Mesons and quarks in nuclei

Nualsar Physics Á335(19a0)395-405 .m worth-BOll~nd Pub2tihing Co ., Amsterdam Not to be reproduced by photoprint or microfilm without written psrmiaeion fron the publiahnr .

MESONS AND QUARKS IN NUCLEI E . OSET Departamento de F~sica Teórica, Universidad de Barcelona Barcelona, Spain

ABSTRACT A short review of the topic of mesons in nuclei is exposed paying particular Special emphaattention to the relationship between several mesonic processes . sis is put into the microscopic pictures that can ultimately relate all these processes with the elementary coupling of mesons to the nuclear hadronic components . The importance of the short range part of the nuclear interaction opens the doors to a more basic understanding in terms of the quark components of nucleons and isobars . 1 . INTRODUCTION In recent years a substantial amount of progress has been made in describing mesonic effects in nuclei in terms of microscopic pictures . The virtue of these pictures is two-fold : on the one hand they provide a description of some physical processes 1n terms of the elementary coupling of mesons to the hadronic components of the nucleus, and on the other hand they allow for a correlation of many mesonic processes in terms of a few basic ingredients characterising this elementary interaction . In this way a unified picture can be obtained by means of which, e .g ., the plon scattering processes can be related to the properties of the nuclear isobar components and these to pion nuclear absorption, which itself should be consistently interpreted inside the same schone . The onset of pion condensation can then be studied as a particular case of the general response of the nucleus to the pion field and similarly the modifications of the hadronic currents inside the nuIn cleus can be interpreted in terms of these nuclear mesonic degrees of freedom . what follows a brief exposition of the present situation wí11 be made trying to accommodate into it most of the contributed papers of the session . 2 . MESON EXCHANGE CURRENTS The basic idea behind the exchange currents is that the mesons responsible for the nucleon-nucleon interaction would introduce some new degrees of freedom, by means of which, external currents would couple to the virtual pions exchanged by the nucleons and to other hadronic components resultin from the strong coupling of the pions to the nucleons, mainly the e(3/2,3/2~ isobar . The traditional field of success of this idea has been in nuclear electromagnetic processes, where the magnetic form factors are larg~ly~ affected by mesonic currents and admittedly well understood in terms of them . ~) As an example let us look at the recent data on electron disintegration of the deuteron at large angles where a Saclay experiment 3 ) has extended the measurements up to q2 ~ 17 fm-~ . The theoretical interpretation would account for the impulse approximation plus the mesonic exchange currents as depicted in fig . 1 which would include the pair term, the pion exchange current and contribution from the eß/2,3/2) excitation . 395

39 6

E . OSET

Fig . 1 . Exchange current terms contributing to the electro-disintegration process in the one-photon exchange approach . (a) pair excitation term ; (b) pion current process ; (c) resonance excitation process . In fig . 2 we can see the (b) (c) experimental points of Sa(a) c1ay 3~ and an earlier experiment ) which goes up to q 2 = 10 fm -2 . The theoretical curves are according to the authors of ref .2) . The effects of the exchange currents are remarkable at large momentum transfers and the agreement of the theory with the experiment quite satisfactory . On the sam~ line ,in a contributed paper,) the effects of the meson exchange currents are investigated for the neuron radiative capture on He . The raction is a selected one where there is a negligible contribution from the single particle operator, so the meson exchange currents are responsible for most of the cross section,which comes in good agreement with experiment . W This apparent success could induce us to think that the same sort of renormalization would hold for other components of the hadronic current, e .g ., the axial nuclear current . In this respect it is very instructive to recall the arguments of Kubodera, Delorme and Rhoö) , who by means of current algebra and in the soft pion limit prove 5 20 10 15 that for t~e isovector vector current Vu the time component q2 (fm-21 goes like 0(p/M) and the space component like 0(1), where p Fig . 2 . Deuteron electrodisintegration at 1s the nucleon momentum and M large angles . Cross section, from 1 to 4 .5 the nucleon mass . The single MeV excitation energy, as a function of the particle operator goes instead quadrimomentum transfer squared . Experimenlike 0(1) for the time compotal points from refs .3 .4) . The curves nent and 0(p/M) for the space are according to the authors of ref . 2 ) . components . This tells us that the space components of the exchange current contribution to Vû are intrinsically enhanced relative to the single particle operator . The results for the reaction seen before are in accordance with this simple power counting picture . For the axial currents, following similar arguments, they find that the time component goes like 0(1), while the space component like 0(p/M), to be compared with 0(p/M) and 0(1), respectively, for the

MESONS AND QUARKS IN NUCLEI

397

single particle operator . In this case it is the time component of the axial current that gets intrinsically enhanced with respect to the single particle operator. This would explain the difficulties in providing an explanation in terms of mesonic exchange currents for the renormalization of the vector axial current, but would open new possibilities of observing large mesonic effects in the time component or equivalently in the axial charge . These arguments based on the low energy theorems and chiral symmetry are model independent and should hold 1n principle for any reaction . A candidate reaction to see these effects would be 16N(O - ) ~ 160 + é + v and its related u capture pro ess. This reaction has been thoroughly studiederecently with ups) and downs) with r~spect to mesonic effects . The authors of ref.7) report in a contribut paper ) that when proper account of nuclear details (core deformation in 1~) is taken, it produces additional effects going in the same direction as those of the mesonic currents and given the experimental errors rathing can be concluded yet. We wí11 came back to this point but let us mention first that there are two other experiments that have been suggested to see the possible mesonic effects in the axial charge . The authors of Ref. 6 suggest as an ideal test, to determine with good precision the asymmetry parameter nt for ßt decay. The sum of these two quantities is dominated by the AD component and would pro~~de interesting information . The suggestion of Bernabeu, Ericson and Jarlskog ) goes in a different direction . They find that u capture at large energy transfers and low neutrino momentum would provide relevant information on the time component of the axial current, which would then be related to the s wave n absorption, provided a smpoth extrapolation from the pion mass to the u mass holds as indicated in ref. ») . 3. GENERAL FRAMEWORK FOR RELATED PIONIC PROCESSES The former paragraph has given us an idea of the incidence of the meson degrees of freedom in some nuclear processes . The pions we saw there,are in a klnematical region (m,~) far away from real pions. In different processes they would appear in different kinenatical regions . To illustrate it let us look at figure 3. A formalism which would give the response function of the nucleus to a pion field in a wide spectrun of m,~ would be most helpful in giving a unified picture of the many related mesonlc processes . These pictures are becoming available and it is worthwhile devoting same attention to then . Let us concentrate on the 3

2

~Cu]

optical branch A - scattering

pionic

atoms

u - capture

Fig. 3.

pion condansates 1

Kinenatical regions for different processes .

398

E . OSET

p wave part of the rrN interaction . One would envisage the nuclear response to the pions as an RPA problem where the pions excite particlehole and isobar-hole components, which afterwards propagate in the nucleus as in fig . 4 . The solution to this problem would ive us the response function R(w,~,~',), (2wT ° R) where now w,~ could span a large kinematical region, provided the appropriate form factors for the meson-hadron vertices are taken into account for off shell mesons . In the spirit of having a microscopic picture, the mesons would now be responsible for the p-h or isobar-hole interaction and thus we would be dealing with a picture where mesons and hadrons would be treated in a democratic way .

Fig . 4 . Nuclear response function to a pion field . The wavy lines stand for the different ingredients of the p-h or isobar-hole interaction in the pionic channel (T - 1 and unnatural parity, Jn - 0 - , 1+ . .) .

This picture has been widely used to study pion scattering in the eß/2,3/2) resonance region . The dominant contribution would come from e -h excitation, while other pieces, including the s wave, would be accounted for by a small background term . This is the so-called isobar-hole model .l2,13,14) Following ref .14) the two basic ingredients in the formalism would be the ~-h interaction and the e selfenergies, as depicted in fig . 5 . To account for W a model is used that allows for n and p meson exchange modified by the Fig . 5 . Response function in the e ß/2,3/2) resonance region . W stands for the e-h interaction, while E stands for the ~ selfenergies .

-. u

++

presence of the nuclear short range correlations . One can then write,

W -q _u +iE

where in addition to the one pion exchange contribution one has some short range pieces included in W'(~,w) :

~ [g'(q.~) *2

"f2

(z)

~1 ~1 " ~z + h'(~,w) S12(q)7 u Apart from a small tensor term, the main ingredient is a spin-spin repulsive term, softly energy and momentum dependent, which gives rise to the EELL effect (g'(~,w) ~ 1/3 would be the "classical" value for the EELL effect) . w'(q,~) '

399

MESONS AND QIIARRS IN NIICLEI

This model c with strong coupling of the p meson to the ~ would give a value g'(O,w - u1 ~ 0.55. ~~ere are claims for a weaker p coupling using Regge trajectory arguments. ) On the other hand, part from the usual quark symmetry arguments invoked for a stronger p-coupl~ingl~) the coupling of photons to ND, with the assumption of vector meson dominance, ]eads to a p coupling which is in perfect agreement with the quark prediction .ló)

The parameter g' plays a major role in pion condensation and related processes and manifests itself in all sorts of pionic processes . The other important ingredient is the e selfenergy for which the model of fig. 6 is used which accounts for the narrowing of the D width due toth~ Pau11 blocking, the intermediate pion absorption and other rescattering effects,~ 4) plus one background energy independent local Hartree potential . The response

+ crossed

function would read (omitting for clarity the crossed D R(w q.q~)

s s,

Fig . 6. Feyrman diagrams for the e selfenergy : (a) Pauli, (b) absorption, (c) reflection .

bubbles)

q'~dH~s'> [~d ss ~-Es á s ~s -E s ~s -W s ~s ]-l

(3)

where s,s' 'are the D-h states, dH the effective coupling of the pion to the e-h co~onents, and Es the D-h single particle energies including the A-Hartree potential and the A free width. In fig. 7 we can see the results for the total cross section in n -160 and e integr~ d cross section for the single charge exchange reaction (,r+,a ) ~ . It is surprising to see in this last reaction the role of the intermediate pion absorption, which increases the cross section by a factor of two to three 1n the resonance region an~ is ess~n~~a1 to get a flat cross section as observed in the analogous reaction 3C(n+,n) N . Similar resultsl8) are obtained for this last reaction using the phenomenological spreading potential of ref .12), We would like to emphasize that, as can be seen in eq . (3), the scattering so there is an interference of process is sensitive to the combination E + W the particle-hole interaction with the e selfenergies and this explains the success in reproducing the scattering data by many different approaches . (See, e.g ., refs . 19-21) for low energy scattering and refs .12,13) in the resonance region where a different W is taken, fittin then E , or equivalently, the e spreading potential, to the scattering data . Two of the contributions22 ) to this Conference, following similar lines to those exposed in the paragraph above, use the isobar hole model to study inelastic and radiative capture and indirectly to obtain information on the isobar nu clear states by projection of these states into different channels . The .response function R(w,q q') is in g neral a highly non~~cal function . However an extrapolation of the model of ref.~4 ) to low energies ) would be suitable for a representation with a Kisslinger optical potential of the type :

Fig . 7. (a total cross section for n~ 1 _fref .l 4 )] . (b) tnte rated cross section for 1 (,r~,,r~)150_fref .l~)l . Free D means no D selfenergy included . Pau11 and total would stand for including fig. 6 (a) in the 0 selfenergy and all diagrams of fig . 6, respectively .

isN( n+~~o)is~

fm47 o~

-.- .-

~b

/

-_ \\\

~i i

~

\

.\ \\

Raâ .Bnárp

MESONS AND QIIARRS IN NUCLEI

~(P)( r) . 4n~i

c0 p(r)

C p2(r) + O

40 1

~

with C ~ (0 .12 +i 0 .08)[û 6] at threshold (w ~ u) . The interference that we poirrted 0out between E and N manifests itself here b~~ween Re C and g','and good fits to low energy scattering and pionic atom data )can be óbtained by increasing g (more repulsion) and Re CO (more attraction) simultan~usly, or vlceversa. Thg best fit to the 2p states in pionic atoms is obtained ) with Im C ~ 0.08 u- , Re CO - 1 .7 Im CO with a fixed value g '= 0.33. If g' 'is set equa4 to zero, a less accurate best fit is obtained for Im CO ~ 0 .04, Re CO - 0.8 Im C0 . A recent analysis 25 ) of low ener a scattering dàta also seems to give support to larger values of g'(g' > 0.5~both for elastic and inelastic scattering to discrete states, together with positive values for Re CO.

At the theoretical level, apart from the prediction of ref. 23 ), there are other values quoted in recent literature . By using a imilar model, but in the infinite matter approximation, a value Im CO ~ 0.045 ~-~b is obtained in ref.26) . Also using the infinite matter approximation but considerigg additional contribution from correlated nucleon pairs a value Im CO ~ 0.16 ù is obtained in ref.27) . Thus there seems to be still ground for further discussion of this problem. An interesting problem opens now, since one can explore with the general response function R(w,~,t)')~ the region of small energy and momentum transfer, which would be the kinematitel region for ß decay. The pion field can then be related to the axial current through PCAC and thus we could investigate the mesonic .effects in the axial current. This problem has been the subject of many earlier investigations .28) More recently the basic mechanism of the pion propagation 1n the nucleus has been applied to study the~~pace component of the axial current for doubly closed shell nuclei t 1 nucleon 9 " 30 ), as shown diagrammatically in fig . 8. The axial vector part of the weak Hamiltonian would be 2 iqx G 6 ta ~ 9A(g 2) v HA ' ~ (Q " 1) 4 ~ ~ é , (5) -~R

with

~ the leptonic current.

The limit w -~ 0 ~ + 0 is particularly easy to handle and it simply reduces to a renormalization of gA . The corrections would be nearly a direct measure of the e-h interaction . Typical corrections obtained with this del pangs from - 10~ ~ - 25~ for + N and 39Ca + K, respectively, for values of g' ~ 0.6, 0.7, 1n good agreement with empirical values . With smaller values of g' 'one would progressively diverge fram .the empirical /r.,,~ -> o determinations of dgA/gA " The renornialization of gp has been Fig " 8 . Renornialization of the studie in the infinite matter approxiaxial vector current. matlon~l) in which case gp simply gets numerically modified but HA continues having the same structure . In a finite nucleus, given that we are now in a situation with >~>~ 0, the mesonic effects cannot be fitted into a simple renormalization of gP and a particular study of each reaction is needed . In view of these results it is now clear that a consistent treatment of mesonic effects in the 0- -~ 0+ reaction, mentioned in~sec . 2, would require a

á02

E . OSET

systematic ana)~sis of the space component as well as the time component of the axial current . ) While the time component seems mainly sensitive to the long range part of the meson exchange, 6 ) the space components, as we have seen, are directly related to the short range nuclear force together with the nuclear isobar degrees of freedom . Intimately related to the short range force in the pionic channels is the question of pion condensates . Such an event would happen in nuclear matter when the production of pions in the N -~ N + .n reaction would be energetically favourable in the medium . This would mean that the pion propagator would have a pole at w - 0 for symmetric nuclear matter or a pole at ~ - u - u (u - chemical potential) for n- condensa~~on in neutron matter . This ntopic p has received a good deal of attention recently )for its astrophysical implications and the possibilities of having new forms of matter at higher densities with nucleons in equilibrium i~~ pion condensates, which could eventually be reached in heavy ion collisions . 3~+ ) The nuclear short range forces balance the medium attraction from the OPE and thus the threshold for the appearance of a ion condensate is strongly dependent on the value of g' .' Detailed calculations 3 ~) show that for values of g'oi0 .4 we would already have pion condensates at normal nuclear matter density, while for values of g' a+ 0 .6 one would need from two to three times nuclear matter density for such an event to take place . In finite nuclei the onset of a pion condensate (corresponding to a singularity in the function R(w,~,~')) would be equivalent to having same pionic excitan - 0 - , .1 , . .) at w = 0 . Such a possibility has also been tions (T - 1 investigated3 ~+~~) and the threshold appears for values around g' °~ 0 .4 as in symmetric nuclear matter . In neutron stars where the densities might be around two to three times the nuclear matter density, pion condensates would be quite licJ~ly to happen and this would have drastic effects in the cooling of neutron stars ) by increasing the cooling rate se~~ra1 orders of magnitude . A recent analysis of the situation in some supernovae )shows that in the case that neutron stars were formed during the collapse of the supernovae SN 1006, Tycho and Cas A the present temperatures deduced from X-ray observations would not be explained in terms of the standard cooling scenarios involving only nucleon degrees of freedom, giving thus a strong support for the existence of pion condensates in those stars . The relative proximity of the pion condensates in normal nuclei has incited much interest in a ser~~s 4~f phenomena (precritical phenomena) which would appear in selected reactions . + ) The idea behind it is that, even if one does not reach the pole of the pion condensate, thus having a singularity for the pion propagator (or R(~,~,~') in finite nuclei), there will be a kinematical region where this propagator will be maximally enhanced . Intuitively we might think that we have come the closest possible to the pion condensate pole . Those reactions that would select the pionic channels of the NN interaction could thus be appreciably enhanced . These "opalescence phenomena" could be found in weak and electromagnetic nuclear interactions as inv4e~i :~gated in ref . 43), in heavy ion collisions44), and in proton scattering . 3) In this last reaction if one excites pion-like states (T = 1, and unnatural parity) we would be selecting the pionic channel of the NN interaction as desired . The predicted enhancement of the cross section becomes a reality around q ~ 2,3 u for 208Pb(p,p')f08Pb(1+) as can be seen in fig . 9 . As could be expected, the magnitude of the enhancement is directly related to the value of g' . Smaller values of g', thus being closer to the pion condensetion threshold, would produce bigger enhancement .

LASSONS AND QIIAERS IN NOCLSI

403

4 . QUARKS IN NUCLEI This topic wí11 be the subject of a plenary session and thus we wí11 be deliberately short here . As has, . been seen in the preceding digressions, the short range part of the nuclear interaction plays a major role in most of the pionlc related processes . But when exploring these small distances one might be checking the structure of the nucle~gs themselves . The MIT bag model )provides a description of the nucleons as a bag of three quarks confined in a radius of around 1 fm . This picture would provide a framework for a more microscopic interpretat~~n 4 ~f short range properties . ~ )

Fig . 9 . Proton inelastic scattering cro section t~ the lowest 1 state in ~~Pb . [ref .4Z)l .

Recently Brown and Rho 4g ) have developed a new model with a "little bag ° where the nucleons would be con fined in a smaller radius of around 0 .3 fm . This model would provide a continuity for the axial-vector current from inside the bag, where it is carried by the quarks, to the, outside of the bag where it is carried by the gradient of the pion field, thus providing a dynamical picture for pion emission or absorption from the nucleons . Work along these lines is in progress and we can expect very interesting developments in the future .

5 . CONCLUSIONS We can draw the following conclusions from the above discussion :

The microscopic pictures, which finally relate the physical phenanena with the elementary coupling of the mesons to the hadronic components of the nucleus, through a consistent magy body scheme, offer a unified description of magy related processes . A skillful combination of different processes can provide relevant information on unknowns of this elementary coupling " coupling constants, form factors . A thorough test of consistency of many different reactions would then be the best check of the manly body microscopic picture used . Such a check of consistency on the available models supports the importance of the short range part of the nuclear lnternction 1n a large number of pionlc processes ranging from elastic scattering, through plonk atoms, to the axial current renornmllzation, plop condensates and precritical phenomena . The importance of these short range pieces opens the door to another level of microscopic understanding in terms of the quark components of the nucleons . New developments in the quark bag models seem most promising . I would like to acknowledge M . Rho and W . Welse for their stimulating suggestions and criticism about several parts of this paper .

REFERENCES 1) 2) 3 4 5 6 7 8 9 10 11 12 13) 14) 15 16 17 18 19 20 21 22 23 24 25 26 28) 29) 30 31 ; 32 33 ; 34 35 36 37 38) 39) 40 41 42 43 44 45 46

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