STUDY OF DEEPLY-BOUND HOLE STATES IN THE Zr-REGION VIA THE ([MATH], 3He) REACTION

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STUDY OF DEEPLY-BOUND HOLE STATES IN THE Zr-REGION VIA THE ([MATH], 3He) REACTION

G. Seegert, A. Pfeiffer, P. Grabmayr, T. Kihm, K. Knöpfle, G. Mairle, G.

Wagner, V. Bechtold, L. Friedrich

To cite this version:

G. Seegert, A. Pfeiffer, P. Grabmayr, T. Kihm, K. Knöpfle, et al.. STUDY OF DEEPLY-BOUND

HOLE STATES IN THE Zr-REGION VIA THE ([MATH], 3He) REACTION. Journal de Physique

Colloques, 1984, 45 (C4), pp.C4-85-C4-89. �10.1051/jphyscol:1984408�. �jpa-00224073�

JOURNAL DE PHYSIQUE

Colloque C4, supplément au n°3, Tome 45, mars 1984

page C4-85

STUDY OF DEEPLY-BOUND HOLE STATES IN THE Zr-REGION VIA THE ( d , He) REACTION

G. Seegert, A. Pfeiffer, P. Grabmayr^ T. Kihm, K.T. Knopfle, G. Mairle, G.J. Wagner+ V. Bechtold* and L. Friedrich*

Max-Planck-Institut ftir Kernphysik, 6900 Heidelberg, F.R.G.

*Kemforschungszentrwn Karlsruhe, IAK II, 7500 Karlsruhe, F.R.G.

Résumé - Le trou proton lf_ ,_ a été localisé par la réaction

""3 86 90 92 92

(d, He) sur Kr, Zr et Mo. Il montre une structure fine très prononcée et une largeur qui augmente avec le carré de son énergie.

Abstract - The complete It . proton hole strength has been lo- calized in the (d, He) reaction at 52 MeV. The second moment of the highly structured strength distribution increases with the square of its energy.

In 1980 our group / l / for the first time determined the spin of an

•+ 3

inner hole state by measuring vector-analyzing powers of a (d. He) reaction. We located and identified a broad "giant-resonance-like"

89

l f

7 /

quasihole state in Y. Its fine structure made it an inter- esting object for a more detailed investigation. We present results

* 3 86 90 92 92 obtained in a study of the (d. He) reaction on Kr, ' Zr and Mo at 5 2 MeV.

The experimental set-up is essentially as described in ref. 1. The numbers of A E - E telescopes has been increased to six. The beam pola- rization of P=0.5 is now continuously monitored by a polarimeter uti- lizing the C(d,d ) C reaction at S

T

. =47 which is located about 1 m downstream of the target.

Fig. 1 shows He-spectra obtained at 6 ,=12.5 from all 4 targets.

One notices typically about 5 strong transitions to low-lying states (note the change of scale) which carry the valence lf_,_, 2p, ,

?

, 2p,,

?

and g

q /

2 strengths. The object of interest here is the broad structure extending between about 3 and 9 MeV of excitation which is dominated

+

present address: Physikalisehes Institut der Universitat Tubingen, 7400 Tubingen, Germany

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984408

C4-86 JOURNAL DE PHYSIQUE

by strength. We assumed a constant background, adjusted to the data at very negative Q-values, which falls of smoothly to zero in the region of isolated groups. Its angular distribution is structure- less and its analyzing power is small.

Fig. 2 shows angular distributions and vector-analyzing powers iTll from 2plI2 and

2p

(left) and fgi2 and f7,,2 (right) transitions on

3/2

8 6 ~ r together with local, zero-range DWBA calculations. Attempts to improve the fit to iTll(o) are in progress. The experimental value of iTll(0) show a near reflection symmetry about zero for j=lf1/2 pairs, which allows a unique spin assignment.

The gross properties of the If hole states: (i) sum rule exhaustion 7/2

(ii) centroid energies and (iii) widths are summarized in table 1.

They are based on strength distributions obtained from the cross section by per- forming DWBA calculations in small energy steps. In parenthesis we add for comparison

(and as a warning!) values based on only one DWBA calculation, performed for the centroid separation energy.

10.0 - _{, ,}

.

_\

I '\ s ~ r l ~ , 3 ~ e 1 8 5 ~ r 8 6 ~ r l a , 3 ~ e 1 8 5 ~ r .

' b

I i Ed = 52 MeV Ed = 52 MeV

l o . P

vamp

' 0 )

-

^{'so' , *<*\}

2 -Ib::

-

0s

...

^.I

k :

^b...:9~m\

P I ,

:: .

^{\ k,'} '

^..,

^{' ! \ I \} *, "" ^{I - +} '

\_I ,

\ _{\ J '} - .

0.01 :

' - E x = 1 2 M V , ; I p m A- E,-OlSr~,v.

a - - - E ~ - O O H E V . I - ~ ~ ~ ~ D - - - E , = ~ ~ M P v J . ? , , , ~

- ,

I

0.5 -

-0.5 -

I

0 10 20 30 LO 0 10 20 30 LO

OCM e~~

4 [MeV)

Fig. 1 - Spectra of ( 6 , 3 ~ e ) Fig.

2 -

Angular distributions for

reactions various subshells

Table 1 - Gross properties of If hole states 7/2

Target zc2s/(2j+l) <Ex>/MeV r / M ~ v ~

02= ~ ( E - < E > ) ? c ~ s / ~ c 2 s b) DWBA for centroid Q-value only

The shell model sum is slightly overexhausted; this deficiency could be remedied e.g. by finite range and nonlocality corrections. The second moments for 9 0 1 9 2 ~ r and

9 2 ~ 0

should be considered equal within the estimated errors. The width for 8 6 ~ r , however, is significantly smaller.

The intermediate structure of the If quasihole in 8 5 ~ r is apparent 7/2

in fig.

3

which shows the strength with background subtraction and DWBA corrections performed. One recognizes intermediate structures at 3.4, 4.0, 5.5 and 7.5 MeV. It is tempting to associate them with doorway states whose decay widths increase with E as does the re-

X

levant level density p(EX) of more complex states. We believe that these intermediate structures contain a clue as to the doorway state mechanism of the quasihole decay.

As a tentative result we present weak

i evidence for excitation of a 2slI2 hole state in 8 9 ~ . The spectrum of fig. 1 when compressed shows a narrow structure of about

3

MeV FWHM at Ex=15 MeV (fig.

4

left) whose angular distribution is compatible with 1=0 transfer (fig. 4 right) considering that the go cross section is an upper limit only. The

9 7 ' 5

Ex IMeVl 3

2slI2 hole strength is exhausted. Yet

the cross section is very small as Fig.

3

- ^lf 7/2 strength compared to the f7/2 group; hence it distribution in 8 5 ~ r would be easy to miss the 1=0 group in

other target nuclei.

JOURNAL DE PHYSIQUE

E,(MeVI

0c.m. ( GRAD)

Fig.

4

- Evidence for a 2slI2 hole state

It is quite striking to realize how little data are available on the spin-orbit splitting of completely filled orbits. But even more is it surprising to learn that a quantity as fundamental as that is far from being understood microscopically. The present data exemplify the problem:

Fig. 5 summarizes the results obtained for the centroid energies. The values for valence shells have been corrected for stripping strengths.

The 2p-orbitals and If-orbitals show about a constant spin-orbit splitting. A Hartree-Fock calculation for using Skyrme 111 forces

/2/

yields very satisfactory results, with the possible exception of the tentatively reported 2s hole state. Note, that the 2s level is indeed expected above the level for whose presence we have no indication in the present analysis. The experimentally determined If spin-orbit splitting contrasts to a result of only 1.5 MeV from BHF- calculations /3/ using a Reid soft core potential. Scheerbaum /3/ has traced the problem back

to

the contribution from spin-unsaturated sub- shells which comes in with a negative sign as a result of its origin from the exchange part of the central and tensor nucleon-nucleon interaction; in second order the tensor part is estimated /4/ to in- crease the spin-orbit splitting to about 3.5 MeV.

Fig.

6

finally, where the square-root of the widths of the If 7/2 quasihole state has been plotted E. the centroid energy (measured relative to the Fermi energy EF), shows that our data are compatible with a relation l ? = a ~ ~ which is expected to hold for infinite Fermi

systems /5/. The slope corresponding to a=1/(15 MeV) fits into the

E = < E > - E F (MeV)

F i g . 5 - C e n t r o i d s e p a r a t i o n e n e r g i e s F i g . 6

-

W i d t h s o f I f

h o l e s t a t e s 7/2

r a n g e o f e m p i r i c a l v a l u e s a v a i l a b l e t o d a t e . We a r e p l a n n i n g e x p e r i - m e n t s o n l i g h t e r n u c l e i t o v e r i f y t h e s t r a i g h t l i n e b e h a v i o u r o f f i g . 6 f o r s m a l l e r v a l u e s o f E.

I n s u m n a r y t h e l f 7 / 2 q u a s i h o l e s t a t e h a s b e e n l o c a l i z e d i n s e v e r a l n u c l e i o f t h e Z r r e g i o n . I t s p u r i t y a n d i t s p r o n o u n c e d f i n e s t r u c t u r e s h o u l d make i t a n i d e a l o b j e c t f o r m i c r o s c o p i c s t u d i e s o f t h e . q u a s i - h o l e d e c a y .

R e f e r e n c e s :

1 - STUIRBRINK A .

g . ,

^{Z .} P h y s i k

A297

( 1 9 8 0 ) 307

2 - BEINER M . , FLOCARD H . , G I A I N.V., a n d QUENTIN P . , N u c l . P h y s .

A238

( 1 9 7 5 ) 29

3

-

SCHEERBAUM R.R., N u c ~ . P h y s .

A257

( 1 9 7 6 ) 77 a n d P h y s . L e t t . B63 ( 1 9 7 6 ) 3 8 1

4 - SCHEERBAUM

RX,

P h y s . L e t t . ( 1 9 7 6 ) 1 5 1

5

-

BERTSCH G.F., BORTIGNON P . F . , a n d BROGLIA R . A . , R e v s . ~ o d . P h y s . 55 ( 1 9 8 3 ) 287

-