(y, n) studies of the giant isovector E2 resonance in lead, cadmium, and calcium

D. W. STORM, 1. HALPERN, C. A. GOSSETT, T. MURAKAMI, D. P. ROSENZWEIG, A N D D. R. TIEGER Nuclc.crr Physics Lnborcriory, Ut~iver.siiy of Wei.shir~gtot~, Seaitlc., WA 981 95, U.S.A.

P. T. DEBEVEC, A. FREYTAG, A N D L. J . MORFORD Dc.pcrrimet~i of' Phy.sics, Ut~iversiiy of Illirrois, Urbnr~a, 1L 61801, U.S.A .

S. A. WENDER Los Alamos Ntriiot~cil Luborcrtory, Los Alamos, NM 87545, U.S.A.

A N D

D. H. DOWELL Deptrritnenf of Physics, Brookhaven Notiot~crl Laborciiory, Upion, NY 11973, U.S.A

Received March 5. 1987

We have measured the angular asymmetry in the (y, n) reaction on natural lead, cadmium, and calcium in the energy region of the isovector quadrupole resonance (20-40 MeV). The asymmetry increases from low values, about 0.2, to high values, 0.6-0.8, where this resonance is expected. This increasing asymmetry is interpreted as resulting from the interference between the El and E2 isovector amplitudes. We have fitted direct-semidirect calculations for lead and cadmium and have obtained resonance energies of 23.5 "- 1.5 and 26.5 2 1.5 MeV for these elements, respectively. For calcium, preliminary results indicate a resonance energy of 34 2 2 MeV. The widths are found to be considerably larger than those of the El resonance.

Nous avons mesure l'asymitrie angulaire dans la reaction (y, n) sur le plomb, le cadmium et le calcium naturels, dans la region d'knergie de la resonance quadrupolaire isovectorielle (20-40 MeV). L'asymCtrie croit ti partir de valeurs basses, environ 0,2, jusqu'a des valeursClevCes, 0,6-0,8, lti ou cette resonance est attendue. Cet accrolssement d'asymCtrle est interpret6 comme le resultat de l'interference entre les amplitudes isovectorielles El et E2. Nous avons fait des calculs directs-semidirects pour le plomb et le cadmium et obtenu pour ces kltments des energies de resonance de 23,5 ? 1,5 et 26,5 2 1,5 MeV, respectivement. Pour le calcium, des resultats prkliminaires indiquent une Cnergie de rCsonance de 34 ? 2 MeV. On trouve que les largeurs sont considerablement plus grandes que celles de la resonance E l .

[Traduit par la revue]

Can. J . Phys. 65, 677 (1987)

1. Introduction The isovector excitation that we have been studying is the

isovector E2 resonance (IVQ). We have been concentrating on measuring the angular asymmetry in the (y, n) reaction. Our experiments have been of a survey nature in an attempt to learn how the properties of the IVQ vary with A. This resonance is expected to occur around E = 1 3 0 / ~ " ' MeV, and to be sub- stantially wider than the giant dipole resonance (GDK) (1 , 2). In a hydrodynamic model, one can picture the protons and neutrons executing collective quadrupole motion, 180" out of phase. There is no spin flipping. This mode can be contrasted with the isoscalar E2 resonance, where the neutrons and pro- tons oscillate together between oblate and prolate shapes. In an inde~endent article model without residual interactions. the energies of both isovector and isoscalar E2 resonances would be the same; namely, 2 f iw (where f iw is the major shell-energy difference). However in the E2 case. the isoscalar resonance involves substantial change in the shape of the average nuclear potential itself along with the particle motion. Hence, the ex- citation energy is lowered. In the isovector E2 case, on the other hand, not only does the nuclear shape not change very much (because protons are filling the space vacated by neu- trons, and vice versa), but the isovector part of the residual nucleon-nucleon (NN) force adds to the restoring force for the oscillation. Thus, the energy is increased substantially.

Why do we use the (y, nj reaction, and why do we measure the angular asymmetry'? In general, it is difficult to observe isovector resonances using hadronic probes, as the isoscalar

force predominates in the reaction. Obviously this workshop presents counter examples, but 1 do not expect examples of (p, n) excitations of El and E2 isovector resonances. The elec- tromagnetic interaction, on the other hand, can excite both isoscalar and isovector states without favoritism.

We measure the angular asymmetry for the (y, n) reaction in terms of the yields at 55" and 125". We define the asymmetry

If we consider the amplitudes for decay radiation occurring when a relatively small resonance is lying on the tail of one of different parity (i.e., the IVQ lying on the high-energy tail of the (GDR), there is an interference between the different parity amplitudes. The interference produces an angular asymmetry in the radiation. This asymmetry gives a.measure of the relative amplitudes involved and thereby enhances sensitivity over an attempt to measure the cross section due to a resonance lying on the tail of a larger one. If one measures the cross section as a function of energy, across a wide resonance, it is difficult to even observe the resonance let alone subtract the poorly known underlying background to determine the parameters describing the resonance. The asymmetry information helps one to deter- mine how to divide the cross section between the resonance of interest and the (opposite parity) background. Thus, the idea is to form a nuclear resonance (which can be done by capture of a nucleon) and observe the asymmetry in the decay photons,

Prililcd In Canada i lniprimC au Canada

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67 8 CAN. J . PHYS. VOL. 65. 1987

and furthermore to do this at various excitation energies, to map out the asymmetry as a function of energy across the resonance. Equivalently, as we have been doing, the inverse reaction can be studied. We chose 55" and 125", where P2[cos(0)] is zero. Then, if the coefficients of P , and higher terms are negligible (as expected with low multipolarity radiation), the angle integrated cross section is the average of the 55" and 125" differential cross sections times 47r.

Finally, we chose to use neutrons rather than charged particles because a charged particle can be captured directly, without involving any resonance, either via an E l or E2 tran- sition. For neutrons, the direct capture is constrained to proceed mainly by E l radiation (so it looks like more of the GDR tail), because the effective charge for neutrons is -Z/A for dipole radiation but -Z/A2 for quadrupole radiation. E2 capture of neutrons is collective, so an observed asymmetry in (n, y) indicates the presence of a collective nuclear excitation. For charged particles, the probability of the direct E2 transition produces an additional asymmetry, which increases with energy (3). Depending on whether photon or neutron beams are available, one can do (n, y) experiments (4, 5) or (y, n) experiments.

The goal of this work is to determine the strength, width, and position of the isovector E2 resonance as a function of A. I will show you that we have observed the resonance in three targets of rather different A's, that we can make fairly definite state- ments about their positions and qualitative statements about the width and strength.

2. Experiment at Illinois We have measured asymmetries in (y,n) on Pb for

20.5-34.5 MeV, on Cd for 20.5-30.5 MeV, and on Ca for 28-39 MeV. Part of this work is in ref. 6. In all cases we find a small (-0.2) asymmetry at the low energies that rises to a large asymmetry (0.5-0.8) over a range of S to 10 MeV. This asymmetry is quite large, because the maximum possible value, 1 .O, corresponds to a zero cross section at 125".

We have been using the University of Illinois mono- chromator to tag the bremsstrahlung beam. Tagged photon rates are about lo7 s- ' , and we tag an energy range of about 10 MeV in 32 bins. The neutron time of flight has been mea- sured using either a single neutron counter (in the earlier experiments) or a unit of three counters (in later runs). There were a number of experimental compromises that we made to obtain these data. The counter unit was placed fairly close (1.5 m) to the target to maximize the solid angle at the expense of energy resolution. The solid angle was 30 msr for the single counter and 90 msr for the triple one. We obtained about 2 ns time resolution, which gave 3-4 MeV energy resolution for neutrons around the ground state (see Fig. 1). We were unable to distinguish ground-state neutrons from those to the lowest excited states, so we combined the lowest few states in the product nucleus by simply putting a cut at a nominal energy in the neutron time-of-flight spectrum. We used a relatively high pulse-height threshold on the neutron counter to minimize background from evaporation neutrons. Pulse-shape discrimi- nation effectively removed photons to the extent that we were unable to observe the gamma flash in the time-of-flight spectrum. The accidental background resulted mainly from neutrons produced in the target by untagged photons.

We have used natural targets of lead, cadmium, and calcium. Because the giant resonances are a fairly generic nuclear phe- nomenon, we do not expect neighboring isotopes to have par-

- 0 100 200 300 400 500

Channel

FIG. 1. A sample time-of-flight spectrum from the measurements on Pb, for a mean photon energy of 23.5 MeV. The time scale is about 0.5 ns.channe1-I. The arrows indicate times for neutrons correspond- ing to various residual excitations.

titularly different giant-resonance parameters. For natural Pb, the Q values for (y, n) on the various isotopes are about the same, so the ground-state neutrons occur at about the same place in the time spectrum. Cadmium has two odd N isotopes totalling 25% abundance. These produce ground- and low- lying-state neutrons with higher energies than the even N isotopes. Thus, we include in our summing the region of the time-of-flight spectrum where these neutrons would lie. The single-hole strengths are expected to be similar in all the isotopes, so that comparisons with calculations to the low-lying single-hole states in the most abundant isotope are reasonably appropriate. Natural (nat) calcium is 97% 40Ca.

The asymmetries obtained for the three targets are shown in Fig. 2. We have also obtained absolute cross sections at the two angles. These are illustrated in Fig. 3. To obtain the cross sections, we have used calculated neutron-counter efficiencies (6). Notice that the asymmetry shows a marked increase with energy in each case, although there is not any particular sign of structure in the cross-section excitation functions.

3. Discussion The asymmetry gives a model-independent measure of the

relative even- and odd-parity amplitudes. We then make the reasonable assumption that one of these amplitudes is the E l (both the direct and giant resonance tail) and that the other is E2 (the IVQ as well as the tail of the isoscalar E2). It is also possible that there may be E3 amplitudes, especially at the higher excitations that we reach.

Because the values of the asymmetry depend on the size of the El amplitude (which is not particularly well known far from the resonance) as well as on the phase between the E l and E2 amplitudes, determination of the precise IVQ amplitude is not altogether unambiguous. everth he less, the rapid-change from small to large values of the asymmetry is a definite indication of passage through a resonance; without a phase change of nearly 1800, such large changes in asymmetry would not occur. Furthermore, because the asymmetry depends on the ratio of even- and odd-parity amplitudes, determination of resonance parameters is much more reliable than techniques that involve unfolding a number of resonant cross sections. In addition to the fact that the 1VQ phase should change through 180" across

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STORM ET AL

1.0

1 " ~ ' I " " I " " I " "

M t ~ d ( y , n ) ( c ) . Ex < 3 MeV

t -

-

I . . . . l . . . . ,

I . ' ' . I . . ' . I ' . . ' I . .

4 0 ~ a ( y ,n) (a') . Ex < 4 M e V

1 1 -

I f f \.li 1; $ i f $ A

FIG. 2. Asymmetries obtained for the three targets. Preliminary data are indicated by Xs. The arrows are at the IVQ resonance energies discussed in this text.

-

the resonance, there are overall relative phases and some ener- gy dependences of the relative phases that are perhaps not possible to predict reliably. We have done both simple classical calculations and direct-semidirect model calculations of the expected asymmetries.

We can write the asymmetry in terms of the 55" amplitudes for reactions involving the even- and odd-parity excitations, At en++ and A- el6-. The asymmetry is then

2AtA-cos(++-+-) - 2cos (~$~-+- ) -

(A t)2 + (A - ) I A t / A - +A-/At

-

To get a large asymmetry, as we have found to be the case especially for Pb above 25 MeV, one must have the ratio of the A's near unity at those energies and the phase difference must be small. This is an interesting and model- independent result of this experiment.

I . . . . I . . . . I . . . . I . . . . .

If we assume that the amplitudes for the reaction consist of an El resonance line centered below the energy of the data plus an E2 resonance located somewhere within the energy range of the data, we can write the amplitudes as Breit-Wigner forms:

The particles .rr and .rrf are opposite. In the simplest picture, we expect the coefficients for the E l and E2 resonances to have a relative phase of zero (6). Then we find that the choice of the standard parameters (see Table 1) for the GDR in lead, along with an IVQ resonance energy of 23.5 MeV, a width of 10 MeV, and a ratio of A,/A, of 0.3 gives good agreement

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CAN. J . PHYS. VOL. 65. I987

FIG. 3. Cross sections obtained for (a) cadmium and (b) lead.

TABLE 1. Giant resonance parameters. Resonance energies are E; widths, r; and fraction of the EWSR exhausted, P . Subscripts d , v,

and s refer to dipole, isovector E2, and isoscalar E2 respectively

Ed rli Pd Ev 1 , P, E, , PI

between this simple prediction and the lead data (see Fig. 4). These parameters correspond to an IVQ strength of 314 times the energy-weighted sum rule (EWSR).

Murakami has done direct-semidirect (DSD) calculations to fit some of the data I have presented. In these calculations, direct capture (mainly E l ) as well as capture via the E l , iso- scalar E2, and isovector E2 resonances are included. The dis- tortions of the neutron wave are obtained using two different sets of optical parameters (7, 8). Murakami has used the Cd and Pb resonance parameters given in Table 1. The giant E l and isoscalar E2 resonance parameters are obtained from the litera- ture (9, lo), while the isovector E2 parameters are adjusted to give reasonable agreement with both our (y, n) data as well as, for the lead case, the (n, y) data of ref. 4. The DSD results are compared with the data in Fig. 5. One of the effects of the optical potential distortions is to introduce a (final-state de- pendent) relative phase shift. When we look at the DSD predic- tions for the individual states in our sum, we see that the asymmetries change fairly sharply and at somewhat different energies. Thus, the summing generates a smearing that is not considered in the simple calculation given above. Con- sequently, a larger width is required in the simple calculation than in the more detailed DSD calculation.

Although we have not yet done any DSD calculations for calcium, the shape of the asymmetry curve is similar to those for lead and cadmium. The calcium asymmetry curve matches

FIG. 4. Classical calculations of the asymmetries (-) and cross sections (.....) for lead, using the parameters mentioned in the text.

the lead one if it is shifted 10.5' MeV, while a 7 MeV shift produces a good match to the cadmium curve. By adding the shifts to the resonance energies obtained for Pb and Cd, we find the Ca IVQ resonance lies at 33.5 to 34 MeV.

In summary, it is clear from the measured asymmetries that some resonant phenomenon is occurring between 20 and 30 MeV, and that we see interference between even- and odd- parity amplitudes. These amplitudes become nearly equal at

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STORM ET AL

FIG. 5 . Direct-semidirect calculations of the asymmetries and cross sections for the cadmium and lead results of the present experiment and for the Pb(n, y) data of ref. 4. The solid curves are calculations using the optical potentials of ref. 7 , while the dashed curves were made using those of ref. 8.

some energies, particularly for leau. We assume that the reso- nance is the IVQ and that it is interfering with the tail of the GDR combined with some direct E l amplitude. Furthermore, we conclude from the calculations for lead and cadmium that the IVQ energies are 23.5 and 26.5 MeV, respectively, with a 1.5 MeV uncertainty. For calcium, the IVQ appears to lie at about 34 MeV. These energies are consistent with the expected A - ' I3 dependence for giant resonance energies. In determining the parameters, we find that there is some correlation between the width and strength. We conclude that the width is about 6 MeV in lead and around 7 MeV in Cd. There is an uncertainty of 2-3 MeV in these widths. The resonances do not appear to exhaust the full EWSR (calculated in the Goldhaber-Teller model) but rather account for about half of it. The DSD model

calculations using these parameters for the IVQ in lead are consistent both with the results obtained in ref. 4 for 'OsPb(n, yo) 'OVb and the present ""Pb(y., n) data summed from the ground state to 4 MeV of residual e~citation.

Clearly higher resolution, to enable separation of discrete final states, is desirable. In the Ca analysis we are pursuing this possibility, because "Ca has a first excited state at 2.47 MeV. In the studies of the inverse reaction, it is possible to unfold the ground and first-excited states from the gamma-ray spectrum, but obtaining sufficient neutron energy to excite the nucleus above the IVQ has been a problem. Finally, we should empha- size that we are interested in continuing the asymmetry studies at higher energies, because the asymmetry responds sensitively to the appearance of resonances of definite parity.

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682 CAN. J . PHYS. VOL. 65, 1987

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