 4934.601~1~ 0.62 5949.14*0.22 6194.14*0.12 6380.820 f 0.061 6496.23 f 0.21 6695.93 * 0.14 6713.0* 1.5 6781.13kO.65 6907.09 * 0.29 7057.81*0.17 7181.77*0.21 7622.05 * 0.78 7691.98 *0.37

1273.3+0.1 2028.2 f 0.3 3067.1*0.3 3623.5+0.5 4839.9 f 0.5 4933.6*0.5 5949.0 f 0.7 6191.4+ 1.1 6380.7 f 0.4 6496.7 f 0.6 6694 f 4 6711*2 6781.4kO.7 6908.1 f 0.7 7057.8 f 0.5 7182*4 7622 * 1 7692 + 4

1273.414*0.014

3oSi nucleus 1640.25 * 0.59 876.91+0.16 -924.14*0.89

6744.7 1 * 0.60 7508.05*0.17 9309.10*0.89

6744.1 zt 0.4 7507.8 * 0.5 9308.3 * 0.6

3’Si nucleus 3611.3* 1.2 830.41 kO.16 -917.1 zto.5

752.9 f- 1.2 3533.77 f 0.28 5281.3*0.6

752.43 f 0.10 3533.7 * 0.2 5282.0 zt 0.4

29Si nucleus 4976.06* 0.17 4220.65 + 0.25 3182.43 ;t 0.50 2625.22kO.15 1409.22 * 0.45 1314.765 * 0.061 300.23 ;t 0.22 55.23kO.12 -131.454*0.060 -246.86 * 0.21 -446.56*0.14 -463.6* 1.5 -531.76kO.65 -657.72 f 0.29 -808.44*0.17 -932.40 f 0.21 -1372.68kO.78 -1442.61 *to.37

4934.563 f 0.013

6380.836 f 0.013

6744.3 19 f 0.059 7508.041* 0.045

“) See comment “) below table 2. “) Q0 values equal to 6249.366 +0.012 keV and 8384.96*0.03 keV from ref. ‘) were used for nuclei 29Si and %, respectively, and the present value 4364.18 f 0.23 keV for the “Si nucleus.

The 33Snucleus. A small admixture of sulphur in our targets allowed us to measure Q-values 3196.60 f 0.17 keV and 706.99 f 0.20 keV, corresponding to two of the most the groundstrongly populated I = 1 states in the reaction 32S(d, P)~~S. Employing state transition Q-value 6417.13 kO.10 keV by Wapstra and Audi ‘) we obtained excitation energies 3220.53 kO.20 keV and 5710.13 f 0.23 keV for these states, respectively. Before comparing these values with the results of the recent (n, y) measurements by Raman et al. 2”) and by Kennett et al. 2g), we shall compare first these two (n, y) sets with each other. Although in both papers very precise excitation and neutron binding energies in 33S are given, the compatibility of these two sets of data is not good. Energies given by Kennett et al. are systematically about 30 ppm smaller than those by Raman et

3. Pi&o?, W. SchCferlingova’/ Speciroscopic information

315

This difference is much beyond the precision given in these two papers and consequently very large consistency factors (square roots of the reduced chi-squares) should be introduced to restore true error estimates. With the aim of comparing our energy evaluations for the mentioned states with those from (n, y) we give here mean values of their excitation energies and the neutron capture state energy, as derived from refs. 28,29), namely, 3220.728* 0.036 keV, 5711.007 f 0.094 keV and 8641.796 f 0.151 keV, where in deriving the true error estimates the consistency factors 2.27, 6.09 and 8.25, respectively, were necessary to be used. The ground-state transition Q0 value 6417.5OkO.29 keV, deduced from these excitation energies and from our corresponding Q-values speaks in favour of neutron binding energy by Raman et al. *‘). The 38Cl nucleus. The (d, p) reaction Q-values and excitation energies of the present experiment are displayed in table 8 together with the excitation energies adopted by Endt and Van der Leun ‘) including also the (n, y) results “). The states are numbered according to ref. “)_ Both sets of excitation energies are quite compatible but the precision in most of our energy determinations, especially for excitations above 3 MeV is much higher. It concerns especially the states which are not populated in the (n, y) reaction (they are identified in the third column of table 8 by the 5 keV error). The excitation energy 3893.39rtO.11 keV, found by us for the state with number 22, differs significantly from the value 3892.3 i 0.3 keV adopted by Endt and Van der Leun (probably erroneously quoted value 3893.2zizO.3keV given by Spits and Akkermans “) from (n, r) experiment). Contrary to the supposition by Endt and Van der Leun the states with numbers 26 and 29 do not correspond to those with excitation energies 4073.2* 0.3 keV and 4405.5 f 1.5 keV observed in (n, y) experiment “>. We obtain for them the excitation energies 4062,98*0.39 keV and 4412.0 f 1.4 keV, respectively. al.

3.3. THE SPECTROSCOPIC STATES

STRENGTHS

AND

ASSIGNED

&VALUES

FOR

OF “Cl

Results of the present DWBA analysis of proton angular distributions from the 37C(1 d f P)~*C~ reaction for 25 states of the 38Cl nucleus below 4.9 MeV excitation are displayed in table 9 together with analogical results quoted from previous papers by Rapaport and Buechner “) and by Fink and Schiffer ‘). States are numbered in the first column in accordance with ref. “). The excitation energies and the absolute differential cross sections at maxima of angular distributions as derived from the present experiment are listed in the second and fourth column of the table, respectively. An inspection of fig. 2 shows that experimental angular dist~butions are quite satisfactorily described by the DWBA calculations and our I-assignments confirm the previous ones 4*5) given in the third column of table 9. The corresponding spectroscopic strengths as evaluated from the present experiment, and

316

3. Piskoi,

W. Schiiferlingovd TABLE

/ Spectroscopic

information

8

Energy levels of 3sCl and (d, p) reaction Q-values “)

Q WV)

E, WV)

N present

present bf

Endt and Van der Leun ‘)

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

3212.39*0.23 3127.83 rt 0.27 2574.39 * 0.6 2265.97 f 0.08 2191.20k0.14 2137.52rtO.17 2098.3 f 1.6 1902.23 i 0.06 1430.8* 1.6 1140.45*0.17 988.5kO.7 930.7 rt 1.6 629.18k0.38 589.75 f 0.28 479.64 f 0.28 345.7 + 0.9 317.6ztO.7 197.89 * 0.30 127.5 * 0.8 61.7110.16 21.3* 1.6 -10.11*0.09 -53.OkO.6 -90.82kO.18 -127.31 kO.23 -179.7OztO.38

670.89 i 0.24 755.4s * 0.28 1309.0 * 0.6 1617.31 *O.lO 1692.08iO.15 1745.76*0.18 1785.0~ 1.6 1981.05 iO.09 2452.5 i 1.6 2742.83 * 0.18 2894.8 f 0.7 2952.6* 1.6 3254.10 * 0.39 3293.53 zt 0.29 3403.64~1~0.29 3537.6rt0.9 3565.7 it 0.7 3685.39 f 0.31 3755.8 10.8 3821.57rt0.17 3862.0 i 1.6 3893.39i0.11 3936.3 i 0.6 3974.10rto.19 4010.59* 0.24 4062.98 f 0.39

671.28*0.10 755.27 * 0.07 1308.83 kO.10 1617.18*0.10 1692.28*0.11 174S.52rtO.14 1784.81 iO.17 1981.02~0.10 2453 f 5 2742.92k0.17 2895.0 f 0.5 2948 f 5 32.50*5 3291*5 3401* 5 3538.4 i 0.7 3564.3 f 0.5 3684.9 i 0.4 3756.3 f 0.4 3822.1 kO.3 3862.4 f 0.5 3892.3 I+= 0.3 ‘) 3936i5 3974.3 * 0.3 4011.3 f 0.3

27 28

-403.20*0.40 -465.7* 1.6

4286.48 i 0.41 4349.0 f 1.6

29 30 31 32

-528.7 k 1.6 -622.7 f 1.6 -929.2 zk1.6 -951.2rt0.5

4412.0* 4506.0* 4812Srt 4834.5 f

1.6 1.6 1.6 0.5

4073.2 f 0.3 4287.410.4 4347 f 5 4405.5 11.2 4505 * 5 4812*5 4834.6 f 0.4

“) See comment “) befow table 2. b, Q0 = 3883.282 f 0.064 keV from the present experiment was used. ‘) Value 3893.2 rtO.3 keV was given in ref. 6).

those from ref. 4), and from ref. 5, are given in the fifth, sixth and seventh columns, respectively. In the last column of the table are given full angular momenta and parities of the states as adopted by Endt and Van der Leun ‘). In our experiment we exposed the natural Cl targets containing appreciable amount of contaminations. Thanks to the high resolution we did not have di~culties with most of the states, but we met problems with some of them. As was mentioned

317

3. PiskoF, W. Schiiferlingova’ / Spectroscopic information TABLE

9

Values of (2/t+ l)S, for the reaction “Cl(d,

N

(ii)

0

0

1 2 3 4 5 6 7 8 10 11 13 14 15 18 19 20 21 22 23 24 25 26 27 32

670.89 755.45 1309.0 1617.31 1692.08 1745.76 1785.0 1981.05 2742.83 2894.8 3254.10 3293.53 3403.64 3685.39 3755.8 3821.57 3862.0 3893.39 3936.3 3974.10 4010.59 4062.98 4286.48 4834.5

I

193 3 193 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

(d~ldfl)Z W/sd -1.1 2.80 3.69 -2.4 11.53 10.19 4.52 -0.4 14.35 12.51 1.92 2.08 3.22 2.45 4.38 2.01 5.39 1.65 14.06 1.77 7.49 3.99 2.77 2.71 3.22

~)~sCl

(24+ l)S, present

ref. 4,

ref. 5,

-, 4.92 “) 10.51 0.90,4.59 8.09 “) 2.84 2.48 1.09 1.21 “) 3.37 2.57 0.37 0.39 0.59 0.44 0.73 0.33 0.88 0.29 “) 2.27 0.29 1.16 0.63 0.43 0.41 0.45 “)

-, 4.24 8.56 0.64,4.12 6.28 2.80 2.44 1.08 0.72 3.52 2.56 0.04 b) 0.28 0.56 0.48 0.68 0.32 1.oo 0.28 2.32 0.24 1.16 0.72 0.48 0.48 0.40

0.12,3.60 7.5 0.56,3.80 5.9 2.0 1.8 0.89 0.94 2.4 1.9 0.33 0.28 0.42 0.35 0.51 0.24 0.65 0.22 1.7 0.16 0.77 0.5 1 0.36 0.30 0.31

25343(1-3)_ (091)) (2-4)) (293)) 3(0-3)_ (O-3) (O-3)_ (O-3)_ (O-3)) (O-3) (l-3)_ (l-3)_ (l-3)) (O-3)_ (O-3) (O-3)) (O-3)_ (O-3)_ (O-3)_

“) Not illustrated in fig. 2; see text. ‘) According to given cross section should be 0.40.

already,

the ground-state

transition

proton

group

was obscured

at forward

angles

by strong proton group corresponding to 36C1. We were able to estimate the I= 3 spectroscopic strength by fitting DWBA curve to few points beyond the main maximum but we could tell nothing about I= 1 component of this state. Analogical situation was with the third excited state where in the main maximum of the angular distribution interfered proton groups originating from carbon and silicon, and with few relatively weakly populated states for which we also found the spectroscopic strengths by fitting DWBA curves to only a few points. All such cases in table 9 are marked by the footnote sign and commented below the table, and are not illustrated in fig. 2. We admit these spectroscopic strengths to be less accurate than the rest; nevertheless they are sufficiently reliable. We also were not able to make definite conclusions about two weakly populated states at 2452.5 and 2952.6 keV excitations presumably corresponding to sd-shell neutron transfers 4,5). Our measurements of

318

respective

3. Piskoi,

proton

groups

W. Schiiferiingovri

ments in both cases, though group originating

in refs. “*“)) interfered energies

information

at angles very near to 0” seem to exclude do not exclude

state given by Fink and Schiffer. the proton

/ Spectroscopic

beyond

the I= 2 assignment

The difficulty

from oxygen about

for the 2452.5 keV

with the 2952.6 keV state was that

(also present

10”. As concerns

3537.6 and 3565.7 keV populated

the 1= 0 assign-

as impurity

in spectra

in ref. “) via the I= 1 transfers

ascribed to the second state in ref. “)) we confirmed for them rather low cross sections.

given

the two states with excitation the I = 1 assignments

(I = 2 was but found

It can be seen from table 9 that the spectroscopic strengths for I = 1 neutron transfers as were determined from the present experiment are in very good agreement with those from ref. “). Concerning the I= 3 transfers the spectroscopic strengths given by Rapaport and Buechner are about 20% smaller than ours. But undoubtedly the inclusion of the finite-range and non-locality corrections into the Rapaport and Buechner DWBA calculations would significantly reduce or fully remove this difference. As we mentioned already in the introduction, the data and results by Fink and Schiffer ‘) are internally contradictory. Employing the spectroscopic strengths given by these authors and their optical potentials, the DWBA calculations result in the systematically smaller values of cross sections at maxima, in comparison with those given in their paper. For instance, the calculation leads to values of 3.0 and 10.0 mb/sr instead of 4.4 and 14.5 mb/sr given by Fink and Schiffer for the first and fourth states, respectively. In any case, the results of Fink and Schiffer are not compatible with ours. Though their differential cross sections at maxima are about 25% higher than ours (at approximately the same deuteron energy), their deduced spectroscopic strengths are 35-40% smaller. According to our investigation of different sets of optical potentials ‘), only the lo-15% difference could be explained by the used sets of optical potentials which differed from ours. The target nucleus 37C1 has the closed (2s, Id) neutron shell and single proton in states arising from the Id,,, orbit. In the (d, p) reaction mainly the negative-parity coupling of the lfT12, 2p3,2 or 2~,,~ neutrons and the Id,,, proton are expected to be populated. According to the simple shell model we should have in 38C1 two quadruplets and one doublet of states containing the lf,,,(l= 3) and 2p,,,, 2p,,, (1= 1) single-particle strengths. The real picture is usually much more complicated. Due to residual interactions the configurations are mixed and each single-particle strength is fragmented in many states of the nucleus. Up to now no realistic shell-model calculations in configuration space with 2slj2, Id,,,, lf7,*, IP,,~ and 2p1,* particles treated as active are available for the nucleus 38C1. To have an idea how many states originating from this configuration space, containing more or less appreciable single-neutron components and should be therefore populated in the nucleus present reaction let us look at the reaction 36S(d, P)~‘S, as the even-even 36S has analogically closed (2s, Id) neutron shell.

3. Pinko?, W. Sch~ferlingova’ / Spectroscopic

In table 10 are displayed observed

results concerning

in the (d, p) reaction

momenta particle

strength

is fragmented

from our recent

by Thorn

of some states was obtained

By inspection

319

states of 37S below 3.5 MeV excitation

as compiled

from the Ed = 18 MeV measurements

information

investigation

et al. 30). Information

in polarization

of the table

we see that although

is contained

in the ground

experiments almost

by Kader et al. 31).

the whole

lf7,* single-

state, the 2p3,* single-particle

at least into three states, namely

ones. In spite of the fact that the 646 keV contains

‘) and

on angular

strength

the 646 keV, 1992 keV and 3262 keV about 70% of the 2p3,z single-particle

strength, the third $- state (containing approx. 15% of 2p,,, single-particle strength) lies at 3262 keV, i.e. at significantly higher energy than the first $- state at 2638 keV containing around 80% of the 2p,,, single-particle strength. The following

conclusions

concerning

the negative-parity

states of 38C1 nucleus

can be made: strength should be contained in the (i) Almost the whole If,,, single-particle lowest quadruplet of states with J” = 2-, 5-, 3- and 4-. (ii) In the energy range up to approximately 4.5-5 MeV the most of the I= 1 single-particle strength should be contained in about 20 states. (iii) For I= 1, J” = I-, 2- states (especially at higher excitations) considerable should be expected. mixing of 2p3,, and 2p,,, configurations If the last fact actually takes place it could make it difficult to identify states with momenta l- and 2 employing the (2Jr+ 1) rule. Nevertheless the sum rules can be applied to the overall 1= 1 single-particle spectroscopic strength. The state at excitation 3442 keV in 37S populated via the 1= 3 transfer in the (d, p) reaction

could be considered

as a parent

of two states at excitations

TABLE 10 Spectroscopic

strengths

in single-particle

I

nucleus

37S

(2Jf1,+ l)S,

J7 ref. 30)

present

ref. 30)

3 1 2 1

3 1 2

7.328 2.796 0.212 0.300

6.16 2.62 0.22 0.15 0.08

(3) 1 1 1 3 1

A (3) 1 1

0.272 1.662 0.568 0.120 0.598 0.340

0.14 1.54 0.60

present 0

646 1398 1992 2023 2515 2638 3262 3355 3442 3493 “) Derived

from polarization

1

experiments

3’).

c;-, F)

around

5 MeV

320

3. Pisko?, W. Schiiferlingovri / Spectroscopic

in 38C1, respective as corresponding character

angular

distributions

tentatively

of which Rapaport

to 1= 3 transitions.

of these states is available,

information

neither

and Buechner

Any further

from the present

“) classified

information experiment

on the nor from

ref. ‘). As concerns interesting

the positive-parity

fact, namely

states we would

that the closure

like to draw attention

of the sd neutron

shell reduces

to a rather the effective

number of neutron holes in the 2~,,~ and Id,,, orbits, i.e. that the components of the type (2sld)“-2(lf2p)2 in the ground-state wave functions are reduced as the sd-shell is filled up. Though in the 34S we have observed ‘) 0.31 2~,,~ and 2.56 Id,,, neutron holes and in the 35C1 we have found ‘) 0.32 2s,,* and 2.66 ld3,2 neutron holes instead of 0 and 2.0 according to the simple shell model, respectively, no I = 0, and only one weak 1= 2 transition has been identified in the 36S(d, P)~‘S reaction, indicating about 0.19 Id neutron hole in the target nucleus 36S. The analogical situation seems true also in the 37C1 nucleus. In fact we were not able with certainty to assign I= 0 or I= 2 to any angular distribution in the reaction 37Cl(d, P)~‘C~, though very small components were not excluded. Applying the sum rules, i.e. that for the particular target nucleus the sum of weighted spectroscopic factors should be equal to its number of neutron holes in subshell j (or 1, when we do not distinguish between different spin orientations), where the weights are the statistical factors (25,+1)/(23,+1) and summation has to be extended over all the final states (whatever the Jr) which can be reached by transfer of a neutron in the subshell j (or in the subshell l), we can check to what degree the If and 2p single-particle strengths are exhausted by the observed I= 3 and I= 1 transfers in the reaction 37Cl(d, P)~*C~ and compare with analogical results for the reaction 36S(d, P)~‘S. The first two l= 3 states in 37S which are presumably the fragmented lf7,* states contain 95% of the lf7,2 single-particle strength. Analogically, for the 38C1 nucleus the sum of weighted spectroscopic factors for five lowest I= 3 states is equal to 7.33 strength is contained in instead of (2j+ 1) = 8, i.e. 91.6% of the lfT12 single-particle these states. Supposing that the fifth observed l= 3 state at 1785 keV excitation is a member of the quadruplet of states arising from coupling of Id,,, proton with a fragment of the lf7,2 I= 3 neutron (2515 keV state in 37S being presumably single-particle orbit, i.e. having J” = f-) then as minimum one I= 3 low-lying state is missed in 38C1 (probable spin should be 4- or 5- as the 2- and 3- components could be fragmented in 2- and 3- members of several 2p multiplets) or the second l= 3 state in 37S has spin %-. The sum of weighted spectroscopic factors for six I= 1 states in 37S amount to 5.786 instead of 2(21+ 1) = 6, i.e. 96.4% of the 2p single-particle strength. Twenty-two I= 1 transitions in the 38C1 nucleus exhaust 95.5% of the 2p single-particle strength. The optical potentials used in DWBA calculations in both cases have the same results for the genealogy “T’~) and could be therefore expected to give consistent 36S(d, P)~‘S and 37Cl(d, P)~~C~ reactions.

3. Piskoi,

We wish to express Franc,

the author

computational the present

W. Schiiferlingova’ / Spectroscopic

our special

of the magnetic

gratitude

to our colleagues,

spectrograph

project

codes, and to Dr. J. KZemCnek, experimental

We acknowledge

material

also valuable

about

321

namely

to Dr. P.

and of some data processing

for their enormous

and for their helpful discussions

information

discussions

DWBA

help in gathering and suggestions.

calculations

with Dr. J.

Cejpek.

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) 29) 30) 31)

A.H. Wapstra and G. Audi, Nucl. Phys. A432 (1985) 1 S. Piskoi, P. Franc, W. SchIferIingova and J. Kieminek, Nucl. Phys. A481 (1988) 269 S. Piskoi, P. Franc, W. Schaferlingova and J. Kieminek, Nucl. Phys. A414 (1984) 219 J. Rapaport and W.W. Beuchner, Nucl. Phys. 83 (1966) 80 C.L. Fink and J.P. Schiffer, Nucl. Phys. A225 (1974) 93 A.M.J. Spits and J.A. Akkermans, Nucl. Phys. A215 (1973) 260 P.M. Endt and C. van der Leun, Nucl. Phys. A310 (1978) 1 P. Franc, J. KIemenek, S. Piskoi and W. Schaferlingova, Czech. J. Phys. B29 (1979) 1084 R. Bauer, J. Kiemenek, S. Piskoi, 2. Svoboda and V. Skaba, Nucl. Instr. Meth. 157 (1978) 83 V. Kroha and K. Putz, 7th Conf. of Czechoslovak Physicists (Czech. Union of Math. and Phys., Prague, 1981) pp. 2-36 P. Franc, J. KIemCnek, S. Piskoi and W. Schiiferlingova, Nucl. Instr. Meth. 211 (1983) 159 F. Ajzenberg-Selove, Nucl. Phys. A449 (1986) 1 F. Ajzenberg-Selove, Nucl. Phys. A468 (1986) 1 T.J. Kennett, W.V. Prestwich, R.J. Tervo and J.S. Tsai, Nucl. Instr. Meth. 215 (1983) 159 A.M.J. Spits and J. Kopecky, Nucl. Phys. A264 (1976) 63 T.J. Kennett, M.A. Islam and W.V. Prestwich, Can. J. Phys. 59 (1981) 93 B. Krusche, K.P. Lieb, H. Daniel, T. von Egidy, G. Barreau, H.G. Borner, R. Brissot, C. Hofmeyr and R. Rascher, Nucl. Phys. A386 (1982) 245 R. Abegg and SK. Datta, Nucl. Phys. A287 (1977) 94 J.A.R. Griffith, M. Irshand, 0. Karban and S. Roman, Nucl. Phys. Al46 (1970) 193 F.D. Becchetti, Jr, and G.W. Greenlees, Phys. Rev. 182 (1969) 1190 P.D. Kunz, Instruction for the use of DWUCK: A distorted-wave Born approximation program, Univ. Colorado report COO-535-606; Algebra used by DWUCK with application to the normalization of typical reactions, Univ. Colorado report COO-535-613 (1970) A.B. McDonald, E.D. Earle, M.A. Lone, F.C. Khanna and H.C. Lee, Nucl. Phys. A281 (1977) 325 L.M. Solin, Ju.A. Nemilov, V.N. Kuzmin and K.I. Zherebtsova, Yad. Fiz. 29 (1979) 289 A. Sperduto, W.W. Buechner, C.K. Bockelman and C.P. Browne, Phys. Rev. 96 (1954) 1316 M.S. Throop, Phys. Rev. 179 (1969) 1011 E.K. Warburton, J.W. Olness and D.E. Alburger, Phys. Rev. B140 (1965) 1202 R. Moreh, W.C. Sellyey and R. Vodhanel, Phys. Rev. C23 (1981) 988 S. Raman, R.F. Carlton, J.C. Wells, E.T. Jurney and J.E. Lynn, Phys. Rev. C32 (1985) 18 T.J. Kennett, W.V. Prestwich and J.S. Tsai, Z. Phys. A322 (1985) 121 C.E. Thorn, J.W. Olness, E.K. Warburton and S. Raman, Phys. Rev. C30 (1984) 1442 H. Kader, H. Clement, G. Craw, H.J. Maier, F. Merz, N. Seichert and P. Schiemenz, Jahresbericht, Technischen Universitat Munchen Annual Report (1982) 33