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Nuclear capture of Σ− hyperons
Nuclear Physics B56 (1973) 617-634, North-Holland Pubhshmg Company
NUCLEAR
CAPTURE
OF 2 2 - H Y P E R O N S
S.P. GOEL* Physics Department, Kurukshetra University, Kurukshetra, India Y. PRAKASH Physics Department, Umverslty o f Jammu, Jammu, India Received 26 February 1973 Abstract The capture at rest of X;- hyperons in emulsion nuclei is studied through Monte-Carlo simulataon. The A ° trapping probability following X;- capture is estimated and compared with the corresponding probablhty following K - capture. The difference in the two probabthties IS explained in terms of the dissimilar energy dlstnbuUons of the A° hyperons produced from the captures of ~:- hyperons and K - mesons Information obtained on the features of the X;- capture star and on the characteristics of the hyperfragments produced from r . - captures is presented.
1. Introduction The rates o f trapping o f A ° hyperons and o f the production o f h y p e r f r a g m e n t s (HFs) and cryptofragments (CFs) following the captures o f Z - hyperons and K mesons have been experimentally estimated b y several authors [ 1 - 1 4 ] . It is reported that the A ° trapping probability following 2;- captures is much smaller than that following K - captures. Marian's calculations [15] and the propane bubble chamber studies [16] of K - absorptions also indicate a rate o f A ° trapping higher than that for 2 ; - absorption in nuclear emulsion. These results are somewhat surprising, for whereas 22- captures always lead to the production o f a A ° hyperon via the reaction 22- + p -->A o + n, thas ts not so for K - captures where a A ° h y p e r o n is produced (directly from K - absorption or mdirectly from 22 conversion) only m ~ 60% o f all K - meson interactions wath nuclear m a t t e r [4]. The energy release is also smaller (~- 80 MeV) m Z - captures than that in K - captures. Thus, the Z - captures, being a more abundant source o f A ° hyperons and having a smaller energy release should be, contrary to experimental results from nuclear emulsion, a richer source o f HFs than the K - captures. The reported slmllarity o f the energy spectra o f A ° hyperons produced from the absorptions o f ~ - hyperons and K - mesons has been used to suggest that any differ* Now at Department of Computer Science, Umverslty of Reading, Reading, England.
618
S.P. Goel, Y. Prakash, Z - capture
Table 1 A° trapping probablhty and rates of HF and CF productton following Z - capture A° trapping probablhty (%)
Rate of produeUon (%) HFs CFs +0.5 -0.4
Medmm
Ref
Remarks
emulsion
[3]
average for all nuclei
13.8 - 15.6 emulsion
[3]
for a sample rich m Z - captures m the heavy nuclei
3.7 ± 0.9
emulsion
[4]
average for all nuclei
3.0 +-0.5
emulsion
[5]
average for all nuclei
3.15 +-0.23
emulsion
[6]
average for all nuclei
emulsion
[6]
C, N, O nuclei
16-+ 3
emulsion
[6]
Ag, Br nuclei
8-14
Z = 40 A = 100 nucleus
[15]
DA= 25 MeV and AN scattering cross section = 22.3 mb
26 +- 5
bubble chamber
[2]
Absorption m neon
2.7
8.5
8.6 - 10
ence in their trapping probabtlities must be due to differences m their creation mechamsm [2, 3, 17]. Martan suggested that Z - hyperons might be captured more toward the outerslde on the nuclear periphery than K - mesons so that the A ° hyperons produced from the former have a better chance o f leaving the nucleus [ 15]. F u t h e r , m a y A ° hyperons produced m K - captures come indirectly from ~ - A conversion which presumably occurs deeper reside the nucleus; hence they have a greater chance o f becoming b o u n d [2]. Thus, the net result is that the A ° trapping probabdity m Z - captures turns out to be smaller than that m K - captures. The results from the hydrogen bubble chamber (having an admixture o f neon) are, however, at variance with those from nuclear emulsion. These results indicate that the A ° trapping probabihty following ~ - capture m neon is higher than the corresponding probabthty following K - captures [ 1 8 - 20]. Available data on A ° trapping probablhty following Z - and K - captures are presented m tables 1 and 2. In the present work, the capture o f ~ - hyperons in emulsion nuclei is studied through Monte-Carlo (MC) slmulataon. The A ° trapping p r o b a b l h ~ is calculated and compared with the corresponding probability similarly calculated for K captures. The calculated A ° trapping probabihty following Z - captures is then compared with the corresponding experimental estimates o f its value obtained from nuclear emulsion. Information is obtained on the features of the ~ - capture star. The characteristics o f the HFs produced from Z - captures are also studied.
[14] I15] 1191
11-+5
52 ± 14
15 - 3 0
9.5 -+ 3.0
absorption m neon
combined results for absorption in hght nuclei
bubble chamber + emulsion
[14]
19.6 -+ 1.8
bubble chamber
average for all freon nuclei
bubble chamber
I14]
19.0-+ 2
Martin's calculations
average for all freon nuclei
bubble chamber
[23]
Z = 40, A = 100 nucl.
average for all freon nuclei
bubble chamber
1221
19 -+ 1.6
combined results for absorption m heavy nuclei
absorption m Br in freon
bubble chamber
[161
51 -+ 1~
bubble chamber + emulsion
absorption m F in freon
absorption In C in propane (C3H8) and freon (CFaBr)
bubble chamber
average for all nuclei
emulsion
[21]
Ag, Br nuclei
emulsion
9_+5
C, N, O nuclei
emulslon
bubble chamber
for K - captures producing AO hyperons
emulsion
[161
[111
for all K - captures
Rema~s
emulsion
Medium
18.5 +- 3.5
30-+ 7
I131
58 -+ 15
41+_7
7+_1 1131
171
30+_7
5-+1
8+-2
[71
CF
HF
(%)
Ref.
Rate of production (%)
A° trapping probablhty
Table 2 A° trapping probabihty and rates of HF and CF production following K - captures
I
M
t~
620
S.P. Goel, Y. Prakash, ~ - capture
2. Monte-Carlo calculation and input parameters 2.1. The procedure o f the calculation For the sake of computational convemence, the procedure of the calculation is d:vided into the following three parts 2. I.I. The mtttal interaction Only the process ~ - + p -->A° + n + 80 MeV is assumed to contribute to the capture of ~ - hyperons. The probabihty of occurrence of the charge-exchange reactaon Z - + p -->Zo + n + 8 MeV is considered to be very small due to phase-space limitation and strong Pauh suppression [4]. Even when this reaction might occur, the very slow ~o hyperon is hkely to be absorbed in the parent nucleus, leading again to the productlon of the A ° hyperon. The absorptaon interaction of K - mesons with single nucleons only is considered m the present work as the probabihty of occurrence of its interaction w:th two nucleons m hehum and heavier nuclei is considered [26] to be relatavely small ( " 17 to 20%). Further, the latter typre of mteraction is expected to produce mostly fast hyperons which are less hkely to be absorbed as compared to the ones produced from the K - meson-smgle nucleon interaction. The K - absorption interacUons with single nucleons simulated in tits work are those gwen by Nikohc [24] and Burhop et al. [25], producing a 7r meson and a A ° or Z hyperon m the final state. The details of the slmulaUon procedure of the capture of K - mesons are to be commumcated separately. The Fermi momentum of the nucleon with which the Z - hyperon or the K meson interacts :s derived from the Fourier transform of its wave functxon. The procedure followed is the same as described by Lokanathan et al. [27]. The energy and momentum of the final-state particles are calculated by assuming that they are distributed lsotroplcally in the cm system. The E - hyperon and the K - meson are assumed to be absorbed from the s state, uniformly anywhere on the nuclear periphery within the (0 - 10)% density region (RI) oI the nuclear matter. 2.1.2. The nuclear cascade The particles produced in the initial interaction are followed, one by one, as they move and undergo scattering interactions inside the parent nucleus. The momentum of the target nucleon with which the mc:dent partxcle interacts is also found from the Fourier transform of its wave functaon [27]. The interaction mean free path is found from the relevant cross sections supphed as input parameters. If after an interaction the energy of a nucleon is found to be less than its Fermi level, the mteracUon is forbidden. If the interactaon is allowed, the energy of both the interacting particles is compared with their respectwe potential-weU depths. A particle having energy less than its potential-well depth is assumed to be absorbed.
s.P. Goel, Y. Prakash, ~ - capture
621
In the case of an absorbed pion or hyperon, ItS entare energy, while m that of an absorbed nucleon, its energy m excess of its Fermi level, is imparted to the nucleus as excitation energy. If the energy of a particle is greater than its potential-well depth, it is further followed and the process is repeated (which results m the development of a nuclear cascade)until all the particles are absorbed or emitted. A parlacle is assumed to be emitted if its energy is greater than its potential-well depth and the next point of lnteract~on falls outside the nucleus. The nature, energy and momentum of every emitted particle are recorded. Each emitted particle ~s assumed to Impart a momentum equal and opposite to its own to the residual nucleus whose mass and charge are adjusted after the emission of each particle. An absorbed ~ hyperon is assumed to interact with a single nucleon and get converted into a A ° hyperon while an absorbed plon is assumed to interact with a pair of nucleons, pp, pn or nn type. The pion absorption Is treated m the manner of Bertini et al. [28]. The particles produced from the absorption of Z hyperons or plons are also followed until they are emitted or absorbed. The absorption of a A ° hyperon is assumed to lead to the production of a HF. It is further assumed that once a A ° is trapped, it remains so even during the ensuing evaporation of the excited nucleus.
2.1.3. The nuclear evaporatTon The nucleus excited due to the energy imparted to it by the absorbed particles ~s assumed to de-excite itself via evaporation. The simulation of the process of nuclear evaporation follows the work of Le Couteur [29], as discussed by Powell et al. [30], and the procedure is identical to that of Smgh et al. [31]. The final momentum of the residual nucleus (henceforth called recoil or HF if a A ° is trapped m it) is obtained from the vector sum of the randomly oriented momenta acqmred by it during the nuclear cascade and the ensuing evaporation. The range corresponding to the final recoil or HF mass, charge and momentum is calculated from the range-energy relations of Heckman et al. [32] as discussed by Key et al. [33]. The calculataons are done separately for ~ - capture m carbon, mtrogen, oxygen, bromine and silver and for K - capture m carbon, bromine and silver. Two hundred events are simulated for each nucleus. The entire procedure is repeated for each nucleus for the initial absorption of ~ hyperons and K - mesons in the (0 - 25)% density region (RII) of the nuclear matter 2.2. Input parameters 2.2. I. The nuclear parameters Following Bernardim et al. [34], the nucleus is represented by a statistical assembly of nucleons and it is considered to be, to start with, m an unexclted ground state composed of non-interactang fermion gases of neutrons and protons m an uniform
622
S.P. Goel, Y. Prakash, ~,- capture
Table 3 Formulae used m the calculation of nuclear parameters Parameter Fermi energy
Formulae used for calculation 2
2
E F = (76.52/ro) (n/A)~ MeV
(EF) Coulomb barrier (C.B.)
C.B. = (Ze2/R) MeV
Potentialwell depth
Dp = E F + B.E. + C.B. MeV Dn = E F + B.E. MeV
Density of nuclear matter (p(r))
p(r) = po/(l+exp((r-c)/a))
Remarks n -- Z for protons n -- (A-Z) for neutrons r o = 1.25 l R =roA~ r o = 1.25 A = 12, 14, 16, 80, 108. The value of C.B. is multaphed by the penetrataon factor 0.7 for protons. Dp = potential well depth for protons Dn = potential weU depth for neutrons B.E.= average binding energy per nucleon Po = nuclear density at centre c = 1.07 A~fm a = 0.55 fm
ReL [ 35 ]
[31]
[ 36 ] [37 }
[38]
potential well wlthm the nucelar volume. The basis of calculation of the various nuclear parameters used in the calculations is summanzed in table 3, The potential-well depth (DA) and the mass of the A ° hyperon are taken to be 32 MeV [39] and 1115.4 MeV, respectively. The potential-well depth of ~ hyperons is taken to be the same as D A whale its value for pions is assumed to be 40 MeV.
2.2.2. The scattenng cross secnons The scattering interactions reside the nucleus are described by the free scattering cross sections except as modified b y the Pauli principle.
2.2.2.1. Nucleon-nucleon scattenng. The total as well as the differential scattering cross sections for the nucleon-nucleon (lap, pn or nn) scattering collisions are taken from Metropolis et al. [40]. The procedure followed is identical to that of these authors.
2.2.2.2. Pion-nucleon scattering. The total scattering cross sections for pion-nucleon scattering collisions are taken from Anderson et al. [41] and the differential scattering cross sections from G o r d m a n et al. [42]. Charge independence is assumed, only s and p waves are considered [43] and the relevant phase shifts are calculated according to the procedure suggested b y Orear [44].
S.P. Goel, Y. Prakash, ~ - capture
623
2.2.2.3. Hyperon-nucleon scattenng. The low energy hyperon-nucleon elastic scattering is predominantly s-wave interaction and it is, therefore, assumed to be lSOtropic m the c.m. system. The total scattering cross sections used m the present calculations are those given by Sechi-Zom et al. [45] for (A°P) interaction, and by Fast et al. [46] for (E+P) and ( E - P ) interactions. It is assumed that the hyperonneutron interaction ts identical to the hyperon-proton one. The (yop) scattering cross section is taken to be equal to the mean of the (E+P) and the ( E - P ) scattenng cross sections. 2.2.3. Frequency o f emission and the momentum o f evaporated partwles The frequencies of emission of the vanous particles likely to be emitted during nuclear evaporation are computed from the evaporataon theory [30] for different nuclear temperatures and three mass regions of the nuclear mass. Out of the particles likely to be emitted during nuclear evaporation, the momenta of 2H, 3H, 3He and 8La, treated as constant, are taken from Key et al. [33] while the momenta of n, p and 4He, treated as variables, are taken from the distributions gwen by Dostrovsky et al. [47]. The detads are given by Slngh et al. [31].
3. Results and discussion The results for RI and RII are generally similar and are, therefore, gwen separately only when there is a special reason for doing so. 3.1. Results o f the simulatton o f nuclear cascade 3.1.1. A°-momentum distribution The momentum distribution of the A ° hyperons produced reside the nucleus from Z - captures is glven in fig. la. This is similar to the momentum distributions of the A ° hyperons emitted from the light and the heavy emulsion nuclei, shown in fig. lb, c. The latter have only an additional low energy tail which is a consequence of the scattering interactions which the A ° hyperons undergo with nucleons inside the nucleus. The distributions are also stmilar for RI and RII. In fig. ld is shown the experimentally estimated distnbution of the momentum of A ° hyperons ermtted from neon (derived from the distribution given by Bugg et al. [18]). This distribution is similar to the distributions shown m fig. lb, c. The broad similanty of all the distributions shown m fig. la, b, c, d could be interpreted as providing evidence in favour of penpheral absorption of Z - hyperons, for the experimentally estunated distribution might be expected to be much more modified If ~ hyperons were captured deeper inside the nucleus and the A ° hyperons interacted much more with the nucleons before being emitted. The energy distributmns of the A ° hyperons produced from the captures of ~ hyperons and K - mesons are not similar (see fig. 2a, b), a result contrary to the as-
624
S.P. Goel, Y Prakash, T_,- capture (a) 60
(0 Iz,., > ill
(I))
¸
40
tl. 0 O
Z
-,.~
20'
200
400
MOMENTUM
OF
0
200
400
A~ HYPERON8 ( M I V / C )
(e)
(d)
60
zc
0
ZOO MOMENTUM
400 OF
0
200
400
Ae.- HYPERON$ (MeV/C)
Fig. 1. Momensum distribution of A ° hyperons. (a) A ° hyperons lmtially produced from I f captures, (13) A ° hyperons emitted from the hght nuclei: (a) A ° hyperons mittally produced from Y-- captures; Co) A ° hyperons emitted from the light nuclei ( 0 - 1 0 ) % density region, - - - - ( 0 - 2 5 ) % density region; (c) A ° hyperons emitted from the heavy nuclei - ( 0 - 1 0 ) % density region, - - - - ( 0 - 2 5 ) % density regton; (d) A ° hyperons emitted from neon.
sumption of several authors [2, 3, 17]. About 70% A o hyperons produced from K captures have energy < 30 MeV while the fraction of such A° hyperons produced from Z - captures is only ~ 30%. The A ° hyperons produced with neutrons in ~ - captures get more energy than those produced with plon in K - captures. Being much lighter, the pions take away much larger energy (nearly eight ttmes) than that available to the A ° hyperons. Thus, despite larger energy release, more of slow A ° hyperons are produced in K - captures as compared to Z - captures.
S.P. Goel, Y. Prakash, ~-capture (o)
625
(b)
30 u) I-
,z 2o > rid i.
o
j
Io
o
zo
,~o
o
eo
E NERGY
OF
\l ~;o
A° - H Y P E R O N $
,~o (MoV)
Fig. 2. Energy dlstrlbutmn of A ° hyperons. (a) A ° hyperons produced from 2;- captures, (b) A ° hyperons produced from K - captures.
3.1.2. Comparison of calculated A ° trappmg probabihttes The calculated values of the A ° trapping probabditles following ~ - and K - captures are presented m table 4. The results for RI and RII are similar, more so in the case of 2;- captures which indicates that the rate o f A ° trapping Is, perhaps, not very senmive to the location o f the initial Z--absorption interaction on the nuclear periphery. The A ° trapping probablhty following Z - capture turns out to be much smaller than that following K - capture. This is in agreoment with experimental results from Table 4 Calculated A ° trapping probability A ° trapping probability Particle
Nucleus
absorbed
2 ; - hyperon
K - meson
(0-10)% density
(0-25)% densRy
region
region
Carbon
13.5 + 3.8
16.0 ± 3.8
Nitrogen
12.5 + 3.8
16.5 + 3.8
Oxygen
13.5 + 3.8
16.5 + 3.8
Bromine
26.0 + 3.8
26.5 + 3.8
Silver
26.5 + 3.8
27.0 ± 3.8
Carbon
33.0 ± 3.8
39.0 + 3.8
Bromine
39.0 + 3.8
50.0 ± 3.8
Silver
41.0 ± 3.8
51.0 + 3.8
Remarks
the probablhty for all the hght nuclei is the same the probablhty Is the same for both the heavy nuclei the probability for mtrogen and oxygen is expected to be the same as for carbon
626
&P. Goel, Y. Prakash, ~ - capture
nuclear emulsion but unlike those from the bubble chamber from absorptaons m neon. The cause of the opposite trend of the bubble chamber result might be m expertmental uncertainties or elsewhere and deserves careful mvest~gatlon. The results of this work are significant in the sense that the A° trapping probabihty following ~ - captures is observed to be less than that followang K - captures even if the capture of )2- hyperons occurs in RII and that of K - mesons occurs in RI (see table 4). This Is contrary to the spirit of Martin's suggestion (see sect. 1). In view of the reported [2, 3, 17] similarity of the energy distributions of the A ° hyperons produced from ~ - and K - captures, the A ° trapping probabihty following 1~- captures should be larger if the ~ - hyperons are captured deeper reside the nucleus than the K - mesons. However, our results indicate (see subsect. 3.1.2) that the energy &stnbutlons of the A ° hyperons produced from ~ - and K - captures are indeed chfferent and therefore, the smaller rate of A ° trapping followang ~ - captures can be explained without revoking the difference m their creation mechanism. Since more of slow A ° hyperons are produced m K - captures than m ~,- captures (70% in the former versus 30% in the latter), their trapping probabihty must obviously be larger in the former even ffboth the K - mesons and the ~ - hyperons were captured in the same density region of the nuclear matter. Our results also indicate that " 30% A ° hyperons are produced from ~ convemon in K - captures. Such A ° hyperons have energy distnbuUon smadar to those produced from )2- capture and are produced deeper inside the nucleus. As expected [2], their trapping probability is larger. 3.1.3. Number o f emitted protons and neutrons No proton is emitted from Y.- captures in the light and the heavy nuclei m ~ 76% and ~ 90% events, respectively. One proton IS emitted m ~ 22% events for the light and ~ 10% events for the heavy nuclei. The emission of two or more protons is rare. In the case of the emission of neutrons, It is observed that the events m which no neutron Is emitted are "" 11% for the hght and ~ 21% for the heavy nucleL One neutron is emitted in "" 70% events for all the nuclei while two neutrons are emitted m 15% and ~ 9% events for the hght and the heavy nuclei, respectwely. The probability of emission of three or four neutrons from any nucleus is very small (~ 4%). 3.1.4. Energy dtstribunon o f protons and neutrons As the initial reaction in 1~- captues is •- + p ~ A ° + n, all the outgoing protons are the result of the nuclear cascade and are consequently emitted with relatively small kinetic energy. All the outgoing protons have energy ~< 50 MeV, their number wtth energy > 30 MeV is only ~ (8-10)% In the case of the hght and ~ (15-20)% in that of the heavy nucleL The calculated energy distributions of outgoing neutrons agree with the corresponding experimental cllstnbution given by Frodesen et al. [4] except that the presence of slow neutrons m the expedrnental chstnbution is not so marked as in the calculated ones. This may be due to meagre statistics or expenmental uncertainties.
S,P. Goel, Y. Prakash, ~ - capture
627
3.1.5. Nudear momentum The nuclei acquire relatively small momentum from the nuclear cascade. The distnbution peaks around "" 300 MeV]c and extends up to "~ 700 MeV/c. This is both an indication as well as a consequence o f the fact that the particles emitted during the nuclear cascade are generally slow and small in number.
3.1. 6. Excitation energy The distribution o f the excitation energy received by the nuclei during the nuclear cascade is shown in fig. 3. The light nuclei do not get any excitation energy in "" 27% events m RI and " 22% events in RII. This indicates that in such events both the A ° hyperon and the neutron produced in Z - capture escape without undergoing any interaction inside the nucleus. The same is true for the heavy nuclei in "~ 15% events m RI as well as RII. The excitation energy tends to be larger for the heavy nuclei because of the larger probablhty o f absorption of particles in such nuclei dunng the nuclear cascade.
3.2. Results o f the stmulatton o f nuclear evaporation In view of the small excitation energy of the nuclei, the results of the nuclear evaporation are not very s~gnificant.
3.2.1. Number o f emitted particles No charged particle is emitted from the light nuclei in "" 60% events and from the heavy nuclei m "" 75% events. One, two and three charged particles are emitted from the light nuclei in "~ 25%, 10% and 4% events, respectively. The corresponding events for the heavy nuclei are 20%, 4% and 1%. From the light nuclei, four charged particles are also emitted occasionally (in "~ 1% events). Neutrons are not emitted from the hght and the heavy nuclei in ~ 50% and ~ 25% 3o
(a)
tb)
-?
I> W Ls. 0
Io
o
"2
zo
io
eo 80
ENERGY {MeV)
0
20
40
60
80
E N E R G Y (MeV)
Fig. 3. Excitation energy received by (a) the hght nucle] and (b) the heavy nuclei: - (0-10)% density region, - - - - (0-25)% density region.
XP. Goel, Y. Prakash, ~ - capture
628
events, respectwely. In the rest of the events, mostly one or two neutrons (in ~ 22% and "-- 15% events, respectively) are emitted from the light nuclei though the maximum number of emitted neutrons could be five for such nuclei. In the case of heavy nuclei, one, two, three and four neutrons are emitted in ~ 20%, 17%, 14% and 13% events respectavely while the maximum number of emitted neutrons could be ten.
3.2.2. Energy of emttted particles Most of the charged particles, I.e., ~> 90% of those emitted from the hght and ~> 80% of those emitted from the heavy nuclei have energy ~< 20 MeV. The rest of the emitted cha~ed particles generally have energy up to 30 MeV though a very small fractaon ( ~ 5 % ) of such particles may have energy up to 40 MeV. Similar features characterize the energy distribution of neutrons also. 3.3. Combined results The combined results of the nuclear cascade and the nuclear evaporation represent a complete simulation of the Z - capture process.
3.3.1. The Z - capture star The distributions of the prongs (Le., the toal number of charged particles, excluding the recoil, emitted during the nuclear cascade and the nuclear evaporation) of the Z - capture star are shown in fig. 4. These distributions do not include the events m whtch the A° hyperon is trapped. It is observed that ~ 54% and "" 69% stars from the light and the heavy nuclei, respectwely, have no prongs. This agrees with the experimental [48] estimates that so
(a)
(b)
6O 1, Ii1 ld
40 !
2O
O
o
~ 4 OF PRONGS
o 2 4 No. OF PRONO8
F i g . 4 . P r o n g d l s t n b u U o n o f s t a r s p r o d u c e d f r o m ~ - c a p t u r e s m (a) t h e h g h t n u c l e i a n d go) t h e heavy nuclei. - ( 0 " - 1 0 ) % d e n s i t y r e g i o n , - - - - ( 0 - 2 5 ) % d e n s i t y regaon.
s.P. Goel, Y. Prakash, X - capture
629
"" 60% 22- absorptions produce zero prong stars. The recent estimate of Junc and Simonovich [49], obtained with restricted detection posslbflitaes, that the production frequency of 22- capture stars on the hght emulsion nuclei is (42.0 --+ 1.9)% is in agreement with our corresponding estimate (46%) but their estimate of(58 -+2.6)% for the same frequency on the heavy nuclei is m disagreement with our estimate (31%) as well as with the earlier experimental [48] esttmate (40%) The calculated prong distributions of the X - capture star are in fair agreement with the experimental distnbutions gwen by Burhop [25]. This agreement lends support to the assumption that the Z - hyperons might be absorbed on the nuclear periphery. The present calculations confirm the experimental results [2, 50] that the 22capture stars containing two or more prongs are predominantly due to captures in the light nuclei while the nunber of charged particles emitted from X - captures m the heavy nuclei is relatively smaller. 3.3.2. Visible energy The wsible energy of the 22- capture star is obtained by taking the sum of the kinetic energy of all the charged particles (all treated as protons as m experimental work) emitted during the nuclear cascade and the nuclear evaporation. As expected, the vislble energy is always less than 80 MeV, m fact, it is generally < 40 MeV. 3.3.3. Recod range The 22- captures in the heavy nuclei always produce recoils of range < 2 lam (actually, < 1 tzm m "" 95% events) whale those m carbon, nitrogen and oxygen produce recods even of range > 20 gtm in ~ 24%, 12% and 5% events, respectavely. Long recoils may be misldentlfied as prongs and consequently m experimental work an event with a long recoil may itself be mlsidenttfied. It may also be mentioned that "~ 75% recoils produced from 22- captures in the light nuclei have range < 10/am. 3.4. Calculated and experimental A ° trappzng probabtlitws
The calculated values of the A ° trapping probabilities followang 22- captures (presented in table 4) are "~ (13 + 3.8)% for RI and "~ (16 + 3.8) for RII m the case ofhght and ~ (26 + 3.8) for RI as well as RII m the case of heavy nuclei. The corresponding experimental values are 8.5% and (16 -+ 3)% for the hght and the heavy nuclei, respectively (see table 1). Taking into account the errors involved, it can be said that the experimental and the calculated results are not in disagreement. This suggests that the absorption of 2;- hyperons occurs on the nuclear periphery. In view of the experimentally estimated value of the A ° trapping probability being closer to the corresponding calculated value for RI in the case ofhght nuclei, it Imght be inferred that the Z - hyperons are, perhaps, absorbed in RI, the (0-10)% density region of nculear matter, though this reference does not get support from the results of ~ - captures in the heavy nuclei.
630
S.P. Goel, Y. Prakash, ~ - capture
Table 5 Calculated production rates of HFs and CFs following ~ - capture Rate of productaon (%) Nucleus
HFs
CFs
RI
RII
RI
RII
Carbon
13.5
16.0
Nitrogen
12.0
16.0
0.5
0.5
Oxygen
12.0
16.0
1.5
0.5
Bromine
1.5
26.0
25.0
Silver
1.0
26,5
26.0
3.5. Producnon o f HFs and CFs The results of this work, presented m table 5, mchcate, m agreement with experimental observations [2-5], that the HFs are produced from 2;- captures mainly in the light emulsion nuclei. Captures in the heavy nuclei generally result m the production of CFs. The percentage of production of HFs from the heavy nuclei is very small. 3.6. Charactensncs o f HFs 3. 6.1. Mass and Charge dtstributlons Fig. 5 shows the mass and the charge distributions of the HFs produced from ~;- captures in the light emulsion nucleL The mass number A of the HFs generally has values from 8 to 11 while the charge Z generally has values from 3 to 6. The mass distnbution is in broad agreement with the calculated mass distribution given by Mora [5]. 3.6.2. Momentum distribution The calculated momentum distributions of the HFs produced from the light nuclei and of the CFs produced from the heavy nuclei peak around 350 MeV/c and extend up to ~ 700 MeV/c (see fig. 6). The HFs and the CFs receive most of their momentum from the nuclear cascade, the contributton of the nuclear evaporation being small (~< 50 MeV/c). The results of the present calculataon are similar to the other available calculated distribution [5]. 3.6.3. Range distrtbutzon The range distribution of the HFs produced~rom the light nuclei is shown in fig. 7a. The range o f ~ 75% HFs is ~< 10 #m. A small number (N 20%) of the HFs has range > 20/lm also (not shown in the figure). The distributaon Is m fair agreement with the experimental and the calculated range &stributions of light HFs grven by Mora [51.
S.P. Goel, Y. Prakash, ~ - capture
631
(0)
20
32
(b)
r-..J I
O)
IZ
,, " _
i
24
tfl r o.
tfl Ik 0
U r
o
Z
I
fn t-z I&l > L,J
L__
V
16
Z0
'-3
0
I,
z
0
4
HF
MASS
2 HF
(A)
4 6 8 CHARGE (m)
Fig. 5. H F m a s s a n d c h a r g e d i s t r i b u t i o n : - ( 0 - 1 0 ) % d e n s i t y region, - - d e n s i t y region. (a) H F mass d i s t r i b u t i o n , (b) H F c h a r g e d i s t r i b u t i o n .
-
(O-25-)%
(b)
32241
(a)
r-7
24 t-
~-~
...
I-
> bl IlL. 0
-'1 e
Z
;-1 -l.
aoo HF
"
4oo
MOMENTUM
aoo
(Me~!
7oo
0
200
CRYPTOFRA@MEN
400
600
7
700
MOMENTUM (MeV C)
Fig. 6. H F m o m e n t u m d i s t r i b u t i o n . - (0-10)% density regmn, - - - - (0-25)% density region. (a) H F s p r o d u c e d f r o m t h e l i g h t nuclei. Co) C F s p r o d u c e d f r o m t h e h e a w nucleL
"°l
S.P. Goel, Y. Prakash, T,-capture
632
(a)
(b)
20" r--1
32
16
~-
~
Z 12 w
P> hi
U.
U.
8
I
II
016
r --J 4
,
Z 24" ILl
> ta
0
(¢1
G
_3
c q
L.
-2. . . . -2 ~
~ ,, ~,,,
•
o
z
4
.
HF
.
Io
RANGE
la
L
~4
~
,8
ao
.
o
(urn)
H g
Fig. 7. I-IF range d l s t n b u t l o n . (a) H F s p r o d u c e d f r o m t h e h g h t n u c l e i region, - - - - (0-25)% m (0-10)%
d e n s i t y r e g i o n , Co) H F s
defislty region,
f r o m : ~ - captures i n ( 0 - 2 5 ) %
a
-
-
o
,
RANGE (0-10)%
(Including CFs) produced from :C-
a
(urn) density
captures
b r o m i n e , - - - - salver. (c) H F s ( i n c l u d i n g C F s ) p r o d u c e d density region
- - o r o m i n e , - - - - silver.
All HFs m RI and ~ 95% HFs in RII produced from 2~- captures m the heavy emulsion nuclei (Ag, Br) have range ~< 1/am (see fig. 7b, c) and are, therefore, classified as CFs. It may, therefore, be concluded that 2~- captures m the heavy nuclei nuclear always produce CFs
4. Conclusion The result of the Monte Carlo simulation of the captures at rest of ~ - hyperons and K - mesons m emulsion nucle: is m agreement with the experimental result from nuclear emulsion that the A ° trapping probabdity following 2~- captures is less than following K - captures. The difference can be explained m terms of the disstmflar energy distributions o f the A o hyperons created in the two cases. The E - capture star has no prongs m ~ 54% events m the hght and "~ 69% events in the heavy nucleL In general, the E - capture star is very small. The E - capture star having two or more prongs (excluding the reeod) is predominantly produced in the light emulsion nuclei.
S.P. Goel, Y. Prakash, ~ - capture
633
References [1] G. Dascola, C. Lambonzlo, S Mora and I. Ortalh, Nuovo Omento 16 (1960) 241. [2] J. Sacton, M.J. Benltson, D.H. Davis, B.D. Jones, B. Sanjeevalah and J. Zakrzewskl, Nuovo Omento 23 (1962) 702. [3] B. Anderson, O. Skjeggestad and D.H. Daws, Phys. Rev. 132 (1963) 2281. [4] A.G. Frodesen, T. Roe and O. Skjeggestad, Nucl Phys 68 (1965) 575. [5] S. Mora, Nuovo Omento 52A (1967) 800. [6] G. Bohm, F. Wysotzkl, M. Csejthey-Barth, J. Sacton, G. Schorochoff, G. Wllquet, A. Thompson, F. Esmael, D. Stanley, D.H. Davis, E.R. Fletcher, S.P Lovell, N.C. Roy, J.H. Wlckens, J.E. Allen, A. Flshwlck, A. Fthpkowskb K. Garbowska-Pmewska and E. Skrzypczak, Acta Phys. Pol A37 (1970) 135. [7] K - European CoUaboratlon, Nuovo Omento 13 (1959) 690. [8] V. Gorge, W. Koch, W. Lmdts, M. Nlkohc, S. Subotlc-Nlkohc and W. Wmzeler, Nucl. Phys. 21 (1960) 599. [9] R. Cester, G. Qsschettt, A. DebenedetU, A. Marzarl Chlesa, G. Rmaudo, C. Deney, K. Gottstem and W. Puschel, Nuovo Omento 22 (1961) 1069. [10] D. Abeledo, L. Choy, R.G. Ammar, N. Crayton, R. Levi Settl, M. Raymund and O. Skjeggestad, Nuovo Omento 22 (1961) 1171. [ 11] D.H. Daws, M. Csejthey-Barth, 3. Sacton, B.D. Jones, B. Sanjeevaaahand J Zakrzewsky, Nuovo Omento 22 (1961) 275. [12] A. Fthpkowskl, E. Arqmt, E. Skrzypczak and A. Wroblewskl, Nuovo Clmento 25 (1962) 1. [13] J. Lemonne, C. Mayeur, J. Sacton, D.H. Davis, D.A. Garbutt and J. Allen, Nuovo Clmento 34 (1964) 529. [14] M. Scejthey-Barth, G. Schorochoffand P. Van Bmst, Nucl Phys B14 (1969) 330. [15] A.D. Martin, Nuovo Omento 27 (1963) 1359. [16] W.L Kmght, F.R. Stannard, F. Opperdaelmer, B. Rickey and R. Wdson, Nuovo Clmento 32 (1964) 598. [17] D.H. Davis and J. Sacton, High energy physics vol. 2, ed. E.H.S. Burhop (Academic Press, London, 1967) 379. [18] W.M. Bugg, G.T. Condo, H.O. Cohn, R.D. McCulloch, N.E. Garrett, L.M. Tucker and J. Moulder, Proc. Int. Conf. on hypernuclear Physics, Argonne National Laboratory (1969) 748. [19] H.O. Cohn, R.D. McCulloch, W.M. Bugg, G.T. Condo, N° Garrett and L.M. Tucker, Plays Letters 27B (1968) 527. [20] W.M. Bugg, G.T. Condo, NoE. Garrett, J.W. Moulder, H.O. Cohn and R.D. MeCulloch, Phys. Letters 31B (1970) 595. [21] G. Sehorochoff-Thesls, University of Brussels (quoted m ref [6]). [22] H. Davas, F. Oppenheimer, W.L. Kmght, F.R. Stannard and O. Treufler, Nuovo Omento 53A (1968) 313. [23] G. Schorochoff, Umverslte hbre de Bruxelles, Bulletin No. 40 (1969). [24] M.M. Ntkohc, Prog. Elem. Particle Cosmic Ray Phys. 8 (1964) 201. [25] E.H.S. Burhop, D.H. Daxas and J. Zakrzewslo, Prog. Nucl. Phys. 9 (1963) 155. [26] Helium Bubble Chamber Collaboration Group, Proc. Int. Conf. on high energy physics, Rochester (1960) 426. [27] S. Lokanathan et al., Clarendon Laboratory, Oxford reports 47/61 and 48/61. [28] Hugo H. Bertml, Phys. Rev. 131 (1963) 1801. [29] Le Couteur, Proc. Phys. Soc. A63 (1950) 259,498. [30] C.F. Powell, P.H. Fowler and D.H. Perkins, The study of elementary particles by the photographls method (Pergman Press, London, 1959) 456.
634
S.P. Goel, Y. Prakash, 7-,-capture
[31 ] Tnyug Smgh, Y. Prakash, K.B. Bhalla and S. Lokanathan, Nuovo Ctmento 68A (1970) 501. [32] H. Heckman, Betty L. Perkins, Wllham G. Simon, Frances M. Smith and Walter H. Barkas, Phys. Rev. 117 (1960)544. [33] A.W. Key, S. Lokanathan and Y. Prakash, Nuovo Qmento 36 (1965) 50. [34] G. Bemardinl, E.T. Booth and S.J. Lindenbaum, Phys. Rev. 88 (1952) 1017. [35] H.A. Bethe and P. Marnson, Elementary nuclear theory (Wiley, New York, 1956) 235. [36] E. Segre, ed., Experimental nuclear physms vol. 2 (Wiley, New York, 1953) 145. [37] R.A. Howard, Nuclear physics (Wadsworth Pubhshmg Company, Belmont, Cahfomla, 1963) 524. [38] R. Hofstadter, Rev. Mod. Phys. 28 (1956) 214, Ann. Rev. Nucl. Scl. 7 (1957) 231. [39] Y. Prakash and S.P. Goel, Nuovo Clmento 51A (1967) 340. [40] N. Metropohs, R. Blvms, M. Storm, A. Turkevlch, J.M. Mallet and G. Fnedlander, Phys Rev. 110 (1958) 185,204. [41] H.L. Anderson, W.C. Davidon and U.E. Kruse, Phys. Rev. 100 (1950) 339. [42] I.I. Gol'dman, V.D. Knvchenkov, V.I. Kogan and V.M. Gahtskn, Problems in quantum mechamcs, translated, edited and arranged by D. ter Haar (Infosearch, London, 1964) 375. [43] W.O. Lock and D.F. Measday, Intermechate energy nuclear physics (Methuen, London, 1970) 119. [44] J. Orear, Phys. Rev. 100 (1955) 288. [45] B. Sectu Zorn, B. Kehoe, J. Twltty and R.A. Bumstem, Phys Rev. 175 (1968) 1735. [46] G. Fast, J.C. Helder and J.J. de Swart, Phys. Rev. Letters 22 (1969) 1453. [47] I. Dostrovsky, P. Rabmovitz, R. Blvlns, Phys Rev. 111 (1958) 1659. [48] B.D. Jones, B. Sanjeevalah, J. Zakrzewskl and D.H. Davis, Nuovo Clmento 19 (1961) 400. [49] M. Junc and J. Slmonovlc, Flzlka (Yugoslavm) 3 (1971) 135. [50] O. Sjeggestadt, quoted by Burhop et al. m ref. [25].
NUCLEAR
CAPTURE
OF 2 2 - H Y P E R O N S
S.P. GOEL* Physics Department, Kurukshetra University, Kurukshetra, India Y. PRAKASH Physics Department, Umverslty o f Jammu, Jammu, India Received 26 February 1973 Abstract The capture at rest of X;- hyperons in emulsion nuclei is studied through Monte-Carlo simulataon. The A ° trapping probability following X;- capture is estimated and compared with the corresponding probablhty following K - capture. The difference in the two probabthties IS explained in terms of the dissimilar energy dlstnbuUons of the A° hyperons produced from the captures of ~:- hyperons and K - mesons Information obtained on the features of the X;- capture star and on the characteristics of the hyperfragments produced from r . - captures is presented.
1. Introduction The rates o f trapping o f A ° hyperons and o f the production o f h y p e r f r a g m e n t s (HFs) and cryptofragments (CFs) following the captures o f Z - hyperons and K mesons have been experimentally estimated b y several authors [ 1 - 1 4 ] . It is reported that the A ° trapping probability following 2;- captures is much smaller than that following K - captures. Marian's calculations [15] and the propane bubble chamber studies [16] of K - absorptions also indicate a rate o f A ° trapping higher than that for 2 ; - absorption in nuclear emulsion. These results are somewhat surprising, for whereas 22- captures always lead to the production o f a A ° hyperon via the reaction 22- + p -->A o + n, thas ts not so for K - captures where a A ° h y p e r o n is produced (directly from K - absorption or mdirectly from 22 conversion) only m ~ 60% o f all K - meson interactions wath nuclear m a t t e r [4]. The energy release is also smaller (~- 80 MeV) m Z - captures than that in K - captures. Thus, the Z - captures, being a more abundant source o f A ° hyperons and having a smaller energy release should be, contrary to experimental results from nuclear emulsion, a richer source o f HFs than the K - captures. The reported slmllarity o f the energy spectra o f A ° hyperons produced from the absorptions o f ~ - hyperons and K - mesons has been used to suggest that any differ* Now at Department of Computer Science, Umverslty of Reading, Reading, England.
618
S.P. Goel, Y. Prakash, Z - capture
Table 1 A° trapping probablhty and rates of HF and CF productton following Z - capture A° trapping probablhty (%)
Rate of produeUon (%) HFs CFs +0.5 -0.4
Medmm
Ref
Remarks
emulsion
[3]
average for all nuclei
13.8 - 15.6 emulsion
[3]
for a sample rich m Z - captures m the heavy nuclei
3.7 ± 0.9
emulsion
[4]
average for all nuclei
3.0 +-0.5
emulsion
[5]
average for all nuclei
3.15 +-0.23
emulsion
[6]
average for all nuclei
emulsion
[6]
C, N, O nuclei
16-+ 3
emulsion
[6]
Ag, Br nuclei
8-14
Z = 40 A = 100 nucleus
[15]
DA= 25 MeV and AN scattering cross section = 22.3 mb
26 +- 5
bubble chamber
[2]
Absorption m neon
2.7
8.5
8.6 - 10
ence in their trapping probabtlities must be due to differences m their creation mechamsm [2, 3, 17]. Martan suggested that Z - hyperons might be captured more toward the outerslde on the nuclear periphery than K - mesons so that the A ° hyperons produced from the former have a better chance o f leaving the nucleus [ 15]. F u t h e r , m a y A ° hyperons produced m K - captures come indirectly from ~ - A conversion which presumably occurs deeper reside the nucleus; hence they have a greater chance o f becoming b o u n d [2]. Thus, the net result is that the A ° trapping probabdity m Z - captures turns out to be smaller than that m K - captures. The results from the hydrogen bubble chamber (having an admixture o f neon) are, however, at variance with those from nuclear emulsion. These results indicate that the A ° trapping probabihty following ~ - capture m neon is higher than the corresponding probabthty following K - captures [ 1 8 - 20]. Available data on A ° trapping probablhty following Z - and K - captures are presented m tables 1 and 2. In the present work, the capture o f ~ - hyperons in emulsion nuclei is studied through Monte-Carlo (MC) slmulataon. The A ° trapping p r o b a b l h ~ is calculated and compared with the corresponding probability similarly calculated for K captures. The calculated A ° trapping probabihty following Z - captures is then compared with the corresponding experimental estimates o f its value obtained from nuclear emulsion. Information is obtained on the features of the ~ - capture star. The characteristics o f the HFs produced from Z - captures are also studied.
[14] I15] 1191
11-+5
52 ± 14
15 - 3 0
9.5 -+ 3.0
absorption m neon
combined results for absorption in hght nuclei
bubble chamber + emulsion
[14]
19.6 -+ 1.8
bubble chamber
average for all freon nuclei
bubble chamber
I14]
19.0-+ 2
Martin's calculations
average for all freon nuclei
bubble chamber
[23]
Z = 40, A = 100 nucl.
average for all freon nuclei
bubble chamber
1221
19 -+ 1.6
combined results for absorption m heavy nuclei
absorption m Br in freon
bubble chamber
[161
51 -+ 1~
bubble chamber + emulsion
absorption m F in freon
absorption In C in propane (C3H8) and freon (CFaBr)
bubble chamber
average for all nuclei
emulsion
[21]
Ag, Br nuclei
emulsion
9_+5
C, N, O nuclei
emulslon
bubble chamber
for K - captures producing AO hyperons
emulsion
[161
[111
for all K - captures
Rema~s
emulsion
Medium
18.5 +- 3.5
30-+ 7
I131
58 -+ 15
41+_7
7+_1 1131
171
30+_7
5-+1
8+-2
[71
CF
HF
(%)
Ref.
Rate of production (%)
A° trapping probablhty
Table 2 A° trapping probabihty and rates of HF and CF production following K - captures
I
M
t~
620
S.P. Goel, Y. Prakash, ~ - capture
2. Monte-Carlo calculation and input parameters 2.1. The procedure o f the calculation For the sake of computational convemence, the procedure of the calculation is d:vided into the following three parts 2. I.I. The mtttal interaction Only the process ~ - + p -->A° + n + 80 MeV is assumed to contribute to the capture of ~ - hyperons. The probabihty of occurrence of the charge-exchange reactaon Z - + p -->Zo + n + 8 MeV is considered to be very small due to phase-space limitation and strong Pauh suppression [4]. Even when this reaction might occur, the very slow ~o hyperon is hkely to be absorbed in the parent nucleus, leading again to the productlon of the A ° hyperon. The absorptaon interaction of K - mesons with single nucleons only is considered m the present work as the probabihty of occurrence of its interaction w:th two nucleons m hehum and heavier nuclei is considered [26] to be relatavely small ( " 17 to 20%). Further, the latter typre of mteraction is expected to produce mostly fast hyperons which are less hkely to be absorbed as compared to the ones produced from the K - meson-smgle nucleon interaction. The K - absorption interacUons with single nucleons simulated in tits work are those gwen by Nikohc [24] and Burhop et al. [25], producing a 7r meson and a A ° or Z hyperon m the final state. The details of the slmulaUon procedure of the capture of K - mesons are to be commumcated separately. The Fermi momentum of the nucleon with which the Z - hyperon or the K meson interacts :s derived from the Fourier transform of its wave functxon. The procedure followed is the same as described by Lokanathan et al. [27]. The energy and momentum of the final-state particles are calculated by assuming that they are distributed lsotroplcally in the cm system. The E - hyperon and the K - meson are assumed to be absorbed from the s state, uniformly anywhere on the nuclear periphery within the (0 - 10)% density region (RI) oI the nuclear matter. 2.1.2. The nuclear cascade The particles produced in the initial interaction are followed, one by one, as they move and undergo scattering interactions inside the parent nucleus. The momentum of the target nucleon with which the mc:dent partxcle interacts is also found from the Fourier transform of its wave functaon [27]. The interaction mean free path is found from the relevant cross sections supphed as input parameters. If after an interaction the energy of a nucleon is found to be less than its Fermi level, the mteracUon is forbidden. If the interactaon is allowed, the energy of both the interacting particles is compared with their respectwe potential-weU depths. A particle having energy less than its potential-well depth is assumed to be absorbed.
s.P. Goel, Y. Prakash, ~ - capture
621
In the case of an absorbed pion or hyperon, ItS entare energy, while m that of an absorbed nucleon, its energy m excess of its Fermi level, is imparted to the nucleus as excitation energy. If the energy of a particle is greater than its potential-well depth, it is further followed and the process is repeated (which results m the development of a nuclear cascade)until all the particles are absorbed or emitted. A parlacle is assumed to be emitted if its energy is greater than its potential-well depth and the next point of lnteract~on falls outside the nucleus. The nature, energy and momentum of every emitted particle are recorded. Each emitted particle ~s assumed to Impart a momentum equal and opposite to its own to the residual nucleus whose mass and charge are adjusted after the emission of each particle. An absorbed ~ hyperon is assumed to interact with a single nucleon and get converted into a A ° hyperon while an absorbed plon is assumed to interact with a pair of nucleons, pp, pn or nn type. The pion absorption Is treated m the manner of Bertini et al. [28]. The particles produced from the absorption of Z hyperons or plons are also followed until they are emitted or absorbed. The absorption of a A ° hyperon is assumed to lead to the production of a HF. It is further assumed that once a A ° is trapped, it remains so even during the ensuing evaporation of the excited nucleus.
2.1.3. The nuclear evaporatTon The nucleus excited due to the energy imparted to it by the absorbed particles ~s assumed to de-excite itself via evaporation. The simulation of the process of nuclear evaporation follows the work of Le Couteur [29], as discussed by Powell et al. [30], and the procedure is identical to that of Smgh et al. [31]. The final momentum of the residual nucleus (henceforth called recoil or HF if a A ° is trapped m it) is obtained from the vector sum of the randomly oriented momenta acqmred by it during the nuclear cascade and the ensuing evaporation. The range corresponding to the final recoil or HF mass, charge and momentum is calculated from the range-energy relations of Heckman et al. [32] as discussed by Key et al. [33]. The calculataons are done separately for ~ - capture m carbon, mtrogen, oxygen, bromine and silver and for K - capture m carbon, bromine and silver. Two hundred events are simulated for each nucleus. The entire procedure is repeated for each nucleus for the initial absorption of ~ hyperons and K - mesons in the (0 - 25)% density region (RII) of the nuclear matter 2.2. Input parameters 2.2. I. The nuclear parameters Following Bernardim et al. [34], the nucleus is represented by a statistical assembly of nucleons and it is considered to be, to start with, m an unexclted ground state composed of non-interactang fermion gases of neutrons and protons m an uniform
622
S.P. Goel, Y. Prakash, ~,- capture
Table 3 Formulae used m the calculation of nuclear parameters Parameter Fermi energy
Formulae used for calculation 2
2
E F = (76.52/ro) (n/A)~ MeV
(EF) Coulomb barrier (C.B.)
C.B. = (Ze2/R) MeV
Potentialwell depth
Dp = E F + B.E. + C.B. MeV Dn = E F + B.E. MeV
Density of nuclear matter (p(r))
p(r) = po/(l+exp((r-c)/a))
Remarks n -- Z for protons n -- (A-Z) for neutrons r o = 1.25 l R =roA~ r o = 1.25 A = 12, 14, 16, 80, 108. The value of C.B. is multaphed by the penetrataon factor 0.7 for protons. Dp = potential well depth for protons Dn = potential weU depth for neutrons B.E.= average binding energy per nucleon Po = nuclear density at centre c = 1.07 A~fm a = 0.55 fm
ReL [ 35 ]
[31]
[ 36 ] [37 }
[38]
potential well wlthm the nucelar volume. The basis of calculation of the various nuclear parameters used in the calculations is summanzed in table 3, The potential-well depth (DA) and the mass of the A ° hyperon are taken to be 32 MeV [39] and 1115.4 MeV, respectively. The potential-well depth of ~ hyperons is taken to be the same as D A whale its value for pions is assumed to be 40 MeV.
2.2.2. The scattenng cross secnons The scattering interactions reside the nucleus are described by the free scattering cross sections except as modified b y the Pauli principle.
2.2.2.1. Nucleon-nucleon scattenng. The total as well as the differential scattering cross sections for the nucleon-nucleon (lap, pn or nn) scattering collisions are taken from Metropolis et al. [40]. The procedure followed is identical to that of these authors.
2.2.2.2. Pion-nucleon scattering. The total scattering cross sections for pion-nucleon scattering collisions are taken from Anderson et al. [41] and the differential scattering cross sections from G o r d m a n et al. [42]. Charge independence is assumed, only s and p waves are considered [43] and the relevant phase shifts are calculated according to the procedure suggested b y Orear [44].
S.P. Goel, Y. Prakash, ~ - capture
623
2.2.2.3. Hyperon-nucleon scattenng. The low energy hyperon-nucleon elastic scattering is predominantly s-wave interaction and it is, therefore, assumed to be lSOtropic m the c.m. system. The total scattering cross sections used m the present calculations are those given by Sechi-Zom et al. [45] for (A°P) interaction, and by Fast et al. [46] for (E+P) and ( E - P ) interactions. It is assumed that the hyperonneutron interaction ts identical to the hyperon-proton one. The (yop) scattering cross section is taken to be equal to the mean of the (E+P) and the ( E - P ) scattenng cross sections. 2.2.3. Frequency o f emission and the momentum o f evaporated partwles The frequencies of emission of the vanous particles likely to be emitted during nuclear evaporation are computed from the evaporataon theory [30] for different nuclear temperatures and three mass regions of the nuclear mass. Out of the particles likely to be emitted during nuclear evaporation, the momenta of 2H, 3H, 3He and 8La, treated as constant, are taken from Key et al. [33] while the momenta of n, p and 4He, treated as variables, are taken from the distributions gwen by Dostrovsky et al. [47]. The detads are given by Slngh et al. [31].
3. Results and discussion The results for RI and RII are generally similar and are, therefore, gwen separately only when there is a special reason for doing so. 3.1. Results o f the simulatton o f nuclear cascade 3.1.1. A°-momentum distribution The momentum distribution of the A ° hyperons produced reside the nucleus from Z - captures is glven in fig. la. This is similar to the momentum distributions of the A ° hyperons emitted from the light and the heavy emulsion nuclei, shown in fig. lb, c. The latter have only an additional low energy tail which is a consequence of the scattering interactions which the A ° hyperons undergo with nucleons inside the nucleus. The distributions are also stmilar for RI and RII. In fig. ld is shown the experimentally estimated distnbution of the momentum of A ° hyperons ermtted from neon (derived from the distribution given by Bugg et al. [18]). This distribution is similar to the distributions shown m fig. lb, c. The broad similanty of all the distributions shown m fig. la, b, c, d could be interpreted as providing evidence in favour of penpheral absorption of Z - hyperons, for the experimentally estunated distribution might be expected to be much more modified If ~ hyperons were captured deeper inside the nucleus and the A ° hyperons interacted much more with the nucleons before being emitted. The energy distributmns of the A ° hyperons produced from the captures of ~ hyperons and K - mesons are not similar (see fig. 2a, b), a result contrary to the as-
624
S.P. Goel, Y Prakash, T_,- capture (a) 60
(0 Iz,., > ill
(I))
¸
40
tl. 0 O
Z
-,.~
20'
200
400
MOMENTUM
OF
0
200
400
A~ HYPERON8 ( M I V / C )
(e)
(d)
60
zc
0
ZOO MOMENTUM
400 OF
0
200
400
Ae.- HYPERON$ (MeV/C)
Fig. 1. Momensum distribution of A ° hyperons. (a) A ° hyperons lmtially produced from I f captures, (13) A ° hyperons emitted from the hght nuclei: (a) A ° hyperons mittally produced from Y-- captures; Co) A ° hyperons emitted from the light nuclei ( 0 - 1 0 ) % density region, - - - - ( 0 - 2 5 ) % density region; (c) A ° hyperons emitted from the heavy nuclei - ( 0 - 1 0 ) % density region, - - - - ( 0 - 2 5 ) % density regton; (d) A ° hyperons emitted from neon.
sumption of several authors [2, 3, 17]. About 70% A o hyperons produced from K captures have energy < 30 MeV while the fraction of such A° hyperons produced from Z - captures is only ~ 30%. The A ° hyperons produced with neutrons in ~ - captures get more energy than those produced with plon in K - captures. Being much lighter, the pions take away much larger energy (nearly eight ttmes) than that available to the A ° hyperons. Thus, despite larger energy release, more of slow A ° hyperons are produced in K - captures as compared to Z - captures.
S.P. Goel, Y. Prakash, ~-capture (o)
625
(b)
30 u) I-
,z 2o > rid i.
o
j
Io
o
zo
,~o
o
eo
E NERGY
OF
\l ~;o
A° - H Y P E R O N $
,~o (MoV)
Fig. 2. Energy dlstrlbutmn of A ° hyperons. (a) A ° hyperons produced from 2;- captures, (b) A ° hyperons produced from K - captures.
3.1.2. Comparison of calculated A ° trappmg probabihttes The calculated values of the A ° trapping probabditles following ~ - and K - captures are presented m table 4. The results for RI and RII are similar, more so in the case of 2;- captures which indicates that the rate o f A ° trapping Is, perhaps, not very senmive to the location o f the initial Z--absorption interaction on the nuclear periphery. The A ° trapping probablhty following Z - capture turns out to be much smaller than that following K - capture. This is in agreoment with experimental results from Table 4 Calculated A ° trapping probability A ° trapping probability Particle
Nucleus
absorbed
2 ; - hyperon
K - meson
(0-10)% density
(0-25)% densRy
region
region
Carbon
13.5 + 3.8
16.0 ± 3.8
Nitrogen
12.5 + 3.8
16.5 + 3.8
Oxygen
13.5 + 3.8
16.5 + 3.8
Bromine
26.0 + 3.8
26.5 + 3.8
Silver
26.5 + 3.8
27.0 ± 3.8
Carbon
33.0 ± 3.8
39.0 + 3.8
Bromine
39.0 + 3.8
50.0 ± 3.8
Silver
41.0 ± 3.8
51.0 + 3.8
Remarks
the probablhty for all the hght nuclei is the same the probablhty Is the same for both the heavy nuclei the probability for mtrogen and oxygen is expected to be the same as for carbon
626
&P. Goel, Y. Prakash, ~ - capture
nuclear emulsion but unlike those from the bubble chamber from absorptaons m neon. The cause of the opposite trend of the bubble chamber result might be m expertmental uncertainties or elsewhere and deserves careful mvest~gatlon. The results of this work are significant in the sense that the A° trapping probabihty following ~ - captures is observed to be less than that followang K - captures even if the capture of )2- hyperons occurs in RII and that of K - mesons occurs in RI (see table 4). This Is contrary to the spirit of Martin's suggestion (see sect. 1). In view of the reported [2, 3, 17] similarity of the energy distributions of the A ° hyperons produced from ~ - and K - captures, the A ° trapping probabihty following 1~- captures should be larger if the ~ - hyperons are captured deeper reside the nucleus than the K - mesons. However, our results indicate (see subsect. 3.1.2) that the energy &stnbutlons of the A ° hyperons produced from ~ - and K - captures are indeed chfferent and therefore, the smaller rate of A ° trapping followang ~ - captures can be explained without revoking the difference m their creation mechanism. Since more of slow A ° hyperons are produced m K - captures than m ~,- captures (70% in the former versus 30% in the latter), their trapping probabihty must obviously be larger in the former even ffboth the K - mesons and the ~ - hyperons were captured in the same density region of the nuclear matter. Our results also indicate that " 30% A ° hyperons are produced from ~ convemon in K - captures. Such A ° hyperons have energy distnbuUon smadar to those produced from )2- capture and are produced deeper inside the nucleus. As expected [2], their trapping probability is larger. 3.1.3. Number o f emitted protons and neutrons No proton is emitted from Y.- captures in the light and the heavy nuclei m ~ 76% and ~ 90% events, respectively. One proton IS emitted m ~ 22% events for the light and ~ 10% events for the heavy nuclei. The emission of two or more protons is rare. In the case of the emission of neutrons, It is observed that the events m which no neutron Is emitted are "" 11% for the hght and ~ 21% for the heavy nucleL One neutron is emitted in "" 70% events for all the nuclei while two neutrons are emitted m 15% and ~ 9% events for the hght and the heavy nuclei, respectwely. The probability of emission of three or four neutrons from any nucleus is very small (~ 4%). 3.1.4. Energy dtstribunon o f protons and neutrons As the initial reaction in 1~- captues is •- + p ~ A ° + n, all the outgoing protons are the result of the nuclear cascade and are consequently emitted with relatively small kinetic energy. All the outgoing protons have energy ~< 50 MeV, their number wtth energy > 30 MeV is only ~ (8-10)% In the case of the hght and ~ (15-20)% in that of the heavy nucleL The calculated energy distributions of outgoing neutrons agree with the corresponding experimental cllstnbution given by Frodesen et al. [4] except that the presence of slow neutrons m the expedrnental chstnbution is not so marked as in the calculated ones. This may be due to meagre statistics or expenmental uncertainties.
S,P. Goel, Y. Prakash, ~ - capture
627
3.1.5. Nudear momentum The nuclei acquire relatively small momentum from the nuclear cascade. The distnbution peaks around "" 300 MeV]c and extends up to "~ 700 MeV/c. This is both an indication as well as a consequence o f the fact that the particles emitted during the nuclear cascade are generally slow and small in number.
3.1. 6. Excitation energy The distribution o f the excitation energy received by the nuclei during the nuclear cascade is shown in fig. 3. The light nuclei do not get any excitation energy in "" 27% events m RI and " 22% events in RII. This indicates that in such events both the A ° hyperon and the neutron produced in Z - capture escape without undergoing any interaction inside the nucleus. The same is true for the heavy nuclei in "~ 15% events m RI as well as RII. The excitation energy tends to be larger for the heavy nuclei because of the larger probablhty o f absorption of particles in such nuclei dunng the nuclear cascade.
3.2. Results o f the stmulatton o f nuclear evaporation In view of the small excitation energy of the nuclei, the results of the nuclear evaporation are not very s~gnificant.
3.2.1. Number o f emitted particles No charged particle is emitted from the light nuclei in "" 60% events and from the heavy nuclei m "" 75% events. One, two and three charged particles are emitted from the light nuclei in "~ 25%, 10% and 4% events, respectively. The corresponding events for the heavy nuclei are 20%, 4% and 1%. From the light nuclei, four charged particles are also emitted occasionally (in "~ 1% events). Neutrons are not emitted from the hght and the heavy nuclei in ~ 50% and ~ 25% 3o
(a)
tb)
-?
I> W Ls. 0
Io
o
"2
zo
io
eo 80
ENERGY {MeV)
0
20
40
60
80
E N E R G Y (MeV)
Fig. 3. Excitation energy received by (a) the hght nucle] and (b) the heavy nuclei: - (0-10)% density region, - - - - (0-25)% density region.
XP. Goel, Y. Prakash, ~ - capture
628
events, respectwely. In the rest of the events, mostly one or two neutrons (in ~ 22% and "-- 15% events, respectively) are emitted from the light nuclei though the maximum number of emitted neutrons could be five for such nuclei. In the case of heavy nuclei, one, two, three and four neutrons are emitted in ~ 20%, 17%, 14% and 13% events respectavely while the maximum number of emitted neutrons could be ten.
3.2.2. Energy of emttted particles Most of the charged particles, I.e., ~> 90% of those emitted from the hght and ~> 80% of those emitted from the heavy nuclei have energy ~< 20 MeV. The rest of the emitted cha~ed particles generally have energy up to 30 MeV though a very small fractaon ( ~ 5 % ) of such particles may have energy up to 40 MeV. Similar features characterize the energy distribution of neutrons also. 3.3. Combined results The combined results of the nuclear cascade and the nuclear evaporation represent a complete simulation of the Z - capture process.
3.3.1. The Z - capture star The distributions of the prongs (Le., the toal number of charged particles, excluding the recoil, emitted during the nuclear cascade and the nuclear evaporation) of the Z - capture star are shown in fig. 4. These distributions do not include the events m whtch the A° hyperon is trapped. It is observed that ~ 54% and "" 69% stars from the light and the heavy nuclei, respectwely, have no prongs. This agrees with the experimental [48] estimates that so
(a)
(b)
6O 1, Ii1 ld
40 !
2O
O
o
~ 4 OF PRONGS
o 2 4 No. OF PRONO8
F i g . 4 . P r o n g d l s t n b u U o n o f s t a r s p r o d u c e d f r o m ~ - c a p t u r e s m (a) t h e h g h t n u c l e i a n d go) t h e heavy nuclei. - ( 0 " - 1 0 ) % d e n s i t y r e g i o n , - - - - ( 0 - 2 5 ) % d e n s i t y regaon.
s.P. Goel, Y. Prakash, X - capture
629
"" 60% 22- absorptions produce zero prong stars. The recent estimate of Junc and Simonovich [49], obtained with restricted detection posslbflitaes, that the production frequency of 22- capture stars on the hght emulsion nuclei is (42.0 --+ 1.9)% is in agreement with our corresponding estimate (46%) but their estimate of(58 -+2.6)% for the same frequency on the heavy nuclei is m disagreement with our estimate (31%) as well as with the earlier experimental [48] esttmate (40%) The calculated prong distributions of the X - capture star are in fair agreement with the experimental distnbutions gwen by Burhop [25]. This agreement lends support to the assumption that the Z - hyperons might be absorbed on the nuclear periphery. The present calculations confirm the experimental results [2, 50] that the 22capture stars containing two or more prongs are predominantly due to captures in the light nuclei while the nunber of charged particles emitted from X - captures m the heavy nuclei is relatively smaller. 3.3.2. Visible energy The wsible energy of the 22- capture star is obtained by taking the sum of the kinetic energy of all the charged particles (all treated as protons as m experimental work) emitted during the nuclear cascade and the nuclear evaporation. As expected, the vislble energy is always less than 80 MeV, m fact, it is generally < 40 MeV. 3.3.3. Recod range The 22- captures in the heavy nuclei always produce recoils of range < 2 lam (actually, < 1 tzm m "" 95% events) whale those m carbon, nitrogen and oxygen produce recods even of range > 20 gtm in ~ 24%, 12% and 5% events, respectavely. Long recoils may be misldentlfied as prongs and consequently m experimental work an event with a long recoil may itself be mlsidenttfied. It may also be mentioned that "~ 75% recoils produced from 22- captures in the light nuclei have range < 10/am. 3.4. Calculated and experimental A ° trappzng probabtlitws
The calculated values of the A ° trapping probabilities followang 22- captures (presented in table 4) are "~ (13 + 3.8)% for RI and "~ (16 + 3.8) for RII m the case ofhght and ~ (26 + 3.8) for RI as well as RII m the case of heavy nuclei. The corresponding experimental values are 8.5% and (16 -+ 3)% for the hght and the heavy nuclei, respectively (see table 1). Taking into account the errors involved, it can be said that the experimental and the calculated results are not in disagreement. This suggests that the absorption of 2;- hyperons occurs on the nuclear periphery. In view of the experimentally estimated value of the A ° trapping probability being closer to the corresponding calculated value for RI in the case ofhght nuclei, it Imght be inferred that the Z - hyperons are, perhaps, absorbed in RI, the (0-10)% density region of nculear matter, though this reference does not get support from the results of ~ - captures in the heavy nuclei.
630
S.P. Goel, Y. Prakash, ~ - capture
Table 5 Calculated production rates of HFs and CFs following ~ - capture Rate of productaon (%) Nucleus
HFs
CFs
RI
RII
RI
RII
Carbon
13.5
16.0
Nitrogen
12.0
16.0
0.5
0.5
Oxygen
12.0
16.0
1.5
0.5
Bromine
1.5
26.0
25.0
Silver
1.0
26,5
26.0
3.5. Producnon o f HFs and CFs The results of this work, presented m table 5, mchcate, m agreement with experimental observations [2-5], that the HFs are produced from 2;- captures mainly in the light emulsion nuclei. Captures in the heavy nuclei generally result m the production of CFs. The percentage of production of HFs from the heavy nuclei is very small. 3.6. Charactensncs o f HFs 3. 6.1. Mass and Charge dtstributlons Fig. 5 shows the mass and the charge distributions of the HFs produced from ~;- captures in the light emulsion nucleL The mass number A of the HFs generally has values from 8 to 11 while the charge Z generally has values from 3 to 6. The mass distnbution is in broad agreement with the calculated mass distribution given by Mora [5]. 3.6.2. Momentum distribution The calculated momentum distributions of the HFs produced from the light nuclei and of the CFs produced from the heavy nuclei peak around 350 MeV/c and extend up to ~ 700 MeV/c (see fig. 6). The HFs and the CFs receive most of their momentum from the nuclear cascade, the contributton of the nuclear evaporation being small (~< 50 MeV/c). The results of the present calculataon are similar to the other available calculated distribution [5]. 3.6.3. Range distrtbutzon The range distribution of the HFs produced~rom the light nuclei is shown in fig. 7a. The range o f ~ 75% HFs is ~< 10 #m. A small number (N 20%) of the HFs has range > 20/lm also (not shown in the figure). The distributaon Is m fair agreement with the experimental and the calculated range &stributions of light HFs grven by Mora [51.
S.P. Goel, Y. Prakash, ~ - capture
631
(0)
20
32
(b)
r-..J I
O)
IZ
,, " _
i
24
tfl r o.
tfl Ik 0
U r
o
Z
I
fn t-z I&l > L,J
L__
V
16
Z0
'-3
0
I,
z
0
4
HF
MASS
2 HF
(A)
4 6 8 CHARGE (m)
Fig. 5. H F m a s s a n d c h a r g e d i s t r i b u t i o n : - ( 0 - 1 0 ) % d e n s i t y region, - - d e n s i t y region. (a) H F mass d i s t r i b u t i o n , (b) H F c h a r g e d i s t r i b u t i o n .
-
(O-25-)%
(b)
32241
(a)
r-7
24 t-
~-~
...
I-
> bl IlL. 0
-'1 e
Z
;-1 -l.
aoo HF
"
4oo
MOMENTUM
aoo
(Me~!
7oo
0
200
CRYPTOFRA@MEN
400
600
7
700
MOMENTUM (MeV C)
Fig. 6. H F m o m e n t u m d i s t r i b u t i o n . - (0-10)% density regmn, - - - - (0-25)% density region. (a) H F s p r o d u c e d f r o m t h e l i g h t nuclei. Co) C F s p r o d u c e d f r o m t h e h e a w nucleL
"°l
S.P. Goel, Y. Prakash, T,-capture
632
(a)
(b)
20" r--1
32
16
~-
~
Z 12 w
P> hi
U.
U.
8
I
II
016
r --J 4
,
Z 24" ILl
> ta
0
(¢1
G
_3
c q
L.
-2. . . . -2 ~
~ ,, ~,,,
•
o
z
4
.
HF
.
Io
RANGE
la
L
~4
~
,8
ao
.
o
(urn)
H g
Fig. 7. I-IF range d l s t n b u t l o n . (a) H F s p r o d u c e d f r o m t h e h g h t n u c l e i region, - - - - (0-25)% m (0-10)%
d e n s i t y r e g i o n , Co) H F s
defislty region,
f r o m : ~ - captures i n ( 0 - 2 5 ) %
a
-
-
o
,
RANGE (0-10)%
(Including CFs) produced from :C-
a
(urn) density
captures
b r o m i n e , - - - - salver. (c) H F s ( i n c l u d i n g C F s ) p r o d u c e d density region
- - o r o m i n e , - - - - silver.
All HFs m RI and ~ 95% HFs in RII produced from 2~- captures m the heavy emulsion nuclei (Ag, Br) have range ~< 1/am (see fig. 7b, c) and are, therefore, classified as CFs. It may, therefore, be concluded that 2~- captures m the heavy nuclei nuclear always produce CFs
4. Conclusion The result of the Monte Carlo simulation of the captures at rest of ~ - hyperons and K - mesons m emulsion nucle: is m agreement with the experimental result from nuclear emulsion that the A ° trapping probabdity following 2~- captures is less than following K - captures. The difference can be explained m terms of the disstmflar energy distributions o f the A o hyperons created in the two cases. The E - capture star has no prongs m ~ 54% events m the hght and "~ 69% events in the heavy nucleL In general, the E - capture star is very small. The E - capture star having two or more prongs (excluding the reeod) is predominantly produced in the light emulsion nuclei.
S.P. Goel, Y. Prakash, ~ - capture
633
References [1] G. Dascola, C. Lambonzlo, S Mora and I. Ortalh, Nuovo Omento 16 (1960) 241. [2] J. Sacton, M.J. Benltson, D.H. Davis, B.D. Jones, B. Sanjeevalah and J. Zakrzewskl, Nuovo Omento 23 (1962) 702. [3] B. Anderson, O. Skjeggestad and D.H. Daws, Phys. Rev. 132 (1963) 2281. [4] A.G. Frodesen, T. Roe and O. Skjeggestad, Nucl Phys 68 (1965) 575. [5] S. Mora, Nuovo Omento 52A (1967) 800. [6] G. Bohm, F. Wysotzkl, M. Csejthey-Barth, J. Sacton, G. Schorochoff, G. Wllquet, A. Thompson, F. Esmael, D. Stanley, D.H. Davis, E.R. Fletcher, S.P Lovell, N.C. Roy, J.H. Wlckens, J.E. Allen, A. Flshwlck, A. Fthpkowskb K. Garbowska-Pmewska and E. Skrzypczak, Acta Phys. Pol A37 (1970) 135. [7] K - European CoUaboratlon, Nuovo Omento 13 (1959) 690. [8] V. Gorge, W. Koch, W. Lmdts, M. Nlkohc, S. Subotlc-Nlkohc and W. Wmzeler, Nucl. Phys. 21 (1960) 599. [9] R. Cester, G. Qsschettt, A. DebenedetU, A. Marzarl Chlesa, G. Rmaudo, C. Deney, K. Gottstem and W. Puschel, Nuovo Omento 22 (1961) 1069. [10] D. Abeledo, L. Choy, R.G. Ammar, N. Crayton, R. Levi Settl, M. Raymund and O. Skjeggestad, Nuovo Omento 22 (1961) 1171. [ 11] D.H. Daws, M. Csejthey-Barth, 3. Sacton, B.D. Jones, B. Sanjeevaaahand J Zakrzewsky, Nuovo Omento 22 (1961) 275. [12] A. Fthpkowskl, E. Arqmt, E. Skrzypczak and A. Wroblewskl, Nuovo Clmento 25 (1962) 1. [13] J. Lemonne, C. Mayeur, J. Sacton, D.H. Davis, D.A. Garbutt and J. Allen, Nuovo Clmento 34 (1964) 529. [14] M. Scejthey-Barth, G. Schorochoffand P. Van Bmst, Nucl Phys B14 (1969) 330. [15] A.D. Martin, Nuovo Omento 27 (1963) 1359. [16] W.L Kmght, F.R. Stannard, F. Opperdaelmer, B. Rickey and R. Wdson, Nuovo Clmento 32 (1964) 598. [17] D.H. Davis and J. Sacton, High energy physics vol. 2, ed. E.H.S. Burhop (Academic Press, London, 1967) 379. [18] W.M. Bugg, G.T. Condo, H.O. Cohn, R.D. McCulloch, N.E. Garrett, L.M. Tucker and J. Moulder, Proc. Int. Conf. on hypernuclear Physics, Argonne National Laboratory (1969) 748. [19] H.O. Cohn, R.D. McCulloch, W.M. Bugg, G.T. Condo, N° Garrett and L.M. Tucker, Plays Letters 27B (1968) 527. [20] W.M. Bugg, G.T. Condo, NoE. Garrett, J.W. Moulder, H.O. Cohn and R.D. MeCulloch, Phys. Letters 31B (1970) 595. [21] G. Sehorochoff-Thesls, University of Brussels (quoted m ref [6]). [22] H. Davas, F. Oppenheimer, W.L. Kmght, F.R. Stannard and O. Treufler, Nuovo Omento 53A (1968) 313. [23] G. Schorochoff, Umverslte hbre de Bruxelles, Bulletin No. 40 (1969). [24] M.M. Ntkohc, Prog. Elem. Particle Cosmic Ray Phys. 8 (1964) 201. [25] E.H.S. Burhop, D.H. Daxas and J. Zakrzewslo, Prog. Nucl. Phys. 9 (1963) 155. [26] Helium Bubble Chamber Collaboration Group, Proc. Int. Conf. on high energy physics, Rochester (1960) 426. [27] S. Lokanathan et al., Clarendon Laboratory, Oxford reports 47/61 and 48/61. [28] Hugo H. Bertml, Phys. Rev. 131 (1963) 1801. [29] Le Couteur, Proc. Phys. Soc. A63 (1950) 259,498. [30] C.F. Powell, P.H. Fowler and D.H. Perkins, The study of elementary particles by the photographls method (Pergman Press, London, 1959) 456.
634
S.P. Goel, Y. Prakash, 7-,-capture
[31 ] Tnyug Smgh, Y. Prakash, K.B. Bhalla and S. Lokanathan, Nuovo Ctmento 68A (1970) 501. [32] H. Heckman, Betty L. Perkins, Wllham G. Simon, Frances M. Smith and Walter H. Barkas, Phys. Rev. 117 (1960)544. [33] A.W. Key, S. Lokanathan and Y. Prakash, Nuovo Qmento 36 (1965) 50. [34] G. Bemardinl, E.T. Booth and S.J. Lindenbaum, Phys. Rev. 88 (1952) 1017. [35] H.A. Bethe and P. Marnson, Elementary nuclear theory (Wiley, New York, 1956) 235. [36] E. Segre, ed., Experimental nuclear physms vol. 2 (Wiley, New York, 1953) 145. [37] R.A. Howard, Nuclear physics (Wadsworth Pubhshmg Company, Belmont, Cahfomla, 1963) 524. [38] R. Hofstadter, Rev. Mod. Phys. 28 (1956) 214, Ann. Rev. Nucl. Scl. 7 (1957) 231. [39] Y. Prakash and S.P. Goel, Nuovo Clmento 51A (1967) 340. [40] N. Metropohs, R. Blvms, M. Storm, A. Turkevlch, J.M. Mallet and G. Fnedlander, Phys Rev. 110 (1958) 185,204. [41] H.L. Anderson, W.C. Davidon and U.E. Kruse, Phys. Rev. 100 (1950) 339. [42] I.I. Gol'dman, V.D. Knvchenkov, V.I. Kogan and V.M. Gahtskn, Problems in quantum mechamcs, translated, edited and arranged by D. ter Haar (Infosearch, London, 1964) 375. [43] W.O. Lock and D.F. Measday, Intermechate energy nuclear physics (Methuen, London, 1970) 119. [44] J. Orear, Phys. Rev. 100 (1955) 288. [45] B. Sectu Zorn, B. Kehoe, J. Twltty and R.A. Bumstem, Phys Rev. 175 (1968) 1735. [46] G. Fast, J.C. Helder and J.J. de Swart, Phys. Rev. Letters 22 (1969) 1453. [47] I. Dostrovsky, P. Rabmovitz, R. Blvlns, Phys Rev. 111 (1958) 1659. [48] B.D. Jones, B. Sanjeevalah, J. Zakrzewskl and D.H. Davis, Nuovo Clmento 19 (1961) 400. [49] M. Junc and J. Slmonovlc, Flzlka (Yugoslavm) 3 (1971) 135. [50] O. Sjeggestadt, quoted by Burhop et al. m ref. [25].