REPRODUCTION C(3W Hadronic Atoms and Ticklish the E2 Nuclear

LA-5994-MS Informal Report UC-34C Reporting Date: May 1975 Issued: June 1975 :C3●

4 @-14 REPORTGOL\-=TION REPRODUCTION C(3W

Hadronic Atoms and Ticklish Nuclei: The E2 Nuclear Resonance Effect

M. Leon

IosWalamos * scientific Laboratory of the University of California LOS ALAMOS, NEW MEXICO 87544 ~“

/\ An Affirmative Action/Equal Opportunity Emplayer

UN ITEIJ STATES ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION CONTRACT W-740 S-ENG. S6 In the interest of prompt distribution, this report was not edited by the Technical Information staff.

Based on an invited paper presented at the Washington, DC, APS Meeting, April 28- May 1, 1975.

PrintedinthoUnitedStatuofAmorka.Awdlahlefrom NationalTachniuxlInformation!kvks U S D.pmtmontof (?-ommuce 52S5PortRoyalRoad Springftold,VA 22151 Pria:titod tipT~.~ Microfiche~.~ HAORONIC ATOMS AND TICKLISH NUCLEI: THE E2 NUCLEAR RESONANCE EFFECT*

M. Leon

ABSTRACT

The E2 nuclear resonance effect in hadronic atoms offers a way to increase the I hadronic informationthat can be obtained from hadronic x-ray experiments. The effect occurs when an atomic deexcitationenergy closely matches a nuclear excitation energy, so that some configurationmixing occurs. It shows up as an attenuation of some of the hadronic x-ray lines from a resonant versus a normal isotope target,

The effect was observed very clearly in pionic cadmium in a recent I.AMPFexperi- , ment. A planned LAMPF experimentwill use the nuclear resonance effect to determine whether the p-wave r-nucleus interactiondoes indeed become repulsive for Z 2 3S as predicted_. The effect also appears in the kaonic molybdenum data taken at LBL because several of the stable molybdenum isotopes are resonant.

A number of promising cases for T-, K-, ~, and Z- atom~ are discussed and a spectacular and potentiallyvery informativeexperiment on p 100MO is proposed.

The motive underlying this subject is the de- sire to increase the strong interactioninformation that can be extracted from the study of hadronic atoms. In muonic atoms, informationabout the size and shape of the nucleus comes from the x rays from transitionsbetween the most tightly bound levels, for which the overlap with the nucleus is signifi- cant. In hadronic atoms, in contrast, the corres- ponding x rays are nearly all missing because the hadron reacts with the nucleus. In fact it is only last remaining hadronic x-ray transition that has any strong interaction informationat all. The sit- Fig. 1. The last, i.e., lowest, x-ray transition uation is sketched in Fig. 1. The most we can hope which contains the strong interaction in- for is some informationon (1] the absorptive width formation. of the upper level, since the ratio of absorptive level, since these are also the shift and width of width and radiative width determines the yield of the last x ray. As the Z of the nucleus increases the last x ray compared to the preceding one; and so do the shift and width, while the yield decreases, (2 and 3) the hadronic energy shift (from the until the line melts into the background. Then purely electromagneticvalue) aid width of the lower there is a gap in Z until the next higher transition

* begins to show a decreased yield, etc. Thus any Based on an invited paper presented at the Washing- additionalhadronic information is very welcome, and ton, D.C. APS Meeting, 28 April-1 May 1975. at least for a few nuclei, the E2 nuclear resonance

1 effect offers an opportunityfor just that. Having set the stage, I can now introduce the main theme. Nuclear excitationby negative muons [(21+1)(21’+1)(21+1)(22’+1)]1/2 bound in atomic orbits is a familiar topic. Since the muon in its lowest orbits gets quite close to, (:::;) (::’){:;:;} o or even inside, the nucleus, the tidal forces are (This equation is included only to satisfy the theo- extremely strong, and thus the probability of excit- retical voyeurs in the audience.) Besides the angu- ing a IItidal~ave!lon the nuclear surface is quite lar momentum factors, we have Q. which is the nuclear large. The situation for negative hadrons is dif- quadruple strength, and ~hich measures the ferent because the hadron is absorbed while most of orbital quadruple strength. This last factor can its wave function is far outside the nucleus; only a easily and quite adequately be evaluated using point small tail penetrates the classicallyforbiddenre- Coulomb wave functions. Q. comes directly from the gion (centrifugalbarrier) to reach the nucleus it- measured Coulomb excitation cross sections [B(E2t) self. As a result, the tidal forces from hadrons values], so the calculationsare independentc$fany are always very weak, so that the probabilityof nu- particular nuclear model. clear excitation is, as a rule, extremely small Everything I have said so far about nuclear But not always, and it is these exceptional resonance applies also to muons, and indeed such cases that I refer to as ‘ticklishnuclei.!! These effects in muonic atoms have been studied for several . exceptions occur for the most part when a resonance years.’ Now I turn to a characteristicthat is condition is satisfied, that is, when an atomic unique to hadrons. I have already mentioned that deexcitation energy is closely matched by a nuclear for hadrons nuclear excitation is much less likely excitation energy. The situation is pictured in than for muons, because the hadron is consumed by the - 112cd, “ere Fig. 2 for the particular example of T nucleus while the hadronic wave function is still the predicted energy difference between the atomic almost completely far outside it. Just this circum- 5g and 3d levels, 618.8 keV,is very nearly equal to stance results in nuclear excitation being very much the ’12Cd nuclear excitation energy of 617.4 keV. easier to detect, in much smaller amounts, for ha- The classical analogy would be to have the period of dronic atoms. This is because the nuclear absorption the hadron in its elliptical orbit match the natural rate increasesvery drastically (by a factor of sever- vibration frequency of the nucleus, so that at every al hundred) for each unit decrease of orbital angular pass through its perigee the hadron strokes the nu- momentum; thus for a decrease of two, the factor cleus at just the right time, and hence builds up a might be --10S. That means a very small admixture large nuclear oscillation. coefficient~ (typically. 1%) can mean a very signi- Quantum-mechanicallythe situation is much ficant induced width: easier to analyze: the noncentral coupling between the hadron and nucleus produces configurationmixing, r~L= la21r~,,t-2 “ so that the energy eigenfunctioncontains a small If this induced width is not small compared to the admixture of excited nucleus-deexcitedatom wave radiative width emptying the original level, we get function: a significantweakening or attenuationof the corres- ponding hadronic x-ray line and any lower lines (Fig. +“ /1-a2 @(5g,0+) + a@(3d,2+) . 2). Thus by comparing the ratio of intensities [at- The admixture coefficient~, which is always very tenuated line/reference(higher) line] from such a small, is given by !Iticklish:isotope to that from a nonresonant, t,isotope of the same element, we get a < 3d,2+ IH I Sg,O+> “lethargic a=i direct measure of the fraction of hadrons absorbed E(3d,2+)-E(5g.0+) “ by the excited nucleus. Note that all corrections H expresses the electric quadruple interaction for level populations,x-ray absorption in the tar- Q between hadron and nucleus, and the matrix element gets, detector efficiencies,etc., drop out when we is in fact given in general byl take this ratio of intensity ratios, which of course

2 4$

Fig. 2. The levels involved in the---nuclear resonance effect for pionic llzCd. The nuclear levels are on the left, the atomic on the L T I right. The 5*4 and 4+3 lines are attenu- 800 1000 12b~ 1400 1600 ated, while the 6+5 line, being unaffected, ICHANNEL serves as a reference line. Fig. 3. Part of the pulse height spectra for pionic makes the experimentsvery easy. l12Cd (above)and lllcd (below). The relevant lines are marked. Let me add that, in contrast to the muon case, there is no chance of observing nuclear Y emission long enough, you can see that the ratio 5+4/6+5 is by the excited nucleus because the hadron destroys smaller in the upper spectrum (112Cd) than in the it much too quickly. lower one (lllCd),which demonstrates the effect. Having presented the main theme, let me now Since lllCd is also ticklish (as we discovered some- show you how it works in a variety of specific cases. what late in the game), we made a second run com- In order to make predictions for this effect, one paring lllcd and llocd. The excitation energies are needs to have some knowledge of the hadronic shifts given in Table II. You can see that the energy match- and widths of the ‘rinner,fvnl,i?-2eigenstates;this ing is nearly as good for lllCd as for 112Cd. For- is obtained by integratingthe Klein-Gordonequation tunately, the ground state spin of 1/2 for lllCd with a phenomenologicalhadron-nucleuspotential. means that the resonance effect is only about half Our predictions for negative pions (for which the as strong as in 112Cd. The results are compared phenomenologicalpotential is fairly well known) cap- with theory in Table III. These results first of all 3 turing on even-even nuclei are shown in Table I. demonstratevery clearly the existence of the nuclear The last column gives the expected attenuationof resonance effect: the ratios are very significantly the line in question. This is defined as different from one. In addition, the agreement with calculation is very good, so that we can be quite

1 confident that we understand the physics. 0 where I is the line intensity for the ticklish What strong interaction information can we ob- Q tain from this kind of nuclear re$onance experiment? nucleus, 10 for a normal one. ‘xperimentally’lQ’10 An attenuationmeasurement places a constraint on is just the ratio of intensity ratios mentioned the complex energy difference, and therefore on the “., above. shift and width produced by the hadron-nucleuspo- Since the largest attenuation is predicted for 112 tential. This is illustratedin Fig. 4, where we Cd, a group of us at Los Alamos (J. N. Bradbury, show the sensitivityof the attenuation to the energy H. Daniel, J. J. Reidy, and myself) ran an experi- shift for the 112Cd/111Cd pair, along with the mea- ment on cadmium isotopes at the biomedical T- beam 4 ● sured value. If the nuclear excitation energies of LAMPF. The experiment involved little more than were known more precisely, the constraint imposed putting the enriched isotope targets in turn into by the experimentwould be much more stringent. the beam, viewing them with a germanium detector In some cases, this type of experiment can give feeding a pulse height analyzer, and comparing the results. Part of the spectra for 112Cd and lllCd !!!l!s&informationOn the strong interaction -by giving us a glimpse of a normally “hidden” level. are shown in Fig. 3. If you look at these spectra

3 TABLE I

ISOTOPES FOR WHICH LARGE PIONIC ATOM NUCLEAR RESONANCE EPFEC1’SARS PREDICTED

E2+– EO+ bvels Enl– En ’,l_2 m’, 1_ 2 Atten. Energy Reference Energy Atten. Nucleus (lceV) mixed (kewb) (lceV) line(s) (keV) line (keV) (%)

112 ,~Cd 617.4 5g–3d 618.8 2.0 5+4 194 6+5 105 52 4+3 424 ‘~Sm 334.1 Sg–4d 337.6 8.4 5+4 326 6+5 176 11 4+3 721 110 ,6Pd 373.8 4f–3p 377.7 29.9 4+3 389 5+4 178 11 46 ~2Ti 983 3d–ls 1037.8 95.4 3+2 254 4+3 88 8 104 ~ Ru 357.7 4f–3p 349.6 26.5 4+3 355 5-+4 163 11

b) Including the strong interaction,finite size, and lowest order vacuum polarization corrections.

TABLE II

NUCLEAR EXCITATIONAND ATfliICDEEXCITATION

ENERGIES FOR PIONIC CADMIUM 0.6-

Levels EnergY Difference (keV) 2 r-Cd Sg + 3d 618.8 + i 1.0 Q .——— ,___ __ 1- Qqz 112 Cd 0+ + 2+ 617.4 + 0.3 3 + 2 111 --——- ——-_ ___ —— — — -— — — Cd+-+; 619.9 i 0.3 K t- 110 Cd 0+ + 2+ 657.7 k 0.3 <~.

AJP $, TABLE III O.o1 1 I I 1 t I 1/ 61Z0 6/8.0 619.o 620.0 621.0 OBSERVED AND PREDICTED INTENSITY Re[E(sg)- E(3d)] (k eV) RATIOS FOR PIONIC CADMIUN Fig. 4. Attenuation as a function of the Sg-3d 5+4 difference for l12Cd as compared 5+4 ;:g~l lCd. Ra : m’ 112Cd ~~ lllCd \ )/( ) 4+3 112cd 4+3 Illcd 5 RB S Thus quite some time ago Ericson et al. predicted (~’ )/( =’ ) that the p-wave pion-nucleus interactionwould

Experiment Z!E!zY change from attractive to repulsive as Z increased o 72 + 0.07 through about 36; the expected behavior is shown in Ra 0.65 + 0.06 - 0.13 6 Fig. 5. This is because the s-wave pion-nucleon + O.ns interaction (which is repulsive) overwhelms the 0.78 t 0.11 0.77 ‘1? - 0.10 attractivep-wave pion-nucleon interaction for larger 111 2’s. This change of sign cannot be observed directly Ra 0.69 + 0.09 0.73 i 0.05 ()m because the absorption in the 3d level means the 111 v 0.81 * 0.10 0.79 * 0.03 3d + 2p transition fades out for Z 2 30. However, for ‘0 ()m I both 104Ru and 110Pd there is a predicted nuclear resonance with the 3p state, so this effect will allow us to determine whether the p-interaction is attractiveor ~epulsive. The heart of the matter 3 for Pd is shown in Fig. 6. There we have plotted lC

contours of fixed attenuation (in percent) in the s

complex energy-differenceplane. The large circle 6 to the right is the prediction of naive extrapola- 4 tion of the observed p-wave energy shifts, while the 2 point at the left is the predicted energy difference

including the p-wave repulsion. There should be no z—~ difficulty in telling 11% from about 2% attenuation Fig. 5. Behavior of the p-wave energy shifts as a and therefore in deciding whether the p-wave force function of 2, showing the predicted sign change (from Ref. 6). is attractive or repulsive. We hope to perform the experimentand answer this question during the next LAMPF running cycle. Proceeding now to heavier hadrons, we first consider kaons; Table IV shows some promising ticklish isotopes.7 (The K-nucleuspotential is only known rather approximately,so there is a corres- ponding uncertainty in the attenuationpredictions.) In particular several isotopes of molybdenum are resonant to kaons. Tables V to VII consider K- molybdenum in more detail. The attenuationsappearing in five of the seven stable isotopes mean that even natural molybdenum should show some attenuation of the 6+5 line. And indeed if one goes back to the K- x-ray survey of Wiegand and Godfrey8 and compares molybdenum with the surroundingelements, the 6+5 iej (keV) line does appear to be depressed by the right amount (TableVI). Fig, 6. Contours of fixed attenuation of the 4f+3d line in llOPd in the complex energy dif- More recently, Godfrey, Lum,and Wiegandg at- ference plane. The abscissa is the real tempted an experiment at LBL on separatedmolybdenum part, the ordinate the imhginary part of the complex energy denominator. isotopes to see the effect. Unfortunatelythey had only 25 hours of K- beam which is not enough for con- will emerge. clusive results. In their data (TableVI), the When the K- reacts with the nucleus, a E- is 9~o, but !3Ven more ‘0 effect appears to show up for released about 10% of the time. These Z’s stop in for “ Mo, which just shouldn’tbe! I am willing to the target and emit x rays of their own. Thus E- 95M0 will behave bet that when more data are taken, x-ray experimentsare feasible, and Table VIII lists itself and show a higher 6+5/7+6 ratio. If not, some promising cases for nuclear resonance effects. then there is something very drasticallywrong with Essentiallynothing is known about the X--nucleus our understandingof the situation, and perhaps the interactionat present, so that actual attenuations only way to fix things up would be to change the spin will certainly not come out to be precisely these and B(E24) value assignments. The values shown in numbers. Here we see that selenium has many ticklish Table VII are from the recent experiment of Barrette isotopes and should be a very instructive system to et al.,10 and you can see that the predicted atten- study. I had hoped to find a case where the energy uations would have to be increased by an order of matching is so close as to be sensitive to the fine 9 magnitude to agree with Godfrey et al. In any case, structure splitting and hence to the Z- magnetic it is clear that the isotopes of molybdenum will be moment, but unfortunatelythere do not seem to be very interestingto investigatefurther, and that any. That is too bad. ultimately a lot of strong interaction information

5 TABLE IV

ISOTOPES FOR MiICH LARGE KAONIC ATOM NUCLEAR RESONANCE EFFECTS ARE PREDICTED.

INTERACTIONPARAMETER - ~= (0.44 + 0.83 i)F.

Levels E r Atten Energy Ref. Energy E2+-EO+ nt-~nt9j,.2 nl, L2 (Id) Nucleus -(w!2_ mixed 4S!!LQ!E(Q 94 871 798.8 24.8 6+s 0.42 284.3 7+6 171.1 0.18 4$0 (6,S)6(4,3) ‘6M0 778 It 798.5 25.2 “ 0.41 “ “ II 0.71

9%0 787.4 !1 798.2 25.S “ 0.41 “ “ II 0,81

loqo 535.5 II 797.9 2S.8 “ 0.40 “ “ 171.2 0.04

832.3 (6,5)6(4,3) 874.9 29.8 6+s 0.42 312.1 7+6 187.9 0.42

1140.2 (6,5)6(4,3) 1105.8 70.4 6+s 0.21 403.5 7+6 243.1 0.42

1426.0 (6,5)6(4,3) 1346.3 126.1 6+3 0.s3 SOS.7 7+6 30s.4 0.15

8+7 0.5s 403.2 276.1 0.42 411.8 (8,7)6(7,5) 406.1 7.8 74 0.13 622.2 w

TABLE V TABLE VII

PREDICTED NUCLEAR RESONANCE EFFECTS IN K- MO CALCULATED CONTRIBUTIONSTO ATTENUATION IN 9%0 EN (keV) = Abundance (%) &s!?!LQ (Leveldata from Ref. 10) 92 15.8 1540 --- Level B(E2+) 1P lo-so e2 ~4 94 9.0 871 18 Energy (keV) ~

95 15.7 786+... 7 3/2+ 204 3.80?0.24 0.1 --- 96 16.5 778 71 7/2+ 766 < 0.013

97 9.5 <4 1/2+ 786 0.325f0.020 4.2

98 23.8 787 81 3/2+ 821 0.060t0.015 0.1

100 9.6 536 4.5 9/2+ 948 5.25 +0.2S 2.8

Natural molybdenum 34% 5/2+ 1057 1.30 *0.07 0.1

TABLE VI

OBSERVED LINE RATIOS AND A’IY’ENUATIONSIN K- MI

6+5 ()—x &?EJil. Z = 38,39,41,45,47,48 0.78i0.08 --- ‘ef” 8 { NAT},O ?, 0.52f0.09 33*14 98M0 0.35Y0.21 55*27 { ‘ef” 9 95M0 0.24*0.14 69+18

Fig. 7. Nuclear resonance effect in -p-100Mo.

6 TABLE VIII

ISOTOPES FOR WHICH LARGE Z- ATOM NUCLEAR RESONANCE EFFECTS ARE PREDICTED.

INTERACTIONPARAMETER”-~= (0.01 + i)F.

L?2+-EO+ Levels R -E r httn Energy Energy nl nl, t-2 nl,J1-2 Ref. Nucleus -@!2- mixed (keV) Jw.L w ‘o m line m Attn

~~Ge 596.0 (7,6) e(5,4) 628.8 12.1 7+6 0.26 23’.3 8+7 154.s 0.78

#e 635.0 (7,6) 8(S,4) 707.6 18.1 7+6 0.21 269.0’ 8+7 174.5 0.s9

,, 78Se 614.2 M 707.3 19.2 0.18 269.2 ,, 174.6 0.40

80Se ,, 666.2 1, 707.2 19.7 0.17 269.3 ,, 174.7 0.70 ,, ,, 82Se 65S.4 ,, 707.0 20.3 0.16 269.4 174.8 0.54

9+8 0.46 201.3 0.16 102 473.0 (9,8)G(7,6) 49S.2 0.2 10+9 143.9 @u 8+7 0.31 293.9 0.21

9+8 0.46 220.1 0.38 lfiPd 555.4 541.5 0.4 10+9 157.3 (9,8)S(7,6) 8+7 0.26 321.3 0.39

9+8 0.45 220.2 0.14 511.7 ,, 541.6 91 IM ,, 106Pd 8+7 0.25 321.4 0.19

9+8 0.45 239.9 l::Cd 617.4 (~,a)e(7.,6), 590.1 0.8 10+9 171.5 0.24 8+7 0.18 350,2

,, II 9+8 0.45 240,0 114Cd 5S8.5 590.2 ,, ,, 0.22 . 8+7 0.18 350.3

126 ~2Te 667.0 (9,8)6’(7,6) 693.4 2.3 9+8 0.42 282.1 10+9 201.6 0.54

128Te ,,”” ,, ,! ,, 743.0 693.s ,, ,, ,* 0.21

130 359.0 S6Ba (9,8)6(8,6) 326.1 6.7 9+8 0.38 327.4 10+9 233.9 0.13

168 10+9 0.42 346.1 68Er 821.1 (10,9)G(8,7) 829.9 2.4 11+10 255.8 0.67 9+8 0.08 483.8 0.61

11+11) 0.45 337.2 l;:Pt 328.5 (ll,lO)&(10,8) 338.0 1.2 12+11 256.3 0.24 10+9 0.23 456.1 0.28

200 Il+lr) 0.44 354.9 80M 367.9 (Ii,IO)G(1O,8) 35S.6 1.8 12+11 269.7 0.13 10+9 0.18 480.0 0.14

11+10 0.43 372.9 2;Pb 899.0 (11,10)6(9,8) 877.3 1.4 12+11 283.4 0.20 10+9 0.14 504.3 0.19

Finally, antiprotons,which I have saved for the vanishing of the 8+7 line, the 9+8 line develops last. Our favorite candidates are shown in Table a complicated structure. Because of the spin of the IX. For 7’Se and 100Mo the attenuation is ~, Fall the lines are doublets (actuallythey are trip- i.e., the line is completelywiped out by the reso- lets, but the third component has negligible inten- 100MO; that dance effect. Note the star next to sity); however, because of the close-couplingthe indicates a hysterical nucleus. Here the admixture 9+81ine inlOOMo becomes a quartet. The predicted parameter ~is —.not small, but instead is - 1. As a structure of this line is shown in Fig. 8. The result, some rather spectacularthings happen. dotted vertical lines show the normal doublet struc- Figure 7 shows the relevant levels. In addition to ture (the fine structure separation is about 300 eV),

7 the solid vertical lines the componentsof the quar- Barnes et al.S). Valuable strong interactionin- tet. The widths of the members vary drastically,and formation could be obtained by careful measurement of this line profjle. As an added bonus, the line the resulting intensity pattern (not— including experimental resolution) is shown. Even when the blur- is in a much more favorable energy region (144 keV), ring produced by experimentalresolution is included, as far as detector efficiency and resolution are con- much of this structurewill remain. The position, cerned, than those last x-ray lines which one nor- widths, and relative strengths of the four components, mally must use to get hadronic information. Thus, and hence the whole line profile, depend on the ha- inmy own completelyunbiased opinion this is the dronic ~-nucleus interaction. This is illust~ated best and most beautiful ~x-ray experiment that one in Fig. 9 which shows the results when we allow the could possibly do. I hope that some experimental- strong interactionparameter to take the values at ists will concur and do it. the comers of the ‘terrorrectangle,”as well as the In summary, I hope that I have managed to con- central value (strong interactionparameter K from vince you that tickling nuclei is not only fun, but instructive.

TABLE IX

rsoTopEs FOR WHICHLARGE~ATC6i NUCLEAR RESONANCEEFFECTS ARE PREDICTED.

INTERACTIONPARAMETER - ii= (2.9 ● 1.5 i)F,

E2+-EO+ Levels E r Ref. nll-Enl,2-2 n!,t-2 Attn Energy Energy Nucleus mixed _@Y!_ (keV) _@!!L M!dQ ‘o J!@!l line _!@!!l Attn 76 ~4Se 559.3 (7,6)6(5,4) S61.4 10.4 7+6 0.34 211.6 8+7 137.2 0.99

:~Mo 871.1 (7,6)G(S,*)” 844.8 S2.1 7+6 “ 0,10 324.1 3+7 210.1 0.67 ‘loo 8+7 0.42 210.2 0.98 ~2Mo S3S.6 (8,7)6(6,S) S34.4 2.2 9+0 144.0 74 0.09 324.2 0.83

I:fiu 3s7.7 (7,6)6(6,4) 328.7 60.1 7+6 0.06 3ss.0 6+7 230.8 0.23

l~e 840.0 (8,7)6(6,s) 818.2 20.0 8+7 0.2s 323.4 9+6 221.4 0.78

148M 9+8 0.43 29S.3 0.80 300.0 (9s06(8s6) 29S.9 S.2 10+9 221.0 60 8+7 0.07 431.2 0.71

1s0 ~pl 336.0 (9,8)6(8.6) 31s.8 7.3 *8 0.42 31s.4 10+9 22S.4 0.26

1LW9 0.43 3S7.6 0.81 l;:Pt 3ss.7 (10,9)6(9,7) 3S8,9 5.7 11+10 264.S 9+8 0.08 .S00.8 0.72

200 8oHg 367.97 (10,9)6(9,7) 377,s 7.7 10+9 0.42 376.S 11+10 278.3 0.43

* Close coupled, perturbation theory inaccurate.

8 i LLL, .’ L L Fig. 9. Structure of the same transition when the interactionparameter ~ is varied to the extremes of its error bars. Z is from Ref. 11. Fig. 8. Structure of the 9+8 transition in –p-100MO. The dotted bars show the original fine structure components in the absence of the nuclear resonance effect, the solid bars the components of the quartet produced by the nuclear resonance effect. The intensity envelope shown results when the appro- priate Lorentziannatural widths are included. Units of the energy scale are arbitrary.

REFERENCES

1. E.G., H. L. Acker, Nucl. Phys. ~, 153 (1966).

2. J. Hiifner,Phys. Lett. ~, 189 (1967).

3. Taken from M. Leon, Phys. Lett. ~, 141 (1974).

4. J. N. Bradbury et al., Phys. Rev. Lett. ~, 31)3 (1975).

5. M. Ericson et al., Phys. Rev. Lett. ~, 1189 (1969).

6. Taken from T.E.O. Ericson, Third Int. Conf. High Energy Physics and Nuclear Structure, ed. S. Devons, p. 448 (Plenum 1970).

7. M. Leon, Phys. Lett. SOB, 425 (1974).

8. C. E. Wiegand and G. L. Godfrey, Phys. Rev. A 9_, 2282 (1974).

9. G. L. Godfrey et al., LBL-3613 (unpublished).

10. J. Barrette et al., Phys. Rev. C lJ, 171 (1975),

11. P. D. Barnes et al., Phys. Rev. Lett. ~, 1132 (1972).