R. Timmermans, Kernfysisch Versneller Instituut, University

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1 1 THE z-emission PUZZLE IN 4 OVER A HE DECAY Author(s) B.F. Gibson, T-5, MS 8283, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM USA R. Timmermans, Kernfysisch Versneller Instituut, University of Groningen, Zernikelaan 25, 9747 AA Groningen, The Netherlands Submitted to. 'roceedings of the "International Conference on Hypernuclear md Strange Particle Physics", Brookhaven National Lab, October DiSTRI3UTION OF THIS DOCUMENT IS UNUMEO b Lor Alamoc National hbomtoty, an m t m t i v e 8ctiorUequelopporhrnity enpdver. is operated by Me Universlty G California I for the US. oepprtment of Energy Under contract W-74OSENG-36. By aaepbya d this article. the publisher recoonizes the U.S. Government retains a nonexclusive, royalty-free license to prblish or reproduce!he published form of the contrikrt~on.or to allow others to do bo. for US. Government purposes. The Los Alamos National Laboratory quests mal the publisher 'dentifythii attide as work performed under the auspioes of the US. Department of Energy. Form ST2629 No R5

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3 The n-emission puzzle in :He decay B. F. Gibsona and R. Timmermansb atheoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545,USA bkernfysisch Versneller Instituut, University of Groningen, Zernikelaan 25, 9747 AA Groningen, The Netherlands The observed [1,2]7r emission from the weak decay of ;He has long been an intriguing puzzle. Experimentally, the 7r to 7r- ratio for ;He decay is about 5%. Because mesonic decay modes of the free A ( p 7r-, n T O ) produce no RS, more complicated mechanisms must be responsible for the 7r decay of :He. Dalitz and von Hippel [3-51 explored two-body decay processes of the type: (i) A 7ro n decay followed by a 7ro p - 7r n charge-exchange reaction, and (ii) C 7r n decay following a A p C n conversion. They concluded that neither process could account for even a 1% 7r decay rate. Dalitz [6] argued that the experimental identification of free C 7r n decay as a p-wave process ruled out the promising explanation coming from von Hippel's calculations [5], which had found that s-wave E decay might yield a sufficiently high rate. Cieplf and Gal [7]re-examined the charge-exchange contribution and concluded that, although up-to-date input parameters yield a 1.2% branching ratio, the charge-exchange mechanism cannot account for the experimental value of about 5%. The ratio of 7r decays to 7r- decays for ;He is defined as R(7r/r-) = I'(iHe I'(iHe all 7r modes) all 7r- modes) The measurement coming from the bubble chamber study by Keyes et al. [2]yielded R(n/n-) = 4.3(1.7)%. Results from Mayeur et al. [l] and from Bohm et al. [8]are quoted as lying within the range 5.4?::;% 5 R(n/n-) 5 6.9?4:;%. Thus, a 7r decay probability of approximately 5(2)% is observed in the experiments. Sacton's review 191 provides a cogent summary, including results from the papers by Mayeur et al. [l] and by Gajewski et al. [lo]. The data are reproduced in Fig. 1 in which one compares the pion kinetic energy spectra for the following four decay processes: :He ;He 2H H : ~ - p ~ H e(a) 7 r n 3H (b) 7r-n 3He (c) 7 r - ~ ~ H (d). J The 7r- spectrum from process (a) is peaked at a kinetic energy of around 30 MeV, as one would expect for 7r-s coming from an underlying A 7r- p free decay; the tail

4 Figure 1. The 7r* kinetic energy distribution from the decays: (a) :He 7r- p 3He, (b) ;He d n 3H, (c) i H - n'n 3He, and ( d ) i H - n - p 3H, as reproduced from Ref. [9]. extends t o 15 MeV. The 7r- decay from process ( d ) is similarly peaked but several MeV higher. The primary strength for ih decay lies in the i H - 7r- 4He analog mode [8], so that the spectrum of (d) contains many fewer events than that of (a). (Krecker et al present a later summary of such 7r- decay data.) Our interpretation of (a) is that one is looking at a process dominated by A - 7rp decay embedded within a very light nucleus; Fermi smearing of the peak is limited. The possible three-body A N 7r- p N decay is less likely to leave behind a bound trinucleon. Specific decay events involving two protons in the final state have been identified [8], but we would expect to see 7r- events with kinetic energies of less than 15 MeV, if 7r-s from three-body decay processes were of importance. The 7r- kinetic energy spectrum for i H into n 3He, process (c), and into p 3H, process (d), look similar to that for (a). We suggest that the two-body (A 7r- p ) decay appearance comes from i H 7r- 4He*, (e) where the 4He*T = 0 states decay equally into n 3He and p 3H. Sacton shows that the two-body decay i H 7r- 4He generates some ten times the number of events that the three-body decay i H 7r- p 3H produces. We infer (i) that the three-body decay modes (c) and ( d ) are closely related, as the number of events for each in Fig. 1 indicates,

5 . d and (ii) that they come primarily from the decay of the T = 0 4He excited states, following emission. This interpretation in terms of strong final-state interactions involved in ( c ) and (d) is supported by Ref. [12], where it is argued that a naive calculation not taking into account resonant final states fails. However, the low-energy?t-s are most likely to come from multi-nucleon final states. The :He T n 3He decay mode (b) is the puzzle. Unlike the 7r- decay spectra, which are peaked according to two-body decay (A 7r- p ) expectations, the & spectrum from the :He T decay is flat in terms of the R energy distribution. Furthermore, it is stated in Ref. [l]that for 7r kinetic energies below 22 MeV multi-neutron final states are likely. Therefore, the label 3H in process (b) and in the caption for Fig. l b should be interpreted as 3H or n 2H or n n H. This is emphasized in Ref. [2], where the final state is labeled nnnp. In addition, we note the paucity of events for pion kinetic energies above that corresponding to the threshold for four-nucleon decay. Finally, Keyes et al. [2] argue that the data suggest the 7r emission process is predominantly s-wave. Therefore, we conclude there is no evidence that the two-body decay of the virtual C,assumed to be operative by von Hippel, can account for the 7r spectrum. It is the large probability for a virtual C which is unique to the :He hypernucleus: The wave function of :He can be written schematically as T- Because of its charge, :He permits the A to make a virtual transition to a E without altering the structure of the nuclear core state, whereas one would anticipate only C(and Eo)transitions in ih. This suggests that the A p C n transition is the key to understanding the T emission. We interpret the flat s-wave T spectrum seen above as evidence for a three-body decay mechanism of the type C N 7r n N replacing the C 7 ~ n free decay unavailable to the deeply bound C. The virtual C N system is offshell; there must be a C N - & n N rescattering to restore the system to on-shell and free the observed TS. We expect both nucleons t o carry off kinetic energy, producing a pion spectrum moreor-less uniformly distributed from zero to the maximum corresponding to a n n 2H final state. One of the two neutrons in the nnn rescattering process could be picked up by the spectator deuteron to produce a triton. Alternatively, the proton in the rnp rescattering process could be picked up by the spectator di-neutron to produce a triton. However, were the 3H final state to play a dominant role in the 7 ~ decay, one would expect to see primarily T events above the nn2h threshold. A threebody decay amplitude of the C N - T n N type, normalized to the theoretically estimated C probability in :He, can explain not only the?r decay branching ratio but also the s-wave angular distribution and the flat energy distribution of the &s. A simple estimate of the C probability in a model calculation [13] for the ihe-ih system yields a probability as large as 14%. Therefore, we assume the C probability in :He to be P(E?) = fip12 = f x 14(6)% = 9(4)%. In order to translate this C probability into an estimate for the branching ratio R(?T/?T-), we must take into account suppression effects due to the Pauli principle for the in-medium decay rates. Dalitz and von Hippel [4] found that, compared to?t- decay, Pauli suppression is about two times

6 stronger for 7r decay of :He. We use this value to estimate the relative importance of Pauli suppression. We assume that, apart from the reduction in phase space, the E decay rate is unmodified in the medium; that is, the C in-medium three-body decay rate is taken to be approximately equal to (i.e., to essentially replace) the two-body free decay rate, except for the phase space difference due to the E being highly virtual. The relevant decay ratio in vacuum which we need is 1 2 r(c T n) / r ( A T- p ) = -r(c) /,r(a) N 2.5, (3) 2 where the A I = 1/2 rule was assumed. Phase space gives an additional factor of the average 7r momentum for in-medium 7r decay of ;He t o its value for E 7r n decay in vacuum. Collecting factors, we estimate 70 1 P(C) x 2.5 x - = 5(3)% 9 R(7r/7r--)N - x (4) 2 l-p(e) 185 where the factor 1/2 is due to the relative Pauli suppression, and we assume that the decay via the virtual Eocomponent is counted primarily in the 7r- decay rate. We suggest that a 7r to 7r- branching ratio R(T/T-)of the order of 5% is a plausible result for any model calculation that includes A - C conversion. Clearly, a more realistic model calculation which includes the charge-exchange channel [7] as well as the Co p 7r n n decay mechanism is called for. The authors wish to acknowledge the key role that Carl Dover played in introducing them to this question. They thank A. Gal for comments relating to the triton final-state. The work of BFG is performed under the auspices of the U. S. Department of Energy. That of RT was included in the research program of the Stichting voor hndamenteel Onderzoek der Materie (FOM)with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). REFERENCES C. Mayeur et al., Nuovo Cim. 44, 698 (1966). G. Keyes et al., Nuovo Cim. 31A,401 (1976). R. H. Dalitz and G. Rajasekharan, Phys. Lett. 1, 58 (1962). R. H. Dalitz and F. von Hippel, Nuovo Cim. 34, 799 (1964). F. von Hippel, Phys. Rev. 136,B455 (1964). R. H. Dalitz, in the Proceedings of the International School of Physics Enrico Fermi XXXVIII, Interaction of High-Energy Particles with Nuclei (Academic Press, New York-London, 1967), p A. Cieplf and A. Gal, Phys. Rev. C 55, 2715 (1997). 8. G. Bohm et al., Nucl. Phys. B9,1 (1969). 9. J. Sacton, in Ref. [6], p W. Gajewski et al., Phys. Lett. 21,673 (1966). 11. U. Krecker, D. Kielczwska, and T. Tymieniecka, Nucl. Phys. A236,491 (1974) Adamovic et al., Lett. Nuovo Cim. 6, 9 (1973). 13. B. F. Gibson, A. Goldberg, and M. S. Weiss, Phys. Rev. C 6, 741 (1972); in Few Particle Problems in Nuclear Interactions (North Holland, Amsterdam, 1972), p. 188.

7 M l l I Nl l l lll 1l 1l l 1 Report Number Publ. Date (11) Sponsor Code (1 8) U C Category (1 9) DOE