p 3 A = 12 C s A = 16 O s d E η m η (MeV)

Transcription

1 PRODUCTION AND DECAY OF ETA-MESIC NUCLEI A. I. L'VOV P. N. Lebedev Physical Institute, Russian Academy of Sciences Leninsky Prospect 5, Moscow 79, Russia Using the Green function method, binding eects on produced -mesons in the two-stage reaction + A! N + +(A )! N +(N) +(A ) are studied. The energy spectrum of the correlated N pairs which arise from decays of 's inside the nucleus is strongly aected by an attractive -nucleus optical potential. Its resonant behavior gives a clear signal of formating intermediate -mesic nuclei. It was found long ago that the S (55) resonance, which lies above the N threshold and is strongly coupled to the N channel, makes the low-energy N interaction attractive and leads to an existence of bound -nucleus systems, the so-called -mesic nuclei. This nding was later conrmed and even strengthened. With contemporary estimates of the N scattering length, ; the -mesic nuclei A are expected to exist for all A. ;5 Studies of the reactions like p + d! He + and d + d! He + have already provided an experimental evidence that the and the nucleus in the nal state experience a strong attraction which manifests itself in a near-threshold enhancement and in a rapid energy dependence of the cross section. 6;7 Nevertheless, a direct observation of bound rather than free etas would be more convincing for a discovery of -mesic nuclei. Since the bound eventually decays through the subprocess N! N, a clear signal for a presence of the stopped etas in nuclei would be in an observation of nal pions and nucleons with almost opposite momenta, with the kinetic energies of about 00 MeV and 00 MeV, respectively, and with the total energy close to m + m N. 8 In the present work, production of such pairs is studied within a simple model which is aimed at learning how the attraction between the eta and the nucleus aects characteristics of the pairs. In accordance with the original suggestion, 8 we consider the two-stage reaction + A! N + +(A )! N +(N )+(A ); () in which the fast nucleon N knocked out in the subprocess (k)+n!(e )+N () escapes from the nucleus, whereas the collides with another nucleon N in

2 the nucleus and perishes producing a pair which also escapes: + N! + N : () Considering the rest of the nucleus as frozen, we write the matrix element of () as T = F (k)f (E ) ZZ e i~ k~r (~r ) ( ) N (~r ) (~r ) ( ) (~r ) ( ) N (~r ) G(~r ;~r ;E )d~r d~r : () Here, are the wave functions of the bound nucleons with the binding energies, and N, N, are the wave functions of the nal particles. F, F are the amplitudes of the reactions () and () which, at energies considered, are approximated by s-waves. The Green function G gives the amplitude of with the energy E = E + E kin N = E + E kin N (5) to propagate from ~r to ~r in the mean eld V (r) of the intermediate nucleus (A ) which can be assumed to be independent on. In the following we also neglect the dependence of E on the hole states, and replace, by their Fermi-gas average hi ' MeV. When a single bound state 0 of the (complex) energy E 0 dominates, the Green function takes the separable form G(~r ;~r ;E ) ' + 0 (~r ) 0 (~r ) ; (6) E E0 which results in the Breit-Wigner resonant behavior of the pair production through the intermediate -mesic nucleus. In such an approximation, the amplitude () depends on the overlap of 0 (r) with the nucleus's nucleons and typically the total cross section of the -mesic nucleus formation by photons is 5{0 b for A = to 6. 9 With the realistic optical potential strength, however, there are several bound states of which are strongly overlapped and act coherently. Also, there is a non-resonance background which describes the process!! in the nucleus with unbound etas. For these reasons Eq. (6) is generally insucient and the full Green function has to be used to describe the reaction (). As an illustration of what may happen, we discuss here the spectral function 0 S(E )=ZZ (~r )(~r )jg(~r ;~r ;E )j d~r d~r ; (7)

3 which describes a global nuclear dependence of the matrix element () squared and averaged over the nuclear states and momenta of the outgoing particles. S(E ) characterizes the nuclear dependence of the total cross section of the two-step transition!! in nuclei. It is proportional to the number of nucleons hit by 's produced somewhere inside the nucleus. This number increases when the has the energy close to a resonance level; such 's are captured by the nucleus and pass a few times across the nucleus before they annihilate or escape. In actual calculations of G and S(E )we use the simple rst-order energydependent potential E V (r;e )= ( p s=m N )f N (E ) (r) with the N scattering amplitude taken from Ref. and with the square-well nuclear density (r) =0:75 0 at r<r A,R A =:A = fm. Such a potential gives the energy of the ground state and its width close to those found in a recent analysis. Typically, the widths are 0 MeV and far less than those found in an older work which seems to overestimate the width's broadening due to the two-nucleon absorption NN! NN in the nucleus. A = C s p A = 6 O s p d E η m η (MeV) E η m η (MeV) Figure : The normalized spectral function S(E) = (6 R A =A )S(E) for the square-well potential representing the carbon and oxygen. Dashed lines: the optical potential is switched o; then S(E) = 9 above the threshold. Dotted lines: the absorption Im V (r) is on. Solid lines: both the attraction Re V (r) and the absorption Im V (r) are on. The resonance-like structures are composed of s, p, d resonances in the -nucleus system. In the absence of the potential V (r), the Green function reads G = e iqr =(r), where r = j~r ~r j and q = E m. Accordingly, S(E )does

4 not depend on E when E >m. At sub-threshold energies, when cannot propagate far from the production point, S(E ) rapidly vanishes. When the absorptive part Im V (r) of the optical potential is taken into account, S(E ) falls down as well. However, it strongly enhances when the attraction Re V (r) is on and the bound states appear. In fact, the resonance-like structure of S(E ) consists of many s, p, d,...wave contributions. See Fig.. The practically important nding is that the non-resonance background in S(E ) is relatively small, so that most of produced N pairs with nearthreshold energies appear from the decay of the resonant -mesic states. Due to the spread in the separation energies,, the inclusive distribution of the total energy E + E N = E + m N + of the pairs is smeared and rather exhibits a single giant peak of the width 0 50 MeV. Such pairs have been recently observed in the experiment performed at Lebedev Institute. Further analysis of their energy distribution may hopefully reveal whether the -mesic nuclei were really found. This research was supported in part by the Russian Foundation for Basic Research, grant Useful discussions with G.A. Sokol are highly appreciated. References. Q. Haider and L. Liu, Phys. Lett. B 7, 57 (986); Phys. Rev. C, 85 (986).. M. Batinic et al., nucl-th/ A.M. Green and S. Wycech, Phys. Rev. C 55, R67 (997).. S.A. Rakityansky et al., Phys. Rev. C 5, R0 (996); S.A. Soanos and S.A. Rakityansky, nucl-th/ V.A. Tryasuchev, Yad. Fiz. [English transl.: Physics of Atomic Nuclei] 60, 5 (997). 6. C. Wilkin, Phys. Rev. C 7, R98 (99). 7. N. Willis et al., Phys. Lett. B 06, (997). 8. G.A. Sokol and V.A. Tryasuchev. Kratkie Soobsh. Fiz. [English transl.: Sov. Phys. { Lebedev Institute Reports], (99). 9. A.I. Lebedev and V.A. Tryasuchev, Yad. Fiz. 58, 6 (995); A.I. L'vov, in preparation. 0. O. Morimatsu and K. Yazaki, Nucl. Phys. A 5, 77 (985); A 8, 9 (988).. J. Kulpa, S. Wycech and A.M. Green, nucl-th/ H.C. Chiang, E. Oset and L.C. Liu, Phys. Rev. C, 595 (988).. G.A. Sokol et al., talk at the th Int. Seminar on High Energy Physics

5 Problems, 7{ August 998, Dubna; to appear in proceedings. 5