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Multiphonon giant resonances: Experimental status and perspectives
NUCLEAR PHYSICS A ELSEVIER
Nuclear PhysicsA599 (1996) 289c-306c
Multiphonon Giant Resonances: Experimental Status and Perspectives Y. Blumenfelda ~Institut de Physique Nucl~aire, IN2P3-CNRS, 91406 Orsay Cedex, France Recently, decisive progress has been made in the search for multiphonon states built with giant resonances. This paper will first focus on the different probes used to excite multiphonon states, and the experimental methods used to characterize these states. Several examples of experiments where the two-phonon giant resonance has been observed are described. The possibility of signing two-phonon strength through its direct decay by particle emission is then discussed in detail, and the results of the ongoing experimental program at GANIL are presented. Finally, the potential of different methods for the future observation of three-phonon states is briefly examined. 1. I N T R O D U C T I O N The nucleus exhibits a large variety of highly collective modes called Giant Resonances (GR)[1]. These resonances are understood as the first oscillator quanta of the collective vibrations. Even though GRs were first discovered almost fifty years ago, the second and higher quanta, named multiphonons, had until recently remained unobserved. Not only is the observation of multiphonon states important for reinforcing the theoretical interpretation of GRs, but their study also provides a unique path towards the investigation of hitherto unknown properties of large amplitude collective motion in nuclei. Of particular interest are the energies of multiphonon states which should allow to gain a handle on the anharmonicities of nuclear excitations [2]. Moreover, multiphonons should represent efficient doorway states towards energy dissipation in heavy ion collisions, and thus be a vital ingredient for our understanding of the dynamics of reactions between heavy nuclei [3]The detailed study of heavy ion inelastic scattering in the early eighties [4] gave the first indication of the existence of multiphonon giant resonances. In these experiments small structures located near the excitation energies expected for multiphonon states were observed in the spectra from reactions induced by Ne, Ar and Ca ions between 10 and 50 MeV/u bombarding energy on various targets (4°Ca, 9°Zr, 12°an, and 2°Spb). However, the interpretation of these structures in terms of multiphonon states remained largely speculative, as no proof of the nature of the bumps could be given. During the last few years, the development of novel experimental techniques coupled to powerful new accelerators has fueled spectacular progress in the field of multiphonon excitations. The two-phonon state has been excited through the nuclear interaction[5], the Coulomb field[6,7], and through double charge exchange reactions[8]. No doubt can 0375-9474/96/$15.00 © 1996ElsevierScienceB.V. All rights reserved. PII: S0375-9474(96)00072-3
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remain concerning its existence. These different methods are now beginning to yield systematic results spanning a large range of nuclear masses. In the past, such systematics have proven to be of the utmost importance for gaining a complete understanding of all types of collective nuclear motion, and they wiU clearly yield much needed new information concerning the two-phonon states. In the near future new more efficient experimental setups should allow to bring to light the elusive higher-order phonon states and in particular the three-phonon GR. The aim of the present paper is to review these fast-paced developments[9,10] and to give some insight into what future studies wiU hold. Section 2 will be devoted to the specificity of the different probes used to excite multiphonon GRs, and to the experimental methods applied to characterize them. The most recent results concerning Coulomb excitation and charge exchange reactions are presented in detail in three other papers of these proceedings[ll-13]. Section 3 consists in a detailed description of the light particle decay method used at GANIL to characterize two-phonon states excited by the nuclear interaction. Very recent results on Ca isotopes are discussed. Finally, section 4 will recap our current knowledge of two-phonon states and indicate some promising paths for the future. 2. E X C I T A T I O N A N D C H A R A C T E R I Z A T I O N STATES
OF M U L T I P H O N O N
2.1. W h a t is a M u l t l p h o n o n S t a t e ?
If a giant resonance (GR) is understood as the first oscillator quantum, multiphonons can be defined as the higher quanta. In a microscopic approach, the giant resonance is described as a coherent superposition of one-particle one-hole (lp-lh) excitations. A multiphonon excitation can then be interpreted as a simultaneous excitation of n identical phonons. In other words, a multiphonon excitation is a giant resonance built on other giant resonances. In a harmonic picture, the different phonons composing a multiphonon state are considered as independent. In such a context the excitation energy of the phonons is predicted to be additive, i.e. a two-phonon GR will have twice the excitation energy of the GR. Following the arguments of [14], the width of the multiphonon state is predicted to be equal to the quadratic sum of the widths of the individual phonons, providing once again that the anharmonicities are small. 2.2. E x c i t a t i o n of M u l t i p h o n o n s t a t e s Multiphonon GRs lle at high excitation energies in the nuclear continuum where the level density is extremely large. The first prerequisite for their observation is to use reactions in which they are excited with very large cross sections and/or high selectivity. Since multiphonons are interpreted as GRs built on others GRs, the excitation of multiphonon states is strongly connected to the properties of their building blocks, the GRs. Thus, in order to determine the best probes for multiphonon studies, it is necessary to briefly recall some aspects of GR excitations. It is well established now[l], that GRs constitute a universal nuclear phenomenon and that they can be excited in a large variety of nuclear reactions involving the electromagnetic, or the strong nuclear interactions. Photonuclear reactions played the main role in the discovery and study of the Isoveetor Giant Dipole Resonance (GDR), while electron
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and light hadron scattering allowed to accumulate information on the properties of the isoscalar giant quadrupole (GQR) and isoscalar giant monopole (GMR) resonances. These three resonances are the most collective GRs and the best known today. More recently, the spinless isovector pion appeared to be an ideal tool to study electric isovector G R s . During the last decade intermediate and high energy heavy ion beams have provided improved conditions for the observation of GRs. In particular, the GRs excited in heavy ion reactions are observed with very large cross sections of the order of barns and excellent peak to continuum ratios[15]. At intermediate energies (30
Inelastic Excitation,~°Ca (~0Ca~0Ca'] /~
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Figure i. Calculated cross sections for 4°Ca + 4°Ca inelastic scattering at various incident energies. (from ref.[17]).
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The large cross sections observed for giant resonances make heavy ions a particularly attractive probe for exciting multiphonon states. Following the previous discussion, the search for the double GQR will make use of intermediate energy "light" heavy ions, e.g. Ne or Ca around 50 MeV/n. The cross-section for two-phonon GQR excitation can be predicted in the framework of a semi-dassical calculation[17]. The result is shown for the 4°Ca + 4°Ca reaction at different incident energies in fig. 1. While the cross sections for both one- and two-phonon states increase dramatically with bombarding energy, the ratio between the first and second peaks drops strongly when going from 10 MeV/u to 44 MeV/u. A bombarding energy around 40 MeV/u is optimal for the detection of the double GQR. At this energy the probability of exciting the double GDR is negligible.
Muttiphonon Excitation 101
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Figure 2. Calculated cross sections for 1, 2 and 3-phonon states in 23Su + 2asU as a function of bombarding energy. (from ref.[lO])
Conditions for the observation of the double GDR will be much more favorable at higher bombarding energy, as illustrated on fig. 2, which shows calculations for the electromagnetic excitation of the single, double, and triple GDR in 2asU + 23aU collisions as a function of bombarding energy [10]. The ratio between the one- and two-phonon states is most favorable around 1 GeV/u, where it has a value of 10. The cross section for the double GDR obtained here is much larger than that predicted for the double GQR at intermediate energies. One can also note that going to energies higher than 1GeV/u will not entail significant advantages. 2.3. C h a r a c t e r i z a t i o n of M u l t i p h o n o n S t a t e s To prove the existence of multiphonon states one must of course use reactions offering large cross sections and good selectivity for their excitation. However, due to the large
Y. Blumenfeld/Nuclear Physics A599 (1996) 289c-306c
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level density in the region of two-phonon states, and to the possible contamination from reaction mechanisms other than pure inelastic scattering, such as pick-up break-up or knock out for example, it is also imperative to devise means to sign the multiphonon strength.
DCX Excitation 3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
10
20
30
40
50
60
70
- O (MeV)
Figure 3. Experimental spectra from the (x +, x-) reaction on 93Nb at 292 MeV. (from ref.[8])
If very selective reactions are used it may be sufficient to systematically measure the characteristics of the observed states over a large range of target nuclei. This is illustrated in the case of pion double charge exchange reactions which can excite only isotensor A T -- 2 transitions. Spectra measured on 93Nb are presented on fig. 3. Despite the good selectivity, a large background is present below the resonances. However, the same reaction was performed on various targets and in all cases the double GDR is observed at the expected Q value with a cross section and angular distribution in agreement with theoretical estimates. Clearly inelastic heavy ion reactions, in which both nuclear and electromagnetic forces come into play, offer no isospin selection. However, beam intensities and cross sections are sufficiently large to allow to perform coincidence experiments and multiphonon states can
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thus be characterized by the measurement of their specific decay channels. If one admits the harmonic approximation, all phonons of a multiphonon state will decay independently, each phonon exhibiting the decay characteristics of the one-phonon GR.
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Figure 4. Sum energy of coincident photon pairs with an energy difference of less than 6 MeV emitted from the 2°9Bi + 2°sph reaction at 1 GeV/u. (from ref.[6])
Figure 5. Excitation energy spectrum obtained for a 136Xe projectile on 2°8pb and 1~C targets at 700 MeV/u (from ref.[7])
A very useful decay channel is the direct 7 decay towards the ground state of the nucleus. In the case of the GDR the branching ratio for direct 7 decay is of the order of 1%. Therefore the double GDR will decay by emitting two 7-rays with a probability of 10 -4. Each photon will carry the energy of one GDR, and both will thus have approximately the same energy. The observation of the double 7 decay was recently used to study the double GDR in 2°Spb[6]. The two-phonon GDR was excited by bombarding a 2°Spb target with a 2°9Bi beam of 1 GeV/u energy at SIS. Two 7-rays in coincidence were observed using the TAPS detector. Peripheral events are selected by requiring that a forward wall (plastic scintillator) detects no charged particles. A structure around 13 MeV was observed in the one-photon energy spectrum and assigned to the GDR in 2°Spb. A spectrum obtained by requiring the coincidence of two 7-rays with an energy difference of less than 6 MeV was constructed and is displayed in fig. 4. A prominent structure is observed at 25.6 + 1 MeV with a width of 5.8 4- 1.6 MeV. This structure has been assigned to the two-phonon GDR in 2°Spb. Assuming that the second phonon has the same branching ratio as the GDR (1.7%), the cross section is found to be 720 mb which is more than a factor 2 larger than the theoretical predictions.
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Another experiment performed at SIS also allowed the observation of the double GDR through Coulomb excitation. The method is to excite collective modes in the projectile using peripheral heavy ion collisions, to measure in coincidence the subsequent neutron and 7-decay of these states and to reconstruct the excitation energy of the projectile. This experiment was performed using a 136Xe beam on 12C and 2°Spb targets[7]. The resulting excitation energy spectra for 136Xe obtained with both targets is displayed in fig. 5 and compared to Weiszacker-Williams calculations[10]. In these calculations, the contribution of the GDR and both isovector and isoscalar GQR is taken into account. The results obtained with a 12C target are used to estimate the nuclear cross section. The calculation reproduces the measured excitation energy spectrum up to 25 MeV. Above, the calculated spectrum drops rapidly while a structure, which is assigned to the double GDR, is clearly observed at 28 MeV in the experimental spectrum, with a width of about 6 -4- 2 MeV. This experiment does not provide an unambiguous signature of the double phonon, but no alternative explanation of the observed structure has been given. New results using the same method with other projectiles are presented elsewhere in these proceedings[11]. In the case of isoscalar resonances, and in particular the GQR, the 7 decay branch is much weaker than for the GDR, and the two 7 decay of the double GQR is too small to be measured. One must then resort to the particle decay in order to characterize the double GQR. This is the object of our experimental program at the GANIL facility, which is described in detail in the following section.
3. L I G H T P A R T I C L E D E C A Y O F T H E D O U B L E
GQR
As GRs are usually located above the particle emission threshold, light particle decay is their main deexcitation channel. As it is well known, particle decay of GRs can occur through various processes [1], mainly the direct decay into hole states of the (A-l) residual nucleus with an escape width F T, and the statistical decay leading to the spreading width, P~. Statistical decay depends only on the excitation energy and angular momentum of the state. Direct decay, on the other hand, can yield information on the microscopic nature of a resonance. Let us use 4°Ca, a proton emitter, as an example to demonstrate the method employed. Fig. 6 sketches the direct decay of a GR and a high lying state in 4°Ca through proton emission. The GR decays towards hole states in 39K. If the high lying state is a onephonon GR it will also decay into hole states through the emission of one high energy proton (dashed arrows). Conversely, if the high lying state is a two-phonon state, since the mixing with other high lying states and the coupling between phonons is expected to be weak [2], each of the two phonons will undergo a direct decay exhibiting the same features as the direct decay of the GR. Two protons will then be emitted. The first proton will populate the GR or (GR ® hole states) in 39K, and the second will deexcite this GR, leading to two-hole states in 38Ar. It is this specific direct decay pattern which can give a signature of a multiphonon state. The prerequisite for this method is that the GR present a sizeable direct decay branch. This limits its usefulness to rather light nuclei (A < 100), since heavy nuclei are known to decay mainly statistically. However, it can be used for both neutron and proton emitters, as will be demonstrated in the following.
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E*(MeV) 35
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]
GR
k~
................ 2.1
~ ................ 2.6 39 K
38Ar
0
0
40
Ca
Figure 6. Schematic decay diagram of one- and two-phonon GRs in 4°Ca.
3.1. E x p e r i m e n t a l M e t h o d We have studied the decay of GRs and high lying states in 4°Ca, and 48Ca, excited in the 50 MeV/u 4°Ca + n~tCa, and 48 MeV/u 2°Ne + 48Ca reactions. Recent data taken on 9°Zr and 94Zr are currently under analysis. The aim is to study the direct decay pattern of the GR and of the excitation energy region where the multiphonon GRs are expected. For this the missing energy spectra for these two decays must be constructed. Consider the reaction P +T-,P +T*(T* ~T'+p) where P and T are projectile and target, and where the excited target decays by emission of a light particle p. The missing energy is then Emi,, = E*(T*) - EpCM - E~em,,where E*(T*) is the initial excitation energy in the target, EpTM the particle energy in the center of mass of the recoiling target, and E~e~ the recoil of the target remnant induced by the particle emission. The excitation energy E*(T*) is obtained from the energy loss of the projectile measured by a spectrometer. At GANIL, the SPEG spectrometer associated with its standard detection system is used[18]. This system consists of two position sensitive drift chambers which, after trajectory reconstruction, yield the focal plane position and scattering angle of the fragment. Particle identification is obtained by combining an energy loss measurement in a large ionization chamber with a residual energy measurement in a thick plastic scintiUator, and the time of flight measured between this scintillator and the cyclotron RF with a resolution of better than 1 ns. An unambiguous mass, charge (Z), and atomic charge (Q) identification of scattered projectiles is achieved. The energy resolution is 800 KeV in the case of the Ca beam and about 400 KeV for the Ne beam. The angular resdution is estimated to be 0.2°. The energy of the coincident light partides must be measured. This is accomplished by surrounding the target with a large number of modules of a particle multidetector. In the case of 4°Ca, which is predominantly a proton emitter, 30 CsI elements of the
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multi-detector array PACHA[19] were placed in the reaction chamber. They were positioned in the reaction plane, covering the whole angular domain with the exception of a small wedge of [-15,+7°] around the beam direction (positive angles are on the same side of the beam as the spectrometer). The total solid angle covered is about 3% of 4z'. The proton energy resolution was about 2%. Threshdds ranged between 1 and 3.5 MeV. In order to be able to sum the spectra from various detectors, a software threshold of 4 MeV protons in the center of mass of the recoiling 4°Ca nucleus was set during the analysis. In the case of 4SCa, which decays preferentially by neutron emission, SPEG was run in coincidence with EDEN, a time of flight neutron multidetector. EDEN is composed of 40 NE213 liquid scintillators[20], which were located outside of the reaction chamber at 1.75 m from the target at backward angles with respect to the beam. They covered a solid angle of about 3% of 4z-. The neutron time of flight resolution is 1 ns which corresponds to an energy resolution of 20 keV for a 1 MeV neutron and 200 keV for a 5 MeV neutron. Neutrons are separated from 7-rays by pulse-shape discrimination. During the analysis a software threshold of 60 KeV electron equivalent was set for the neutron detectors. This threshold was determined from calibration runs with a 241Am source. The appropriate efficiency correction was applied to the neutron spectra. In the following the main points of our investigations wiU be illustrated with results from the 4°Ca + 4°Ca experiment. Some recent unpublished results from the neutron-decay experiments will also be shown.
800
1500
600 1000 0 400 C)
500
200 0
0
20
40
60
0 80 E*
100
Figure 7. Inelastic spectrum from the 4°Ca + 4°Ca reaction at 50 MeV/u with two different energy binnings. The dashed llne is the measured contribution from the pick-up break-up of one proton.
3.2. Reaction M e c h a n i s m s Fig. 7 presents the inclusive inelastic spectrum from the 4°Ca + 4°Ca reaction. The GR, split into two components centered at 14 and 17.5 MeV, is clearly observed. An multipole analysis similar to that described in reL[15] shows that the GQR is the dominant constituent of both these components in the angular domain studied. The higher excitation
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energy region appears as a broad continuum upon which one may observe some small structures, in particular around 34 MeV excitation energy. Random phase approximation calculations situate a large amount of the high multipolarity strength in this region where semi-classical calculations also predict the excitation of the two-phonon GQR[21].
V ~
•
-900
~~
~
...-0
+90 o
Figure 8. Invasiant cross section plot for protons emitted in 4°Ca + 4°Ca inelastic reactions at 50 MeV/u. the arrow indicates the velocity of the projectile-like fragment.
Before searching for signatures of high energy collective states it is important to understand the general features of the inelastic spectrum, and to determine the reaction mechanisms contributing to the inelastic cross section. For this, light particle coincidence measurements represent a powerful tool. Fig. 8 shows a density plot of the invariant proton cross section in the (VII, V±) velocity plane in coincidence with inelastically scattered 4°Ca without any selection on the excitation energy deposited. One immediately realizes the potential of coincidence experiments at this bombarding energy : protons emitted by the projectile and the target-like nuclei can easily be separated in velocity space. First of all, the high energy protons measured in two detectors on the left hand side of the beam are due to elastic scattering on the hydrogen contaminant of the target. An almost isotropic component of low velocity protons centered around the recoiling target nucleus reflects the decay of states excited in the target through inelastic scattering. In the forward direction an accumulation of fast moving protons is observed, which indicates the presence of the pick-up break-up mechanism (PUBU)[22]. The contour lines depict the result of a Monte Carlo simulation including both PUBU and inelastic excitations and reproduces very well the main trends of the data. More surprisingly, in the upper right
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quadrant a strong enhancement of high energy protons is observed, emitted at angles too large to be ascribed to PUBU processes. This is indicative of a new mechanism which will be further discussed below, but is not yet well understood. By comparing the proton spectra measured at forward angles with the Monte-Carlo simulation it is possible to infer the total proton pick-up break-up contribution to the inclusive inelastic spectrum[23], and the result is displayed on fig. 7. Since, in the present reaction~ the neutron PUBU cross section is estimated to be much smaller than the proton one, we conclude that the PUBU accounts for less than half of the cross section in the high excitation energy region.
300
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100 0 400
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0
100 50
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15 E-'(MeV)
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Figure 9. Missing energy spectra for the GQR (left) and double GQR (right) excitation energy regions. The schematic drawings indicate the proton detection angles considered in the top and bottom figures.
To understand the remainder of the coincidence cross section the missing energy spectra for two excitation energy regions are displayed on fig. 9. The first region ( a ) and c) ) between 12 and 20 MeV encompasses the GQR, while the second region ( b ) and d)) at higher excitation energy should contain the two-phonon strength. The spectra are presented for detectors located in the upper right quadrant ( a ) and b) ) where unexpected high energy protons were observed in the invariant cross section plot, and for detectors in the backward hemisphere (c) and d) ), where only decay from the target is expected. None of the spectra presented here contain any contribution from PUBU reactions. The solid lines are calculations performed with the code CASCADE, which represent the statistical part of the decay. These calculations have been normalized so as to never overshoot the data. First, a sizeable direct decay branch of the GQR is observed, accounting for approximately 30% of the total decay, which populates the ground state and the first excited
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state in 39K. This direct decay is comparable in strength in the forward and backward hemispheres, as expected from decay of a giant state. The behavior of the decay from the higher excitation energy region is very different. At backward proton angles some small structures superimposed on a broad statistical bump are observed but no direct decay to the hole states in 39K is present. For the forward detectors, however, the direct population of a9K hole states dominates the missing energy spectrum. The very strong anisotropy of this component, and its asymmetry with respect to the direction of the recoiling target, rule out an interpretation in terms of direct decay of a specific high lying state. It must rather be due to a new fast mechanism for proton emission which is not yet well understood. Note that fast neutron emission presenting analogous characteristics was observed in inelastic 170 + 2°Spb coUisions at 84 MeV/u[24]. In order to achieve a better understanding of this intriguing process, systematic measurements in different systems are planned in the near future at the AGOR cyclotron. 0 < E,,z
a)
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Forward
200
minus Backward
20
40
60
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40
60
80 E'(MeV)
Figure 10. Inelastic spectra in coincidence with protons emitted in the backward (top) and forward (middle) directions and subtraction of these two spectra (bottom) which shows the contribution of the new fast proton mechanism. Left panel is for all protons and right panel for final state energies less than 8 MeV in 39K.
To extract the contribution of this new mechanism to the inelastic spectrum, the inelastic spectrum in coincidence with backward detectors, where only target decay is present, was subtracted from the spectrum in coincidence with forward detectors, after suitable
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normalization for the solid angles of the particle detectors. The two inelastic spectra, and the subtracted spectrum are shown on fig. 10, both with (right panel) and without (left panel) gating on discrete final states in 39K (E*(39K < 8 MeV). The two subtracted spectra are very similar, confirming that the fast mechanism mainly populates the low-lying hole states of 39K. The contribution of this mechanism to the inelastic spectrum sets in at around 20 MeV excitation energy and therefore does not pollute the GR region. Its maximum is located near 30 MeV. Above, this contribution decreases but remains present up to excitation energies as high as 80 MeV. Very roughly, this fast proton emission mechanism makes up 25% of the inelastic cross section between 20 and 60 MeV excitation energy. The decay of highly excited target states will now be investigated, in order to search for clues of multiphonon excitations.
3.3. Signature of t h e t w o - p h o n o n G Q R in 4°Ca In Fig. l l a ) , the 4°Ca inelastic spectrum in coincidence with backward emitted protons is displayed. This condition effectively eliminates contributions from PUBU reactions and fast processes. Such a spectrum must be corrected for the multiplicity of emitted protons [19]. For example, when the two-proton decay channel is open, the probability to detect a coincidence event will be greater than when only the one-proton channel is accessible. When the solid angle for particle detection is small, as in the present experiment, this probability goes simply as the multiplicity of protons above the detection threshold. The correction was performed by calculating the proton multiplicity as a function of excitation energy, taking into account the detector thresholds, using two statistical codes (CASCADE and LILITA), and dividing the measured spectrum by this multiplicity. The result depends very little on the choice of the evaporation code. The multiplicity function calculated with the code LILITA is shown in fig. 11a). The corrected spectrum is displayed in fig. llb). In such a correction, the main assumption is that particle emission is purely statistical and the direct contribution is neglected. This will tend to slightly overestimate the proton multiplicity. We estimate the systematic error using this assumption to be about 20 %. In this coincidence spectrum a very prominent structure at twice the GQR excitation energy shows up, which is barely visible in the inclusive spectrum. To roughly estimate the characteristics of this structure, several polynomial fits of the background were subtracted. An example is shown as a solid line in fig. 11b), and the result, fitted by a gaussian, is displayed on the bottom of the figure. The width of the structure is estimated to be 9 MeV. Concerning the cross section, a ratio of 8 between the giant resonance and the structure at 34 MeV was extracted from this fit. However, other fits, where the background is drawn closer to the data, can yield ratios as high as 15 with narrower widths. These characteristics are compatible with the multiphonon model [21] which predicts a ratio of 15 and a width for the two-phonon state equal to v/2 times the width of the one-phonon state [14]. However, theoretical calculations for this energy region predict the presence of both the two-phonon state and other high lying giant resonances. Therefore, it is difficult to demonstrate the existence of the two-phonon state simply by studying the characteristics of the observed structure. In order to sign the presence of two-phonon strength, a study of the decay of the structure is called for. Fig. 12a). shows the missing energy spectrum for the region of the
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800 600 o
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+++ 1
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400 200 0
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E Figure 11. a) Inelastic spectrum in coincidence with backward emitted protons. The solid line is the multiplicity correction (see text); b) top: Inelastic spectrum after correction for multiplicity. The solid line is an arbitrary background; b) bottom: spectrum after background subtraction. The solid line is a gaussianfit.
GQR. As discussed before, direct decay to the ground and first excited state in agK clearly shows up in addition to the statistical decay component. For excitation energies in 4°Ca around 34 MeV, corresponding to the structure, the missing energy spectrum (Fig. 12b) shows peaks at 8.3 and 10.9 MeV corresponding to the population of the GS and the 2.6 MeV state in 39K, which were shown above to be due to the fast proton emission mechanism. The other very striking feature, however, is the presence of peaks located about 17 MeV above the GS, which corresponds to the GR energy in 39K (see upper scale) superimposed on a broad contribution. The calculated statistical decay spectrum corresponding to this energy region is shown by the histogram. At these large missing energies, two protons can be emitted, while only one is detected. If the first emitted proton is detected, peaks in the missing energy spectrum mean that a small number of states must be preferentially populated in 39K. In the same way, if we detect the second emitted proton, which populates 3SAr, peaks will show up only if the initial excited nucleus, 4°Ca, has decayed through particular states in 39K, to well defined low lying states in 3SAt. This is precisely the picture expected for the direct decay of a two-phonon state (cf. discussion
of fig. 6). A simulation of such a two phonon direct decay has been done with the following
Y. Blumenfeld /Nuclear Physics .4599 (1996) 289e-306c
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d,.. ~~,~,1~ ~ ~
I
b)
0
o/
A
g~
10
80
30
E~U(MeV)
Figure 12. a): Experimental missing energy spectrum for the GQR region in 4°Ca. Solid line is the statistical decay calculation. b): Same as a) for the region of the double phonon. c): Simulated missing energy spectrum
9.9
19.9
29.9 E~ss(MeV)
Figure 13. Same as Fig. 12 in the case of 4SCa.
for the two-phonon direct decay.
assumptions. The GQR is composed of two peaks centered at 14 and 17.5 MeV with widths (FWHM) of 2 MeV, making up 40% and 60% of the total GQR cross section respectively. A two-phonon state is constructed by randomly picking each phonon among the two components. As observed for the GR in 4°Ca (Fig. 12a), the direct decay of each phonon is assumed to populate only the GS and the first excited hole state of the daughter nucleus (39K or 3SAr). The decay probability to the GS and the first excited state were set equal. The experimental resolution of 800keV was taken into account. The calculation has been done for a 100% direct decay but we checked that the main features remain unchanged for a smaller direct decay branch. The result of the simulation is presented in fig. 12c). The various decay combinations should give rise to ten peaks, the positions of which are shown by bars. However, due to the experimental resolution and the GR width, the final result exhibits only 4 peaks which are in remarkable agreement with
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those observed in the experimental missing energy spectrum (Fig. 12b). This comparison conclusively demonstrates the presence of two-phonon strength.
3.4. Two-phonon strength in 4SCa In the case of 48Ca, which decays predominantly by neutron emission, the same method was applied, replacing the proton detection system by the EDEN neutron array, as described in section 3.2. Figure 13a) shows the missing energy spectrum for the GR region in 4sca, along with the corresponding statistical decay calculation. Again a sizeable direct decay branch is observed, this time mainly populating the ground state of 4rCa, with possibly a very small branch towards the first excited hole state. The missing energy spectrum for the double-phonon region (fig. 13b) displays features very similar to the 4°Ca case, a branch towards low-lying states due to fast forward moving neutrons, and structures superimposed on the statistical bump. The simulation calculation, which takes into account the double-humped structure of the GR in 4sca, and assumes that all the direct decay of the GR proceeds towards the ground state, shows structure in good agreement with the experimental data, providing the fingerprint of the two-phonon state in 4sca. 4. C O N C L U S I O N S A N D P E R S P E C T I V E S The last five years have seen a rapid evolution of the field of multiphonon giant resonances, progressing from the existence of a few scattered speculative results to unquestionable experimental evidence of two-phonon states. From the extended body of experimental results available today, a coherent picture of the properties of two-phonon excitations in nuclei can be drawn. Collective nuclear vibrations built with giant resonances appear as mostly harmonic motions. Indeed, the energy of the observed two-phonon states do not exhibit sizeable deviations from the harmonic prediction E2 = 2E1. This leads to the conclusion that anharmonicities will show up only when larger deformations will be reached, i.e. for a large number of excited phonons. The weakness of the interaction between phonons is confirmed by the measurement of the width of the two-phonon states, which is close to the independent phonon limit F2 = v~F1. The narrow width of the two-phonon state indicates that it can be considered, instead of a unique state coupled to the continuum at the energy E2, as a tensorial product of two independent states of energy El. A remarkable confirmation of the independence of the phonons is given by the measurement of the direct decay pattern of the double GQR in several nuclei. A remaining open problem concerns the cross section of the double phonon states. The particle decay method employed at GANIL does not allow a precise extraction of the cross section. First results from Coulomb excitation indicated an excess of cross section of about a factor two with respect to the harmonic approximation, but more recent measurements on other nuclei seem to be in agreement with calculations[ll,12]. More systematic measurements are clearly needed to resolve this problem. The main challenge of the field is now to observe three-phonon giant resonances, which is a difficult task due to the very small cross sections predicted, and the rather large width of these states. Amongst the methods employed for the two-phonon studies, double charge exchange reactions cannot excite triple phonon states because of trivial selection rules.
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The branching ratio of triple 7 decay would be of the order of 10 -s, making a three 3' experiment practically impossible. The most promising path seems to be the particle decay method, because of the sizeable direct decay branch in light nuclei. However, the present experimental set-ups, with a particle detection efficiency of less than 3%, cannot meet the challenge. A straightforward way to increase the efficiency for charged particle detection would be to combine the spectrometer with a 47r charged particle array. This would also allow to detect simultaneously all particles emitted from a multiphonon state, leading to a more precise understanding of its decay. These studies would however be restricted to light nuclei which decay predominantly by charged particle emission. Such an experiment would be feasible at GANIL under excellent conditions by combining the SPEG spectrometer with the very powerful INDRA array[25]. 5. A C K N O W L E D G E M E N T S I wish to thank my colleagues D. Beaumel, N. Frascaria, I. Lhenry, V. Pascalon-Rozier, J.C.Roynette, J.A.Scarpaci, and T. Suomij£rvi from Orsay for their constant involvement in the GANIL experimental program and for innumerable discussions. I would like to acknowledge particularly our very fruitful collaboration with Adriaan van der Woude from KVI, which I hope will continue in the future despite his very nice retirement ceremonies which took place during the conference. REFERENCES
1. A. van der Woude, Prog. Part. Nucl. Phys. 18 (1987) 217. 2. D. Beaumel and Ph. Chomaz, Ann. Phys. (N.Y.) 213 (1992) 405. 3. R.A. Broglia et al., Phys. Lett. 61B (1978) 331. 4. N. Frascaria et al., Nucl. Phys. A474 (1987) 253. 5. J . A . Scarpaci et al., Phys. Rev. Lett. 71 (1993) 3766. 6. J. Hitman et al., Phys. Rev. Lett. 70 (1993) 533. 7. R. Schmidt et al., Phys. Rev. Left. 70 (1993) 1767. 8. S. Mordechai and C. F. Moore, Nature 352 (1991) 393. 9. Ph. Chomaz and N. Frascaria, Phys. Rep. 252 (1995) 275. 10. H. Emling, Prog. Part. Nucl. Phys. 33 (1994) 729. 11. J. Stroth: these proceedings. 12. T. Aumann et al., these proceedings. 13. S. Mordechai and C.F. Moore, these proceedings. 14. Ph. Chomaz and N.V. Giai, Phys. Lett. B282 (1992) 13. 15. T. Suomij/irvi et al., Nucl. Phys. A509 (1990) 174. 16. P. Roussel-Chomaz et al., Phys. Left. B209 (1988) 187. 17. F. Catara et al., Nucl. Phys. A471 (1987) 661. 18. L. Bianchi et al. Nucl. Inst. Meth. A276 (1989) 509. 19. J.A. Scarpaci, PhD Thesis, Orsay (1990), report IPN0-T-90-04 (Orsay). 20. H. Laurent et al. Nucl. Inst. Meth. A326 (1993) 517. 21. Y. Blumenfeld and Ph. Chomaz, Phys. Hey. C38 (1988) 2157. 22. Y. Blumenfeld et al., Nucl. Phys. A445 (1985) 151. 23. J.A. Scarpaci et al., Phys. Left. B258 (1991) 279.
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24. A. van den Berg et al., Nucl. Phys. A578 (1994) 238. 25. J. Pouthas et al., Nucl. Inst. Meth. A357 (1995) 418.
Nuclear PhysicsA599 (1996) 289c-306c
Multiphonon Giant Resonances: Experimental Status and Perspectives Y. Blumenfelda ~Institut de Physique Nucl~aire, IN2P3-CNRS, 91406 Orsay Cedex, France Recently, decisive progress has been made in the search for multiphonon states built with giant resonances. This paper will first focus on the different probes used to excite multiphonon states, and the experimental methods used to characterize these states. Several examples of experiments where the two-phonon giant resonance has been observed are described. The possibility of signing two-phonon strength through its direct decay by particle emission is then discussed in detail, and the results of the ongoing experimental program at GANIL are presented. Finally, the potential of different methods for the future observation of three-phonon states is briefly examined. 1. I N T R O D U C T I O N The nucleus exhibits a large variety of highly collective modes called Giant Resonances (GR)[1]. These resonances are understood as the first oscillator quanta of the collective vibrations. Even though GRs were first discovered almost fifty years ago, the second and higher quanta, named multiphonons, had until recently remained unobserved. Not only is the observation of multiphonon states important for reinforcing the theoretical interpretation of GRs, but their study also provides a unique path towards the investigation of hitherto unknown properties of large amplitude collective motion in nuclei. Of particular interest are the energies of multiphonon states which should allow to gain a handle on the anharmonicities of nuclear excitations [2]. Moreover, multiphonons should represent efficient doorway states towards energy dissipation in heavy ion collisions, and thus be a vital ingredient for our understanding of the dynamics of reactions between heavy nuclei [3]The detailed study of heavy ion inelastic scattering in the early eighties [4] gave the first indication of the existence of multiphonon giant resonances. In these experiments small structures located near the excitation energies expected for multiphonon states were observed in the spectra from reactions induced by Ne, Ar and Ca ions between 10 and 50 MeV/u bombarding energy on various targets (4°Ca, 9°Zr, 12°an, and 2°Spb). However, the interpretation of these structures in terms of multiphonon states remained largely speculative, as no proof of the nature of the bumps could be given. During the last few years, the development of novel experimental techniques coupled to powerful new accelerators has fueled spectacular progress in the field of multiphonon excitations. The two-phonon state has been excited through the nuclear interaction[5], the Coulomb field[6,7], and through double charge exchange reactions[8]. No doubt can 0375-9474/96/$15.00 © 1996ElsevierScienceB.V. All rights reserved. PII: S0375-9474(96)00072-3
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remain concerning its existence. These different methods are now beginning to yield systematic results spanning a large range of nuclear masses. In the past, such systematics have proven to be of the utmost importance for gaining a complete understanding of all types of collective nuclear motion, and they wiU clearly yield much needed new information concerning the two-phonon states. In the near future new more efficient experimental setups should allow to bring to light the elusive higher-order phonon states and in particular the three-phonon GR. The aim of the present paper is to review these fast-paced developments[9,10] and to give some insight into what future studies wiU hold. Section 2 will be devoted to the specificity of the different probes used to excite multiphonon GRs, and to the experimental methods applied to characterize them. The most recent results concerning Coulomb excitation and charge exchange reactions are presented in detail in three other papers of these proceedings[ll-13]. Section 3 consists in a detailed description of the light particle decay method used at GANIL to characterize two-phonon states excited by the nuclear interaction. Very recent results on Ca isotopes are discussed. Finally, section 4 will recap our current knowledge of two-phonon states and indicate some promising paths for the future. 2. E X C I T A T I O N A N D C H A R A C T E R I Z A T I O N STATES
OF M U L T I P H O N O N
2.1. W h a t is a M u l t l p h o n o n S t a t e ?
If a giant resonance (GR) is understood as the first oscillator quantum, multiphonons can be defined as the higher quanta. In a microscopic approach, the giant resonance is described as a coherent superposition of one-particle one-hole (lp-lh) excitations. A multiphonon excitation can then be interpreted as a simultaneous excitation of n identical phonons. In other words, a multiphonon excitation is a giant resonance built on other giant resonances. In a harmonic picture, the different phonons composing a multiphonon state are considered as independent. In such a context the excitation energy of the phonons is predicted to be additive, i.e. a two-phonon GR will have twice the excitation energy of the GR. Following the arguments of [14], the width of the multiphonon state is predicted to be equal to the quadratic sum of the widths of the individual phonons, providing once again that the anharmonicities are small. 2.2. E x c i t a t i o n of M u l t i p h o n o n s t a t e s Multiphonon GRs lle at high excitation energies in the nuclear continuum where the level density is extremely large. The first prerequisite for their observation is to use reactions in which they are excited with very large cross sections and/or high selectivity. Since multiphonons are interpreted as GRs built on others GRs, the excitation of multiphonon states is strongly connected to the properties of their building blocks, the GRs. Thus, in order to determine the best probes for multiphonon studies, it is necessary to briefly recall some aspects of GR excitations. It is well established now[l], that GRs constitute a universal nuclear phenomenon and that they can be excited in a large variety of nuclear reactions involving the electromagnetic, or the strong nuclear interactions. Photonuclear reactions played the main role in the discovery and study of the Isoveetor Giant Dipole Resonance (GDR), while electron
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and light hadron scattering allowed to accumulate information on the properties of the isoscalar giant quadrupole (GQR) and isoscalar giant monopole (GMR) resonances. These three resonances are the most collective GRs and the best known today. More recently, the spinless isovector pion appeared to be an ideal tool to study electric isovector G R s . During the last decade intermediate and high energy heavy ion beams have provided improved conditions for the observation of GRs. In particular, the GRs excited in heavy ion reactions are observed with very large cross sections of the order of barns and excellent peak to continuum ratios[15]. At intermediate energies (30
Inelastic Excitation,~°Ca (~0Ca~0Ca'] /~
[ta=:
0
~=Qo
O!01
Excitation Energy E(HeV) lOO~:
F
O~o~
100F~.. . . .
~JA=n,,v
~ Excitation
f A
t#=.u,~
o I ~ ~- ~ Energy E(HeV)
~,
Figure i. Calculated cross sections for 4°Ca + 4°Ca inelastic scattering at various incident energies. (from ref.[17]).
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The large cross sections observed for giant resonances make heavy ions a particularly attractive probe for exciting multiphonon states. Following the previous discussion, the search for the double GQR will make use of intermediate energy "light" heavy ions, e.g. Ne or Ca around 50 MeV/n. The cross-section for two-phonon GQR excitation can be predicted in the framework of a semi-dassical calculation[17]. The result is shown for the 4°Ca + 4°Ca reaction at different incident energies in fig. 1. While the cross sections for both one- and two-phonon states increase dramatically with bombarding energy, the ratio between the first and second peaks drops strongly when going from 10 MeV/u to 44 MeV/u. A bombarding energy around 40 MeV/u is optimal for the detection of the double GQR. At this energy the probability of exciting the double GDR is negligible.
Muttiphonon Excitation 101
~
N-2
10 0
.... 2-.-._..$
"~""
Z
b
i0 -I
-
-
~
238U+238LI
_." "*"
/ i0.-z 10
$
N=~
,
i
,
,Illl~i
i
i
Incident Energy
,
i i,iiii
1
,
.
10 Etob
,,,,
10 2
(GeV/u)
Figure 2. Calculated cross sections for 1, 2 and 3-phonon states in 23Su + 2asU as a function of bombarding energy. (from ref.[lO])
Conditions for the observation of the double GDR will be much more favorable at higher bombarding energy, as illustrated on fig. 2, which shows calculations for the electromagnetic excitation of the single, double, and triple GDR in 2asU + 23aU collisions as a function of bombarding energy [10]. The ratio between the one- and two-phonon states is most favorable around 1 GeV/u, where it has a value of 10. The cross section for the double GDR obtained here is much larger than that predicted for the double GQR at intermediate energies. One can also note that going to energies higher than 1GeV/u will not entail significant advantages. 2.3. C h a r a c t e r i z a t i o n of M u l t i p h o n o n S t a t e s To prove the existence of multiphonon states one must of course use reactions offering large cross sections and good selectivity for their excitation. However, due to the large
Y. Blumenfeld/Nuclear Physics A599 (1996) 289c-306c
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level density in the region of two-phonon states, and to the possible contamination from reaction mechanisms other than pure inelastic scattering, such as pick-up break-up or knock out for example, it is also imperative to devise means to sign the multiphonon strength.
DCX Excitation 3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
10
20
30
40
50
60
70
- O (MeV)
Figure 3. Experimental spectra from the (x +, x-) reaction on 93Nb at 292 MeV. (from ref.[8])
If very selective reactions are used it may be sufficient to systematically measure the characteristics of the observed states over a large range of target nuclei. This is illustrated in the case of pion double charge exchange reactions which can excite only isotensor A T -- 2 transitions. Spectra measured on 93Nb are presented on fig. 3. Despite the good selectivity, a large background is present below the resonances. However, the same reaction was performed on various targets and in all cases the double GDR is observed at the expected Q value with a cross section and angular distribution in agreement with theoretical estimates. Clearly inelastic heavy ion reactions, in which both nuclear and electromagnetic forces come into play, offer no isospin selection. However, beam intensities and cross sections are sufficiently large to allow to perform coincidence experiments and multiphonon states can
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thus be characterized by the measurement of their specific decay channels. If one admits the harmonic approximation, all phonons of a multiphonon state will decay independently, each phonon exhibiting the decay characteristics of the one-phonon GR.
-L
~'~" Decay
~2,o
IneLastic Excitation
GD=
tph
2ph
HIIY"T,. ,t 0
80 '\,~L
-20 16 L~0 24 ~
32. 36 40
~
20
30
4C
"
10 " \ ' " ~ t 16
I
o 10
20
30
ExeltatlwEnC'rlWE (l~ev)
40
50
El"E2 I -< 6 M e V ~ 20 24 28 32 36 40 44 Sum Energy EI+E 2(MeV)
Figure 4. Sum energy of coincident photon pairs with an energy difference of less than 6 MeV emitted from the 2°9Bi + 2°sph reaction at 1 GeV/u. (from ref.[6])
Figure 5. Excitation energy spectrum obtained for a 136Xe projectile on 2°8pb and 1~C targets at 700 MeV/u (from ref.[7])
A very useful decay channel is the direct 7 decay towards the ground state of the nucleus. In the case of the GDR the branching ratio for direct 7 decay is of the order of 1%. Therefore the double GDR will decay by emitting two 7-rays with a probability of 10 -4. Each photon will carry the energy of one GDR, and both will thus have approximately the same energy. The observation of the double 7 decay was recently used to study the double GDR in 2°Spb[6]. The two-phonon GDR was excited by bombarding a 2°Spb target with a 2°9Bi beam of 1 GeV/u energy at SIS. Two 7-rays in coincidence were observed using the TAPS detector. Peripheral events are selected by requiring that a forward wall (plastic scintillator) detects no charged particles. A structure around 13 MeV was observed in the one-photon energy spectrum and assigned to the GDR in 2°Spb. A spectrum obtained by requiring the coincidence of two 7-rays with an energy difference of less than 6 MeV was constructed and is displayed in fig. 4. A prominent structure is observed at 25.6 + 1 MeV with a width of 5.8 4- 1.6 MeV. This structure has been assigned to the two-phonon GDR in 2°Spb. Assuming that the second phonon has the same branching ratio as the GDR (1.7%), the cross section is found to be 720 mb which is more than a factor 2 larger than the theoretical predictions.
Y. Blumenfeld/Nuclear Physics A599 (1996) 289c-306c
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Another experiment performed at SIS also allowed the observation of the double GDR through Coulomb excitation. The method is to excite collective modes in the projectile using peripheral heavy ion collisions, to measure in coincidence the subsequent neutron and 7-decay of these states and to reconstruct the excitation energy of the projectile. This experiment was performed using a 136Xe beam on 12C and 2°Spb targets[7]. The resulting excitation energy spectra for 136Xe obtained with both targets is displayed in fig. 5 and compared to Weiszacker-Williams calculations[10]. In these calculations, the contribution of the GDR and both isovector and isoscalar GQR is taken into account. The results obtained with a 12C target are used to estimate the nuclear cross section. The calculation reproduces the measured excitation energy spectrum up to 25 MeV. Above, the calculated spectrum drops rapidly while a structure, which is assigned to the double GDR, is clearly observed at 28 MeV in the experimental spectrum, with a width of about 6 -4- 2 MeV. This experiment does not provide an unambiguous signature of the double phonon, but no alternative explanation of the observed structure has been given. New results using the same method with other projectiles are presented elsewhere in these proceedings[11]. In the case of isoscalar resonances, and in particular the GQR, the 7 decay branch is much weaker than for the GDR, and the two 7 decay of the double GQR is too small to be measured. One must then resort to the particle decay in order to characterize the double GQR. This is the object of our experimental program at the GANIL facility, which is described in detail in the following section.
3. L I G H T P A R T I C L E D E C A Y O F T H E D O U B L E
GQR
As GRs are usually located above the particle emission threshold, light particle decay is their main deexcitation channel. As it is well known, particle decay of GRs can occur through various processes [1], mainly the direct decay into hole states of the (A-l) residual nucleus with an escape width F T, and the statistical decay leading to the spreading width, P~. Statistical decay depends only on the excitation energy and angular momentum of the state. Direct decay, on the other hand, can yield information on the microscopic nature of a resonance. Let us use 4°Ca, a proton emitter, as an example to demonstrate the method employed. Fig. 6 sketches the direct decay of a GR and a high lying state in 4°Ca through proton emission. The GR decays towards hole states in 39K. If the high lying state is a onephonon GR it will also decay into hole states through the emission of one high energy proton (dashed arrows). Conversely, if the high lying state is a two-phonon state, since the mixing with other high lying states and the coupling between phonons is expected to be weak [2], each of the two phonons will undergo a direct decay exhibiting the same features as the direct decay of the GR. Two protons will then be emitted. The first proton will populate the GR or (GR ® hole states) in 39K, and the second will deexcite this GR, leading to two-hole states in 38Ar. It is this specific direct decay pattern which can give a signature of a multiphonon state. The prerequisite for this method is that the GR present a sizeable direct decay branch. This limits its usefulness to rather light nuclei (A < 100), since heavy nuclei are known to decay mainly statistically. However, it can be used for both neutron and proton emitters, as will be demonstrated in the following.
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E*(MeV) 35
oecay' ~ ~""'GR'"'"' t ~ 7 . 5 17.5
]
GR
k~
................ 2.1
~ ................ 2.6 39 K
38Ar
0
0
40
Ca
Figure 6. Schematic decay diagram of one- and two-phonon GRs in 4°Ca.
3.1. E x p e r i m e n t a l M e t h o d We have studied the decay of GRs and high lying states in 4°Ca, and 48Ca, excited in the 50 MeV/u 4°Ca + n~tCa, and 48 MeV/u 2°Ne + 48Ca reactions. Recent data taken on 9°Zr and 94Zr are currently under analysis. The aim is to study the direct decay pattern of the GR and of the excitation energy region where the multiphonon GRs are expected. For this the missing energy spectra for these two decays must be constructed. Consider the reaction P +T-,P +T*(T* ~T'+p) where P and T are projectile and target, and where the excited target decays by emission of a light particle p. The missing energy is then Emi,, = E*(T*) - EpCM - E~em,,where E*(T*) is the initial excitation energy in the target, EpTM the particle energy in the center of mass of the recoiling target, and E~e~ the recoil of the target remnant induced by the particle emission. The excitation energy E*(T*) is obtained from the energy loss of the projectile measured by a spectrometer. At GANIL, the SPEG spectrometer associated with its standard detection system is used[18]. This system consists of two position sensitive drift chambers which, after trajectory reconstruction, yield the focal plane position and scattering angle of the fragment. Particle identification is obtained by combining an energy loss measurement in a large ionization chamber with a residual energy measurement in a thick plastic scintiUator, and the time of flight measured between this scintillator and the cyclotron RF with a resolution of better than 1 ns. An unambiguous mass, charge (Z), and atomic charge (Q) identification of scattered projectiles is achieved. The energy resolution is 800 KeV in the case of the Ca beam and about 400 KeV for the Ne beam. The angular resdution is estimated to be 0.2°. The energy of the coincident light partides must be measured. This is accomplished by surrounding the target with a large number of modules of a particle multidetector. In the case of 4°Ca, which is predominantly a proton emitter, 30 CsI elements of the
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multi-detector array PACHA[19] were placed in the reaction chamber. They were positioned in the reaction plane, covering the whole angular domain with the exception of a small wedge of [-15,+7°] around the beam direction (positive angles are on the same side of the beam as the spectrometer). The total solid angle covered is about 3% of 4z'. The proton energy resolution was about 2%. Threshdds ranged between 1 and 3.5 MeV. In order to be able to sum the spectra from various detectors, a software threshold of 4 MeV protons in the center of mass of the recoiling 4°Ca nucleus was set during the analysis. In the case of 4SCa, which decays preferentially by neutron emission, SPEG was run in coincidence with EDEN, a time of flight neutron multidetector. EDEN is composed of 40 NE213 liquid scintillators[20], which were located outside of the reaction chamber at 1.75 m from the target at backward angles with respect to the beam. They covered a solid angle of about 3% of 4z-. The neutron time of flight resolution is 1 ns which corresponds to an energy resolution of 20 keV for a 1 MeV neutron and 200 keV for a 5 MeV neutron. Neutrons are separated from 7-rays by pulse-shape discrimination. During the analysis a software threshold of 60 KeV electron equivalent was set for the neutron detectors. This threshold was determined from calibration runs with a 241Am source. The appropriate efficiency correction was applied to the neutron spectra. In the following the main points of our investigations wiU be illustrated with results from the 4°Ca + 4°Ca experiment. Some recent unpublished results from the neutron-decay experiments will also be shown.
800
1500
600 1000 0 400 C)
500
200 0
0
20
40
60
0 80 E*
100
Figure 7. Inelastic spectrum from the 4°Ca + 4°Ca reaction at 50 MeV/u with two different energy binnings. The dashed llne is the measured contribution from the pick-up break-up of one proton.
3.2. Reaction M e c h a n i s m s Fig. 7 presents the inclusive inelastic spectrum from the 4°Ca + 4°Ca reaction. The GR, split into two components centered at 14 and 17.5 MeV, is clearly observed. An multipole analysis similar to that described in reL[15] shows that the GQR is the dominant constituent of both these components in the angular domain studied. The higher excitation
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energy region appears as a broad continuum upon which one may observe some small structures, in particular around 34 MeV excitation energy. Random phase approximation calculations situate a large amount of the high multipolarity strength in this region where semi-classical calculations also predict the excitation of the two-phonon GQR[21].
V ~
•
-900
~~
~
...-0
+90 o
Figure 8. Invasiant cross section plot for protons emitted in 4°Ca + 4°Ca inelastic reactions at 50 MeV/u. the arrow indicates the velocity of the projectile-like fragment.
Before searching for signatures of high energy collective states it is important to understand the general features of the inelastic spectrum, and to determine the reaction mechanisms contributing to the inelastic cross section. For this, light particle coincidence measurements represent a powerful tool. Fig. 8 shows a density plot of the invariant proton cross section in the (VII, V±) velocity plane in coincidence with inelastically scattered 4°Ca without any selection on the excitation energy deposited. One immediately realizes the potential of coincidence experiments at this bombarding energy : protons emitted by the projectile and the target-like nuclei can easily be separated in velocity space. First of all, the high energy protons measured in two detectors on the left hand side of the beam are due to elastic scattering on the hydrogen contaminant of the target. An almost isotropic component of low velocity protons centered around the recoiling target nucleus reflects the decay of states excited in the target through inelastic scattering. In the forward direction an accumulation of fast moving protons is observed, which indicates the presence of the pick-up break-up mechanism (PUBU)[22]. The contour lines depict the result of a Monte Carlo simulation including both PUBU and inelastic excitations and reproduces very well the main trends of the data. More surprisingly, in the upper right
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quadrant a strong enhancement of high energy protons is observed, emitted at angles too large to be ascribed to PUBU processes. This is indicative of a new mechanism which will be further discussed below, but is not yet well understood. By comparing the proton spectra measured at forward angles with the Monte-Carlo simulation it is possible to infer the total proton pick-up break-up contribution to the inclusive inelastic spectrum[23], and the result is displayed on fig. 7. Since, in the present reaction~ the neutron PUBU cross section is estimated to be much smaller than the proton one, we conclude that the PUBU accounts for less than half of the cross section in the high excitation energy region.
300
a)
" ~t~
t
b)
=o2 0 0
ham 100
50
100 0 400
t
c)
~d)
"~ 300 o
0
100 50
o 200
lOO 10
15 E-'(MeV)
10
20
30 E-'(MeV)
Figure 9. Missing energy spectra for the GQR (left) and double GQR (right) excitation energy regions. The schematic drawings indicate the proton detection angles considered in the top and bottom figures.
To understand the remainder of the coincidence cross section the missing energy spectra for two excitation energy regions are displayed on fig. 9. The first region ( a ) and c) ) between 12 and 20 MeV encompasses the GQR, while the second region ( b ) and d)) at higher excitation energy should contain the two-phonon strength. The spectra are presented for detectors located in the upper right quadrant ( a ) and b) ) where unexpected high energy protons were observed in the invariant cross section plot, and for detectors in the backward hemisphere (c) and d) ), where only decay from the target is expected. None of the spectra presented here contain any contribution from PUBU reactions. The solid lines are calculations performed with the code CASCADE, which represent the statistical part of the decay. These calculations have been normalized so as to never overshoot the data. First, a sizeable direct decay branch of the GQR is observed, accounting for approximately 30% of the total decay, which populates the ground state and the first excited
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Y Blumenfeld /Nuclear Physics A599 (1996) 289c-306c
state in 39K. This direct decay is comparable in strength in the forward and backward hemispheres, as expected from decay of a giant state. The behavior of the decay from the higher excitation energy region is very different. At backward proton angles some small structures superimposed on a broad statistical bump are observed but no direct decay to the hole states in 39K is present. For the forward detectors, however, the direct population of a9K hole states dominates the missing energy spectrum. The very strong anisotropy of this component, and its asymmetry with respect to the direction of the recoiling target, rule out an interpretation in terms of direct decay of a specific high lying state. It must rather be due to a new fast mechanism for proton emission which is not yet well understood. Note that fast neutron emission presenting analogous characteristics was observed in inelastic 170 + 2°Spb coUisions at 84 MeV/u[24]. In order to achieve a better understanding of this intriguing process, systematic measurements in different systems are planned in the near future at the AGOR cyclotron. 0 < E,,z
a)
I
0 < g~ < 8 MeV
b) Backward
200
Protons
,
,
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I ,,
I
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Forward
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I
L
f)
e)
Forward
200
minus Backward
20
40
60
80
Z "(Meg)
20
40
60
80 E'(MeV)
Figure 10. Inelastic spectra in coincidence with protons emitted in the backward (top) and forward (middle) directions and subtraction of these two spectra (bottom) which shows the contribution of the new fast proton mechanism. Left panel is for all protons and right panel for final state energies less than 8 MeV in 39K.
To extract the contribution of this new mechanism to the inelastic spectrum, the inelastic spectrum in coincidence with backward detectors, where only target decay is present, was subtracted from the spectrum in coincidence with forward detectors, after suitable
Y Blumenfeld/Nuclear Physics A599 (1996) 289c-306c
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normalization for the solid angles of the particle detectors. The two inelastic spectra, and the subtracted spectrum are shown on fig. 10, both with (right panel) and without (left panel) gating on discrete final states in 39K (E*(39K < 8 MeV). The two subtracted spectra are very similar, confirming that the fast mechanism mainly populates the low-lying hole states of 39K. The contribution of this mechanism to the inelastic spectrum sets in at around 20 MeV excitation energy and therefore does not pollute the GR region. Its maximum is located near 30 MeV. Above, this contribution decreases but remains present up to excitation energies as high as 80 MeV. Very roughly, this fast proton emission mechanism makes up 25% of the inelastic cross section between 20 and 60 MeV excitation energy. The decay of highly excited target states will now be investigated, in order to search for clues of multiphonon excitations.
3.3. Signature of t h e t w o - p h o n o n G Q R in 4°Ca In Fig. l l a ) , the 4°Ca inelastic spectrum in coincidence with backward emitted protons is displayed. This condition effectively eliminates contributions from PUBU reactions and fast processes. Such a spectrum must be corrected for the multiplicity of emitted protons [19]. For example, when the two-proton decay channel is open, the probability to detect a coincidence event will be greater than when only the one-proton channel is accessible. When the solid angle for particle detection is small, as in the present experiment, this probability goes simply as the multiplicity of protons above the detection threshold. The correction was performed by calculating the proton multiplicity as a function of excitation energy, taking into account the detector thresholds, using two statistical codes (CASCADE and LILITA), and dividing the measured spectrum by this multiplicity. The result depends very little on the choice of the evaporation code. The multiplicity function calculated with the code LILITA is shown in fig. 11a). The corrected spectrum is displayed in fig. llb). In such a correction, the main assumption is that particle emission is purely statistical and the direct contribution is neglected. This will tend to slightly overestimate the proton multiplicity. We estimate the systematic error using this assumption to be about 20 %. In this coincidence spectrum a very prominent structure at twice the GQR excitation energy shows up, which is barely visible in the inclusive spectrum. To roughly estimate the characteristics of this structure, several polynomial fits of the background were subtracted. An example is shown as a solid line in fig. 11b), and the result, fitted by a gaussian, is displayed on the bottom of the figure. The width of the structure is estimated to be 9 MeV. Concerning the cross section, a ratio of 8 between the giant resonance and the structure at 34 MeV was extracted from this fit. However, other fits, where the background is drawn closer to the data, can yield ratios as high as 15 with narrower widths. These characteristics are compatible with the multiphonon model [21] which predicts a ratio of 15 and a width for the two-phonon state equal to v/2 times the width of the one-phonon state [14]. However, theoretical calculations for this energy region predict the presence of both the two-phonon state and other high lying giant resonances. Therefore, it is difficult to demonstrate the existence of the two-phonon state simply by studying the characteristics of the observed structure. In order to sign the presence of two-phonon strength, a study of the decay of the structure is called for. Fig. 12a). shows the missing energy spectrum for the region of the
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800 600 o
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Pa)1
l++++
4°Ca(4°Ca, 4°Ca
+++ 1
|
400 200 0
09
10 .o v
'0 ..........
b "0
20
40
60
E Figure 11. a) Inelastic spectrum in coincidence with backward emitted protons. The solid line is the multiplicity correction (see text); b) top: Inelastic spectrum after correction for multiplicity. The solid line is an arbitrary background; b) bottom: spectrum after background subtraction. The solid line is a gaussianfit.
GQR. As discussed before, direct decay to the ground and first excited state in agK clearly shows up in addition to the statistical decay component. For excitation energies in 4°Ca around 34 MeV, corresponding to the structure, the missing energy spectrum (Fig. 12b) shows peaks at 8.3 and 10.9 MeV corresponding to the population of the GS and the 2.6 MeV state in 39K, which were shown above to be due to the fast proton emission mechanism. The other very striking feature, however, is the presence of peaks located about 17 MeV above the GS, which corresponds to the GR energy in 39K (see upper scale) superimposed on a broad contribution. The calculated statistical decay spectrum corresponding to this energy region is shown by the histogram. At these large missing energies, two protons can be emitted, while only one is detected. If the first emitted proton is detected, peaks in the missing energy spectrum mean that a small number of states must be preferentially populated in 39K. In the same way, if we detect the second emitted proton, which populates 3SAr, peaks will show up only if the initial excited nucleus, 4°Ca, has decayed through particular states in 39K, to well defined low lying states in 3SAt. This is precisely the picture expected for the direct decay of a two-phonon state (cf. discussion
of fig. 6). A simulation of such a two phonon direct decay has been done with the following
Y. Blumenfeld /Nuclear Physics .4599 (1996) 289e-306c
o
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.
.
.
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Figure 12. a): Experimental missing energy spectrum for the GQR region in 4°Ca. Solid line is the statistical decay calculation. b): Same as a) for the region of the double phonon. c): Simulated missing energy spectrum
9.9
19.9
29.9 E~ss(MeV)
Figure 13. Same as Fig. 12 in the case of 4SCa.
for the two-phonon direct decay.
assumptions. The GQR is composed of two peaks centered at 14 and 17.5 MeV with widths (FWHM) of 2 MeV, making up 40% and 60% of the total GQR cross section respectively. A two-phonon state is constructed by randomly picking each phonon among the two components. As observed for the GR in 4°Ca (Fig. 12a), the direct decay of each phonon is assumed to populate only the GS and the first excited hole state of the daughter nucleus (39K or 3SAr). The decay probability to the GS and the first excited state were set equal. The experimental resolution of 800keV was taken into account. The calculation has been done for a 100% direct decay but we checked that the main features remain unchanged for a smaller direct decay branch. The result of the simulation is presented in fig. 12c). The various decay combinations should give rise to ten peaks, the positions of which are shown by bars. However, due to the experimental resolution and the GR width, the final result exhibits only 4 peaks which are in remarkable agreement with
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those observed in the experimental missing energy spectrum (Fig. 12b). This comparison conclusively demonstrates the presence of two-phonon strength.
3.4. Two-phonon strength in 4SCa In the case of 48Ca, which decays predominantly by neutron emission, the same method was applied, replacing the proton detection system by the EDEN neutron array, as described in section 3.2. Figure 13a) shows the missing energy spectrum for the GR region in 4sca, along with the corresponding statistical decay calculation. Again a sizeable direct decay branch is observed, this time mainly populating the ground state of 4rCa, with possibly a very small branch towards the first excited hole state. The missing energy spectrum for the double-phonon region (fig. 13b) displays features very similar to the 4°Ca case, a branch towards low-lying states due to fast forward moving neutrons, and structures superimposed on the statistical bump. The simulation calculation, which takes into account the double-humped structure of the GR in 4sca, and assumes that all the direct decay of the GR proceeds towards the ground state, shows structure in good agreement with the experimental data, providing the fingerprint of the two-phonon state in 4sca. 4. C O N C L U S I O N S A N D P E R S P E C T I V E S The last five years have seen a rapid evolution of the field of multiphonon giant resonances, progressing from the existence of a few scattered speculative results to unquestionable experimental evidence of two-phonon states. From the extended body of experimental results available today, a coherent picture of the properties of two-phonon excitations in nuclei can be drawn. Collective nuclear vibrations built with giant resonances appear as mostly harmonic motions. Indeed, the energy of the observed two-phonon states do not exhibit sizeable deviations from the harmonic prediction E2 = 2E1. This leads to the conclusion that anharmonicities will show up only when larger deformations will be reached, i.e. for a large number of excited phonons. The weakness of the interaction between phonons is confirmed by the measurement of the width of the two-phonon states, which is close to the independent phonon limit F2 = v~F1. The narrow width of the two-phonon state indicates that it can be considered, instead of a unique state coupled to the continuum at the energy E2, as a tensorial product of two independent states of energy El. A remarkable confirmation of the independence of the phonons is given by the measurement of the direct decay pattern of the double GQR in several nuclei. A remaining open problem concerns the cross section of the double phonon states. The particle decay method employed at GANIL does not allow a precise extraction of the cross section. First results from Coulomb excitation indicated an excess of cross section of about a factor two with respect to the harmonic approximation, but more recent measurements on other nuclei seem to be in agreement with calculations[ll,12]. More systematic measurements are clearly needed to resolve this problem. The main challenge of the field is now to observe three-phonon giant resonances, which is a difficult task due to the very small cross sections predicted, and the rather large width of these states. Amongst the methods employed for the two-phonon studies, double charge exchange reactions cannot excite triple phonon states because of trivial selection rules.
Z Blumenfeld/Nuclear Physics A599 (1996) 289c-306c
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The branching ratio of triple 7 decay would be of the order of 10 -s, making a three 3' experiment practically impossible. The most promising path seems to be the particle decay method, because of the sizeable direct decay branch in light nuclei. However, the present experimental set-ups, with a particle detection efficiency of less than 3%, cannot meet the challenge. A straightforward way to increase the efficiency for charged particle detection would be to combine the spectrometer with a 47r charged particle array. This would also allow to detect simultaneously all particles emitted from a multiphonon state, leading to a more precise understanding of its decay. These studies would however be restricted to light nuclei which decay predominantly by charged particle emission. Such an experiment would be feasible at GANIL under excellent conditions by combining the SPEG spectrometer with the very powerful INDRA array[25]. 5. A C K N O W L E D G E M E N T S I wish to thank my colleagues D. Beaumel, N. Frascaria, I. Lhenry, V. Pascalon-Rozier, J.C.Roynette, J.A.Scarpaci, and T. Suomij£rvi from Orsay for their constant involvement in the GANIL experimental program and for innumerable discussions. I would like to acknowledge particularly our very fruitful collaboration with Adriaan van der Woude from KVI, which I hope will continue in the future despite his very nice retirement ceremonies which took place during the conference. REFERENCES
1. A. van der Woude, Prog. Part. Nucl. Phys. 18 (1987) 217. 2. D. Beaumel and Ph. Chomaz, Ann. Phys. (N.Y.) 213 (1992) 405. 3. R.A. Broglia et al., Phys. Lett. 61B (1978) 331. 4. N. Frascaria et al., Nucl. Phys. A474 (1987) 253. 5. J . A . Scarpaci et al., Phys. Rev. Lett. 71 (1993) 3766. 6. J. Hitman et al., Phys. Rev. Lett. 70 (1993) 533. 7. R. Schmidt et al., Phys. Rev. Left. 70 (1993) 1767. 8. S. Mordechai and C. F. Moore, Nature 352 (1991) 393. 9. Ph. Chomaz and N. Frascaria, Phys. Rep. 252 (1995) 275. 10. H. Emling, Prog. Part. Nucl. Phys. 33 (1994) 729. 11. J. Stroth: these proceedings. 12. T. Aumann et al., these proceedings. 13. S. Mordechai and C.F. Moore, these proceedings. 14. Ph. Chomaz and N.V. Giai, Phys. Lett. B282 (1992) 13. 15. T. Suomij/irvi et al., Nucl. Phys. A509 (1990) 174. 16. P. Roussel-Chomaz et al., Phys. Left. B209 (1988) 187. 17. F. Catara et al., Nucl. Phys. A471 (1987) 661. 18. L. Bianchi et al. Nucl. Inst. Meth. A276 (1989) 509. 19. J.A. Scarpaci, PhD Thesis, Orsay (1990), report IPN0-T-90-04 (Orsay). 20. H. Laurent et al. Nucl. Inst. Meth. A326 (1993) 517. 21. Y. Blumenfeld and Ph. Chomaz, Phys. Hey. C38 (1988) 2157. 22. Y. Blumenfeld et al., Nucl. Phys. A445 (1985) 151. 23. J.A. Scarpaci et al., Phys. Left. B258 (1991) 279.
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24. A. van den Berg et al., Nucl. Phys. A578 (1994) 238. 25. J. Pouthas et al., Nucl. Inst. Meth. A357 (1995) 418.