Spectroscopy of 15O by use of the 13C(3He, n)15O reaction

1 2.A:2.F

1

iVuclear Physics A183 (1972) 625-639;

@

North-HollandPublishing

Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

SPECTROSCOPY

OF %

BY USE OF THE 13C(3Me, n)150 REACTION

P. D. GEORGOPULOS

+, W. A. LOCHSTET and E. BLEULER

Department of Physics, The Pennsylvania State University, University Park, Pennsyluania 16802, USAtt

Received 29 November

1971

A&!&a&: Coefficients of fractional parentage (2-c.f.p.) were extracted from theoretical calculations for the 13C(3He, n)150 reaction. These 2-c.f.p. were used in DWBA calculations to obtain the direct reaction part of the cross section. Angular distributions were taken for the l%J3He, n) I50 reaction at 6 MeV, and fitted with an incoherent sum of direct and compound parts. Oneparticle-two-hole strengths were suggested for the first six positive-parity states. The positiveparity 10.28 MeV state is suggested to have a spin of % or greater. E

NUCLEAR REACTIONS 13(J3He, n), E = 6 MeV; measured a@,, 8). I50 deduced levels, L, spectroscopic factors. DWBA and CN analysis, enriched target.

1. Iutroduction The investigation of the 13C(3He, n)l 5O reaction at 6 MeV was undertaken to test coefficients of fractional parentage (2-c.f.p.) extracted from theoretical calculations. This was accomplished by comparing calculated and experimental relative differential cross sections for the first nine states in 15Q . The importance of employing such an extraction in analyses of two-particle transfer reactions lies in the fact that the magnitudes as well as the relative phases of the coefficients play a role in the theory “). This is in contrast to single-nucleon transfer reactions, where only the absolute values of the components are of importance. Although several recent studies of this reaction have been made ‘-‘), their principal objectives were to extract spectroscopic strengths by employing primarily only the dominant configurations of the states in their analyses. This approach is in contrast to the approach taken in the present study. Moreover, the investigation was used to determine to what extent the reaction mechanism could be described by an incoherent summing of direct and compound processes. Previous studies of this reaction to the ground state in this energy region [refs. 5 - ‘)I showed characteristic forward peaking suggestive of the direct process, but the compound contribution may not be ignorable. Ritter et al. have employed such a combined analysis on the 14N(d, n)’ 5O reaction at 5.35 MeV, and have indicated its necessity “). t Present address: Delaware County Campus, The Pennsylvania State University. ++ Supported in part by a grant from the National Science Foundation. 625

626

P. D. GEORGOPULOS

et al.

Selection rules for the direct (‘He, n) reaction have been given several times ‘, ’ “). The two stripped protons are coupled to total angular momentum J,, spin S, = 0 and isospin T, = 1. For the 15C target with J” = $-, the negative-parity states of I50 are populated by even total orbital angular momentum transfers (E,) where L, = J,, while the positive-parity states are populated by L, = Jt = odd.

2. Experimental

procedure

Since the angular distributions for the 1”C(3He, n)1-50 reaction reported earlier from this laboratory “) were affected by large statistical errors, it was decided to remeasure them with improved equipment. The measurements were carried out by means of a fast neutron time-of-flight spectrometer at flight paths of 3 and 6 m. The 6 MeV 3He beam from the CN Van de Graaff accelerator was chopped within the terminal into pulses with a FWHM of 3.5-4 ns duration at a repetition rate of 5 MHz. Average beam currents in the range of 160 nA were used. Neutrons were detected by a NE 213 liquid scintillator, 12.7 cm diam and 2.5 cm thick, viewed by a 58 DVP photomultiplier tube. The counter was shielded by lead and mounted on a movable table. Three signals were taken from the tube. The anode furnished start pulses for an Qrtec 437 time-to-amplitude converter (TAC). Pulses from the 14th dynode were fed into an Elron PSD-1, n-y discriminator, while linear pulses were derived from the 12th dynode by a Hewlett Packard 5554A chargesensitive preamplifier. Signals from both lines were fed into a coincidence unit, the output of which gated the input of a TMC 1024-channel analyser, with one half the memory used to store the TAC spectrum. The lower cut-off of the spectrometer was determined by the charge-sensitive preamplifier line. Beam bursts were detected by a capacitive pick-off located within the beam line. Alternate pick-off pulses triggered the “stop” input of the TAC, thus producing a double TAC pulse-height spectrum. This provided a direct conversion from channels to time, since the spectrum in the lower channels was time shifted from the one in the upper channels by 200 ns. An absolute time reference was established in the spectrum by noting the peak channel numbers of groups corresponding to y-rays emitted from the target; these prompt y-rays were used since their flight time was known. A monitor counter was used for normalization during all the runs. Another TAC was introduced into the system for this counter. Targets were prepared by evaporating a layer in the range of 40 pg/cm’ of elemental carbon enriched to 91.8 % in “C onto tantalum backings. Individual target thicknesses were determined by observing the ‘%(p, y)i4N resonance at J!$ = 1.7476 MeV [ref. “)I. The shapes of the resonances ascertained that the targets were of uniform thickness within the beam spot area, while the FWHM of the resonance determined their thickness to about 10 %. The energy loss in the targets, as used, was 32 keV for 6 MeV 3He ions. The sensitivity of the primary counter to neutrons was determined utilizing three reactions. An absolute sensitivity to neutrons with energies of 1.7 to 9 MeV was ob-

621

I50 SPECTROSCOPY

mined from the use of the 2H(d, n)3He reaction I’) while the relative efficiencies were extracted from the cut-off at 1.2 MeV to 1.9 MeV by employing the 7Li(p, n)7Be reaction 13) and the 13C(p, n)13N reaction ’ “). Since 9 to 13 MeV neutrons are produced reaching the ’ 5O ground state, it was necessary to rely on a calculation of the efficiency in this region ’ “). Since the calculation reproduced quite well the behaviour of the experimental efficiency in the region between 1.2 to 9 MeV, it was used to determine the efficiency in the upper region where it decreased linearly from 9 to 13 MeV by a factor of 0.76. I

I

I

I

I

I

I

250

300

2400

I

I-

t

4

150

200 CHANNEL

Fig. 1. Time-of-fright

2

-

NUMBER

spectrum at 6 m with overlap of low and high neutron energy ranges.

Data were collected with flight paths of 3 m, with only the 0.00, 10.28 and 10.46 MeV states being cleanly resolved. The flight path was increased to 6 m for the analysis of the other states. Two runs with slightly differing flight paths were also needed at each angle for the 6 m data since at these distances the low-energy neutron groups overlapped with both the high-energy groups and the prompt y-rays. A typical spectrum is shown in fig. 1. To obtain intensities, the background subtracted from each peak was determined from the slowly varying intensity between the peaks. At forward angles, the groups from the 10.28 and 10.46 MeV states rose above a mound due to -the 13C(3He, np)14N reaction. Since the target material contained 8.2 % 12C, a large neutron group resulted from the 12C(3He, n)140 ground state reaction which masked the 150 8.28 MeV state at forward angles. Thus an angular distribution was taken employing a natural carbon target and the ’ 4O contribution was subtracted out from the ’ 5O spectrum.

628

P. D. GEORGOPWLOS

et al.

The neutrons leaving 150 in its 10.28 MeV level have nearly the same energy as neutrons from the ’ 60(311e, n)18Ne reaction. At angles greater than 30” these groups would be resolved, and no evidence was found for the I60 reaction. The contaminant neutrons would follow a forward-peaked L, = 0 pattern (0’ -b O+), but since the spectra obtained down to 10” have narrow groups which are not shifted toward the positions of the I60 neutrons, this possible conta~nation has been ignored. The quadruplet of states near 9.6 MeV excitation in I50 were not adequately resolved and were not considered in the analysis. 3. halysis 3.1. TWO-c.f.p.

CALCULATUJN

Since the direct-~teractio~ mechanism assumes that the final nuclear state is formed by adding a pair of nucleons to the inert target, the finaf-state wave function must be expressed with the aid of two-nucleon coefficients of fractional parentage defined by the following expression:

where the non-, zero- and t-subscripted quantum numbers refer to the residual nucleus, target nucleus and transferred nucleon pair, respectively, and where the square brackets denote vector coupling. The p - (n,, ZI,.jl, %*,Z,,j,) refers to the nature of the transferred pair. In order to fulfill the req~rements of the dir~t-interaction computer code DWUCK 16) employed, the two transferred particles having good quantum numbers j, and j,, were coupled to total angular momentum Jt. Explicitly, the above coefficients are calculated by

h% x ~E’t,~‘~,$t~tw(Lo,

dmq;

la,

;;pm~

L,

I,

;L’,

L,)

W(S,, *, S, 4; S’, S,) W(T,, 3, T, 3; T’, T,) 5

;j,

where f = 2 J-l- 1 and 6 = (L’S’T’, IIs,tl; LST). The leading two terms are the expansion coefficients of the basis wave functions for the target and the residual nucleus, respectively, and the third term is the I-c.f.p. relating the p”* part of the ‘.% basis wave function to the target basis wave function. This expression assumes that the l 3~ ground state wave function is of a pure p-shell nature. This assumption was made in the detailed intermediate coupling calculations of Kurath ’ 7), Boyarkina 18) and Varma and Goldhammer I’). In the latter two cases the wave functions were expressed in a L-S representation suitable for use in the

629

I50 SPECTROSCOPY

present analysis. Cohen and Kurath, in subsequent analyses, have employed their wave functions in calculating 1-c.f.p. and 2-c.f.p. for the p-shell nuclei 2o, ‘I). For the A. = 15 nuclei, intermediate coupling calculations have been made for the positive-parity states by Halbert and French 22), Zhusupov et al. 23), Hsieh and Horie 24), and Lie et al. 25), while core-polarization studies in ’ 5O have been made by Shukla and Brown “): For these positive-parity states, the classic cumulation of Halbert and French was considered in the 2-c.f.p. analysis. This calculation which has been used in the comparison of the single nucleon transfer analysis to I50 by Alford and Purser 27), seems to give a reliable account of the low-lying positive-parity states. The wave functions were given in a concise and convenient form for combining them with the 13C wave functions. They were expressed in terms of a basis set which was composed of 10 lp particles (pl’ E’) with total orbital~spin-isospin quantum numbers (L’, S’, T’) and partition [Xl, coupled to either a 2s or a Id shell particle (II, sl, tl) with resultant quantum numbers (L, S, J, T). Following Cohen and Kurath 21), the negative-parity states of ’ 5O were treated as pure lp single-hole shell-model states. In order to make the above expression compatible with the single-hole wave functions, the A = 15 expansion ~oe~~ients A& were replaced by the (plllplop} geometric c.f.p. Along with the 2-c.f.p. calculated by Cohen and Kurath for the negative-parity states, the 2-c.f.p. calculated presently for the first nine states in A = 15 t are shown in tables 1 and 2. All were used in the DWBA calculations. TABLE 1

Two-c.f.p. E,, in “0 (MeV)

for stripping to negative-parity

JCB

states in A = 15, using p nucleons only

Tt = 1

Configurations

of transferred

pair

.__

-

0.00

Q-

J* = 0

6.18

23-

Jt = 2

p;pt -0.1382 +0.1330 1-0.1440 p*p.?Z -0.0135 +0.0260 +0.0168

p#% - O.OG76”) +0.0821b) +0.0502’) P@; -0.0401 10.0478 +0.0400

“) Results of Cohen and Kurath, ref. 21). The change in sign is irrelevant. b, Calculated from the 13C results of Goldhammer, ref. 19). ‘) Calculated from the 13C results of Boyarkina, ref. I*). t While the phase convention for the coefficient of fractional parentage employed in both the Boyarkina and Goldhammer calculations is that of Jahn and van Wieringen 28) corrected in ref. zs), that of Nalbert and Frenchis not. Therefore, since all c.f.p. defined in the latter are negative, it was necessary to change the sign of those pi * components in the IsO wave functions that corresponded to a positive
630

et al.

P. D. GEORGOPULOS TABLE 2

Two-c.f.p. for stripping to positive parity states in A = 15, using the results of Halbert and Frenck 2z) E

in I50 &eV)

Jf n

Tt = 1

Jt = 1 5.18

zr+

7.55

*+ z

6.79

3+ ‘z

8.28

4’

5.24

5+ 2

6.86

5+ Y

7.28

H+

Configurations

P&

-0.1788 -0.1929

“)

bj

+0.1053 +0.1098 -0.2610 -0.2751 -0.0345 -0.0357 Jt = 3

p+ds +0.1929 +0.2088 -0.1008 -0.1053 +0.2784 +0.2937

of transferred

pgs* 1-0.0780

p+d+ -0.0585 -0.0624 -0.0201 -0.0207 -0.0534 -0.0573 +0.0162 $0.0165

+0.0438 +0.0228 +0.0255 +0.0036 +0.0033

p*dg -0.0315 -0.0273 -0.0114 -0.0069 -0.0180 -0.0174

P& -0.0405 -0.0303 -0.0363 -0.0411 -0.0087 -0.0147

pair

p3ds f0.0027 -0.0012 -0.0057 -0.0057 -0.0048 -0.OQ30 -0.0024 -0.0009

+0.0597 +0.0309

psd9 -0.0189 -0.0180 +o.oooo +0.0009 -0.0366 +0.0318 10.0582 +0.0333

“) Upper numbers calculated with the 13C wave functions of Goldhammer, ref. 19), “) Lower numbers calculated with the 13C wave functions of Boyarkina, ref. Is).

TABLE 3

Optical-model

b) H2 “) Nl “) N2 d,

used in DWBA analysis “)

,

Set label Hl

parameters

(M&)

(2)

(fzl)

(MI!)

(;n$

(fz)

-176 -105 - (49.3 -0.33 &) - (62.9 -0.3 E,)

1.14 1.10 1.25

0.70 0.80 0.65

-18.5 -16.8 0

1.75 1.80 1.25

0.80 0.70 0.70

1.40 1.40 1.25

0 0 23

2.5 0 5.5

1.17

0.75

0

1.26

0.58

1.25

43

6.0

“)

1.25

0.65

bound states

1.25

“) Sets Hl and Nl were used in ref. 3), but improperly ‘) Ref. ‘). “) Ref. 30). d, See text. ‘) Fitted to binding energy.

a. = 25

quoted there.

3.2. DWBA ANALYSIS Direct-reaction

cross

sections

were calculated

using the two-particle

of the computer code DWUCK 16). The optical-model shown in table 3. The form of the potentials used is U(r) = UC(r)+ vf(x)+iJvy-(x’)+iW’

$.f(Y)+

parameters

v, (jy

transfer option considered are

2 &s $r(x). *

= (1-k e”)- 1 and x = (r - T,A.~)/~and where UC(r) is the potential of a uniformly charged sphere of radius I*&“, The E?1 and H2 parameter sets for ’ “C-t- 3Hz were taken from the polarization studies of the 13C(3He,n)150 reaction 7), both being averaged sets. The neutron set Nl is that given by Rosen 30). The neutron set N2 is that from ~e~~hett~ and Greeniees ’ “) as used in ref. 7)t except that the real well depth was modified and made a function of the neutron energy. Based on the fittings of the fisst nine states the H2Nl and H2N2 combinations were eonsidered in all subsequent analyses, giving essentially similar results. For the bound states of a partieular Bevel,the proton binding energies were taken as one half the two-Briton separation energy for that level. 30th zero-range and ~~~te~range (R = 0~59 fm) options were used, in addition to a non-local correction with p, = 0.85 fm and &nf: = 0.25 fm. where f(x)

The compound calculation was based on the causer-F~shba~h fo~~~srn as found in ref. 32)q All energ~t~c~~y possible n, p9 3He, 4He exit channels were considered (about 130). Trans~ss~~n coefEcients were extracted from a modified version of the computer code DWUCK ’ 6)1 employing ~~ti~~-~otentia~ parameters appropriate to the entrance and exit channels. These are listed in table 4. For a given rmdeus, N x P(S) of the N levels of unknown spin in an energy interval were selected at random and assigned spin J, where P(J) CC(2Jf I)exp(-- (J+$)‘/2cr2), G = 1.5 and c B(J) =: 1 [ref. ‘“)I. Levels of unsown parity were assigned random parities with an eqtaal ~robabi~~t~ of 7t = 2.

Y

Channel

(MeV)

sHe + 12Ca) 3He+13Cb) n-j- %c)

- 148.5 - 176.0 - (49.3 -0.33 &) -(53.X -0.33 Ep)

p+=N=)

1.74 1.14 125

0.38 0.70 0.65

1.25

Q.65

-0.68 -18.5 0 0

1.74 1.75 1.25

0.38 0.80 0.70

1.74 1.4 1.25

0 0 23

0 2.5 5.5

1.25

0.70

1.25

30

5.5

“) Ref. 39).

‘) lie& ‘). The difference in reaction cross sections is small between the Hl and 82 sets. ‘) Ref. 3Q). 3.4. ~METB-XQDOF CO~~A~I~~

~~~~~~~~

WITH THEORY

incoherent summing of the theoretical direct-reaction and ~om~ou~d-~L~cleus cross sections was used, employing a constant reduction factor for the compoundnucleus cont~bu~on~ The factor was used to take into account the inadequacy of the An

632

B. D. GEORGOPULOS

et al.

causer-~eshbach theory in reducing the compound fo~a~on cross section. This is needed since the theory assumes that the incident Aux goes into formmg the compound state exclusively but in actuality some of it is fed into the direct-reaction channel. A least-squares fitting routine was employed to fit the following expression to each experimental angular distribution: da --.-ED d%., with the added constraint 0 2 C 5 1 being imposed. In the case of unresolved ~OLIblets (5.X8-5.24 MeV, 6.79-6.86 MeV) a single C-value was used for both states. However, different ~~compo~ents could be obtained for each state in the doublet, since the orbital transfer of the two protons for each was d~erent. Analysis of this type on the 6.18, 7.28 MeV and the 8.74 MeV states suggested that the C-coefhcient have a value of about 0.2. Subsequent fittings were made with this further constraint on the other states, since a variable reduction factor did not seem warranted in view of the crudeness of the summing procedure. In order to compare the experimental results with the theoretical calculations, the direct-interaction part was written as doD’ .-=D dQ =N da,, d%wucK g = 55, n, = =lO,

(2Jf1) (2J,+1)(2Jo+l)

sg[C$ _:

_;I” -,

dg

dSt,wu,:

7$=+,

where s represents a “strength factor” (we prefer not to use “spectroscopic factor”) and where g is due to the antisymmetrization of the wave functions used to calculate the 2-c.f.p. [ref. “)I. The isospin coupling coefficient is needed, since these wave functions do not specify the charge state of the systems they characterize. The square of this coefficient for the (3He, n) reaction to the T = 4 states in ’ 5O is 3. Normalizati.on factors N, one for each of the three sets of 2-c.f.p. employed for each potential set, were obtained from the results for the ground state transition by assuming a strength factor of one. This was done since this term is not known for two-particle transfer reactions involving 3Me as the incident particle. Strength factors differing from one would indicate inadequacies in the wave functions used to characterize the states. This procedure is analogous to the method of extracting spectroscopic factors in single-nucleon transfer reactions. 4. Results

Extracted angular distributions including all relative errors are shown in fig. 2. The differential cross section at 0” for the ground state was found to be in agreement with the excitation function given by Din and Weil “) while general agreement was

633

5

t:!~!::::I!!:l::~ Exe = 7.55 MeV

i-SUM

DI + SUM CN

5t-

4

I 00

300

600

SO”

120”

i50*

5”

Sm.

30°

60°

SO*

e C.“.

120°

t50°

.05 0”

30”

60°

90° e c-m.

120°

150a

Fig. 2. Angular d~s~ri~ot~o~s with curves from an incoherent comb~~a~io~ of DI and CN calc~a~~o~s, for C = 0.2 (see text).

634

P. D. GEORGOPULQS

et al.

found with the 6 MeV forward-angle data of Hinderliter and Lochstet “). There is also general agreement with the 6.2 MeV results of Etten and Lenz “). The direct-interaction contributions plotted in fig. 2 are those employing potential sets H2 and Nl, with the finite-range correction, while the compound-nucleus contributions plotted have been reduced by the C-coefficient of 0.2. As was mentioned previously, this value was determined on the basis of best fits for the 6.18, 7.28 and 8.74 MeV states. Minimum x2 fits were obtained for the ground state, 5.2 and 6.8 MeV doublets, and the 8.28 MeV state at C-values less than 0.1, with the D-coehicients going negative for values of C of0.3 and greater. A minimum x2 fit with C = 0.3 was obtained for the 7.55 MeV level. For either a C = 0.2 or 0.3, the fits for this level were poor. Based on this analysis, a C = 0.2 seemed like a reasonable choice for all the states. Although the fits to the forward angles are generally good, the calculation seemed to underestimate the back-angle contributions. A possible explanation lies in the fact that interference terms consisting of combinations of compound-nucleus and direct-interaction amplitudes, neglected in the formalism, could play a major role and show at these angles. Indeed, this should be expected according to the following estimates of the density and widths of the levels of the compound nucleus 160 at an excitation energy of 27.6 MeV. At excitation energies of 18.7 to 23.8 MeV, Temmer found a mean level width of 230 keV [ref. ““)I. By extrapolation to 27.6 keV, the mean level width is found to be 320 keV [ref. 3“)I. The relation between average level width and level density 37), with the transmission coefficients found in the HauserFeshbach calculation, yields a level density of about 0.4 keV_‘. Thus, the effective number of levels contributing to the reaction amplitude is about 320 x 0.4 = 130. This would seem sufficient for the averaging over J implied in the Hauser-Feshbach calculations, but the target thickness of 32 keV is grossly inadequate for averaging over the phases of the contributing amplitudes and thus the sum of the interference terms does not vanish. Since the spins and parities for the first ten states in I50 are known 38), the total orbital angular momentum transfers (L,) are also known. The shapes of the DWBA cross sections, as expected, were strongly dependent on L,. Although different configuration amplitude sets produced rather slight differences in the shapes of the angular distributions, the magnitudes were definitely affected. Strength factors for each set of amplitudes compiled employing H2Nl and H2N2 sets, both with the finite-range option of Cl.69fm, are listed in table 5 along with the normalization factors N. Zero-range calculations did not change the strength factors by more than 10 % from the ones found with the finite-range option. 5. Discussion

As stated in subsect. 3.4, strength factors s = 1 are expected if the wave functions for the target and the final nucleus are correct (and if the reaction mechanism is described correctly). The spread of the s-values listed in table 5 is thus rather disappoint-

635

I50 SPECTROSCOPY

ing and is an indication that the particular set of wave functions chosen for investigation is at least partly deficient. 5.1. NEGATIVE-PARITY

STATES

The coefficients of fractional parentage listed in table 1 for the three sets of 13C wave functions are fairly close to each other for the p+p+ and p&p+ pairs, but show variations by nearly a factor of 2 for the pg+ pairs. The relative strength factors for the 6.18 MeV state given in table 5 show a similar variation, from about 0.50 to 0.80. The Cohen-Kurath 13C wave function, which results in the value of s closest to one, might be considered the best choice. This conclusion, however, is probably not warranted because of the 2p-3h and perhaps 4p-.5h admixtures in the negative-parity 150 states ““). Since the 2p-3h component can be reached in the (3He, n) reaction, the complete calculation would include transfer of p2 and (s, d)2 proton pairs, with unpredictable results. In view of the sensitivity of the two-particle transfer cross section to small changes in the wave functions, the values of s obtained for the 6.18 MeV level, with any of the three 13C wave functions, may indicate that the 2p-3h component in these “0 states is small. 5.2. POSITIVE-PARITY

STATES

As can be seen from table 2, the dominant 2-c.f.p. to the f’-$’ and $+G’ states are those which one would expect from the stripping of 2 protons into a 13C target nucleus with a dominant configuration [~(lp+)-~ v(lp+)-I], namely the p+s+ and p+d, configurations, respectively. The only noticeable deviation arises in the description of the 8.28 MeV $’ state. Employing the Goldhammer basis set for 13C in the TABLE 5 Results of the DWBA

=c

w.f.

Goldhammer

Pot. sets Norm. factor states (MeV) 0.00 5.18 5.24 6.18 6.79 6.S6 7.28 7.55 8.28

analysis Boyarkina

H2Nl

H2N2

H2Nl

H2N2

N2Nl

H2N2

570 s

500 s

1.00

1.00

0.79

0.82

Jrr

N Lt

510 s

440 s

680 s

590 s

*-

0

$+

&23+

1 3 2 1

g+ 7t H z1+ z3+

3 3 1 1

1.00 0.015 0.13 0.49 0.019 1.96 “) 1.00 0.082 0.96 8.8 0.1oa>

1.oo 0.025 0.20 0.51 0.025 2.7 1.6 0.13 1.2 12.3 0.17

1.00 0.011 0.097 0.61 0.020 20.0 0.29 0.055 1.5 65.0 0.11

1.00 0.019 0.15 0.64 0.025 25.0 0.81 0.081 1.9 92.0 0.16

;+

H

Cohen and Kurath

“) With I50 wave functions switched (see text).

636

P. D. GEORGOPULOS et al.

2-c.f.p. calculation for this state, the major amplitude corresponded to the pgds configuration, while the Boyarkina set gave equal strengths to the p+d+ and pBs3 configurations. These differences were then passed on to the direct-interaction calculation where quite different strengths were obtained (table 5). In both cases the strength factors were greater than one. As can be seen from the same table, a small strength factor was extracted for the other 4’ state, namely the 6.79 MeV state. The ’ 5Q wave functions were then reversed between the two states, resulting in desired increases and decreases in the strengths of the 6.79 and 8.28 MeV levels, respectively. IIowever, the 14N(3He, d)” 5Q studies of Alford and Purser 27) indicate a preference for the original ordering: the 6.79 MeV level is populated by I, = 0 transfer with an intensity in excellent agreement with that derived from the Halbert-French wave function. This agreement would be lost if the wave functions were switched, since the transition to the 8.28 MeV level shows a weak 1, = 2 transfer only. The argument is weakened by the fact that this transition has only about 20 % of the expected strength, which leads to the suggestion that the Halbert and French model may be inadequate at the higher excitation energies “‘). 0 ur results would indicate that perhaps both 3* states are inadequately described. The s-values listed in table 5 are based on lp-2h wave functions for the positiveparity states. They must, of course, be considered to contain 3p-4h and higher con~gurations. If the 13C ground state is considered as having three holes and if core excitations are small, as suggested by the excitation energy of 3 MeV for the first excited state in 13C, then only the lp-2h components would be populated by the (3He, n) reaction. Assuming that these components are given correctly by the Halbert and French wave functions, one can try to explain s-values less than 1 by a reduced lp-2h strength. Table 6 compares our experimental results with the theoretical values of Lie, Engeland and Dahll ““) and of Shukla and Brown ““). There is some correlation, especially if we use the switched wave functions for the 3’” states, but the experimental strengths for the 7.28, 5.24 and even the 5.18 MeV level must be considered as being much too low. It should be re-emphasized that the absolute values of s depend on the arbitrary normalization of the ground state transition. Perhaps introduction of 3p-4h components could make appreciable differences in the structure of the lp-2h components. In any event it would be interesting to employ the “0 wave functions of Lie et al. ““) in the 2-c.f.p. calculation to see if their prescribed lp-2h strengths can be reproduced by our methods. 5.3. HIGHER STATES

Three states above the nine analysed were also studied, with the unresolved 8.9 MeV doublet and the 9.6 MeV quadruplet groups in 15O not being considered since no new information concerning individual states could be extracted. The 8.74 MeV state which has J” = 3’ was fit well with an L, = 1 transfer. For pure p&s* and p+d$ transfer configurations, the strength factors would be 0.048 and 0.091, respectively.

637

I50 SPECTROSCOPY TABLE 6 The Ip-2h strengths of the low-lying positive-parity Present “)

State (MeV) 5.P8 5.24 6.79

4’ 2s+ ++

6.86 7.28 7.55 8.28

8’ s+ a+ $+

2 13 2 > 1OOd) 100 S 96 > 100 10 d)

Shukla and &own b>

states of I50 (%) Lie et aI. 3

50 50 50

35 82 83

50 50 50 50

83 9X 99 55

*) Based on Goldhammer 19) plus Halbert and Frenchz2) H2N1, and normalized to the ground state. “1 Ref, 26). “) Ref. z5). d> With I50 wave function switched (see text).

cakulations

with potential

sets

No previous spin assignment has been made for the 10.28 MeV state which has been assigned a positive parity 3‘)_ The L, = 1 transfer is incompatible with the shape of the angular distribution, indicating a spin of 2 or greater for this state (Lt = 3 or larger). For the 10.46 MeV state, assignments of ($, s)- have been made by Snelgrove and Kasby in their analysis of the 160(p, d)“‘O reaction 40). Shirk et al. suggest a (3, $)from their (p, y) work ‘I). Based on the shapes of the angular distributions, a L, = 2 rather than a L, = 0 assignment seems indicated in the present study. Subsequent analysis by Shirk et al. 42) suggested, however, that this state may be in fact a doublet with about 7 keV separation. In this case, the present analysis would be inadequate. For both the 10.28 and 10.46 MeV states, the addition of compound-nucleus contributions played a small role in rejecting the L, = 0,1 angular distributions.

It is felt that the sensitivity of the DWBA to calculated 2-c.f.p., employed in analysing experimental results and extracting spectroscopic strengths, is such as to warrant the full use of these amplitudes and not just the use of the dominant configurations. This is due to the fact that the magnitudes of the cross sections are rather sensitive to all components. Since the shapes of the angular distributions are not a strong function of the components, analyses for determining orbital angular momentum transfers can be made without ambiguity. This can be seen in the present analysis of the 10.28 state. The combining of the direct-interaction and the corn~o~~nd-nuclear calculations was found to be a necessary feature in describing this reaction at this energy. It was

638

P. D. GEORGOPULOS

et al.

argued that disagreement at back angles might be explained by including interference terms. A reduction factor, presumed constant, of 0.2 was found indicating a smaller than expected component for the compound-nucleus process. However, mod~cations of the Hauser-Feshbach formalism have been made 43)1with over-all decreases in the compou~ld cross sections being found “1. Hence the value of 0.2 should be taken as an empirical value. For several final states, the magnitude of the observed stripping cross sections disagrees strongly with that predicted on the basis of the Halbert and French wave functions for “0 which are of pure lp-2h character. It appears that the 5.18, 5.24 and 7.28 MeV states, as well as perhaps the 8.28 MeV level, have large 3p4h strengths. The authors wish to thank Drs. E. C. Halbert and I’. Goldhammer for their wave functions and useful suggestions and Drs. P. D. Kunz and I?. Rost for their aid with the DWBA code. We are also indebted to Dr. N. Freed for his s~m~ating discussion, and the Breazeale Nuclear Reactor for the loan of a TAC.

References 1) N. K. Glendenning, Phys. Rev. 137 (1965) I3102 2) J. L. Nonsaker, W. J. McDonald, G. C. Neilson and T. II. Hsu, Int. Gonf. on properties ofnuclear states, Montreal, Canada, 1969, contribution 8.51 3) II. F. IEnderliter and W. A. Lochstet, Nucl. Phys. A163 (1971) 661 4) M. P.Etten and G. Ii. Len%, Bull. Am. Phys. Sot. 16 (1971) 489 and private ~omm~icatio~ 5) V. K. Deshpande, II. W. Fulbright and J. W. Verba, Nucl. Phys. 52 (1964) 457 6) G. I.% Din and J. ,L. Weil, Nucl. Phys. 73 (1965) 161 7) D. C. DeMartini and T. R. Donoghue, Bull. Am. Phys. Sot. 14 (1969) 1229; D. G. DeMartini, Ph.D. thesis, Ohio State University, 1969, unpublished .S) R. C. Ritter, E. Sheldon and &I. Strang, Nuci. Pbys. Al49 (1970) 609 9) N. K. Glendenning, Nucl. Phys. 29 (1962) 109 10) B. G. Harvey, Nuclear structure and nuclear reactions, Proc. of the ninth summer meeting of nuclear physicists Aught-September 1964, vol. 2, ed. N. Cindro (The Federal Nuclear Commission of Yugoslavia, 1964) p. 65 11) 5. B. Marion, Rev. Mod. Phys. 38 (1966) 660 12) J. E. Brolley and 5. L. Fowler, Fast neutron physics, part 1, ed. J. B. Marion and 5. L. Fowler (Interscience, New York, 1960) p. 73 13) P. R. Bevington, W. W. Rolland and II. W. Lewis, Phys. Rev, X21 (1961) 871 14) C. Wong, J. D. Anderson, S. D. Bloom, J. W. IvIcGlure and B. D. Walker, Phys. Rev. 123 (1961) 598 1.5) T. B. Grandy, Fh.D. thesis, University of Alberta, 1967, unpublished; C. D. Swartz and G. E. Owen, Fast neutron physics, part 1, ed. J. B. Marion and 5. L. Fowler (Interscience, New York, 1960) p. 211 16) P. D. Kunz, University of Colorado DWBA code DWUCK, 1969, ~In~ublisbed 17) D. Kurath; Phys. Rev. 101 (1956) 216 18) A. N. Boyarkina, Izv. Rkad. Nauk SSSR (ser. fiz.) 28 (1964) 337 19) S. Varma and P. Goldh~er~ Nncl. Phys. Al25 (1963) 69; P. Goldhammer, private communication 20) S. Cohen and D. Kurath, Nucl. Phys. AlO1 (1967) 1 21) S. Cohen and D. Kurath, Nucl. Phys. A141 (1970) 145 22) E. C. Halbert and J. B. French, Phys. Rev. PO5 (1957) 1563; E. C. IIalbert, Ph.D. thesis, University of Rochester, 1956, ~publ~sbed; E. C. Nalbert, private communication

I50 SPECTROSCOPY 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43)

639

M. A. Zhusupov, V. V. Karepetyan and R. A. Eramzhyan, JINR-P04-3178, 1967, p. 19 S. T. Hsieh and H. Horie, Nucl. Phys. A151 (1970) 243 S. Lie, T. England and G. Dahll, Nucl. Phys. A156 (1970) 449 A. P. Shukla and G. E. Brown, Nucl. Phys. All2 (1968) 296 W. P. Alford and K. H. Purser, Nucl. Phys. Al32 (1969) 86 H. A. Jahn and H. van Wieringen, Proc. Roy. Sot. A209 (1951) 502 J. P. Elliott, J. Hope and H. A. Jahn, Phil. Trans. Roy. Sot. A246 (1953) 241 L. Rosen, Proc. 2nd Int. Symp. polarization phenomena of nucleons, ed. Huber and Schopper (Birkhauser Verlag, Base& Switzerland 1966) p. 253 F. D. Becchetti and 6. W. Greenlees, Phys. Rev. 182 (1969) 1190 W. Hauser and H. Feshbach, Phys. Rev. 87 (1952) 366 F. P. Brady, J. A. Jungerman and J. C. Young, Nucl. Phys. A98 (1967) 241 A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1446 G. M. Temmer, Phys. Rev. Lett. 12 (1964) 330 T. Ericson and T. Mayer-Kuckuk, Ann. Rev. Nucl. Sci. 16 (1966) 183 M. A. Preston, Physics of the nucleus (Addison-Wesley, Reading, Mass., 1963) p. 508 F. Ajzenberg-Selove, Nucl. Phys. Al52 (1970) 1 H. M. Kuan, S. S. Hanna and M. Hasinoff, Bull. Am. Phys. Sot. 12 (1967) 52 J. L. Snelgrove and E. Kashy, Phys. Rev. 187 (1969) 1246 D. G. Shirk, S. Fiarman, N. Y. Wei and H. M. Kuan, Bull. Am. Phys. Sot. 16 (1971) 489 H. M. Kuan, private communication P. A. Moldauer, Phys. Rev. 135 (1959) B642