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Direct reactions with heavy ions
NuclearPhysics A400(1983)153c-170c.O North-HollandPublishing Co., Amsterdam Not to bereproduced byphotoptitor microfilm without written permission from
153c
thepublisher.
DIRECT
REACTIONS Masayasu
Institute
WITH
HEAVY
IONS
ISHIHARA
of Physical and Chemical Wako-shi, Saitama, Japan
Research
Abstract: Several aspects of quasi-elastic scattering in heavy-ion reactions with projectiles of A < 20 and E = 10 to 20 MeV/ nucleon are discussed emphasing properties associated with simple direct transfer mechanisms. Studies both of reaction mechanisms and of spectroscopy are treated. The discussion of reaction mechanisms is centered on the applicability of DWBA descriptions to quasi-elastic continuum spectra. Recent results on particle correlations, which reveal the importance of sequential ejectile breakup, and those on spin polarizations in very massive transfer reactions, which set a new constraint in interpreting the reactions, are also mentioned. Two types of spectroscopy with quasi-elastic reactions are discussed. One is the spectroscopy of cluster states, and the other is spectroscopy using particle-gamma coincidences. With regard to the former, latest results relating to the exotic "C transfer reaction, 12C('60,a)24Mg, are reviewed, and a recent observation in ('2c,11 B) reactions is mentioned to depict a new prospect of spectroscopy on highly-lying single particle states. With regard to the latter, several unique possibilities arising from recent experiments are summarized.
1.
Introduction
Although the title of this report should cover a vast field of heavy ion physics, I shall restrict myself to fairly narrow aspects of the field. The main emphasis of this report will be placed on those binary heavy-ion reactions leading to highly excited final states in the continuum region, while the large bulk of studies dealing with low-lying discrete final states will be barely touched. This is not to denigrate the significance of the studies on lowlying states, which have consistently constituted a major domain of heavy-ion physics, but rather to stress new prospects for the studies on highly excited final states, which have increased in importance as higher-energy projectiles became available. The type of reactions to be discussed should be further specified; we shall discuss the so-called quasi-elastic process in heavyion collisions with projectiles in the energy range of = 10 to 20 MeV/nucleon. We will concern ourselves mainly with strippingtype reactions. Such quasi-elastic processes may be distinguished from more complicated processes like deep inelastic scatteringorpre-equilibrium reactions by referring to the diagrams shown in fig. 1. The diagram at the right indicates a process in which the ejectile b emerges from a complex of projectile plus target so that the nucleons constituting the ejectile can originate from both projectile and target. Deep inelastic scattering and, more typically, pre-equilibrium reactions may be categorized by such processes. On the other hand, the quasi-elastic process may have more relevance to the diagram at the left, where the ejectile retains some memory of its history that it originally belonged to the projectile. If the quasi-elastic process is of this nature, there should be some possibility for the process
M. ISHIHARA
154c
Fig.
1.
Schematic
diagrams
of heavy
ion direct
reactions,
A
(a,b).
to be described as a relatively simple reaction to which directreaction theories such as the DWBA may be applied. So far there have been several different approaches proposed to describe the quasi-elastic process: one of the successful descriptions is that of the "sum-rule model"'), by which some gross properties of the process have been consistently accounted for on This is discussed in the the basis of macroscopic considerations. report by Siemssen, and therefore I shall emphasize the alternative approach which incorporates the microscopic treatment in terms of DWBA theories. The remainder of this report will be divided into two parts: in Section 2 recent studies on direct reaction mechanisms will be of DWBA theories to energybriefly reviewed, where applicability In Section 3, dissipative heavy ion reactions is a central subject. some prospects will be surveyed on two types of spectroscopic studies exploiting characteristics of heavy ion quasi-elastic processes. All studies involved are still in a premature stage of development, but one can anticipate some promising possibilities of the field.
2. 2.1
Direct
reaction
mechanism
THE GROSS PROPERTIES KINEMATICAL MATCHING
for quasi-elastic
OF QUASI-ELASTIC CONDITIONS
PROCESSES
scattering AND
Before moving to the microscopic treatment of quasi-elastic processes in terms of DWBA, it may be instructive to glance over the gross properties of these processes and to realize to what extent This they bear features characteristic of direct transfer reactions. may be done by referring to the kinematical matching conditions'), whose importance in determining reaction amplitudes has been verified from earlier studies3) on heavy-ion direct transfer reactions leading to discrete final states. According to Brink'), the kinematical matching conditions consist of two requirements, i.e., the conservation of total angular momentum and the conservation of linear momentum of the transferred particle (see fig. 2). The consequences of these conditions are on the average, the transferred particle should preferensimple: Then tially have the same velocity as the incident projectile. optimum values of Q and angular momentum transfer are predicted as
QoPt = m eff
(v2/2)
(3)
DIRECT
REACTIONS
WITH HEAVY
IONS
155c
k,= mv/fi
-
X,/R,
Aks
k,
AL=
x2 - X,
+
... (1)
- X,/R,=0 ‘/zko(R,
-R2)
+ Q.,,R/liv
=O
Fig.
. ..(2)
2. Kinematical matching conditions for heavy-ion cluster fer reactions. The notation is the same as in ref. 2.
trans-
and
ALoPt =
m
(vR
2
) = (mR2/uiR)ki
.
(4)
Naturally these values are proportional to the mass of the transferred particle. In detail, the matching conditions depend on the value of Al, which is the z-component of orbital angular momentum carried by the transferred particle before transfer in the rest frame of the projectile. This should give rise to a particular Q-value dependence of spin polarization for an ejectile in a stripping reaction. There are many dataavailable from earlier studies which show how these expectations are realized in quasi-elastic reactions. The fact that the optimum Q-value follows the predicted trends rather well has been known since the work of ref. 4). Fig. 3 illustrates the situation for angular momentum transfer, where y-ray multiplicities measured5) for different final channels are plotted versus the In contrast to the result for deep inelastic mass of ejectile. components, the data for quasi-elastic components follow the V-shaped pattern as anticipated from eq. 4. A more crucial test of the influence of matching conditions may be providedIt ejectile polari1 Mo(l'N, "B) shows zation6) (see fig. 4). in The 12B polarization a characteristic Q-value dependence, changing its sign with Q-value. This arises from the interplay between positive and negative Xl components, whose relative strengths vary for different Q-value regions as shown by individual cross sections calculated') by using the matching conditions. The evidence so far given is all in accord with kinematical conditions and strongly suggests the importance of a simple direct reaction mechanism for the quasi-elastic process. 2.2
ANALYSES OF QUASI-ELASTIC OF DWBA THEORIES
PROCESSES
IN TERMS
Among several studies dealing with DWBA theories8-'3), I shall mainly refer here to work by Udagawa and Tamura. These authors have developed two alternatives for DWBA theories applied to the quasiThe one may be termed as "(multiple) transfer elastic process. reaction" formalism") (denoted by A) which is in the spirit a straightforward extension of the usual DWBA theory with modifications introduced so as to deal with continuum final states. The other option is named "breakup fusion" formalism1'f'2) (denoted by B), in which a transfer reaction is described as a process due to
M. ISHIHARA
156c
0 0
2
4
MASS
6
6
IO
OF LIGHT
12
14
16
18
PRODUCT
Fig. 3. Gamma-ray multiplicity M, versus mass of ejectile observed5) in q3Nb + 120 MeV "N; average values of transferred angular momentum are shown. The solid,circles and open circles indicate, respectively, My at the centers of quasi-elastic and deep inelastic bumps in the energy spectra. The solid line represents the prediction from the matching conditions and the dotted line corresponds to the sticking condition. breakup of the projectile followed by fusion of one of the fragments The processes implied by these two formalisms may with the target. sound very different, but in reality could be very similar to each other according to the formal theoretical foundations. So far the transfer reaction formalism has been primarily applied to few-nucleon transfer reactions while the breakup fusion formalism has mainly been applied to more massive transfer reactions. Leaving the theoretical details to original papers, several examples of DWBA analyses are given below to show how far these The first example is again theories can reproduce experimental data. concerned with results of "B polarization measured") in one- and the seven-nucleon transfer reactions (fig. 5). As anticipated, theoretical result (using formalism A) for the one-nucleon transfer nicely reproduces both the energy and polarization spectra. It is more remarkable that the calculation can account for a large portion of the spectra even for the ("F, "B) reaction involving sevenThis result indicates that a simple direct mechnucleon transfer. anism strongly persists in fairly massive transfer reactions although contributions from more complicated mechanisms become apparent as well. This aspect has been further examined") for a more massive transfer reaction, 1s1Ta('4N,a), by applying the formalism B in treating energy and angular distributions (fig. 6). The theoretical curves seem to be consistent with the high-energy portion of the spectrum at different angles, although the large part of the spectrum The calculation indicates that the peak of the is left unexplained. energy spectrum of 'OB direct transfer is located at energies higher than that for the beam velocity while the breakup source-strength corresponding to the lower energy portion may be contributing to the This feature has relevance") to the well cx transfer channel.
DIRECT
REACTIONS
WITH HEAVY
E lab= 90
IONS
MeV
IO)
1.0
157c
I
QOP
+05-
cbl
P
/ _+=+I-
0
-0.5
[ 60
-50
-40 Q
-30
-20
-10
(MeV)
(b) 3pecti"a of '*B at 20° in the Fig. 4. Energy (a) and polarization reaction at 90 MeV incident energy61'). P is defined "'Mo('~N, “B) to be positive for PI Iki x kf. Experimental points are compared with theoretical curves (solid line) calculated') on the basis of matching The three dotted lines in (a) represent calculated cross conditions. sections for individual components of (111= 2,X1) in the order of from right to left. Xl = +2, 0, -2
*o-
(b)
10
-30
40
60
80
100
E,(MeV)
120
140
160
40
60
80
100
Eb
Ix,
140
160
(MN
5.. Energy and polarization spy;$;;(o$ '*B iI;l,th,; r-;a&~o;~v14 33Pa at 149 MeV and Th(13C,'*B) ). F, "B) Solid lines indicate the theoretical results in terms of the "trans(see text). fer reaction" formalism
Tf
9.
158c
M. ISHIHARA
Energy spectra of alpha particles Fig. 6. reaction at 115 MeV. Spectra calculated") formalism are shown by solid lines.
in the 181Ta('4N,n)'91Pt using the breakup fusion
established trend that smaller incident partial waves are more responsible for a moremassive transfer process. It may be worth while to cite a third example of DWBA analysis not only to give further support for the theory but also to show the ability of the theory to indicate some extra mechanism participating in quasi-elastic scattering. This is shown in fig. 7, where energy and angular distributions are compared for three c1 transfer reactions on the same &OCa target but with different projectiles16). The theoretical calculations using formalism A fit these distributions However, the very nicely in the case of "N and 13C projectiles. theoretical result clearly deviates from the experiment, especially induced reaction at forward angles. For the "Ne reaction, for "Ne the existence of a mechanism characterized by a forward peaked angular distribution, in addition to the usual direct transfer mechanism, is implied. One can immediately think of two plausible mechanisms relevant one is direct projecto the forward peaked component for "he; tile breakup and the second is the sequential breakup of the inelas6O final channe 1. tically excited projectile, both leading to the c1 + These two processes can be distinguished by looking at correlations between c1 and 160, and such experiments were performed by several groups'7-20). Fig. 8 shows the result taken for the 40Ca + *'Ne where coincidence yields reaction at 149 MeV by Shimoda et al."), The are plotted versus relative energy of the coincident particles. spectra are dominated by discrete lines corresponding to excited levels of "Ne, with no appreciable trace of the continuum components Similar conclusions which should be seen in case of direct breakup. are consistently obtained for the same reaction at different incident energies (130, 210 MeV) and for the *'Ne bombardment on a heavier Thus one can reasonably conclude that target "'Pb at 149 MeV. sequential rather than direct breakup is universally the primary mechanism for the forward peaked component.
DIRECT
REACTIONS
WITH
HEAVY
159c
IONS
.
%,(
. .
“Ne l6O) ?, 262 i&V
(to the left) and angular distributions (to Energy spectra Fig. 7. alpha-transfer reactions on the same the right) obtained for three "Ca ta:qet with different projectiles, 'ONe, I&N, 13Cwith= 8_5MeV/ Solid lines indicate calculated results based on the nucleon 1. The shaded areas in the energy spectra transfer reaction formalism. from an extra process. l6O) represent contributions of ("Ne, ExtzONe) I4 I I I
I8 I
0.0
I
I
I
I
I
(MeV) IO 6 I
(7.2’.-14.8’, , I1.5’.52.9’,
0.4
0.2 0.1 1
I’I 12
8 E,-o
Fig. 8. reaction the axis
4
0
(MeV)
"0 correlation in the 40Ca(20Ne,a'60)40Ca Results of u vs. Coincidence cross sections are pryjected at 149 MeVzO). 0. of relative kinetic energy, EU_O, between 01 and
on
160~
M. ISHIHARA
The vanishing strength observed for the direct breakup process does not necessarily contradict the notion of the breakup fusion formalism, which presumes the reaction to start with projectile breakup. According to the theoretical analysis I'),the breakup dominantly occurs at a relatively close distance of colliding nuclei so that the breakup source-strength primarily ends with subsequent fusion, leaving little strength available for three-body final channels. The examples shown above almost represent the present status of understanding of quasi-elastic reactions in terms of DWBA theories. In spite of several successes achieved, previous theoretical attempts only treat some specific aspects arbitrarily chosen and use various formalisms for different situations. To obtain a more unified perspective of quasi-elastic scattering, it is certainly desirable to examine the whole range of phenomena more systematically with a single formalism. A preliminary attempt along this line is already in progress by using formalism B15). In general, the breakup fusion formalism appears to have a better prospect than the transfer reaction formalism, since it can avoid direct manipulation of wave functions for unbound final states in the continuum region, which have to be dealt with in the latter formalism only with considerable ambiguities. The main physical ingredient for the former formalism scatis the optical potential, and detailed studies on quasi-elastic tering may provide some information about the form of potential in interior regions. 2.3
EXTRA COMMENTS ON VERY MASSIVE TRANSFER OR CHANNELS OF LIGHT PARTICLE EMISSIONS
REACTIONS
The DWBA analysis discussed in 2.2 indicates strong participation of some mechanisms other than the simple direct transfer mechanism for very massive transfer channels, i.e. for reactions involving light ejectiles. Indeed, a variety of mechanisms have been considered to account for the light-particle emission21) with different emphasis In order to pin down the relevant depending on the energy region. mechanisms for the region of = 10 MeV/nucleon, more experimental data The observation of spin on various properties are certainly needed. polarization of ejectile and/or residual nucleus may provide such information. measured for Fig. 9 shows recent results of2golarizations protons in the giNb(::~~pb\l;eaction ) (fte. 9(b)) and for the targetN,a) reaction The proton like residue in the ) (fig. 9(c)). polarization for the non-equilibrium component is consistently positive with values of = 20% over the whole range of proton energy, indicating the occurrence of negative-angle deflections in the reactions. for the c1 emitting reaction On the other hand, the polarization shows a more complicated energy dependence (angular dependence is is negaIn contrast to the proton case, the polarization weaker). tive for a wide range of lower energies with maximum (in absolute Posivalue) at energies a little higher than that of beam velocity. tive polarization occurs only at the highest energies. This difference is indicative of at least two different mechanisms participating in very massive transfer reactions, one represented by that for the (14N,p) reaction and the other to be characterized by negative polarThe dominance of the latter ization (positive deflection angle). 5gTb(7Li,n) reaction at 49 MeV by mechanism is suggested for the the observed polarization23 ) of target-like residue, which was found to be negative and nearly constant at P 2 -0.4 for different enerWe conjecture that the mechanism implied by the breakup fusion gies. formalism is very likely to be relevant to this particular reaction.
DIRECT
REACTIONS
WITH
HEAVY
161c
IONS
-0.2
-0.2
reactions involv9. Spin polarizations observed in 14N induced rotbns determined") by The polarization of ing light ejectiles. I? N,p) reaction at 95 MeV the double scattering method in the g3Nb( for the laboratory angle Op = 20° is shown vs. proton energy in (b). Differences between the forward and backward energy spectra shown in The Ep dependence of (a) may represent non-equilibrium components. to the polarization can be accounted for by attributing P ^- +22% non-equilibrium component and zero polarization to the remainder, i.e., the equilibrium component. The average polarization of the target-like residues in the 15'Tb( '\N,ol) reaction ) from circular polariat 115 MeV determinedz3 zation of gamma rays is shown in (c) by the contour plot in the plane of energy vs. angle of the alpha particle. The polarization results shown above certainly provide a new set of constraints for any appropriate theories to accomodate, and attempts to develop theoretical descriptions to account for the observed features are desirable.
3.
Prospects
for
spectroscopic
studies
We obtain hintsz4) of the types of spectroscopy to be pursued with energy-dissipative direct heavy-ion reactions by consulting again the kinematical matching conditions. Fig. 10 shows energy vs. spin diagrams for the residual nucleus in heavy ion transfer reactions, where the usual yrast band (solid line) and the band of states with configuration of target plus transferred cluster (dashed line) are indicated. The states of molecular resonances are thereThe region corresponding to fore represented by the latter line. Its optimum kinematical matching conditions is marked by a bold X. location relative to those bands can vary significantly from reaction to reaction. For the case of (I) the region of matching hits the area close to the bands, therefore giving rise to the expectation that cluster states nearby would be populated selectively. In that case, the corresponding structures may show up even in the highly excited continuum region in the energy spectrum of ejected particle. The studies aiming at this type of particle spectroscopy are described in subsection 3.1.
M. ISHIHARA
162~
1
Yrast
-
-
Cluster config.
8oc’5=Tb(‘4N,al’6=Yb .E,4N=
115 MeV
SO-
Fig. 10. Diagrams of excitation energy Ex vs. spin J for the residual nucleus produced in transfer reactions to illustrate the location of the kinematically matched region (indicated by cross) relative to the yrast band (solid line) and the band of cluster configurations (dashed The two dotted lines in line). each of the diagrams correspond to the two requirements (eqs. (1) and (2)) of matching conditions. Two typical situations are given ") by the '2C(160,a)24Mg reaction (I) and the 15gTb('4N,a)16gYb reaction (II,). Residual nuclei free from subsequent particle emissions may be formed if they are populated in the region between the solid and dash-dot lines in (IIb).
In many reaction systems like the case of (II,), the matching region lies deeply inside of the domain of high level density, therefore allowing the final residual nuclei eventually to decay by the Here one can measure emission of gamma rays as well as particles. y-rays in coincidence with ejectiles, where features characteristic of direct reactions can be exploited in order to distinguish from The the usual in-beam y-ray spectroscopy using fusion reactions. prospects for such spectroscopy are described in subsection 3.2. 3.1
3.1.1
SPECTROSCOPY Transfer
OF CLUSTER of massive
TRANSFER
REACTIONS
clusters
As a most prominent work in this category, one can quote the experiment done at Texas A&M25), where "C transfer on a "C nucleus was studied in the 12C('60,a) 24Mg reaction by looking at inclusive c1 As shown in fig. 11(a), a number of small structures are spectra. observed on top of the huge continuum distribution, which after This feature was background substraction appear as in fig. 11(b). and the discrete lines were conjectured to in fact anticipatedz6), be associatedwithexcitation of molecular-resonance-like states. In fact, the excitation energies of these lines nicely fit those of the molecular states identified via study of excitation functions in the 12c + 12C inelastic scatteringz7). The above conjecture, however, has been challenged by two major criticisms which argue for very different mechanisms to account for
DIRECTREACTIONSWITHHEAVYIONS
Q+‘*cI~+)+‘~c(~+I
0
IO
20
30
40
163~
td)
50
Ea(c.m.) (MeV) results3') on the 12C('60,a)24Mg reaction at Fig. 11. Experimental Alpha particles are always detected at 5.5O. 142.4 MeV. (a) Singles energy spectrum of alpha particlesz5). (b) Singles spectrum after subtraction of continuum backgroundz5). (c) Spectrum of alpha particles corresponding to the final channel This is obtained by integratof CY + (24Mg* + '*C(g.s.) + "C(2+)). ing coincidence cross sections, where the coincidence data for c1 at 5.5O and "C at 30°-480 are used and three-body kinematics involving "Mg nucleus are assumed. an intermediate + (d) Same as in (c) for the final channel of a + (24Mg* + "C(2+) "c(2+)). to the finalchannelof (e) Spectrum of alpha particles corresponding It is obtained in a similar way 12C(g.s.) + ('60X -+ '2C(g.s.) + a). as for (c) and (d) but based on coincidence data for cx at 5.5O and "C at 8O-l8O, which nicely followed three-body kinematics expected for the relevant final channel. (f) Spectrum of alpha particles corresponding to the final channel of 'Be(g.s.) + ("Ne* + 160(g.s.) + a) obtained from 160 + c1 coincidence data.
164~
M. ISHIHARA
the phenomenon. One attributes the observed structures to excitation of the molecular resonance states via compound- but not directreaction process"), and the other to sequential c1 decay of excited projectile-like fragments formed via some direct reaction processes"). In particular, evidence for the importance of the latter mechanism has been obtained"r 31) in recent experimental investigations of the bombarding energy dependence of the peak energies of the resonance-like structures. More decisive information on the breakup of projectile-like fragments can be obtained by observing correlations between a particles and heavy fragments. The experiment performed at 0saka3') provides most extensive data for such correlations, which showed that the sequential breakup is certainly very important. One of the new findings of the study is that the breakup of excited "Ne formed by an c1 pickup reaction is even more siqnificant than that of inelassupposed to be the tically excited 160, which has been persistently This finding appears to give-a reasonable account main contributor. for the puzzling question why resonance-like structures in the alpha spectra are weaker33) for, e.g., the 13C + I60 reaction than for the I60 reaction. A recent studv3\) of '60(12C.BBe)20Ne reveals C+ that the cross section of the CY transfer for the i6O i "C reaction is stronger than that for the '60('3C,qBe)20Ne reaction. The correlation data further providedarough estimate of the strengths of the sequential breakup components which can be directly compared with the strengths in the singles spectrum (see figs. 11(e) and (f)). The breakup components, particularly due to "Ne*, are strong but not sufficiently to account for the whole strengths in the singles. Thus it is still possible that the cluster transfer process is contributing to the phenomenon to some extent. An attempt to elucidate this last aspect has also been made at Osaka by looking at the correlation of the c1 particle with "C detected at relatively backward angles in order to observe the correlation in the "C - "C final channel, to which the molecular states of "Mg strongly decay. lTairly st:Tng coincidence cross C(2+) and "C(2+) + "C(2+) sections are observed for both C9.s. + as shown in figs. 11(c) and (d), a though the relation of those events with the molecular states is not yet definite. More studies along this line are desirable to further elucidate the intriguing possibility that the reactions represent massive-cluster transfer. 3.1.2
One-nucleon transfer high-spin states
to high-lying
In the previous subsection an exotic reaction of massive cluster transfer was discussed. For reactions involving the transfer of fewer nucleons, one can anticipate more significance of simple direct trasnfer mechanisms so that the spectroscopy of cluster transfer may This anticipation indeed appears to be correct for onework better. nucleon transfer reactions, according to our recent studies3') at Texas A&M. 144Sm('2C,11B)'45Eu Fig. 12 shows the "B spectrum observedinthe reaction at 180 MeV. Besides several discrete lines at lower excita(indicated by a and b in tion, we see prominent gross structures fig. 12) in the region of excitation energy Ex = 6-8 MeV, which are This spectrum clearly distinguishable from the underlying continuum. reminds us of the spectrum recently observed in the 14*Sm(*He,t) reaction36). Indeed, the peaks a and b correspond in energy to those lines seen in the (4He,t) reaction, which were assigned to lh 9/2 and li 13/2 single particle states within the major shell one 5% above Thus the gross peaks in the heavy-ion reaction the Fermi surface.
DIRECT
REACTIONS
WITH HEAVY
IONS
165~
2000. '44Sm('2C , “B) 14’Eu
i
E = IEOMeV
t
0
100
200 channel
300
400
reaction at Fig. 12. Energy spectrum of "B in 144Sm('2C,"B)'45E~ The centers of two peaks indicated by a and b correspond 180 MeV35). to excitation energies of = 6.0 and 2 7.5 MeV, respectively. may also be associated with those high-lying high-spin states. In earlier studies of heavy-ion reactions, such peaks have never been incident energy recognized 37,38), probably because of insufficient or the contamination caused by kinematically broadened peaks, which frequently arise from ejectile excitations and obscure the energy Such contaminating peaks appear spectrum at the region of interest. only weakly at lower excitation energies for the case of the "B ejectile. The strong population of high-energy particle states found in proton transfer reactions may open a new field of spectroscopy analogous to but complementing the studies of deep-hole states. The heavy-ion reaction used has been found to have some advantage over the ($He,t) reaction, yielding much stronger population of high-lying states compared to low-lying states. One can speculate on additional advantages such as j-selectivity. Studies to explore such aspects are presently in progress. 3.2
GAMMA-RAY
SPECTROSCOPY
IN HEAVY
ION DIRECT
REACTIONS
The first experiment of this category was made at IPCR by rast line in coincidence with forward observing y cascades along the emitted alpha particles in the Y "Tb(14 N,axny)Yb reactions3'). It was anticipated that the (14N,n) reaction occurs via a peripheral direct reaction and populates residual states in a fairly confined R range around the optimum A&-value predicted from the matching conset a ditions. If this is the case, the reaction can automatically high-spin window on the entry states of y cascades, enhancing relative strengths of y transitions in high-spin yrast region. Those of most massive transfer channels are favoured in producing the window at highes.t spin values, as seen from fig. 3. Such expectations have turned out to be essentially fulfilled. As shown in fig. 13, relative intensities of high-spin transitions are largely enhanced for the forward alpha emission (direct reaction component) as compared
166c
M. ISHIHARA
Fig. 13. Relative gamma-ray intensity for transitions along yrast bands measured in coincidence with high-energy forward alpha particles (top) and with backward alpha particles (bottom) in the 15sTb(‘4 N,axny)AYb reactions at 95 MeV3'). No appreciable side feeding is observed below I = 10 for the "direct" component. to the case of the backward alpha emission (fusion reaction component). Research using the above technique has been used to study level schemes in yrast regions"). Here a crucial question is whether the method can ever be competitive in producing useful data with studies made by the usual technique incorporating fusion reactions. The primary disadvantage of using direct reactions is inefficiency in gaining statistics partly due to its smaller cross section and partly due to limitations in detection efficiency of coincidence particles. In order to compensate for those deficiencies, particular features of heavy-ion direct reactions should be exploited. Several experiments have been performed recently to explore such possibilities, and some promising aspects have been observed as listed below. 1) Formation of a high-spin window: this is the aspect stressed in the study of the 15'Tb(14N,a) reaction. The average R value of the window has been examined in other reactions by measuring y-ray multiplicities, and fairly large L values were indicated for channels associated with emission of p, d, t as well as c14'--lt3). In particular, the observation made at ORNL43) appears to be interesting of the entry states created in (fig. 14). The averagespinvalue massive transfer reactions could sometimes appreciably exceed the If this conclusion range of critical II values for fusion reactions. is correct, use of such reactions may have considerable merit in investigating very-high-spin states in the yrast region. The measurement of the coincident particle provides an easy to a particular final means") to identify y rays corresponding nucleus among various possible channels permitted via sequential This corresponds to measuring excitation particle evaporation. functions in the case of fusion reactions, and simplifies the experimental procedure considerably (see fig. 15).
DIRECT
REACTIONS
Fig. 14. Average values of transferred angular momentum for partial fusion reactions (two-body massive transfer reactions) determined from gamma multiplicity measurements are compared with the critical angular momentum R,, for fusion reactionsQ3).
WITH HEAVY
IONS
167~
Fig. 15. Comparison of cross sections of different final channels following the 15 gTb ( 1 li N,a) reaction at 115 MeV4') determined from y-ray intensities as a function of energy of coincident alpha particle detected at 15O.
The features of 1) and 2) can also be used for fusion reactions by sum-energy spectrometers and/or multiplicity-filter detector arrays. Use of the particle-y technique, however, can avoid introducing such complicated instrumentation. the direct reaction creates spin orien3) Spin orientation: tations in residual nuclei preferentially along the direction normal Thus the maximum allowed alignment could be the reaction plane. larger than in fusion reactions, giving rise to larger asymmetry of y emissions and therefore to higher sensitivity in multipolarity assignments. Moreover, direct reactions can produce non-vanishing polarizations which can seldom be obtained with fusion reactions. The magnitudes of spin alignment (Pzz) and polarization (P,) of residual nuclei have been studied for quasi-elastic reactions in 1% + lsqTb collisions at 115 MeV as a function of atomic number of ejectilek5). The results obtained (fig. 16) indicate that fairly for the region of large P,, and P, are indeed produced, particularly ejectile corresponding to medium-mass transfer. 4) Well defined entry states (or regions) for y cascades: direct reactions can sometimes populate excited states stable with Depending on energy respect to particle emission (see fig. lU(IIb)). resolution for the particle spectrum and on level density of the residual nucleus, the entry states for the y cascade can be defined either as an isolated level or as a region of excited states with a This feature, which is not obtained in specific excitation energy. usual fusion reactions, facilitates selection of particular flow Moreover, thoseentry statesmaybeofa particulines of y cascades. of direct reactions. lar nature, being chosen by selectivities
M. ISHIHARA
16%~
15’-j-b+ 14N at IrSMeV
Fig. 16. Alignment Pzz (solid circles) andpolarization P, (open circles) for the tarqet-like resi-
~i:l”~~~~~~~~~
“:~ -06t-
mined
based on out-of-plane
par-
i
Experiments pursuing this aspecthavebeen reportedrecently46"7f, where y-rays following high-spin particle states were measured in one-nucleon transfer reactions of Er(160,150) and Er("C,"C), proving the usefulness of the technique in studying states otherwise inaccessible. of the particle-y spectroscopy As stated before, applicability This situation is mainly hampered by inefficient data collection. may be largely improved by using higher energy projectiles, since, e.g., the angular distribution of ejectiles at higher energies tends to be more confined along the beam direction, leading to a larger Thus altogether detection efficiency for the coincident particle. the prospects for particle-y spectroscopy appear to be bright. Acknowledgement The author acknowledges discussionswith H. Kamitsubo, T. Inamura, T. Nomura, H. Utsunomiya, K. Ieki at IPCR, K. Nagatani at INS, K. Katori, T. Fukuda, T. Shimoda at Osaka University, E. Takada, T. I am greatly Murakami, and D. Haenni at Texas A&M University. indebted to T, Udagawa at University of Texas for discussions Of Special thanks are due to the theoretical aspects of the paper. data group of Osaka University, who have provided some expeximental This work was partly supported by the foundaprior to publication. for non-energy sciences. tion of Japan-U.S. collaboration References 1)
2) 3)
41
J. Van Driel, S. Gonggrijp, J. Wilcvnski, K, Siwek-Wilczinska, D.C.J.M: Hageman, R.V.F. Janssens, J. Lukasiak, and R.H. Siemssen, Phys. Rev. Lett. 45 (1980) 606. D.M. Brink, Phys. Lett. 4OBr1972) 37. N. Anyas-Weiss, J.C. Corxl, P.S. Fisher, P.N. Hudson, A. Menchaca-Rocha, D.J. Millener, A.D. Panagiotou, D.X. Scott, D. Strottman, D.M. Brink, B. Buck, P.J. Ellis, and T. England, Phys. Lett. Cl3 (1976) 2241. P.J. Siemens, J.P. Bondorf, D.H.E. Gross, and F. Dickmann, Phys. Lett. 36% (1971) 24.
DIRECT
5)
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25) 26) 27)
28) 29)
30)
REACTIONSWITH
HEAVY
IONS
169c
M. Ishihara, J. Numao, T. Fukuda, K. Tanaka, and T. Inamura, Features of Heavy Ion Collisions, Proc. Symp. on Macroscopic p. 617. Argonne, 1976, ed. D.G. Kovar (ANL Report ANL-PHY-76-2) K. Sugimoto, N. Takahashi, A. Mizobuchi, Y. Nojiri, T. Minamisono, M. Ishihara, K. Tanaka, and H. Kamitsubo, Phys. Rev. Lett. 39 (1977) 323. K. Tanza, M. Ishihara, H. Kamitsubo, N. Takahashi, A. Mizobuchi, and K. Sugimoto, J. Phys. Sot. Japan Y. Nojiri, T. Minamisono, 44 suppl. (1978) 825. c Kishimoto and K.-I. Kubo, Texas A&M Cyclotron Institute Annual Report (1977) p. 58. R. Shyam, G. Baur, F. Rosel, and D. Trautmann, Phys. Rev. Cl9 (1979) 1246. T. Udagawa and T. Tamura, Phys. Rev. Lett. 41 (1978) 1770; T. Udagawa and T. Tamura, Proc. Symp. on Continuum Spectra in Heavy Ion Collisions, San Antonio, 1979, ed. T. Tamura, J.B. Natowitz, and D.H. Youngblood (Harvard Academic Publishers) p. 155. T. Udagawa and T. Tamura, Phys. Rev. Lett. 45 (198b) 177. Udagawa, D. Price, and T. Tamura, Phys. ztt. 116B (1982) 311. T. A. Kasano and M. Ichimura, Phys. Lett. 115B (1982) 81. M. Ishihara, T. Shimoda, H. Frahlich, H. Kamitsubo, K. Nagatani, T. Udagawa, and T. Tamura, Phys. Rev. Lett. 43 (1979) 111; M. Ion ColliIshihara, Proc. Symp. on Continuum Spectra inHeavy ed. T. Tamura, J.B. Natowitz, and sions, San Antonio, 1979, D.H. Youngblood (Harvard Academic Publishers) p. 89. T. Udagawa, private communication. H. Frijhlich, T. Shimoda,' M. Ishihara, K. Nagatani, T. Udagawa, 1518. and T. Tamura, Phys. Rev. Lett. 42 (1979) A.C. Shotter, A.N. Bite, J.M. Wouters, W.P. Rae, and J. Cerny, Phys. Rev. Lett. 46 (1981) 12. N. Takahashi, T. Yamaya, and K. Nagatani, E. Takada, T. ShiGda, Phys. Rev. C23 (1981) 772. Biirgel, M. Clover, C.H. Egelhaaf, H. Fuchs, A. H. Homeyer, E Gamp, D. Kovar, and W. Rauch, Proc. Int. Symp. on Selected Aspects of Heavy Ion Reactions, Saclay, 1982, ed. M. Martinot; p. 128. and C. Ngo, communication, T. Shimoda et al., unpublished. See, e.g., D.K. Scott, Nucl. Phys. A354 (1981) 375~. T. Sugitate, T. Nomura, M. Ishihara, Y. Gono, H. Utsunomiya, K. Ieki, and S. Kohmoto, Nucl. Phys. A388 (1982) 402. K. Ieki, M. Ishihara, T. Inamura, and S. Kohmoto, unpublished. E. Takada, Ph.D thesis, 1981, Texas A&M Cyclotron Institute (unpublished). K. Nagatani, T. Shimoda, D. Tanner, R. Tribble, and T. Yamaya, Phys. Rev. Lett. 43 (1979) 1480. M. Ichimura, E. Tzada, T. Yamaya, and K. Nagatani, Phys. Lett. 1OlB (1981) 31. T.M. Cormier, J. Applegate, G.M. Berkowitz, P. Braun-Munzinger, P.M. Cormier, J.W. Harris, C.M. Jachcinski, and L.L. Lee, Jr., Phys. Rev. Lett. 18 (1977) 940. M.M. Coinbra, N. Carlin Filho, T.M. Cormier, A. Szanto de Tolez, and P.M. Stwertka, Phys. Rev. Lett. 47 (1981) 632. W.D. Rae, R.G. Stokstad, B.G. HarveyyA. Dacal, R. Legrain, J. Mahoney, M.J. Murphy, and T.J.M. Symons, Phys. Rev. Lett. 45 (1980) 884; D. Branford, M.J. Levine, J. Barrette, and S. Kubono, Phys. Rev. C23 (1981) 549. P.M. Stwertka, T.M. crmier, M. Herman, N. Nicolas, A. Szanto de Toledo, M.M. Coimbra, and N. Carlin Filho, Phys. Rev. Lett. -49 (1982) 640.
17oc
31)
32)
33) 34) 35) 36)
37) 38)
39) 40) 41) 42) 43)
44)
45) 46) 47)
M. ISHIHARA
T. Murakami, E. Ungricht, N. Takahashi, Y.-W. Lui, Y. Mihara, R.E. Neese, E. Takada, D.M. Tanner, T.E. Tribble, and K. Nagatani, to be published in Phys. Lett. T. Shimoda, S. Shimoura, T. Fukuda, M. Tanaka, H. Ogata, I. Miura, E. Tanaka, M.-K. Tanaka, K. Takimoto, and K. Katori, submitted to Phys. Lett. N. Takahashi, T. Yamaya, R.E. Tribble, E. Takada, Y.-W. Lui, D.M. Tanner, and K. Nagatani, Phys. Lett. 108B (1982) 177. T. Murakami et al., unpublished. E. Takada, M. Ishihara, T. Murakami, E. Ungricht, Y.-W. Lui, R. Tribble, Y. Toba, and Y. Mihara, unpublished. S. Gales, C.P. Massolo, S. Fortier, E. Gerlic, J. Guillot, E. Hourani, J.M. Maison, J.P. Schapira, B. Zwieglinski, P. Martin, and V. Comparat, Phys. Rev. Lett. 48 (1982) 1593. S.T. Thornton, D.E. Gustafson, J.L?. Ford, Jr., K.S. Toth, and D.C. Hensley, Phys. Rev. Cl3 (1976) 1502. C. Olmer, M. Mermaz, M. Buenerx C.K. Gelbke, D.L. Hendrie, J. Mahoney, D.K. Scott, M.H. Macfarlane, and S.C. Pieper, Phys. Rev. Cl8 (1978) 205. T. Inaiii&a, M. Ishihara, T. Fukuda, T. Shimoda, and K. Hiruta, Phys. Lett. 68~ (1977) 51. D.R. Haenni, T.T. Sugihara, R.P. Schmitt, G. Mouchaty, and U. Garg, Phys. Rev. C25 (1982) 1699. H. Yamada, D.R. Zoi?iowksi, S.E. Cala, A.C. Kahler, J. Pierce, and T.T. Sugihara, Phys. Rev. Lett. 43 (1979) 605. K.A. Geoffroy, D.G. Sarantites, M.L.3albert, D.C. Hensley, D.A. Dayras, and J.H. Barker, Phys. Rev. Lett. 43 (1979) 1303. H. Yamada, C.F. Maguire, J.H. Hamilton, A.V. Ramaya, C.D. Hensley, M.S. Halbert, R.L. Robinson, F.E. Bertrand, and R. Woodward, Phys. Rev. C24 (1981) 2565. H. Utsunomiya, T. Nomu=, M. Ishihara, Y. Gono. T. Sugitate, K. Ieki, and S. Kohmoto, 1980 IPCR Cyclotron Progress Report, Vol. 14, p. 19. K. Ieki, M. Ishihara, T. Inamura, and S. Kohmoto, unpublished. P.D. Bond, J. Barette, C. Baktash, C.E. Thorn, and A.J. Kreiner, Phys. Rev. Lett. 46 (1981) 1595. A.J. Kreiner, P.DTBond, C. Baktash, J. Barrette, C.E. Thorn, and M.T. Collins, Phys. Rev. C25 (1982) 866. -
153c
thepublisher.
DIRECT
REACTIONS Masayasu
Institute
WITH
HEAVY
IONS
ISHIHARA
of Physical and Chemical Wako-shi, Saitama, Japan
Research
Abstract: Several aspects of quasi-elastic scattering in heavy-ion reactions with projectiles of A < 20 and E = 10 to 20 MeV/ nucleon are discussed emphasing properties associated with simple direct transfer mechanisms. Studies both of reaction mechanisms and of spectroscopy are treated. The discussion of reaction mechanisms is centered on the applicability of DWBA descriptions to quasi-elastic continuum spectra. Recent results on particle correlations, which reveal the importance of sequential ejectile breakup, and those on spin polarizations in very massive transfer reactions, which set a new constraint in interpreting the reactions, are also mentioned. Two types of spectroscopy with quasi-elastic reactions are discussed. One is the spectroscopy of cluster states, and the other is spectroscopy using particle-gamma coincidences. With regard to the former, latest results relating to the exotic "C transfer reaction, 12C('60,a)24Mg, are reviewed, and a recent observation in ('2c,11 B) reactions is mentioned to depict a new prospect of spectroscopy on highly-lying single particle states. With regard to the latter, several unique possibilities arising from recent experiments are summarized.
1.
Introduction
Although the title of this report should cover a vast field of heavy ion physics, I shall restrict myself to fairly narrow aspects of the field. The main emphasis of this report will be placed on those binary heavy-ion reactions leading to highly excited final states in the continuum region, while the large bulk of studies dealing with low-lying discrete final states will be barely touched. This is not to denigrate the significance of the studies on lowlying states, which have consistently constituted a major domain of heavy-ion physics, but rather to stress new prospects for the studies on highly excited final states, which have increased in importance as higher-energy projectiles became available. The type of reactions to be discussed should be further specified; we shall discuss the so-called quasi-elastic process in heavyion collisions with projectiles in the energy range of = 10 to 20 MeV/nucleon. We will concern ourselves mainly with strippingtype reactions. Such quasi-elastic processes may be distinguished from more complicated processes like deep inelastic scatteringorpre-equilibrium reactions by referring to the diagrams shown in fig. 1. The diagram at the right indicates a process in which the ejectile b emerges from a complex of projectile plus target so that the nucleons constituting the ejectile can originate from both projectile and target. Deep inelastic scattering and, more typically, pre-equilibrium reactions may be categorized by such processes. On the other hand, the quasi-elastic process may have more relevance to the diagram at the left, where the ejectile retains some memory of its history that it originally belonged to the projectile. If the quasi-elastic process is of this nature, there should be some possibility for the process
M. ISHIHARA
154c
Fig.
1.
Schematic
diagrams
of heavy
ion direct
reactions,
A
(a,b).
to be described as a relatively simple reaction to which directreaction theories such as the DWBA may be applied. So far there have been several different approaches proposed to describe the quasi-elastic process: one of the successful descriptions is that of the "sum-rule model"'), by which some gross properties of the process have been consistently accounted for on This is discussed in the the basis of macroscopic considerations. report by Siemssen, and therefore I shall emphasize the alternative approach which incorporates the microscopic treatment in terms of DWBA theories. The remainder of this report will be divided into two parts: in Section 2 recent studies on direct reaction mechanisms will be of DWBA theories to energybriefly reviewed, where applicability In Section 3, dissipative heavy ion reactions is a central subject. some prospects will be surveyed on two types of spectroscopic studies exploiting characteristics of heavy ion quasi-elastic processes. All studies involved are still in a premature stage of development, but one can anticipate some promising possibilities of the field.
2. 2.1
Direct
reaction
mechanism
THE GROSS PROPERTIES KINEMATICAL MATCHING
for quasi-elastic
OF QUASI-ELASTIC CONDITIONS
PROCESSES
scattering AND
Before moving to the microscopic treatment of quasi-elastic processes in terms of DWBA, it may be instructive to glance over the gross properties of these processes and to realize to what extent This they bear features characteristic of direct transfer reactions. may be done by referring to the kinematical matching conditions'), whose importance in determining reaction amplitudes has been verified from earlier studies3) on heavy-ion direct transfer reactions leading to discrete final states. According to Brink'), the kinematical matching conditions consist of two requirements, i.e., the conservation of total angular momentum and the conservation of linear momentum of the transferred particle (see fig. 2). The consequences of these conditions are on the average, the transferred particle should preferensimple: Then tially have the same velocity as the incident projectile. optimum values of Q and angular momentum transfer are predicted as
QoPt = m eff
(v2/2)
(3)
DIRECT
REACTIONS
WITH HEAVY
IONS
155c
k,= mv/fi
-
X,/R,
Aks
k,
AL=
x2 - X,
+
... (1)
- X,/R,=0 ‘/zko(R,
-R2)
+ Q.,,R/liv
=O
Fig.
. ..(2)
2. Kinematical matching conditions for heavy-ion cluster fer reactions. The notation is the same as in ref. 2.
trans-
and
ALoPt =
m
(vR
2
) = (mR2/uiR)ki
.
(4)
Naturally these values are proportional to the mass of the transferred particle. In detail, the matching conditions depend on the value of Al, which is the z-component of orbital angular momentum carried by the transferred particle before transfer in the rest frame of the projectile. This should give rise to a particular Q-value dependence of spin polarization for an ejectile in a stripping reaction. There are many dataavailable from earlier studies which show how these expectations are realized in quasi-elastic reactions. The fact that the optimum Q-value follows the predicted trends rather well has been known since the work of ref. 4). Fig. 3 illustrates the situation for angular momentum transfer, where y-ray multiplicities measured5) for different final channels are plotted versus the In contrast to the result for deep inelastic mass of ejectile. components, the data for quasi-elastic components follow the V-shaped pattern as anticipated from eq. 4. A more crucial test of the influence of matching conditions may be providedIt ejectile polari1 Mo(l'N, "B) shows zation6) (see fig. 4). in The 12B polarization a characteristic Q-value dependence, changing its sign with Q-value. This arises from the interplay between positive and negative Xl components, whose relative strengths vary for different Q-value regions as shown by individual cross sections calculated') by using the matching conditions. The evidence so far given is all in accord with kinematical conditions and strongly suggests the importance of a simple direct reaction mechanism for the quasi-elastic process. 2.2
ANALYSES OF QUASI-ELASTIC OF DWBA THEORIES
PROCESSES
IN TERMS
Among several studies dealing with DWBA theories8-'3), I shall mainly refer here to work by Udagawa and Tamura. These authors have developed two alternatives for DWBA theories applied to the quasiThe one may be termed as "(multiple) transfer elastic process. reaction" formalism") (denoted by A) which is in the spirit a straightforward extension of the usual DWBA theory with modifications introduced so as to deal with continuum final states. The other option is named "breakup fusion" formalism1'f'2) (denoted by B), in which a transfer reaction is described as a process due to
M. ISHIHARA
156c
0 0
2
4
MASS
6
6
IO
OF LIGHT
12
14
16
18
PRODUCT
Fig. 3. Gamma-ray multiplicity M, versus mass of ejectile observed5) in q3Nb + 120 MeV "N; average values of transferred angular momentum are shown. The solid,circles and open circles indicate, respectively, My at the centers of quasi-elastic and deep inelastic bumps in the energy spectra. The solid line represents the prediction from the matching conditions and the dotted line corresponds to the sticking condition. breakup of the projectile followed by fusion of one of the fragments The processes implied by these two formalisms may with the target. sound very different, but in reality could be very similar to each other according to the formal theoretical foundations. So far the transfer reaction formalism has been primarily applied to few-nucleon transfer reactions while the breakup fusion formalism has mainly been applied to more massive transfer reactions. Leaving the theoretical details to original papers, several examples of DWBA analyses are given below to show how far these The first example is again theories can reproduce experimental data. concerned with results of "B polarization measured") in one- and the seven-nucleon transfer reactions (fig. 5). As anticipated, theoretical result (using formalism A) for the one-nucleon transfer nicely reproduces both the energy and polarization spectra. It is more remarkable that the calculation can account for a large portion of the spectra even for the ("F, "B) reaction involving sevenThis result indicates that a simple direct mechnucleon transfer. anism strongly persists in fairly massive transfer reactions although contributions from more complicated mechanisms become apparent as well. This aspect has been further examined") for a more massive transfer reaction, 1s1Ta('4N,a), by applying the formalism B in treating energy and angular distributions (fig. 6). The theoretical curves seem to be consistent with the high-energy portion of the spectrum at different angles, although the large part of the spectrum The calculation indicates that the peak of the is left unexplained. energy spectrum of 'OB direct transfer is located at energies higher than that for the beam velocity while the breakup source-strength corresponding to the lower energy portion may be contributing to the This feature has relevance") to the well cx transfer channel.
DIRECT
REACTIONS
WITH HEAVY
E lab= 90
IONS
MeV
IO)
1.0
157c
I
QOP
+05-
cbl
P
/ _+=+I-
0
-0.5
[ 60
-50
-40 Q
-30
-20
-10
(MeV)
(b) 3pecti"a of '*B at 20° in the Fig. 4. Energy (a) and polarization reaction at 90 MeV incident energy61'). P is defined "'Mo('~N, “B) to be positive for PI Iki x kf. Experimental points are compared with theoretical curves (solid line) calculated') on the basis of matching The three dotted lines in (a) represent calculated cross conditions. sections for individual components of (111= 2,X1) in the order of from right to left. Xl = +2, 0, -2
*o-
(b)
10
-30
40
60
80
100
E,(MeV)
120
140
160
40
60
80
100
Eb
Ix,
140
160
(MN
5.. Energy and polarization spy;$;;(o$ '*B iI;l,th,; r-;a&~o;~v14 33Pa at 149 MeV and Th(13C,'*B) ). F, "B) Solid lines indicate the theoretical results in terms of the "trans(see text). fer reaction" formalism
Tf
9.
158c
M. ISHIHARA
Energy spectra of alpha particles Fig. 6. reaction at 115 MeV. Spectra calculated") formalism are shown by solid lines.
in the 181Ta('4N,n)'91Pt using the breakup fusion
established trend that smaller incident partial waves are more responsible for a moremassive transfer process. It may be worth while to cite a third example of DWBA analysis not only to give further support for the theory but also to show the ability of the theory to indicate some extra mechanism participating in quasi-elastic scattering. This is shown in fig. 7, where energy and angular distributions are compared for three c1 transfer reactions on the same &OCa target but with different projectiles16). The theoretical calculations using formalism A fit these distributions However, the very nicely in the case of "N and 13C projectiles. theoretical result clearly deviates from the experiment, especially induced reaction at forward angles. For the "Ne reaction, for "Ne the existence of a mechanism characterized by a forward peaked angular distribution, in addition to the usual direct transfer mechanism, is implied. One can immediately think of two plausible mechanisms relevant one is direct projecto the forward peaked component for "he; tile breakup and the second is the sequential breakup of the inelas6O final channe 1. tically excited projectile, both leading to the c1 + These two processes can be distinguished by looking at correlations between c1 and 160, and such experiments were performed by several groups'7-20). Fig. 8 shows the result taken for the 40Ca + *'Ne where coincidence yields reaction at 149 MeV by Shimoda et al."), The are plotted versus relative energy of the coincident particles. spectra are dominated by discrete lines corresponding to excited levels of "Ne, with no appreciable trace of the continuum components Similar conclusions which should be seen in case of direct breakup. are consistently obtained for the same reaction at different incident energies (130, 210 MeV) and for the *'Ne bombardment on a heavier Thus one can reasonably conclude that target "'Pb at 149 MeV. sequential rather than direct breakup is universally the primary mechanism for the forward peaked component.
DIRECT
REACTIONS
WITH
HEAVY
159c
IONS
.
%,(
. .
“Ne l6O) ?, 262 i&V
(to the left) and angular distributions (to Energy spectra Fig. 7. alpha-transfer reactions on the same the right) obtained for three "Ca ta:qet with different projectiles, 'ONe, I&N, 13Cwith= 8_5MeV/ Solid lines indicate calculated results based on the nucleon 1. The shaded areas in the energy spectra transfer reaction formalism. from an extra process. l6O) represent contributions of ("Ne, ExtzONe) I4 I I I
I8 I
0.0
I
I
I
I
I
(MeV) IO 6 I
(7.2’.-14.8’, , I1.5’.52.9’,
0.4
0.2 0.1 1
I’I 12
8 E,-o
Fig. 8. reaction the axis
4
0
(MeV)
"0 correlation in the 40Ca(20Ne,a'60)40Ca Results of u vs. Coincidence cross sections are pryjected at 149 MeVzO). 0. of relative kinetic energy, EU_O, between 01 and
on
160~
M. ISHIHARA
The vanishing strength observed for the direct breakup process does not necessarily contradict the notion of the breakup fusion formalism, which presumes the reaction to start with projectile breakup. According to the theoretical analysis I'),the breakup dominantly occurs at a relatively close distance of colliding nuclei so that the breakup source-strength primarily ends with subsequent fusion, leaving little strength available for three-body final channels. The examples shown above almost represent the present status of understanding of quasi-elastic reactions in terms of DWBA theories. In spite of several successes achieved, previous theoretical attempts only treat some specific aspects arbitrarily chosen and use various formalisms for different situations. To obtain a more unified perspective of quasi-elastic scattering, it is certainly desirable to examine the whole range of phenomena more systematically with a single formalism. A preliminary attempt along this line is already in progress by using formalism B15). In general, the breakup fusion formalism appears to have a better prospect than the transfer reaction formalism, since it can avoid direct manipulation of wave functions for unbound final states in the continuum region, which have to be dealt with in the latter formalism only with considerable ambiguities. The main physical ingredient for the former formalism scatis the optical potential, and detailed studies on quasi-elastic tering may provide some information about the form of potential in interior regions. 2.3
EXTRA COMMENTS ON VERY MASSIVE TRANSFER OR CHANNELS OF LIGHT PARTICLE EMISSIONS
REACTIONS
The DWBA analysis discussed in 2.2 indicates strong participation of some mechanisms other than the simple direct transfer mechanism for very massive transfer channels, i.e. for reactions involving light ejectiles. Indeed, a variety of mechanisms have been considered to account for the light-particle emission21) with different emphasis In order to pin down the relevant depending on the energy region. mechanisms for the region of = 10 MeV/nucleon, more experimental data The observation of spin on various properties are certainly needed. polarization of ejectile and/or residual nucleus may provide such information. measured for Fig. 9 shows recent results of2golarizations protons in the giNb(::~~pb\l;eaction ) (fte. 9(b)) and for the targetN,a) reaction The proton like residue in the ) (fig. 9(c)). polarization for the non-equilibrium component is consistently positive with values of = 20% over the whole range of proton energy, indicating the occurrence of negative-angle deflections in the reactions. for the c1 emitting reaction On the other hand, the polarization shows a more complicated energy dependence (angular dependence is is negaIn contrast to the proton case, the polarization weaker). tive for a wide range of lower energies with maximum (in absolute Posivalue) at energies a little higher than that of beam velocity. tive polarization occurs only at the highest energies. This difference is indicative of at least two different mechanisms participating in very massive transfer reactions, one represented by that for the (14N,p) reaction and the other to be characterized by negative polarThe dominance of the latter ization (positive deflection angle). 5gTb(7Li,n) reaction at 49 MeV by mechanism is suggested for the the observed polarization23 ) of target-like residue, which was found to be negative and nearly constant at P 2 -0.4 for different enerWe conjecture that the mechanism implied by the breakup fusion gies. formalism is very likely to be relevant to this particular reaction.
DIRECT
REACTIONS
WITH
HEAVY
161c
IONS
-0.2
-0.2
reactions involv9. Spin polarizations observed in 14N induced rotbns determined") by The polarization of ing light ejectiles. I? N,p) reaction at 95 MeV the double scattering method in the g3Nb( for the laboratory angle Op = 20° is shown vs. proton energy in (b). Differences between the forward and backward energy spectra shown in The Ep dependence of (a) may represent non-equilibrium components. to the polarization can be accounted for by attributing P ^- +22% non-equilibrium component and zero polarization to the remainder, i.e., the equilibrium component. The average polarization of the target-like residues in the 15'Tb( '\N,ol) reaction ) from circular polariat 115 MeV determinedz3 zation of gamma rays is shown in (c) by the contour plot in the plane of energy vs. angle of the alpha particle. The polarization results shown above certainly provide a new set of constraints for any appropriate theories to accomodate, and attempts to develop theoretical descriptions to account for the observed features are desirable.
3.
Prospects
for
spectroscopic
studies
We obtain hintsz4) of the types of spectroscopy to be pursued with energy-dissipative direct heavy-ion reactions by consulting again the kinematical matching conditions. Fig. 10 shows energy vs. spin diagrams for the residual nucleus in heavy ion transfer reactions, where the usual yrast band (solid line) and the band of states with configuration of target plus transferred cluster (dashed line) are indicated. The states of molecular resonances are thereThe region corresponding to fore represented by the latter line. Its optimum kinematical matching conditions is marked by a bold X. location relative to those bands can vary significantly from reaction to reaction. For the case of (I) the region of matching hits the area close to the bands, therefore giving rise to the expectation that cluster states nearby would be populated selectively. In that case, the corresponding structures may show up even in the highly excited continuum region in the energy spectrum of ejected particle. The studies aiming at this type of particle spectroscopy are described in subsection 3.1.
M. ISHIHARA
162~
1
Yrast
-
-
Cluster config.
8oc’5=Tb(‘4N,al’6=Yb .E,4N=
115 MeV
SO-
Fig. 10. Diagrams of excitation energy Ex vs. spin J for the residual nucleus produced in transfer reactions to illustrate the location of the kinematically matched region (indicated by cross) relative to the yrast band (solid line) and the band of cluster configurations (dashed The two dotted lines in line). each of the diagrams correspond to the two requirements (eqs. (1) and (2)) of matching conditions. Two typical situations are given ") by the '2C(160,a)24Mg reaction (I) and the 15gTb('4N,a)16gYb reaction (II,). Residual nuclei free from subsequent particle emissions may be formed if they are populated in the region between the solid and dash-dot lines in (IIb).
In many reaction systems like the case of (II,), the matching region lies deeply inside of the domain of high level density, therefore allowing the final residual nuclei eventually to decay by the Here one can measure emission of gamma rays as well as particles. y-rays in coincidence with ejectiles, where features characteristic of direct reactions can be exploited in order to distinguish from The the usual in-beam y-ray spectroscopy using fusion reactions. prospects for such spectroscopy are described in subsection 3.2. 3.1
3.1.1
SPECTROSCOPY Transfer
OF CLUSTER of massive
TRANSFER
REACTIONS
clusters
As a most prominent work in this category, one can quote the experiment done at Texas A&M25), where "C transfer on a "C nucleus was studied in the 12C('60,a) 24Mg reaction by looking at inclusive c1 As shown in fig. 11(a), a number of small structures are spectra. observed on top of the huge continuum distribution, which after This feature was background substraction appear as in fig. 11(b). and the discrete lines were conjectured to in fact anticipatedz6), be associatedwithexcitation of molecular-resonance-like states. In fact, the excitation energies of these lines nicely fit those of the molecular states identified via study of excitation functions in the 12c + 12C inelastic scatteringz7). The above conjecture, however, has been challenged by two major criticisms which argue for very different mechanisms to account for
DIRECTREACTIONSWITHHEAVYIONS
Q+‘*cI~+)+‘~c(~+I
0
IO
20
30
40
163~
td)
50
Ea(c.m.) (MeV) results3') on the 12C('60,a)24Mg reaction at Fig. 11. Experimental Alpha particles are always detected at 5.5O. 142.4 MeV. (a) Singles energy spectrum of alpha particlesz5). (b) Singles spectrum after subtraction of continuum backgroundz5). (c) Spectrum of alpha particles corresponding to the final channel This is obtained by integratof CY + (24Mg* + '*C(g.s.) + "C(2+)). ing coincidence cross sections, where the coincidence data for c1 at 5.5O and "C at 30°-480 are used and three-body kinematics involving "Mg nucleus are assumed. an intermediate + (d) Same as in (c) for the final channel of a + (24Mg* + "C(2+) "c(2+)). to the finalchannelof (e) Spectrum of alpha particles corresponding It is obtained in a similar way 12C(g.s.) + ('60X -+ '2C(g.s.) + a). as for (c) and (d) but based on coincidence data for cx at 5.5O and "C at 8O-l8O, which nicely followed three-body kinematics expected for the relevant final channel. (f) Spectrum of alpha particles corresponding to the final channel of 'Be(g.s.) + ("Ne* + 160(g.s.) + a) obtained from 160 + c1 coincidence data.
164~
M. ISHIHARA
the phenomenon. One attributes the observed structures to excitation of the molecular resonance states via compound- but not directreaction process"), and the other to sequential c1 decay of excited projectile-like fragments formed via some direct reaction processes"). In particular, evidence for the importance of the latter mechanism has been obtained"r 31) in recent experimental investigations of the bombarding energy dependence of the peak energies of the resonance-like structures. More decisive information on the breakup of projectile-like fragments can be obtained by observing correlations between a particles and heavy fragments. The experiment performed at 0saka3') provides most extensive data for such correlations, which showed that the sequential breakup is certainly very important. One of the new findings of the study is that the breakup of excited "Ne formed by an c1 pickup reaction is even more siqnificant than that of inelassupposed to be the tically excited 160, which has been persistently This finding appears to give-a reasonable account main contributor. for the puzzling question why resonance-like structures in the alpha spectra are weaker33) for, e.g., the 13C + I60 reaction than for the I60 reaction. A recent studv3\) of '60(12C.BBe)20Ne reveals C+ that the cross section of the CY transfer for the i6O i "C reaction is stronger than that for the '60('3C,qBe)20Ne reaction. The correlation data further providedarough estimate of the strengths of the sequential breakup components which can be directly compared with the strengths in the singles spectrum (see figs. 11(e) and (f)). The breakup components, particularly due to "Ne*, are strong but not sufficiently to account for the whole strengths in the singles. Thus it is still possible that the cluster transfer process is contributing to the phenomenon to some extent. An attempt to elucidate this last aspect has also been made at Osaka by looking at the correlation of the c1 particle with "C detected at relatively backward angles in order to observe the correlation in the "C - "C final channel, to which the molecular states of "Mg strongly decay. lTairly st:Tng coincidence cross C(2+) and "C(2+) + "C(2+) sections are observed for both C9.s. + as shown in figs. 11(c) and (d), a though the relation of those events with the molecular states is not yet definite. More studies along this line are desirable to further elucidate the intriguing possibility that the reactions represent massive-cluster transfer. 3.1.2
One-nucleon transfer high-spin states
to high-lying
In the previous subsection an exotic reaction of massive cluster transfer was discussed. For reactions involving the transfer of fewer nucleons, one can anticipate more significance of simple direct trasnfer mechanisms so that the spectroscopy of cluster transfer may This anticipation indeed appears to be correct for onework better. nucleon transfer reactions, according to our recent studies3') at Texas A&M. 144Sm('2C,11B)'45Eu Fig. 12 shows the "B spectrum observedinthe reaction at 180 MeV. Besides several discrete lines at lower excita(indicated by a and b in tion, we see prominent gross structures fig. 12) in the region of excitation energy Ex = 6-8 MeV, which are This spectrum clearly distinguishable from the underlying continuum. reminds us of the spectrum recently observed in the 14*Sm(*He,t) reaction36). Indeed, the peaks a and b correspond in energy to those lines seen in the (4He,t) reaction, which were assigned to lh 9/2 and li 13/2 single particle states within the major shell one 5% above Thus the gross peaks in the heavy-ion reaction the Fermi surface.
DIRECT
REACTIONS
WITH HEAVY
IONS
165~
2000. '44Sm('2C , “B) 14’Eu
i
E = IEOMeV
t
0
100
200 channel
300
400
reaction at Fig. 12. Energy spectrum of "B in 144Sm('2C,"B)'45E~ The centers of two peaks indicated by a and b correspond 180 MeV35). to excitation energies of = 6.0 and 2 7.5 MeV, respectively. may also be associated with those high-lying high-spin states. In earlier studies of heavy-ion reactions, such peaks have never been incident energy recognized 37,38), probably because of insufficient or the contamination caused by kinematically broadened peaks, which frequently arise from ejectile excitations and obscure the energy Such contaminating peaks appear spectrum at the region of interest. only weakly at lower excitation energies for the case of the "B ejectile. The strong population of high-energy particle states found in proton transfer reactions may open a new field of spectroscopy analogous to but complementing the studies of deep-hole states. The heavy-ion reaction used has been found to have some advantage over the ($He,t) reaction, yielding much stronger population of high-lying states compared to low-lying states. One can speculate on additional advantages such as j-selectivity. Studies to explore such aspects are presently in progress. 3.2
GAMMA-RAY
SPECTROSCOPY
IN HEAVY
ION DIRECT
REACTIONS
The first experiment of this category was made at IPCR by rast line in coincidence with forward observing y cascades along the emitted alpha particles in the Y "Tb(14 N,axny)Yb reactions3'). It was anticipated that the (14N,n) reaction occurs via a peripheral direct reaction and populates residual states in a fairly confined R range around the optimum A&-value predicted from the matching conset a ditions. If this is the case, the reaction can automatically high-spin window on the entry states of y cascades, enhancing relative strengths of y transitions in high-spin yrast region. Those of most massive transfer channels are favoured in producing the window at highes.t spin values, as seen from fig. 3. Such expectations have turned out to be essentially fulfilled. As shown in fig. 13, relative intensities of high-spin transitions are largely enhanced for the forward alpha emission (direct reaction component) as compared
166c
M. ISHIHARA
Fig. 13. Relative gamma-ray intensity for transitions along yrast bands measured in coincidence with high-energy forward alpha particles (top) and with backward alpha particles (bottom) in the 15sTb(‘4 N,axny)AYb reactions at 95 MeV3'). No appreciable side feeding is observed below I = 10 for the "direct" component. to the case of the backward alpha emission (fusion reaction component). Research using the above technique has been used to study level schemes in yrast regions"). Here a crucial question is whether the method can ever be competitive in producing useful data with studies made by the usual technique incorporating fusion reactions. The primary disadvantage of using direct reactions is inefficiency in gaining statistics partly due to its smaller cross section and partly due to limitations in detection efficiency of coincidence particles. In order to compensate for those deficiencies, particular features of heavy-ion direct reactions should be exploited. Several experiments have been performed recently to explore such possibilities, and some promising aspects have been observed as listed below. 1) Formation of a high-spin window: this is the aspect stressed in the study of the 15'Tb(14N,a) reaction. The average R value of the window has been examined in other reactions by measuring y-ray multiplicities, and fairly large L values were indicated for channels associated with emission of p, d, t as well as c14'--lt3). In particular, the observation made at ORNL43) appears to be interesting of the entry states created in (fig. 14). The averagespinvalue massive transfer reactions could sometimes appreciably exceed the If this conclusion range of critical II values for fusion reactions. is correct, use of such reactions may have considerable merit in investigating very-high-spin states in the yrast region. The measurement of the coincident particle provides an easy to a particular final means") to identify y rays corresponding nucleus among various possible channels permitted via sequential This corresponds to measuring excitation particle evaporation. functions in the case of fusion reactions, and simplifies the experimental procedure considerably (see fig. 15).
DIRECT
REACTIONS
Fig. 14. Average values
WITH HEAVY
IONS
167~
Fig. 15. Comparison of cross sections of different final channels following the 15 gTb ( 1 li N,a) reaction at 115 MeV4') determined from y-ray intensities as a function of energy of coincident alpha particle detected at 15O.
The features of 1) and 2) can also be used for fusion reactions by sum-energy spectrometers and/or multiplicity-filter detector arrays. Use of the particle-y technique, however, can avoid introducing such complicated instrumentation. the direct reaction creates spin orien3) Spin orientation: tations in residual nuclei preferentially along the direction normal Thus the maximum allowed alignment could be the reaction plane. larger than in fusion reactions, giving rise to larger asymmetry of y emissions and therefore to higher sensitivity in multipolarity assignments. Moreover, direct reactions can produce non-vanishing polarizations which can seldom be obtained with fusion reactions. The magnitudes of spin alignment (Pzz) and polarization (P,) of residual nuclei have been studied for quasi-elastic reactions in 1% + lsqTb collisions at 115 MeV as a function of atomic number of ejectilek5). The results obtained (fig. 16) indicate that fairly for the region of large P,, and P, are indeed produced, particularly ejectile corresponding to medium-mass transfer. 4) Well defined entry states (or regions) for y cascades: direct reactions can sometimes populate excited states stable with Depending on energy respect to particle emission (see fig. lU(IIb)). resolution for the particle spectrum and on level density of the residual nucleus, the entry states for the y cascade can be defined either as an isolated level or as a region of excited states with a This feature, which is not obtained in specific excitation energy. usual fusion reactions, facilitates selection of particular flow Moreover, thoseentry statesmaybeofa particulines of y cascades. of direct reactions. lar nature, being chosen by selectivities
M. ISHIHARA
16%~
15’-j-b+ 14N at IrSMeV
Fig. 16. Alignment Pzz (solid circles) andpolarization P, (open circles) for the tarqet-like resi-
~i:l”~~~~~~~~~
“:~ -06t-
mined
based on out-of-plane
par-
i
Experiments pursuing this aspecthavebeen reportedrecently46"7f, where y-rays following high-spin particle states were measured in one-nucleon transfer reactions of Er(160,150) and Er("C,"C), proving the usefulness of the technique in studying states otherwise inaccessible. of the particle-y spectroscopy As stated before, applicability This situation is mainly hampered by inefficient data collection. may be largely improved by using higher energy projectiles, since, e.g., the angular distribution of ejectiles at higher energies tends to be more confined along the beam direction, leading to a larger Thus altogether detection efficiency for the coincident particle. the prospects for particle-y spectroscopy appear to be bright. Acknowledgement The author acknowledges discussionswith H. Kamitsubo, T. Inamura, T. Nomura, H. Utsunomiya, K. Ieki at IPCR, K. Nagatani at INS, K. Katori, T. Fukuda, T. Shimoda at Osaka University, E. Takada, T. I am greatly Murakami, and D. Haenni at Texas A&M University. indebted to T, Udagawa at University of Texas for discussions Of Special thanks are due to the theoretical aspects of the paper. data group of Osaka University, who have provided some expeximental This work was partly supported by the foundaprior to publication. for non-energy sciences. tion of Japan-U.S. collaboration References 1)
2) 3)
41
J. Van Driel, S. Gonggrijp, J. Wilcvnski, K, Siwek-Wilczinska, D.C.J.M: Hageman, R.V.F. Janssens, J. Lukasiak, and R.H. Siemssen, Phys. Rev. Lett. 45 (1980) 606. D.M. Brink, Phys. Lett. 4OBr1972) 37. N. Anyas-Weiss, J.C. Corxl, P.S. Fisher, P.N. Hudson, A. Menchaca-Rocha, D.J. Millener, A.D. Panagiotou, D.X. Scott, D. Strottman, D.M. Brink, B. Buck, P.J. Ellis, and T. England, Phys. Lett. Cl3 (1976) 2241. P.J. Siemens, J.P. Bondorf, D.H.E. Gross, and F. Dickmann, Phys. Lett. 36% (1971) 24.
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HEAVY
IONS
169c
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