LOW ENERGY PIONS in NUCLEAR PHYSICS Mannque Rho

LOW ENERGY PIONS IN NUCLEAR PHYSICS Mannque Rho

To cite this version:

Mannque Rho. LOW ENERGY PIONS IN NUCLEAR PHYSICS. Journal de Physique Colloques, 1972, 33 (C5), pp.C5-155-C5-169. 10.1051/jphyscol:1972512. jpa-00215114

HAL Id: jpa-00215114 https://hal.archives-ouvertes.fr/jpa-00215114 Submitted on 1 Jan 1972

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Calloque C5, supplement au no 8-9, Tome 33, ~oOt-Septembre 1972, page C5-155

LOW ENERGY PIONS IN NUCLFAR PHYSICS

Mannque RiiO Service de Physique Theorique, CEN-Saclay - France

Rdsumd - On discute d'une faqon unifide 1es effets despiuns virtuels en physique nu- c- et l'rnteraction dwpions r&ls avec les noyaux & basse dnergie en termes du th&oreme de pions mous. Lcs sujets trait& de cette manihre sont les sufvants : les phd- nomisnes de courant d'echange, les rcgles de some reliant ceux-ci aux quantitds mesurdescims lesexperiences a haute hergie, la production, l'absorption et la diffusion despions par 1.2s noyaux prhs du seuil, et Itextraction & partir des donndes d'atomes X-m8siques des il~formationssur la symktrie chirakbrisec dans l'inter~ctionforte.

Abstract - The effect of virtual pions in low-energy properties of nuclei and the interaction wxth nuclei of low-energy real pions are discussed in terms of the information extracted from the exact soft-pion limit. The subjects treated in this way are the exchange current phenomena, the sum rules connecting these to quantities measurable in high energy sxperiments, the production, absorption and scattering of pions near threshold, and the extraction from x-mcsic data of an Information on the rhiral symmetry breaking in strong rnteract ion Hamiltonfan.

I - IE*"TROWCTION - The pion was predicted in 1935 on the longest range part of it. Thus the pion by Yukawa and discovered in the laboratory in 1947. plays an essential role here just as the small mass It fs now well-known that just as the photon media- of pion plays a crucial role in the theories of tes the atomic and molecular forces, the pion me- elementary particle physics. The aim of this talk diates the nuclear force, responsible mainly for is to discuss the relevance of pions to nuclear the long range part. The pion mediating such force physics in as unified manner as it is possible to- is virtual just as the photon mediating the atomic day. Let me first explain what I mean by a unified and molecular forces is. However a pion can also be ma.-iner. The pion is a pseudoscalar object, spin produced if sufficient energy is given or it can be zero and parity-1 and may be described besides its absorbed by releasing energy. We say that the pion quantum numbers by the mmentum four vector -* invalved in this Latter process is real, i.e., on qk= (q i ) . A real plon satisfies the mass-shell q0 its mass shell.Just as the real photon has no mass, condition the pion 1s almost massless, in any case the smal- q2 = q2-q2 :-m2 . (1) lest among the known hadrons. This fact is quite X imf)ortant as we shall see later. The non-zero mass, However a virtual pion need not satisfy this. In however small it may br, turns out to raise many fact one defines a virtual pion by the fact that 2 2 interesting questions. For these reasons, even after q differs front -m7[. Suppose a pion is exchanged so many years of research on pions, we still try to between two nucleons as in a two-nualeon scattering learn more about them and will continue to do so. process of Fig.1. Here the pion is space-like. This means simply that in my metric qL: is a positive Nuclear Physics bas developed on the con- quantity. Now if all the nucleons are inside a nu- cept of potential. Much of low-energy properties cleus (in other words, within the Fermi sea), then studied in nuclear laboratories depend intimately

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972512 even by a virtual pion. Nevertheless this one plays a very important role for pion physics and has also a great deal of relevance even for interactigns with nuclei. The point corresponding to q =m 0 T( and lGl= 0 evidently describes a real pion at, rest and we call it the threshold. A pion being exchanged in a nucleus docs not have well-defined 121, and qo . They range over a considerable spread in although may be localized within a small Fig.1 (GI , qo One-pion exchange graph in N-N collision strip. On the average, a single-pion exchange is

4> centered around q2-m; , so the point relevant for q2 is usually small compared with q6 which is of nuclei ("1n nucleie* in the plot) is for convenience o:der of a few ( kf )2 where kf is the Fermi mo- put at m4 As we will emphasize again and again, mentum, roughly two pion mass. So one can say that 7i . we are interested in the phenomena where the long in a nucleus range one-pion-exchange picture is relevant. 2 q2 rv m (2 > X There has been a considerable progress in

Both points (1) and (2) are not too far from the both nuclear and subnuclear physics in describing point where q2 = 0 , certainly if one considers the threshold process involving nucleons starting these on the ather hadron scale, namely nucleon from the soft-pion limit. Like the soft-photon for which is as large as 7m It seems only natural which low-energy theorems are well known, the soft X . then to treat both cases (1) and (2) together, ho- pion limit gives us a model-independent result, ping that it makes some sense. quite similar in many aspects to the soft-photon results. The major progress concerns then the link between this point and the physical threshold. Now it seems reasonable to think that if one can go in 4 the q direction in the /q/ vs. qo plane, one should 1 Physical Threshold also bi able to go in GI direction. Thus one would expect that the soft-pion limit is as relevant to the threshold as to the nuclear matter region.

This talk deals thus on a same footing the pion which is exchanged between nucleons and the pion which is produced or captured or scatters by nucleons or nuclei, The major advantagedte pion in nuclear physics is that it generates the potential which governs a great deal of nuclear dy- namics as well as it can be used as a probe, different from the usual nuclear or efectromagnctic pro- bes.

I1 - PlON CLOUD - What takes place when two nucleons approach each other at close distance is not k~ownat all. But we think we know a little about I have dram in Pig.2 the points in the what happens when they are at a large distance, say 1:1 1:1 vs. qo plot where the phenomena of our inte- mare than one pion Compton wave length apart. Around rests lie. The origin where I:/ = 0 , qo= 0 is cal- this range and beyond it, one pion exchange is impor- led the "soft-pion limit" which is cloarly an unphy- tant. sical mathematical point. This may not be reached MW ENERGY PIONS ... C5-157

We also know that each nucleon carries a Now how many mesons are exchanged on the average ? meson cloud srctund it. Suppose now two nucleons ap- One can have a rough idea about this by looking at proach each other at a distance at which two clouds the contribution to the norm of the basic Heitler- can overlap. The question one inay ask is, what is London state coming from one, two, ... meson ex- the distribution of meson clouds when there is a changes. This is shown in Fig.4. Clearly, at largo simulated creation and annihilation of pions ? distances, one-meson exchange seems enough. This is -1 There must be a certain distortion but this must certainly so for r > m As the distance becomes 71 . depend upon the distance. The only treatment on smaller, more and more pions are exchanged as one this question that I know of which has some credibi- would expect. lity 1s that of Cutkosky published some 14 years agoC1I. It is based on the Heitler-London model based on the static approximation. In this model, pat- terned after molecular structure, the simulated exchange of pions as well as the excitation of nucleon resonances can be correctly taken into account. The static model tells us that a nucleon carries,on the average, about 3 pions. Thus nun-interacting system of two nucleons would contain roughly 6 pions in the cloud. As the exchange occurs due to interactions, the distribution of meson clouds is expected to be distorted. Cutkosky investigated this question and found that the deviation of the average number of pions in deuteron from that of two iso- lated nucleons was small at large distance, typical- Fig.4 ly $ to 1- pion at the distance of one-pion Campton The ono-, two-, and three-meson contributions to 2 the norm of the basic state in deuteron. wave length. This feature is shown in Fig.3. As one would expect, the deviation increases as the distan- This description may be too crude and ce becomes shorter. We may note that the increase of perhaps too model-dependent for us to take it se- meson clouds may be associated with attraction and riously, But it may be correct at least qualitati- vice versa. vely. How can we check these features ? If we dis- turb weakly a two- or many-nucleon system, i.e. Dtv~tlOnof Meson Cl6uds in Deutlron I a nucleus, then first of all some effects may show these meson exchange phenomena and secondly they may be sensitive only to the one-pion exchange domain. One of such effects we know is the meson- exchange current in the electromagnetic and weak processes in nuclei, I shall try to show you whether we can combine all these concepts (soft-pions, meson cloud , exchange currents, etc ...) into a sensible and unified picture.

111 - MESON EXCHANGE CURRENTS - The modification in the moson distribution must show up in some phenomena, although the effect may be small in general. Let us now examine whether it makes sense to talk about one pion exchange and a soft pion. One can do this with the old problem, the meson exchange con-

Fig.3 tribution in magnetic dipole moment and magnetic P stands for parallel spin states and 0 for the or- thogonal spin state. C5-158 M. RHO

dipole transition. One can read in text books that the presence of exchange potentials requires the presence of meson exchange multi-particle currents. In its absence, the current would not satisfy the continuity equation. Thus the magnetic moment calculated with the usual single-particle operators is expected to differ from the true value, the experimentally measured dipole moment. The same would be true also for the transition matrix element.

a. Spectacular Agreement Let us consider the simplest case recently studied by Riska and Brown [2 ] namely the thresh- -old capture of neutron

At low energies, this process goes predominantly via Fig.5 the isovector magnetic dipole operator and brings V stands for a vector meson (p or 0) and N* nu- out the main feature we want to study. For many cleon isobars. Note that Fig.(a) can also be given by a pair graph. years, a discrepancy of about 10% in the cross-section has been a glaring embarrassment to the nuclear where the (3,3) resonance (hereafter called h(1236)) theorists. More specifically if one takes the conven- is taken for N* does not contribute and Fig.S(c) tional single-particle operator and a sophisticated is small, so the low energy theorem would be a very wave function seriously, all that theorists can do good description. The 3~1state of deuteron inva- is lidates scnewhat this nice feature. Nonetheless 0- = 302.5 2 4.0 mb (4a) even with the full components of the wave function, theory already 6.6% comes from the first two graphs and whereas experimentalists tell us that it is the rest from Fig.S(d). That the nucleon resonance A contributes non negligibly via the D-state indi- cates that in such a situation, the pion is no lon- So there is a disagreement. Can this 9.5% discrepan- ger so soft. This is not surprising, since the D- cy which one usually ascribes to ths meson exchange state can be generated by the OPEP tensor force, so correction be described by one-pion exchange and this sort of contribution amounts essentially to a soft-pion description of the exchanged pion ? The two-pion exchange, each of the pions far from the correction calculated by Riska and Brown which co- soft-pion point. What counts here is that this can be calculated as shown by the result. This is not mes out to be miraculously close to the discrepancy always the case however as we will see below. (i.e. 9.5%) answers these questions, the first affirmatively and the second more or less also. Here b. Less Spectacular, but Still Impressive is how. The above success naturally suggests that one could expect similar agreements in static magne- If the one-pion-exchange dominance makes tic moments. The deuteron magnetic moment is iso- sense, then in the small photon momentum limit (or scalar, so it is too difficult from the point of in the soft-pion limit1 one would expect that only view r am taking. The other nuclei extensively stu- the first two graphs in Fig.5 contribute signifi- died recently are the isodoublets 3~ and 3He cantly and the last two negligibly for the isovec- . Trying to understand the magnetic moments of these tor transition (this is the consequence of low-ener- two nuclei is really an old problem. What motivates gy theorems). If the wave functions for both the us to look into these again is this. The above exam- bound and unbound systems were in relative S state 1 ple suggests that the two-body current is reliably (i.e. 3~1 and So respectively), then Fig.5cd) LOW ENERGY PIONS .. . C5-159

given by something like Fig.5, generalized to arbi- the low-energy theorem, in particular, the soft- trary initial and final two-body states. It appears pion description seems weakencd a little becauseof also reasonable to approximate the exchange current a possibly sizable A contribution (see, however, by a two-body current alone even in the tri-nucleon the remark made in the subsmrion d. ). systcm. Then the mechanism studied above, generali- In anticipation of what is to come, I zed to an arbitrary state, must be applicable to the (2) must say that this remarkable agreement for three-nucleon doublets. Furthermore, the recent de- 6pV is more disturbing than pleasing. The reason is velopment of Faddeev technique allows one to obtain thzt one would expect 6$) to overshoot the ex- reliable three-nucleon bound state wave functions perimental discrepancy more than the result (6). which were not possible before.

These two ingredients were brought toge- c. Still Successful ther by Harper, Kim, Tubis and ~hof31 . The Faddeev Another place qhcre the one-pion-exchange solution with the Reid soft-core potential leads to approximation seems to work well is in predicting the wave function probabi3ities P = 89.7% , the anomalous orbital moment in heavy nuclei. Long S PS, r 8.6% time ago ?5], it was predicted on the basis of the = 1,770 , PD with s,s',D standing for the fully symmetric S , mixed symmetric S and D pianic exchange current of Fig.S(b) (others do not states respectively [4], For this wave function, contribute) that a nucleon i:: nucleus has an orbi- the discrepancy bctween experiment and single-parti- tal gyromagnetic ratio which is different by about cle momcnts is 10% from that of a free nucleon : i.e., eff - ge - ge + 6ge for proton

- - g for neutron

Let me recall that the experimental values are with ge 1 and 6geg 0.1 . This has been recent- p = 0.426 and c: = 2.553 , thus the deviations ly verified by Yamazaki et a1 in a series of beau- amount to 1% and 16% respectively. tiful experiments [a] . By measuring the magnetic moxents of high spin excited states in medium and The calculation of Harper et a1 [3] takes heavy nuclei, they have succeeded in pinning down into account all four graphs of Fig.5 (generalized to these three-body nuclei of spin and isospin 12 ). For the isoscalar moment, only the diagram (c) with Sge (proton) = 0.09 4 0.03 (81 V = p contributes, whereas for isovector moment, Sge (neutron) 0.06 3.04 the diagrams (a), (b) and (d) with A and (c) with = . w can contribute. The calculated results are There are some controversies as to whether this remarkable success of the one-pion-exchange term is not accidental. For instance, Fujita et a1 [7] argue th.zt the mesonic contribution to Sge should be really 0.2 rather than 0.1 and what the in nice agreement with (5). The isoscalar exchange cxperlmentersmeasure is not the mesonic correction moment is a difficult thing to calculate because it alone but the mesonic correction plus a correction is small and gets important contribution from heavy mesons, so our number may not be very meaningful, coming from short-range correlation which is clai- med to be about -0.1 In such argument, the pion but the agreement with the isovector moment is quite . significant. One finds that the contribution from exchange contribution is not clearly enough ; a Fig.J(d) becomes more substantial, amounting to consistent treatment requiring multimeson exchanges about 4% of the total exchange correction, than in will be necessary. The controversy of this type is the slow neutron capture case. The moral here is however problematic and will not be resolved soon, that the one-pion-exchange picture is still good but because as soon as two or more mesons are being exchanged, there is no systematic way of disentan- Fig.5Cd) with N*= A , N: 1(1470) , N; 1(1520) gling short-range correlation and meson-exchange 5' Z 2'2 is found to give far too large value, effects, a point repeatedly emphasized by J.S. Bell ,5(2 IN [81 . 15% . Here the D-atate contribution dominates; in pa:ticular the S-D cross term with A interme- d. Disaster : Gamow-Teller Matrj.,: Element diate state is devastatingly large, i.e., 12% . Things are not always as ropy as they Even granting a large error to the experimental looked above. Let us replace the electromagnetic matrix element which is itself somewhat controver- current by the weak axial current with a small four sial, bc2) of 15% seems ridiculously huge. Since momentum k as an external disturbance. This is it is the A which is responsible, there must be the case for edecay, more precisely a Gamow-Teller something wrong in treating this object. matrix element. If the axial current is represented by the wiggly line in Fig.5 (with no restrictions e. A Way Out on the initial and final states), then the graph Green and Schucan [11 ] proposed a way out (b) does not contribute and (a) is negligible, so of this difficulty by making the following observa- the contributions come mainly from the graphs (c) tion. Although it lies 300 MeV above the nucleon, and (d). It should be pointed out that there is a A is an excited state of the latter. Therefore in great deal of difference between the axial current calculating mesonic corrections, both should be and the electromagnetic current : whereas Figs.S(c) treatcd on a same footing. Not only Fig.5(d) in and (d) appear as corrections to the soft-pion re- whicit the A coordinate is essentially transformed sults in the electromagnetic case, they constitute away, but also terms from which it cannot be trans- some of the main contributions given by the soft- formed away should be taken into account explicitly. pion theorem in the axial case. One can demonstrate As a consequence, the effective current should be this using the PCAC hyputhesis that we shall not go renormalized accordingly. They demonstrate their into [9]. Let me just mention that what is needed point by a simple model in which the A degree of a is something like (- T ) whcre TgL is a pion- freedom is put in a generalized wave function. This ak 7l k* production amplitude in N-N collision. It should thec cut down the A contribution. thus requires a p-wave amplitude. In the approxima- A need for such renormalization is clcar. tion of one-pion exchange, this invalves simply the But unfortunately a simple model consideration is p-wave x-N scattering amplitude. Or in terms of not good enough for a quantitative calculation of pion production via an axial current, the main con- small effects. It is not clear how to do this for tr-;bution comes from Figs.S(c) and (d). Thus if one the effective two-body current in a satisfactory confines oneself to one-nion exchange and if the way. The Cutkosky model considered above takes care pion can be considered to be soft, then Figs.5cc) of this problem for the deuteron, but a generaliza- and (d) are a model-independent description of the tion to many-body systems has not been studied yet. mesonic currents in the Gamow-Teller matrix element. Any attempt for a satisfactory theory should leave An application of this theory to the the magnetic moment relatively untouched, while re- triton edecay ducing by a large amount the &decay matrix element. This is not achieved in the Green-Schucan picture.

f. Experimental Probe of Exchange Currents was made by Fischbach, Harper, Kim, Tubis and Cheng As a way of justifying my discussion of [lo], using the same Faddeev solution whtch proved the virtual pion effects in this conference and to be successful for the magnetic moment. The dis- also connecting the above domain to the real pion crepancy between the experimental G-T matrix ele- world, let us see whether there are any experiments ment and the single-particle operator value is which bear directly on the effects that I have been kn3wn to be G~~~w6% . The theoretical prediction talking about. It seems fair to say that at this based on the graphs of Fig.S(c) with V r p and moment there exists no such experiment which is con- LOW ENERGY PIONS ... C5-161

viacing enough. But there is some indication that and from which one can extract an effective two- with imagination and hard work, one might find some. body operator corresponding to the exchange current. The argument needed in relating (12) to (13) invol- An instructive example is the anomalous ves PCAC and low-energy theorems, so we shall not gyromagnetic ratio be . Surprisingly enough, this elaborate on the method. The essential point is quantity can be related to an experimentally measu- that one can extract the full matrix elements (mea- red quantity. According to Fujita and Hirata [7], ning one- and two-body current matrix elements) of the relation we want is the process (13) from a precise knowledge of the process (121, although the connection is not as direct as Blin-Stoyle et al originally thought (there is an extra correction to the result of Blin-Stoyle where zl(w) is the nuclear dipole photoabsorption Y et a1 if one uses judiciously the low-energy theo- cross section. The origin of this formula is the rem associated with PCAC [14]). It should be clear Bethe-Levinger dipole sum rule. The exchange correc- by now that once we know the amplitude for (131, it tion (to the TKR sum rule) in this sum rule is found can also be used as an effective current for heavier to be related to the quantity 2bge . One can also nuclei. Unfortunately, the lack of precise low- write this using the Gell-Mann, Goldberger and Thir- energy data on (12) does not allow this interesting ring sum rule [12] to replace the right hand side application yet. with high-energy information only, i.e., Another interesting way of confronting the mesonic correction with high energy experiments was suggested by M. Ericson [15]. Using a dispersion relation for the x-nuclear scattering amplitude where { and aP are the cross-sections for photo- (AK+ -A -) and making some approximations, she ma- Y x production of pions from p and n respectively and nnged to write a sum rule $ photoabsorption cross-sect ion in nucleus A = N+Z Y and IEl implies only the electric dipole part be included.

The right hand side of Eq. (10) is of course known, the integral being fairly well saturated Here fx is the chsrged pion decay constant, w by the giant dipole resonance. Eq.(lO) would thus is some value above threshold (m ) , C (w) the + x 2 lead to bges0.2 already mentioned above. The total R-nucleus scattering cross-section at lab 2 right-hand side of Eq.(ll) as it stands does not energy w , and fA is the sum of pion-nucleus- seem to be measurlble. But it is suggestive of the 2 nucleus coupling f fai . The integral on kind of sum rule one can write down. f the right-hand side goes over and above the (3,3) Similar approaches are possible for meso- resonance region, so contains no low-energy (1.e. nic corrections in Gamow-Teller matrix elements. One 2 threshold) contribution. This fA has the property suggestion [13] is to relate the process (now you see the relevance of this talk) that if there were no exchange current effect, it -wo:~ld be the same as the one nucleon value, namely 2 fmN zx 0.08 . Given high-energy x-nuclear data, 2 ~q.(14)would enable one to obtain fA . The quan- to the two-body decay process tity on the left-hand side being a constant, the 2 deviation of fA from f2 will then be reflected xNN in the integral. Since fi is related to the simi- which may not be realized in laboratories but is lar sum of Gamow-Teller matrix elements via PCAC, known to initiate the "hydrogen burningt' in stars Eq. (14) is essentially a su,n rule for the latter (the first step in producing helium from hydrogen) also. Unfortunately Eq.(14) can say nothing on the I2 C5-162 M. RHO

individual transitions we are particularly interes- cussions given above to think nucleons (free or ted in. Also the relation to Gamow-Teller matrix bound) carrying their own (virtual) meson clouds. elements is obtained through PCAC which may be in They are virtual in the sense that they are off considerable error in nuclei. The presence of ano- the mass-shell. But would it not be possible to malous thresholds makes the naive Coldberger-Trei- strip one off and put it on the mass-shell by sup- man relation highly doubtful in nuclei, although plying appropriate energy and momentum ? '$Tore spe- they can be treated appropriately [16 1. These two cifically, one might imagine the pion production are disadvantages. Nevertheless when we get to know as something like a stripping similar to the fami- enough about the axial strengths (Camow-Teller liar (d,p) reaction. Consider the process strengths) in nuclei and have enough data on the n- nuclear scattering around and above the (3,3) resonance region, this may prove to be a powerful tool. at the energy region appropriate for threshold pion

g. Summary production. Can one picture the outgoing pion as This is then how the situation is with playing a similar role as the proton in (d,p) reac- the virtual pion in nuclei. Unlike the structure of tion ? This is probably not the question in mind hadronswhere infinite numbemof virtual particles when Dahlgren et a1 at Uppsala performed the expe- seem to be needed to describe it, it seems to re- riments [I?] quire only one-pion-exchange to describe a lot of low-energy properties of nuclei in which the mesonic degree of freedom is explicitly needed. The verti- ces needed for such description seem to be given rather well in terms of soft-pion amplitudes. Also with 185 MeV protons, but it is certainly an appro- it looks feasible in the nbar future to "measure" priatz question to ask when one looks at the expe- the virtual meson effects with high energy particles rimental results. Let me show you a differential which will become available in the meson factories cross-section curve which they obtained at 40° la- being constructed. boratory angle (Fig.6). This I consider is rather impressife in its simplicity. Some states are exci- IV - RE& PION PROCESSES - Even if we theorists ted clearly and some states not at all. Thus besi- may talk about soft pions with zero mass, in reality, des the simple nature of excitation mech%nis:n, the- we have to provide at least 140 MeV to produce them re inust be some sort of strong selectivity operative in laboratories. This is a very low energy for par- in the react ion. ticle physicists, but high energy for nuclear physicists. It is small on a hadronic scale, but large on the scale of nuclear excitations. Pions interacting with other hadrons cannot see the structure of the othersat low energy. In contrast a low-energy - pion will see at least a part of the structure of - LOO i - nucleus as it scatters or is produced from, or ab- -5 300 - sorbed by, a nucleus. These differences make the %E - study of nucleus a lot more interesting and color- 200 - ful. In this part of the talk, I would like to turn 100 - to the processes occurring at or near the "threshold point" in Fig.2 . 0 -

EXCITATDN ENERGY a. Pion Production in Nucleon-Nucleus Colli- Fig.6 d2cr si~n The experimental differential cross-section -dn dE It was found to be profitable in the dis- for dl85 M~V)+ 12c( a.s) + x+ + I3c* at 45O scattering angle (~ef.[171). MWENERGY PIONS ... C5-163

I have heard that there are several theoretical school [ 181 (unlike electro- or photo-production calculations being performed at present but I have of pion, there is a delicate point as to how one not seen any. So let me just describe how one would should take the soft-pion limit in this case. This expect a specially simple picture to emerge in a is a technical matter). naive sof i:-pion picture. Recall the reaction I think we need some detailed theoretical calculations and more experiments such as an,w- (17) lar distributions of well-separated individual discussed before in another co~~text.In the soft- levels to verify whether or not the simple pictur,e pion limit, to which one hopes the situation to ap- which seems to emerge is really tenable. But if it ply for pions with low kinetic energy, it turns out bears out to be so, it may be solnewhat of a puzzle. that a soft pion is radiated just as soft bremss- The reason is this. Although the soft-pion limit trahlung photon does from the external lcgs of the is a workable first step in all the processes we two initial protons (see Fig.7). One usually works consider, it is never the entire story. From theo- in the refcrenoe system where pion is at rest, so retical point of view, making the finite mass cor- in this frame both the projectile proton and the rection always brings in non-negligible modifica- target proton radiate the pion. tion, at least in nuclei. A sojhisticated mass extrapolation (going from zero to = 140 MeV) wo;lld tell us that some of the corrections would n' be very important. For instance, in the reaction (17), it is known that a mechanism where pion is P d emitted from more complicated structure , is very important. One of such mechanisms is shown in Fid.9.

Fig.7 Tne graphs contributing in the soft-pion limit n' to p+p -+ x'd near pion threshold.

If one considers heavier targets like the process (16), the radiation from the target can be ignored (in the case of 12c, it vanishes identically becau- Fig.9 The correction to the soft-pion limit for p+p + se of the spin-parity consideration). Therefore the

X++d which is known to be very. important~ even process, in that limit, can be described by the fa- at small pion energies, where ------stand for other graphs such as A excitation. miliar stripping diagram (Fip.8). In deference to the Maryland school, I must add here the soft-pion Here the blob hides details. The emitted X+ could limit I am referring to is the one in which kinema- be coming from a decay P +ZX in which one pion tics are done correctly ; i.e. that of Maryland is absorbed by a nucleon and the other emitted or it could arise from virtual excitation and deexci- - tation of nucleon isobars. The mechanism of this sort would presumably prevent a clean excitation of well-defined states or at least distort the pictu-

13c. 13C. 12C__.a_ re somewhat. Also a X- production would not be la1 I bl terribly suppressed. Yet the experiments seem to - indicate that the X production is much less obser- Fig. 8 T.le soit-pion description (a) of p+12c n++13c* ved than expected- Are we unduly worried about the com ared with the stripping process (b) corrections ? Is it possible that what is important d+18C -r p+13c* . for two-nucleon system is somehow not so for heavier nuclei ? Or are we all deceived ? We will have the answer very soon.

200111111111111111( b. Photoxoduction of Pion Continuing our discussion of production events- carbon processes, the next item is the electromagnetic production. One can produce pions with electron (virtual photon), real photon or with neutrino (weak process). Very littie has been done on the low- energy electro- and neutrino-productions from nuclei. The utility of the latter for nuclear structure is at present doubtful, so let us forget it :?ere. As for electroproduction, there are some expe-

.. . - ~ ~ riments and calculations for the region just above Ey (MeV) the quasi-elastic peak, with pions being produced near and slightlf above the threshold. There is a difficulty in understanding this region [ 191, but perhaps it may be entirely nuclear structure effect. Let me concentrate on the photoproduction or rati~er the inverse process, the radiative pion absorption

This has been extensively studied recently mainly for the reason of experimental ease. It is difficult to do photoproduction of pions near threshold, but stopped pions in atomic orbits are easier to F1g. 10 work with. Lots of theoretical [20] and experimental Energy spectrum of photons following radiative pion capture in 12c : (a) before and (b) after [21] works have been done on this matter, with the subtracting direct interaction mechanism. ~ef.[ll]. aim to check two things : 1) whether or not the soft-pion picture makes sense ; 2) whether or not

the giant resonmoe !hi& is predicted to be there is -9 -P where E is the photon polarization vector, k actually there. From the theoretical point o.P view the photon momentum, 2 the spin operator acting the giant resonance is a closed problem ; I think on the involved nucleon. the only thing that remains to be done is purely experimental (see Fig.10). As for the first question, the works of M. Ericson and her coworkers [22] neatly clarify the situation : the soft-pion limit is just the driving term in the Born series, the higher order terms (i.e. the finite mass correction) bringing in the distortion of pion due to the nuclear field. Thus the soft-pion amplitude, a model- Fig. 11 independent object, plays an essential role in sor- Soft-pion limit for the radiative pion capture Process. (a) represents the case where the fi- ting out the existing less rigorous theories. nal particle stays in the nucleus ; (b) the case where a nucleon gets kicked off in a direct In the strict soft-pion limit, everything process. vanishes except the contribution coming from Fig.11

with the operator If the final nucleon gets kicked off (Fig.ll(b)), this represents quasi-elastic process ; otherwise the final state is a bound or an unbound state LOW ENERGY PIONS .. .

(mainly giant resonance). If one makes a correction to order m7(M , then other well-defined diagrams contribute changing the operator (19) by 10-20% . Further corrections, i. e. the multiple scattering, lead to a distorted pion wave as already mentioned. The pions captured from the atomic s-orbit are tru- ly slow, so the operator (19) is a good operator. From the work of Foldy and Walecka [23], we know that an operator of this sort will have a large matrix element to some particular states,namely the giant resonances. On the other hand, the pions from p-orbit are not so soft and corrections to Eq.(19) Fig. 12 Graph for %-nuclear scattering. a and p are in addition to the finite mass correction discussed isospin indices and Ai and Af initial and final above should be made. Then the nice feature of the nuclei. operator like Eq. (19) is expected to be less pra- make the notation convenient (it is not difficult minent. Since capture occurs more often from the p- to generalize to arbitrary isospins). There are orbit than from the s-orbit for other than lightest then T(" amplitudes nuclei, a clean experiment observing giant resonances in a more convincing way would imply that either Eq.(19) stays dominant or the corrective terms beha- ve also like Eq.(19). Needless to say, the situation where T(-) is called charge antisymmetric ampli- will not be so clean anymore. tude, T(+) charge symmetric amplitude. This defines all the quantities we need below. It is clear that the picture nicely fits in with that used for the proton-induced production. Our interest centers once more on the ca- To see this, it is better to look at the inverse se where pions have very small kinetic energy ; i.e. process, the photoproduction. In the soft-pion li- the s-wave pions. In fact, let us set from the start the 3-molxnta equal to zero, -'tq q 0 Then of mit, the photon kicks off a 7L- or %+ from a neu- = = . course real pions satisfy q = q: .= mx but for tron or a proton which is converted to a proton or 0 , q: q: a neutron. The converted nucleon has to find an un- the moment, we imagine that q = is a variable, filled shell because the exclusion principle does which can be let to approach zero, i.e. the soft- not allow it to stay in the filled shells. The dif- pion limit. In this limit, we know what Tap is for X-nuclear as well as x-N scattering from many ference from the proton-induced process is that he- years of work done by other people [24] : for a re the final nucleus has the same mass as the ini- nucleus A, tial nucleus, thus exciting particle-hole states.

c. %-Nuclear Scattering A pion, because of its unit isospin, can Here T is the isospin operator far the nucleus have single or double charge exchange in addition Y and MA the nuclear mass, is the so-called to its diagonal (in charge) scattering. So it is cAA necessary to consider the charge states explicitly 'lo-commutator", which nobody really knows about its in the amplitude Tap for (see Fig.12) size except that many people feel that the nucleon counterpart UNN should be small. We will come back to this object later.

where a, p run over 1,2,3 or +,-,O and If one looks at the charge exchange pro- Ai*Af are initial and final nuclear states. I shall not cess discuss at all the double charge exchange process. 1 Then we can specialize to an isospin target to -2 C5-166 M. RHO

this unknown c-coinmutator does not contribute, +so needed to clarify the reac tion mechanism. the amplitude in the limit is simply T+ for 7i- - If the impact of the result Eq.(22) on scattering. This result is usually referred to as nuclear physics seems not too impressive at this "universal" since the mplitude does not depend moment, it has on the other hand a far reaching upon any other quantities than isospin. Now how consequence on one very fundamental question in close is this object to the physical quantity, say subnuclear physics. I would like to end this talk a(-) ? For the nucleon, this the scattering length by describing th.at I think to be an important feed- is really very good if one replaces qo by mX . back of nuclear physics to another branch of phy- The experimental value for (1+4p/%) a(-) is sics. This is the story of the C-canmutator in -1 - 1 0.10 mx , while the theory gives 0.09 mZ . Whnt Eq.(22). It is a subject all by itself and I can- about nuclei ? As bQ. Ericson and coworkers[25] poin- not possibly give justice to it in this short pe- ted out, it does not make sense to compare the soft- riod of time. Let me just try to explain in a few pion result directly to experimental numbers. Rather words what it is all about. it should be taken as the Born term in the Born se- We have seen many cases in n -nuclear ries. Indeed if one calculates the Dorn term with interactionswhere a zero-mass pion concept makes the X-nuclear potential of Krell and Ericson [26] a good sense. (Of course this is a folklore with which describes the S-mesic atom data rather well, (- 1 -1 particle physics.) One believes that this success one finds (1 + mdmA) ag,,rn to be 0.088 mK to be (-) has to do with the small mass of pion. But what compared to the soft-pion value (1+ m7i/mA) asoft = 0.09 mi1 a beautiful agreement. The rest of makes it small ? Or alternatively what makes it as the Born series, which corresponds to finite mass mxch as 140 MeV ? Since much of what we understand correction, just gives rise to the distortion of about the low-energy properties of strong inter- pion wave just as in the photoproduction case. action hang on this fact, this is an extremely important problem. It turns out that the c-commu- What do we do with this nice feature of tator for the nucleon, CTNN , contains an essential threshold pion scattering ? What do we learn from information on the breaking of the relevant symme- it on nuclear structure ? try referred to as chiral symmetry 1281. In the One might be tempted to stretch the ener- exact chiral symmetry limit which wvuld be achieved gy region and to apply the simple reault to low- if the pion mass were zero, UNN would be zero. In energy pions already available in some laboratories. fact, OiN is of the forin The appearance of T operator is very suggestive. 2 If the picture still held at an incident pion energy of WeV or so, would it not be cm ideal tool to excite analog states ? The trouble with this pos- where Ao(x) is the axial charge density (the ti- sibility is that tho 8-wave amplitude to which the me component of the weak interaction axial current) soft-pion theorem applies is not expected to be ade- and HSB is the symmetry breaking Hamiltonian. The quate for 30 lev pions. The p-wave contribution commutator would vanish in the symmetry limit. In- should undmbtedly be important. In any event des- direct though it may be, CNN carries the informa- pite the theoretical expectation that the clean pic- tion on the symmetry breaking mechanism HSB . No- ture be blurred somewhat, it is nevertheless an te that this term survives In the limit qo *O , interesting possibility to see analog states by thes so it is really a soft-pion K-N amplitude, There- process. Indeed the recent experiment by Alster et fore it is difficult to get at. One can get a good a1 la71 on 91~r(K*,X0)91~b* where the sequential idea of how difficult it is by looking at the disa- process "Nb* * + p is looked at seems to greements between various calculations which I ha- indicate that such experiments are feasible and lf- ve compiled in Fig. 13. The rm , obtained in dif- kely to tell us a lot about nuclear structure in ferent methods from X-N and K-N data all of which the near future. More refined experiments will be involve off-shell extrapolation ranges from about MWENERGY PIONS ...

distortion. So the mass extrapolation po- ses no serious problem. (c) There exists a potential theory to guide us and further to enable us to separate out electromagnetic effects from strong interaction effects. (d) The greatest advantage with nuclei is the Pnuli exclusion principle. This suppresses by a large amount corrections needed to extrapolate the physical amplitude to the soft-pion limit. This makes the error in the extrapolation much less than with nu- Fig.13 cleons where there is no such suppression. Search for true G-commutator. We have indicated by by a hatched area a rough range of ~7 favored by the model of Gell-Xann, Oakes and NN~enner The CNN found in this method is (see ~ef.[28] ). dNN = 34 MeV (24) 20 MeV to 110 MeV .The structure of HSB changes drastically from the lowest value to the highest which is indicated in Fig.13 by a star . It is clo- value. For instance the smallest value favors the ser to the lower limit, which is also favored by a chiral SU(2)xSU(2) symmetry (the breaking of which currently fashionabie model 1281. There are several gives the pion mass) over the SU(3) symmetry (the approximations made in getting this value. However breaking of which brings about the mass differences we are sure that 0-m should not differ much from in the octet baryons)whereas with cHN= 110 MeV , (24) even if such approximations are avoided. The SU(3) would be considered a better symmetry than main question seems to be how to convince the parti- SU(2)xSU(2) unless one introduces an extra scalar cle physiciistLs that this is more reliable than theirs ! particle (referred IQasadilaton). It is a general feeling among experts that the latter is not a palatable scheme, but none of the calculations is V - CQNCLUSION - I have treated only the low-ener- convincing enough to settle this controversy. gy properties of x-nuclear interaction. The picture appears consistent and to a large extent successful. M. Ericson and I and others have sugges- Now there remains the higher energy and larger mo- ted recently that the X-nuclear data extracted from mentum precesses, which seem to be completely dis- IX-inesic atom can give a more reliable information joint from the low-energy domain. But there must on this 1291. We argue that we can easily obtain be a link. Our future homework will be then to find tbe nuclear c-commutator (the same as Eq. (23) a way to unify all these phenomena together into a where nucleons are replaced by nuclei) and then consistent picture. extrapolate CkA to the nucleon value CNN . There are several reasons why we think that nuclei are better suited in providing this information.

(a) While the data for the charge symmetric X-N amplitude :ire notoriously bad at low energy, we have quite reliable data for t:?e x-nuclear scattering from the K-mesic a tom. (b) The charge antisymmetric amplitude in x- nuclear scattering is well understood in terms of the soft-pion limit as the Born term and the corrections as the pion wave M. RHO

REFERENCES

[I] CuTKOSXY (R.E. ), Phys. Rev., 1958 9,1027 ; [ 161 JARLSKW (C. ) and YNDURAIN (F. J. 1, CERN Pre- ibid, 1959, *,1272. print TH 1492 (1972). [a] RISKA (D.0.) and BROWN (G.E.), Phys. Letters, [17] DAHLGREN (S.), GRAI~TsTR~M(P.), H~ISTAD(B.) 1972, E, 193 and references given there. and ASBERG (A.), Proceedings of the Interna- [3] HARPER (E.P. ), KIM (Y.E. 1, TUBIS (A. ) and tional Seminar on K-nucleus Interactions, RHO (H.), Phys. Letters (to be published). (Ed. by BECKER (F.) and BOUNPN (P.)), Univer- [4] HARPER (E.P.), KIM (Y.E.) and TUUIS (A.), sit6 Louis Pasteur, Strasbourg (1971). Pfrys. Rev. Letters, 1972, 28, 1533. [ 181 BANERJEE (M.K. ), LEVINSON (C.A. ), SHUSTER (M.D.) [5] MIYAZAWA (H.), Prog. Theor. Phys., 1951, 6, and ZOLLMAN (D.A.), Phys. Rev., 1971, C3, 509 801. and to be published. [6] YAMAZAKI (T.), NOMURA (T.), KAMH (U.), INAMURA [19] MOIiIZ (E.J.) et al, Phys. Rev. Letters, 1971, (T.), HASHIZUMA (A.) and TENDOW (Y.), Phys. -26, 445 ; SMITH (R.) and MONIZ (E.J.), to be Rev. Letters, 1970, 24, 317 ; published. YAMAZAKI (T,), NONRlRA (T.), NAiiAMIYA (S.) and [20] See for coinplete references, FIGUREAU (A. ), KATOH (T.), Phys. Rev. Letters, 1970, 25, 547. Strasbourg Conference Proceedings, ~ef.I171 ; [7] FUJITA (J.) and HIRATA (M.), Phys. Letters, also ERTCWN (M.) and RHO (M.), Physics Reports 1971, E, 237 ; (to be published). FUJITA (J.), YAMAGE (S.) and HIRATA (M.), E2t 1 TRUOEL (P. >, S trasbourg Conference Proceedings, (unpublished), 1972. ~ef.[ 171. [8] BELL (J.S. ), private communication. [22] ERICSON (M.) and FIGUREAU (A. ), Nucl. Phys. [9] C-B (M.) and RHO (M. ), Nucl. Phys., 1971, 1969, E,621 ; for a review, see ERICGON (M.) -A163, 1. and RHO (M. 1, Ref. [ 201. [ 101 FIS~HEACH (E. ), HARPER (E.P. ), KIM (Y.E. 1, [231 FOLDY (L.) and WALECKA (J.D. 1, Nuavo Cimmto, TUBIS (A.) and CHEW (W.K.), Phys. Letters, 1964, 34, 1026. 1972, 388, 8 . See also RISKA (O.D.) and [241 ADLER (S.L.) and DASHEN (R.), Current Algebras BItOWN (G.E.), Phys. Letters, 1970, E, 662, and applications to Particle Physics (Benjamin who gets about the same amount. Inc., New York, 1968). [ 111 GREEN f A.M. ) and SCHUCAN (T.H. ), Nucl. Phys. E25] See ERICSON (M.) and RHO (M. 1, Ref.[20] ; (to be published) ; also BROWN (G.E.), private FIGUREAU (A,), Thesis, UniversitB de Lyon, 1970. communication. [26] KRELL (M.) and ERICSON (T.E.O.), Nucl. Phys., [ 121 GELL-MAW (M.), GOGIlBERGER (M.L.) and THIRRING 1969, Blf, 521. (W.), Phys. Rev., 1954, 95, 1612. (271 AtSTER (J. 1, ASHERY (D. 1, YAW (A.I.), DUCLOS [13] BLIN-STQYLE (R. J. ) and TINT (M. ), Phys. Rev., (J.), MILLER (J.) and MOXNESTER (M.A.), Phys. 1967, 160, 803. Rev. Letters, 1972, 28, 313. [la] OHTSUBO (H.), FUJITA (J.) and TAKEDA ((2.1, [28] RENNER (8. ), Springer Tracts in Modern Physics, Prog. Theor. Phys., 1970, 44, 1596 ; 1972, 2, 120. RHO (M.), 1972 (unpublished). [29] ERICSON (M.) and RHO (M.), Phys. Letters, 1971, [15] ERICSON (M. ), Annals of Phys. (N.Y. ), 1971, 63, -36B, 93 ; see also ~ef.E20] ; GEN~INI (P.), 562. Univ. of Lecce preprint, 1971 ; KUMG (W.T.), BANERJEE (M.K.) and LEVPNSON (c.A.), Univ. of Maryland preprint, 1972. LOW ENERGY PIONS ...

DISCUSSION

G. RIPKA (Saclay) M, RHO (Saclay) You discussed the question whether the pion The present situation of the second class cur- product ion react ion mechanism is similar or rent problem is not any better than before, 1 not to the pick-up (p,d) reaction. Coudn't you can only say that Kubodera, Delorme and myself get that information by checking whether the have been able to derive a formula which can same states are selectively excited in the be easily checked by experiments and which may two reactions ? clarify the situation when experiments become available. On the experimental side, Prof. N. RHO (Saclay) Wilkinson has been reexamining the experimental There are some kinematic differences between data and also the possible nuclear effects wi~ich the two reactions. I do not see any compelling may be crucial in this matter. In short, at the reasons why they should excite the same states, present moment, the presence or absence of the except perhaps at a situation when the kinema- second-class current is not settled. tics resemble. I was told that high-energy (d,p) resembles indeed the (p,;) reaction. GRUNBAUM (Karlsruhe) How to explain only soft pion behaviour in nu- C.M. NEWSTEAD (Karlsruhe) cleus, if for nucleon electromagnetic proper- For those of us who are non-specialists, could ties (charge, magnetic radii), the agreement you please summarize the current position of with soft pion is poor ? second class currents vis-a-vis your theoretical predictions and Prof. Wilklnson's work 7 M. RHO (Saclay) It would be foolish to apply soft pion ideas to the nucleon properties. I am afraid that you did not understand my theme.