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Nuclear capture of K− meson at rest
Volume 13, number 3
PHYSICS LETTERS
NUCLEAR
CAPTURE
OF K"
1 December 1964
MESON
AT REST
*
G T CONDO Physics Department, Unzve~,szty of Tennessee, Knoxwlle , Tennessee and R. D HILL Physzcs Department, Unzverszty of Illtnots, U~'bana, lll~nozs Received 10 November 1964
Recent experiments on the absorption of K" mesons at rest Indicate that those events leading to the emission of ~.~ pairs are more frequent m the light nuclel (C, N, O) than in the heavy nuclei (Ag, Br) of nuclear emulsion W e will attempt to demonstrate that these observations are inconslstent with the rather wide-spread impression that K- mesons are captured m heavy nuclel by an exclusively peripheral process In a number of investigations of Yo* (1405 MeV) production in nuclear emulsion, Frisk [1], Barbaro-Galtieri et al. [2], S a m m a n et al. [3] and Ismail et al. [4] have all found that the light nuclei (C~ N, O) are responsible for approximately 0.60 of the K- capture events whose only charged prongs (other than possibly a short recoil fragment) are a r.~ pair. These observations are strongly supported by other emulsion work m which Auger electrons have been used to distinguish K- captures m light and heavy nuclei Thus, II the data of Nicolic et al. [5], Csejthey-Barth and Sacton [6]~ Isma11 et al. [4] and Condo et al. [7] a r e c o m bined, it is found that 0 65 ~ 0.05 of all charged ~.# events o r i g i n a t e in light nuclei. On the b a s i s of s t r a i g h t K - c a p t u r e , however, c a l c u l a t i o n s by Hill [8] have shown that only 0.37 of the events would be expected to o c c u r m the light nuclei. E x p e r i m e n t a l v e r d i c a h o n of these c a l c u l a t i o n s has been p r e s e n t e d by C s e j t h e y - B a r t h and Sacton [6] for K - c a p t u r e s and by P e v s n e r et al [9] for the case of , - a b s o r p t i o n s . Thus, d it is a s s u m e d that t h e r e is no f u n d a m e n t a l difference in the v a r i o u s K - - n u c l e o n r e a c t i o n a m p l l t u d e s in light and heavy n u c l e l , we a r e led to i n f e r that the a m o u n t of c h a r g e d hyperon c o n v e r s i o n ()'. + N A + N) in heavy n u c l e i Is c o n s i d e r a b l y l a r g e r than in light nuclei. * This work was supported in part by the U S. Atom]c Energy Commission under Contract AT(11-1)-1195
Values of relative Z --*A conversion probabilItles, C L and CH, in light and heavy nuclei respectively, can be evaluated from the two experimental results" (i) ~ 0 65 of all Z~ events emerge from light nuclei and (il)~ 0.60 of all ~.~ pairs are created in heavy nuclei These values, together with a nuclear emulsion average C, which is determined by the relative numbers of light and heavy nuclei m emulsion, are shown in table I
Table 1 RelaUve conversion probabd~ties for E hyperons m hght and heavy nuclm
CL CH C
0 0 63 0 37
02 0.71 0 51
03 0,75 0 57
04 0 78 0.63
05 0 82 0 69
075 0 91 0 83
A particular set of conversion probabilities can be chosen from table I if a further datum partly experimental, partly calculable - can be obtained W e require an estimate of the number of K'-capture events in nuclear emulsion which emit Z~ pairs as a fraction of the number of Z hyperons that are actually produced. The required estimate was arrived at in the following manner. W e have assumed that 0.20 of all K- interactions do not emit ~ mesons [11], that 0.55 of all single nucleon interactions occur on a proton [10] and that 0.45 of these proton interactions yield a charged ~ pair. This last-named figure m a weighted avarage of the relative hyperon cross section for I¢- momenta between [12] 125 and 250 MeV/c. The use of the "in-flight" data is inteded to compensate approximately for the Fermi motion of the capturing nucleon Thus ~ 0 20 of all Kstars might be expected to produce a charged ~.~ pair, whereas experimentally the European KCollaboration [13] found, aRer correcting for ob271
Volume 13, number 3
PHYSICS LETTERS
s e r v a t l o n a l and e x p e r i m e n t a l b i a s e s , that a p p r o x i m a t e l y 0 10 of all K - s t a r s y ie ld ~.~ p a i r s We t h e r e f o r e e s t i m a t e that the a v e r a g e ~ - A c o n v e r sion p r o b a b i l i t y m n u c l e a r e m u l s l o n is ~ (0 50 ± 0 1) T ab l e 1 then s u g g e s t s that CH ~ 0 70 and CL 0 18 The q u e s h o n of i n t e r e s t is now w h e t h e r these conversion probabIhtles are reasonable The m o d el n o r m a l l y p r o p o s e d f o r the c a p t u r e of K- m e s o n s by a t o m i c nucle~ e n v i s a g e s a Km e s o n c a s c a d i n g t h r o u g h the Bohr o r b i t s of s m a l l e c c e n t r i c i t y and e v e n t u a l l y u n d e r g o i n g n u c l e a r a b sor pti o n , e i t h e r f r o m a 5g l e v e l in heavy n u c l e i (.4 ~- 100) o r f r o m a 3d l e v e l in h g h t n u c l e i (A ~14) This model, as was f i r s t pointed out by J o n e s [10], l m p h e s that the K- i n t e r a c t i o n v o l u m e is f a r out on the n u c l e a r p e r i p h e r y w h e r e the nucleon de nsi t y is ~ 0 10 of its c e n t r a l value It is f r o m p r e c i s e l y such a c a p t u r e p r o c e s s , e s p e c i a l l y f r o m the 5g l e v e l In heavy n u c le i, that one mxght e x p e c t to o b s e r v e w e l l - c o r r e l a t e d ~ p a i r s It was the o b s e r v a t i o n of t h e s e p a r r s , now m a i n l y a t t r i b u t e d to h g h t nuclei, that lent c r e d e n c e to this p e r i p h e r a l mode l of K - - m e s o n c a p t u r e On the b a s i s of p e m p h e r a l c a p t u r e (from the 5g o r b i t fo r A - 100 and the 3d o r b i t f o r A -~ 14), it is difficult to u n d e r s t a n d how the c o n v e r s i o n p r o b a b l h h e s can d , f f e r between light and h e a v y nuclei by as l a r g e a f a c t o r as 3 or 4 t o 1 In fact, we have c a r r i e d out a p p r o x i m a t e Monte C a r l o type c a l c u l a t i o n s using Y. - A c o n v e r s i o n c r o s s s e c t i o n s of the o r d e r of 100 mb and we would e x p e c t the c o n v e r s i o n p r o b a b i l i t y to be p r o b a b l y no m o r e than 25% l e s s m h g h t nuclet than m heavy n u c l e i It would s e e m to us that the m o s t h k e l y e x p l a n a h o n of this d~screpancy ~s that the ~ - A c o n v e r s i o n p r o b a b i l i t y IS s t r o n g l y i n c r e a s e d m heavy nuclei b e c a u s e of c e n t r a l n u c l e a r c a p t u r e of the K- m e s o n Again, using rough Monte C a r l o type c a l c u l a t i o n s we fred that c a p t u r e of K- m e s o n s f r o m s, p o r d s t a t e s m heavy n u c l e i l e a d s to ~ - A c o n v e r s i o n p r o b a b i l i t i e s of > 0 90 Thus, ff K - c a p t u r e o c -
272
1 December 1964
c u r s f r o m p r e p o n d e r a n t l y d o r f s t a t e s in light n u cl ei , and ff c a p t u r e s in heavy n u c l e i o c c u r app r o x i m a t e l y half the t i m e f r o m s, p or d s t a t e s and the o t h er half of the t i m e f r o m g s t a t e s , we find that the y i el d of ~ p a i r s in light and heavy n u c l e i is a p p r o x i m a t e l y 3 to 1 M e c h a n i s m s f o r allowing p a r t of K - - m e s o n c a p t u r e in heavy n u c l e i to o c c u r In such low an g u l ar m o m e n t u m s t a t e s of the m e s i c atom have been p r o p o s e d by M c C a r t h y and P r o w s e [14] in o r d e r to explain the high m u l t i nucleon c a p t u r e r a t e and by Condo et al [7] m o r d e r to explain the low A u g e r e l e c t r o n e m i s s i o n i n t en si t y In fact, the amount of c a p t u r e f r o m s, p and d s t a t e s of heavy n u c l e i that Is r e q m r e d to account f o r the r e d u c h o n of A u g e r e l e c t r o n e m i s sion is quite c o n s i s t e n t with the amount of low an g u l ar m o m e n t u m c a p t u r e needed to explain r e duction of r.~ e m i s s i o n f r o m heavy n u c l e l 1 ~ Frisk, Ark. fb~r Fys 24 (1963) 221 2 A Barbaro-Galherl, F M Smith and J W Patrick, Physics Letters 5 (1963) 63 3 A Samman, J. P Gerber and H Braun, Physics Letters 6 (1963) 200 4 A Z.M Isma11, S Lokanathanand Y Prakash, Nuovo elmento 33 (1964) 25 5 M N1coh0, Y E1senberg, W Koch, M Sclmeeberger and H Winzeler, Helv. Phys Acta 33 (1960) 221 6 M. Csejthey-Barth and J Sacton, Unlverslt~ de Bruxelles, Inshtut de Physique- Services de Physique Nucl~aire et de Metrologie Nucl~a~re, Bulletin No 4, August 1962 (unpublished) 7 G T.Condo, R D H~II and A D Martin, Phys Rev 133 (1964) A1280 8 R D Hall, Suppl Nuovo mmento 19 (1961) 83 9 A.Pevsner, R.Strand, L Madansky and T Toohlg, Nuovo cimento 19 (1961) 409 10 P B Jones, Phil. Mag 3 (1958) 33 11 G T Condo andR D Hill, Phys Rev 129 (1963) 388 12 W E Humphrey and R R Ross, Phys Rev 127 (1962) 1305 13 B. Bhowm~k et al , European K Collaborahon, Nuovo mmento 13 (1959) 690 14 I E McCarthy and D J Prowse, Nucl Phys 17 (1960) 96
PHYSICS LETTERS
NUCLEAR
CAPTURE
OF K"
1 December 1964
MESON
AT REST
*
G T CONDO Physics Department, Unzve~,szty of Tennessee, Knoxwlle , Tennessee and R. D HILL Physzcs Department, Unzverszty of Illtnots, U~'bana, lll~nozs Received 10 November 1964
Recent experiments on the absorption of K" mesons at rest Indicate that those events leading to the emission of ~.~ pairs are more frequent m the light nuclel (C, N, O) than in the heavy nuclei (Ag, Br) of nuclear emulsion W e will attempt to demonstrate that these observations are inconslstent with the rather wide-spread impression that K- mesons are captured m heavy nuclel by an exclusively peripheral process In a number of investigations of Yo* (1405 MeV) production in nuclear emulsion, Frisk [1], Barbaro-Galtieri et al. [2], S a m m a n et al. [3] and Ismail et al. [4] have all found that the light nuclei (C~ N, O) are responsible for approximately 0.60 of the K- capture events whose only charged prongs (other than possibly a short recoil fragment) are a r.~ pair. These observations are strongly supported by other emulsion work m which Auger electrons have been used to distinguish K- captures m light and heavy nuclei Thus, II the data of Nicolic et al. [5], Csejthey-Barth and Sacton [6]~ Isma11 et al. [4] and Condo et al. [7] a r e c o m bined, it is found that 0 65 ~ 0.05 of all charged ~.# events o r i g i n a t e in light nuclei. On the b a s i s of s t r a i g h t K - c a p t u r e , however, c a l c u l a t i o n s by Hill [8] have shown that only 0.37 of the events would be expected to o c c u r m the light nuclei. E x p e r i m e n t a l v e r d i c a h o n of these c a l c u l a t i o n s has been p r e s e n t e d by C s e j t h e y - B a r t h and Sacton [6] for K - c a p t u r e s and by P e v s n e r et al [9] for the case of , - a b s o r p t i o n s . Thus, d it is a s s u m e d that t h e r e is no f u n d a m e n t a l difference in the v a r i o u s K - - n u c l e o n r e a c t i o n a m p l l t u d e s in light and heavy n u c l e l , we a r e led to i n f e r that the a m o u n t of c h a r g e d hyperon c o n v e r s i o n ()'. + N A + N) in heavy n u c l e i Is c o n s i d e r a b l y l a r g e r than in light nuclei. * This work was supported in part by the U S. Atom]c Energy Commission under Contract AT(11-1)-1195
Values of relative Z --*A conversion probabilItles, C L and CH, in light and heavy nuclei respectively, can be evaluated from the two experimental results" (i) ~ 0 65 of all Z~ events emerge from light nuclei and (il)~ 0.60 of all ~.~ pairs are created in heavy nuclei These values, together with a nuclear emulsion average C, which is determined by the relative numbers of light and heavy nuclei m emulsion, are shown in table I
Table 1 RelaUve conversion probabd~ties for E hyperons m hght and heavy nuclm
CL CH C
0 0 63 0 37
02 0.71 0 51
03 0,75 0 57
04 0 78 0.63
05 0 82 0 69
075 0 91 0 83
A particular set of conversion probabilities can be chosen from table I if a further datum partly experimental, partly calculable - can be obtained W e require an estimate of the number of K'-capture events in nuclear emulsion which emit Z~ pairs as a fraction of the number of Z hyperons that are actually produced. The required estimate was arrived at in the following manner. W e have assumed that 0.20 of all K- interactions do not emit ~ mesons [11], that 0.55 of all single nucleon interactions occur on a proton [10] and that 0.45 of these proton interactions yield a charged ~ pair. This last-named figure m a weighted avarage of the relative hyperon cross section for I¢- momenta between [12] 125 and 250 MeV/c. The use of the "in-flight" data is inteded to compensate approximately for the Fermi motion of the capturing nucleon Thus ~ 0 20 of all Kstars might be expected to produce a charged ~.~ pair, whereas experimentally the European KCollaboration [13] found, aRer correcting for ob271
Volume 13, number 3
PHYSICS LETTERS
s e r v a t l o n a l and e x p e r i m e n t a l b i a s e s , that a p p r o x i m a t e l y 0 10 of all K - s t a r s y ie ld ~.~ p a i r s We t h e r e f o r e e s t i m a t e that the a v e r a g e ~ - A c o n v e r sion p r o b a b i l i t y m n u c l e a r e m u l s l o n is ~ (0 50 ± 0 1) T ab l e 1 then s u g g e s t s that CH ~ 0 70 and CL 0 18 The q u e s h o n of i n t e r e s t is now w h e t h e r these conversion probabIhtles are reasonable The m o d el n o r m a l l y p r o p o s e d f o r the c a p t u r e of K- m e s o n s by a t o m i c nucle~ e n v i s a g e s a Km e s o n c a s c a d i n g t h r o u g h the Bohr o r b i t s of s m a l l e c c e n t r i c i t y and e v e n t u a l l y u n d e r g o i n g n u c l e a r a b sor pti o n , e i t h e r f r o m a 5g l e v e l in heavy n u c l e i (.4 ~- 100) o r f r o m a 3d l e v e l in h g h t n u c l e i (A ~14) This model, as was f i r s t pointed out by J o n e s [10], l m p h e s that the K- i n t e r a c t i o n v o l u m e is f a r out on the n u c l e a r p e r i p h e r y w h e r e the nucleon de nsi t y is ~ 0 10 of its c e n t r a l value It is f r o m p r e c i s e l y such a c a p t u r e p r o c e s s , e s p e c i a l l y f r o m the 5g l e v e l In heavy n u c le i, that one mxght e x p e c t to o b s e r v e w e l l - c o r r e l a t e d ~ p a i r s It was the o b s e r v a t i o n of t h e s e p a r r s , now m a i n l y a t t r i b u t e d to h g h t nuclei, that lent c r e d e n c e to this p e r i p h e r a l mode l of K - - m e s o n c a p t u r e On the b a s i s of p e m p h e r a l c a p t u r e (from the 5g o r b i t fo r A - 100 and the 3d o r b i t f o r A -~ 14), it is difficult to u n d e r s t a n d how the c o n v e r s i o n p r o b a b l h h e s can d , f f e r between light and h e a v y nuclei by as l a r g e a f a c t o r as 3 or 4 t o 1 In fact, we have c a r r i e d out a p p r o x i m a t e Monte C a r l o type c a l c u l a t i o n s using Y. - A c o n v e r s i o n c r o s s s e c t i o n s of the o r d e r of 100 mb and we would e x p e c t the c o n v e r s i o n p r o b a b i l i t y to be p r o b a b l y no m o r e than 25% l e s s m h g h t nuclet than m heavy n u c l e i It would s e e m to us that the m o s t h k e l y e x p l a n a h o n of this d~screpancy ~s that the ~ - A c o n v e r s i o n p r o b a b i l i t y IS s t r o n g l y i n c r e a s e d m heavy nuclei b e c a u s e of c e n t r a l n u c l e a r c a p t u r e of the K- m e s o n Again, using rough Monte C a r l o type c a l c u l a t i o n s we fred that c a p t u r e of K- m e s o n s f r o m s, p o r d s t a t e s m heavy n u c l e i l e a d s to ~ - A c o n v e r s i o n p r o b a b i l i t i e s of > 0 90 Thus, ff K - c a p t u r e o c -
272
1 December 1964
c u r s f r o m p r e p o n d e r a n t l y d o r f s t a t e s in light n u cl ei , and ff c a p t u r e s in heavy n u c l e i o c c u r app r o x i m a t e l y half the t i m e f r o m s, p or d s t a t e s and the o t h er half of the t i m e f r o m g s t a t e s , we find that the y i el d of ~ p a i r s in light and heavy n u c l e i is a p p r o x i m a t e l y 3 to 1 M e c h a n i s m s f o r allowing p a r t of K - - m e s o n c a p t u r e in heavy n u c l e i to o c c u r In such low an g u l ar m o m e n t u m s t a t e s of the m e s i c atom have been p r o p o s e d by M c C a r t h y and P r o w s e [14] in o r d e r to explain the high m u l t i nucleon c a p t u r e r a t e and by Condo et al [7] m o r d e r to explain the low A u g e r e l e c t r o n e m i s s i o n i n t en si t y In fact, the amount of c a p t u r e f r o m s, p and d s t a t e s of heavy n u c l e i that Is r e q m r e d to account f o r the r e d u c h o n of A u g e r e l e c t r o n e m i s sion is quite c o n s i s t e n t with the amount of low an g u l ar m o m e n t u m c a p t u r e needed to explain r e duction of r.~ e m i s s i o n f r o m heavy n u c l e l 1 ~ Frisk, Ark. fb~r Fys 24 (1963) 221 2 A Barbaro-Galherl, F M Smith and J W Patrick, Physics Letters 5 (1963) 63 3 A Samman, J. P Gerber and H Braun, Physics Letters 6 (1963) 200 4 A Z.M Isma11, S Lokanathanand Y Prakash, Nuovo elmento 33 (1964) 25 5 M N1coh0, Y E1senberg, W Koch, M Sclmeeberger and H Winzeler, Helv. Phys Acta 33 (1960) 221 6 M. Csejthey-Barth and J Sacton, Unlverslt~ de Bruxelles, Inshtut de Physique- Services de Physique Nucl~aire et de Metrologie Nucl~a~re, Bulletin No 4, August 1962 (unpublished) 7 G T.Condo, R D H~II and A D Martin, Phys Rev 133 (1964) A1280 8 R D Hall, Suppl Nuovo mmento 19 (1961) 83 9 A.Pevsner, R.Strand, L Madansky and T Toohlg, Nuovo cimento 19 (1961) 409 10 P B Jones, Phil. Mag 3 (1958) 33 11 G T Condo andR D Hill, Phys Rev 129 (1963) 388 12 W E Humphrey and R R Ross, Phys Rev 127 (1962) 1305 13 B. Bhowm~k et al , European K Collaborahon, Nuovo mmento 13 (1959) 690 14 I E McCarthy and D J Prowse, Nucl Phys 17 (1960) 96