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A note on the interpretation of isotope shifts
Volume 20, number 6
A
NOTE
PHYSICS LETTERS
ON
THE
INTERPRETATION
1 April 1966
OF
ISOTOPE
SHIFTS
D. N. STACEY
Clarendon Laboratory, Oxford Received 12 March 1966
It is pointed out that in tin observed irregular changes in the mean square radius of the nuclear charge distribution cannot be reconciled with the common assumption that such irregular changes are due solely to the effects of nuclear deformation.
F i e l d - d e p e n d e n t isotope shifts a r e to a good a p p r o x i m a t i o n p r o p o r t i o n a l to d i f f e r e n c e s in the m e a n s q u a r e r a d i u s ( ~ ) of the proton charge d i s t r i b u t i o n between isotopes. If ( r 2) w e r e a smoothly v a r y i n g function of N, the isotopes of a m e d i u m - h e a v y or heavy e l e m e n t would be spaced a p p r o x i m a t e l y equidistantly on a w a v e - n u m b e r s c a l e in the s p e c t r a l l i n e s of that e l e m e n t . Obs e r v e d d e p a r t u r e s f r o m equal spacing in s p e c t r a l l i n e s of the r a r e - e a r t h e l e m e n t s w e r e i n t e r p r e t e d by B r i x and K o p f e r m a n n [1] in t e r m s of an i r r e g u l a r l y v a r y i n g n u c l e a r deformation; s u b s e q u e n t m e a s u r e m e n t s of d e f o r m a t i o n s by the method of Coulomb excitation have shown that isotope shift r e s u l t s for heavy e l e m e n t s can be accounted for at l e a s t s e m i - q u a n t i t a t i v e l y in this way. In consequence, i r r e g u l a r v a r i a t i o n s in isotope shifts have f r e q u e n t l y been a t t r i b u t e d solely to the effects of the changing n u c l e a r d e f o r m a t i o n f r o m isotope to isotope; the d e f o r m a t i o n may be of e i t h e r the s t a t i c or v i b r a t i o n a l type. F o r m u l a e for the f i e l d - d e p e n d e n t shift b a s e d on this a s s u m p t i o n have often b e e n quoted [2-8] and in s o m e c a s e s used to d e r i v e d e f o r m a t i o n s of n u c l e i for which t h e r e a r e data f r o m isotope shift e x p e r i m e n t s but not f r o m Coulomb excitation [2-4]. We wish to point out, however, that in the atomic s p e c t r u m of tin, m a r k e d i r r e g u l a r i t i e s in the isotope shifts have b e e n o b s e r v e d which a r e i m p o s s i b l e to explain in t e r m s of n u c l e a r d e f o r m a tion. T h r e e sets of m e a s u r e m e n t s e x i s t [9-11], each for a different s p e c t r a l line, and the m o s t p r o b a b l e values of the r e l a t i v e field shifts a r e as follows [11]: Mass
numbers Relative
shifts
644
T h e s e r e l a t i v e shifts a r e the changes in (r 2) between s u c c e s s i v e isotopes as f r a c t i o n s of that o c c u r r i n g between l l 2 S n and l l 4 S n . The d e f o r m a t i o n s of the tin isotopes a r e all v e r y s m a l l , and n e a r l y equal; it can e a s i l y be shown that they cannot account for m o r e than a s m a l l f r a c t i o n of the field s h i f t s . In p a r t i c u l a r , t h e r e is a s y s t e m a t i c (though not r e g u l a r ) d e c r e a s e in 5(rZ)/SN over the range of isotopes which is shown by the isotope shift r e s u l t s and which cannot be explained in t e r m s of the s m a l l changes in d e f o r m a t i o n . In o r d e r to do so, it would be n e c e s s a r y to a s s u m e that the n u c l e a r d e f o r m a t i o n s of tin a r e as shown in the continuous curve in fig. 1, in which t h e r e is obvious d i s a g r e e m e n t with the Coulomb exitation data [12, 13] shown in the b r o k e n c u r v e . Thus, in the even isotopes of tin, the r a d i a l charge d i s t r i b u t i o n changes in a way which exhibits specific shell effects. While these effects a r e p a r t i c u l a r l y s t r i k i n g in tin as a r e s u l t of the e x t r e m e l y s m a l l d e f o r m a t i o n s of the isotopes, they a r e c l e a r l y not confined to this e l e m e n t . In other e l e m e n t s , p a r t i c u l a r l y c a d m i u m and t e l l u r i u m , effects of this kind will be d i s c u s s e d in
~0
112-114114-116 116-118 116-129 120-122 122-124 MMf.f NV~mE~
1
0.99
0.72
0.74
0.61
O°26
Fig. I .
Volume 20, number 6
PHYSICS LETTERS
a l a t e r p a p e r [14] t o g e t h e r with d e t a i l s of the a r g u m e n t s p r e s e n t e d h e r e . The r e s u l t s f o r tin, howe v e r , p r e s e n t the m o s t d i r e c t e v i d e n c e that i r r e g u l a r v a r i a t i o n s in isotope shifts can a r i s e f r o m r a d i a l as well as d e f o r m a t i o n e f f e c t s , and any a t t e mpt to i n t e r p r e t i s o to p e shifts s a t i s f a c t o r i l y m u s t take this f a c t into account.
References 1. P. Brix and H. Kopfermann, Z. Phys. 126 (1949) 344. 2. A.S.Meligy, S.Tadros and M.A.E1 Wahab, Nucl. Phys. 16 (1960) 99. 3. A.R. Striganov, V.A. Katulin and V.V. Eliseev, Optik i Spektr. 12 (1962) 171 (Optics and Spectr. 12, 91. 4. A. R. Striganov, A. F. Golovin, M.P. Gerasimova, Optik i Spektr. 14 (1963) (Optics and Spectry (USSR) (Engl. Transl.) 14 (1963) 3.
INVESTIGATION
IApril 1966
5. N.J.Ionesco-Pallas, Physics Letters 6 (1963) 93. 6. E.E. Fradkin, Zh. Eksper. Teor. Fiz. 42 (1962) 787; Soviet Physics J E T P 15 (1962) 550. 7. F.A. Babushkin, Zh. Eksper. Teor. Fiz. 44 (1963) 1661; Soviet Physics J E T P 17 (1963) 1118. 8. F.A. Babushkin, Zh. Eksper. Teor. Fiz. 45 (1963) 1478; Soviet Physics J E T P 18 (1964) 1022. 9. K.Murakawa, J. Phys. Soc. Japan 9 (1954) 876. 10. W. R. Hindmarsh and H. G. Kuhn, Prec. Phys. Soc. A 68 (1955) 433. 11, D.N. Stacey, Proc. Roy.Soc. A280 (1964)439. 12. D. G. Alkhazov et al., Zh. Eksper. Teor. Fiz. 33 (2957) 1036; Soviet Physics JETP 6 (1958) 1036. 13. P.H. Stelson and F. K. McGowan, Phys. Rev. 110 (1958) 489. 14. W.H. King, H.G. Kuhn and D. N. Stacey (to be published).
ON THE FINE STRUCTURE OF SIX BALMER-SERIES OF DEUTERIUM
LINES
OF T H E
L. CSILLAG
Central Research Institute for Physics, Budapest Received 9 March 1966
We have measured the wavelengths of the apparent doublet components of six Balmer lines of deuterium. The value of the Rydberg constant resulting from our measurement is in good agreement with that accepted up to now.
The quantum t h e o r y of o n e - e l e c t r o n a t o m s which has b e e n w o r k e d out in g r e a t d e t a i l could be p r o v e d to be v a l i d with the help of o p t i c a l and m i c r o w a v e t e c h n i q u e s with high a c c u r a c y f o r e n e r g y l e v e l s of low main quantum n u m b e r s . F o r e x c i t e d l e v e l s of high m a i n quantum n u m b e r s h o w e v e r , the v a l i d i t y of the t h e o r y could be shown only by an a n a l y s i s of the w a v e l e n g t h data of the l i n e s of u n r e s o l v e d fine s t r u c t u r e [1,2]. F o r a m o r e convincing c o n f i r m a tion of the t h e o r y f u r t h e r high p r e c i s i o n m e a s u r e m e n t on the l i n e s of r e s o l v e d fine s t r u c t u r e a p p e a r a ll the m o r e n e c e s s a r y as in the c a s e of highly excited levels certain considerations make small d e v i a t i o n s f r o m t h e o r y a p p e a r p o s s i b l e [3]. We have t h e r e f o r e c a r r i e d out w a v e l e n g t h m e a s u r e m e n t s on the l i n e s D~ - D~ which had up to now not b e e n d e t e r m i n e d with a p p r o p r i a t e a c c u r a c y . Ou r r e s u l t s showed that the wave n u m b e r s of the o p t i cal l y r e s o l v a b l e c o m p o n e n t s a g r e e with those c a l c u l a t e d t h e o r e t i c a l l y within a m e a s u r i n g
e r r o r of 2 x 10-3 c m - 1 . Thus, the t h e o r y c o r r e c t l y d e s c r i b e s - at l e a s t to the g i v en a c c u r a c y the l o c a t i o n and s t r u c t u r e of the l e v e l s up to the m a i n quantum n u m b e r n = 9. In addition, it now b e c a m e p o s s i b l e to d e t e r m i n e the R y d b e r g const an t with a much s m a l l e r e r r o r . As light s o u r c e p u r e d e u t e r i u m gas of 0.03 T o r t p r e s s u r e was u s e d and e x c i t e d in highf r e q u e n c y r i n g - d i s c h a r g e , the tube being cooled by liquid n i t r o g e n . A F a b r y - P e r o t i n t e r f e r o m e t e r c o m b i n e d with a q u a r t z s p e c t r o g r a p h e n s u r e d an a p p r o p r i a t e r e s o l u t i o n . As w a v e l e n g t h s t a n d a r d s we used the 198Hg l i n es 4358. 3 3 7 5 ~ and 4046. 5716 A [4]. F u r t h e r d e t a i l s of o u r m e a s u r e m e n t s will be r e p o r t e d e l s e w h e r e [5]. Tab l e 1 s u m m a r i z e s o u r e x p e r i m e n t . The t h i r d c o l u m n contains the m e a s u r e d r e s u l t s . All the Bal. m e r - l i n e s i n v e s t i g a t e d c o n s i s t of s e v e n c o m p o nents, h o w e v e r , only two g r o u p s of t h r e e o r four c o m p o n e n t s e a c h could be r e s o l v e d by o u r o p t i cal
645
A
NOTE
PHYSICS LETTERS
ON
THE
INTERPRETATION
1 April 1966
OF
ISOTOPE
SHIFTS
D. N. STACEY
Clarendon Laboratory, Oxford Received 12 March 1966
It is pointed out that in tin observed irregular changes in the mean square radius of the nuclear charge distribution cannot be reconciled with the common assumption that such irregular changes are due solely to the effects of nuclear deformation.
F i e l d - d e p e n d e n t isotope shifts a r e to a good a p p r o x i m a t i o n p r o p o r t i o n a l to d i f f e r e n c e s in the m e a n s q u a r e r a d i u s ( ~ ) of the proton charge d i s t r i b u t i o n between isotopes. If ( r 2) w e r e a smoothly v a r y i n g function of N, the isotopes of a m e d i u m - h e a v y or heavy e l e m e n t would be spaced a p p r o x i m a t e l y equidistantly on a w a v e - n u m b e r s c a l e in the s p e c t r a l l i n e s of that e l e m e n t . Obs e r v e d d e p a r t u r e s f r o m equal spacing in s p e c t r a l l i n e s of the r a r e - e a r t h e l e m e n t s w e r e i n t e r p r e t e d by B r i x and K o p f e r m a n n [1] in t e r m s of an i r r e g u l a r l y v a r y i n g n u c l e a r deformation; s u b s e q u e n t m e a s u r e m e n t s of d e f o r m a t i o n s by the method of Coulomb excitation have shown that isotope shift r e s u l t s for heavy e l e m e n t s can be accounted for at l e a s t s e m i - q u a n t i t a t i v e l y in this way. In consequence, i r r e g u l a r v a r i a t i o n s in isotope shifts have f r e q u e n t l y been a t t r i b u t e d solely to the effects of the changing n u c l e a r d e f o r m a t i o n f r o m isotope to isotope; the d e f o r m a t i o n may be of e i t h e r the s t a t i c or v i b r a t i o n a l type. F o r m u l a e for the f i e l d - d e p e n d e n t shift b a s e d on this a s s u m p t i o n have often b e e n quoted [2-8] and in s o m e c a s e s used to d e r i v e d e f o r m a t i o n s of n u c l e i for which t h e r e a r e data f r o m isotope shift e x p e r i m e n t s but not f r o m Coulomb excitation [2-4]. We wish to point out, however, that in the atomic s p e c t r u m of tin, m a r k e d i r r e g u l a r i t i e s in the isotope shifts have b e e n o b s e r v e d which a r e i m p o s s i b l e to explain in t e r m s of n u c l e a r d e f o r m a tion. T h r e e sets of m e a s u r e m e n t s e x i s t [9-11], each for a different s p e c t r a l line, and the m o s t p r o b a b l e values of the r e l a t i v e field shifts a r e as follows [11]: Mass
numbers Relative
shifts
644
T h e s e r e l a t i v e shifts a r e the changes in (r 2) between s u c c e s s i v e isotopes as f r a c t i o n s of that o c c u r r i n g between l l 2 S n and l l 4 S n . The d e f o r m a t i o n s of the tin isotopes a r e all v e r y s m a l l , and n e a r l y equal; it can e a s i l y be shown that they cannot account for m o r e than a s m a l l f r a c t i o n of the field s h i f t s . In p a r t i c u l a r , t h e r e is a s y s t e m a t i c (though not r e g u l a r ) d e c r e a s e in 5(rZ)/SN over the range of isotopes which is shown by the isotope shift r e s u l t s and which cannot be explained in t e r m s of the s m a l l changes in d e f o r m a t i o n . In o r d e r to do so, it would be n e c e s s a r y to a s s u m e that the n u c l e a r d e f o r m a t i o n s of tin a r e as shown in the continuous curve in fig. 1, in which t h e r e is obvious d i s a g r e e m e n t with the Coulomb exitation data [12, 13] shown in the b r o k e n c u r v e . Thus, in the even isotopes of tin, the r a d i a l charge d i s t r i b u t i o n changes in a way which exhibits specific shell effects. While these effects a r e p a r t i c u l a r l y s t r i k i n g in tin as a r e s u l t of the e x t r e m e l y s m a l l d e f o r m a t i o n s of the isotopes, they a r e c l e a r l y not confined to this e l e m e n t . In other e l e m e n t s , p a r t i c u l a r l y c a d m i u m and t e l l u r i u m , effects of this kind will be d i s c u s s e d in
~0
112-114114-116 116-118 116-129 120-122 122-124 MMf.f NV~mE~
1
0.99
0.72
0.74
0.61
O°26
Fig. I .
Volume 20, number 6
PHYSICS LETTERS
a l a t e r p a p e r [14] t o g e t h e r with d e t a i l s of the a r g u m e n t s p r e s e n t e d h e r e . The r e s u l t s f o r tin, howe v e r , p r e s e n t the m o s t d i r e c t e v i d e n c e that i r r e g u l a r v a r i a t i o n s in isotope shifts can a r i s e f r o m r a d i a l as well as d e f o r m a t i o n e f f e c t s , and any a t t e mpt to i n t e r p r e t i s o to p e shifts s a t i s f a c t o r i l y m u s t take this f a c t into account.
References 1. P. Brix and H. Kopfermann, Z. Phys. 126 (1949) 344. 2. A.S.Meligy, S.Tadros and M.A.E1 Wahab, Nucl. Phys. 16 (1960) 99. 3. A.R. Striganov, V.A. Katulin and V.V. Eliseev, Optik i Spektr. 12 (1962) 171 (Optics and Spectr. 12, 91. 4. A. R. Striganov, A. F. Golovin, M.P. Gerasimova, Optik i Spektr. 14 (1963) (Optics and Spectry (USSR) (Engl. Transl.) 14 (1963) 3.
INVESTIGATION
IApril 1966
5. N.J.Ionesco-Pallas, Physics Letters 6 (1963) 93. 6. E.E. Fradkin, Zh. Eksper. Teor. Fiz. 42 (1962) 787; Soviet Physics J E T P 15 (1962) 550. 7. F.A. Babushkin, Zh. Eksper. Teor. Fiz. 44 (1963) 1661; Soviet Physics J E T P 17 (1963) 1118. 8. F.A. Babushkin, Zh. Eksper. Teor. Fiz. 45 (1963) 1478; Soviet Physics J E T P 18 (1964) 1022. 9. K.Murakawa, J. Phys. Soc. Japan 9 (1954) 876. 10. W. R. Hindmarsh and H. G. Kuhn, Prec. Phys. Soc. A 68 (1955) 433. 11, D.N. Stacey, Proc. Roy.Soc. A280 (1964)439. 12. D. G. Alkhazov et al., Zh. Eksper. Teor. Fiz. 33 (2957) 1036; Soviet Physics JETP 6 (1958) 1036. 13. P.H. Stelson and F. K. McGowan, Phys. Rev. 110 (1958) 489. 14. W.H. King, H.G. Kuhn and D. N. Stacey (to be published).
ON THE FINE STRUCTURE OF SIX BALMER-SERIES OF DEUTERIUM
LINES
OF T H E
L. CSILLAG
Central Research Institute for Physics, Budapest Received 9 March 1966
We have measured the wavelengths of the apparent doublet components of six Balmer lines of deuterium. The value of the Rydberg constant resulting from our measurement is in good agreement with that accepted up to now.
The quantum t h e o r y of o n e - e l e c t r o n a t o m s which has b e e n w o r k e d out in g r e a t d e t a i l could be p r o v e d to be v a l i d with the help of o p t i c a l and m i c r o w a v e t e c h n i q u e s with high a c c u r a c y f o r e n e r g y l e v e l s of low main quantum n u m b e r s . F o r e x c i t e d l e v e l s of high m a i n quantum n u m b e r s h o w e v e r , the v a l i d i t y of the t h e o r y could be shown only by an a n a l y s i s of the w a v e l e n g t h data of the l i n e s of u n r e s o l v e d fine s t r u c t u r e [1,2]. F o r a m o r e convincing c o n f i r m a tion of the t h e o r y f u r t h e r high p r e c i s i o n m e a s u r e m e n t on the l i n e s of r e s o l v e d fine s t r u c t u r e a p p e a r a ll the m o r e n e c e s s a r y as in the c a s e of highly excited levels certain considerations make small d e v i a t i o n s f r o m t h e o r y a p p e a r p o s s i b l e [3]. We have t h e r e f o r e c a r r i e d out w a v e l e n g t h m e a s u r e m e n t s on the l i n e s D~ - D~ which had up to now not b e e n d e t e r m i n e d with a p p r o p r i a t e a c c u r a c y . Ou r r e s u l t s showed that the wave n u m b e r s of the o p t i cal l y r e s o l v a b l e c o m p o n e n t s a g r e e with those c a l c u l a t e d t h e o r e t i c a l l y within a m e a s u r i n g
e r r o r of 2 x 10-3 c m - 1 . Thus, the t h e o r y c o r r e c t l y d e s c r i b e s - at l e a s t to the g i v en a c c u r a c y the l o c a t i o n and s t r u c t u r e of the l e v e l s up to the m a i n quantum n u m b e r n = 9. In addition, it now b e c a m e p o s s i b l e to d e t e r m i n e the R y d b e r g const an t with a much s m a l l e r e r r o r . As light s o u r c e p u r e d e u t e r i u m gas of 0.03 T o r t p r e s s u r e was u s e d and e x c i t e d in highf r e q u e n c y r i n g - d i s c h a r g e , the tube being cooled by liquid n i t r o g e n . A F a b r y - P e r o t i n t e r f e r o m e t e r c o m b i n e d with a q u a r t z s p e c t r o g r a p h e n s u r e d an a p p r o p r i a t e r e s o l u t i o n . As w a v e l e n g t h s t a n d a r d s we used the 198Hg l i n es 4358. 3 3 7 5 ~ and 4046. 5716 A [4]. F u r t h e r d e t a i l s of o u r m e a s u r e m e n t s will be r e p o r t e d e l s e w h e r e [5]. Tab l e 1 s u m m a r i z e s o u r e x p e r i m e n t . The t h i r d c o l u m n contains the m e a s u r e d r e s u l t s . All the Bal. m e r - l i n e s i n v e s t i g a t e d c o n s i s t of s e v e n c o m p o nents, h o w e v e r , only two g r o u p s of t h r e e o r four c o m p o n e n t s e a c h could be r e s o l v e d by o u r o p t i cal
645