GIANT RESONANCES BUILT ON HIGHLY EXCITED STATES

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GIANT RESONANCES BUILT ON HIGHLY EXCITED STATES

K. Snover

To cite this version:

K. Snover. GIANT RESONANCES BUILT ON HIGHLY EXCITED STATES. Journal de Physique

Colloques, 1984, 45 (C4), pp.C4-337-C4-350. �10.1051/jphyscol:1984426�. �jpa-00224092�

JOURNAL DE PHYSIQUE

Colloque C4, supplCment au n03, Tome 45, mars 1984 page C4-337

GIANT RESONANCES B U I L T ON HIGHLY EXCITED STATES

K . A . Snover

Department of Physics, University of Washington, Seattle, WA 98195, U,S.A.

Resume - On passe en revue les proprietes des resonances dipolaires geantes btities sur des etats nucleaires excitPs, en mettant l'accent sur les resul- tats recents. Les reactions ( P , ~ ) non-statistiques sur les noyaux legers et les reactions statistiques de particules composites sur les noyaux legers et lourds sont discut6es.

Abstract: - .- The properties of giant dipole resonances built on excited nuclear states are reviewed, with emphasis on recent results.

Nonstatistical (p,y) reactions in light nuclei, and statistical complex-- particle reactions in light and heavy nuclei are discussed.

A great deal of excitement and progress has been made in the last few years in the study of Giant Dipole Resonances built on highly excited states, or excited-state GDRS. I%e new results come primarily from observations of high energy y-rays produced in the radiative capture of nucleons and compxite projectiles colliding with a variety of different target nuclei. Because real photons are observed, El radiation dominates. Relatively little is known about giant resonances of other multipolarity built on excited states: because of time limitation, I will restrict myself primarily to Giant Dipole Resonances.

It is now clear that high energy y-rays from the decay of the GDR are produced in essentially all energetic nuclear reactions. In contrast to ground state-GDR excitation by inelastic scattering or photon absorption, in which the energy transferred to the nucleus goes into the GDR excitation, energetic nuclear collisions produce highly excited, fused systems in which part of the energy goes into the GDR vibration and the rest of the energy goes into other £0- of nuclear excitation. l%e decay of the W R produces the high energy y-ray leaving the nucleus usually in an excited state. The interesting new physics lies in the way in which the properties of the GDR are mdified in highly excited nuclei.

The basic expectation was given originally by Brink,l who proposed that every exited nuclear state should have a GDR built upon it, with properties which should not depend strongly on the details of the nuclear state. Recent experiments confirm this expectation, and provide new information about the properties of highly excited nuclei.

Two distinct methods of forming GDRs built on excited states are known: 1) proton (and neutron) capture, in which the GDR is induced directly by the dipole multipole of the ; , . ; , nucleon-nucleon interaction, the same interaction which provides the restoring force for the collective GDR vibrations, and 2) complex particle capture, which produces thermally equilibrated hot; nuclei in which part of the excitation energy is contained in GDRs built on states of lower energy.

The fundamental distinction between these two types of reactions was realized years ago by Halpern and c ~ l l e a g u e s . ~ Recent proton capture experiments at intermediate energies in light nuclei have provided new insight into the ( p a y ) reaction as well as the nature of excited-state GDRs. The predominantly

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984426

C4-338 JOURNAL DE PHYSIQUE

nonstatistical nature of (p,y) permits one to examine the microscopic structure of the GDR, and also to produce particularly Simple residual states. 'fie statistical GDR decay mechanism offers the possibility of studying a wide varzety of different systems under different conditions.

Much of our present understanding stems from comparing different reactions leading to the same system; this is illustrated in the light nucleus 2 a ~ i in Fig. 1. l%e 'i-342 + ^{Z 5 ~ g} reaction channel3 produces a statistical-like y-ray spectrum without structure at high energies, whereas the p + z 7 ~ 1 channelQ forming Z B ~ i * at the same excitation energy produces considerably more high- energy y-rays per nuclear reaction, with substantial structure indicatinq selective population of specific final states. The statistical component of p +

2 7

A 1 is comparable to that of 3 ~ e + ^"Mg and hence is small compared to the nonstatistical component of (p,y) at high energies. [An interesting recent experiment makes use of the statistical component of (p,y) at low energies in a heavy nucleus to test the Brink hypothesis. J

Fig. 1 - Gamma-rays from p + ^{2 7 ~ 1 (Ref. 4)} and 3 ~ e + ^{2 5 ~ g (Ref. 3).}

The vertical scale is a l d o / dE where o is the total reaction

cross section. R Y Y R

1 ) Proton (neutron) capture: The GDR in (p,y) and (n, y ) reactions which populate low-lying levels of light nuclei has been studied for years. In general the excited-state GDRs are located at approximately the same y-ray resonance energy as the ground-state GDR. Often the structure in the GDR varies greatly from one case to the next, as it does for neighboring ground-state WRs.

Recently, the (p,y) reaction to highly excited final states has been studied at high bombarding energies, up to 100 MeV, in light nuclei. These new data, along with simple calculations described below, have led to a new understanding of the simplicity of the (p,y) reaction through the GDR.

Energetic (p,y) reactions excite GDRs built on states which look like a

single proton coupled to the target ground-state. These excited-state GDRs have

a resonance energy similar to the ground-state GDR, but often have considerably

broader widths. I'he y-decay of the GDR then leaves the nucleus in the simple

configuration corresponding to a single excited proton coupled to the target

ground state. Relative to the ground-state of the residual nucleus, these are 1

particle-1 hole (lp-lh) configurations in which the hole configuration

corresponds to the target nucleus; i.e., the same configurations as are made in proton stripping reactions. l'his is illustrated schematically in Fig. 2. These qualitative features were suggested by the experiments of Blatt and colleague^.^

At intermediate (E - ^{30-50 MeV)} energies the "~(p, y)lilc reactione' strongly populates unresolved states at P Ex - 19 MeV believed to be primarily of [ld,/,,

- +

lp ,/,I configuration; the energy dependence of the cross section shows a broad resonance centered at E " 30 MeV, corresponding to E 2 23 MeV, the same y-ray

P Y

resonance energy as the ground-state GDR. However, the extremely large ( r ^{' 20}

MeV) width of this resonance has made it difficult to be certain that it is indeed due to the GDR. m e proof that GDRs built on l p l h states dominate the (p,y) reaction was shown in Ref. 4. Fig. 3 demonstrates the close correspondence between the final states made in (p,y) and the states made in ( 3~e,d), while Fig. 4 demonstrates that the energy dependence of the cross section for populating these states shows resonances ( G D R s ) all centered at approximately the same y-ray energy, E = 20 MeV, the energy oE the ground-state O R .

Y

Fig. 2 - Schematic diagram of proton capture. The proton incident on a hole state (target nucleus) induces a collective p-h excitation (a) which decays (b) leaving the residual nucle- us in a Ip-lh state (c). The cap- tured proton also participates in the collective excitation through a term in (b) (not shown) which looks like the entrance channel, with a single proton excited.

2 7 (p, ~ ~ r ) 2 8 ~ i '

Fig. 3 - 27~l(py)28~i spectrum compared with proton stripping strength (Ref. 4).

Fig. 4 - u(9O0) vs. Ey for

27~l(p,y)28~i*, where E ~ = E ~ ~ + Q - Ex. f

Each data set is labelled Ey the final-

state energy Efx, in 2 8 ~ i (Ref. 4 ) .

C4-340 J O U R N A L DE PHYSIQUE

The integrated resonance strengths o(y,po)dE, derived from the measured (p,y) cross sections using detailed balance, have been determined empirically to have a remarkable simple quantitative relation to the proton stripping spectroscopic factors C S ' in the mass region A " 28. To a good approximation

where the constant of proportionality K = 22 MeV-mb is approximately independent of the configuration of the captured proton.4 This holds not only for

2 7

~ l ( p , y ) ~ ~ s i populating a wide variety of final states of different spin and particle-hole con£ iguration, but also for Z8~i(p, y)"~, which populates single- proton final states that are the weak-coupling analogs of the "si particle-hole multiplets. Thus, although the capture process proceeds via an intermediate resonance (the GDR), the integrated strengths exhibit the character of a direct reaction.

The magnitude of K may be understood in a simple manner.4" Neglecting collective effects, a simple direct emission model calculation using harmonic oscillator matrix elements yields

where

Here Nx = p or n corresponding to the ejection of a proton or a neutron X X into channel x, n and P are the principal and orbital quantum numbers of the ejected nucleon, [cZS]zp is the spectroscopic factor, qZ is the recoil effective charge and is equal to (N/A)' for proton emission and (z/A)' for neutron emission, and the constant factor 4rrZeZn/3~c = 40 MeV-mb. Knp is just the pure single-nucleon ejection cross section. ' Thus KZs =

ZsKld ⁼ 25 and Klf = 30 MeV-mb for ZS,/~, Id and If proton ejection from Si. Fig. 5 shows that this

3/2 7 / 2

works very well for the (y,p ) strengths deduced from "kl(p,y) and r8si(p,y)

0

using experimental czs-values. On the average, the simple model overpredicts the integrated strengths by "15% which is within experimental error.

why should a simple direct emission model account so well for the integrated (y,p ) strengths when we know experimentally that the reaction

0

proceeds via the GDR? The answer is best understood by appeal to the extreme

Fig. 5 - Solid bars: experimental re- sults from Ref. 4. Open bars: calcu- lated results (Eqns. 2 and 3) using experimental (see Ref. 4 ) S ' C values.

' 0 2 4 6 8 10 12 14

schematic model of the GDR. In this model, all possible microscopic dipole excitations (see Fig. 6 ) are present in the GDR with amplitudes proportional to their dipole matrix elements. The schematic model intensity is then KnP Vnp for the sum of all excited configurations of the form nQ - n'P', where Vnp is the initial-state occupancy (before dipole absorption) of orbital nQ. If we neglect rearrangement processes, then in the limit where all excited dipole configurations decay into the continuum with equal barrier transmission, one arrives again at Eqns. (23 and 1331

l'his simple model may be applied to recently mea~ured'~ proton decay branching ratios for the ground-state GDR in Z s ~ i . Since the total dipole strength in this model is the classical dipole sum rule, 60 NZ/A MeV mb, the branching ratio for decay to channel px is just K n p ( ~ Z ~ ] ~ p / 6 0 ~ ~ / ~ . Fig. 7 demonstrates that the simple model works very well in describing these branching ratios.

E:( (MeV)

= ? = ^{- -}

- - - -

- - - -

E 1 . ~ - m + + n ^{- - - -} -I- ^{- -}

- - - -

Fig. 6 - Schematic diagram of the inverse y-excitation process for a lp-lh state. Only the first term

on the right hand side contributes 2+ lf 3+ 7+ 5+3+ l+ r 5+

2 2 2 E ^{2 2 2 2 2}

to po emission.

J"

Fig. 7 - Solid bars: experimental branch- ing ratios (BR) for the proton decay of the GDR built on the ground-state of 2 8 ~ i (Ref. 10). Open bars: calculated BRs using experimental (see Ref. 10) C~S-values.

Thus we have achieved a remarkably simple understanding of the nucleon

decay strengths for both the ground-state GDR in "si and for excited-state GDRS

observed in (p,y) in this mass region, in terms of the microscopic configurations

involved in the GDR. These comparisons provide striking confinnation that the

microscopic nature of the GDR is given correctly by simple theory. Cases in

light nuclei where the simple model fails (sudh as where photonucleon

strength to p-l states in mass-15 is less than the strength to p-+ statesiL

whereas the simple model would predict it to be greater) indicate 7 3/2 ; e need to

relax the extreme approximation of neglecting barrier penetration differences for

different channels. It will be interesting to see if a universal description of

nucleon decay strengths of the GDR in light nuclei can be achieved with this

microscopic schematic model approach. Such a description would lay the

groundwork for a better understanding of the GDi? in heavier nuclei where both

statistical and nonstatistical decays are important in reactions involving

protons and neutrons.

C4-342 JOURNAL DE PHYSIQUE

our understanding of the relation between integrated (p,y) strengths and spectroscopic factors means that the (p,y) reaction can be used as a tool for studying single-proton strength in light nuclei. At high excitation energies in the continuum, where states are often broad and overlapping, the extraction of spectroscopic strength by conventional proton stripping reactions is highly problematical, whereas analysis of the (p,y) reaction is much simpler. A good illustration of this is the 19 MeV complex of p-h states in + Z ~ . In spite of the wide attention given to this problem, the level structure of IZc in this energy region is still not well understood. However, the ll~(p,y) strengths over the GDR built on these levels (Fig. 8 ) gives a clear indication of the spectroscopic strength contained in this region. Fig. 9 demonstrates the correspondence between integrated (y,p ) cross sections and spectroscopic strength for the low-

0

lying states in +'c; the integrated (y,p ) strength of = 330 M~V-mbe for the 19

0

MeV Complex may then be used to infer E(ZJ+~)C'S "330/25 = 13. From experiment and from the shell model, one expects most of the [d,/,, - 1

P ^{3/2 1} strength for J ~ . T-4-,1 and 4-,0 ( E ( Z J + ~ ) C ~ S = 9) plus some of the 3 ,1 and 2-,1 strength (E(2J+1 ) C ' S = 6 ) in this complex, in good agreement with the inferred value.

The width of the GDR broadens considerably with the excitation energy of the final state upon which it is built. The fact that the integrated strengths are given correctly by the simple model indicates that spreading width contributions are small. Naively one would not expect much of the increase to be due to escape width increase either, since in a weak-coupling model of the GDR built on excited states, the excited-nucleon decay energies do not change appreciably with excitation energy (excited-state GDRs tend to decay by nucleon emission to excited states in the residual nucleus). The additional width may be due to fragmentation of the GDR strength. This conclusion is supported by GDR

LEVELS in "C

~f (MeV)

120 0 5 10 15 2 0 25

I I I

1

1 . / , ^{, , , , , , ,}

0 >c >a 'I\ , j

r.13, '"" ""

Fig. 9 - Solid bars: experimental re- Fig. 8 - Top half: 11~(p,y)12~ spec- sults from Ref. 12 [x 0.8 as recom- trum. Bottom half: Excitation mended in Collins et al., Phys. Rev.

curve for " y I 9 " , from Ref. 6. The - C26, 332 (198211 and Ref. 6. Open dashed line shows the shape assumed, bars: calculated results using exper- along with W(O) given in Ref. 6, for imental (Ref. 13) C~S-values.

the /o(y ,po)dE estimate (see text).

width differences observed for (p,y) on A and A + 1 tarqets for analogous reactions involving the same transferred proton configuration. For example r "

12 M ~ V + for the GDR in Z7~l(p,y)28~i(f,,2 x d-+ ) while r " 6 M~V' Lor the GDR in

28 5/2

~i(~,y)~~~*(f,,,), even though the energetics of the two reactions are very similar. In t d a b s e n c e of GDR fragmentation, one would expect these widths to be comparable.

Complex Particle Capture The universal presence of GDR excitations in thermally equilibrated hot nuclei is now clear from a variety of recenL experiments. This was observed in the y-ray spectra from the statistical decay of medium-heavy compound nuclei formed in +Dm-induced r e a c t i ~ n s , ~ ~ which showed an enhancement or "bump" for E " EGDR determined by the average behavior of the GDR built on excited states. 'The enhancement occurs because the GDR vibration energy, and hence also the y-ray energy is, to a first approximation, independent of excitation energy and nuclear species (for neighboring nuclei) and hence all high energy gamma decays tend to peak near a common energy. l'he very fact that the GDR is seen strongly in decays of equilibrated nuclei implies that on the average, the GDR built on excited states has a total decay strength which is largely statistical.

In contrast to the relatively intense yield of low energy y-rays emitted after the initially hot nucleus has cooled to near or below particle threshold, the high energy y-rays must be emitted in competition with particle evaporation.

By analogy with ground-state photon absorption, it is easy to derive the y-ray strength functioni5 for the statistical decay of the GDR built on excited states:

where rJ is the El radiative width between individual levels for a decay J - ^Jo

where 1 ^{= J or} * ^{1, p (E )} is the density of initial states, EG and l ' are the J i

energy and width of the GDR, and s:~ represents the fraction of the excited-state

GDR strength which decays statistically (in units of the classical dipole sum rule). ss - ^{r l / r .} SE1 where SEl is the GDR strength and r = r+ + ^{T t}

where r+ El 1s the spreading width and rl is the escape width of the excited-state

GDR .

It is particularly interesting to contrast statistical and nonstatistical reactions in the same system, so for this purpose I go back to the case of 2 a ~ i formed in z 5 ~ g + ^{3 ~ e} reactions, and compare with z 7 ~ l + p. Fig. 10 shows that the structureless 3 ~ e + ^{2 5 ~ g} spectra change very slowly with bombarding energy.

The cross section is very large below particle threshold (E c 10 MeV) while at higher energies a structureless yield is apparent in ' t h e region of E Statistical model calculations (Fig. 10) using a version of the code CASCADE Es modified to include y-decays from the initial compound nucleus and to include the GDR strength function are in good agreement with the data for GDR strength function parameters E = 20, and r = 12 MeV. The accurate description of the

G

measured spectral shapes over a factor of loe variation in intensity is a

remarkable achievement. Fig. 11 shows the sensitivity of the calculated curves

to changes in the GDR parameters. Fig. 12 shows that the high energy y-ray

intensity arises primarily from the decay of the initial Z a ~ i compound nucleus

before any particles are emitted. Thus the high energy y-yield directly probes

the properties of the initial compound nucleus. The agreement in magnitude

C4-344 JOURNAL DE PHYSIQUE

between the experiment and the statistical model calculation in the GDR region (Ey - ^{15 MeV and} greater) indicates sE1 - ^1-1.3. Since we expect SE1 ' 1, as is known for the ground-state GDR, this requires TJ. / r to be of order unity. Thus, on the average, the GDR built on an ensemble of all excited states decays mostly statisrlcally. This is to be contrasted with the GDRs built on l p l h states excited in (pay), which, as we have seen, decay nonstatistically. Indeed, w e d on the (p,y) results one might not have expected to see predominantly statistical excited-state GDR decays in light nuclei. The distinction appears to be that GDRs built on simple states such as lp-lh states decay mostly nonstatistically whereas GDRs built on the average state at high energies, which is considerably more complicated, decay mostly statistically. One might have expected that the GDRs which decay mainly statistically would be narrower, owing to the absence of the direct, or nonstatistical decay mode for these resonances. However, this is apparently not the case: at similar excitation energies, the total widths for these two types of G D R ~ are comparable ( e .g . ^{, for 'a~i*} - ^{34 MeV, r} - ^{12 MeV).}

Ey (MeV) E, (MeV)

t Fig. 10 (above left) - Gamma-ray produc-

tion cross section for 3 ~ e plus 2 5 ~ g . The smooth curves are statistical model cal- culations with the indicated GDR para- meters (Ref. 3).

Fig. 1 1 (above right) - Examples of CASCADE calculations for different GDR parameters (Ref. 3).

Fig. 12 (ri ht) - A decomposition of the

calculated %le - 2 5 ~ g spectrum. Each

curve is labelled by the particle emitted

preceeding the y-ray (Ref. 3).

For E ( 3 ~ e ) > 20 MeV there is an excess of yield at E " 20 MeV which cannot be explained by a statistical calculation. Angular distributions show some Y

for#ard/backwarcl asymmetry [even at low E( 'lie)] which increases with increasing E( 3 ~ e ) . These two features indicate non-negligible nonstatistical contributions at higher energies. This shows that one must be cautious when using light complex projectiles for statistical studies! There are only a few known examples of nonstatistical complex particle capture through the GDR.~' Given the success of the (p,y) analysis discussed above, it would be interesting to try to understand such reactions in terms of the spectroscopic factors for complex particle transfer.

A stu~3~~' of L Z + ~ gives direct evidence in support of El dominance in the statistical emission of high energy y-rays. These data (Fig. 13) show a strong inhibition of high energy E " EG ' 20 MeV y-emission relative to that observed in **Mg + ^{'He. The} inhibition Y. follows from the expectation that dipole y-emission in self-conjugate nuclei should be inhibited from T=O initial states, since such decays must necessarily change isospin and since the density of T-1 final states at moderate excitation energies is much less than T-4 final states.

Thus the high energy y-yield from " C + + ' o , Which populates T=O initial compound states, should be much less than that from 2 5 ~ g + ^{' I i e} which populates equally both 1- and lkl initial states. At low E the spectra from the two reactions are similar, since the emission of a particle preceeding the y-decay tends to Y

wash out the effects of isospin. Shown in Fig. 10 are CASCADE calculations for both pure and completely mixed isospin, along with a calculation in which isospin mixing increases linearly with energy, with a value of 3% for the initial

28 Si*(Ex -- 3 4 MeV) compound nucleus. Thus compound nuclear isospin is still relatively pure in this case! Here E2 emission is not negligible, being of order 15% in the high energy region (Fig. lo ).

0 10 20 30 40

Gornmo E n e ~ g y ( M e V )

F i g . 13 - Gamma r a y s from 1 2 c + 160, ~ ( ' ~ 0 ) = 40 MeV, E ( ~ * s ~ * ) = 34 MeV.

CASCADE c a l c u l a t i o n s : s o l i d l i n e - c o m p l e t e l y mixed i s o s p i n , l o n g dash - 3%

i s o s p i n mixing, s h o r t d a s h - p u r e i s o s p i n , a l l c u r v e s E l + E2; l o n g - s h o r t d a s h

- E2 o n l y ( R e f . 18).

C4-346 JOURNAL DE PHYSIQUE

Statistical GDR Dc2CayS in Medium and Heavy Nuclei There are a number of new s t u d i e ~ ~ ~ - ~ ~ of statistical GDR decays following collisions of complex projectiles ( A = 12 and greater) with medium and heavy nuclei. All experimental spectra show a bump at E ' EG corresponding to excited-state statistical GDR decays. The interesting physics lies in the properties of the GDR strength Y

function in different systems, and its dependence on properties of highly excited nuclei such as excitation energy, spin and perhaps also nuclear deformation.

Figs. 1 4 and 15 show recent Oxford measurements2' of y-decay spectra from excited

6 3 76 A S

Cu, Kr and IZ7cs compound nuclei formed in IZc and 0-induced reactions.

High energy y-rays were detected in a large 25x30 cm NaI with an active anticoincidence shield, in coincidence with low-energy y-rays (from near the end of the decay cascade) detected in a small NaI "trigger" detector located near the target. Time-of-flight pemitted accurate separation of y and neutron-induced events. In the singles measurements in light nuclei described previously, neutron backgrounds were negligible as verified by pulsed beam time-of-flight.

Barrette and sandorfiz3 have emphasized the importance of using such a detector in order to minimize the response function distortion of the spectrum shape due to lineshape tails, and to obtain good cosmic-ray background suppression and hence clean spectra at high E.

v"

Fig. 14 - Gamma ray spectra from the decay of 7 6 ~ r * at Ex = 53.9 MeV (top), 46.3 MeV (middle) and 44.0 MeV (bottom).

Circles are 180 = 5 8 ~ i data and crosses are 12c + 6 4 ~ n . The cross section scale applies to the 180 data; the 12c

+ ^{6 4 ~ n} data has been normalized to the 180 + ^{5 8 ~ i} data. The solid curves are statistical model calculations with the indicated GDR parameters (Ref. 24).

Fig. 15 - Observed high energy y-ray intensities for the decay of three different compound nuclei: Top:

1 2 7 ~ s (Ex = 48.4 MeV), crosses 12c +

l151n, circles ' 0 ' + 1 0 9 ~ g ; Middle:

7 6 ~ r (Ex = 53.9 MeV), crosses 12c +

6 4 ~ n , circles 180 + 5 8 ~ i ; Bottom:

6 3 ~ u (Ex = 54.3 MeV), crosses 12c +

5 1 ~ , circles 180 + 4 5 ~ c . The solid

curves are statistical model calcu-

lations with the indicated GDR para-

meters (Ref. 24).

Fig. 16 shows a c a l c u l a t e d spectrum decomposition i n t o i n d i v i d u a l components f o r 7sKr*. As i n t h e e a r l i e r example, t h e y-decay of t h e i n i t i a l compound nucleus is t h e s t r o n g e s t component a t l a r g e Ey, whereas most o f t h e low- e n e r g y y-rays are produced a f t e r s e v e r a l p a r t i c l e s have been e m i t t e d . , Although t h e p r o b a b i l i t y ( p e r MeV) o f high energy y-emission p e r cascade is small, "few x t h e compound formation c r o s s s e c t i o n i s l a r g e ( u c = 715 m t ~ i n Fig. 1 6 ) and t h i s r e s u l t s i n a l a r g e y-production c r o s s s e c t i o n u -; uc . ry / r ^" hundreds o f

@/mv a t E _y - _=G' Y

Evidence i n f a v o r o f t h e dominance o f i n i t i a l compound nucleus decays a t h i g h E h a s been r e p o r t e d by s e v e r a l groups. A Copenhagen group2+ h a s o b t a i n e d d i f f e r e n c e s p e c t r a f o r Y ON^ + 180 and + 4 8 ~ d + 170 where E ( I 7 0 ) was a d j u s t e d t o form l e 5 E r a t an energy lower t h a n + s e ~ r b y approximately t h e energy o f a s i n g l e evaporated neutron; t h e r e s u l t i n d i c a t e s t h a t 30-40% o f t h e GDR s t r e n g t h i n l s e ~ r decays come from t h e i n i t i a l contpound nucleus. A t rookh haven,^^ y-y decay c o i n c i d e n c e s t u d i e s o f + I ' O T ~ u s i n g Ge(Li) and l a r g e N a I d e t e c t o r s show t h a t a h i g h energy y is most l i k e l y t o be e m i t t e d e a r l y i n t h e decay cascade. A t

~ e i d e l b e r g " a charged p a r t i c l e - y c o i n c i d e n c e s t u d y o f +'o + "Ni shows c l e a r l y t h a t t h e e f f e c t i v e t e m p e r a t u r e o f t h e observed p r o t o n s p e c t r a is l e s s when a high-energy y is i n coincidence, i n d i c a t i n g y-emission most o f t e n preceeds proton e v a p o r a t i o n . Also, t h e proton/alpha r a t i o i n t h e e v a p o r a t i o n spectrum i n c r e a s e s when a h i g h e n e r g y y-ray c o i n c i d e n c e is r e q u i r e d , 2 s i n d i c a t i n g W R decays from low s p i n i n i t i a l s t a t e are most p r o b a b l e . l%e p r e f e r e n c e f o r low-spin W R decays is a f e a t u r e o f CASCADE c a l c u l a t i o n s which a r i s e s from t h e f a c t t h a t t h e f i n a l state l e v e l d e n s i t y is g r e a t e s t f o r low J . l l l e W R decays average o v e r f i n a l - s t a t e s p i n , w i t h t h e r e s u l t t h a t a n g u l a r d i s t r i b u t i o n s a r e n e a r l y i s o t r o p i c a t h i g h E

is not p o s s i b l e a t t h i s time t o p r e s e n t a c o n s i s t e n t q u a n t i t a t i v e p i c t u r e o f t h e p r o p e r t i e s o f t h e GDR s t r e n g t h f u n c t i o n i n h i g h l y e x c i t e d n u c l e i . Although a number o f experiments have been performed, i n s e v e r a l c a s e s t h e a n a l y s i s is s t i l l i n p r o g r e s s while i n some o t h e r c a s e s t h e i n t e r p r e t a t i o n is based on a comparison o f d a t a w i t h approximate e x p r e s s i o n s u s i n g e f f e c t i v e t e m p e r a t u r e f a c t o r s , t h e accuracy o f which i s d i f f i c u l t t o judge.

Fig. 16 - Decomposition of the calcu- lated spectrum into individual compon- ents. The curves are labelled by the particles emitted preceeding the y-ray

(Ref. 24).

C4-348 JOURNAL DE PHYSIQUE

Several different experiments suggest downward shifts of EG in highly excited systems. I'he measured Spectra of Figs. 14 and 15 are well described by CASCADE calculations in which the W R energy EG is 1-1.5 MeV lower and the width

r is comparable or somewhat ( ' 2 MeV) broader than the g.s.-GDR in the same or neighboring nuclei. This is illustrated in the case of g 3 ~ ~ * in Pig. 15, for which the best single-lorentzian calculation is shown along with a curve showing the expected shape based on the ~.S.-GDR parameters.26 In each case the data shown in Figs. 14 and 15 are the superposition of results from both and IZc entrance channels, which show identical spectral shapes, thus confirming the hypothesis that the y-decays come from a thermally equilibrated compound nucleus. In principle, such decays could lead to different spectrum shapes if the GDR strength function depends on angular momentum, since these two channels bring in different amounts of angular momentum [AP(mean) ' 6 - 8 R ] . Hence the GDR is insensitive to small spin differences, indicating &EG/GP < 0.05-0.1 MeV per unit of angular momentum.

Recent Brookhaven dataz3 have also been compared with realistic UISCADE calculations; the results (Fig. 17) show downward EG shifts for "0 + " ~ i and

I B

o + = * ~ i , while measurements of 2 9 ~ i + + Z 4 ~ n are consistent with no shift and

34 S + '30~e data indicate evidence for an upward shift in EG. Also the El strengths required to fit the data are considerably less that 1 for all but the heaviest case, which is indeed puzzling, since the g.s.-C;DR strengths are typically 1-1.5 classical sum rules in this mass region. So far, this is the only experiment in medium or heavy nuclei which is sensitive to sS

~ l '

Fig. 17 - Gamma-ray spectra from four fusion reactions. The observed cross sections have been divided by the total reaction cross section to obtain the vertical scale. The solid curves are CASCADE calculations with the indicated GDR parameters (Ref. 23).

GAMMA RAY ENERGY ( M e V 1

Ifhe Strasbourg resultsr0 on Z s ~ i + lZOsn and the Heidelberg resultsL2 on

3 1

S + l Z 8 ~ e suggest downward EG shifts, although in these cases a detailed comparison has not yet been made with statistical model calculations. The Heidelberq and Brookhaven S + Te reactions form neighboring Er isotopes at similar excitation energies and thus one would expect similar GDR parameters; the fact that there are such large apparent differences in EG for these two cases suggests experimental problems. The Heidelberg experiment, performed with a N a I crystal ball, also suggests a substantial spin dependence, L\EG ^" several MeV downward over the range of L (initial) up to 60 i i , which is much larger than theoretical e~~ectations.~' The Copenhagen groupZL has also been studying statistical GDR decays in rare earth nuclei (including Er) with a spin spectrometer, so one may hope that an experimental consensus on these matters will emerge before long.

several e ~ p e r i m e n t s ' ~ ' ~ ~ ' ~ ~ ~ " show evidence for excited-state GDR widths that are broader than typical g . s . 4 R widths. In the work of Draper et al., ^{L 9} who looked at C;DR decays following deep--inelastic scattering, there is evidence

for such a broadening, as the case in the 2 s ~ i + ^{i'4~n and 3 4} + ^~ 1 3 0 ~ e Brookhaven data.'" One interesting possibility, not yet realized, is that GDR decay studies at high energy and spin may teach us about the average defonnaiion of rapidly rotating nuclei. 'Phis is based on an analogy with statically deformed cold nuclei for Which the GDR is known to split into two components corresponding to GDR vibrations along the long and the short axes of the deformed nucleus. lhere is the possibility, but no solid evidence yet, that some of the abSerPed broadening may be related to deformation. One may still hope to see experimentally a spectrum shape which requires a 2-component GDR strength function1

Conclusion while a great deal of exciting new progress has been made in the past two years in the study of GDRs built on excited states, many puzzles remain. The broadening of both statistical and nonstatistical excited-state GDRS in light nuclei is not understood. It will be interesting to see the (p,y) reaction used to explore high-lying single-proton distributions in light nuclei and also to explore further the interesting transition between nonequilibrated and equilibrated GDR decay modes. The new area of statistical GDR decay studies in complex-particle collisions, begun in earnest only a few years ago, is just beginning to offer quantitative information on the nature of the GDR in highly

excited systems. Now that the initial euphoria of discovery of this phenomenon has passed, it is clear that a lot of hard work lies ahead both in experimental measurement and interpretation, in order that GDR parameters may be reliably extracted from complex reaction data1

1 am indebted to my colleagues who have shared in this work, including D.H. Dowell, E.F. Garman, A.M. Sandorfi, M.N. Harakeh, G. Feldman, J.L. Osborne, and R. Loveman.

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