Exotic bound states of strange hadrons

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  • This article was downloaded by: [Carnegie Mellon University] On: 10 November 2014, At: 04:16 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Contemporary Physics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tcph20 Exotic bound states of strange hadrons G. Backenstoss a c d & J. Zakrzewski b e a University of Karlsruhe , Germany b CERN , Geneva, Switzerland c CERN , Geneva, Switzerland d University of Basle , Switzerland e University of Warsaw , Warsaw, Poland Published online: 20 Aug 2006. To cite this article: G. Backenstoss & J. Zakrzewski (1974) Exotic bound states of strange hadrons, Contemporary Physics, 15:3, 197-225, DOI: 10.1080/00107517408210789 To link to this article: http://dx.doi.org/10.1080/00107517408210789 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the âContentâ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/ terms-and-conditions http://www.tandfonline.com/loi/tcph20 http://www.tandfonline.com/action/showCitFormats?doi=10.1080/00107517408210789 http://dx.doi.org/10.1080/00107517408210789 http://www.tandfonline.com/page/terms-and-conditions http://www.tandfonline.com/page/terms-and-conditions
  • CONTEMP. PHYS., 1974, VOL. 15, NO. 3, 197-225 Charge z Hadron number -1 -1 -1 -1 +1 0 0 Exotic Bound States of Strange Hadrons G. BACKENSTOSS University of Karlsruhe, Germany* and CERN, Geneva, Switzerland and J. ZAKRZEWSKIT CERN, Geneva, Switzerland SUMMARY. A negatively charged strange hadron can be bound by the electromagnetic interaction in the Coulomb field of a nucleus to form an exotic atom. De-excitation of such an atom occurs with the emission of X-rays whose energies, line widths, and int,ensities have been measured. Deviations from the electromagnetio level soheme ere observed for lower-lying states owing to the strong interaction of a hadron with a nucleus. When the wave function of a hadron begins to overlap with the nuclear density distribution, the hadron undergoes nuclear absorption via the strong inter- action. The 6nal outcome of such a process is the formation of a A hyperon which may be bound in a nucleus by the strong interaction. An exotic nucleus, or a hyper- nucleus, is thus formed making it possible to study the A-nucleon interaction. Excited states of hypernuclei decaying via weak, electromagnetic, or strong interaction have been observed and ere extensively studied. Investigation of exotic atoms and hypernuclei provides basic information on the properties of strange hadrons, their interaction with nucleons, and the structure of the nuclear surface. Baryon Spin Isosph Strange- Mass B JP I S /MeV number parity ness mh 0 0- Q -1 493-691 1 1 1 -1 1197.34 -2 1321.29 -3 1672.5 0 3 4 Q 1 B+ 1 3' 1 &+ 1 9+ 0 938.259 0 939.553 -1 1115.69 0 1. Introduction An ' ordinary ' atom consists of a positive nucleus which interacts electro- magnetically with negative electrons in bound atomic states. Already in 1947 Wheeler (1947) suggested that also other negative particles may be captured by the nucleusta form an ' exotic ' atom. The particle in question may be either a lepton, e.g. a muon (p-meson), or a hadron, e.g. a pion (r-meson) or a kaon (K-meson). The properties of such exotic atoms have recently been reviewed by Burhop (1969) and (1970); and in particular those of muonic atoms by Devons and Duerdoth (1968) and Wu and Wilets (1969), and those of pionic atoms by Backenstoss (1970), whose articles contain references to earlier work in this field. The reader is referred to these articles for details of both theoretical aspects and experimental procedures that are common to all exotic atoms. The present review will be concerned with bound atomic and nuclear states of strange hadrons only, i.e. mesons and hyperons of negative strangeness, where so Table 1. Properties of stable hadrons Mean life T / S 1.2 x 10-8 1.5 x 10-l'J 1.7 x 10-lo 1.3 x 10-10 stable 0.92 x 108 2*5+ 10-lO * Now University of Basle, Switzerland t Visiting scientist on leave from the University of Warsaw, Warsaw, Poland. 0.p. 0 D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 198 G. Backenstoss and J . Zakrzewski far only a few recent conference reports exist (Ericson 1971, Backenstoss 1971, Koch 1973, Wycech 1973). Table 1 (a) summarizes the relevant properties of negatively charged strange hadrons (Lasinski et al. 1973). All these particles are stable against decays via strong interaction, and their lifetimes are long enough for them to become incorporated in atoms and survive many atomic transitions lasting, in all, of the order of 10-12-10-10 s. When, as the result of these processes, the mean distance of the hadron becomes comparable to the radius of the nucleus, strong interaction sets in and the hadron undergoes strong nuclear capture processes in a time < 10-l6 s. An ' ordinary ' nucleus is a multihadron state of protons and neutrons bound by strong interaction, with a baryon number equal to its mass number, B = A , and with strangeness S=O. However, none of the strange hadrons shown in table 1 (a) can be stable against strong interaction in a nucleus. This is because such inter- actions conserve the quantum numbers of table 1 (a ) and, for the particles at rest, the energy conservation allows for the following transformations t o occur, whose final outcome is the formation of one or more A hyperons: K-+N-+X or A+ T , -X+N+A+N in nuclear matter, (la) K-+2N-+X or A+N, uX+N+A+N in nuclear matter, S-+p+A+A, (3) Q-+pn+A+h+A, (4) where N stands for a nucleon, a proton p, or a neutron n. On the other hand, the A hyperon, when at rest, remains stable against strong interaction in the presence of nucleons, since there is no such process possible consistent with energy conserva- tion. This arises from the fact that the A hyperon is the lightest of all strange baryons. Its relevant properties, together with those of the nucleons, are given in table 1 ( b ) . Since the A-N interaction is attractive, the A hyperon can become bound to nucleons to form an ' exotic ' nucleus, or a hypernucleus, until i t decays via weak interaction in time of the order of the mean life of the A hyperon, 10-lo s. This is very long compared with the characteristic time for strong interaction processes, about 10-23s. A hypernucleus is thus a multihadron state of nucleons and A hyperons with strangeness S#O which is stable against strong interaction transfor- mations. These are the structures that have been extensively studied ever since their original dis- covery in 1952 by Danysz and Pniewski (1953). Double hypernuclei with two bound A hyperons, and S= -2, have also been observed (Danysz et al. 1963, Prowse 1966). For recent surveys of hypernuclear physics, and for references to earlier work, the reader should see Davis and Sacton (1967), Dalitz (1969)) and Pniewski (1971). Much attention has recently been given to both theoretical and experimental aspects of bound atomic states of strange hadrons, K- mesons, and X- hyperons. Their study can provide information of a fundamental nature related to the properties of the hadrons themselves, e.g. their masses, magnetic moments, and internal struc- ture. It is also a source of information on the low-energy hadron-nucleon interaction and on the structure of the nuclei, with heavy hadrons particularly sensitive to the nuclear surface. In this respect the nuclear capture of strange hadrons, e.g. K- mesons, might be thought of as a probe of the nuclear periphery, as discussed earlier by Wilkinson (1959). The study of bound nuclear states of A hyperons, resulting from the nuclear capture of strange hadrons from bound atomic states, is the main source of information about the h-N and A-h interaction. This stems from the fact that, owing to their short lifetime, there are no beams of low-energy A hyperons available. Thus A-N If one A hyperon is bound in a nucleus, its strangeness S= -1. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 199 Bohr energyt Hadronic atom E B = Eo(mh/me)ZP /keV K- 13.1 Za s- 31.8 Zs r- Y 35.2 Za Q- 44.5 zs scattering experiments are difficult to perform, and it is just the nuclear bound states of A hyperons that make it possible to learn of the properties of the A-N interaction. In the present survey attention will be drawn to the most recent developments in the field of exotic bound states of strange hadrons. Electromagnetic tmnsitions between atomic bound states of K- mesons and C- hyperons have been observed and are being extensively studied at the moment. Once these particles are captured by nuclei, A hyperons can be produced and trapped in nuclear fragments to form nuclear bound states, the hypernuclei. Experiments to detect transitions between excited states of hypernuclei are now under way in several laboratories. It is expected that these two new spectroswpies-an atomic and nuclear one, respectively -which have recently grown up in this field, will broaden our knowledge comider- ably in the time to come. 2. Atomic bound states 2.1. General picture The atomic levels between which the observed X-ray transitions occur originate from the interaction of the nuclear Coulomb field with the negative particles and are basically the same as the levels of the ordinary electronic atoms. Hence, for a start, the simple Bohr formulae lead to a good understanding of their properties: Bohr radius? Principal quantum aB = (m,/mh)(u,/Z) number of the atomic capture state I h 54.712 31 22.612 48 20.5lZ 51 16.212 57 tValues are given for &II infinitely heavy nucleus; for an ordinary hydrogen atom Eo=13.6eV; a,=5.3x104fm. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 2 00 a. Backenstoss and J . Zakrxewski For the properties of hadronic atoms discussed later, the energy levels must be calculated more exactly, which is done by mmns of the Klein-ordon or Dirac equations for a boson or a fermion, respectively. For a point charge nucleus, the solutions have the form E n.J - --!!&($)a[l+ 2 ($)*(L j + 4 -:)-. . .I, where j = l for a spin-zero boson while j= 1 f 4 for a spin-half fermion, 1 being the angular momentum quantum number. Thus, for a K-meson, the energy levels of an exotic atom are singlets, whereas for a hyperon they are doublets. Several electromagnetic corrections have to be applied to the solutions (6) arising from the finite size of the nuclear charge AE,s, radiative corrections, of which vacuum polarization AEvp is dominating, and electron screening AEs (for details me, for example, Backenstoss 1970). The energy value of a level in an exotic atom, with all electromagnetic effects taken into account, can finally be written as where in all cases the dominating term is EKG,D, the solution (6) of the Klein- Gordon or Dirac equations, respectively. Actually the fist two terms of the right- hand side of eqn. (7) and the Grst-order part of the third term are calculated simul- taneously by solving numerically the wave equation with the corresponding poten- tials. All information obtained on exotic atoms originates from the observation of X-ray transitions. Since the atom is formed in a highly excited state with nw (m,/m J1I2, these X-rays are naturally present. De-excitation of all exotic atoms occurs via electromagnetic tramitions between energy levels with the tranefer of energy to an electron by the Auger effect or with its release in the form of X-rays. Calculations of these cascades have been performed by several authors (Eisenberg and Kessler 1963, Rook 1970). The f i s t process prevails in the earlier stages of the cascade while the second one dominates for states with smaller n, i.e. larger energies. The particular selection rules for these prooesses, Al= & 1 with Al= -1 favoured, An as small as possible for the Auger transition, and An as large as com- patible with A1 = -1 for the X-ray emission, tend to drive the hadron towards states of maximal 1-values, l=n-1. Once a state (n,l=n-1) a ' circular orbit ' has been reached, the only electromagnetic transitions that can occur are of the type (n:n-l)+(n-l,n-2)-+(n-2,n-3), etc. For states with small n-values, radiative El transitions dominate, until the hadron reaches a state for which nuclear absorption becomes a competing process (see Section 3) which rapidly takes over. 2.2. Experiments The Grst observation of K- mesonic X-rays from helium waa made in 1965 by Burleson et al. (1965) and, since then, several papers have been published on experi- mental studies of kaonic atoms (Wiegand and Mack 1967, Wiegand 1969, Backenstoss et al. 1970a, Kunselman 1971)) opening up a new field of atomic spectroscopy of strange hadronic atoms. Experimental arrangements in these studies are similar t o those used to measure muonic or pionic X-rays. Solid-state lithium-drifted germanium [Ge(Li)] detectors are mainly used, giving an energy resolution AEIEw Exotic atoms are formed essentially with the negative particles at rest, while the particles are produced typically at energies of several hundred MeV. Hence the beam particles must be slowed down in a moderator, which results for hadrons in a substantial loss of particles owing to strong interactions in flight. Quantitatively the problem is much more difficult for the strange hadrons than for pions. Protons of 20 GeV hitting a target produce 3 orders of magnitude more pions than kaons. Since the lifetime of the kaons is only half that of the pions, and, contrary to the situation for pions, the relativistic time dilatation is less important for the heavier kaons, the loss due to decays in a slowing-down kaon beam is large. In order to in the 100 keV region. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • U D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 202 0. Backenstoss and J . Zakrzewski 0 , obtain the best possible stopping rates per gram of mat'erial, one must optimize the momentum of the kaon beam where the production of kaons increases while the decay rate decreases with the momentum and the strong interaction losses increase with momentum as a coneequence of the thicker moderator needed to stop the kaons. The optimum momentum was found at about 700-800MeV/c for a beam of about 15 m length, about the minimum length compatible with the require- ments imposed by separation and shielding, where less than 5 per cent of the kaons survive to enter the moderator. I n view of the large abundance of pions, a t least a partial separation of kaons and pions is needed. This can be provided by degra- dation of a momentum-selected beam where the energy loss depends on the mass of the particles, or more efficiently by an electrostatic separator. In fig. 1 an electrostatically separated kaon beam a t the CERN proton synchrotron is shown as an example. In a typical experiment carried out a t CERN by the CERN-Karlsruhe-Heidelberg group (Backenstoss et al. 1970 a), about 800 K- mesons per burst of the proton synchrotron (PS) were brought to rest in a target of 8 g cm-e thicknesa and 6 cm x 8 cm area. The number of T- mesons passing through the target was about 100 times larger. Hence an eficient rejection factor for pions by the beam telescope is required. This can be achieved by two Cerenkov counters in anticoincidence and a positive signature by pulse-height discrimination in the last three thin scintillation counters where the slow kaons give much larger pulses. Thus a reduction factor of lo5 for pions has been obtained. The insert of fig. 1 illustrates the arrange- ment of the beam telescope and the Ge(Li) detectors. The cross-shaped target -#Id+ I 1 1 I 1 1 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 I 0 0 110 120 130 140 150 160 N (D OD t ln t (D I m -3 1: I I U In I 1 In OD I I (v m I= t 1 c In- %* U OD t + I m U c- In' I t-W T I I' Energy / keV Fig. 2. K-mesonic spectrum in ,,P from 0-200 keV. The transitions shown are I
  • Exotic Bound States of Strange Hadrons 203 minimizes self-absorption of X-rays at a target thickness required to be 5-8 g cm-l owing to the widths of the range curve. The Cu and C are moderators to slow down the kaons. The X-ray spectrum of kaonic phosphorus is given in fig. 2, as an example (Backenstoss et al. 1972 a). Because of its short lifetime, a hyperon beam would be useless for producing C hyperonic atoms, since all C- would decay before being captured by atoms. However, according to eqns. (la) and (lb), C- hyperons are produced by strongly interacting K- mesons. About 8-10 per cent C- are produced per stopped K- with an energy of about 20 MeV. These C- are rapidly stopped in the neighbourhood of their origin and thus form C hyperonic atoms. Therefore Z hyperonic X-ray spectra are observed simul- taneously with the kaonic spectra as demonstrated in fig. 2. For C- hyperons the situation is even more difficult. 2.3. Energies The identification of the exotic X-ray transitions is mainly done on the basis of their energies as calculated accordmg to eqns. (6) and (7). The measurement of the energies is performed by calibrating with radioactive y-ray standards or known pionic X-ray transitions. Pionic X-rays are also shown as present in fig. 2, not as a consequence of an incomplete rejection of the telescope trigger but because of the pions produced by reaction (la). If one aims at high-precision energy measurements, precautions must be taken particularly when using radioactive y-rays as described elsewhere (Backenstoss et al. 1971). Furthermore, the identification of the X-ray transition is facilitated by the typical pattern provided by the X-ray series as known Table 3. Examples of the energies and intensities of kaonic X-ray transitions Element c S Ba Cransit ion 6 4 5 4 7+3 6+3 5+3 4-3-3 3+2 6 4 5 4 4+3 l l + l O 10+9 9 4 8+7 7+6 B e d /keV I c a s c § (per cent) Inlea , . (per cent) 150t 10.2 41.2 37.9 32-3 22.1 63.312 62-73 f 0.08 7.99 1.94 5.61 16-24 98.60 115.41. 74.9 162.094 161.56 f 0-06 9.47 100.4 9.46 f 0.37 100.00 f 1.9 75.9 f 2.2 71.539 71.571 f 0.027 96.775 96.781 2 0.016 135.438 135.423 f 0.016 197.810 197.790 f 0.017 305.321 305.331 f 0.025 60 76 88 100 58k5 83f7 10054 I I t E , , and Emens. are equal within the experimental error which is always
  • 204 G. Backenstoss and J . Zakrrzwski from ordinary X-ray spectroscopy. Hence the identification can always be based on a particular sequence of lines. For example, in table 3 measured energies of kaonic X-ray transitions are given and compared with calculeted values obtained according to eqns. (6) and (7). The Klein-Gordon energy as well as the electromagnetic corrections can be cal- culated with a precision considerably higher than the experimental error in the energy. This can be clearly demonstrated, for example, for muons and pions. If one selects X-ray transitions where the strong interaction effect discussed in Section 3 is negligible-that is for sufficiently high n-values-the mass of the K- meson can be determined. From the suitable transitions in kaonic Au (7 < n c 12) and Ba ( 6 < n c l l ) , the K- mass has been determined (Backenstoss et al. 1973): WZK-= (493.691 & 0.040) MeV. This represents a reduction of the error by a factor of 4 compared with earlier measure- ments derived from the K+-+3r decay. 7 - 6 - 5 - - CI P '4- c - 3 - 2 E 2 2 - Y, 3 0 L 1 - c zr I rn - I i 5; 'p i i d c Fig. 3. X-ray lines from K, Z, and T atoms obtained from stopping K- mesons in l,C1 (Baakenstoss et al. 1970 b). The first unambiguous observation of X-ray transitions in Z hyperonic atoms was made in 1970 at CERN (Backenstoss et al. 1970 b), although two single lines ascribed to transitions in such atoms, the 6h-+5g transition in potassium (Wiegand 1969) and the 6h+5g transition in sulphur (Backenstoss et al. 1970a), had previously been noted and some lines in kaonic spectra of Li and Be had been claimed as X-lines (Berezin 1970). On the other hand, Backenstoss et al. (1970 b) have observed a series of X-ray transitions of the type n+n-l, n-l-tn-2, etc., in Z hyperonio atoms of sulphur, chlorine, and zinc. In fig. 3 two clearly visible X-ray lines from D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 205 31 ISp Z hyperonic chlorine are shown. Alw in fig. 2, Z hyperonic phosphorus lines are present. In table 4 examples of energy measurements of X-ray transitions in Z hyperonic atoms are presented. The calculated values of the transition energy with corrections for finite size and vacuum polarization are in good agreement with the measured ones. The errors in the case of Z hyperonic X-ray energies are considerably larger than those for kaonic X-ray energies, due to the much poorer statistics of the Z lines. Even beyond the reach of the strong interaction the hadron moves in an electric field of lo1* V cm-l in heavy elements. Following a suggestion of Iachello and Land6 (1971) this could be used to determine whether hadrons could be polarized. Ericson and Hiifner (1972) investigated, in addition, the effect due to the nuclear polarizability, both being connected with a level shift of the atomic states. The precision measurements for the kaon mass have yielded a limit for the kaon polariz- ability (Backenstoss et al. 1973) of aK < 0.02 (fm)3 with 90 per cent confidence. 8+7 33-07 7+6 50.92 6+5 84-68 Table 4. Examples of the Z-hyperonic X-ray energies, intensities and Z/K ratios. 33.3 f 0.4 50.8 f 0.2 84.7 f 0.2 71 88 100 55 & 23 76+ 15 l o o f 9 I c , , c . t (Per Erne,,. cent) /keV 4 68f11 73*4 100 f 4 7 ~~ 72-55 f 0.20 105.64 f 0.06 162.75 f 0.17 69 83 100 I ZiNb +See footnote of Table 3. arc = arK+O.05. 9-44 72.36 8+7 105-65 7+6 163.01 2.4. Intensities Since both K- and Z- X-rays are measured simultaneously in the same spectrum, their relative intensities provide a measure for the number of Z- produced per stopped K- meson provided the pro erties of the cascade are accounted for. The relative intensities of kaonic and Ehyperonic X-ray lines have been measured. Examples for these intensities corrected for the energy-dependent X-ray absorption and detector efficiency are given in column 6 of tables 3 and 4 for K- and Z- atoms, respectively. They can be compared with cascade calculations assuming the hadron being captured a t a state n = 29 with a population nearly proportional to the statistical factor P,,,~(22+1)eu', where OL is an adjustable parameter close to zero (1.1 ~ 0 . 1 ) . In column 5 of tables 3 and 4 the intensities thus calculated are shown. The experi- mental data are satisfactorily reproduced. Furthermore, the decay of C- before being captured, and depending on the target material, must be considered. More details are given elsewhere (Bunaciu 1973, Backenstoss et al. 1974 a). In column 7 of table 4 the Z yields per stopped kaon derived from a comparison of all transitions of the two X-ray cascades are given. These numbers show an increase for light nuclei and a slow decrease with increasing 2. There exists agreement with the measurements of the European K- Collaboration (Bhowmik et al. 1959) who obtained the value of (8.1 f 1-3) per cent as the rate of the X- hyperons produced in the capture a t rest of K- mesons by nuclei of the photographic emulsion. The rates of the Z- hyperons emitted and brought to rest per K- mesons stopped in a given element have been calculated by Zieminska (1971) and the results are shown in fig. 4 D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 206 G. Backenstoss and J . Zakrzewski together with the data obtained from X-rays. Although the calculations seem to overestimate the rates as compared with the observed values, they indicate that even for a heavy nucleus, e.g. uranium, one can expect quite a large probability of the formation of C hyperonic atoms, only about 50 per cent smaller then that for a light nucleus, e.g. carbon. Recently X hyperonic transitions have also been observed in Brookhaven for Pb and U. In principle, from measurements of X-ray transitions in heavy C hyperonic atoms, it should be possible to measure the magnetic moment of the C- hyperon since the energy levels in such atoms are doublets as the result of the fine structure splitting (Fox et al. 1973). 10 20 30 LO 50 I I I I rn a, = a,+0.05 A a r = a K Calculated (Zterninska) L I I I I I I BC P Ca TI Zn Nb Cd Ba Atomic number 2 Fig. 4. Comparison of calculated and experimental I (Z ) / I (K) . The calculated points inolude The measured values are nuclear correlations; in the lower limit they are neglected. evaluated assuming QE =ux or QZ =a=+ 0.05. 3. Strong interaction effects The electromagnetic bound states of a hadron in an exotic atom are affected by its short-range strong interaction with a nucleus. When a hadron is in a state with a large n-value, i.e. a t a large distance from the nucleus [see eqn. (5b)], the effects of this interaction are negligible. However, with the de-excitation of the hadronic atom, the hadron reaches lower n-states in which its wave function begins to overlap the nucleon density distribution. In such states the effects of strong interactions begin to play an important role, causing deviations from the level scheme determined by the electromagnetic interactions discussed in Section 2. Already one or two transitions further down the strong interaction overwhelms the electromagnetic interaction so strongly that the entire concept that leads to atomic states must be revised. Therefore, strong interaction effects are only observable where they contribut'e a small perturbation to the Coulomb field. The influence of strong interactions shows up in a shift of energy levels A E N , a broadening of the levels I' a, and a decrease of the observed X-ray yield Y. The latter two are due to nuclear absorption from the lower and from the upper level of an X-ray transition, res- pectively. The strong interaction energy shift AEN is determined experimentally as DN=Ernea s.-Eern, (8) the difference between the values of the energy measured Erne,,., and that calculated with the inclusion of all electromagnetic corrections E,, of eqn. (7). D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 207 The level width due to strong interaction r a is related to the rate of the nuclear absorption W B : Since, as mentioned above, the strong interaction sets in very rapidly, I' a of the lower level is 2-3 orders of magnitude larger than that of the upper level of a transition (n,l)+(n- 1,l-1). Hence the Lorentzian width determined from the observed line shape of the X-ray transition after unfolding it from the instrumental one, assumed to be Gaussian, measures I? a of the lower level (n- 1,l- 1). 3.1. Shi;fts and widths of energy levels The first measurments of the kaonic level shift and line width, from direct obser- vation of the X-ray line, were obtained at CERN for the 4f-+3d transitions in sulphur (Backenstoss et al. 1970 a). In table 5 more data on the strong interaction shifts and widths are presented. The broadening of the line beyond the instrumental widths due to the Lorentzian widths can easily be seen for the kaonic 4+3 transition in fig. 2. r,=Rw,. (9) Table 5. Comparison of measured with calculated strong interaction effects in- kaonic atoms r.m.s. radius Ifm Element 2.45 2.42 2.45 3.188 3.244 3.335 I'ransition 3+2 3+2 3+2 4+3 4+3 4+3 -208 f 35 0.09 - 167 35 1.49 -590 f 80 0.09 -330 & 80 - 0.50 - 550 k 60 - 1.56 -770 f 400 0-12 810 f 100 0.43 700 k 80 - 0.48 1730 f 150 -0.10 1440 k 120 1.82 0.81 3800 f 1000 0.34 2330 k 200 - - 0.98 k 0.19 1.20 1.94 k 0.33 1-07 3.25 k 0.41 5.69 k 1-5 - 1.32 -1.41 The first lines in colums 4 4 show experimental values and their errors. The italic numbers give the deviation (experiment-calculation) in unitt of the experimental error. The calculations are performed with the potential eqn. (12) and the parameter eqn. (13). No such measurements have yet been obtained for Z atoms. The reason is not only the fact that the intensities of C lines are more than 10 times weaker than for kaonic lines, but that owing to the heavier mass the strong interaction effects set in a t larger (n,Z) values. Hence the increase of the effects from (n,Z) to (n- 1,Z- 1) is smaller than for kaons which means, that for a given X-ray yield, the shifts and widths are smaller. (This becomes obvious from a comparison of figs. 5 and 6 discussed below.) 3.2. Intensity attenuation The width of the upper level of a transition, in general over two-three orders of magnitude smaller than that of the lower level, can be determined by measuring the yield Y of an X-ray transition defined as, D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 208 G. Backenstoss and J . Zakmewski - - I l l n 7 O8r 04 - 0. 08 - OL - 0 0 8 - OL- 0 08 - O L - 0 . 08 - 0 6 . 0 0 8 - OL 0 V(8h-71) Y(71 ~ 6h) i l \ V ( 6 h - 59) V(L1 - 3d) V(M - 2p) 3 5 10 15 20 25 30 35 40 &5 50 55' 60 65 50 75 80 85 90 where W,, W,, and W , are the X-ray, Auger, and nuclear absorption rates from the upper level, and P is the population of this level. If Y is measured and P, W,, and W, are known, one can obtain from this relation the nuclear absorption rate W a, and hence the width of the upper level: Figure 5 shows Wiegand's results (1969) of the systematic study of X-ray transitions in kaonic atoms as a function of the atomic numer Z of an element, carried out throughout the periodic table. The lines represent the calculated yields from Ericson and Scheck (1970) discussed below. The outstanding feature of this figure is the decrease of intensity of a particular X-ray transition (n,n--l)-+(n-l,m-2) as one moves towards larger atomic numbers 8, with the subsequent disappearance of this transition at a certain value of Z. Whereas the termination ofthe X-ray series is the most striking feature of hadronic atoms as compared with leptonic atoms, the exact determination of absorption widths from intensity measurements remains the most difficult experimental part. Either the population P in eqn. (10) has to be known, for which a detailed knowledge of the atomic cascade is required, or P must be determined by measuring the tran- sitions feeding this level. The advantage of the latter method (eqn. 11) where the r , = rx(p/ Y--i)-rA. (11) W,( x 10'4) s-l Yield W,( x 1014) s-l r ,/eV Transition 4+3 6 4 6+5 9 4 I Atomic n u m b e r Z Fig. 5. Yields of kaonic X-rays versus 2. The solid curves are calculated values obtained perturbatively using point Coulomb wavefunctions and Imk=O.7 fm (Ericson and Scheck 1970). The experimental points are taken from Wiegand (1969). 0.915 15.47 21-44 105.70 Table 6. Intensity attenuation of X-atomic X-rays Y , X-ray and absorption rates W , and W a, respectively, and absorption width r a. 0.47 f 0.18 0-03 f 0.01 6-2 f 3.4 0.41 0.22 9.9 f 6-4 0.65 f 0.42 44f52 2.90 f 3.5 Element C C Ti Ba Yield Y 6 6 f 9 71 11 68 f 14 70 f 25 I I I I I D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 209 quantity PI Y involves only the measurement of relative intensities, is described in a recent paper (Backenstoss et al.) 1974 b). The data thus obtained are included in table 5 for kaons, and similar results for X- atoms in table 6. For kaons it means that three strong interaction effects are available for one nucleus, which provides constraints for the possible theoretical models. For Z atoms, on the other hand, these measurements constitute the first and only observations so far of strong inter- action effects. 3.3. Theoretical treatment All the strong interaction effects discussed above can be calculated provided the hadron-nucleus interaction is described by an optical potential. The complex potential is introduced simultaneously with the extended Coulomb potential and the vacuum polarization potential in the corresponding wave equation which is then solved numerically with a computer (Krell and Ericson 1969). T h e rather compli- cated behaviour for strong potentials as required here has been discussed by Krell (1971). The theoretical data given in the tables are calculated in this way. Y i d d .* Atomic number Z yields; the right-hand scale to widths. Fig. 6. Yields and widths of kaonic X-ray transition versus 2. The left-hand scale refers to Yield Y* Width ' I r/ koV Atomic number Z Fig. 7. Yields and widths of Chyperonic X-ray transitions (as in fig. 6). D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 210 G . Backenstoss and J . ZakrzewsTci As an example, in figs. 6 and 7 the yields Y and the absorption widths F a for various transitions as a function of Z are given for K and X atoms, respectively. It can be noted that only certain windows in the Z region exist within which strong interaction effects are measurable. These windows are determined on the low-Z side by the fact that ra becomes too small, whereas a t the kigh-Z side the yields become too small. It should be emphasized that the strong imaginary part produces a shift corres- ponding to a repulsive potential which may compensate the shift produced by an attractive real potential. Hence perturbation treatment may lead to very wrong results. The availability of more detailed experimental data on hadronic atoms has recently also prompted theoretical studies of kaonic atoms by several authors (Ericson and Scheck 1970, Bethe and Siemens 1970, Revai 1970, Krelll971, Wycech 1971, Bardeen and Torigoe 1971, Koch and Sternheim 1972, Alberg, Henley and Wilets 1973), whereas so far very little has been done for Z atoms. Firstly, the kaonic atom data are more complete and precise than the Z atomic data, and moreover the elementary K-N interaction is better known than the corresponding 2-N interaction. Secondly, at present it i s not obvious which theoretical approach should be followed, and which would describe the observed phenomena best. But there is a variety of suggestions as to how to construct such a potential. The des- cription of the interaction between the K- meson and the nucleus is made difficult, however, because of the existence of a bound state of the kaon-proton system, the Y0*(1405) resonance, a t an energy of 27 MeV below the kaon-proton threshold. Its influence on the kaon capture process has been indicated by Burhop (1967) and discussed by Bloom et al. (1969). It has been taken into account in most of the papers quoted above. It was, however, rather tempting to try first an approach (Ericson and Scheck 1970) which proved to be successful for pionic atoms (Backenstass 1970). Ericson and Scheck have constructed a kaon-nucleus potential proportional to the matter density p and related to the free KN scattering length A : The reason is twofold. In a11 cases the kaon-nucleus interaction is described by an optical potential. where mK and mN are kaon and nucleon mass, respectively; p is the reduced kaon- nucleus mass; A, and A , are the complex isospin components of the scattering length; and pn and pp are the neutron and proton densities, respectively. Compared with the pionic atoms, the situation seemed to be simpler. Since the KN p-wave inter- action is small, no strong non-local part should be present, and since single-nucleon capture dominates for kaons the two-nucleon absorption dominating in the pion case could be neglected. The potential (12) with the experimentally known scattering lengths (Ebel et al. 1970) could explain the early yield measurements without resorting to an extended neutron distribution (Bethe and Siemens 1970). 3.4. Comparison of theory and experiment However, with more precise data becoming available including level shifts and natural line widths, the scattering length appraoch was unable to explain these data. It could be shown (Backenstoss et al. 1972 a, Seki 1972) that assuming the structure of the potential as in eqn. (12), only an attractive real part could fit all the data, whereas the scattering lengths would produce a repulsive potential. A n explanation was given by Bardeen and Torigoe (1971) who took into account the change of sign of the scattering amplitude below threshold due to the presence of the Y* resonance. A recent fit to the strong interaction effects on light nuclei (5
  • Exotic Bound States of Strange Hadrons 21 1 where A = 9 A,+$ A , for T = 0 nuclei. The corresponding value obtained from the scattering length is (-0-42+i0.7) h. Whereas it became clear that the treatment successfully applied to pionic atoms is far too simple to explain the observed effects in kaonic atoms, it seems to be too early to assess properly the pertinent theoretical work, since no real good fit to the data has been achieved so far. But a recent conference review by Wycech (1973) might be mentioned. Koch and Sternheim (1972) try to construct the potential by superimposing elementary KN potentials in place of the scattering length. Alberg, Henley and Witels (1973) find that non-local and off-energy-shell effects are appreci- able and derive an equivalent local potential which differs sigrdicantly from the shape of the matter density. The question of how reliably the strong interaction effects in kaonic atoms can be treated theoretically must be solved before further information can be drawn from the measurements. There are essentially two different subjects which might then benefit from the study of kaonic atoms. If one succeds in relating the properties of the K-nucleus potential to the elementary KN interaction, one could measure this interaction at the threshold complementing the scattering results obtained at higher energies. The question regarding the relevance of bound systems such as Y* inside the nuclei may then be asked (Wycech 1971). Secondly, the kaon may be used as a test particle for the structure of the nuclei, as emphasized earlier (Wilkinson 1959, 1960, 1961, 1967). However, the relative strength of the K a to the K-p interac- tion depends on the influence of the resonances below threshold (Y*). A recent fit to the kaonic X-ray data of P, S, and C1 using the experimentally determined potential parameters (13) and assuming p,(r) = p,(r) gave some indication (Backenstoss et al. 1974 b) that the matter distribution in the radial region between 3 and 7 fm, which is particularly sensitively probed by the kaon, falls off more steeply than the so far accepted best Fermi-type charge distribution derived from electron scattering. However, such a statement is subject to all the reservations attached to the par- ticular model described above. The existence of a neutron excess in the surface of heavy nuclei has been discussed in connection with the analysis of the nuclear capture of K- mesons on nuclei of the photographic emulsion (Davis et al. 1967, Burhop 1967, Bugg et al. 1969, Burhop et al. 1969, Wiegand 1969, Bethe and Siemens 1970, Wycech 1971, Bardeen and Torigoe 1971, Burhop 1972). In fact, the experimental results of Davis et al. (1967) obtained with the photographic emulsion technique suggest that the ratio of the fraction of K- meson captured on a neutron relative to that on a proton is much larger for heavy than for light nuclei; about five times larger for silver than for carbon. This result has recently been confirmed from a study of antiprotons stopping in plates of carbon, titanium, tantalum, and lead located in a hydrogen bubble chamber (Bugg et al. 1973). Therefore, precise measurements in heavier kaonic atoms may be indicated. However, it is too early to judge whether an empirical adjustment of the potential parameters to light nuclei will be adequate for drawing conclusions concerning the surface of heavier nuclei, from strong interaction effects of their kaonic spectra or whether a full understanding of the theoretical aspects of the K-nucleus interaction will be required. For Z hyperonic atoms the nuclear absorption for C , Ca, Ti, and Ba could be determined (Bunaciu 1973, Backenstoss et al. 1974 a). All the questions concerned with the theoretical treatment of kaonic atoms are even more open in the case of Z atoms. Hence it might be an accident that the effect can be explained by the approach equivalent to that of eqn. (12) with a complex scattering length derived by Gell, Alexander and Stumer (1970) from ZN scattering data. If the approach would be correct-which might be plausible because the %nucleus interaction takes place in regions where the nuclear density is less than 1 per cent of the central density-it could mean a reduction of the ambiguities contained in the analysis of Gell et al. (1970). Finally, it should be pointed out that investigations on antiprotonic atoms (Backen- stoss et al. 1972 b, Barnes et al. 1972)-not discussed here in the context of strange hadrons-are extremely important in order to complement kaonic data, being experimentally easier to handle than Z hyperonic atoms. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 212 G . Backemtoss and J . Zakrzewski 4. Nuclear bound states When a K- meson reaches the critical state from which electromagnetic transitions are no longer observed, it is removed from that state by the strong nuclear absorption. As a result, a A hyperon may be produced via one of the processes (1) and, owing to its attractive interaction with nucleons, it can become bound to form a hyper- nucleus in either a ground or an excited state. A ground state of a hypernucleus is often considered, in a phenomenological approach ( Gal et al. 1971, 1972), as a structure consisting of a core nucleus with a A hyperon bound to it in its lowest state. In this approach, an excited hypernuclear state may be described as an excitation of the core nucleus or a state with the A hyperon not being in its lowest level. targets hypernuclei targets 61 : L LI 7 ~ i 3 4He s-shell L AH -.- .-.-.-.-.-.- 9 Be 5 ,He 7'%' ,Li ,Be 9Be - - I4N I6O .. p- shell .-.-.-.-.-.-.-.-. -._ 0 ! O i 1. - . -. -. Fig. 8. Twenty-one uniquely identified hypernuclei and some species, at present not identified (marked as ciroles), which together with their core nuclei should be stable against a fast decay. All hypernuclei which might be produced by K- mesons with a given target are placed above the corresponding broken line after Pniewski (1973), based on the data of the European K- Colleboration (Juri6 et al. 1973, European K- Coll. 1974). Ground-state configurations of hypernuclei (fig. 8) are, of course, unstable against the A hyperon decay via the weak interaction A+N+?I, or A+N+N+N, a week interaction process occurring in nuclear matter only. When a negatively charged pion is emitted, an event can often be uniquely identified in the photographic emulsion, and it is through the study of such mesonic decays that most of our information has been obtained, consisting primarily of the A binding, or separation energies, BA in hypernuclei. The ground-state values of B A for light hypernuclei have thus been determined in a most systematic study by the European K- Collaboration (JuriC et al. 1973) as given in table 7. Their dependence on the hypernuclear mass number A is shown in fig. 9. In these investigations, beams of K- mesons interacting a t rest have been used to produce hy-pernuclei. This is by far the most copious source of hypernuclei (Zakrzewski 1964, Burhop et al. 1964) with about 10 per cent or 50 per cent of kaon captures that occur in the emulsion on carbon, nitrogen and D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 213 13- U - 11- oxygen, or bromine and silver, respectively, leading to the trapping of A hyperons in nuclear matter. In principle, en excited state of a hypernucleus may decay either through (i) the strong interaction with the emission of baryons, a A hyperon, a nucleon, (ii) the weak interaction with or without the emission of a pion (an isomeric (iii) the electromagnetic intersotion with the emission of a photon (a y decaying an a particle, etc. (a resonant state); or state); or state). 9- 8- 7- B,, /MeV 6- S- 3 Hypsrnuclear mass number A Fig. 9. Variation of the BA values with the hypernuolear mass numbers (JuriO et aZ. 1973). U.P. P D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 214 G. Backenstoss and J . Zakrzewski The study of these decay processes constitutes a new field of research, that of hypernuclear spectroscopy, which has recently attracted much attention stemming from the fact that low-momentum K- meson beams of high intensity have become available for counter experiments. The presentation of the results of these experi- ments will be our main concern in the rest of this survey. 4.1. Strong interaction decay To date, hypernucleus excited states decaying via the strong interaction have been studied with pion spectroscopy techniques by determining the kinetic energy of charged rr mesons originating together with hypernuclei from strangeness-exchange two-body reactions of K- mesons with target nuclei: K-+AZ-+T-+AZ for kaon momenta2 0. (14) In this way, the existence of such a state has now been firmly established for the Y C hypernucleus. It was first observed in 1969, using the emulsion technique by the European K- Collaboration (Bohm et al. 1970). Figure 10, taken from the work of the Collaboration (JuriC et al. 1972) based on greatly increased statistics, 3 5 3 0 25 m : 2 0 Y * Y e 0 L 15 Y 0 E 3 z 10 5 0 n : : I , , . f l .,r',hn , 1 E Z 155 156 157 158 Tx p r o d / M e V 3 20 GO 80 100 120 1LO Tn p r o d / M c V Fig. 10. Kinetic energy distribution of pions from reaction K-+ '*C +r-+ lH+ XB. Curve (a) represents the three-body phase space, curve ( b ) an impulse model and curve (c) an impulse model including a possible contribution of N*(1236) (JuriO et al. 1972). D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 215 shows a pronounced peak in the kinetic energyt distribution of pions coming from the K- meson abaorptions on carbon with the production of the YB hypernucleus and a proton. It was interpreted in terms of a two-step reaction involving the production of a resonant particle-unstable state of the FC hypernucleus, followed by its strong interaction decay into a proton and a TB hypernucleus: K-+Y!+r-+FC* strong interaction decay -lH+yB mesonic decay L, r-+other particles. The binding energy of the A hyperon in the excited state of the F C hypernucleus, â¬31, and the natural width of this state wer0 obtained from this observation to be 0.1 With the assumption that the (unknown) A binding energy of the ground state FC is equal to that of its mirror EB hyper- nucleus, B*(FC) = BA(FB), the excitation energy of the resonant state was estimated as E , , = B A ( ~ C ) - B ~ = l l MeV. The F C resonance production was studied by Faessler et al. (1973) in a counter experiment a t CERN. The momenta of the production pions resulting from the K- meson absorption at rest in a carbon target were measured using a bending magnet and arrays of plastic scintillators and multiwire chambers. The pion momentum distribution (fig. 11) was interpreted by the authors in terms of the production of the ground and excited states of FC, with the position of the peak around 261 MeV/c corresponding to the A binding energy of about zero MeV, the value being consistent with that obtained in the emulsion experiments$. These 0.2 MeV and less than 1 MeV. Fig. 1 r I I I 1000 - L )(-,1Zc -n-.hO . l l C .......... ............. Ln-." ---- u - z: n' ."g . . . . . . . . . . L * '\ ,... 'ii 500 5, ,,, .." .\, . z 0 225 250 275 300- Momentum of TT-mesons / MeV/c, -1. Spectrum of m- memured with 8 x 108 K- stopped in lac. The insert shows the spec- trum above 250MeVlc after subtreotion of a smooth baokground. The dashed curve8 are calculated contributions to the background not normalized to the experimental data (Faessler et al. 1973). +The error in the determination of the pion kinetic energy, deduced from kinematic oonsider- ations, was estimated to be about 0.1 MeV for this energy range (Bohm et al. 1970, JuriO et 02. 1972). $It should be mentioned that, since the widths of the peaks are about 6 MeV/c, whioh is the instrumental resolution, there is no way of excluding the possibility that more than one narrow state contributes to the peak around 261 MeV/c. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 216 70 60- 50 40 30 20- a. Backenstoss and J . Zakmewski - - - - I I I I I I I 10 20 30 - lo -30 -20 -10 0 12 Mlssing mass minus of ,,C ,,C excitat ion energy/ MeV 12 (a) 8ot- resolution Instr' (FWHM) I l l 1 I l l 1 1 1 1 1 I 1 l l l l l l L 0 10 20 Exc i ta t ion energy of 'EC/MoV (b ) Fig, 12. (a) Raw data for the run 1 with the lac target (10- thick target scintillators); ( b ) Excitation energy of "C 8s resulting from a preliminary analysis of the data (Bonazzola et aZ. 1973). A D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 217 states seem to have been produced with similar ratee, comparable to the rate for the TC resonance found in the emulsion experiment, 3 x lo-' (JuriC et al. 1972). On the other hand, no definite indication of the production of YC in its ground state was observed by the European K- Collaboration (1974). If the counter experiment result is correct, this might be explained in terms of an observational loss; another possibility would be the domination of the T O mode in the F C ground-state decay that could not be observed in the emulsion (European K- Collaboration, 1974). Apart from studies with stopping K- mesons, experiments are under way in which beams of fast kaons are used to produce hypernucleus states via reaction (14). A n experiment with kaons of 390 MeV/c momentum has just been completed at CERN by Bonazzola et al. (1973). Momenta of incident kaons and pions emitted in the forward direction were measured with a double magnetic spectrometer consisting of a single magnet with a target in the middle and arrays of multiwire proportional counters to determine particle trajectories. The missing mass was then calculated: M , = { r ~ ~ + w k z ) - ~ ~ ~ - (P~-P,)~ i l l2 , E being the total energy of a particle with rest mass M and momentum p (c= l), end the hypernucleus excitation energy was obtained by subtraction of its ground state mass E , , = M , - - M ( ~ Z ) . Preliminary results (Bonazzola et al. 1973) of this experiment are shown in fig. 12, where the excitation energy spectra for a carbon target are shown before and after background subtraction. Although the statistics are poor, according to these authors there is an indication for the production of both the ground and excited states of TC at about 10 MeV?, in a ratio of about 1 : 4. If this were confirmed in future experiments, it could contribute significantly to our understanding of the mechanism of the hypernucleus production. Figure 13 shows preliminary results for an oxygen target, interpreted by the above-mentioned authors in terms of the production of the 20 excited states at about 12 MeV and, perhaps, around 20MeV, although in the latter case the background conditions were less known. There were many speculations on (Dalitz and Levi-Setti 1963) and searches in the emulsion experiments (e.g. European K- Collaboration 1974, Zakrzewski 1971) for other particle-unstable hypernuclear resonances, but none was found. In par- ticular, no definite indications for either the ?N or TO excited states were seen, although in the former case the situation is less clear, and the possibility of the exis- tence of an excited state less sharp than that of YC cannot be ruled out. Many of these problems may hopefully be solved with an experiment now in preparation at CERN where, with the use of a double magnetic spectrometer composed of two magnets and multiwire proportional counters, a much improved momentum resolution is envisaged (Povh 1973). Again, K- mesons with momentum of about 0.9 GeV/c will be used, the reason for utilizing beams of fast kaons resulting from the fact that, with a T- meson from reaction (14) being emitted in the forward direction, the momentum transfer to the A hyperon can be quite small, whereas i t is about 250 MeV/c for the kaon absorption at rest. In this situation, hypernucleus excited states can readily be produced with the replacement of a nucleon in the target nucleus with a h hyperon. When a p-shell nucleon is replaced by a A hyperon in the same spin state, an excited hypernucleus state may arise. In fact, as an explanation of the 't\'C resonance, the binding of a p-wave A hyperon to the core nucleus was proposed by Dalitz (1969), whereas a strangeness analogue state was suggested by Kerman and Lipkin (1971). "he possibility of the existence of such states, similar to isobaric analogue states known in nuclear spectroscopy, was discussed by Lipkin (1965), Feshbach and Kerman (1966), and Kisslinger (1967) even before the observation of the ,i"C hypernucleus resonance. Strangeness analogue +Since the instrumental energy resolution is about 6 MeV, the remark given in the preceding footnote is valid also in this case. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 218 G. Backenstoss and J . Zakrxewski statefl would arise in strangeness-exchange reactions of kaons with nuclei when a kaon was transformed into a pion and a nucleon into a A hyperon without changing the wave function. The classification (Kerman and Lipkin 1971) of these states under the SU(3) symmetry of the Sakata model (Sakata 1956), in which all multi- baryon states would be composed of the basic triplet, proton, neutron, and A hyperon, would lead to an estimate of their production cross-sections (Deloff and Piekarz 1973). However, because ofthe strong breaking ofthe A-nucleon exchange symmetry required by the model, objections have been raised (Dalitz 1969) as to the validity of this approach. Thus i t is evident that from the theoretical point of view the situa- tion is far from being clear, and more experimental results are needed on production cross-sections and excitation energies of various hypernuclear species. With im- proved momentum resolution it should also be possible to measure A binding energies for hypernuclei unidentified up to now with the emulsion technique. A rich field of research is still to be explored before we come to a better understanding of both hypernuclear structure and A-nucleon interaction. I I I I I I , , I I I I I I E x c i t a t i o n anorgy ofâ:O/MoV Excitation energy of 1 6 0 a s resulting from a preliminary analysis of the data. 0 10 20 Fig. 13. A 4.2. Weak interaction decay â When the lifetime of a hypernucleus excited state is comparable with that of a free A hyperon, of the order of IO-lO s, the decay via the weak interaction may occur in competition with the electromagnetic y transition. The weak decay of such an isomeric state would then lead to an apparently smaller value of the A binding energy when analysed as if the hypernucleus decayed from its ground state, an assumption made in computing BA values from the studies with the nuclear emulsion. It was just such an observation of an anomalously broad BA distribution for the :He hypernuclous that led Pniewski and Danysz (1962) to suggest that hypernuclear isomerism is an explanation. The ;He isomeric state would be derived from the D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 219 parent state of the 6He core nucleus at 1.7 MeV, where the details of the :He level scheme, indeed the very existence of the 2He isomeric states, strongly depend on the characteristics of the &nucleon interaction (Gal et al. 1971, 1972). However, the present experimental data of the European K- Collaboration (Juri6 et al. 1973), shown in fig. 14 for hypernuclei with mass numbers equal to 7, do not provide any definite evidence for the existence or non-existence of an isomeric state of :He, although the B A distribution for :He seems to be broader than for the other species. Also, no tail appears towards smaller values in the BA distribution of the i L ihypernucleus, another candidate for hypernuclear isomerism considered by Pniewski et al. (1967). The direct observation of y-rays with the counter technique would solve the problem of hypernuclear isomerism if the partial lifetime of the hyperisomeric state was not too long. 2 4 6 8 6, /MeV Fig. 14. Distributions of the BA values for the mass 7 hypernuclei: (a) uniquely identilied :He from the experiment desoribed by Jurii: et al. (1973); ( b ) world data for ;He; (c) i L i from theexperiment described by Jurii: et al. (1973); ( d ) ;Be from themmeexperiment (Jurii: et al. 1973). 4.3. Electromagnetic interaction decay The first successful counter experiment on short-lived excited states of hyper- nuclei decaying via the electromagnetic interaction with the y emission was performed at CERN by Bamberger et al. (1971). Their experimental set-up, shown in fig. 15 contained NaI crystals as y detectors and a Cernekov counter to observe production pions of kinetic energies exceeding 160 MeV. K- mesow were stopped in several targets, notably 6Li and 7Li, and fig. 16 shows the y spectra observed for these latter materials. In both spectra there is a peak at about 1-09 MeV, ascribed by the authors to electromagnetic y transitions in the 2H and/or :He hypernuclei produced in the multibody reations K-f8Li,7Li-+ iH#, fiHe#+other particles - t iH, iHe+y. All other possible sources of such a line were ruled out by the authors in the dis- cussion of the results. There seems to be another peak at about 1.42 MeV and, if it were a hypernuclear line, it could result only from the excitation of the same hypernuclei, iH, ;He. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 220 G. Backenstoss and J . Zakrzewski Fig. 16. Set-up of the beam telescope, target and NaI counters. S,, S,, S,, S,, s,, 8,, g, and 6, -plastio scintillation counters; el, o,-threshold Cerenkov counters; C,-Cerenkov counter for fast pion detection (Bamberger et al. 1971). 2L - 20 - ln 5 16- U r 7 j 1 2 - 3 z 8 - L - 05 1.0 1.5 2.0 0.5 1.0 1.5 2.0 Energy / MoV Fig. 16. Prompt y spectra obtained with OLi and 'Li targets (Bamberger et al. 1971). D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • Exotic Bound States of Strange Hadrons 221 Bamberger et al. (1971) stress, however, that the origin of this line is ambiguous. The intensities of these two lines are (0.33 f 0.05) per cent and (0.10 f 0.03) per cent or (0-09fO.03) per cent and (0.05+0.03) per cent per stopping K- meson in a 'Li or 6Li target, respectively. No y line was observed in coincidence with high-energy pions in the case of the 7Li target, indicating that the two-body reaction leading to iLi* in a y decaying state K-+'Li+r-+ iLi+ - h + Y , has a small production rate, less than 0.05 per cent per stopping K- meson. The origin of the AH, ;He excitation is interpreted in terms of the spin dependence of the A-N interaction. If the spin J , of a core nucleus is different from zero, it can couple with the spin of the A hyperon to give the value J , f 4. The hypernucleus ground and excited states thus can be explained as a spin doublet, the excitation being due to the spin-flip of the A hyperon and mainly depending on the A-nucleon spin-spin interaction. This is the situation in the case of the 2H and :He hyper- nuclei with spin J=O for their ground state, the A spin being coupled antiparallel with that of the core nucleus, J ,= 9 in each case. The i H * and :He* excited states Table 7. BA compilation Hypernuclide Number of events 204 155 279 1784 31 see fig. 17 226 35 6 787 68 8 222 4 2 10 73 87 6 3 14 0.13 f 0.05 2-04 f 0.04 2.39 f 0.03 3-12 f 0.02 4-25 f 0.10 5-58 f 0.03 5.16 f 0.08 7-16 f 0.70 6.80 f 0.03 6.84 f 0.05 8-53 f 0.15 6.71 f 0.04 7-88 f 0.15 9.11 f. 0.22 8-89 f 0.12 10.24 f 0.05 11.37 f 0.06 11-69 f 0.12" 12-17 & 0.33 13.59 0.15" * See Jurid et al. (1973) and European K- collaboration (1974) for discussion. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
  • 222 G. Backenstoss and J . Zakrzewski with spin values J=l are expected to be particle stable (Tang 1969); they would decay via the electromagnetic M1 y transition, the excitation energy thus giving the best information on the spin dependence of the A-N interaction. Although the ground states of 2H and :He form an isospin doublet, there is a difference in their A binding energies (see table 7), ascribed to the charge symmetry-breaking effects in the interaction of the A hyperon with nucleons (Raymund 1964); hence the excita- tion energies of their excited states may also be different (see, for example, Tang 1969). In fact, detailed calculations were made by Bamberger et al. (1973) of the A- nucleon interaction parameters utilizing the new experimental information. The authors used as the input data the emulsion values of BA for i H , i H , and AHe and, additionally, the 1-09MeV line from the counter experiment assigned in turn to :-H* or :He*. The best fit to the A-proton elastic scattering cross-qpctions a t low energies was carried out, the results of the calculations indicating both a rather strong spin dependence of the A-N interaction and a pronounced charge symmetry-breaking effect. While the excitation energy of the other hypernucleus, :He* or i H , turned out to be 1.2-1.4 MeV for the best-fit parameters, this approach was clearly based on a specific phenomenological model (Herndon and Tang 1967). Any inconsistency with future experimental data would be an indication of the limits of applicability of these phenomenological considerations. Thus it would be of great interest to ascertain whether the 1.42 MeV line does exist and is of hypernuclear origin. For this purpose an experiment has been pro- posed a t CERN by the Lyon-Warsaw group, with an enlarged distance between the target and the y detector t o allow for a better time separation of the background y transitions induced in the y detector by fast neutrons originating in a target. Further, with a range telescope to detect the decay pions with the kinematic energy of 53 MeV, it will also be possible to ascribe the observed lines t o either i H or ;He. If the y line a t 1.09 MeV (or 1.42 MeV) were observed in coincidence with such pions, this would be a signature of the i H hypernucleus decay via the two-body mode iH-tr-+*He. The proper assignment of the y lines would thus remove the ambiguity in the calculations of the A-nucleon interaction parameters. 5. Conclusions The study of the atomic and nuclear bound states of strange hadrons, i.e. the hadronic atoms and the hypernuclei respectively, has been greatly advanced by the availability of improved low energetic K-meson beams particularly designed for this purpose. The experimental investigations, though still in a pioneering stage, have shown their relevance to a considerably broad field of physics and have prompted substantial theoretical efforts. The strong interaction between the hadrons and the nucleus shows up in the properties of the atomic and nuclear levels such as energy and width, and in the binding energy of hypernuclei. It is connected to the elemen- tary hadron-nucleon interaction and to the structure of the nuclei. Hence the study of the elementary interaction a t almost zero energy and the study of the nuclear structure in terms of a shell model as well as in terms of the distribution of the protons and neutrons particularly a t the nuclear surface, may be facilitated. Ques- tions as to the existence and behaviour of excited strange baryons such as the Y* in nuclear matter may be tackled and the interaction of A hyperons in nuclei can be investigated in a unique way which is of importance in view of the non existence of the Pauli principle for Aâs in nuclei. Finally the strong Coulomb field of the nucleus provides a unique tool to measure the properties of charged hadrons such as their masses, their magnetic moments and their ability to be polarized. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14
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  • Exotic Bound States of Strange Hadrons 225 Wu, C. S., and WILETS, L., 1969, Annu. Rev. Nuclear Sci., 19, 527. WYCECH, S., 1971, Nuclear Phys., B, 28, 541, and 1973, Proc. 5th Int. Conf. on High-Energy ZAKRZEWSKI, J., 1964, Proc. I d . Conf. on Hyperfragments, St-Cergue, 1963 (CERN 6 6 1 , 1964), p. 89, and 1971, Warsaw University report ZFD/71/8/1971. See also European K- Col- laboration (1974) for earlier work. ZIEMINSKA, D., 1971, Phys. Letters, B, 37, 403. Physics and Nuclear Structure, Uppsala, 1973, in press. The Authors: Gerhard Backenstoss obtained his doctorâs degree from the University of Freiburg, Germany, in nuclear physics. After some research work in semiconductor physics a t the Bell Telephone Laboratories and in elementary particle physics at the Carnegie Institute of Technology in Pittsburgh he joined 1959 the CERN laboratory in Geneva, where he participated in many experiments in the fields of elementary particles and nuclear structure also after an appointment at the University of Karlsruhe in 1966. In the last years the efforts of his group were mainly devoted to the study of muonic and pionic atoms followed by the first observations of antiprotonic and 1 hyperonic X-rays for which he received the German Rontgen prize in 1970. He is now professor of physics at the University of Bade, Switzerland. Janusz Zakrzewski was born in Cracow, Poland, in 1932. He studied at the University of Warsaw, taking the degree of MSc in 1957. Staying in England in the years 1958-1901, he carried out research a t the University of Bristol where he obtained his PhD in 1961. He spent a year in the USA as the Enrico Fermi scholar at the University of Chicago in 1965-1966. As a visiting scientist, he stayed several times at CERN in Switzerland for a few months. His work has been in the field of experimental elementary particle and high energy physics, in par- ticular K meson and hypernuclear physics and high energy nuclear fission. He has been work- ing a t the University of Warsaw since 1956, and was appointed Professor of Physics in 1971. He was elected the Dean of the Faculty of Physics in 1972. D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 0 4: 16 1 0 N ov em be r 20 14