The proton shell closure at 14C

2.B : 2.G

Nuclear Physics A324 (1979) 53-62; © North-Holland Publlahing Co., Amsterdam Not to be reproduced by photoprint or mictoSlm without written permission from the publisher

THE PROTON SHELL CLOSURE AT "C f R. R. SERCELY, R. J. PETERSON and P. A. SMITH

Nuclear Physics Laboratory, University of Colorado, Boulder, CO 80309 and E. R. FLYNN

Los Alamos Scientifrc Laboratory, Los Alamos, NM 87553 Received 26 June 1978 (Revised 12 March 1979) Abstract : Data for the "C( 3 He, d)'sN and "C(t, `He)' 3H reactions arecompared to DWBA calculations to measure the spectroscopic factors for p,iZ and p3î2 proton transitions. Crood fits are found for the stripping data, as well as to similar stripping data on' 2C. These results lower the previous value forproton p3 ~ 2 hole strength in' `C by a factor of two, indicating that theneutron closure of thep-shell has provided a very good proton closed shell at "C . Stripping results to low-lying positive parity states in "N are interpreted within aNilsson scheme, whichreproduces the experimeptal results, but which requires a large deformation for the s-d orbitals . E

NUCLEAR REACTIONS "C(sHe, d), E = 25 .4 MeV; "C(t, `He), E = 23 .0 MeV; measured a(B), "N, ' 3N deduced spectroscopic factors, goodness of proton shell closure.

1. Introdactioo The large deformation found for t2C requires an extensive admixture of the p~ and p~ single-nucleon orbitals . Since t4C, with a closed neutron p-shell, is observed not to have a large deformation t), it is reasonable to investigate whether the p-shell proton orbitals are mixed in this nucleus as they are in ' ZC. This question is best answered by the study of single-proton transfer reactions on a t4C target . A previous z) (3He, d) stripping study on t ~C suffered from a low-beam energy and lacked an absolute normalization . The angular distribution for the weak ~- state lacked data points and was not fit well enough by DWBA calculations to provideconfidence in the spectroscopic factor which is to be used to determine the shell closure. The (d, 3He) proton pickup reaction on t4C has limited utility for determining the p~F spectroscopic factor because no states of spin ~- presently are known in t 3B [refs . 3,4)] . The only such proton pickup reaction that has been studied to that nucleus suffered from poor resolution s). t

Supported in part by the US Department of Energy . 53

R . R . SERCELY et al.

S4

We have remeasured the ' 4C( 3 He, d)'SN spectroscopic factor to the ~- state with a higher beam energy, better statistics and a better DWBA analysis. In addition, the (t, 4He) proton pickup reaction has been studied, populating two known candidates for ~- states in 13 B, although no new information on the spins of these states is obtained. The result of these examinations is a more definitive statement on the closure of the proton p~ subshell in '°C than was previously possible. This experimental ' 4C proton wave function may be applied to the study ofthe structure of levels studied by other reactions using'"C as a target, for instance testing models for' 60 by the 14C(3He, n) 160 reaction 6). Z. The éxperiment and DWBA analysis

The t4 C target used was about 15 pg/~z thick, mounted on a 1 mg/cmZ gold foil . This target has been previously used in reaction studies ' " '), and the target thickness which determines the overall normalization is known to ± 15 ~. The

14

z

~~

3 He,d)

10 deg .

400

0 U H O

100

900

CHANNEL NUMBER

100

- 6400 N

Z v H 0

15 N

1600

N

n âV >

~

_ ~

w

A

N

M

N

v~ 5 e"

= m

±

N

,Nd

si

J ~i

400 I

-

I

IL Ia. .

900 10 0 Fig . 1 . Two portions of a spectrum for the ( 3He, d) ieaction on' 4C. The lmown states of "N are noted.

(3He, d) stripping reaction was performed at a beam energy of 25.4 MeV, low enough to avoid generating many reaction deuterons from the gold backing. The 3 He beam was obtained from the University of Colorado AVF cyclotron, and the reaction was studied with the "beam-swinger" spectrometer system 8), with data taken at angles as small as zero degrees. At small angles, no charge collection was possible for the beam, and the current was estimated by catching some beam on upstream slits, and assuming that the ratio of this beam to the beam on target was constant over runs of a few minutes duration . This ratio was observed not to vary over 5 ~ for periods of hours for runs at larger angles . The energy resolution for bound final states was found to be 35 keV (FWHM) for the 1°C target on its gold backing and 20 keV for a free-standing 1Z C target . The absolute cross sections for the 12 C target are in agreement with those measured at a beam energy of 24.68±0.15 MeV [ref. 9)] . Fig. 1 shows a sample of the data for 1S N; higher lying regions of the spectrum were not investigated since an earlier study of the iaC(d, n) 15 N reaction indicates almost no l = 1 spectroscopic strength beyond 7 MeV [refs. to. i 1)] . The important transition is that to the ~- state at 6.32 MeV, which should have zero cross section if the p t proton shell is filled for the target. The (t, a) data were taken with a 23 .00 MeV triton beam from the Los Alamos Scientific Laboratory three-stage accelerator and the same 14C target . A resolution of 20 keV (FWHM) was obtained, but the large kinematic effects across the acceptance angle of the Q3D spectrometer 12 ) yielded strongly skewed peak shapes, as only the quadrupole element of the kinematic correcting multipole was used in T~ 1

Optical model parameters used for the DWBA prodictions of figs . 2, 3 and 4 3

V (MeV) rR (fm) ae (fm) W (MeV) (fm) r, a (fm) aw, (MeV) r, (fm) a, (fm) V,,,, (MeV) r,,°, (fm) a,,°. (fm) r° (fm) .i fI'homas) ß (nonlocal)

He')

t b)

-154 .7 1 .20 0.72 -39.6 1 .40 0.88 o

-151 .9 1.24 0.665 -28.05 1 .24 0.64 0

-10 1 .20 0.72 1.13

0

0

Bound p 1 .15 0.55

1 .13 25 0

'He °)

d °)

-217 1 .30 0.58 -28.0 1.5 0.32

1.3

-87.4 1.15 0.79 -4 .41 1 .33 0 .612 54 .a 1 .33 0.612 -13 0.98 1 .00 1 .50

0.2

0

Finite range lengths of 0.77 fm and 2.0 fm were includod for the transfer interaction for the (3He, d) and (t, a) reactions. ~ Ref. ls). °) Ref. i~). °) Ref. i6) . 7 Ref. i3) .

56

R. R. SERCELY et al.

an attempt to keep the energy calibration valid for several targets. It was thus not possible to separate cleanly the four small states of 13B near 3 .5 MeV. Two of these are possible candidates for a ~- hole states s " a " i s). The data indicate that none of the four states has (t, a) cross section at any angle ever exceeding 4 ~ of the yield to the ~- ground state. The DWBA analysis of the (3 He, d) data on both 1 ZC and 14C was performed with the computer code DWUCK 14) using 3He optical model parameters obtained by fits to elastic scattering data 1 s) and deuteron parameters from a global analysis of elastic data i b). These parameters are listed in table 1 . A (mite range parameter of0.77 fm was used for the pickup interaction. The only data from the (t, a) reaction analyzed in detail are for the ground state. The triton optical model parameters were obtained by refitting "data" obtained from an optical model calculation using the parameters given in ref. "). This was done to reduce the large difference between the values of rR in the triton and 4He optical potentials (taken from ref. ia)) so as to provide better "well matching ." The geometry for the binding well of the transferred proton was taken from electron scattering results i9) on light nuclei . If the diffuseness parameter is allowed to increase to 0.70 fm, as used in the distorting potential, the predicted pt cross section to the 15N ground state increased by 50 %, so that the extracted spectroscopic factor drops by a factor of 1 .5. An earlier examination z°) of the sensitivity of the spectroscopic factors to the optical model parameters chosen to distort the initial and final wave functions found a range of nearly a factor oftwo for the ground state of 13 N. These sensitivities form a warning that the correct absolute values for spectroscopic factors cannot be obtained . In addition, unbound final states were treated as being just barely bound in the DWBA analysis, which is guaranteed to overestimate the spectroscopic factors for several levels in ' 3N. The stripping DWBA predictions and data were compared by the expression 14) : d~

(data) = 4.42CZS ~ (DWBA)

(3He, d),

where S is the spectroscopic factor and CZ is the isospin factor, equal to unity for izC and for'4C. The limit for stripping into a totally empty shell is unity with this 3 normalization. The (t, a) data were compared to the DWBA predictions by'°) d~l

(data) _ ~+ 1 ~(DWBA)

(t, a)

In this normalization, the spectroscopic factor for pickup from a full shell is 2j+ 1, withj the total angular momentum of the transferred proton .

3. Negative parity states The proton stripping data and DWBA predictions to known a) ~- and ~- states of 3N and t SN are shown in fig. 2. Very good fits to the ~- ground states are found, while that to the ~ - state of ' SN shows some deviation from the large angle data.

la w a °1

E

a01

0

10 20 30 40 50 60 70

Fig. 2. Data and DWBA predictions for negative parity excitations in ' 3 N and ' 3N are compared . The }+ and }- states of "N cannot be resolved. T~sr e 2 Spectroscopic factors measured in the present work to known states of "N and 'sN compared, after renormalization, to the Nilsson predictions for ß = -0 .3 (ß = -0 .1 for negative parity states in "N) Excitation

J'

S~

Renormalized') S

States of "N 0 5.276 5.299 6.323 7.155 7.301

}}+ }+ }}+ ~}+

2.76 1 .3 0.70 0.10 0.047 0.012

0.97 0.45 0.25 0.03 0.017 0.0042

States of 0 2.365 3.511 3.547

}}+ }}+

0.81 0.23 (0.69) (1 .76)

"N

b

)

Previous work

1 .65 0.9 0.58 0.3 0.13 0.18 `)

0.70-1.25 0.25

} 0 .16

Predictions for S Nilsson ")

shell model °)

0.90 0.33 0.60 0.05 0.12 0.023

0.83

0.60 0.60 0.20 0.33

0.61

0.08

weak coupling ~)

0.59 0.19 0 0

0.19

') The renormalization factor is computed by demanding that the sum of all 1 = 1 proton stripping spectroscopic factors to "N be unity. °) Rd ~~ . b) Rd.'s. °) See text . °) Rd. _'). ~) Rd 2').

R. R. SERCELY et aJ.

58

The first ~- state of t 3 N is not resolved from the ~+ state, since both unbound states are about 50 keV wide . The data are fit by a sum of 1 = 1 and 1= 2 curves as shown separately by the broken curves and together as the solid curve. These two shapes are quite similar, and reliable measurements of either spectroscopic factor are not possible . The values extracted for the spectroscopic factors S are listed in table 2. The isospin factor is removed to provide a clear comparison of the results for the two targets. The spectroscopic factors in table 2 for ' sN are found tQ be too large, since the sum of all ~- and ~- strength should be unity. A column is also listed in table 2 containing spectroscopic factors renormalized to reach this proper sum . The spectroscopic factors for the ~- and ~- states are compared to the results of other experiments in table 2. The present result for the ground state of t 3 N is within the range previously reported from the ( 3He, d) reaction Z ~, but the spectroscopic factor for the lowest unbound ~- state is exaggerated, as expected from the treatment of the transferred proton wave functions to,zo) . The renotmalized proton spectroscopic factors for t sN are comparable to those derived from the (d, n) reaction' ° ) for the lower states, but are much weaker than those previously claimed for the higher excited states . This indicates a greater contribution from nondirect processes for the low energy (d, n) reaction . Predicted spectroscopic factors for the 1 = 1 transitions were listed by Cohen and Kurath Zt ) ; these are compared to the data in table 2. The weak coupling predictions zz) do not permit a simple prediction for the l = 1 stripping strengths. The (t, 4 He) data to the ~- ground state of t3 B are shown in fig. 3. The DWBA prediction doés not fit these data well, but the spectroscopic factor extracted is S(~) = 5.7, near that expected for a filled p} shell. The limit for the p~r spectroscopic

v a E

b v

10

20

30

40

50

60

Fig . 3 . The proton pickup reaction' 4C(t, a)l'B provides the data shown for the }- ground state of' 3 B. Higher excited states are very weakly populated. The solid curve is a DWBA prediction, using the parameters listed in table 1 .

factor (to either of the known negative parity states 3 " °) near 3 .5 MeV) is S(~) = 0.05, and would be zero if, in fact, neither has a spin of -}- . Even if one does have the proper spin, the spectroscopic factor is probably an overestimate, since the cross sections are as small as those to the positive parity states, and it is likely that multistep processes are important. These results are interpreted as confirming the general features noted from the ' 4C( 3 He, d) data, namely that the p~ proton shell is quite full and the p~ proton shell quite empty for the t4C target. 4. The positive parity states Prominent proton stripping should be found for the s-d shell, as it is completely empty above either target in the simple model followed in this analysis . Data for several known s) Z+, Z+ and Z+ states of 'sN are compared to DWBA predictions in fig. 4. A known a) ~+ state at 7.567 MeV in ' SN was excited only very weakly,

E

b v

Fig. 4. Data and DWBA predictions for known positive parity states of ' 3N and ' °N are compared . The small angle data provide a good measure of the ! = 0 component for the unresolved doûblet in "N .

which confirms the small role of multistep processes on the t4 C target for the ( 3 He, d) reaction . Quite a large spectroscopic factor for this ~+ state is quoted from the (d, n) work ' °), emphasizing again the non-direct nature of that reaction at such a low energy . The spectroscopic factors for the present data are listed in table 2, also renormalized in the case of t4 C. Data for the ~+ excited state of t 3N are also shown. The fits are good, even for this unbound state. The weak coupling scheme ss) permits a calculation of the 1 = 0 and 1 = 2

60

R. R. SERCELY et al.

stripping spectroscopic factors when laC is considered to be formed by two 1p holes in 160. These results are listed in table 2, and found to be in good. agreement with the data. The spectroscopic factor for the 1sN -~+ state was computed for a bound proton, but nonetheless compares well with the result obtained when the proper unbound nature of the state is used 2 °). Although an extreme sensitivity to the wave function of the transferred proton is expected 11) because this -~+ is unbound by only 421 keV [ref. a)]. The comparison to the proper calculation is more striking for the ~+ state, where the present result even exceeds the sum rule limit . A convenient context in which to compare the stripping data for even and odd parity states in laN and 1sN is found in the Nilsson scheme z<-ae) , It is known that 1ZC is strongly deformed, and the single proton structure above laC would also reflect any deformation of this core . For negative deformations the lowest ~+ state is the K = ~+ [202] band head, and a band built on the K = ~ + [220] orbit will be found above this . The spectroscopic factors are predicted 26) to be [2/(2j+ 1)] ~c~~ 2 , where the coefficients c~ are the single particle components of good j in the deformed nucleon wave function . These are tabulated in ref. zs) . Since the proper sum rule is not found for our spectroscopic factors, these have been renormalized in table 2 so as to obtain a unit sum of l = 1 strengths to 1 SN. The sixth column shows the predicted spectroscopic factors for positive parity states at ß = -0.3 . The comparison of relative spectroscopic factors and excitation energies is improved by going to yet more negative deformations so as to allow the decoupling parameter to invert the order of the ~-+ and ~+[220] states, but this shift of the ~+ state is also affected by rotational-particle coupling with the higher ~+ state. It is worth noting that the sum of the two observed ~-+ spectroscopic factors is very near that of the two predicted values . The predicted spectroscopic factor for the [211] K = ~+ band head is an order of magnitude larger than that for the [220] K = ~} ~+ band member. Since the observed result is. even weaker than the weaker prediction, the [211] K = ~+ band head must lie higher. The same predictions are also applied to the first few l aN states in table 2. The agreement is about as found for 1 sN, and the yield to the -}+ state indicates a similar deformation. These results imply a similar deformation near ß = -0.3 for the positive parity states of laN and 1 sN. The spectroscopic factors also agree with the weak coupling predictions z3), but this congruence is built into the coexistence model for 160 [ref. z')] . S. The p! shell dosore The p~ proton stripping strength to 1 sN is much less than that observed for the }- ground state. This result is consistent with the very weak pickup to any candidate for a }- state in 13B . It is not feasible to use the present stripping results for a similar comparison for the 1zC target, since the relevant ~- state of 1sN is both unbound and unresolved . The ratio of strengths for the p~ and p} stripping on laC is a factor

of two smaller than the limit set by ref. Z ), and thus in better agreement with the prediction listed in table 4 of that work. The sum rule analysis for occupation numbers Z1), using the renormalized spectroscopic factors for 14C from table 2, can be used for the p~ orbitals for both targets. This provides
62

R. R. SERCELY et al.

13) R. Middleton and D. J. Pollen, Nucl . Phys. 51 (1964) 50 14) P. D. Kunz, DWUCK (unpublished) 15) J. L. Duggan, J. Y. Park, S. D. Danielopoulos, R. D. Miller, J. Lin, M. M. Duncan and R. L. Dangle, Nucl . Phys. A151(1970) 107 16) C. M. Perey and F. G. Perey, Nucl . Data Tables 10 (1972) 539 17) F. Hinterberger,G. Meule, U. Schmidt-Rohr, P.Turek and G. J. Wagner, Nucl . Phys . A106 (1968)161 18) P. Gaillard, R. Bouché, L. Feubrais, M. Gaillard, A. Guichard, M. Gusakow, J. L. Leonhardt andJ. R. Piztie, Nucl . Phys . A131 (1969) 353 19) C. W. de Jager, H. de Vries aad C. de Vries, Atomic Data and Nucl . Data Tables 14 (1974) 479 20) H. T. Fortune, T. J. Gray, W. Frost and N. R. Fletcher, Phys. Rev. 179 (1969) 1033 21) S. Cohen and D. Kurath, Nucl . Phys . A101 (1967) 1 22) S. Lie and T. Engaand, Nucl . Phys . A169 (1971) 617 23) S. Lie, T. England and G. Dahll, Nucl . Phys . A156 (1970) 449 24) S. G. Nilsson, Mat. Fys. Medd . Dan. Vid. Selsk. 29 (1955) no. 16 25) J. P. Davidson, Collective models of the nucleus (Academic Press, NY, 1968) 26) G. R. Satchler, Ann. of Phys. 3 (1958) 275 27) A. P. Shukla and G. E. Brown, Nucl. Phys . 51 (1964) 50