Volume 44B, number 1 PHYSICS LETTERS 2 April 1973

SHELL MODEL CALCULATIONS ON THE POSITIVE PARITY STATES IN 20Ne

J.M. IRVINE, G.S. MANI, V. PUCKNELL Schuster Laboratory, University of Manchester, UK

and

A. WATT, R.R. WIIITEHEAD Department of Natural Philosoph)', Universit.v of Glasgow. UK

Received 8 February 1973

The results of an extended shell model calculation in the space spanned by the 0pl/2 orbital and the whole of the sd-shell for the nucleus :"ONe are presented. The positions of the (4p-0h), (6p-2h) and (8p-4h) bands are located and the results are compared with recent experiments.

In recent years a large amount of discussion had centered around the possibility of low lying ( 8 p - 4 h ) levels in 20Ne. These have been predicted in terms of the quartet model by Arima et al. [1]. Middleton et al. [21 have argued, based on their experinaental re- suits of angular distribution and excitation function for the reaction 12C(12C,a) 20Ne, that the observed

levels at 7.20 MeV (0 +) and 7.83 (2 +) have the quartet configuration (220): that is, a configuration with two sd-shell alpha particles outside the 12C core. Nagatani et al. [31 have studied the reaction 12(,.-( 14N, 6Li ) 20Ne and conch, de that the 6.72 MeV (0+), the 7.44 MeV (2 + ) and the 9.90 MeV (4 +) levels belong to tile (4p Oh) baud while the 9.08 MeV (4 + ) and the 12.19 MeV (6 +) states belong to the 8 p - 4 h band with K+0 + Recently Vogt [4], on the basis of the observed re- duced widths for alpha decay of these levels, has pos- tulated that the levels at 7.20 MeV (0+), 7.83 MeV (2+), 9.08 MeV (4 +) and 11.94 MeV (8 +) excitation behmg to the ( 8 p 4h) band while tile 6.72 MeV (0+), 7.42 MeV (2 +) and the 9.99 MeV (4 + ) levels are mem- bers of the 4 p - 0 h band. The transition probabili ty of the I 1.04 MeV (8 +) to the 8.78 MeV (6 + ) transition is 7.5 -+ 2.5 W.u. which, on the other hand indicates that the lowest 8 + level is a member of the ground state band. All these arguments leave the problem of where the(bp 2h) band would be located. AIsomost of the arguments to ascribe the(Sp 4h) configt, ration to these levels depend on assumption regarding the reac- tion mechanism which for heavy ion reactions are not well understood. Thus the motivation for the present

work was to perform a shell model calculation for

20Ne based on the 12C core in order to establish the positions of the (4 0 h ) , ( 6 p - 2 h ) and the ( 8 p - 4 h ) bands of the sd-shell. Since a complete calculation of eight particles in this rnodel space becomes rather large, tile (4p-- Oh), ( 6 p 2h) and ( 8 p - 4 h ) bands were calculated separately by restricting the occupation of the 0Pl/2 orbital. Thus band mixing is neglected in the present work. To economise on computer time the lowest energy levels of each band were calculated with M=0 and higher spin states were obtained from calculations with M=6 or 8, as described in ref. [5]. The G-matrix derived from the Reid potential by Siemens [6] and computed by Irvine and Pucknell [7] was used as the two body interaction. The single par- ticle energies were obtained by adjusting them so that the spectra of mass 15, 16 and 17 were reproduced with the above interaction when corrections for core breaking were incorporated. The resultant single par- ticle energies are given in table 1 and are very close to the experimental single particle energies of 13C.

Following Negele [8] the values of starting energies were obtained using the following prescription. For occupied states the starting energies were taken to be the Hartree-Fock energies, while for unoccupied states the starting energies were equated to kinetic energies.

Table 1 Single particle energies used in the present calculation

0pl,,2 0.0 MeV 0ds, 2 5.1 MeV 1 s 1,,2 3.0 MeV I 0d3/2 8.25 MeV

16

Volume 44B, number 1 PIIYSICS LETTERS 2 April 1973

2°Ne

15,0

> .

i35.O

4 5 . 0

9* 8"

m S O

m 6 * 2" ~ 6 "

6*

- - S" - - 6" 1:2 .2:2 - - 4 " ¢ . 2 0 : 2

- - 8" 3" 2 ;2 ~ 8 " - - 2 " 2

- - 8 " 2" 0~.

9" 4" _ 6 " - - 0 : 2 I " ~ ~ 2 "

- - e " 2,.,::~o.. 3",1 - - - - 8 " 0 ~ ' - - ....'~. + 4 5;I 4"1

- - 0 " ~ . 2 1 ~3~'4. 4 . 2".1 7:1 6 ' r . ~ . m m . , u ~ r - ~ - m m . . 2 . 0".1 "4",1 '"

. 4" _. 3",I- 8 . , I . - : ) S'.I / J / ~ " . 3",1 4" 6" ~ 4 ~ s " II')- 4" 2",1 - - , ~ , - I'.1.

P ~ " - - ~ 3 ' 2 " _ _ ~ ' ~ 3 " 2" 4",a - -4" '~" "2" ~ 0 ° 2" 3",1 - - 2 - ,

6* 2" - - 2 " . 2" ~ 2

2" - - 0 " ~ 0 "

O*

4*

2*

O*

- - 4"

~ 2 "

m 0 •

EX FI'. 4p-Oh 61) -2h ~ - 4 h T - 0 4p-Oh EXPT. T - O T • O T - O +~ pority T- I .T - 2 T- I .T, 2

Stoics Stoics Stores Levels Levels Levels

2;2

- - 0 : 2

.0".I i . - - I '-~| .I

IT.I) I;I- (T-l)

- - ~ ( 4 : 1 ) 12"), I - - 2" I

Fig. 1. The calculated spectrum for 2°Ne positive parity levels compared with experimental data. The energy scale is with reference to the U 2 C core.

In the case o f partially occupied orbits a mean value

o f the starting energy was obta ined using the above

prescript ion. Thus the different bands had different

starting energy values. These in t roduced a difference

of around one to two MeV in the binding energy of

the ground state. It was observed that the best fits to

17

~61ume 44B, number 1 PHYSICS LETTERS 2 April 1973

the experimental data were obtained when the start- ing energies were not altered when calculating differ- ent bands. Hence we have adopted for all the bands tile values calculated using the above prescription for the (4p-0h) band. The results of the calculation are presented in fig. 1. The calculated binding energy of the ground state of 20Ne with respect to the 12C core

was -41.5 MeV which agrees very well with the ex- perimental value of -4.1.0 MeV. The calculations in- dicate that the (6p-2h) band is 5 -7 MeV lower than the (8p-4h) band, and at 1 l.l MeV for the (4p Oh) band as compared to the experimentally observed lowest 8 + state at 11.95 MeV. This makes it likely that the lowest g+ state is (4p- Oh). Vogt's argument for a low-lying superband requires that the states at 7.196 MeV (0+), 7.834 MeV (2 +) and 9.08 MeV (4 +) are also (8p 4h), while our results indicate that they may well be (6p--2h). There is thus no compelling evidence for an (8p 4h) band in 20Ne, unless one can find arguments 1o show that the mixing of higher configurations would raise the (6p-2h) states and lower the (8p-4h) ones. The assignment of (6p-2h) structure to the 7.196 MeV (0 +) and 7.834 MeV (2 + ) would not be in contradiction with the results of the 12C( 12C, a) 20Ne reaction [2] or the 12C( 14N, 6Li) 20Ne reaction since the reaction mechanism for these heavy ion transfer reactions are not well understood.

The broad 0 +, T=0 and 2 +, T=0 levels at 8.6 MeV and 8.8 MeV excitation observed in experiments do not appear in the present calculations. These levels, from considerations of their alpha-widths which are close to Wigner limit, are thougJlt to be due to four

particles in the (fp) shell with 160 as core and hence would not be reproduced in our present calculation. In fig. I, the calculated T = 1 and T=2 states are corn- pared with experiment. The calculation predicts larger numbers ofT= 1 states than have been observ- ed experimentally. In these calculations only (4p-0h) configurations were raken into account. The agree- ment of the observed T= 1 and T=2 levels with the corresponding calculated ones are reasonable though it would be necessary to include the (6p-2h) and (8p-4h) configurations before any detailed compari- son could be made.

The authors take this opportunity to thank Dr Zacharov of Daresbury Nuclear Laboratory and Mr Walkinshaw of the Rutherford High Energy Labora- tory for the use of the computers at these laborato- ries.

References

[ 1 ] A. Arima, V. Gillet and J. Ginocchio, Phys. Rev. Lett. 25 (1970 1043.

[2] R. Middleton, J.D. Garrett and tt.T. Fortune, Phys. Rev. Lett. 27 (1971) 950.

[3] K. Nagatani, M.J. Le Vine, T.A. Belote and A. Arima, Phys. Rev. Lett. 27 (1971) 1071.

[4] E. Vogt, Phys. Lett. 40B (1972) 345. [5] R. Whitehead, Nucl. Phys. A182 (1972) 290. [6] P. Siemens, Nucl. Phys. A141 (1970) 225. [7] Irvine and Pucknell, Nucl. Phys. A159 (1970) 513. [8] J. Negele, Phys. Rev. CI (1970) 1260. [9] F. Ajzenberg-Selove, Nucl. Phys. AI90 (1972) 1.

18