Hole states of 20F and 20Ne

I

2-G

I

Nuclear Physics A228 (1974) 382-392; Not to be reproduced

by photoprint

@

North-Holland

or microfilm

without

written

Publishing

Co., Amsterdam

permission

from the publisher

HOLE STATES OF ‘OF AND “Ne G. F. MILLINGTON, Department

of Physics,

J. R. LESLIE

and

Queen’s University,

W. McLATCHIE

Kingston,

Ontario,

Canada

and G. C. BALL,

W. G. DAVIES

Chalk River Nuclear Laboratories, Chalk River, Received

and

Atomic Ontario, 3 May

J. S. FORSTER

Energy of Canada Limited, Canada 1974

Abstract: The structure of the low-lying states of ‘OF has been investigated with the reaction ZINe(d, 3He)ZoF induced by 26 MeV deuterons. Spins, parity assignments and spectroscopic factors for the populated states are compared with the predictions of the Nilsson model and recent shell-model and projected Hartree-Fock calculations. The reaction ‘lNe(d, t)ZoNe, of the studied simultaneously, excites strongly the T = 1 states in Z”Ne which are analogues low-lying states of ‘OF. The spectroscopic factors of parent and analogue are consistent to within 20 % for states excited by a single Z-transfer.

E

NUCLEAR REACTIONS ZINe(d, 3He), E = 26 MeV, measured (T(E~“~, 0). 20F deduced levels, I,, P, spectroscopic factors. Enriched ZINe target. ZINe(d, t), E = 26 MeV, measured o(E,, 0). “‘Ne deduced levels I,, Jr, spectroscopic factors. Enriched “Ne target.

1. Introduction Although experimental studies of ‘OF were first reported two decades ago ‘) surprisingly little spectroscopic information was available until recent theoretical calculations “-“) renewed interest in this nucleus. Existing information for 20F, recently summarized by Ajzenberg-Selove 6), shows that among the states below 2 MeV of excitation there is only one candidate for a negative-parity state, that at 1824 keV. On the other hand two recent and rather different calculations 4, ‘) predict the existence of four negative-parity states in this energy region. The calculation of Johnstone et al. “) describes the low-lying negative-parity states of 20F as lp3 and Ip,. proton holes coupled to the model states of “Ne and suggests the possible utility of the proton pick-up reaction “Ne(d, 3He)20F for exciting such states. The present paper reports the I-values and spectroscopic factors obtained in such a study and compares them with theoretical predictions where available. Since the present work was begun, determinations of the linear polarization of of .7” = 1- and 2- to the states at transition y-rays in 20F have given assignments 984 keV and 1309 keV, respectively 7*8). Ref. “) suggests J” = 5+ for the state at 1824 keV. 382

*OF AND “Ne

383

2. Experimental

Neon gas isotopically enriched to 91.5 % in ‘INe was contained in the gas cell shown in fig. 1. The cell is constructed of aluminum with 2.5 [trn Havar windows on the beam entrance and exit ports and 3.8 pm aluminized mylar windows on the sides. The end posts were constructed to prevent the beam from striking the epoxy adhesive holding the windows in place.

-

ORTEC

SCATTERING

_ GAS __ _..ICELL _-.. -

-

CHAMBER

Fig. I. Schematic of the scattering chamber, gas cell, and detection system.

AE

Centreof forget cell

E

E

~“~~~~~ h2 THE

= height of second cotlimater

DIMENSIONS

OF

THE

DETECTOR

TELESCOPES

Fig. 2. Detailed view of detection system.

Reactions in the gas were induced by a beam of 26 MeV deuterons from the upgraded Chalk River MP tandem accelerator. Reaction products were detected in solid-state counter telescopes of dimensions shown in fig. 2 and mass identified by a computer code written for the on-line PDF-l computer “).

384

G. F. MILLINGTON

er al.

The 3He and triton spectra from one of the detector telescopes at Qlab= 16” are shown in fig. 3.

Ed

-26

HeV

‘lab. = 16”

1000

800 Channel

I200

0

no.

*‘Ne(d.r)*%!e

200

0 600

Channel

no.

800

1000

Fig. 3. Triton and 3He spectra at etzb = 16” overlaid to illustrate states excited in 2cNe and 20F.

1200

the correspondence

between

3. Analysis 3.1. ANGULAR

DISTRIBUTIONS

A Gaussian fitting routine was used to extract peak centroids and areas. The energy calibration of the spectra was based upon the peaks corresponding to states “) at 655.9540.15 keV and 1309.22+0.16 keV in 20F for the 3He spectra and states “) at 5621.7&2 keV, 742424 keV and the lowest T = 1 state lo) at 1027113 keV in “Ne for the triton spectra. Excitation energies in 20F were determined to within t_ 10 keV and in all cases the states were identified with known levels. In the case of “Ne, level energies for strong transitions were also determined to + 10 keV. 3.2. DWBA CALCULATIONS

Distorted wave Born approximation (DWBA) calculations were carried out with the code of Nelson and Macefield ‘I). The opticaI-model parameters used for the

‘OF AND

385

*“Ne

incident deuterons were those of Satchler for 26 MeV deuterons on 24Mg, reported in the compilation of Hodgson “). The triton and 3He parameters were assumed to parameters are shown be the same and were taken from ref. 13). The optical-model in table 1. Calculations were done in the local finite-range (LFR) approximation with the interaction range set equal to 1.25 fm. TABLE 1 The DWBA

parameters

used in the analysis of the 21Ne(d, 3He)ZoF and ZINe(d, t)ZoNe reactions

V

(MeV)

(t!L)

(fz)

“)

93.6

1.0

0.9

b,

144.06

1.55

0.51

*OF

1.2

0.65

n +20Ne

1.2

0.65

dSZINe 3He+ZoF

W (MeV)

25.92

V

WD (MeV)

(Lz)

(Fi)

(fz)

27.6

1.436

0.5

1.3

1.2

1.4

1.4

(M$

$ij

(zj

6.4

1.2

0.65

6.4

1.2

0.65

t +“Ne PTI

“) Ref. lz).

1.3

b, Ref. 13).

The experimental angular tions to extract spectroscopic

distributions information

were compared with the DWBA by use of the relation

calcula-

do

(6)

dR exp

DWBA ’

is the calculated differential where S is the spectroscopic factor and (da/dQ),,,, cross section for pick-up of a nucleon from the sub-shell described by quantum numbers I and j. The quantity C is the Clebsch-Gordan coefficient for coupling the isospin of the final state and the picked-up nucleon to that of the target. In the present experiment C2 = 3 for pick-up into states of *OF and C2 = 3 and 1 for pick-up into T = 1 and T = 0 states in “Ne, respectively. The normalization, N, is taken from the calculation of Bassel l4 ) and has the values 2.95 and 3.33 for (d, 3He) and (d, t) reactions, respectively. For single Z-value transitions values of C’S were extracted by normalizing the DWBA calculations to the major maxima of the experimental differential cross sections. For distributions requiring two Z-values a least squares fitting procedure was used to fit the sum of the predicted DWBA distributions to the first 11 experimental points. The fits were restricted to these points because of the general failure of the DWBA calculations to reproduce the experimental secondary maxima. 4. Results and discussion 4.1. THE

REACTION

*‘Ne(d,

3He)ZoF

The 3He spectrum obtained at t&, = 16” is shown in fig. 3; it can be seen that most approximately of the pick-up strength to 20F lies below 2.5 MeV. The resolution,

G. F. MILLINGTON

386

et al.

100 keV FWHM, is not sufficient to resolve completely the doublet peak corresponding to states at 984 and 1057 keV. The components of this peak were extracted using a coupled Gaussian fitting routine in which the separation and widths of the peaks were kept fixed. The experimental angular distributions and the DWBA predictions are shown in

.

G.S

2+

0.17

CofM

Angle

Fig. 4. Angular distributions of 3He groups from the reaction ZINe(d, 3He)ZoF. Experimental points arc represented by dots and DWBA predictions by solid lines. Groups are labelled by the corresponding excitation energy in keV.

fig. 4. As adequate

fits to the angular distributions corresponding to states at 984, 1309 and 1843 keV could be achieved only for 1 = 1 transfer, these states can be immediately assigned negative parity. A state at 1824 keV exists in the spectrum of 20F and may be expected to contribute to the peak at E, = 1843 keV. However, a

Z°F

AND

387

Z”Ne

recent linear polarization measurement “) of the y-decay of the state at 1824 keV indicates that it has J” = 5+ and so would require an I = 4 transfer. Previous measurements of mixing ratios 15*16) and lifetimes 17-lg) restrict the spin assignments for the 984, 1309, and 1843 keV states and combined with the present results they imply J” = l- for the 984 keV state and J” = 2- for the states at 1309 and 1843 keV. McGrory and Wildenthal ‘) have pointed out that the states of ‘OF below about 3 MeV can be all accounted for by four rotational bands; two positive-parity bands (K” = l’, 2+) formed by coupling a proton in the 4’ [220] Nilsson orbital to a neutron in the 3’ [21 I] orbital and two negative-parity bands (K” = 1 -, 2-) formed by coupling a neutron in the $‘[21 I] orbital to a proton in a 3- [IO11 orbital. The measured spectroscopic factors reported here allow us to examine this model more closely. The method of calculation of spectroscopic factors for pick-up from Nilsson orbitals into pure rotational states has been shown by Satchler 20) to be C2S = where the subscripts if K, = 0 or K2 = and final states is pick-up or neutron from a completely

S2[Tl I
(sr2~Q,)IJ2K2)12~j2,n,~n,~ l12,

1 and 2 refer to target and residual state respectively; g2 = 2 0 and is unity otherwise. The shape overlap term for the initial assumed to be unity. The isospin factor [T] is unity for proton pick-up from an orbital empty of protons but for neutron pick-up full orbital it is

VI = I12. Since the reduced width coefficients cjln2+n,l are available in tabular form 21) it is a straightforward exercise to compute the values of C’S associated with pure model configurations. Values of C2S for the 21Ne(d, 3He)20F reaction are shown in column TABLE 2

Experimental values of CzS for EX GeV)

0 656 823 984 1057 1309 1843 2044 2195

.I”

I

czs exp.

2+ 3+ 4+ I-

0+2 2 2 1

1+ 22-

0+2 1 1 0+2 2

0.24+0X3 0.66 0.26 0.84 0.08+0.25 0.86 0.69 < 0.01+0.15 0.16

‘OF

compared to model calculations Nilsson

CZS

model

K, J”

czs

2, 2+

0.25+0.13

2,3+ 2,4+

“)

0.70 0.19+0.05 0.93

1,2-

0.28 0.06+0.25 0.32

1,2+ 1,3+

‘).

shell model 0.35

0.37 0.24

1, I1,1+ 2,2-

“) Calculated via the Nilsson model with /I? = 0.25. “) From ref. 24). ‘) Ref. 23) calculated with the wave functions of ref.

PHF b,

0.75

1.25

‘)

10.25 0.71 0.25 0.59 0.17 -LO.03 0.72 0.23 0.007+0.13 0.002

388

G. F. MILLINGTON

el al.

11601

I 0”

,‘!I

I

20”

40”

20”

,

I

40”

I

,

0”

20”

,

,

40’

C of M. Angle t)*“Ne corresponding Fig. 5. Angular distributions of triton groups from the reaction “Ne(d, excitation analogues of low-lying states in z°F. Groups are labelled by the corresponding in keV.

4 of table 2. The identification

to the energy

of the rotational states in 20F is shown in column 5, and the calculated spectroscopic factors in column 6. These factors are a function of the nuclear deformation for which the value /I = 0.25 for ‘OF has been taken from the quadrupole moment (Q, = 0.29 b) derived from the transition strength (B(E2) = IO+ 1 e2 * fm4) of the 823 keV (4+) to ground state (2+) transition 22). In general it can be seen that this simple model provides a fair account of the pick-up strengths in this reaction. The spectroscopic factors predicted by the shell-model calculations of Wildenthal 5*23) for positive-parity states also give a reasonable account of the observed values (table 4); however, the simple Nilsson model predictions are not noticeably inferior. The spectroscopic factors for negative-parity states are equally well described by 4*24), the Nilsson model and the shell the projected Hartree-Fock calculations model 5,23). The sharing of the I = 1 strength between the two 2- levels is not reproduced by any of the calculations.

‘OF AND 4.2. THE

REACTION

A typical triton

*‘Ne(d,

spectrum

‘ONe

389

t)‘ONe

is shown in fig. 3. Reliable

triton

data were accumulated

in only one of the detector telescopes and this telescope was not sufficiently thick to stop tritons from levels below 5 MeV of excitation in 2oNe. The angular distributions of the triton groups above 5 MeV excitation are shown in figs. 5 and 6. Values of C’S were extracted as already described and appear in tables 3 and 4. 4.2.1. T = I states in 2oNe. Fig. 3 is drawn so that the ground-state group of ‘OF lies above the lowest T = 1 group 10,25) in “Ne. Several states appear strongly

5785

7027

b

200

I-

1

\

7424

2+

9084

(4’)

2+

40’

I 0’

I,

C. of :.

0

,I 40’

ANGLE

0

/ 20’

Fig. 6. Angular distributions of triton groups from the reaction TT= 0 states. Groups are labelled by the corresponding

/ 20’

, 404

“Ne(d, t)ZaNe corresponding excitation energy in keV.

to

390

G. F. MILLINGTON

et a[.

TABLE 3 Extracted

values of C2S for states in 20F and their analogues

Z°F (k%)

*ONe

1

20Ne J”

in Z”Ne

czs

K10271

(k%)

(keV) 0

10271-c 3 “) 10880+10 11086+10

2+ 3+ 4+ 11+ 222+

656 823 984 1057 1309 1843 2044 2195

11270

0 609 815 999

11601~10 12100~10

1330 1829

(3+)

0+2 2 2 1 0+2 1 1 2 2

0.24qO.58 0.66 0.26 0.84

0.52

0.08 +0.25

0.03+0.18 0.86 0.69

0.50 0.43

0.15 0.16 1=0+2 2.38

Sums: “) From

0.08+0.25 0.42 0.18

I= 1 2.39

/=0+2 1.14

I= 1 1.45

ref. lo).

TABLE 4

The T = 0 states of Z”Ne seen in the reaction Present

work I

J% (keV)

5622*f 5785 i

2 4

1 1

7424*&

4

0+2

& 9

0+2

Previous n/j”)

CZS

8839 (9084 (9357

i 8 rt21) r) *17)

: 1

0.02 0.03 0.05 0.07 0.005 0.023 0.33 5 0.12 5 0.1

(9913

119)

2

< 0.16

10385 (10880

f12 +lo)

1 1

7827

lpt

1p+

0.08 0.13

E. (keV) “)

t)20Ne Theory

work

J” ‘)

5622+ 5785&

2 3

31-

7424&

4

2+

7834+

4

2+

8850+ 5 90401 5 (9340-c 30) 9950& 6 9990f 10 10401+ 5 10836

“Ne(d,

I-

c=s

‘)

C2S

K. Jr

5 0.053 5 0.067

1,1-

0.34

0.11 0.01 0.002 0.11 0.35

1.2-

0.14

0.02

1, 3-

0.02

4+ 1+ 4+ 33-

0.038

* These energies were used for the calibration of the triton spectrum. “) The values of nb are not assignments but represent the values used in the DWBA “) From ref. 6). “) From ref. 31). d, Calculated with the Nilsson model with p = 0.25. ‘) From refs. 5*23). r) The bracketed values in this column indicate that the triton peak shows characteristic of more than one state being populated.

calculation.

broadening

*OF AND

Z”Ne

391

in the triton spectrum above this group and have similar energy spacing and angular distributions to corresponding states in ‘OF This leads us to identify them as anawere logues in 2oNe of the low-lying levels in “, . The triton angular distributions calculated with the same transferred angular momentum components as their parent states. However, the peak at E, = 10880 keV was fitted with a mixed 1 = 1 f2 distribution (fig. 5) since Ajzenberg-Selove “) indicates a 3- state at 10836 keV which could contribute to, and be unresolved from, this peak. The angular distribution of the peak at E, = 11270 keV is a mixture of I = 0, 1 and 2, an expected result if it is the analogue of the 984/1057 keV doublet seen in the 3He spectrum. The values of C2S for all the analogue states of fig. 5 are shown in table 3 and it can be seen that the ratio of the values of C2S (20F) to C’S (“Ne) is close to 2. This is to be expected since the spectroscopic factors (S) should be the same for the states in 20F and their analogues in 20Ne and the values of C2 in the ratio of 2 : 1. For the states with only a single Z-component and for which the uncertainties in fitting procedure are small the ratio is about 1.6 and reasonably constant. In view of the uncertainty associated with the bound-state wave function calculated for the analogue states, the agreement of the ratio (to within 20 %) with the theoretical value is satisfactory. The results for T = 1 states are summarized in table 3. Three T = 1 states had previously been assigned in 2 ‘Ne The 10271 keV state had been assigned ’ ‘) as the analogue of the “F(J” = 2+) ground state. States 26,27) at 11080 keV (J” = 4+) and 10853 keV (J” = 3+) have also been assigned T = 1, consistent with our results. Finally, a state in the region of 11250 keV has been assigned J” = 1’ by some authors 28P2g) and J” = l- by others 2 5,26). The presence of the analogues of the 984 keV (J” = l-) and 1057 keV (J” = 1’) states in 20F in this region may explain these apparent discrepancies. 4.2.2. T = 0 states in 2oNe. The interpretation of the states seen in 20Ne is somewhat complicated by the impurity reaction 22Ne(d, t)‘rNe which accounts for two of the peaks in the triton spectrum of fig. 3 and may contaminate some of the other peaks. In these cases the spectroscopic factors (C2S) in table 4 are indicated as upper limits. The angular distributions of the triton groups from T = 0 states in 20Ne are shown in fig. 6 and the values of C2S and excitation energies in 20Ne extracted from these data are shown in table 4. It is well known that the structure of 2o Ne shows a pronounced rotational nature; five rotational bands (K” = Of, 2-, O-, O+, O+) have been identified below 10 MeV. In the Nilsson model two T = 0 negative-parity bands of K” = l-, 2- produced by coupling a +- [loll hole to a $‘[202] particle are expected in “Ne. The second of these bands may be identified with the band beginning at 4968 keV. A candidate for the head of the K” = 1 - band is seen at 8839 f 8 keV in the present work. The Nilsson model (with p = 0.25) predicts a pick-up strength to this state of C2S = 0.34, the shell-model calculation of ref. ““) gives C2S = 0.35 and the experimental value is C2S = 0.33.

392

G. F. MILLINGTON

ef al.

1 The triton group corresponding to an excitation in **Neof9357~17keVhasani= distribution and is a possible candidate for the second (J” = 2-) member of this band. However, such an identification is clouded by possible interference ‘“) from the 5691 and 5780 keV levels in *lNe. Either of the two 3- states at 10401 keV and 10836 keV in ‘*Ne could be a candidate for the 3- member of the K” = I- rotational band; however, the state at 10401 keV has a C’S closer to the predicted rotational model value. 4.3. CONCLUSIONS

The 21Ne(d, 3He)20F reaction has confirmed the negative parity assignments for the levels at 984,1309 and 1843 keV in 20F. In addition two new T = 1 analogue levels at 11601 keV and 12100 keV in **Ne have been identified from the *lNe(d, t)**Ne reaction. The spectroscopic factors for pick-up of a nucleon from *lNe are in fairly good agreement with the available calculations. References 1) H. A. Watson and W. W. Buechner, Phys. Rev. 88 (1952) 1324 2) M. R. Gunye and C. S. Warke, Phys. Rev. 156 (1967) 1087 3) E. C. Halbert, J. B. McGrory, B. H. Wildenthal and S. P. Pandya, in Advances in nuclear physics, vol. 4, ed. M. Baranger and E. Vogt (Plenum, New York, 1971) 4) 1. P. Johnstone, B. Caste1 and P. Sostegno, Phys. Lett. 34B (1971) 34 5) J. B. McGrory and B. H. Wildenthal, Phys. Rev. C7 (1973) 974 6) F. Ajzenberg-Selove, Nuct. Phys. A190 (1972) 1 ‘7)K. A. Hardy and Y. K. Lee, Phys. Rev. C7 (1973) 1441 8) D. S. Longo, J, C. Lawson, L. A. Alexander, B. P. Hichwa and P. R. Chagnon, Phys. Rev. C8 (1973) 1347 9) B. Hird and R. W. Ollerhead, Nucl. Instr. 71 (1969) 231 10) T. K. Alexander, B. Y. Underwood, N. Anyas-Weiss, N. A. Jelly, J. Sztics, S. P. Dolan, M. R. Wormald and K. W. Allen, Nucl. Phys. Al97 (1972) 1 11) J. M. Nelson and B. E. F. Macefield, Atlas Program Library report no. 17, Oxford University Nuclear Physics Laboratory, unpublished 12) P. E. Hodgson, Adv. in Phys. 15 (1966) 329 13) J. M. Joyce, R. W. Zurmiihfe and C. M. Fou, Nucl. Phys. Al32 (1969) 629 14) R. H. Bassel, Phys. Rev. 149 (1966) 791 15) G. A. Bissinger, R. M. Mueller, P. A. Quin and P. R. Chagnon, Nucl. Phys. A90 (1967) 1 16) P. A. Quin, G. A. Bissinger and P. R. Chagnon, Nucl. Phys. A155 (1970) 495 17) J. R. Leslie, W. McLatchie, R. M. Hutcheon and G. F. Millington, to be published 18) T. Holtebek, R. Stromme and S. Tryti, Nucl. Phys. Al42 (1970) 251 19) R. L. Hershberger, M. J .Wosniak and D. J. Donahugh, Phys. Rev. 186 (1969) 1167 20) G. R. Satchler, Ann. of Phys. 3 (1958) 27.5 21) J. P. Davidson, Collective models of the nucleus (Academic Press, New York, 1968) appendix D 22) J. G. Pronko and R. W. Nightingale, Phys. Rev. C4 (1971) 1023 23) B. H. WiIdenthal, private communication 24) 1. P. Johnstone, private communication 25) J. D. Pearson and R. H. Spear, Nucl. Phys. 54 (1964) 434 26) J. John, J. P. Aldridge and R. H. Davis, Phys. Rev. 181 (1969) 1455 27) B. T. Lawergren, A. T. G. Ferguson and G. C. Morrison, Nucl. Phys. A108 (1968) 325 28) R. C. Ritter, J. T. Parsons and D. L. Bernard, Phys. Lett. 28B (1969) 588 29) W. L. Bendel, L. W. Fagg, S. K. Numrich, E. C. Jones andH. F. Kaiser,Phys. Rev. C3 (1971) 1821 30) C. Rolfs, H. P. Trautvetter, E. Kuhlmann and F. Reiss, Nucl. Phys. A189 (1972) 641 31) A. J. Howard, J. G. Pronko and R. G. Hirko, Nucl. Phys. A150 (1970) 609