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The neutron-deuteron scattering lengths
Volume 36B, number 3
THE
P H YSI CS L E T T E R S
NEUTRON-DEUTERON
SCATTERING
6 September 1971
LENGTHS
W. DILG, L. K O E S T E R and W. N I S T L E R P h y s i k - D e p a r t m e n t d e r Technischen UniversiNit Miinchen, Germany Received 13 July 1971
New measurements of the n-d coherent scattering amplitude and epithermal cross section are reported. The results aeoh = 6.672+0.007 fm, (;free = 3.390:~0.012 b, are inconsistent with the scattering lengths, proposed by Van Oers and Seagrave. From the present data one obtains a 2 = 0.65 ±0.04 fro, a 4 = 6.35 ±0.02 fm for the doublet and quartet n-d scattering lengths, respectively.
Low e n e r g y n -d s c a t t e r i n g i s c o m p l e t e l y d e s c r i b e d by two p a r a m e t e r s , the q u a r t e t and doublet n e u t r o n - d e u t e r o n s c a t t e r i n g l e n g t h s a 4 and a2, r e s p e c t i v e l y . Of p a r t i c u l a r t h e o r e t i c a l i n t e r e s t i s the l a t t e r v a l u e , which p r o v i d e s , t o g e t h e r with the t r i t o n binding e n e r g y , a s e n s i t i v e t e s t for n u c l e a r t h r e e - b o d y c a l c u l a t i o n s [1]. E x p e r i m e n t a l i n f o r m a t i o n on the s c a t t e r i n g le n g th s h a s been obtained so f a r f r o m m e a s u r e m e n t s of the n - d c o h e r e n t s c a t t e r i n g amplitude [2,3] and the i n c o h e r e n t [4] and f r e e total [5,6] c r o s s s e c t i o n s ; f r o m the o r t h o - and p a r a - d e u t e r i u m c r o s s s e c ti ons [7]; f r o m the a n g u l a r v a r i a t i o n of slow neut r o n s c a t t e r i n g f r o m d e u t e r i u m g a s [8] and f r o m a s c a t t e r i n g e x p e r i m e n t i n v o l v i n g p o l a r i z e d neut r o n s and d e u t e r o n s [9]. A few y e a r s ago Van O e r s and S e a g r a v e [10] analysed the a v a i l a b l e d a t a and obtained the v a l u e s (set 1) a 2 =0.15+0.05fm, a 4 = 6 . 1 3 ± 0 . 0 4 fm. They a r e based on the m e a s u r e d v a l u e s [3,4], a c o h = a 4 + ½a2 = 6.21+0.04 fm, (;inc = 2~(a4-a~.)2 = 2 . 2 5 + 0 . 0 4 b and imply ~ f r e e = ~ ~(a~+½a2) -2 3 . 1 5 ± 0 . 0 4 b. T h i s set has been widely a c c e p t e d up to now, in spite of v a r i o u s unexplained d i s c r e p a n c i e s with p r e v i o u s r e s u l t s , like a 2 / a 4 = 0 . 1 2 ± 0 . 0 4 [8], a 2 = 0 . 5 7 ± 0 . 1 4 f m , a 4 = 6.47±0.14 f m [ 7 ] , (;free = 3 . 4 4 ± 0 . 0 6 b [ 5 ] and 3.38 ± 0.05 b [6]. R e c e n t l y , the e x p e r i m e n t a l b a s i s of set 1 b e c a m e s t i l l m o r e doubtful by a new m e a s u r e m e n t of the c o h e r e n t a m p l i t u d e , p e r f o r m e d at this l a b o r a t o r y [11] y i e l d i n g a c o h = 6.70± 0.05 fm, which c o n s i d e r a b l y d i f f e r s f r o m the r e s u l t in r e f . [3]. To r e s o l v e the d i s c r e p a n c i e s d e s c r i b e d above, i m p r o v e d m e a s u r e m e n t s of a coh and (;free have been c a r r i e d out, which allow a r e e v a l u a t i o n of the n - d s c a t t e r i n g lengths. F o r the d e t e r m i n a t i o n of a f r e e , t r a n s m i s s i o n m e a s u r e 208
m e n t s w e r e p e r f o r m e d on heavy w a t e r , fused q u a r t z (i.e. SiO2) and s i l i c o n e with 130 eV neut r o n s . F r o m t h ese r e s u l t s the oxygen and deut e r o n f r e e total c r o s s s e c t i o n s w e r e deduced. The method, e x p e r i m e n t a l a r r a n g e m e n t and p r o c e d u r e used for a c c u r a t e d e t e r m i n a t i o n of 130 eV c r o s s s e c t i o n s with cobalt r e s o n a n c e neut r o n s have been p r e v i o u s l y d e s c r i b e d [12]. The p u r i t y of the heavy w a t e r used w as 99.79 + 0.02 m o l go D20, based on i s o t o p i c a n a l y s e s by d i f f e r ent m e t h o d s (IR s p e c t r o s c o p y , p y c n o m e t r y , NMR). T r a n s m i s s i o n m e a s u r e m e n t s on t h r e e s a m p l e s (3-6 g / c m 2) y i e l d e d r e s u l t s c o n s i s t e n t within 0.2%. The t r a n s m i s s i o n data have been a n a l y s e d taking into account (1) b e a m attenuation in the (1 m m ) q u a r t z windows of the s a m p l e cont a i n e r s ; (2) b e a m attenuation in a i r d u r i n g s a m p l e - o u t m e a s u r e m e n t s ; (3) d e a d - t i m e counting l o s s e s ; (4) d e t e c t o r " i n - s c a t t e r i n g " (which was n e g l i g i b l e , see r e f . [12]); (5) the m a s s s p e c t r o s c o p i c a l l y d e t e r m i n e d 1 8 0 / 1 6 0 r a t i o in c a l c u l a t i n g the n u m b e r of m o l e c u l e s p e r cm2; (6) the c r o s s - s e c t i o n c o n t r i b u t i o n due to the H 2 0 contamination. The l a t t e r h as been c o n t r o l l e d by l a t e r r e - a n a l y s i s ( p y c n o m e t r y , NMR) of the s a m p l e s u sed , which y i el d ed D 2 0 abundances l e s s than 0.05go below the f i r s t r e s u l t s . Thus a value 99.76± 0.05 m o l go could be a s s u m e d f o r all s a m p l e s d u r i n g the t r a n s m i s s i o n e x p e r i m e n t . T h i s led to an a v e r a g e (;(D20, 130 eV) = 10.54 + 0.02 b, the e r r o r * mainly a r i s i n g f r o m the H 2 0 c o r r e c t i o n . The c o m b i n a t i o n Si/SiO2 i s well suited to obtain the oxygen c r o s s s e c t i o n as the c r o s s - s e c tion d i f f e r e n c e f r o m m e a s u r e m e n t s on so l i d s, * All e r r o r s quoted correspond to 33 statistical and estimated systematic uncertainties.
Volume 36B, number 3
PHYSICS LETTERS
6September 1971
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Fig. 1. Reflectivity from heavy water (99.63 mol % D20 ) as a function of the neutron height of fall. s i n c e ~(Si) i s s m a l l c o m p a r e d with cr(SiO2) and b e c a u s e s a m p l e s of both m a t e r i a l s a r e a v a i l a b l e in e x c e l l e n t c h e m i c a l p u r i t y and h o m o g e n e i t y . A p r e v i o u s l y r e p o r t e d [12] m e a s u r e m e n t on Si y i e l d i n g ~ S i , 130 eV) = 2.0442 + 0.0018 b, h a s been p e r f o r m e d on s e m i c o n d u c t o r g r a d e single c r y s t a l s . F o r the SiO2 we u s e d o p ti c a l q u a r t z g l a s s I n f r a s i l I * * in the f o r m of p l a t e s with polished surfaces. Transmission measurements on d i f f e r e n t s a m p l e s (3-10 g / c m 2) y i e l d e d r e s u l t s c o n s i s t e n t within s t a t i s t i c s with an a v e r a g e a(SiO2, 130 eV) = 9.566+0.013 b. F r o m the above d a t a we obtain the c r o s s s e c t i o n ~free(O) = 3.76 1 + 0 . 0 0 7 b a,ld ~free(D) = 3 . 3 9 0 + 0 . 0 1 2 b. T h i s r e s u l t i s u n a f f e c t e d by m o l e c u l a r binding e f f e c t s , which a r e n e g l i g i b l e at the n e u t r o n e n e r g y u s e d :~. The c o h e r e n t s c a t t e r i n g a m p l it u d e of D 2 0 w a s d e t e r m i n e d by m e a n s of m i r r o r r e f l e c t i o n of slow n e u t r o n s f r o m heavy w a t e r and f r o m v a r i o u s m i x t u r e s of h eav y and light w a t e r with the n e u t r o n - g r a v i t y r e f r a c t o m e t e r [15,16]. The o r i g i n a l heavy w a t e r with a p u r i t y of 99.79 :e 0.02 mol % D 2 0 and the m i x t u r e s w e r e handled with g r e a t c a r e in o r d e r to avoid depletion. In addition the D 2 0 content of the l i q u i d s has been d e t e r m i n e d b e f o r e and a f t e r the r e f l e c t i o n m e a s u r e m e n t s by ** From Heraeus-Schott Quarzsehmelze, Hanau. Impurities quoted: metallic <10 ppm, H <0.3 ppm (based on IR transmission). In the epithermal limiting case one has ff/~free = 1 + fl E, see ref. [13] and experimental observations on H20: ref. [14]. For D20 fi should be smaller by a factor of about 3 than for H20.
o.'~
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Fig. 2. The n-d scattering lengths a2 and a4 given by the intersection of lines representing the coherent, incoherent and free scattering values. m e a s u r i n g the density. The m e a s u r e d r e f l e c tivity of n e u t r o n s f r o m a m i r r o r of heavy w a t e r (99.63 ± 0.04 m o l % D20) i s given in fig. 1. The e x p e r i m e n t led to a value f o r the c r i t i c a l height of fall h o = 1610.67 + 0.33 m m . T h i s m e a s u r e m e n t y i e l d s , af t er c o r r e c t i o n f o r the H 2 0 - c o n t a m i n a t i o n , a value f o r the c o h e r e n t s c a t t e r i n g amplitude of the D 2 0 m o l e c u l e a coh = 19.148 + 0.015 fm. The c o h e r e n t s c a t t e r i n g amplitude of oxygen could be c a l c u l a t e d f r o m the m e a s u r e d ~free(O) b ecau se the i n c o h e r e n t s c a t t e r i n g and the binding e f f e c t s a r e n e g l i g i b l e . Taking into account a contribution of the n e u t r o n e l e c t r o n s c a t t e r i n g based on a s c a t t e r i n g a m p l i tude a ne = -0.00146 fm p e r e l e c t r o n (only F o l d y i n t e r a c t i o n ) one obtains acoh(O) = 5.804 ± 0.007 fm, which l e a d s to the bound s c a t t e r i n g length of the d e u t e r i u m atom acoh(D) = 6.672 + 0.007 fm. T h i s value a g r e e s with (but i s c o n s i d e r a b l y m o r e a c c u r a t e than) the p r e v i o u s l y [11] r e p o r t e d r e s u l t a c o h = 6.70 + 0.05 fm obtained by m e a n s of the balanced r e f r a c t i v e index method. It d i s a g r e e s with the L i v e r m o r e value [3] a c o h = 6.21 + 0.04 fm. Using t h ese new e x p e r i m e n t a l data one finds a 2 = 0.65m0.04 fro, a 4 = 6.35+0.02 fm, ain c = 2 . 0 4 + 0 . 0 3 b. T h e s e r e s u l t s a g r e e , as shown in fig. 2, with the r e s u l t s f o r atot, (a2,a4) and a 2 / a 4 given in r e f s . [5], [7] and [8], r e s p e c t i v e l y . The deviation f r o m the v a l u e s f o r a i n c given in r e f . [4] i s 5 t i m e s the standard e r r o r . We b e l i e v e that u n c e r t a i n t i e s in the H 2 0 co n t am i n at i o n may be r e s p o n sible f o r this d i f f e r e n c e . The new v a l u e s f o r a 4 and e s p e c i a l l y for a 2 209
Volume 36B, n u m b e r 3
PHYSICS
are in agreement (as well as the triton binding e n e r g y ) w i t h t h e r e s u l t s of s e p a r a b l e - m o d e l c a l c u l a t i o n s i n c l u d i n g a t e n s o r c o m p o n e n t [1].
References [1] L. M. Delves and A. C. Philipps, Revs. Mod. Phys. 41 (1969) 497. [2] C.G. ShuIl, E.O. Wollan and W. C. Koehler, Phys. Rev. 83 (1951) 700. [3] W. Bartolini, R.E. Donaldson and D. J. Groves, Phys. Rev. 174 (1968) 313. [4] W. GissIer, Z. KristaIIographie 118 (1963) 149. [5] E. Fermi and L. Marshal|, Phys. Rev. 75 (1949) 578. [6] Brookhaven National Laboratory Report BNL 325, 2nd ed. (1964).
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LETTERS
6 S e p t e m b e r 1971
[7] S.J. Nikitin et al., F i r s t Geneva Conf. 2 (1955) 81. [8] D. C. H u r s t and J. Alcoek, Can. J. Phys. 29 (1951) 36. [9] V. P. Alkimenkow et al., Phys. L e t t e r s 24B (1967) 151. [10] W. T. H. Van Oers and J . D. Seagrave, Phys. L e t t e r s 24B (1967) 562. [11] L. K o e s t e r and H. U n g e r e r , Z. Physik 219 (1969) 300. [12] W. Dilg and H. Vonach, Z. Naturf. 26a (1971) 442. [13] G.C. Wick, Phys. Rev. 94 0954) 1228. [14] E.MeIkonian, Phys. Rev. 76 (1949) 1744; W. B. Jones, Phys. Rev. 74 (1948) 364. [15] H. M a i e r - L e i b n i t z , Z. Angew. Phys. 14 (1962) 738. [16] L. Koester, Z. Physik 182 (1965) 328 and 198 (1967) 187.
THE
P H YSI CS L E T T E R S
NEUTRON-DEUTERON
SCATTERING
6 September 1971
LENGTHS
W. DILG, L. K O E S T E R and W. N I S T L E R P h y s i k - D e p a r t m e n t d e r Technischen UniversiNit Miinchen, Germany Received 13 July 1971
New measurements of the n-d coherent scattering amplitude and epithermal cross section are reported. The results aeoh = 6.672+0.007 fm, (;free = 3.390:~0.012 b, are inconsistent with the scattering lengths, proposed by Van Oers and Seagrave. From the present data one obtains a 2 = 0.65 ±0.04 fro, a 4 = 6.35 ±0.02 fm for the doublet and quartet n-d scattering lengths, respectively.
Low e n e r g y n -d s c a t t e r i n g i s c o m p l e t e l y d e s c r i b e d by two p a r a m e t e r s , the q u a r t e t and doublet n e u t r o n - d e u t e r o n s c a t t e r i n g l e n g t h s a 4 and a2, r e s p e c t i v e l y . Of p a r t i c u l a r t h e o r e t i c a l i n t e r e s t i s the l a t t e r v a l u e , which p r o v i d e s , t o g e t h e r with the t r i t o n binding e n e r g y , a s e n s i t i v e t e s t for n u c l e a r t h r e e - b o d y c a l c u l a t i o n s [1]. E x p e r i m e n t a l i n f o r m a t i o n on the s c a t t e r i n g le n g th s h a s been obtained so f a r f r o m m e a s u r e m e n t s of the n - d c o h e r e n t s c a t t e r i n g amplitude [2,3] and the i n c o h e r e n t [4] and f r e e total [5,6] c r o s s s e c t i o n s ; f r o m the o r t h o - and p a r a - d e u t e r i u m c r o s s s e c ti ons [7]; f r o m the a n g u l a r v a r i a t i o n of slow neut r o n s c a t t e r i n g f r o m d e u t e r i u m g a s [8] and f r o m a s c a t t e r i n g e x p e r i m e n t i n v o l v i n g p o l a r i z e d neut r o n s and d e u t e r o n s [9]. A few y e a r s ago Van O e r s and S e a g r a v e [10] analysed the a v a i l a b l e d a t a and obtained the v a l u e s (set 1) a 2 =0.15+0.05fm, a 4 = 6 . 1 3 ± 0 . 0 4 fm. They a r e based on the m e a s u r e d v a l u e s [3,4], a c o h = a 4 + ½a2 = 6.21+0.04 fm, (;inc = 2~(a4-a~.)2 = 2 . 2 5 + 0 . 0 4 b and imply ~ f r e e = ~ ~(a~+½a2) -2 3 . 1 5 ± 0 . 0 4 b. T h i s set has been widely a c c e p t e d up to now, in spite of v a r i o u s unexplained d i s c r e p a n c i e s with p r e v i o u s r e s u l t s , like a 2 / a 4 = 0 . 1 2 ± 0 . 0 4 [8], a 2 = 0 . 5 7 ± 0 . 1 4 f m , a 4 = 6.47±0.14 f m [ 7 ] , (;free = 3 . 4 4 ± 0 . 0 6 b [ 5 ] and 3.38 ± 0.05 b [6]. R e c e n t l y , the e x p e r i m e n t a l b a s i s of set 1 b e c a m e s t i l l m o r e doubtful by a new m e a s u r e m e n t of the c o h e r e n t a m p l i t u d e , p e r f o r m e d at this l a b o r a t o r y [11] y i e l d i n g a c o h = 6.70± 0.05 fm, which c o n s i d e r a b l y d i f f e r s f r o m the r e s u l t in r e f . [3]. To r e s o l v e the d i s c r e p a n c i e s d e s c r i b e d above, i m p r o v e d m e a s u r e m e n t s of a coh and (;free have been c a r r i e d out, which allow a r e e v a l u a t i o n of the n - d s c a t t e r i n g lengths. F o r the d e t e r m i n a t i o n of a f r e e , t r a n s m i s s i o n m e a s u r e 208
m e n t s w e r e p e r f o r m e d on heavy w a t e r , fused q u a r t z (i.e. SiO2) and s i l i c o n e with 130 eV neut r o n s . F r o m t h ese r e s u l t s the oxygen and deut e r o n f r e e total c r o s s s e c t i o n s w e r e deduced. The method, e x p e r i m e n t a l a r r a n g e m e n t and p r o c e d u r e used for a c c u r a t e d e t e r m i n a t i o n of 130 eV c r o s s s e c t i o n s with cobalt r e s o n a n c e neut r o n s have been p r e v i o u s l y d e s c r i b e d [12]. The p u r i t y of the heavy w a t e r used w as 99.79 + 0.02 m o l go D20, based on i s o t o p i c a n a l y s e s by d i f f e r ent m e t h o d s (IR s p e c t r o s c o p y , p y c n o m e t r y , NMR). T r a n s m i s s i o n m e a s u r e m e n t s on t h r e e s a m p l e s (3-6 g / c m 2) y i e l d e d r e s u l t s c o n s i s t e n t within 0.2%. The t r a n s m i s s i o n data have been a n a l y s e d taking into account (1) b e a m attenuation in the (1 m m ) q u a r t z windows of the s a m p l e cont a i n e r s ; (2) b e a m attenuation in a i r d u r i n g s a m p l e - o u t m e a s u r e m e n t s ; (3) d e a d - t i m e counting l o s s e s ; (4) d e t e c t o r " i n - s c a t t e r i n g " (which was n e g l i g i b l e , see r e f . [12]); (5) the m a s s s p e c t r o s c o p i c a l l y d e t e r m i n e d 1 8 0 / 1 6 0 r a t i o in c a l c u l a t i n g the n u m b e r of m o l e c u l e s p e r cm2; (6) the c r o s s - s e c t i o n c o n t r i b u t i o n due to the H 2 0 contamination. The l a t t e r h as been c o n t r o l l e d by l a t e r r e - a n a l y s i s ( p y c n o m e t r y , NMR) of the s a m p l e s u sed , which y i el d ed D 2 0 abundances l e s s than 0.05go below the f i r s t r e s u l t s . Thus a value 99.76± 0.05 m o l go could be a s s u m e d f o r all s a m p l e s d u r i n g the t r a n s m i s s i o n e x p e r i m e n t . T h i s led to an a v e r a g e (;(D20, 130 eV) = 10.54 + 0.02 b, the e r r o r * mainly a r i s i n g f r o m the H 2 0 c o r r e c t i o n . The c o m b i n a t i o n Si/SiO2 i s well suited to obtain the oxygen c r o s s s e c t i o n as the c r o s s - s e c tion d i f f e r e n c e f r o m m e a s u r e m e n t s on so l i d s, * All e r r o r s quoted correspond to 33 statistical and estimated systematic uncertainties.
Volume 36B, number 3
PHYSICS LETTERS
6September 1971
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;.65
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Fig. 1. Reflectivity from heavy water (99.63 mol % D20 ) as a function of the neutron height of fall. s i n c e ~(Si) i s s m a l l c o m p a r e d with cr(SiO2) and b e c a u s e s a m p l e s of both m a t e r i a l s a r e a v a i l a b l e in e x c e l l e n t c h e m i c a l p u r i t y and h o m o g e n e i t y . A p r e v i o u s l y r e p o r t e d [12] m e a s u r e m e n t on Si y i e l d i n g ~ S i , 130 eV) = 2.0442 + 0.0018 b, h a s been p e r f o r m e d on s e m i c o n d u c t o r g r a d e single c r y s t a l s . F o r the SiO2 we u s e d o p ti c a l q u a r t z g l a s s I n f r a s i l I * * in the f o r m of p l a t e s with polished surfaces. Transmission measurements on d i f f e r e n t s a m p l e s (3-10 g / c m 2) y i e l d e d r e s u l t s c o n s i s t e n t within s t a t i s t i c s with an a v e r a g e a(SiO2, 130 eV) = 9.566+0.013 b. F r o m the above d a t a we obtain the c r o s s s e c t i o n ~free(O) = 3.76 1 + 0 . 0 0 7 b a,ld ~free(D) = 3 . 3 9 0 + 0 . 0 1 2 b. T h i s r e s u l t i s u n a f f e c t e d by m o l e c u l a r binding e f f e c t s , which a r e n e g l i g i b l e at the n e u t r o n e n e r g y u s e d :~. The c o h e r e n t s c a t t e r i n g a m p l it u d e of D 2 0 w a s d e t e r m i n e d by m e a n s of m i r r o r r e f l e c t i o n of slow n e u t r o n s f r o m heavy w a t e r and f r o m v a r i o u s m i x t u r e s of h eav y and light w a t e r with the n e u t r o n - g r a v i t y r e f r a c t o m e t e r [15,16]. The o r i g i n a l heavy w a t e r with a p u r i t y of 99.79 :e 0.02 mol % D 2 0 and the m i x t u r e s w e r e handled with g r e a t c a r e in o r d e r to avoid depletion. In addition the D 2 0 content of the l i q u i d s has been d e t e r m i n e d b e f o r e and a f t e r the r e f l e c t i o n m e a s u r e m e n t s by ** From Heraeus-Schott Quarzsehmelze, Hanau. Impurities quoted: metallic <10 ppm, H <0.3 ppm (based on IR transmission). In the epithermal limiting case one has ff/~free = 1 + fl E, see ref. [13] and experimental observations on H20: ref. [14]. For D20 fi should be smaller by a factor of about 3 than for H20.
o.'~
- -
Fig. 2. The n-d scattering lengths a2 and a4 given by the intersection of lines representing the coherent, incoherent and free scattering values. m e a s u r i n g the density. The m e a s u r e d r e f l e c tivity of n e u t r o n s f r o m a m i r r o r of heavy w a t e r (99.63 ± 0.04 m o l % D20) i s given in fig. 1. The e x p e r i m e n t led to a value f o r the c r i t i c a l height of fall h o = 1610.67 + 0.33 m m . T h i s m e a s u r e m e n t y i e l d s , af t er c o r r e c t i o n f o r the H 2 0 - c o n t a m i n a t i o n , a value f o r the c o h e r e n t s c a t t e r i n g amplitude of the D 2 0 m o l e c u l e a coh = 19.148 + 0.015 fm. The c o h e r e n t s c a t t e r i n g amplitude of oxygen could be c a l c u l a t e d f r o m the m e a s u r e d ~free(O) b ecau se the i n c o h e r e n t s c a t t e r i n g and the binding e f f e c t s a r e n e g l i g i b l e . Taking into account a contribution of the n e u t r o n e l e c t r o n s c a t t e r i n g based on a s c a t t e r i n g a m p l i tude a ne = -0.00146 fm p e r e l e c t r o n (only F o l d y i n t e r a c t i o n ) one obtains acoh(O) = 5.804 ± 0.007 fm, which l e a d s to the bound s c a t t e r i n g length of the d e u t e r i u m atom acoh(D) = 6.672 + 0.007 fm. T h i s value a g r e e s with (but i s c o n s i d e r a b l y m o r e a c c u r a t e than) the p r e v i o u s l y [11] r e p o r t e d r e s u l t a c o h = 6.70 + 0.05 fm obtained by m e a n s of the balanced r e f r a c t i v e index method. It d i s a g r e e s with the L i v e r m o r e value [3] a c o h = 6.21 + 0.04 fm. Using t h ese new e x p e r i m e n t a l data one finds a 2 = 0.65m0.04 fro, a 4 = 6.35+0.02 fm, ain c = 2 . 0 4 + 0 . 0 3 b. T h e s e r e s u l t s a g r e e , as shown in fig. 2, with the r e s u l t s f o r atot, (a2,a4) and a 2 / a 4 given in r e f s . [5], [7] and [8], r e s p e c t i v e l y . The deviation f r o m the v a l u e s f o r a i n c given in r e f . [4] i s 5 t i m e s the standard e r r o r . We b e l i e v e that u n c e r t a i n t i e s in the H 2 0 co n t am i n at i o n may be r e s p o n sible f o r this d i f f e r e n c e . The new v a l u e s f o r a 4 and e s p e c i a l l y for a 2 209
Volume 36B, n u m b e r 3
PHYSICS
are in agreement (as well as the triton binding e n e r g y ) w i t h t h e r e s u l t s of s e p a r a b l e - m o d e l c a l c u l a t i o n s i n c l u d i n g a t e n s o r c o m p o n e n t [1].
References [1] L. M. Delves and A. C. Philipps, Revs. Mod. Phys. 41 (1969) 497. [2] C.G. ShuIl, E.O. Wollan and W. C. Koehler, Phys. Rev. 83 (1951) 700. [3] W. Bartolini, R.E. Donaldson and D. J. Groves, Phys. Rev. 174 (1968) 313. [4] W. GissIer, Z. KristaIIographie 118 (1963) 149. [5] E. Fermi and L. Marshal|, Phys. Rev. 75 (1949) 578. [6] Brookhaven National Laboratory Report BNL 325, 2nd ed. (1964).
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[7] S.J. Nikitin et al., F i r s t Geneva Conf. 2 (1955) 81. [8] D. C. H u r s t and J. Alcoek, Can. J. Phys. 29 (1951) 36. [9] V. P. Alkimenkow et al., Phys. L e t t e r s 24B (1967) 151. [10] W. T. H. Van Oers and J . D. Seagrave, Phys. L e t t e r s 24B (1967) 562. [11] L. K o e s t e r and H. U n g e r e r , Z. Physik 219 (1969) 300. [12] W. Dilg and H. Vonach, Z. Naturf. 26a (1971) 442. [13] G.C. Wick, Phys. Rev. 94 0954) 1228. [14] E.MeIkonian, Phys. Rev. 76 (1949) 1744; W. B. Jones, Phys. Rev. 74 (1948) 364. [15] H. M a i e r - L e i b n i t z , Z. Angew. Phys. 14 (1962) 738. [16] L. Koester, Z. Physik 182 (1965) 328 and 198 (1967) 187.