Pionic M X-rays of 166, 168Er and 176Hf

Volume 143B, number 4, 5, 6

PHYSICS LETTERS

16 August 1984

P I O N I C M X-RAYS O F 166'168Er A N D 176Hf ~ Y. T A N A K A , R.M. S T E F F E N Department of Physics, Purdue University, West Lafayette, I N 47907, USA

E.B. S H E R A , W. R E U T E R 1, M.V. H O E H N Los Alamos National Laboratory, Los Alamos, N M 87545, USA

and

J.D. Z U M B R O Department of Physics, Princeton University, Princeton, N J 08544, USA

Received 28 March 1984 The X-ray energies and widths of the pionic 4f ~ 3d transitions (M X-rays) of 166'16SEr and 176Hf have been measured. The measured widths [ F(166Er) = 19.7(0.9) keV, F(16SEr)= 19.4(1.0) keV, and F(176Hf) = 27.8(4.3) keV] are in good agreement with theoretical calculations, and suggest that anomalous widths, if they exist, begin at or above Z = 73.

T h e p i o n - n u c l e u s strong interaction in pionic atoms causes b o u n d pionic levels to be shifted in energy a n d to be b r o a d e n e d . These energy shifts a n d widths are usually analyzed in terms of an optical potential [1,2]. The optical potential contains the s- a n d p-wave scattering lengths of the ~r-N scattering a m p l i t u d e (modified to include multiple scattering of the pion). It also c o n t a i n s an i m a g i n a r y term, which is p r o p o r t i o n a l to the square of the nuclear mass density, to describe pion absorption b y two nucleons. This theory has successfully explained the m a j o r features of pionic atom data with a global set of optical potential parameters [2]. However, recent experiments [3-6] ,1 on pionic 23Na, 181Ta, 2°sPb, This work was supported by the US Department of Energy. All work was carried out as Los Alamos National Laboratory. 1 Present address: Department of Physics, University of Ti~bingen,Ti~bingen,West Germany. ,i The very recent work of d'Achard van Enschut et al. [7] which was published after the present paper was submitted, also shows anomalously small 3d-state widths and shift in Pt and Au.

a n d 2°9Bi indicate widths of pionic transitions b e t w e e n deeply b o u n d pionic states that are 1 . 5 - 3 times smaller than predicted b y theory (see fig, 1). These discrepancies c a n n o t be explained within the framework of a n optical model with reasonable variations of the potential parameters [8-11], a n d if confirmed would imply a failure of our u n d e r s t a n d i n g of p i o n a b s o r p t i o n b y the nucleus. With the hope of better u n d e r s t a n d i n g the exp e r i m e n t a l situation, we measured the M a n d N X-rays of pionic 166"168Er a n d 176Hf. These isotopes occur in a mass range where a serious systematic discrepancy appears to begin (fig. 1), yet their M X-ray widths a n d intensities make them more tractable experimentally than, for example, isotopes in the Pb region. The experiments were performed at the biomedical c h a n n e l of the Los A l a m o s M e s o n Physics Facility. T h e target a r r a n g e m e n t , Ge(Li) spectrometer, a n d d a t a acquisition system have b e e n described in detail in previous papers [13,14]. We used as targets 19.2 g of 166Er (96.2% enrichment), 19.1 g of 168Er (95.5% enrichment), a n d 6.1 g of 176Hf (68.7% enrichment), all in the form of oxides. The 7-ray spectra

0 3 7 0 - 2 6 9 3 / 8 4 / $ 0 3 . 0 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

347

Volume 143B, number 4, 5, 6

PHYSICS LETTERS

100-

j.,"

0 i

j.....

10

°

-.- '"

1 50

60

7 0'

8 'o

90

I00-

.- --" ~L~ ¸¸ ¸ ¸ ¸

¸

0

10"

• present data 1 50

0

70

80

90

Z Fig. 1. Strong interaction widths r of the pionic 4f ~ 3d transitions (upper figure) and strong interaction energy shifts of the same transitions (lower figure). The figures include the present results for 166Er and 176Hf (black circles), data from ref. [4] (open circles), data from ref. [5] (squares), and data from table 1 of ref. [12] (triangles). (Points without error bars have errors smaller than the size of the plotted point.) The energy shifts are measured with respect to the electromagnetic values of the pionic atoms with the finite size effect of the charge distribution included. Theoretical calculations using the optical potential parametrization of Krell and Ericson [2] are shown by dotted lines.

f r o m 60 Co a n d t98Au were r e c o r d e d s i m u l t a n e o u s l y with the p i o n i c d a t a for energy calibration. T h e y - r a y spectra from 5aCr, 6°C0, n°Ag, a82Ta, a n d 199Au were also m e a s u r e d in a s e p a r a t e run to p r o v i d e further i n f o r m a t i o n for energy calibration. T h e energy c a l i b r a t i o n was b a s e d on a q u a d r a t i c i n t e r p o l a t i o n of the o b s e r v e d channel p o s i t i o n s of these y - r a y lines. T h e y-rays f r o m the Ge(n, n') reaction occur348

16 August 1984

ring in the Ge(Li) d e t e c t o r cause a significant b a c k g r o u n d in the X - r a y spectrum. The p e a k s from this reaction are b r o a d a n d they have long tails t o w a r d higher energies due to the nuclear recoil energy received in the scattering process. In the present e x p e r i m e n t the 835 keV y - r a y from the 72Ge(n, n') reaction o v e r l a p p e d the M X - r a y line of pionic erbium. However, the y-rays from this r e a c t i o n could be a l m o s t c o m p l e t e l y suppressed relative to the X - r a y spectra b y setting app r o p r i a t e l y n a r r o w time gates on the G e d e t e c t o r spectra, thereby using the n e u t r o n time-of-flight f r o m target to Ge(Li) d e t e c t o r to d i s c r i m i n a t e against n e u t r o n - p r o d u c e d b a c k g r o u n d events. The M X - r a y w i d t h of 176Hf was affected b y the 177Hf target i m p u r i t y because of its large a b u n d a n c e (14.9%) and b e c a u s e of its b r o a d line width d u e to q u a d r u p o l e hyperfine splitting. The hyperfine-split s p e c t r u m of the M X-rays of 177Hf was calculated b y using the g r o u n d - s t a t e q u a d r u p o l e m o m e n t value of ref. [15] a n d the theoretically c o m p u t e d t76Hf-177Hf isotope shift; this s p e c t r u m was then s u b t r a c t e d from the e x p e r i m e n t a l 176Hf spectrum. Fig. 2 shows the p i o n i c M X - r a y spectra of t66A68Er a n d 176Hf. A m o n g the nuclear y-rays o b served in this experiment, the 835 keV y - r a y from the 72Ge(n, n') reaction and the 844 keV y - r a y f r o m the 27Al(n, n') reaction were identified in the s p e c t r a of b o t h t66Er a n d 168Er. S u b t r a c t i o n of the 835 keV y - r a y from the e r b i u m spectra was s t r a i g h t f o r w a r d because the p o s i t i o n a n d the shape of this line were k n o w n from a s e p a r a t e measurement. The 1014 keV y - r a y from the 27Al(n, n') r e a c t i o n was also identified in the 176Hf spectrum. These y-rays f r o m the G e ( L i ) d e t e c t o r were easily identified b y c o m p a r i n g the p r e s e n t s p e c t r a a n d those taken s i m u l t a n e o u s l y with a wider time-gate setting. T h e origin of o t h e r n e a r b y y-rays, s o m e of which are visible in fig. 2, is n o t clear, though they are p r o b a b l y y-rays f r o m the target following p i o n absorption. A n a l y s i s of the M a n d N X - r a y spectra is b a s e d o n the c o n v e n t i o n a l m e t h o d of line fitting [13]. T h e fitting function was c o m p o s e d of a linear b a c k g r o u n d a n d a g a u s s i a n - c o n v o l u t e d lorentzian with e x p o n e n t i a l tails. T h e gaussian width a n d the e x p o n e n t i a l tail p a r a m e t e r s were d e t e r m i n e d b y

V o l u m e 143B, n u m b e r 4, 5, 6

PHYSICS LETTERS

16 A u g u s t 1984

Table 1 T r a n s i t i o n energies, s t r o n g - i n t e r a c t i o n e n e r g y shifts a) c, a n d w i d t h s F of the p i o n i c X - r a y t r a n s i t i o n s of 166"168Er a n d 176Hf. Nucleus

( 4 f ~ 3d transitions ) 166Er 168Er 172 H f (5g ---* 4 f transitions) 166E r 16s Er 176 H f

Transition

Experiment

e n e r g y (keV)

c(keV)

F(keV)

~(keV)

C a l c u l a t i o n b) F(keV)

873.2(0.3) 872.2(0.3) 982.0(1.0)

- 17.3(0.3) - 16.3(0.3) - 20.7(1.0)

19.7(0.9) 19.4(1.0) 27.8(4.3)

- 14.6 - 14.2 - 19.1

17.3 17.2 26.8

392.699(33) 392.702(33) 441.098(11)

- 0.344(33) - 0.343(33) - 0.562(11 )

-0.278 - 0.280 - 0.469

a) T h e listed e n e r g y shifts are d u e to the s t r o n g i n t e r a c t i o n only; t h e y are n o t the s u m o f s t r o n g i n t e r a c t i o n a n d C o u l o m b finite size shifts. b) T h e o p t i c a l p o t e n t i a l of Krell a n d E r i c s o n [2] w a s u s e d in the c a l c u l a t i o n .

1100 166

/L,J.J 9OO-

800

i

i

850

900

i

1000U] Z

800-

0 0

600-

~

168

I

i

rllll~l"l~' '~r'l ~''''r

800

zr

k0.

i

i

r

850

900

950

,5OO

176 i

400-

1

i

i

Hf

!

i

3OO

900

f

i

i

950

1000

1050

ENERGY

(keV)

Fig. 2. Pionic M X - r a y s p e c t r a of 166'168Er a n d 176Hf. T h e solid c u r v e s r e p r e s e n t o u r fits to the spectra, o b t a i n e d b y u s i n g a f u n c t i o n c o m p o s e d of a linear b a c k g r o u n d ( s h o w n d o t t e d ) p l u s a g a u s s i a n - c o n v o l u t e d l o r e n t z i a n with e x p o n e n t i a l tails. T h e p e c u l i a r s t r u c t u r e s o n the l o w - e n e r g y sides of the 166j68Er lines a r e d u e to the 835 keV "/-rays f r o m the 72Ge(n, n ' ) r e a c t i o n w h i c h h a v e l o n g tails t o w a r d s h i g h e r energies.

fitting the T-ray spectra of 6°Co and 198Au. The energy shifts and widths thus obtained are shown in table 1 and in fig. 1 (black circles). The quoted errors include the statistical fitting error (including variations due to assuming linear or quadratic spectral backgrounds) and the errors due to uncertainties in subtracting the nuclear T-rays. The error also includes a possible y-ray peak at 965 keV of 176Hf (which would decrease the M X-ray width of ]76Hf by 2.2 keV). The present M X-ray results for 16SEr are in agreement with previous data [5]; c = 18.0(1.3) keV ,2 and F = 19.5(13.0) keV. The isotope effect, a well-known feature of the X-rays of light pionic atoms [16], was observed in the measured energy shifts of 166'168Er. To compare the present results with calculation, the pionic atom binding energies and eigenfunctions were computed numerically with the computer program PION [17]. The pion-nucleus strong interaction was represented by the optical potential of Krell and Ericson [2]. The binding energies were corrected for vacuum polarization effects, self-energy effects, electron screening, and relativistic recoil. The corrections also included the effects of the nuclear polarization due to high-lying giant resonances. The nuclear polarization energies were estimated from muonic values [18], modified for the pion mass ( - 2 0 0 eV in the 3d states of Hf). Calculated results are shown in table 1 and in ~c2 C a l c u l a t e d f r o m the t r a n s i t i o n e n e r g y o f ref. [5].

349

Volume 143B, number 4, 5, 6

PHYSICS LETTERS

fig. 1 ( d o t t e d lines). T h e e x p e r i m e n t a l v a l u e s f o r the widths and energy shifts are slightly larger than the calculated values but are entirely consistent with existing theory, in contrast to the anomalous M X-ray widths previously reported for pionic atoms [4-6] in this mass region. E x p e r i m e n t s a r e c u r r e n t l y b e i n g p l a n n e d t o extend the region studied to pionic atoms of higher Z for which the apparent discrepancy with theory becomes progressively more pronounced.

References [1] M. Ericson and T.E.O. Ericson, Ann. Phys. 36 (1966) 323. [2] M. Krell and T.E.O. Ericson, Nucl. Phys. B l l (1969) 521. [3] A. Olin et al., Nucl. Phys. A312 (1978) 361.

350

[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

16 August 1984

J. Konijn et al., Nucl. Phys. A326 (1979) 401. C.J. Batty et al.,, Nucl. Phys. A355 (1981) 383. G.A. Beer et al., Bul. Am. Phys. Soc. 28 (1983) 966. J.F.M. d'Achard van Enschut et al., Phys. Lett. 136B (1984) 24. E. Friedman and A. Gal, Nucl. Phys. A345 (1980) 457. T.E.O. Ericson and L. Tauscher, Phys. Lett. l12B (1982) 425. R. Seki, Phys. Rev. C26 (1982) 1342. C.J. Batty et al., Nucl. Phys. A402 (1983) 411. A.R. Kunselman et al., Phys. Rev. C15 (1977) 1801. E.B. Shera et al., Phys. Rev. C14 (1976) 731. Y. Yamazaki et al., Phys. Rev. C18 (1978) 1474. Y. Tanaka et al., Phys. Rev. Lett. 51 (1983) 1633. I. Schwanner et al., Phys. Lett. 96B (1980) 268. Y. Tanaka, computer program PION, unpublished. Y. Tanaka, computer program MUON2, unpublished.