Pion-nucleus interactions: Experiments

Nuclear Physics A374(1982)377c-399c. ® North-Hound Publishing Co., Amsterdam Not ro bo reproduced by photoprint or microfibn without written permission from the oublishcr .

PION-NUCLEUS INTERACTIONS

: EXPERIMENTS

D . DEHNHARD School of Physics and Astronomy University of Minnesota Minneapolis, Minnesota Abstract : Recent experimental results on pion-nucleus elastic and inelastic scattering and pion-induced single - and double-charge-exchange reactions are discussed . 1 . Introduction To this session 57 contributions have been submitted which range from lowenergy ~r-nucleus scattering to double-charge-exchange reactions at a few GeV/c to n-nucleon interactions at a few hundred MeV/c . It is clearly impossible to do justice to all of these coptributions . Fortunately Q . IngramlJ has already discussed many subjects in pion-nucleus interactions so that I can concentrate on just a few things such as elastic and inelastic scattering (ES and IS) and single-and double-charge-exchange reactions (SCX and DCX) . i will place some weight on what I consider to be some of the highlights in ~r-nucleus interactions, particularly with respect to nuclear structure . 2 . Recent Pion-Nucleon and Pion-Deuteron Experiments 2 .1 . PION-NUCLEON ELASTIC SCATTERING One of the basic ingredients of any microscopic description of pion-nucleus interactions is a set of precisely determined pion-nucleon phase shifts . Recent measurements by Sadler et a1 . 2 ) (contrib . H10) of the elastic scattering crosssection a - for n + p anima+for ,r+ + p from 378 MeV/c to 687 MeV/c span the ene,~gy region between the most prominent pion-nucleon resonance, the T = 3/2, J = 3/2+ or [3,3] resonance (1232 MeV) and the three T _= 1/2 resonances with J~ = 1/2 (1470 MeV), J n = 3/2 (1520 MeV), and J~ = 1/2 (1535 MeV) 3 ) . The authors of ref . 2 report general agreement between the measured differential cross-sections and the predictions of phase shift analyses based on earlier work . However, they also found 10 to 15% deviations, especially at the minima of the angular distributions at large m~ nta . A comparison was made of the new ES data with n + p -" ~ + n SCX results using the triangular relationship (see fig . 1) . Within experimental errors the vSCX falls between the upper and lower limits, i .e ., these data show no evidence for a break-down of charge invariance . Brekenev et a1 .5) (contrib . H7) present data from measurements of the polarization parametér~ in ~+ + p elastic scattering between T~ = 510 MeV (634 MeV/c) and 580 MeV (706 MeV/c) which cannot be reproduced with existing phase shifts . Present n-nucleus studies are being done mainly in the region of the [3,3] resonance and below . However, it will be very intriguing to extend the present work to the region of the T = 1/2 resonances for which the 7r - (,r+) interact with protons(neutrons) but not with neutrons (protons) in contrast to the T = 3/2 resonances for which ~ (~r+) interact more strongly (by a factor of ~ 3) with the neutrons (protons) than with the protons (neutrons) . Although the above-mentioned work was motivated mainly from a particle physicist's point of view, it lays the necessary groundwork for ~r-nucleus studies in this energy region . Even for the well-studied energy region up to T.~ c 200 MeV (P = 310 MeV/c) further ~r-nucleon data would be very useful, in particular polarization data to pin down the spin-dependent part of the 7r-nucleon interaction . It remains to be seen how 377c

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D. DEHNHARD

- K- H -- CMU-LBL 10

~L 1

i.~

I

Qb

~

I

II 11

I

I

Q2 -Q2 -Ob COS (Bcr)

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Figure 1 Differential cross-sections for SCX ~ + p -. ,r° + n and the upper and lower limits 0 .5~~ ± ~I2 due to the triangular relationship (contrib . H10) . much the new phase shifts to be extracted from ref. 2 and 4 and similar work will affect present work on the n-nucleus interaction . 2 .2 ELASTIC PION-DEUTERON SCATTERING If charge symmetry holds for the ~r-nucleon system, ~+ and n elastic scattering from the deuteron should have identical cross s~c~ions .except for small Coulomb effects . Three contributions to this session6> >J report on experimental results below 600 MeV/c, and two of these6 .P~ also show comparisons with theoretical predictions which assume charge symmetry but include Coulomb-nuclear interference effects . The good-statistics data 6 ) of Masterson et al . (contrib . H8) (fig .2) are consistent with charge symmetry to within (0 .~+~ .5)% after simple Coulomb corrections . There is, however, an indication for âsystematic deviation from the charge-symmetry predictions around e(c .m) = 100° and 120° . This deserves further study: Unf4 tunately, there is not suffi:cien~ time to discuss the very recent evidence9 ~ for a di-baryon signal in ~~ + d elastic scattering . I assume that these results will be covered in the session on di-baryon resonances . I also hope that the authors of Contributions H9 and H35 will be aüle to discuss the large amount of data now being accumulated .on ~r-helium scattering . 2 .3 . PION ABSORPTION ON THE DEUTERON The only n-absorption experiment I will mention is the ~ + d i p + ~ reacti~l as recently summarized and supplemented by new measurements by . Ritchie et al . )(contrib . 47) . An understanding of ~ absorption is another important

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379c

_ Figure 2 Asymmetry An = (a - - a+)/(a + a+) for e elastic scattering from deuterium . For details of legend see contrib . H8 (ref .6) . ingredient for microscopic theories of the n-nucleus interaction and ~++d ~ p+p is the simplest such process . Fig. 3 shows the ~+ + d + p + p results of many different groups . There appears to be a break between the data below and above 80 MeV which is not indicated by any of the calculations . The predicted cross-sections from different calculations increase uniformly with energy around 80 MeV. In addition, the calculations that fit the 150 MeV peak cross section fail badly at low energy and calculations that do reasonably well at low energy miss the maximum at 150 MeV . It appears that further data need to be taken before the 80 MeV anomaly can be assumed to be real . If it is real, it is clear that there is still much to be learned about this basic ,r-absorption process . 3 . Pion-Nucleus Elastic Scattering (ES) 3 .1 . GENERAL REMARKS There exists now a large body of data on ,r-nucleus ES in the region of the f3,3] resonance . At resonance the angular distributions are daninated by diffraction effects . Thus qualitative agreement between theory and experiment can be obtained with any model that makes the nucleus sufficiently strongly absorptive . Nevertheless, the details of highly precise data in the whole angular range appear to contain sufficient information to test various model predictions (see below) . The recent trend among experimentalists (see ref . 11 and references therein) has been to get away from th t~ongly absorbing region . Several abstracts contributed to this session12 ~1~~~4) are on ES at pion energies between 20 and 80 MeV . At these energies the nucleus is more transparent so that one would hope that some details of the neutron and proton densities are more easily detectable . However, first-order opts"cal potentials which are fairly successful at resonance

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D . DEHNHARD

are quite inadequate at the low energies . The theoretical treatment of secondorder terms (e .g . due to true pion absorption and correlations) is still at its beginning, but these data should be very useful in the development of microscopic theories .

E Z O

H

U W N N O ß` U

H O H

0

50

100

150

200

PION LABORATORY ENERGY (Met

Figure 3 Total cross section of the n+ + d -+ p + p reaction below 200 MeV . Far details of legend see ref . 10 (Ritchie et al .) At present, the data are analysed mostly by phenomenological optical potentials . The form and energy dependence of these potentials are derived from the n-N t matrix and nuclear densities, but the strengths of the s and p-wave terms in the potentials are treated as adjustable parameters . Such treatments have the advantage of providing a simple procedure for generating distorted waves for use in distorted wave impulse approximation (DWIA) calculations . In addition, the energy dependence of the phenomenological parameters might give hints regarding the nature of processes not included in the optical model calculations . The effect of second-order terms on elastic scattering between 40 and 340 MeV has recently been studied by Liu and Shakinl5) . These authors start from a parameter-free first-order optical potential and treat second-order terms on a phenomenological basis . The eXtratted parameters show strong resonance behavi~r and great similarity for rr + 1zC and ,r + 160 . The resonance behavior of the p terms may be relevan to present theories of DCX reactions . Another example~2 J for the usefulness of phenomenological approaches is the analysis of the 20-50 MeV ES data of Obenshain et al . (contrib . H3) . The 20 MeV data require a significantly larger s-wave absorptive strength than the 30-50 MeV results and those predicted by theory . However, the 20 MeV absorption appears to be consistentl6) with pionic atom data . The reason for the unexpectedly large

PION-NUCLEUS INTERACTIONS : EXPERIMENTS

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s-wave absorption is not yet understood . Other recent experimental workl3) on ES is concentrating on the far-forwardangle region (contrib . H4) to exploit the Coulomb-nuclear interference in order to determine the phase of the nuclear scattering amplitude . A programl7) of ES measurements at 100 MeV (contrib . H14) is directed towards a study in a region that is already dominated by the [3,31 resonance . However, T, . = 100 MeV is sufficiently far from the center .~f the resonance so that the real part of the scattering amplitude a(k) = k-1 e~ sind plays a major role . Here ~ is the --nucleon phase shift and k is the pion's c .m . momentum . (At resonance & a ./2 so that a(k) is essentially purely imaginary) . These data will fill the gap between the regions (20-80 MeV and 130-250 MeV) which have been covered extensively already . 3 .2 . RECENT LARGE-ANGLE DATA AND PREDICTIONS Of special interest to present analyses of data near the (3,31 resonance are the pecent very-large-angle (140 ° -180 ° ) measurements of the Omicron collaborationl8)(contrib . H6) of 160 + n- ES at 114, 163, and 240 MeV (fig . 4) . These data complement earlier results of Albanese et al .l9) below 140° There are only very few earlier large-angle data, e .g . thoséo~Chabloz et a1 .20) for 12C + -+ at 162 MeV . (See also references in ref . 18) . At the far-~äc~ard angles the differential cross-sections are not as much dominated by diffraction effects as at forward angles . Present - -nucleus ES theories differ widely in their predictions at the farbackward angles . In fig . 5 two predictions t60 (.n-.a-1 of the isobar-doo nvay mod 1 (or ,~-hole model) 2 ~f Hirata et al .tl~ and Freedman et al . 1 are compâréd with 160 + n+ data at ~3 MeV and a simple first-order optical model calculation with the code PIPIT .23) . 114 MeV There is a very large difference between ~ 163 MeV the isobar-doorway model of ref . 22 and ~ .zaoMev the PIPIT result at the far backward angles. b Unfortunately, the curve from ref . 21 does e not extend into this angular region and neither ref . 21 nor 22 give predictions for 160 + n- for a direct comparison with the resultsl 8 )of contribution H6 . However, o.ol Coulomb effects are not likely to remedy ~. the significant differences between the wo . leo^ calculations of ref . 22 and the experiment (Ref . 18) . More recent calculations lg )(fig .6) with the phase shifts for the peripheral partial waves fixed ~~ the values of the Figure 4 isobar-doorway model )and the phase Differential cross-sections for shifts for the central partial waves trea16 O + n elastic scattering at ted as free paramg ters give an excellent T = 114 163, and 240 Mey at fit to the datalçl up to 140 ° , but again lârge angl es ( contrib .H6)18), the isobar-doorway model results differ greatly from the PIPIT results at very large angles . Furthermore, strongly different results can be obtained for the large angles with the same model by adjusting the central wave amplitudes while maintaining a fit to the other angles . It is quite instructive to compare the scattering matrix elements for different model predictions . As in ref . 21 we use T L = (SL-1)/2i where the S = exp(2idL) are the usual S-matrix elements and the dL are the ,r-nucleus phase sifts . Fi . 7 shows Argand plots of TL from optical model calculations with the code PIRK2~) (a) without and (b) with an energy shift of 0E _ -30 .6 MeV in deriving the ,r-nucleus potential from the n-nucleon phase shifts . Such energy shifts appear to provide a convenient way of parameterizing a large part of the inadequacies of a simple first-order, zero-range, on-shell, optical potential calculation . Very

t~

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D . DEHNHARD

Bc .m . (degrees) Figure 5 16 0 + n+ elastic scattering data at 163 MeV (ref . 19) and isobar-doorway model predictions of ref . 21 (broken line) and ref .22 (solid line) .

Figure 6 16 0 + n+ data and calculations of ref . 19 .

PION-NUCLEUS INTERACTIONS : EXPERIMENTS

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0 .6

Figure 7 Argand plot of TL = [exp'(2idL) - 1]/2i for 160 + ~+ elastic scattering at 163 MeV . a) PIRK calculation without energy shift, b) PIRK calculation with energy shift, and c) Isobar doorway model prediction of ref . 21 . good fits over a wide range of inci~e 6 nt energies and target mass numbers were ) using an energy shift near -30 MeV . obtained by Cottingame and Holtkamp The points in fig . 7 connected by the solid line (c) are from the isobarL doorway model of ref. 21 . It is clear that the TL of the "energy-shifted" calculations resemble closely those of the 0-hole model for the peripheral partial waves . However, there are quite significant differences between the TL from the three calculations (a), (b), and (c) for the more central partial waves . Calculations (not shown) with the momentum-space code PIPIT without an energy shift fall somewhere between the curves (a) and (b) . The cross sections calculated with the above T~ values are shown in Fig . 8 together with the data . It appears that the large improvement in the fit (b) with an energy shift versus the calculation (a) without a shift is due to the large changes in the real parts of the T~ for the peripheral partial waves . It is likely that large-angle data, although they are very sensitive to several parameters, will provide further and much needed constraints to theoretical predictions especially for the more central partial waves . Both at S .I .N . and LAMPF. there are plans to extend present incomplete angular distributions into

D . DEHNHARD the far backward region .

10 3 102 10 1

v

10~

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10 1

E

U

16~ (~+~ .~ +) 16~

T-tr =163 MeV isobar-doorway --- PIRK with Eshift _ ._ . PIRK w/o Eshitt

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\~ .~ . C

10 2 10 3

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lo ecm

b

(deg)

Figure 8 Differential cross sections for 16 0 + ~+ elastic scattering at 163 MeV ; a, b, and c as for Fig . 7 . 3 .3 NEUTRON RADII FROM PION-NUCLEUS ELASTIC SCATTERING Until very recently, there has been considerable activity 26,2 ~) using n+ and n- ES to extract neutron radii or, somewhat less ambitiously, differences between neutron radii of adjacent isotopes . In most of this work the proton point distribution is assumed to be known from electron scattering and n + and ~ ES are then fittedpp by varying the neutron distribution . The response to these studies has ranged from enthusiastic support to skepticism . Possibly as a reaction to the criticism, not a single contribution to this session reports on a determination of a neutron radius (see, however, contrib . D8, F17, F18, etc) . In my opinion this trend will be reversed within the next few years as present theories on n-nucleus interactions are being improved . I even dare to say that many of the results obtained so far will hold their own since the uncertainties in treating ~r-nucleus scattering are very similar for ~rr} and n - and should çancel to a large extent in comparative studies of ~+ and n - ES . Zeidman et a1 .z 8 ) derive differences Qr tween th rms radii of the neutron and protô distributions j2 for 4 8Ca (0 .12 fm ± 0 .05 fm) and RO Pb (0 .07 fm ± O .U7 fm) Dr = 1 ~~ - < r2 >l e which are considerably smaller than the values Qm a DDHF calculation29)(0 .19 fm for 4 8Ca and 0,2 fm for 208pb), The pion values~~) agree with more recent theoretical estimates3 0 ) (0 .14 fm for 48Ca and 0 .13 fm for 208Pb) . For 4 8Ca the value from an early analysis of $00 MeV proton scattering 31)(Or = q .23 fm) is much larger than from ,r± scattering, but the more recent analysis32) of the same proton data and new data at a lower energy (500 MeV) suggests that there are sizeable nuclear matter corrections which have to be understood before Dr values can be extracted reliably . It should be kept in mind that rms radius differences of the order of 0 .1 to 0 .2 fm are significant . For 48Ca a decrease in the neutron rms radius by 0 .1

PION-NUCLEUS INTERACTIONS : EXPERIMENTS

38 5c

fm corresponds to an increase in the central density of about 10% . 33 ) . Thus work on neutron radii measurements will continue . Especially fruitful should be the attempts to obtain consistent results from pion, proton, neutron, alpha, and electron scattering at several incident energies as well as from pionic and muonic atoms . 4 . Pion-Induced Single-and Double-Charge-Exchange Reactions 4 .1 . SINGLE-CHARGE EXCHANGE REACTIONS (SCX) Perhaps the most sensitive method of deriving neutron ground-state densities p for T > 0 nuclei from ,r-nucleus interactions should be provided by the (~+~ .~o) single-charge-exchange reaction leading to the isobaric-analog state (IAS) oß~h3 5 target ground state . Several reviews on the ,r-induced SCX have appeared ~ ) so that I can restrict myself to a few basics and some recent developments . Assuming isospin invariance, the ,r-nucleus optical potential may be written

where Tn and T are the isospin operators for the pion and the target, respectively . The Up , U1, and Up are complicated functions of the nuclear density, the n-nucleon t-matrix, and the ~r-nucleus reaction mechanism . In lowest order U1 is proportional to p n - p . It is the driving term f r the direct SCX reaction to the IAS . Previous to t~e data of H .4j Baer et a1 .~6)(n+,,r°) reactions had been studied by ~~dio-activity methods . 3 ~ . For T3C(n+,pro) severe difficulties were encountered) in the attempts to interpret the large total cross-sections and their energy dependence . Although the new good-resolution data with the Los Alamos ~r° spectrometer37)(contrib . H23 and H24) are lower in absolute cross-sections (Q ~ 0 .80 ± 0 .15 mb instead of the previous 0 .95 ± 0 .15mb at resonance)there are still difficulties in reproducing the experimental values . For example, Hirata38) gets a = 0 .3 mb using the ~-hole model . These difficulties suggest that the (,r+,~) reaction is not a simple one-step SCX process . If this were correct SCX to the IAS would not be ve~,~ valuable in extracting pn - pp . . Johnson and Siciliano )have recently developed a unified approach to ES and SCX and DCX reactions to IAS and double-IAS using isotensor terms in addition to the isoscalar and isovector terms . They abandoned the N/Z density scaling of many other studies (i .e . p n = N/Z pp where pp is taken from electron scattering) in favor of more realistic densities . They also demonstrated the high sensitivity of SCX to small changes in the well parameters used in calculating the proton and neutron ground-stat d s 'es and to higher or~er terms (p ) in the density . Figut~ 9 shows data~0~~~~~~1. and calculations 4 3 for 180 + ~ ES, 18 U(n + ,~o ) SCX, and 180(~rr~,,r-) DCX (the latter to be discussed in Section4 .2) .The broken lines were obtained using p = N/Z pp . The solid lines are from a calculation in which p n and were deriveâ from wave functions calculated in a Woods-Saxon we 11 which producespp a p consistent with electron scattering . For the neutrons all well parameters were ~Cept the same except for the symmetry term . In this calculation p n sticks out beyond p more than for simple N/Z scaling and the SCX cross-sections are affected dramatically but ES is changed only very little . This calculation fits the only preliminary data point fo 180(n + ,~o) at 5 ° (Lab) of Doron et a1 . 41 ) . This model is now being applied to the ~3 C problem . If ~he 13C problem can-6e solved by use of more realistic densities and perhaps p terms it will be a major step in proving that SCX reactions to IAS provide a sensitive method of extracting the differences between the proton and neutron densities in the ground state . 4 .2 . DOUBLE-CHARGE-EXCHANGE REACTIONS (DCX)

Several recent peviews on DCX reactions exist44 , 45 , 46 ), pne of the mot promising recent developments has been the successful fit by Greene et al 3)

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18 0( to the ,+ ,~r ) DCX angular distribution at 164 MeV (Fig . 9 dash-dotted line) by the inclusion of p2 terms in the optical potential . Previous theoretical work treated the DCX as a two-step SCX due to the two-fold application of the isovector U~ term in the optical potential and could not reproduce the position of the first mim mum . The isotensor term Up had been left out in these calculations since its lowest order ~~~ is second order in p a2d it had been assumed to be small, Johnson and Siciliano have pointed out that p terms affect magnitude and shape of the DCX cross-sections . They depend very strongly on the ratio of the isotensor to isoscalar coefficients in the optical potential . The authors of refs . 39 and 43 succeeded in reproducing the position of the first minimum in the angular distribution which could not be explained 4 ~) by the U1 term alone . A preliminary fit to the 180 (,r+,n ) data with a U 2 term and p2 terms in Uô and U1 had already been shown in ref . 45 . Work on fitting the excitation function42) at 6~ a b = 5 ° for 180 0+,~ ) is underway . Although the successful fit of the anomalous-small-angle minimum may be considered a big step in the understanding of DCX, the model of ref . 39 does not treat non-analog transitions which, at some energies, have cross sections comparable to those of the double-IAS transitions .

E

v b v

Figure 9 Differential cross-sections for 180 + rr + ES (ref . 40), SCX (ref . 41) and DCX (ref . 42) reactions at 164 MeV . Calculations of ref. 43 (see text) .

180 0+ ,~ ) excitation function An attempt to interpret the shape of the result of an interference of a di~ect double-IAS amplitude from an early DCX theory48) (whiçll includes some 2n order effects) and a non-analog amplitude led after the 1 b0(rr+ ,~ ) cross sections is discussed by S . J . Greene _et _a1 .4 in contribution H27 . Further evidence for the shortcomings of conventional approaches to DCX

as a giodel!2 is

PION-NUCLEUS INTERACTIONS : EXPERIMENTS

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provided by the recent observation by Seth et a1 . 49 ) of a DCX-cross-section ratio R = Q( 4 8Ca)/a(42Ca) of R s 2 ± 1 in scarpcontrast to the prediction of R ~ 20 without consideration of p2 terms (contribution H28) . 5 . Pion Inelastic Scattering (IS) + + 5 .1 . (~ ,n - ')ON N = Z NUCLEI

For transitions between states of good isospin, pion IS on N = L nuclei should yield the same cross-sections for ~+ and ~ (except for small Coulomb effects) . However large asymmetries A = (Q- - a )/(a - + a+) were observed experimenta11y50,51j for 12C and 160 for a number of states . These results were in terpreted as due to isospin mixing o~ a 4 - doublet 50) and a 1+ doublet 50) in C and a triplet of 4 - states5l) in 1 O . .Fpr 160, there exists now ~ complete set of data on pion5 l)(Fig . 10), electron 52 )(fig . 11), and proton 53 (fig . 11) scattering for the unnatural parity transitions to the "stretched" 4- states near 19 MeV . The pion data required only a negligibly small DT = 0 admixture in the transition to the 18 .98 MeV, T = 1 state but DI = 1 admixtures 5 ~f . ~ ± 25v in the )V transitions to the two T = 0 states at 17 .79 MeV and 19 .80 Me Use of these isospin mixed tr~p$ition densities has a rather dramatic effect on the (e,e') predictions . 54 ~ .The cross section for one state (17 .79 MeV) increases by a factor of 5 . For the other state (19 .80 MeV) it decreases by a factor of about 10 . This is due to the strong enhancement of the DT = 1 piece in the transition density amplitude in transverse magnetic transitions . The ~T = 1 piece then interferes with the ~T = 0 piece, constructively for the 17 .79-MeV state and destructively for the 19 .80-MeV state . However, for (p,p') to the T = O,states, the DT = 1 admixture has only a small effect since the DT = 1 and ~l = 0 parts of the nucleon-nucleon force at 135 MeV are not as different as the 4T = 1 and DT = 0 spin-dependent parts of the electron-nucleon interaction . The good agreement between the DWIA calculations and the data for the three different probes is strong support for the contention that the transitions to these stretched states are well understood as simple particle-hole (p-h) excitations . Similarly, good agreement was obtained in an analysis 55) of (e,e'),(p,p'), and (~r, ,r') data for the exc'tation of the states of the If7/2 d6I/2T6- stretched configuration in ~BSi . + + 5 .2 . (~r- ,n - ') ON N ~ Z NUCLEI 5 .2 .1 . 26Mg(T~,~') : A ~+ -enhanced collective transition T ical examples for pion IS on N ~ Z nuclei are ~he work on 180 (refs. 4~ 56) and ~gMg (re~~ 56,57) . In Fig . 12 the 26 Mg (0+ -~ 21) data of Wiedner et al and Zichy et al . /)are shown together with a DWIA calculation5 7 ) using a co-TTective form ~ctôr . The cross-section ratio is R = a(n+)/a(n") = 1 .6 . A ratio R = 1/9 is expected if this transition would involve solely a recouplin~q of the two "valence" neutrons . However, in the simple shell model the lowest 2 state in 2 Mg is due to the recoupling of the two proton holes in the "closed-shell" nucleus 28 Si . This model would lead to a ratio R = 9 . The experimental value of R = 1 .6 is consistent with the collective nature of this transition, i .e . many proton and neutron components contribute . Still, a significant component in the transition amplitude must be due to the (d /2)ß+P -~ (d5/2)Z+ P transition leading to the (~+~n+~) enhancement . Similar reductions of the fro 56 nucleon value of R due to the collectivity of the transitions have been seen 4 ~ )for 180 and other cases . 5 .2 .2 . 13C(n,,~,)13C(g .5 MeV) . A pure neutron particle-hole transition The first evidence 58 , 59 ) for a ratio R -1 = 9 .indicating a pure neutron p-h transition was found for the odd-A nucleus 13C . .(Fig . 13a) . Here a transition

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Differential cross sections for 160(n±,,r±) at 164 MeV to 4 - states (ref .51,b5) IÔ 2

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Figure 11 _ Transverse magnetic form factor for excitation of 4 states in 16 0 (ref . 52) (left) and differential cross sections for 16 0(p,p') at 135 MeV to states (ref . 53) (right) . Theoretical curves : ref . 54 .

4

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PION-NUCLEUS INTERACTIONS : EXPERIMENTS

to a state at 9 .5 MeV was identified as due to a simple p3/2 + d5/2 neutron excitation . A high-spin state (J~ = 9/2+) had been predicted60) at this energy as due to the weak coupling of a d5/2 neutron to the ~irst excited state in 12 C(2+) . The only way to reach thisf(2+, T = 0) ® ( d5/2) 19~2+ state in a one-step p-h excitation is by the promotion of a p3/2 neutron fro(n a f(2+ ,T = 0) ® (p3/2)nl~/2_ component in the 13C ground state to shell . This simple picture wa confirmed by two shell model calculationst ~ 622which

61

yielded la~~ neutron transition density amplitudes, An = 0 .63561 nd An = 0 .666 ~ but vanishingly small proton amplitudes, = 0 .001 1~ and AP Ap = 0 .00362) . If only transitions from the p to sd shell are considered, the transition to this state can proceed only by an orbital angular momentum transfer to the nucleus DL = 3, a spin transfer DS = 1 and a tptal angular momentum transfer 0J = i3 like fo63 tF~e "stretched" 4- states in 1ZC a65 160. 66 C(e,e) 4) and ~ 3 C(p,p ) data at 547 MeV )and 800 MeV )are now also available for this state . They strongly support the simple particle-hole excitation suggested above . In (e,e') a strong M4 transition is observed and fitted very well with a harmonic oscillator parameter b = 1.5 fm .63)(Fig . 13b) . We have used a transition density very close to the one from the (e,e') analysis in a DWIA calculation for (~r,~r') with the code of Lee .67) . The result is the broken line in Fig . 13a . The predicted cross sections peak at a larger angle than the ( ,r,~') data and are generally too large when normalized to the (e,e') absolute normalization which indicates about 70% of the theoretically predicted 6 l) p3/2 + d5/2 strength . Like Lee68) in his early calculations for this transition we find a much better fit (Fig . 13a, solid lines) to the n data with b = 1 .67 fm (not corrected for recoil) However, the overall normalization using the shell model transition densities68) is now ~ 0 .5 and not ~ 1 .0 as in ref . 68 . The new value of 0 .5 is partially due to a renormalization of the preliminary data by a factor of 0 .75 and partially caused by a 30% increase in the DWIA calculation due to the use_of different distortions . This reduced strength is now more in line with data for other transitions to stretched states55)(16p and 28Si) . Work on the proton data is in progress . 5 .2 .3 . 13C(,r,~r') : Transition to the 1/2+ state at 3 .09 MeV For the natural-parity, collectively-enhanced transitions to the 3/2 and 5/2- states and several other states the DWIA calculations of Lee and Kurath67,68) do very well if enhancement factors consistent with electromagnetic transition rates are used . (For a summary of the 13C results see ref. 59) . There are, however, a number of significant discrepancies between theory and experiment for the "single-particle" 1/2* (3 .09 MeV) and 5/2* (3 .85 MeV) states (fig . 14) . In the simple shell model the e states are due to the coupling of a+ 2s1/2 . and ld5/2 neutron, resp ., to the 1~C core . I will discuss the I/2- + 1/2 transition ~n same detail since it demonstrates once more the power of comparisons of (,r,n'), (p,p') and (e,e') data . The shell model calculation61,68) predicts this transition to be mainly due to a lpl/2 + 2s1/2 neutron excitation but there are other non-negligible components, especially a lp3/2 + ld5/2 transition amplitude that interferes destructively with the lpl/2 + 2s amplitude . The n- data are reproduced quite nicely /2 in this model68)~but the ~ data are about a factor of 3 to 5 larger than the prediction . This suggests that the neutron part of the transition is correctly described by the shell model but not the proton part . This tentative conclusion is supported by aimilar discrepancies in electron scattering . In (e,e') the experimental longitudinal form factor63) (due to the interaction with the nuclear charges) (fig . 15) is about a factor of 5 larger than from theory . The discrepancy between theory and experiment is much smaller for the transverse form factor which, according to the model, is largely due to the interaction with the magnetic moment of the neutrons . This indicates again that the neutron part is better understood than the proton part . A large discrepancy between theory and experiment was also found in 547 MeV (p,p') data . 6 5) . The consistent deviations from theoretical prediction for all

390c

D. DEHNHARD

Fig . 12 . O~fferential cross sections for 26 Mg(n , , r') at T.~ = 180 MeV (ref . 56,57)

q (fm ~)

L

N

Fig,13a. left Differential cross sections for 13C(n-,,r±'~ at 162 MeV to the 9 .5 MeV state. {see text) ( data of ref, 59) Fig .13b . (ri ght) Transverse magnetic form factor for 13C(9,5 MeV) . Data of ref. 63 and 64 . Calculations of ref . 63 .

- b=1.67fm _- b=1.46fm 30

60 '

i ' 90 ,

9~ r~ (Degrees)

` 120

PION-NUCLEUS INTERACTIONS : EXPERIMENTS

391c

Fi gure 14 Differential cress-sections for 13C(ß±,~r±') at 162 MeV to 1/2+ (3 .09 MeV) and 5/2+ (3 .85 MeV) states, (ref . 59) .

Figure 15 Longitudinal (left) arld transverse (right) form factors for 13 C ß .09 MeV, 1/2+ ), (ref . 63) .

39 2c

D . DEHNHARD

three probes make it quite likely that it is the nuclear structure part of the calculations that is the problem rather than the DWIA analysis of these data . 5 .2 .4 . Large ~+/,~ asymmetries in llg(~~~~) Like the transition to the "stretched" st~te in 13 C(9/2+ ),a similar pureneutron pg/2 ~ d5/2 transition is expected in 1B to an 11/2+ "stretched" configuration . Indeed ,such a state was observed at 14 .04 MeV by Geesamam et al . (contrib . H15) . It displays a very large ~- enhancement (Fig . 16) . Transitions to several other states also show large asymmetries, some being more strongly, excit d b ,r+ than ~- . These data are now being compared with DWIA calculations~ 7 + 6~) using shell model transition densities6 7,b8,61) . 14C(,~,n') 5 .2 .5 . : Strong cancellations of neutron and proton components in the transition In a recent (~r,~r') experiment69) on 14 C by D .B . Holtkamp et al . (contrib . H17) cross section ratios R (or R-1 ~ considerably larger than 9 were ~~und . C . The Fig . 17 shows a spectrum at Blab = 42 near 8 MeV excitation energy in second 2+ state at 8 .32 MeV is quite prominently excited by ,r+ but is not

W Z 2 Q 2 U

100

r z

0 U

100

EXCITATION ENERGY (Mev)

Figure 16 ~gectra from ,r+ and ~ scattering from B at162 MeV and 70°(Lab),(ref .69) .

EXCITATION ENERGY (MeV) Figure 17 l ~pectra for n+ and ~ scattering from Cat 164 MeV and 42 ° (Lab), (ref . 70) .

PION-NUCLEUS INTERACTIONS : EXPERIMENTS

393c

visible in the n spectrum . In contrast, the first 2+ state is almost equally excited by ~+ and ~ . At a larger momentum transfer ( 8]ab = 66°, Fig . 18)

4 wC 2 200 ELASTIC I

_ 3_ 2 , . g .7_ 7,0 8 .3 10.4 11 .7

15.1

4_ 17.3 164 MeV 66°

150

~r ,

100 Z

m 50

Y 0

6 .7 7.0 8.3 10.4 11 .7

tn

H Z O 120 U 80

15 .1

17 .3

a l Î2

0

5

~I ~' Y""fil~~~r'~I~'~~~~~r~~~ 10 15 ~0 25

EXCITATION ENERGY (MeV)

Figure 18 Same as Fig . 17 but at 66 ° (Lab) . a state at 11 .67 MeV is seen only by n' and a state at 17 .26 MeV is observed essential~,~ only by ,r+ . The C(n,~r') data for the 2~ state at 8 .32 MeV give a lower limit for the value of R > 26 at 42 ° (Lab) and for the 2i state at 7 .01 MeV the ratio is R = 1 .1 . The lack of any observable cross-section in (~ ,n ') for the 22 state at 42° (Lab),which is near the maximum of well known DL = 2 transitions ,can be interpreted as due to an almost complete cancellation of the neutron and proton parts of the transition amplitudes, An and Ap, respectively . For the ~ cross section to be zero th~ simple plane-wave-impulse approximation result for a- ~ ~3An + App suggests an amplitude ratio A /A n = -3 . Such a ratio can be understood as a çonsequence of two facts : a rélatively sm211 neutron 4)adm~~Cture L. (lp) - (2sd1) n] to-the principal proton 2~omponent(1~ P in 2~he g .s . of C and thè almost complète mixing of the (lp)p+ andL(1p) - (2sld) confi]2+ gurations in the two 2+ states near 8 MeV . (see e .g . ref . 71) . Due to the relative phases of the two components in the wave functions the interference o~ the neutron and proton parts will be constructive for the transition to one 2 state and destructive for the other . Because of distortions and because the

394c

D. DEHNHARD

(sd) 2n and (p) -2 p form factors have slightly different radial dependences,the destructive interference of the two parts will be angle dependent. Indeed,there are small ~ cross sections indicated for the 8 .32 MeV state at some angles sugges ~ng an an ular distribution shape very different from the data for the 2i . state 7 .01 MeV) which result from a constructive interference . For the 2~ state in (,r+,~r+')the destructive interference is much smaller than for (~r ,n-') and the angular distribution shape is affected only slightly . DWIA calculations by S. Chakravarti72) using weak-coupling-model predictions73) for the transition density amplitudes reproduce the data for both 2+ states very nicely (fig . 19) .

14C (~r +, ,r +'

EX =7.01MeV

î

+ 21

N

É t0 -t E

~C7

b 10_ 2

)

8.32 MeV 2p

- Preliminary

40

DWIA 60

80

20

40

60

g0

9~.m .(Degrees)

Figure 19 Differential cross-sections for 14C(ß±,n±') at 164 MeV to the 7 .01 MeV (2i) and 8 .32 MeV (22) states, (refs 70 and 72) . Thus pion IS allows an unusually sensitive test of small admixtures in nuclear wavefunctions . The same kind of interference effect appears to be responsible for the highly asymmetric cross sections for the two states at 11 .67 and 17 .26 MeV mentioned above . Based on the angu]7~ distributions for these states (not shown) and theoretical estimates of Kurath ~ we propose these to be 4- stretched states . 5 .2 .6 . Excitation functions for pion inelastic scattering at constant momentum transfer In the energy region of 13 ;31 resonance dominance (T .~ ~ 100 to ~ 300 MeV) the different energy dependences of the spin-dependent and spin-independent parts of the pion-nucleon force provide a very sensitive method of discriminatin between DS = 1 (spin transfer to the nucleus) and DS = 0 transitions75+76,70 . At constant momentum tran~fer the energy dependence of DS = 0 transitions is expected to follow ~ simple cos e dependence and DS = 1 transitions are expected to follow sin 9 in the fixed-scatterer approximation . The scattering angle 6 at constant q is only a function of the incident pion energy .

PION-NUCLEUS INTERACTIONS : EXPERIMENTS

395c

Some results for 12 C and 13 C have been shown at the Va ouver conference .78 ) Fig . 20 contains the data of Seestrom-Morris et a1 .77) for ~~C + n+ IS to the

Figure 20 Excitation functions ld for 13C(n+,~rr+') at q = 1 .1 - t~'fm-l for a 3/2- state at to the 9/2+ state 3 .68 MeV and C(~ ,,r - ') at q = 1 .4 h'fm at 9 .50 MeV . 3/2- state which is dominated by the DS = 0 transition density amplitude67 ) . The excitation function follows the simple cos2 e relation and is fitted extremely well by a DWIA calculation with a collective form factor . The data for the 9/2+ state follow a sin e dependence inst king confirmation of the pure DS = 1 nature of this transition as derived5~~ from the large asymmetry and q-dependence of the cross sections at 162 MeV . Since natural-parity transitions are usually dominated by DS = 0 and since unnatural-parity transitions can proceed only by 0S = 1 (if Fermi motion corrections are neglected) it appears safe to say that the strong signal for DS = 1 versus 4S = 0 as indicated by these data will find extensive applications in nuclear structure physics . Use of (~r,~r'1 excitation functions in searches for DS = i giant resonances (contrib . H18) 79) should be particularly promising . 5 .2 .7 . An anomalous excitation function for

12C(~,,~')12C(1+,T

= 1, 15 .11 MeY)

Very recently, Morris et al~ have reported work on excitation functions for 1 C(~,T~') to the two 1+sties at 12 .71 MeV (T = 0) and 15 .11 MeV (T = 1) . Since these states are of unnatural parity their excitation functions should follow a simple singe relation, i .e . the cross-sections at constant q (e .g . at fhe first maximum in the angular distribution) should decrease from T~ = 100 MeV to T.~ = 225 MeV . This expected behavior is observed for the T = 0 state but not for the T = 1 state (fig . 21) . The particle-hole structure of the two 1+ states is very similar67) . Thus for f3,3] resonance dominance, the T = 0 state should be excited four times more strongly than the T = 1 state if the transition is due

396c

D . DEHNHARD 12 C(~rr,a') IZ C

q=124Me1//c

R ~ 4rT(15 .11) Q(12 .711 2

12C(n,~') Figure 21 Excitation functions for at q = U .b3 h'fm 1 for 1+ states at 12 .71 and 15 .11 MeV . Top : Ratio R = 4x(15 .11 MeV)/x(12 .71 MeV) . Bottom : Differential crosssections x for the two states . Curves : DWIA calculations, (for details see ref.BD) . to a simple particle-hole excitation . However, this is the case only at lower energies . At resonance the two states are excited with comparable strength . Morris, et al .suggest that these data are an indication of a e=Yiole admixture in the T= I-state at 15 .11 MeV . (A n-hole configuration can couple only to T = 1 or 2. Thûs it would play, no role in the T = 0 state) . If this suggestion is confirmed ,it would be one of the more fascinating results in nuclear structure physics in recent years .

PION-NUCLEUS INTERACTIONS : EXPERIMENTS

39 7c

6 . Conclusion Data taken and to be taken in the next few years at the meson facilities for elastic and inelastic ~ scattering and for ,r-induced single-and double-chargeexchange reactions provide a base for a deeper understanding of the properties of the nucleus than attainable with conventional probes alone . Precise elastic scattering measurements done over the whole angular range and at many energies place constraints on the parameters of microscopic models of ~r-propagation in the nucleus . Problems with (n+ ,n°) single-charge exchange to the isobaric analogue of the target ground state are currently being solved . This reaction might give the most sensitive method of determining the distribution of the neutron excess pn -pp . (,r+ , ) double-charge-exchange data now show strong evidence for the importance of an isotensor term in the optical potential Its microscopic interpretation in terms of nucleon correlations and other fundamental nuclear properties constitutes a challenge to nuclear theory . Inelastic scattering enables a separation of the neutron and proton parts of the transition density. For example, recent (~r, ,r') results on the carbon isotopes has yielded informatiôn on isospin mixing, a pure-neutron excitation, strong cancellations of the neutron and proton parts of the transition density and also on strongly different excitation functions for DS = 1 and 4S = 0 transit'ons . A very recent report of an anomalous ~T = 1, oS = 1 excitation function in1~C(~r,~r') 1 (15 .1 MeV) shows an indication for a new and intriguing aspect of nuclear structure.

n

X

Acknowledyements Finally I must mention at least a few of the people who contributed in various ways to this report . J . Alster, R. Boudrie, D . Fitzgerald, R . Freedman, S . Greene, D . Holtkamp, R . Hicks, C . Morris, B . Preedom, F. Petrovich, M. Sadler, E . Siciliano, D . Sober, and B . Zeidman supplied experimental data and/or calculations prior to publication . H . Thiessen, J . Amann, R. Boudrie, D. Holtkamp, C . Morris, and S . Seestrom-Morris made it a pleasure to use the EPICS facility at LAMPF . In addition to these colleagues, H . Baer, B . Bayman, S . Chakravarti, W . Cottingame, P . Ellis, M . Franey, G. Hoffmann, D. Kurath, and H . Lee provided many helpful discussions . Special thanks are due to Mrs . L . Cordova and Mrs . B . Parent for their help in preparing this manuscript . This work was supported in part by the United States Department of Energy . References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

Q. Ingram, Invited talk, presented at this conference M.E . Sadler et al ., Contribution H10 Particle Data Group, Rev . Mod . Phys . 52 (1980) S1 D.H . Fitzgerald et al ., Proceedings o~the Baryon 1980 Conference, Toronto, ed . by N . Isgur V .S . Bekrenev et al ., Contribution H7 T.G . Masterson et al ., Contribution H8 and to be published in Phys . Rev .Lett . R .C . Minehart et al ., Contribution H9 B . Balestri et al ., Contribution H11 J . Bolger et al ., Phys . Rev . Lett . 46 (1981) 167 B .G . Ritchie et al ., Contribution HST and preprint . See also contributions to Session A for ref . to the inverse reaction, p+p-.~r++d B .M . Preedom et al ., Phys . Rev. C23 (1981) 1134 F .E . Obenshain et al ., Contributiôn H3 H . Degitz, Contribution H4 . For earlier work see, e .g ., G .S . Mutchler et al ., Phys . Rev . C11 (1975) 1873 M . Kaletka,~ntribution H13 L .C . Liu and C .M . Shakin, Phys . Rev . C19 (1979) 129 H . McManus, Private Communication in rß .12 L. Antonuk, Contribution H14 E . Bason et al ., Contribution H6 and preprint

398c 19) 20) 21) 22) 23) 24) 25) 26)

27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 55) 56) 57) 58)

D. DEHNHARD J .P . Albanese et al ., Nucl . Phys . A350 (1980) 301 B . Chabloz et al ., Phys . Lett . 81B~379) 143 M . Hirata et al ., Ann . Phys . 12(1979) 205, and Y . Horikawa, M . Thies, and F . Lenz, Nucl . Phys . A345 (19$6j 386 R .A . Freedman, G .A . hfilTer, and E .M . Henley, preprint R .A . Eisenstein and F . Tabakin, Comp . Phys . Comm . 12 (1976) 237 R .A . Eisenstein and G .A . Miller, Comp . Phys . Comm.8 (1974) 130 W .B . Cottingame and D .B . Holtkamp, Phys . Rev . Lett . ~3 (1980) 1828 See for example : Proceedings of the Eighth Internatiônal Conference on High Energy Physics and Nuclear Structure, Vancouver, August 1979, ed . by D .F . Measday and A .W . Thomas, Nucl . Phys . A335 (1980), and contributed papers, unpublished J . Alster, in Proceedings of the Workshop on Nuclear Structure with Intermediate-Energy Probes, Los Alamos, Jan . 14-16, 1980, p .119 B . Zeidman, Proceedings of the 14th LAMPF Users Group Meeting, Los Alamos, Oct . 27-28, 1980, p .91, and B . Zeidman et al ., Phys . Rev . Lett . _40 (1978)1316 J .W . Negele and D . Vautherin, Phys . Rev . C5 (1972) 1471 J . Dechargé and D . Cogny, Phys . Rev . C21 ßf980) 1568 L . Ray, Phys . Rev . C19 (1979) 1855,an3~.W . Hoffman, see ref .27, page 99 L . Ray et al ., Phys.îFev . C23 (1981) 828, and G .W . Hoffmann, Private commnunication M .J . Jakobson et al ., Phys . Rev . Lett . 38 (1977) 1201 J . Alster and s . Warszawski, Phys . Rev . -52C (1979) 87 and references therein Proceedings of the LAMPF Workshop on Pio~ingle Charge Exchange, Los Alamos, Jan . 22-24, 1979, ed . by H . Baer, J . Bowman, and M . Johnson, LA-7892-C, unpublished H .W . Baer et al ., Phys . Rev . Lett . 45 (1980) 982 A . Doron et al ., Contributions H23 an3 H24 M . Hirata, Preprint M .B . Johnson and E .R . Siciliano, Preprint S .G . Iverson et al ., Phys . Rev . Lett . 40 (1978) 17, and Phys . Lett . _82B(1979) 51 ; See also C . Lunke et al ., Phys . Létt . 78B (1978) 201 A . Doron et al ., to be published and J . Alstér, Private Communication S .J . Greene et al ., Phys . Lett . _88B (1979) 62, and S .J . Greene, Preprint and Contribution H27 S .J . Greene, M .B . Johnson, and E .R . Siciliano, Private Conmunication . For another calculation that succeeded in reproducing the small-angle minimum see contribution G37 K . K . Seth, ref .35, page 201, and K .K . Seth, Proceedings of the LAMPF Workshop on Intermediate Energy Nuclear Chemistry, Los Alamos, June 23-27, 1980, unpublished . G .R . Burleson, ref . 27, page 195 K . K . Seth et al ., Phys . Rev . Lett . 43 (1979) 1574 S .J . Greene, Ph . D . Thesis, Univ . o~Texas (1981) G .A . Miller and J .E . Spencer, Ann . Phys . 100 (1976) 562 K .K . Seth et al ., Contribution H28 C .L . Morris et al ., Phys . Lett . 86B (1979) 31, and C .L . Morris et al ., Phys . Lett . 99B (1981) 387 D .B . Holtkamp et al ., Phys . Rev . Lett . 45 (1980) 420 C . Hyde, Private Communication to F . Petrovich R .S . Henderson et al ., Aust . J . Phys . 32 (1979) 411 F . Petrovich and W .G . Love, Proceedings International Cônference on Nuclear Physics, Berkeley, Aug . 1980 ed . by R .M . Dianand and J .O . Rasmussen, Nucl . Phys . A254 (1981) 499c D .B . HolTamp, W .B . Cottingame, D . Halderson, J .A . Carr, and F . Petrovich, to be published C .A . Wiedner et al ., Phys . Lett . 78B (1980) 26 M . Zichy, Ph . D . Thesis, ETH ZUricl, 1980 D . Dehnhard et al ., Phys . Rev . Lett . _43 (1979) 1091, and E . Schwarz et al ., Phys . Rev . Lett . 43 (1979) 1578

PION-NUCLEUS INTERACTIONS : EXPERIMENTS 59) 60) 61) 62) 63) 64) 65) 66) 67) 68) 69) 70) 71) 72) 73) 74) 75) 76) 77) 78) 79) 80)

39 9c

S .J . Seestrom-Morris, Ph . D . Thesis, Univ . of Minnesota, 1981 A.M . Lane, Rev . Mod . Phys . 32 (1960) 519 D.J . Millener and D . Kurath,Nucl . Phys . _A255 (1975) 315, and D . Kurath, Private Communication J .F . Dubach, see ref .27, page 72 R. Hicks, Private Communication D .I . Sober, Private Communication S .J . Seestrom-Morris and M .A . Franey, Private Communication G .S . Blanpied, Private Communication T.-S .H . Lee and D . Kurath, Phys . Rev . C21 (1980) 293 T .-S .H . Lee and D . Kurath, Phys . Rev . l'2'f (1980) 1670 D .F . Geesaman et al ., Contribution H15 D .B . Holtkamp et al ., Contribution H17 and preprint N .F . Mangelson et al ., Nucl . Phys . A117 (1968) 161 S . ~Chakravarti, Private Communication P .J . Ellis, Private Communication D . Kurath, Private Communication W .B . Cottingame et al ., Bull . Am . Phys . Soc . 24 (1979) 821, and to be published E .R . Siciliano and G .E . Walker, Phys . Rev . C23(1981) 2661 S .J . Seestrom-Morris et al ., Phys . Rev . Lett ._46 (1981) 1447 H .A . Thiessen, Ref .26, page 329 C .F . Moore et al ., Contribution H18 C .L . Morris et al ., Preprint