Non-normal-parity states in A = 7 and 8 nuclei

1.D.I: ]

Nuclear Physics A208 (1973) 61--76; (~) North-Holland Publishing Co., Amsterdam

I

N o t to be r e p r o d u c e d by p h o t o p r i n t or microfilm without written permission from the publisher

I.E.I

NON-NORMAL-PARITY

S T A T E S I N A -- 7 A N D 8 N U C L E I

A. ASWAD t and H. R. KISSENER Zentralinstitut fiir Kernforschuny, Bereich 2, Rossendorf bei Dresden, DDR

and H. U. JAGER tt and R. A. ERAMZHIAN Joint Institute of Nuclear Research, Dubna, USSR

Received 22 February 1973 Abstract: Shell model calculations taking into account all non-spurious 1 t~m excitations have been performed for A = 7 and 8 nuclei. The Hamiltonian has been taken from similar investigations of nuclei at the upper end of the lp shell. Level schemes, El radiative widths, and spectroscopic factors for single-nucleon scattering and the knock-out of a ls proton have been calculated. Good agreement with reported data has been obtained. The properties of new predicted levels are discussed. Cross sections of (y', p), (?', n) and the inverse reactions involving nuclei with A = 6, 7 and 8 are analysed using R-matrix theory.

I. Introduction

Shell m o d e l calculations o f the n o n - n o r m a l - p a r i t y states in A = 13 a n d 14 nuclei have been recently p e r f o r m e d t). All 1 h~o excitations have been considered in these calculations. The spurious states due to c.m. m o t i o n are exactly removed. The residual interaction between nucleons in the l p shell was t a k e n from the p a p e r by C o h e n a n d K u r a t h 2). F o r the interaction between unequivalent nucleons a force ( C A L ) obtained by Gillet et al. 3) in a fit to the o d d - p a r i t y levels in 4°Ca has been a d o p t e d . G o o d a g r e e m e n t o f the p r e d i c t i o n s o f this m o d e l with the available d a t a has been obtained. The full space o f n o n - s p u r i o u s 1 he0 excitations is expected to form a r e a s o n a b l e basis for a unified d e s c r i p t i o n o f the n o n - n o r m a l - p a r i t y states in l p shell nuclei. A p a r t f r o m the p a p e r o f W o n g a n d R o w e 4) on the giant resonance in ~2C, such calculations have n o t yet been r e p o r t e d for A = 7-12 nuclei. It is o f some interest to check the a p p l i c a b i l i t y o f the m o d e l o f ref. l) to these nuclei. I n the present p a p e r a c o m p l e x spectroscopic investigation o f the n o n - n o r m a l - p a r i t y states in 7Li a n d SBe, using this model, is p e r f o r m e d . Unlike A = 13, 14 nuclei, little experimental i n f o r m a t i o n on 7Li a n d 8Be is available. S o m e o d d - p a r i t y levels have been o b s e r v e d in SBe a r o u n d 20 M e V excitation energy. The r e p o r t e d 7Li s p e c t r u m does not contain e v e n - p a r i t y assignments (states * Oa leave of absence from the University of Damascus, Damascus, Syria. *t Permanent address: Zentralirlstitut fiir Kernforschung, Bereich 2, Rossendorf bei Dresden, DDR. 61

A. ASWAD et al.

62

with unknown parity appear above 12 MeV). Besides, the nucleus 8Be is unstable and its giant resonance can only be investigated by the inverse photo-nuclear reaction 7Li(p, ~). Starting from the Hamiltonian of ref. 1), the individual properties of the lowest non-normal-parity states and the gross structure of these states in the giant resonance region are investigated. The level positions, the spectroscopic amplitudes for singlenucleon transfer and partial radiative widths F~ (El) are compared with the available data in sect. 3. Recent measurements on the VLi(7, p)6He, 7Li(~, n)6Li and 7Li (P, 70,1) 8Be reactions are analysed in sect. 4. Spectroscopic factors for the knock-out of a ls proton in the 9Be(p, 2p)SLi reaction are presented in sect. 5. All experimental data quoted without reference are taken from ref. 5). 2. Details of the calculation

In the A = 7, 8 systems the configuration space of all 1 h~o excitations, (Is) 4 (lp) a - 5(2s, ld) l and (ls)3(lp) A- 3, contains a large amount (up to 30 %) of spurious states due to c.m. motion. They are eliminated by means of the Elliott-Skyrme technique 6). The Hamiltonian used for the A = 7 and 8 nuclei differs from the Hamiltonian applied in ref. 1) to the A = 13 system only by the position of the ls shell. Levels with noticeable (ls) - t admixture appear in the A = 13, 14 and A = 7, 8 systems at about the same excitation energies. But in the former case they give only a small contribution to the dipole sum. Thus, our choice of the hole energy ets could not be immediately substantiated by experiment. In 7Li the main peak of the photoabsorption cross section is formed by (ls)-1 states. The peak position measured by Denisov et al. 7) is reproduced with good accuracy (see sect. 4) if the difference between the lp~ particle energy and the ls hole energy (referring to a 4He core) is assumed to be elp~--els : 22 MeV. This value, accepted throughout the present paper, is suggested by the binding energies of A = 3, 4, 5 nuclei: [21.54 MeV (3He-SHe) (~IP~--el~)~x" = [21.78 MeV (3H-SLi). The calculations have been performed for the following J~; T values: A = 8: A=7:

J" = 0 - , 1 - , 2 - , 3 - ; T = 0, 1 and J ~ = ½ + , - ~ + , ~+; T = ½ , ~.

J~ = 4 - ; T =

0

The normal-parity wave functions entering in transition matrix elements are those of Cohen and Kurath z) (case (8-16)2BME). The spectroscopic amplitude for singleparticle transfer is defined as reduced matrix element of a Fermi creation operator, +

t

v

t

v

S~(Nlj ) = (A, E, J, M, T, T3lCmim, l A - 1 , E , J , M , T , T~) , ( J'M'jm[JM)(T'T3½tITT3 )

NON-NORMAL-PARITY

STATES

63

in accordance with ref. s). The radiative widths are calculated, as usual, using the long-wavelength approximation. The contributions of the nucleon magnetic moments to electric multipole radiation are neglected. No effective charge is assumed, and an oscillator length of 1.45 fm is adopted. The analysis of photo-nuclear reactions was performed using R-matrix theory, as was done in ref. 32). Only El transitions are considered. In the calculation of level widths and decay branches only the primary nucleon channels were taken into account. Integrated cross sections have been converted into cross sections by spreading the contributions from the excited levels of the target nucleus over non-interfering Breit-Wigner lines of proper position and shape.

3. Low-lying non-normal-parity states 3.1. T I l E N U C L E U S

8Be

Odd-parity states in 8Be have been observed as resonances in single-nucleon scattering and (p, 7) reactions. Such experiments provide information on level positions, spin and parity assignments, reduced widths and radiative widths. The calculated quantities are summarized in three tables. Table 1 gives the positions of predicted TABLE l Predicted excitation energies o f n o n - n o r m a l - p a r i t y states in SBe J~r; T 1-; 2-; 2-; 1-; 0-; 1-; 4-; 0- ;

0 0 1 0 0 1 0 1

Eth (MeV)

j~r; T

Eth (MeV)

17.46 18.36 19.38 19.66 19.97 20.16 20.60 20.98

3-; 0 1-; I 1-;0 3-; 0 2-; 0 3-; 1 2-; 0

21.68 22.12 23.73 23.77 23.79 24.22 24.46

odd-parity states below E x = 24.5 MeV. The spectroscopic amplitudes relating these states to the ground and first excited states in 7Li and 7Be are presented in table 2. Table 3 contains the partial radiative widths for the allowed E1 transitions to the lowest 8Be levels. The ls hole configuration contributes less than 8 % to the normalization of the states presented in fig. 1 except for the (3- ; 0)1 states where it amounts to 23 %. The isospin mixture effects which are well known 13) for the even-parity states in 8Be are beyond the scope of this model. In the calculated level scheme also appear closely spaced levels with the same Jn values and of similar structure but with different isospins which might be mixed by the Coulomb interaction (e.g. the 2= states at 18.36 MeV and 19.38 MeV). Comparing the model predictions with the reported data (fig. 1) some correspondence seems to be obvious. The theoretical 2 - ; T = 0 state at 18.36 MeV consisting

64

A. ASWAD

et al.

TABLE 2 Spectroscopic amplitudes for the odd-parity states in aBe J~; T

E,. (MeV)

(~- ; ½h S½(2s)

0-;0 0-;1 1-;0 1-;1 2-;0 2-;1 3-;0 3-;1 4-;0

19.97 20.98 17.46 19.66 23.73 20.16 22.12 18.36 23.79 24.46 19.38 21.68 23.77 24.22 20.60

S~(ld~)

--0.6804 0.2659 --0.1880 --0.6434 --0.6176 --0.8131 0.2793 --0.2401 0.8404

0.5308 --0.1217 --0.3170 0.2586 --0.4338 --0.3605 --0.7347 0.0901 0.3200 0.2441 --0.0499 --0.2335 0.8858

(½-; ½), S~(ld~_)

S~-(2s)

--0.3496 0.3267 0.0122 0.2987 --0.0454 --0.2059 0.0288 0.0924 --0.1944 --0.3277 --0.0895 --0.0745 --0.5796 0.2996

0.8662 --0.8788 0.1722 0.7836 --0.1376 --0.5767 0.5617

S~i(Ida)

--0.3446 --0.0091 0.5763 0.3005 --0.4091 --0.4929 0.6923

S~(ldk)

0.1616 0.2060 --0.1724 --0.1105 --0.0764 0.0522 0.1324 0.2144 --0.0400

TABLE 3 Partial radiative widths/'7 (El) of the odd-parity T = 1 levels in aBe J~; T

Eth (MeV)

/,7 (eV) (0 + ; 0)1

2-; 1-; 1- ; 3-; 2-; 1-; 3-; 2-;

1 1 1 1 1 1 1 1

19.38 20.16 22.12 24.22 24.95 25.37 25.45 26.25

5.0 1.7 × 103 7.8 x 102

(2 + ; 0)1 0.057 47 1.7 × 10a 3.8 x 102 1.1 ×102 34 2.6x 103 62

m a i n l y o f a 2s n u c l e o n c o u p l e d to the g r o u n d state o f A = 7 s h o u l d be the c o u n t e r p a r t o f the b r o a d r e s o n a n c e w i t h J ~ = 2 - ; T = (0) (l = 0) w h i c h has b e e n o b s e r v e d i n 7Li(p, n ) e x p e r i m e n t s at Ep = 1.9 M e V . I n the elastic s c a t t e r i n g o f p r o t o n s a J ~ = 4 - r e s o n a n c e has b e e n o b s e r v e d at a n e x c i t a t i o n e n e r g y o f 20.9 M e V . It has b e e n suggested 14) t h a t this level is a n a l m o s t p u r e single-particle state o f the c o n f i g u r a t i o n ( l s ) 4 ( l p ~ ) 3 + l d ~ . T h e c a l c u l a t i o n yields a J " = 4 - state w i t h the s a m e s t r u c t u r e at Eth = 20.6 M e V . T h e lowest p r e d i c t e d 3 - state a p p e a r s at Eth = 21.68 MeV. This result agrees w i t h the s p i n a n d p a r i t y a s s i g n m e n t for the 21.4 M e V level recently p r o p o s e d by L a u r a t 9). O n a c c o u n t o f the large r a d i a t i v e w i d t h the theoretical 1 - ; T = 1 state at Eth = 22.12 M e V c a n be a s s i g n e d to the 21.6 M e V level k n o w n as g i a n t d i p o l e r e s o n a n c e

N O N - N O R M A L - P A R I T Y STATES

65

based on the ground state. In 7Li(p, ~) reactions a broad peak has also been observed at E x ~ 23.6 MeV which is interpreted as E1 giant resonance related to the first excited state. Because of the approximately isotropic angular distribution an s-wave proton capture (and hence, a J~ = 1-, 2 - assignment for this compound state) seems most probable. According to the calculation a 3 - ; T = 1 state (Eth = 25.45 MeV) gives the largest contribution to the giant resonance based on the (2+; T = 0)1 level. Investigations 2o-12.25) of the 7Li(p, n2) reaction in the vicinity of its threshold revealed the presence of s-waves. A 1- level which explains the s-wave contribution has been assumed by Bevington et al. 22) first at Ep ~ 2.5 MeV. In a following paper [ref. 15)] another position Ep = 3.55 MeV of this level was suggested. However, the more recent investigations by Thornton et al. ~0) and Presser et al. 12) confirmed that the 1- resonance appears at Ep ~ 2.30 MeV (E, ~ 19.5 MeV). The model predicts at E,h = 19.66 MeV also a 1-; T = 0 state having the structure A = 7, (½-)1 plus 2s nucleon. In the 7Li(p, ~) reaction the yield of the transition to the first excited state shows a broad resonance at proton energy of about 2.1 MeV, where no resonance structure was observed in the yield of the ground state transition. F r o m the analysis of angular distributions and from arguments based on transition probabilities, Nilsson and Bergqvist 16) concluded that it is only possible to restrict the assignments for the corresponding 19.05 MeV level to J~ = 1+, 2 +, 3 +. In a shell model calculation for the normal-parity states Barker 13) interpreted the 19.05 MeV level as member of an isospin-mixed 3 + doublet. But, this assumption could not be substantiated by the 22.12

1-~1

( 0.70;0.23~Q021

( 1 - ) / ~ 21'68

3-,0

(0.46,0.30; 0.02)

/

21.6

.J

21.4 20.9

34"

20.98

0-;1

( 0.78,0,06;0.11)

- - ' \ ~

20.60

4",0

{ 0.13~0.86,0.02)

20.16 19.97 I9.66 1938

1- ;1 0-;0 1-,0 2-3

( 0.75~0.14~0.06) (0.75,0.08;0.12 } (0.69,0~4,0.13) (0.71,0.22;0.03)

18.36

2-~0

(0.66,0.28;0.03)

17.46

1-;0

(0 50,036~0.06)

19.5 19.05

1- J

189

2- \ .

EXP

TH.

Fig. 1. Comparison of reported and calculated odd-parity levels in SBe below 23 MeV. The experimental spectrum given in ref. s) has been modified by the results of Laurat 9), Thornton et aL lo), Bevington et al. i t ) and Presser et al. xz) for the states at 20.36, 21.4 and 19.5 MeV. The expectation values for the particle numbers in the 2s, ld{ and ld{ shells enclosed in parentheses on the right-hand side of the diagram indicate the structure of the corresponding wave functions.

66

A. ASWAD et al.

investigations of Callender and Browne 17) on the 3 + doublet. In the t°B(d, ~)SBe reaction they observed only one particle group. A possible explanation is that the 8Be states at 19.05 and 19.22 MeV do not have the same spin and parity, and that the lower level has a pure T = 1 character. With respect to the 7-decay properties of the predicted non-normal-parity states there is only one possible candidate for an explanation of the 19.05 MeV level. The radiative widths of the 1-; T = 1 state at Eth = 20.16 MeV for transitions to the ground state (F~.(E1) = 5 eV) and to the first excited state (FT(E1) = 47 eV) differ by one order of magnitude. In the reported data no indications have been found for some low-lying odd-parity states in 8Be which are predicted by the model (fig. 1). The theoretical (1-; 0)1 state appears in the vicinity of the 7 L i + p threshold. The E1 transitions from this state to the lower T = 0 states are isospin-forbidden. The two additional 0 - states have a large spectroscopic amplitude to the first excited state of the A = 7 system. But, in the 7Li(p, Pl) and 7Li(p, nl) reactions they should be weakly excited (see table 2), and the characteristic L -¢: 0 terms of the differential cross section are influenced by J " = 0 - states only by interference with other levels. Apart from the uncertainties of the model it seems to be reasonable that these states have not been observed in the single-nucleon scattering and (p, 7) experiments which provided so far nearly all information about odd-parity states in SBe. 3.2. THE A ~ 7 SYSTEM Some new investigations of the level scheme of mass-7 nuclei have been recently published. The states in 7Li and 7Be at 9.7 and 9.3 MeV, respectively, were assigned as -~- ones 18,19). In the 6Li(n, p)6ne(0) and 6El(n, n')6Li(3.56) reactions Presser e t a l . 20) identified a-3z-; T = ½ resonance at 10.25 MeV. Taking into account these new data, all levels observed in 7Li and 7Be up to an excitation energy of about 12 MeV have odd parity and can be arranged in isospin multiplets. The model predicts the lowest even-parity state at E~h = 11.52 MeV which is roughly in line with this experimental information. In theoretical investigations performed in a highly truncated configuration space a lower position of such levels was obtained. By simple estimates on the position of pure (2s) 1, (ld,~) 1, (ld~) 1 and (Is) -1 states Lane 2~) and Neudachin et al. 22) found the lowest even-parity state at about 2 and 8 MeV, respectively. In the rotational model calculations by Chesterfield and Spicer 23) this level appears at 9.4 MeV. Levels in 7Li of unknown parity have been observed in photo-reactions and in electron scattering. The reported peak positions in the lower part of photo cross sections (10 MeV < E x < 20 MeV) differ widely [see table 7.5 of ref. 5) and refs. 2,) and 25, 27)]. It is not yet possible to compare theoretical properties of individual states with experimental data. The predicted properties of the lowest even-parity states in A = 7 nuclei, which might be useful as guide for further experiments, are presented in table 4. In the model used, the deviations between calculated and observed excitation ener-

NON-NORMAL-PARITY STATES

67

TABLE 4 The predicted structure of the lowest even-parity states in the mass-7 system 2J 2 T

Eth (MeV)

F'7(EI) (eV) g.s. transition

1 1 11.52 3 1 12.63 5 1 14.01 1 1 14.97 3 1 15.43 1 1 16.41 1 3 16.43 5 1 16.55 3 1 16.6l I 1 17.24 5 1 17.32 5 3 19.52 3 3 20.25

27 0.30 34 96 3.9 94 4.4 x 102 7.3 0.081 5.5~102 l.lxl0 z 7.0>101 44

Mean hole number

(1 +; 0)x S~(2s)

S½(ld~)

(3+; 0)l S~(ld~)

S ~-(2s)

S½(Id.~) S~(ld~)

Is 0.49 0.07 0.35 0.11 0.48 0.18 0.09 0.23 0.05 0.22 0.16 0.03 0.06

0.3673 --0.8689

--0.0925 0.2042

0.7184 0.0477 --0.2278 0.0130 0.0452 --0.1237

--0.1965 0.3522 --0.3034

--0.0312 0.0533 0.0251 --0.1219 --0.0029 0.3170

0.6319

0.2483 --0.3470 --0.2707 0.1390 0.0820 0.2727

All states with E~h < 18.8 MeV and the lowest J = ~+, ~+', T -

0.1932 0.2096 --0.1563 --0.0129 0.1158 --0.4118 --0.0252 0.2485 0.3633 0.0816

--0.1895 0.0194 0.0015 --0.1741 0.0815 --0.1167

:~ states are given. ~

gies s h o u l d be larger in the A = 7 case t h a n in the A = 8, 13, 14 ones. The H a m i l t o n i a n contains an effective force [ ( 8 - 1 6 ) 2 B M E ] o f C o h e n a n d K u r a t h 2) which has been f o u n d by fitting the d a t a f r o m A = 8 t h r o u g h A = 16. A p p l y i n g this H a m i l t o n i a n to states o f the type ( l s ) g ( l p ) Z ( 2 s , l d ) * the energy deviations f r o m e x p e r i m e n t s h o u l d be, at least, similar to those o b t a i n e d by C o h e n a n d K u r a t h for 6Li. Therefore, d e v i a t i o n s o f a b o u t 2 M e V can be expected. The spectroscopic a m p l i t u d e s a n d m e a n particle n u m b e r given in table 4 indicate the c o m p l e x structure o f the low-lying even-parity states in A = 7 nuclei. O n l y two states [(~+; ½)1 a n d (½+; ½)z], which s h o u l d be strongly excited in the 6 L i + n channel, are predicted. A n o t h e r striking p r o p e r t y is the occurrence o f states with a s t r o n g a d m i x t u r e o f ls holes. I n the A = 7 case those states o f the c o n f i g u r a t i o n ( l s ) 3 ( l p ) 4 are energetically f a v o u r e d which c o n t a i n four nucleons in the l p shell a r r a n g e d in a n c~-cluster with the Y o u n g scheme [4]: ](ls)-l,

J1 = T1 = ½; ( 1 p ) 4 1 4 ] ,

Sz =

J ~ ; T = ½), ( L 2 = 0, 2, 4; J= = ½+, ~z+, {+, ½+, 9+).

T2 = 0, L 2 ;

Therefore, three low-lying states with J~ = ½+, 3 + , 52+; T = ½ have a l s hole adm i x t u r e o f m o r e t h a n 30 ~ . This p r o p e r t y , p r e d i c t e d also by simpler m o d e l s 21-23), c a n n o t be directly c h e c k e d by the (p, 2p) r e a c t i o n since there is no stable A = 8 target. These c o n s i d e r a t i o n s show that p h o t o - r e a c t i o n s are the best tool to investigate the e v e n - p a r i t y states in A = 7 nuclei. But p r o b a b l y it is n o t possible to identify in such reactions all existing levels. The p a r t i a l widths for E1 transitions to the g r o u n d

68

A. A S W A D e t al.

state (see table 4) range from very small values up to a few hundred eV. At Eth ~ 16.4 MeV and Eth ~ 17.3 MeV closely spaced states with large radiative widths are predicted. 4. Photo-nuclear reactions 4.1. T H E 7Li G I A N T R E S O N A N C E

A number of experimental data which are related to the 7Li giant resonance have been reported. The (Y, P), (~', n) and more complicated reactions were investigated by Denisov 7), Hayward 26), Bashanov 25), Manuzio 29), Garfagnini 30) and Wong 3~) who provide also further references. Fig. 2 shows the calculated total E1 absorption cross section compared with an estimate taken from ref. 7). The structure of the strongest dipole states can be found j d dE ( MeV" rob)

[

- -

10!

6 rob)

]1[

total

______ Tf "1z2

i

exp.

t~tlllJi

Denisov

/

i 20[

]0

I

1

calc El Scmorai

0 1 i

10

i

l,__1 i

i

f

i

i

i

,

i

~

2Q

i

i

~

[

i

. . . .

30

[

,

~

i

,

j

40

i

i

i

i

[

i

i

,

I

50 E ~(MeV)

Fig. 2. Photo-absorption cross section in VLi. (a) Present calculation. The vertical bars denote integrated cross sections (left scale), the solid line gives the cross section (right scale); the dashed line s h o w s the contribution o f levels with isospin ~-. (b) Experimental data f r o m D e n i s o v e t al. 7); cq and cr2 are the contributions o f the valence nucleon (lp -+ (2s, lsd)) and core excitations (Is -+ lp). (c) Calculation by El Samarai et al. 34).

69

NON-NORMAL PARITY STATES TABLE 5 Structure of the strongest dipole states in 7Li (jzr = ~_+, ~+, z~+, T = ½ and ~:) 7Li levels

E

2J 2T ~trydE

(MeV) 18.9 19.5 21.0 22.2 30.3 34.7 36.9 37.7 37.9

Contribution of configuration (in ~o)

5 5 5 5 3 3 3 3 5

(MeV-mb)

1

5 11 5 5 4 5 15 10 12

16.0 25.3 53.5 52.6 4.1

1 3 1 3 3 1 3 3 3

2

3

4

5

36.4 20.5 10.1 4.8 8.7 16.2 5.4

6 10.1 7.3

7

8

33.0 7.6 4.2 7.2 11.1

48.5

6.3

10

11

9.1

16.5

3.5 4.2

I0.7

3.2

12

11.3 11.7 28.6 13.1 4.4 13.6

4.1 11.8

9

15.0 36.9 43.5 29.9 53.1

9.5 19.6 17.8 54.5 18.1

6.2 3.0 6.8 8.8

Contributions < 3~ (including those from the configurations (p½)Z(2s)l and (ls)-l(p~) 4) have been omitted. The ground state consists of 58~ (pk) 3, 16.4~o (pk)2(p~) 1 and 25.6~ (pk)~(p½)2. Configurations are assigned as follows: 1 ----(pk)2(d~)~ 2 (p~)2(dk)l 3 ~ (p~)2(2s) 1 4 ~ (p+)2(d~)l 5 ~ (pk)2(dk)'

6 ~(p~)~(p½)l(d~)X 7 ~ (p~)X(p~)l(d~)l 8 ~(p~)~(p~)~(2s) 1

9 "~ 10 z 11 ~ 12 ~

(Is)- l(pk) 4 (ls)-l(p?~)3(p01 (ls)-X(p~_)2(p~_)2 (Is)-J(pk)l(p.~) 3

f r o m table 5. The 7Li giant resonance is roughly divided into two parts. A g r o u p o f p e a k s a r o u n d 20 M e V is mainly due to l p -~ (2s, l d ) nucleon excitation. The b r o a d d o m i n a t i n g structure a r o u n d 40 M e V is mostly due to ls ~ l p core excitations. This c o n f i g u r a t i o n a l splitting is clearly seen in the experimental curves 7). The calculation provides, however, small strength at excitation energies a r o u n d 30 M e V a n d a b o v e 45 MeV. F o r the i n t e g r a t e d a b s o r p t i o n cross section the value 140 M e V . m b is obt a i n e d which is in the range o f the experimental value 7) f a z MeVa(ET)d E = 1")2 +30 M e V " mb. 1~J_2o th U n l i k e the cases A = 14 [ref. 3z)] a n d A = 13 [ref. 33)], no a d d i t i o n a l splitting o f dipole states with isospin T< a n d T> is f o u n d for 7Li, a l t h o u g h the p e a k a r o u n d 40 M e V is d o m i n a t e d b y T = ~- levels. The integrated cross sections for transitions into these g r o u p s o f levels have the same o r d e r o f m a g n i t u d e . F r o m a geometrical consideration [(TT, IOITT)E/(TT, 10IT+ 1, T ) 2 = T ] one expects for ~ , ( T = ½)/~(T = ~2) a ratio o f 1 : 2. The calculated a b s o r p t i o n p a t t e r n is also c o m p a r e d with an earlier calculation by E1 S a m a r a i et al. 34) which was p e r f o r m e d in the L-S coupling scheme using the s u p e r m u l t i p l e t a p p r o x i m a t i o n a n d Serber forces. I n ref. 34) the a b s o l u t e p o s i t i o n o f the dipole states was fixed by assigning the lowest ~:+; ~} level to an o b s e r v e d m a r k e d p e a k in the 7Li(7, p ) r e a c t i o n at E x ~ 12.5 M e V [ref. 35)]. El S a m a r a i et al. get no

70

A. ASWAD

et al.

dipole strength above 30 MeV, and also their calculated dipole sum is well above the experimental value. In the present paper the lowest ~+; { level is predicted at ~ 20 MeV. Also, the Cohen-Kurath wave functions provide strong M1 absorption lines between 9 and 17 MeV. Next, the nucleon decay of the giant resonance is considered. The calculated cross sections given here are upper limits. This is because the decay channels to levels of non-normal parity in 6He and 6Li and also the decay with emission of complex particles are neglected. These effects are significant only in the energy region of the main peak at ~ 40 MeV. This is due to the ls hole components decaying to nonnormal-parity levels in A = 6, and to the spatial symmetry of the dipole states in this energy region which favours the ( 1 + 3 + 3 ) decay. The neutron emission is the most important decay mode of the 7Li giant resonance. The calculation yields a ratio of about 5 : 2 for the integrated (7, n) and (7, P) branches. The total (7, n) cross sections reported by different authors are partly contradictory. Low-resolution measurements 2 6, Z5, 3 6) s h o w a s m o o t h increase from jddE

(MeV

rob)

~(mb

', i i r ] ~

t

, i , , , , ] , , , , I ....

",

7Li

,", / \ ~

j , rr

( ~-,po

, i , , , ,

)6He

,",

~ l',J ',/', I" /I Fr, I ~J ~ ,,' ~ / ~

exp

o ,_.,

~

10

. . . .

i

,

,~,

,

,

(~,Po

i

[

20

. . . .

]

. . . .

+

]

30

'

Pl

[

)

'

'

/~

I

. . . .

]

ZO

I ' ' 1 1

E ~- (MeV)

Fig. 3. Partial 7Li(7', p) and (7, n) cross sections. The experimental data (dashed curves) are taken from ref. 7).

N O N - N O R M A L - P A R I T Y STATES

71

threshold (7.25 MeV) to .~ 3 mb at ~ 18 MeV photon energy and a slow decrease towards 50 MeV, whereas older data 37) show pronounced minima at 17.5 and 25 MeV. Marked peaks around 16 and 17 MeV are found by (y, n) with higher resolution 26) and at 16 MeV by the electro-excitation 3t). Of particular interest are partial cross sections of the decay to individual levels in the residual nuclei. Measurements of photo-nucleon emission spectra 7,29, 30) have provided qualitative assignments of peaks in the particle distributions to possible combinations of levels in the target and final nuclei. Denisov 7) gives qualitative results for the VLi(7, Po, 1) 6 H e reactions. However, no quantitative branching ratios for decay to individual levels in the residual nuclei are established with confidence up till now. Fig. 3 shows the preliminary experimental and calculated cross sections for the (7, P) and (7, n) decays of 7Li to the ground and first excited states in 6He and 6Li, respectively. A group of levels around 20 MeV decays preferably to these levels. In the (7, Po) reaction several narrow lines were observed in this region. The calculation provides qualitatively the position of these lines but not the observed fine structure; the calculated level widths are of the order of 5 MeV. Also, the calculated integral (7, Po) cross section between 10 and 30 MeV is smaller than the value obtained by the activation method 7). On the other hand, the calculated decay 7Li(7, Pt) to the first excited state in 6He (2 +, 1.7 MeV) has the same shape and order of magnitude in this energy region, and the sum of strengths (y, P 0 + P t ) is comparable with the experimental one 7). Experimental determination of the (7, P) and (7, n) branching ratios would be a good check on this model calculation. Tentative calculated branching ratios are given in table 6 which reflects the favoured population of T = 1 levels compared with T = 0 ones. TABLE 6 Branches of VLi(y, p) and VLi(7, n) to the lowest levels in A ~ 6 (in ~ of the integrated photoabsorption cross section) 6He

g.s.

1st. e.s. 2+

(~)

5

10

6Li

g.s.

1st. e.s.

2nd. e.s.

3rd. e.s.

4th. e.s.

1+;0

3+;0

0+; 1

2+;0

2+; 1

5

7

7

4

16

(%o)

2nd. e.s. (1 +, 1)th....

unassigned

5

9 unassigned 32

The main peak in the photo-absorption curve at 38 MeV contains strong components with ls hole structure. The nucleon decay of these levels proceeds mainly to non-normal-parity levels of the A = 6 nuclei. The spatial symmetry of these dipole states will be dominated by the partitions [3, 3, 1], [3, 2, 1, 1 ] etc. Hence, this group of states decays preferably by complex particle emission, which is in agreement with

72

A. A S W A D e t al.

experiment showing a high yield for p + 2 t decay at these photon energies 7). Since the isospin of these dipole states is mainly T = ~, the neutron decay to low-lying 6Li levels with T = 0 is suppressed. 4.2. THE aBe P H O T O - R E S O N A N C E

In fig. 4 the calculated El photo-resonances in SBe above the g.s. and the first excited 2 + state (2.9 MeV) are presented in order to get some systematics on the model description of photo-absorption in lp shell nuclei as a function of the mass num>(6dE ( Me'V. rob)

6(mb)

i

8Be

i

photo obsorphon

10

first

2+ ~

1- 2- 3- ; T = I

2 10

I

0 . . . .

[

20

. . . .

~

. . . .

I

30

. . . .

I

. . . .

I

40

. . . .

,fo I EX 8Be

( MeV )

Fig. 4. Calculated photo-resonances in SBe above the ground state and the first excited 2+; 0 state.

ber. Comparing this figure with the corresponding curves for A = 14 [ref. 32)] a n d A = 7, a gradual shift of dipole strength from the upper to the lower peak with increasing A is noted. This is evident from the number of basic states of the types (ls)4(lp)A-5(2S, ld) 1 and (ls)3(lp) A-3, respectively. Comparing the two photo-resonances above the ground and first excited states, one notes a shift in the first maximum of 3.5 MeV which is just the calculated energy of the first level (2+; 0) using Cohen-Kurath wave functions. The experimental energy of this level is 2.9 MeV. The high-energy maximum shows the same energy shift. The structure of the dominating dipole states is given in table 7. Unlike the cases A = 7 and 14, the high-energy peak does not contain states with dominating ls hole structure. It is of interest to study the distribution of the ls hole strength for nuclei in the middle of the lp shell. The cross sections for the inverse reactions 7Li(p, 7o,1) [ref. 28)] leaving the abe

NON-NORMAL-PARITY

73

STATES

TABLE 7 Structure o f the strongest dipole states in aBe (j~r = 1 - ; T ~ 1) abe levels

1:

J'~

(MeV)

(MeV.mb)

22.1 25.4 28.2 31.7 36.1 36.9 37.5 38.3 38.4 38.8

41 14 8 8 13 11 22 9 9 9

C o n t r i b u t i o n o f configurations (in ~ ) 1

2

3

4

5

6

7

8

9

10 11

10.8 27.9 7.2 28.5 5.4 8.7 5.0 47.2 3.1 3.8 6.6 6.0 11.8 8.8 4.2 5.1 20.8 3.7 7.7 18.6 12.2 13.5 4.8 3.8 8.7 3.5 14.2 19.6 15.6 13.0 3.8 9.6 5.6 26.7 3.7 24.6 3.3 17.9 5.1 14.3 5.8 13.7 8.6 4.1 7.8 4.3 4.8 14.4 7.6 11.5 21.1 6.6 18.7 7.3 17.2 4.9 4.0 6.7 5.2 12.6 32.1 3.3 5.2 5.4 9.9 16.2 6.1 3.3 16.5 9.8 3.0 15.5

12

13

/4

15

6.9 3.5 3.7 13.6 15.1 8.2 12.3 7.3 13.5 8.4 3.2 9.4 12.3 7.7 10.3 4.0

C o n t r i b u t i o n s < 3 ~ (including those f r o m the configurations (p{)3(d~_)l a n d (ls)-l(p~_)l(p,~) *) have been omitted. T h e g r o u n d state is 4 5 ~ (p~)% 1 6 . 2 ~ (p{)a(p~)l, 3 4 ~ (pk)2(p½) 2 a n d 4 . 6 ~ (p¢)4. Configurations are assigned as follows: 1 2 3 4 5 6

=~: ~ ~ ~

(pk)3(d~)' (pk)3(d~)~ (pk)3(2s)l (p~)2(p~:)~(d~)l (pk)2(p~)l(dk) t (pk)2(p~)'(2s)'

7 8 9 10 11

~ ~~~~

(pk)'(p¢)a(d~) ' (p~:)'(p½)Z(d/r)~ (pk)~(p½)2(2s)~ (p~_)3(d/_)l (p_})3(2s)l

12 - ( I s ) - ' ( p ~ ) 5 13 ~ ( l s ) - l ( p ~ ) 4 ( p ~ ) ~ 14 (ls)-~(pk)3(pk) 2 15 ~_ ( l s ) - l ( p ~ ) Z ( p ~ ) 3

nucleus in the g.s. and first excited state are shown in fig. 5. G o o d agreement is obtained in the positions of the peaks. The magnitude of the calculated cross section

Me',/ #b

r

ub Hs~b 7Li (P, ~c ';SBe

,..~.~ ',~'-----.....~

29(

20

2

/I

9

I

," tt ~."

108~

" ' , 7Li (: ~I) ~Be

"'.,

~ 29

02 3C

Lx , 8Be )

Fig. 5. The 7Li(p,7) reactions leading to the g r o u n d state and the first excited 2+; 0 state in 8Be. D a s h e d curves: experiment 2s); solid lines: this calculation.

74

A. ASWAD et al.

(divided by 4n) is somewhat lower than the experimental one 28). One should notice however, that the angular distribution for energies around the main maxima is biased in the direction 0 = 90 ° at which the experiment was performed. The narrow peaks observed below 20 MeV might be due to M1 de-excitation. The calculation with Cohen-Kurath wave functions provides 0.75 MeV •mb M1 strength which is almost concentrated in two peaks at 17 and 19 MeV excitation energies.

5. The 9Be(p, 2p)SLi reaction The (p, 2p) reaction with light nuclei provides information on the position of levels with a (ls)3(lp) a - 3 structure. The summed-energy spectrum for the knock-out of a ls proton from 9Be has a broad peak at a separation energy E S of about 30 MeV. The angular behaviour of the peak studied by Tyr6n et al. 27) reveals that it consists of at least two components. Tyren et al. assumed in the analysis of their experiment two levels at Es = 25.4, 32.3 MeV and the same occupation number N = 1.0 for both components.

o.:1 S 0.5

10

,2",T-1:

10 0.2 S

20 Ex(SLi)/MeV

15

I

rl

Ex(SLi)/MeV 15

I I,iIi

,1-iT.l:

Fig. 6. Calculated spectroscopic factors S for separation of a Is nucleon from the 9Be ground state. For comparison the level positions and occupation numbers N assumed by Tyr6n et al. 27) in the analysis of their 9Be(p, 2p)SLi experiment are also presented.

The spectroscopic factors for this process have been calculated (see fig. 6). Compared with the assumptions of Tyr6n et al., a more complicated distribution of the strengths is obtained. However, two groups of levels with large spectroscopic factors also appear. Fig. 6 indicates that the Hamiltonian used (which is fixed a priori) reproduces the positions of high-lying ls hole levels excited by the (p, 2p) reaction with energy deviations of about 2 or 3 MeV. The same accuracy has been found in the investigation of photo-reaction data on Is hole levels (see sect. 4).

N O N - N O R M A L - P A R I T Y STATES

75

6. Conclusions

The non-normal-parity states in A = 7, 8 nuclei have been investigated in the configuration space of all non-spurious 1 h~o excitations. A Hamiltonian well describing such states in nuclei at the upper end of the lp shell has been adopted. In the energy region where the lowest odd-parity levels appear (E x -~ 20 MeV) the compound nucleus SBe has many resonances. Information on level positions and level parameters can be obtained only by a complex many-level R-matrix fit. The model used reproduces the characteristic properties (parent structure, radiative widths) of all reported odd-parity levels with good accuracy. Deviations of the calculated excitation energies from experimental ones are less than 1 MeV. A discussion of the additionally predicted states gives some reasons that these states have not yet been observed. In 7Li the even-parity states predicted between I I and 18 MeV have no simple parent structure. Excitations of the types lp --+ (2s, ld) and Is -+ lp are strongly mixed. Individual level properties cannot be compared with experimental ones because even-parity assignments have not yet been reported. The model provides the lowest non-normal-parity state just in the energy region where levels of unknown parity appear in the present-day spectrum. The 7Li giant resonance is roughly divided into two parts with quite different decay properties. The experimentally established configurational splitting is reproduced by the model. The calculated total E1 absorption cross section consists in the main of two peaks around 20 and 38 MeV. They are due to lp --+ (2s, ld) and ls --+ lp nucleon excitations, respectively. Contrary to earlier calculations the main contribution to the dipole sum comes from levels above 30 MeV. Cross sections and branching ratios for decay to several low-lying levels in 6He and 6Li have been predicted. The calculated cross sections for the inverse photo reactions 7 Li(p, 7o, ~) are in good agreement with the reported data. The spectroscopic factors for the knock-out of a ls nucleon in the 9Be(p, 2p)SLi reaction have been calculated, In agreement with the investigations of Tyrdn et al. z v), two groups of levels with large spectroscopic factors are predicted. The good overall agreement between the experimental and the calculated quantities (i.e. energy levels, spectroscopic factors, photo-reaction data), presented in this paper, gives us confidence that the model predictions can be a useful basis for further experiments on non-normal-parity states in 7Li and 8Be. References 1) 2) 3) 4) 5) 6)

H. U. J~iger, H. R. Kissener and R. A. Eramzhian, Nucl. Phys. AI71 (1971) 16; AI71 (1971) 584 S. Cohen and D. Kurath, Nucl. Phys. 73 (1965) l V. Gillet and E. A. Sanderson, Nucl. Phys. 54 0964) 472 S. S. M. Wong and D. J. Rowe, Phys. Lett. 30B (1969) 150 T. Lauritsen and F. Ajzenberg-Selove, Nucl. Phys. 78 (1966) 1 J. P. Elliott a~ad T. H. R. Skyrme, Proc. Roy. Sac. A232 (1955) 561

76 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)

23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37)

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