A study of the level structure of 20Ne from the (3He, d) reaction on 19F

2.G

l

NuclearPhysics A267 (1976) 205-216; (~) North-HollandPublishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

A STUDY OF THE LEVEL STRUCTURE OF 2°Ne F R O M THE (3He, d) REACTION ON 19F H. M. SEN GUPTA t T. A. BELOTE and D. ROAF

Nuclear Physics Laboratory, University of OxJbrd, Oxford Received 5 April 1976 Abstract: The ~9F(3He, d) reaction has been studied at E3Hc = 16 MeV and angular distributions have been measured for several levels up to E. ~ ! 1 MeV. The data were analyzed in terms of the DWBA and CCBA calculations and spectroscopic factors were obtained. Results are compared with previous (3He, d) experiments, as well as the theoretical predictions.

E I

NUCLEAR REACTION ~gF(3He, d), E = 16 MeV; measured a(Ed, 0). 2°Nelevels deduced

C2S.

I

]

I

1. Introduction A considerable amount of effort has been expended in studying the level structure of 2°Ne, as summarized by Ajzenberg-Selove ~). The theoretical investigations have been carried out in terms of the Nilsson model and SU(3) classification of the nuclear shell model. The experimental information has been derived from (d, n), (3He, ~), (d, t), (3He, d), (p, t), heavy ion reactions, etc. The (3He, d) reaction is one of the most useful means of extracting spectroscopic information on the levels of 2°Ne. Such a reaction is in general expected to proceed through a direct stripping process. But the large deformation of 2°Ne certainly calls for the inclusion of inelastic effect in particle transfer reaction in particular for the so-called '~]-forbidden" transitions. In a previous paper on the ~gF(3He, d) reaction 2) (henceforth to be referred to as paper I), the importance of such a second order process was studied for the lowest three members of the ground-state rotational band ( K ~ = 0+~ and it was thus possible to account for the observed structureless angular distribution for the 4.25 MeV level ( j r = 4+). Other (3He, d) experiments on 19F are due to Siemssen et al. 3) at 10 MeV, Obst and Kemper 4) at 21-23 MeV and Betts et al. 5) at 18 MeV. There appears some discrepancies between the last two measurements in that some levels observed in one are not observed in the other. As~an example, we quote the unresolved doublet 9.95 and 9.99 MeV l-ref. 4)] and the 9.86 MeV level of ref. 5). It is not clear whether the same level has been differently labelled, although the difference in excitation is beyond experimental error. t Permanent address: Department of Physics, University of Dacca, Dacca, Bangladesh. 205 Aullust 1976

206

H . M . SEN GUPTA et al.

The present work is a continuation of paper I and is concerned with higher excited levels in 2°Ne (Ex > 4.25 MeV). All the levels that are missing in one or the other of refs. 4.5) are found in the present work. Angular distributions have been measured for levels up to E~ ~ 11 MeV and the results have been analyzed in terms of the DWBA and CCBA models.

2. Experimental procedure The experiment was carried out with a beam of 16.0 MeV 3He particles from the tandem Van de Graaff accelerator of the University of Oxford, Oxford. The target was CaF2 deposited on to a thin carbon foil. The scattered particles were momentum analyzed in a multigap magnetic spectrograph and detected in Ilford L4 emulsion 25 #m thick. Data were extracted from the same set of exposures as paper I and the experimental procedure has been detailed there.

3. Results and discussion 3.1. EXPERIMENTAL DATA

A typical spectrum of deuteron at 30°(lab) is shown in fig. 1. As the energy levels in 20 Ne are fairly well established, no attempt was made in the present work to obtain them and we have taken those from the compilation of Ajzenberg-Selove a) except for the 9.86 MeV level; this is not included in the compilation, but has been observed in a recent tgF(3He, d) work 5). Angular distributions were obtained for most of the levels in fig. 1 up to E x ~ 11 MeV; for those marked A in table 3, cross-section data could be obtained at a few angles only and were not considered suitable for theoretical analyses. A broad level at ,~ 8.3 MeV was found by Betts e t al. 5) with F ~ 800 keV, which is the same as the level ~ 8.6 MeV of Ajzenberg-Selove 1). Such a broad group could be hidden in the background, which could include other broad levels ofref. 1). In addition several levels (all known ~)) are seen on a background, which increases with increasing excitation. 3.2. DWBA AND CCBA ANALYSES

The DWBA calculations were performed using the code DWUCK of Kunz. The parameters of the optical model potentials are the same as in paper I and are reproduced in table 1 ; only spherical potentials were used for the DWBA calculations. The entrance channel parameters were fixed from the 3He-agF elastic scattering data at 16 MeV (paper I), while those of the exit channel are from Hinterberger e t al. 6), again used in paper I. The bound state wave functions were obtained by allowing the proton to be moving in a Woods-Saxon well of r v = 1.25 fm, av = 0.65 fm and

19F(3He, d)2°Ne

207

u~

.",,%.

0

r.

r~

.....

:; LU

7 v)

~"

~~ _ ~ . : ~ ~...,.,.. - . - = . - - , _ -.::'. ".,....

~

._.,.~L_.~.~.._..~

~

:"

. .:". ..'~ '. ,.

•

".'77........ ~ .

e

"----

,..,... -

.

'--~--'~

~.--v 2

-

I

w m SL'O ~13d $)13Y'~11

208

H . M . SEN GUPTA

et al.

2 = 25 with (real) depth adjusted to reproduce the observed binding energies. Local zero range (LZR) calculations were performed for both the potentials A and D for 3He (table 1) having respectively the volume and surface absorption form factor. The non-local finite range (NLFR) effects in the local energy approximation 7) were however considered (arbitrarily) for potential A using the nonlocality ranges /3~I~c = 0.2 fm, /3d = 0.54 fm and /~p = 0.85 fm and finite range parameter of 0.770 fm. TABLE 1

Parameters of the optical model potentials V

rV

(MeV) (fro)

3He+19F d+2°Ne bound state 3He+lgF

153.1 76.4 a) 149.0

1.25 1.25 1.25 1.25

av

W

W'

rw

(fm) (MeV)(MeV) (fro)

0.689 0.745 0.650 0.713

21.9 9.66 20.6

aw

V~.o.

r ....

(fm) (MeV)(fm)

a ....

1.31 0.925 1.25 0.716

5.3 1 . 1 2 0.689 6.0 1.25 0.745 ~=25 1.05 0.808 5.3 1.13 0.713

(fro)

Parameter set

1.4 1.3 1.2 1.4

A B C D

~2

(fro)

r¢

0.3 0.40 0.3

W and W' refer to volume and surface absorption respectively. *) A.djusted to reproduce the measured separation energy. TABLE 2

Spectroscopic factor for the first excited K" = 0 + band from CCBA calculations (2J+ 1)C2S

Excitation (MeV)

J~

pot A 6.722 7.422 9.99

0+ 2+ 4+

0.39 0.39 0.032

pot D 0.38 0.39 0.037

The CCBA calculations were carried out in the zero range approximation using the code CHUCK of Kunz. The spectroscopic amplitudes of Obst and Kemper 4) based on the Nilsson model were used and the three lowest members of a rotational band in both entrance and exit channels were explicitly coupled through inelastic excitation, all allowed transitions between any two levels being taken as shown in fig. 9 of ref. 4). To start with, the coupled channel calculations were'carried out for the K ~ = 0 + band, (6.722 MeV as band head) using both the 3He potentials A and D (table 1) and the spectroscopic factors obtained were as shown in table 2. The reason for the choice of the band was that two members, namely 6.722 and 7.424 MeV, are strongly excited in the (3He, d) reaction and the experimental data are thus most accurate and the third member (9.99 MeV) is a "j-forbidden" transition. The result is rather insensitive to the choice of potential and we arbitrarily selected the 3He

tgF(3He, d)2°Ne

209

TABLE 3 S u m m a r y of ~gF(3He, d) reaction Excitation (MeV)

(2J+

2" ~) 0 1.634 4.247 4.968 5.622 5.785 6.722 7.006 7.17 7.20 7.424 7.834 8.447 8.6 c) 8.72 8.775 8.850 9.04 9.12 9.34 9.489 9.859 ~) 9.95 9.99 10.26

nO"")

b) 0 1.63 4.25 4.96 5.62 5.78 6.72 7.00 7.16

b)

1 b)

II b)

ns (0.03) (0.09) 0.16 0.52

0.79 0.06

2sit z lds/2 ns 1p3/2 1f7/2 2p3~ 2sl/2 1f7/2 lfT<2

0.27 2.17 0.014 0.065 0,080 0.37 0.16 0.43

0.30 1.43 0.08 0.021 0.10 0.10 0.39 0.12 0.12

7.42 7.85 8.48 8.6 8.74 8.80 8.86 9.05 9.13 9.33 9.51 9.86 9.95 10.01 10.26

0+ 2+ 4+ 2310+ 430+ 2+ 2+ 50+ 16+ 14+ 3(1, 2, 3) + 2+ 3+(1, 2) + (1 +) 4+ 2+; T = 1

ld5/2 lds/z ns A ns ns 2p~t2 ns ns ns ns lds~ z ns ns lds/z

0.61 0.081

0.39 0.046

10.40

10.42

3-

A

10.548 10.579 10.836 10.853

10.54 10.58 10.83 10.86

4+ 2+ 2+ (2+); T = 1

A lds/2 A ldsj 2

11.08

11.08

(4 + ; T = 1)

A

III

I)C2S IV d)

V ~)

0.30 2.10 0.0 0.040 0.12 0.13 0.25 0.081

0.43 1.90 0.0 0.040 0.028 0.12 0.22 0.11

0.60 0.06

0.60 0.045

0.42

0.13 ns (0.01)

0.014 0.033

0.04 f) 0.03 f) 2.37

1.62 0.032 0.11

0.07

0.081

0.05 0.05 f) 2.82

1.73

In the table I, III, IV, V denote D W B A local zero range and II denotes CCBA. A denotes that the crosssection data are available over a narrow range o f data. ") Ref. 1). b) Present work. °) Ref. ~). d) Ref. 4). e) See text. f) For Ids/2 transition s). *) Orbital for direct transfer.

potential A for all subsequent CCBA calculations. Since the //4 values are not accurately known (paper I), 1t4 is taken to be zero. The results of the present analyses (DWBA and CCBA) are summarized in table 3; also included for comparison are the (2./+ 1)C2S values from refs. 4, s). The levels

210

SEN G U P T A et al.

H.M.

marked A are the ones for which angular distributions could bc measured at a few angles only, as stated earlier. The remaining angular distributions including levels showing no direct stripping characteristics (designated ns in table 3) are displayed in fig. 2. The DWBA spectroscopic factors for the two 3He potentials are about the same and fits are of similar quality, though in one or two eases the agreement was slightly better for the surface absorption potential. The inclusion of N L F R effects gives spectroscopic factors about 40 % smaller than the LZR cases, the fit being not much 0.1

\,~

Ex = 4. 968

,-

e,,

6.722

0.011

o.,

0.1

',,\ ~/,~

0.01

t|

\/

//

¢~ '~,~

X

Ex : " / . 0 0 6

-/ ~,,,

', ~t~%#sJ" %%'%%

b" Ex = 5.785

0.1

"

'~

\"\

Ex = 7.17 * 7 . 2 0

,]o. •

V

0.01

\ t

s

\,/

l

0.001 0

30

I

60

I

90

\

0%

\ JO.O

120

ecru s (deg) Fig. 2a.

l 30

I 60

I 90

120

19F(3He' d)2ONe

2L1

improved. The present DWBA spectroscopic factors are usually closer to those of Obst and Kemper 4) than to Betts et al. 5) and Siemssen et al. a). A few test runs were taken with the potential pazameters of ref. 5) (including those of bound state) for the levels 6.722, 7.17, 9.86 and 10.86 MeV and the (2J+ 1)C2S values are respectively 0.34, 0.62, 2.18 and 2.35 as against those shown in table 3. The CCBA fits are better than the DWBA ones as expected and the angular distributions to the so-called "j-forbidden" transitions are well accounted for. The spectroscopic factors from CCBA analyses are usually smaller than those of the

,°I 1.0[

Ex = 7.42/,

~

0.1

Ex = 8.72 0

0 0 o

o

0.01

Ex

= 8.78

o

~

.

o

~

0.1

o

o

o 0

0

0

0

0

0

0

~

l

s

Ex = 7.83/-

°"F \

1,0

P-:

0.01

~

~

Z

E~-- 8.8~

0.1 O 0 0

0 0

. / f *',~ o

EX= 8.~7

0.'

o

0.01

~t

o o

o o

0.01 0

0

I

:310

I

o

\

I

I

90

120

0

Ocms(deg )

Fig. 2b,

30

60

go

120

212

H.M. SEN GUPTA et

al.

LZR DWBA analyses, the difference being quite appreciable for the 7.17 and 7.424 MeV levels. Sample DWBA (LZR 3He potential A) calculations were carried out for the 7.424, 7.834, 9.86, 10.26, 10.58 and 10.85 MeV levels for assumed ld~ transitions and (2J+ 1)C2S values are 0.65, 0.087, 1.83, 0.13, 0.093 and 2.03 respectively as against the values 0.61, 0.081, 1.62, 0.11, 0.081 and 1.73 for l d l transition. 3.3. DISCUSSION Several rotational bands have been proposed in 2°Ne [refs. 8,9)-1, of which the ones with K ~ = 0 ÷, 2-, 0-, 0 ÷, 0 ÷ and 0 ÷ with respective band heads at excitations of 0, 4.968, 5.785, 6.722, 7.20 and 8.6 MeV are well established below excitations of 0.1

0.11

0

0

0

0

0

Ex = 9.49 o

g

[).01~-

0.01

0.1 Ex

0 0

0

1i ~

= 9.12

Ex = 9 . 8 7

0 0

JD A

-~

°l

0 0

0.01

1.0t

o

Ex = 9.3/,

0.1t

o

o

o G

o

o

o

Ex = g . 9 5 o O

O O

O O

,4 0.01

0.001 0

0.11

J

t

30

60

1 90

120

).Off 0

Ocms ( deg )

Fig. 2c.

Ex = 9 . g 9

30

60

90

120

~9F(aHe, d)2°Ne

213

10 MeV. The spectroscopic factors from different theoretical calculations 3,4, 9, 10), are shown in table 4 for a comparison with those of the relevant levels from (3He, d) reaction [present work and refs. 3-5)]. The first three members of the ground-state rotational band (K ~ = 0 ÷) were studied at length in paper I. For the sake of completeness a reanalysis was done with transition amplitudes of Obst and Kemper ~) as for all other levels in the present work. The spectroscopic factor for the ground-state transition, in agreement with refs. 3, ~), is smaller than the collective model and shell-model values. Those for the 1.63 MeV are in excellent agreement with one another being much less than the experimental results of ref. ~). The fourth member of the band, the 8.78 MeV level (J* = 6÷), has a structureless angular distribution (fig. 2). There is no direct transition from ground state, nor a transition from the entrance channels considered in the 1.0 o

Ex = 10.26

%

o~ o

0.1

o

I

o

o

0

1.(

a~ Ex = 1 0 . 5 8

%

E 0.

I

b"-E u

0

0 %%

,, ¢t

Ex = 10. 853

Xo t

1.0

o

o

9

0.! 0

30

50

0

120

ecrns (dcg I Fig. 2d. Fig. 2. Measured angular distributions to levels in 2°Ne as shown with a comparison to theoretical analyses. The solid line is from CCBA analysis and the broken line is from DWBA analysis using potential parameters of table ! (3He potential A was used).

H. M. SEN G U P T A et al.

214

TABLE 4

Comparison of spectroscopic factors between experiment and theory Excitation (MeV) ") 0 1.634 4.247 4.968

b)

5.785 6.722 7,006 7.17

0+ 2+ 4+ 2310+ 43-

7.20

0+

7.424 7.834 8.72

2+ 2+ 1-

5.622

( 2 J + 1)C2S

j~

0.27 2.17

c)

0.014 0.065 0.080 0.37 0.16 0.43

0.30 1.43 0.08 0.021 0.10 0.10 0.39 0.12 0.12

0.61 0.081

0.39 0.046

~)

(0.03) (0.09) 0.16 0.52

~)

f)

0.30 2.10 0.0

0.43 1.90 0.0

0.040

0.040 0.028

0.12 0.13 0.25 0.08

0.12 0.22 0.11

0.60 0.06

0.60 0.045

0.42

~)

,)

j)

i)

k)

0.31 3,15 =< 1,8

0.59 1.40

0.65

0.41 1.60

0.86 2.36

0,0

0.0

0.0

<= 0,05

0,15 0,014 0.57 0,26 0,009 0,42 0.27 0.75 0.75

0.0

0.0

0.0

0.0

_< 0.28 0,15 0,47

__<0.23 =< 0.64 < 0,027

0.79 0.06

~) Ref. 1). b) D W B A (present work). e) D W B A [ref. 4)]. f) CCBA [ref. 4)]. ~) Shell model 9). J) Nilsson model 3).

0.80

2.25

0,40

0,00 0.50 0.00 0.15

0.24 0.22 0.0 0.77 0.0 0.75

0.19 0.34

0.0 0.20 0.0 0.07

c) CCBA (present work), d) D W B A [ref. 5)]. s) D W B A [ref. a)]. h) Collective model 4). k) Shell model SU(3) [ref. 10)].

sd shell and one needs the ~+ and ~+ 2 members of the 19F ground-state band (K ~ = ½+) to reach this level. This has not been done in the present work. The K ~ = 2- band with the 4.968 MeV level as the band head is assumed to be 5p-lh. The levels are weakly populated in (3He, d) reaction, as against the strong excitation of the 4.968 MeV level in pickup reactions 11-13), thus supporting the presence of a hole. The 7.006 MeV member (J~ = 4-) of the band was observed in ref. 4) and in present work and the angular distribution is fairly well given by the CCBA analysis. The 8.45 MeV level (J~ = 5-) has a non-stripping angular distribution, while the still higher member 10.609 MeV level (J" = 6-) has not been observed in any (3He, d) work. The next band is the K ~ = 0- band with the 5.785 MeV level as the band head. The observed small strength of the 5.785 MeV level compared to the prediction of the collective model has been explained by Obst and Kemper 4) by considering the fact that too much weight is put on the p-shell contribution, whereas the transition is mostly into the If t shell. The small CCBA spectroscopic factor for the 7.17 MeV, J~ = 3- level compared to that of DWBA calculations can be accounted for in a similar way; the DWBA assumes a direct 1fi transition to this level, as against the 2p transition for the 5.785 MeV level. The 10.257 MeV level (J" = 5-) if excited is not resolved from the 10.26 MeV level (J" = 2 +, T = 1). All three members of the first excited K ~ = 0 + band are excited in the present experiment. The angular distributions are fairly well reproduced by theory. The 9.99 MeV level (J" = 4 +) with no direct stripping angular distributions is well

tgF(aHe, d)2°Ne

215

accounted for by the CCBA analysis. The spectroscopic factors for the 6.722 MeV level from the present work and from ref. 4) are close to each other and are in good agreement with the collective model value, whereas those from refs. 3, 5) are larger but nearer to the shell-model prediction. The C 2 S values from CCBA calculations for the 7.424 MeV level given by both the surface and volume absorption 3He potentials are smaller than all the DWBA values. The lowest member of the next higher K s = 0 ÷ band, namely the 7.20 MeV level is probably not excited in any (3He, d) work and the group labelled as the 7.17 and 7.20 MeV doublet has been attributed entirely to the former level from a consideration of the shape of the angular distribution. The angular distribution for the 7.834 MeV member of this band (jR = 2 +) is well reproduced by both DWBA and CCBA theory, but the spectroscopic factor is an order of magnitude smaller than the collective model value; the shell model on the other hand predicts a vanishingly small C2S value. The "j-forbidden" 9.04 MeV level (J" = 4 ÷) is again well accounted for by the coupled channels analysis. There is no clear indication in the present experiment for the excitation of any member of the K s = 0 ÷ band with the 8.6 MeV level as band head. The level is assumed to be broad with F ,~ 800 keV [refs. 1,5)]; we observe a narrow level at the correct excitation and observe several known levels sitting on a large background, as stated earlier. The 10.548 MeV level belonging to this band is significant only at a few angles. Finally, about a possible K s = 1- band. Such a band is predicted from Nilsson model by coupling a 2!-[101] hole to a 2~+[202] particle, as is the K s = 2- band (with 4.968 MeV as the band head). From 21Ne(d, t) work 13) the levels 8.850 (8.839), 9.340 (9.357) and 10.401 (10.385) MeV t are considered to be good candidates for this band with J~ = 1-, 2- and 3- respectively. The angular distribution for the 8.850 MeV level in (3He, d) reaction [ref. 5) and present work] is typical of lp = 1 transfer and is consistent with J~ = 1- assignment 1). The 9.34 MeV level is not observed by Obst and Kemper 4). It is an lp = 2 transition according to Betts et al. 5); the present angular distribution is however not typical of any direct transfer reaction. The next level has not been observed by Betts et al. 5) and is just outside the range of excitation in ref. 4). In the present work, cross-section data could be obtained at a few angles only so that no conclusion can be arrived at. Although the assignment of the K s = 1 - band by Millington et al. 13) is based on data over a narrow range of angles, the weak excitation of the levels in (3He, d) reaction nevertheless favour the hole character of the proposed band. 4. Conclusions

Most of the levels excited in one or the other of previous (aHe, d) work are observed in this experiment. No clear evidence is found for the existence of a broad level at t The excitations in parentheses are due to Millington et al. 13).

216

H . M . SEN GUPTA et al.

,~ 8.6 MeV, but we observed several known levels on a rather large background, the background increasing with increasing excitation. The 9.86 MeV level observed by Betts et al. s) but not quoted in ref. 1) is clearly established. Angular distributions are fitted better by the CCBA than the DWBA analyses. The second order process via collective inelastic excitation is quite successful in accounting for the transitions that are forbidden to direct stripping and the CCBA analysis is thus imperative for the deformed nuclei 19F and 2°Ne. The spectroscopic factors obtained in the present work are closer to those of ref. 4) than to those of refs. 3,5). The different theoretical predictions a,,,9, to) do not agree amongst themselves and in some cases the differences are so large that comparison with experiment is not probably meaningful. The authors are indebted to Prof. P. D. Kunz for the DWUCK and CHUCK programmes. They would like to thank Dr. D. Sinclair for helpful discussion and advice in the analyses and Dr, D. J. MiUener for communicating his results before publication. One of the authors (H.M.S.G.) would thank the Royal Society for a grant and the University of Dacca, Dacca for granting leave; he appreciates the hospitality of Profs. Sir Denys Wilkinson and K. W. Allen at Oxford. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

F. Ajzenberg-Selove, Nucl. Phys. A190 (1972) 1 T. Vertse, A. Dudek-Ellis, P. J. Ellis, T. A. Belote and D. Roaf, Nucl. Phys. A223 (1974) 207 R. H. Siemssen, L. L. Lea, Jr., and D. Cline, Phys. Rev. 140 (1965) B1258 A. W. Obst and K. W. Kemper, Phys. Rev. C8 (1973) 1682 R. R. Betts, H. T. Fortune and R. Middleton, Phys. Rev. CII (1975) 19 F. Hinterberger, G. Mairle, U. Schmidt-Rohr, G. J. Wagner and P. Turek, Nucl. Phys. A I I I (1968) 265 K. K. Seth, J. Picard and G. R. Satchler, Nucl. Phys. A140 (1970) 577 N. Marquardt, W. yon Oertzen and R. L. Walter, Phys. Lett. 35B (1971) 37 J. B. McGrory and B. H. Wildenthal, Phys. Rev. C7 (1973) 974 D. J. Millener, private communication (1976) R. R. Betts, H. T. Fortune and R. Middleton, unpublished, quoted in ref. s) D. K. Olsen, T. Udagawa, T. Tamura and R. E. Brown, Phys. Rev. Lett. 29 (1972) 1178 G. F. Millington, J. R. Leslie, W. McLatchie, G. C. Ball, W.G. Davies and J. S. Forster, Nucl. Phys. A228 (1974) 382