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Excitation of multiphonon states through heavy ion inelastic scattering
NUCLEAR PHYSICS A ELSEVIER
Nuclear Physics A649 (1999) 225c-234c
Excitation of multiphonon states through heavy ion inelastic scattering J.A. Scarpaci a aInstitut de Physique Nucl~aire, IN~P3-CNRS, 91406 Orsay Cedex, France Multiphonon states built with giant resonances have been observed with several probes in the last few years. In this paper we will first describe the different methods to excite multiphonon states, and then concentrate on heavy ion inelastic scattering performed at intermediate energies in coincidence with light emitted particles. Reaction mechanisms participating to the inelastic channel will be described and a newly observed mechanism will be characterized in detail. The direct decay method used to sign the multiphonons will be presented and the latest results on Zr nuclei will be shown. 1. I N T R O D U C T I O N Multiphonon states built with giant resonances have been observed with several probes on a large variety of nuclei[I,2]. 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 and the cross sections of multiphonon states which should allow to gain a handle on the anharmonicities of nuclear excitations [3,4]. The two-phonon state has been excited through the nuclear interaction[5], the Coulomb field[6,7], and through double charge exchange reactions[8]. We will present in section 2, a detailed description of the light particle decay method used at GANIL to characterize two-phonon states excited by the nuclear interaction. Reaction mechanisms involved in the inelastic channel will be described in section 3 and a newly observed mechanism characterized in more detail. Section 4 will be devoted to the study of particle decay of excited states such as the giant resonances and leading to the signature of the double phonon. In particular the latest experiments on Zr and Ni isotopes will be presented. 2. L I G H T P A R T I C L E E M I S S I O N 2.1. E x c i t a t i o n of M u l t i p h o n o n states 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 [9], from which the direct decay into hole states of the (A1) residual nucleus with an escape width F t, and the statistical decay leading to the spreading width, F ~. Statistical decay depends only on the excitation energy and angular 0375-9474/99/$ see front matter © 1999 ElsevierScience B.V. All rights reserved. PII S0375-9474(99)00066-4
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J.A. Scarpaci /Nuclear Physics A649 (1999) 225c-234c
momentum of the state. Direct decay, on the other hand, can yield information on the microscopic nature of a resonance and yield fingerprints for the observation of double phonons. E*IMeV) 35.
17..~
,
o.
1 .................
,
39K
2.6 (;s
3SAt
°Ca
Figure 1. Schematic decay diagram of one- and two-phononGRs in 4°Ca.
Fig. 1 sketches the direct decay of a GR and a high lying state in a°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 [3], 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 SSAr. 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. 2.2. E x p e r i m e n t a l
Method
We have studied the decay of GRs and high lying states in 4°Ca, 48Ca, 9°Zr, 94Zr and 58Ni excited in the 50 MeV/u 4°Ca + n~tCa, 48 MeV/u 2°Ne + 4SCa, 44 MeV/u 36At + 9°Zr and 94Zr, and 44 MeV/u a°Ar + SSNi reactions. 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 E,uss - E*(T*) - EpTM - E~m, where E*(T*) is the initial excitation energy in the target, E c g the particle energy in the center of mass of the recoiling target, and 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
J.A. Scarpaci /Nuclear Physics A649 (1999) 225c-234c
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by a spectrometer. At GANIL, the SPEG spectrometer associated with its standard detection system is used[10]. 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 energy of the coincident light particles is performed by surrounding the target with a large number of modules of a particle multidetector. In the case of proton emitters such as 4°Ca and SSNi, 30 CsI elements of the multi-detector array PACHA[ll] were placed in the reaction chamber. The total solid angle covered is about 3% of 47r. The proton energy resolution was about 2%. Thresholds ranged between 1 and 3.5 MeV. In the case of 4SCa and 9°,94Zr, which decays preferentially by neutron emission, and also for 5SNi, SPEG was run in coincidence with EDEN, a time of flight neutron multidetector. EDEN is composed of 40 NE213 liquid scintillators[12], which were located outside of the reaction chamber at 1.75 m from the target around it. They covered a solid angle of about 3% of 47r. 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.
3. Reaction Mechanisms The inelastic channel, defined by the detection of the intact projectile, is fed not only by target excitations through the inelastic scattering of the projectile, but also by other reaction mechanisms that leave the ejectile intact. This is clearly seen the velocity plot of protons detected in coincidence.
3.1. Proton velocity plot Figure 2 shows a density plot of the invariant cross section for protons in the (Vpar,Vp¢r) velocity plane, in coincidence with the inelastic channel, for the 4°Ca (4°Ca, 4°Ca + p) reaction. The ejectile is detected after the spectrometer on the right side of the beam which average velocity is shown in the plot. In the forward direction, an accumulation of fast moving protons centered around the ejectile velocity is observed which is characteristic of the presence of the pick-up break-up mechanism. An almost isotropic component of low velocity protons centered around the recoiling target nucleus reflects the decay of the target. At negative angles, around -50 ° , the yield is strongly enhanced by recoiling protons stemming from the elastic scattering on the hydrogen contaminant of the target. The knock-out of protons from the target gives rise to proton emission around the recoiling angle (around -80°). Finally, another interesting enhancement is observed around +40 ° where fast protons of kinetic energy up to 50 MeV are detected. This new component, which cannot be accounted for by the decay of the projectile nor the target and is not consistent with the knock-out process, will be extensively discussed in the following part of this paper[13]. 3.2. Angular correlations Angular correlation of neutrons feeding the ground state (GS) of the daughter nucleus, 57Ni was extracted from the reaction 5SNi(4°Ar, 4°Ar + n) ran at 44 MeV per nucleons, and is presented in Fig.3, for the full acceptance of the spectrometer and for apparent excitation energies between 12 and 80 MeV. The proton angles are shown in the laboratory
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JA. Scarpacil Nudear Physics A649 (1999) 225c-234c
0.15 Pick-up Break-up Elasticscattering on H y d ~ n ~
i ',
I .:.,~
,Iv
I
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12 < E* < 80
4°Caejectile ../New Mechanism
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FWI-IMffi 62 °
;Z o.os
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I
~ Neutrons :~ i. :
•
,:
i
........................ ." +90°
Target
,~ Target decay
Figure 2. Experimental invariant cross section of protons for 4°Ca (4°Ca, 4°Ca + p) reaction, represented in the (Vp~r,Vper) plane. Contour plot: Monte Carlo simulation of the target decay and of the proton pick-up break-up.
0.00
I
-120
,
"~.%~...
I
0
,
hb
I
120
O~ Figure 3. Angular correlations for neutrons feeding the GS of the 5rNi daughter nuclei in the 5SNi(4°Ar, 4°Ar + n) reaction.
system. Besides an almost isotropic component which could result from the decay of the target, a very strong peak is observed around +40 ° on the same side of the beam as the ejectile. This component is thus not compatible with the target decay which should either be isotropic or show a symmetry around the recoiling target direction, around -80 °. It is not compatible either with the pick-up break-up nor with the knock out processes expected respectively around 0 ° and -80 °. Azimuthal angular correlations could also be extracted for the reaction 4°Ar + SSNi, and it was observed that the ejectiles detected in coincidence had about the same azimuthal angle as the particle detected on the same side of the horizontal plane. This strong correlation between the proton and the ejectile seems to demonstrate that the proton has been pulled out of the target as the projectile passed by, thus the name given to this mechanism: the towing mode. Contrarily to the pick-up break-up process, where we assume a transfer followed by a statistical decay of the A+I ejectile, the particle does not stick to the projectile long enough to get fully boosted to the projectile velocity. The velocity of the observed light particles are not centered around the ejectile velocity. 3.3.
Calculation
A calculation has been performed to infer the evolution of a particle wave function when two potentials brush past each other. The time dependent SchrSdinger equation was solved in a three dimensional space using Wood-Saxon potentials. It describes the evolution of a wave function initially in the target potential at rest when the projectile passes by at a given impact parameter. Figure 4 shows the density probability for a 3s wave function initially bound in the target potential by 8.7 MeV, when the projectile has passed by at an impact parameter of 8 Fermi at 44 MeV per nucleon. We observe that besides the large probability that the particle remains in the target (73%) and some
J.A. Scarpaci /Nudear Physics A649 (1999) 225c-234c
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probability that it is transfered to the projectile (1.4%), there is a sizeable probability (21%) of particle emission at an angle around 40 ° on the same side of the beam as the projectile, reproducing the experimental observation.
\GR Inclusiveinelasticspectrum ~ / Targetexcitation o~ / / Knock-out TowingMode
o: N / Z
P ~ Q-
10;
I i;; i'--. !
0 Figure 4. Result of the time dependent SchrSdinger calculation (see text for more details).
I
hm
20
I
I
II
40
~'% L
60
"1 I
10"
80 IO0 E* (MeV)
Figure 5. Inclusive inelastic spectrum for the ~SNi (4°Ar, 4°Ar') reaction, decomposed in its differents reaction mechanisms.
3.4. C o n t r i b u t i o n t o t h e inelastic s p e c t r u m The contribution of the new mechanism was extracted by comparing the inelastic specmm~ in coincidence with particles emitted in the forward direction with the one in coincklcnce with backward emitted particles. In the former, both the target decay and the new mechanism contribute whereas in the later one only target decay is present. The contribution of the new mechanism to the inelastic spectrum is centered around 30 MeV ['or both particle emission. Figure 5 shows the inclusive inelastic spectrum (histogram). All components contributing to this spectrum are shown. The inelastic spectrum in coincidence with backward eufission of neutrons or protons normalized to 4rr reflects the excitation of the target. This contribution, shown with open circles, dominates the spectrum up to excitation encrgics of about 30 MeV. The contribution of the new mechanism sets in above 20 MeV and its cross section is of the same order as the target excitation for excitation energies above 40 MeV. The large plateau observed around 60 MeV comes from the neutron pickup break-up contribution[14] and the knock out process gives rise to a peak around 25 MeV. The full inelastic cross section has been disentangled in four reaction mechanisms.
J.A. Scarpaci /Nuclear Physics A649 (1999) 225c-234c
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Target excitations, pick-up break-up, knock-out and towing mode. In order to study target excitations and decays it is clear that we should concentrate on backward emitted nucleons. The decay of highly excited target states will now be investigated, in order to search for clues of multiphonon excitations. 4. D i r e c t d e c a y o f G R s - S i g n a t u r e o f t h e t w o - p h o n o n
GQR
To explain in detail the procedure, we will present the data obtained for the 4°Ca + 4°Ca reaction. In Fig. 6a), the 4°Ca inelastic spectrum in coincidence with backward emitted protons is displayed. Proton multiplicity calculated with CASCADE is also shown [11] and the spectrum corrected for this multiplicity is displayed in fig. 6b). In this coincidence spectrum a very prominent structure at twice the GQR excitation energy shows up, which is barely visible in the inclusive spectrum (not shown). 4o 40 ~o Ca( Ca Ca+p)
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I
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i[i : [:J:il ,*[ ~ ; r ~ ] ~ [ 20 30 40
................. 50 E * ( M e V )
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Figure 6. a) Inelastic spectrum in coincidence with backward emitted protons. The solid line is the multiplicity correction (see text); b) Inelastic spectrum after correction for multiplicity. The solid and dashed line are arbitrary backgrounds; c and d) spectrum after background subtraction. The solid line is a gaussian fit.
lO
~
3O Emiss (Mev )
Figure 7. Missing energy spectra for the decay of the GR in 4°Ca (a), and the decay of the double phonon region (b). Solid histograms are the calculated statistical contribution. (c) is a simulation of the direct decay expected for the double phonon.
In order to estimate the characteristics of this structure, several polynomial fits of the background were subtracted. Two examples of backgrounds are shown as solid and dashed lines in Fig. 6(b), and the result of their subtraction from the spectrum, fitted by
JA. Scarpaci/Nuclear Physics .4649 (1999) 225c-234c
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Gaussians, are displayed on Fig. 6(c) and Fig. 6(d). From these two subtracted spectra, the energy of the structure is found to be 34.8 + 0.5 MeV, the FWHM 8.8 +2 MeV and the cross section 15+8 times smaller than the giant resonance cross section. These characteristics are compatible with the multiphonon model[15] which predicts a two-phonon state at twice the energy of the GR, a width equal to v ~ times the width of the onephonon state and a cross section ratio of about 20 between the GR and the double phonon [16]. However, theoretical calculations for this energy region predict the presence of both the two-phonon state and other high lying giant resonances[17]. Although, the structure observed appears to be a good candidate for a double quadrupole phonon excitation, a detailed study of its decay and a comparison with the direct decay pattern of the GQI~, is needed to confirm this hypothesis. Fig. 7a). shows the missing energy spectrum for the region of the GQR. As discussed before, direct decay to the ground and first excited state in 39K 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. 7b) 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 aSAr, 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 38At. This is precisely the picture expected for the direct decay of a two-phonon state (cf. discussion of fig. 1). A simulation of such a two phonon direct decay has been done with the following 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. 7a), 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 38Ar). 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 and also for 30% direct decay. The results of the simulation are presented in fig. 7c). The various decay combinations give rise to ten peaks, the positions of which are shown by bars. After convolution by tile experimental resolution and the GR width, the final result exhibits only 4 peaks which are in remarkable agreement with those observed in the experimental missing energy spectrum (Fig. 7b). For the simulation performed with 30% direct decay, the peaks still persist but are less pronounced. This comparison conclusively demonstrates the presence of two-phonon strength.
J..A. Scarpaci/Nuclear Physics A649 (1999) 225c-234c
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4.1. D i r e c t d e c a y e x t r a c t i o n One should be aware that the extraction of the percentage of direct decay is not an unambiguous task. There are many reasons for that, the main reason being the background under the GR. Indeed, the percentage of direct decay that we extract from the GR region can be written as: bg
o'~o~
GR
atoe
where %~0 and %DO are the percentage of direct decay of the background and the GR respectively, eba, aria and atot are the cross section of respectively the background, the GR and the sum of background plus GR. In case the background has the same direct decay behaviour as the GR, the extracted value for the direct decay of the GR region (see Fig.7(a)) is the correct GR direct decay percentage. If on the contrary the background decays purely statistically, then the GR direct decay should be %DD = %~D ..... which in case of the 4°Ca + 4°Ca reaction would cr R be twice as much as the extracted va~ue of 30%, since the background accounts for half of the cross section in the GR region. Futhermore, one should take into account the fact that we only measure protons above 4 MeV due to experimental threshold problems. How the low energy protons will affect the precentage? Are they statistical proton? Finally the normalization of the Cascade statistical calculation is optimize to never overshoot the data, which gives an upper limit for the statistical decay contribution, hence a lower limit for the direct decay. This shows that the extraction of the direct decay percentage is a very hazardous business, and the value to be use for the direct decay simulation remains a very open question.
4.2. T w o - p h o n o n s t r e n g t h in 48Ca a n d 9°'94Zr In the case of 4SCa and 9°'94Zr, which decay predominantly by neutron emission, the same method was applied, replacing the proton detection system by the EDEN neutron array. Figure 8 shows the inelastic spectra in coincidence with backward emitted neutrons for 9°'94Zr. A peak is clearly present at 27 MeV excitation energy in 94Zr, which is twice the excitation energy of the GR. As for 9°Zr, a peak is observed which can be fitted by two peaks, one at 22 MeV and the other at 28 MeV. The latter is at the position expected for the double phonon. Figure 9a) shows the missing energy spectrum for the GR region in 48Ca and 9°'94Zr, along with the corresponding statistical decay calculations. A small direct decay branch is observed, to the ground state only for 4SCa and 9°Zr, but also to excited states around 4 MeV for 94Zr. The missing energy spectrum for the doublephonon region is shown in Fig. 9b) together with the simulation. For 4SCa and 9°Zr, the simulation shows two main structures in good agreement with the experimental data, providing the fingerprint of the two-phonon state in these nuclei. For 94Zr, the signature is less clear. This is mainly due to the direct decay of the GR which feeds several states in 93Zr, blurring the decay pattern for the two phonon decay. The ~8Ni decay was also studied through both neutron and proton, but the results suffer the same problem as for 94Zr since the GR decays through several unresolved states of 57Ni and 57C0 respectively, leading to a structureless direct decay component. This shows another limit of the method which needs not only a sizeable direct decay branch but also well separated hole states in the daughter nuclei.
J.A. Scarpaci/Nuclear Physics A649 (1999) 225c-234c
m
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Figure 8. Inelastic spectra in coincidence with backward emitted neutrons for 9°'94Zr o
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Figure 9. Missing energy spectra for the decay of the GR in 4SCa (a), 9°Zr (b) and 94Zr (c), and the decay of the double phonon regions (c,d,e).
5. C O N C L U S I O N S
AND PERSPECTIVES
Inelastic scattering of medium energy heavy ions have provided a large amount of data which gives a coherent picture of the properties and decay of two-phonon excitations. The excess of cross section in the missing energy spectra is well reproduced by a simulation of the two-phonon direct decay based on the measured direct decay Of the giant resonance providing an elegant proof of its existance. Furthermore, these inelastic measurements in coincidence with light emitted particles have allowed for the first time to fully disentangled the inclusive inelastic scattering spectrum in the different reaction mechanisms. The main challenge of the multiphonon 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. It seems however a general belief that these three-phonon states should be looked for since they would give us a better handle on the anharmonic-
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J.A. Scarpaci /Nuclear Physics A649 (1999) 225c-234c
ity of the nucleus. Amongst the methods employed for the two-phonon studies, double charge exchange reactions cannot excite triple phonon states because of trivial selection rules. The branching ratio of triple 7 decay would be much too small, making a three 0/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 4~r 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[18]. 6. A C K N O W L E D G E M E N T S I wish to thank my colleagues D. Beaumel, Y. Blumenfeld, N. Frascaria, I. Lhenry, V. Pascalon-Rozier, L. Petizon, J.C. Roynette and T. Suomij/irvi from Orsay and also my friends and colleagues from GANIL, Ph. Chomaz, D. Lacroix and P. Roussel-Chomaz for their constant involvement in the GANIL experimental (and theoretical) program and for innumerable discussions. I would like to acknowledge particularly our very fruitful collaboration with Adriaan van der Woude from KVI. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
Ph. Chomaz and N. Frascaria, Phys. Rep. 252 (1995) 275. T. Aumann, B.F. Bortignon and H. Emling Annu. Rev. Nucl. Part. Sci. 1998, Vol. 48 D. Beaumel and Ph. Chomaz, Ann. Phys. (N.Y.) 213 (1992) 405. R.A. Broglia et al., Phys. Lett. 61B (1978) 331. J.A. Scarpaci et al., Phys. Rev. Lett. 71 (1993) 3766. J. Ritman et al., Phys. Rev. Lett. 70 (1993) 533. R. Schmidt et al., Phys. Rev. Lett. 70 (1993) 1767. S. Mordechai and C. F. Moore, Nature 352 (1991) 393. A. van der Woude, Prog. Part. Nucl. Phys. 18 (1987) 217. L. Bianchi et al. Nucl. Inst. Meth. A276 (1989) 509. J.A. Scarpaci et al., Phys. Rev. C56, 3187 (1997) H. Laurent et al. Nucl. Inst. Meth. A326 (1993) 517. J.A. Scarpaci et al., Phys. Lett. B428 (1998) 241. J.A. Scarpaci et al., Phys. Lett. B258 (1991) 279. Ph. Chomaz and N.V. Giai, Phys. Lett. B282 (1992) 13. F. Cataraet al., Nucl. Phys. A471 (1987) 661. Y. Blumenfeld and Ph. Chomaz, Phys. Rev. C38 (1988) 2157. J. Pouthas et al., Nucl. Inst. Meth. A357 (1995) 418.
Nuclear Physics A649 (1999) 225c-234c
Excitation of multiphonon states through heavy ion inelastic scattering J.A. Scarpaci a aInstitut de Physique Nucl~aire, IN~P3-CNRS, 91406 Orsay Cedex, France Multiphonon states built with giant resonances have been observed with several probes in the last few years. In this paper we will first describe the different methods to excite multiphonon states, and then concentrate on heavy ion inelastic scattering performed at intermediate energies in coincidence with light emitted particles. Reaction mechanisms participating to the inelastic channel will be described and a newly observed mechanism will be characterized in detail. The direct decay method used to sign the multiphonons will be presented and the latest results on Zr nuclei will be shown. 1. I N T R O D U C T I O N Multiphonon states built with giant resonances have been observed with several probes on a large variety of nuclei[I,2]. 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 and the cross sections of multiphonon states which should allow to gain a handle on the anharmonicities of nuclear excitations [3,4]. The two-phonon state has been excited through the nuclear interaction[5], the Coulomb field[6,7], and through double charge exchange reactions[8]. We will present in section 2, a detailed description of the light particle decay method used at GANIL to characterize two-phonon states excited by the nuclear interaction. Reaction mechanisms involved in the inelastic channel will be described in section 3 and a newly observed mechanism characterized in more detail. Section 4 will be devoted to the study of particle decay of excited states such as the giant resonances and leading to the signature of the double phonon. In particular the latest experiments on Zr and Ni isotopes will be presented. 2. L I G H T P A R T I C L E E M I S S I O N 2.1. E x c i t a t i o n of M u l t i p h o n o n states 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 [9], from which the direct decay into hole states of the (A1) residual nucleus with an escape width F t, and the statistical decay leading to the spreading width, F ~. Statistical decay depends only on the excitation energy and angular 0375-9474/99/$ see front matter © 1999 ElsevierScience B.V. All rights reserved. PII S0375-9474(99)00066-4
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J.A. Scarpaci /Nuclear Physics A649 (1999) 225c-234c
momentum of the state. Direct decay, on the other hand, can yield information on the microscopic nature of a resonance and yield fingerprints for the observation of double phonons. E*IMeV) 35.
17..~
,
o.
1 .................
,
39K
2.6 (;s
3SAt
°Ca
Figure 1. Schematic decay diagram of one- and two-phononGRs in 4°Ca.
Fig. 1 sketches the direct decay of a GR and a high lying state in a°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 [3], 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 SSAr. 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. 2.2. E x p e r i m e n t a l
Method
We have studied the decay of GRs and high lying states in 4°Ca, 48Ca, 9°Zr, 94Zr and 58Ni excited in the 50 MeV/u 4°Ca + n~tCa, 48 MeV/u 2°Ne + 4SCa, 44 MeV/u 36At + 9°Zr and 94Zr, and 44 MeV/u a°Ar + SSNi reactions. 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 E,uss - E*(T*) - EpTM - E~m, where E*(T*) is the initial excitation energy in the target, E c g the particle energy in the center of mass of the recoiling target, and 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
J.A. Scarpaci /Nuclear Physics A649 (1999) 225c-234c
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by a spectrometer. At GANIL, the SPEG spectrometer associated with its standard detection system is used[10]. 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 energy of the coincident light particles is performed by surrounding the target with a large number of modules of a particle multidetector. In the case of proton emitters such as 4°Ca and SSNi, 30 CsI elements of the multi-detector array PACHA[ll] were placed in the reaction chamber. The total solid angle covered is about 3% of 47r. The proton energy resolution was about 2%. Thresholds ranged between 1 and 3.5 MeV. In the case of 4SCa and 9°,94Zr, which decays preferentially by neutron emission, and also for 5SNi, SPEG was run in coincidence with EDEN, a time of flight neutron multidetector. EDEN is composed of 40 NE213 liquid scintillators[12], which were located outside of the reaction chamber at 1.75 m from the target around it. They covered a solid angle of about 3% of 47r. 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.
3. Reaction Mechanisms The inelastic channel, defined by the detection of the intact projectile, is fed not only by target excitations through the inelastic scattering of the projectile, but also by other reaction mechanisms that leave the ejectile intact. This is clearly seen the velocity plot of protons detected in coincidence.
3.1. Proton velocity plot Figure 2 shows a density plot of the invariant cross section for protons in the (Vpar,Vp¢r) velocity plane, in coincidence with the inelastic channel, for the 4°Ca (4°Ca, 4°Ca + p) reaction. The ejectile is detected after the spectrometer on the right side of the beam which average velocity is shown in the plot. In the forward direction, an accumulation of fast moving protons centered around the ejectile velocity is observed which is characteristic of the presence of the pick-up break-up mechanism. An almost isotropic component of low velocity protons centered around the recoiling target nucleus reflects the decay of the target. At negative angles, around -50 ° , the yield is strongly enhanced by recoiling protons stemming from the elastic scattering on the hydrogen contaminant of the target. The knock-out of protons from the target gives rise to proton emission around the recoiling angle (around -80°). Finally, another interesting enhancement is observed around +40 ° where fast protons of kinetic energy up to 50 MeV are detected. This new component, which cannot be accounted for by the decay of the projectile nor the target and is not consistent with the knock-out process, will be extensively discussed in the following part of this paper[13]. 3.2. Angular correlations Angular correlation of neutrons feeding the ground state (GS) of the daughter nucleus, 57Ni was extracted from the reaction 5SNi(4°Ar, 4°Ar + n) ran at 44 MeV per nucleons, and is presented in Fig.3, for the full acceptance of the spectrometer and for apparent excitation energies between 12 and 80 MeV. The proton angles are shown in the laboratory
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JA. Scarpacil Nudear Physics A649 (1999) 225c-234c
0.15 Pick-up Break-up Elasticscattering on H y d ~ n ~
i ',
I .:.,~
,Iv
I
"
12 < E* < 80
4°Caejectile ../New Mechanism
I
I "
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FWI-IMffi 62 °
;Z o.os
Knoc
I
~ Neutrons :~ i. :
•
,:
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........................ ." +90°
Target
,~ Target decay
Figure 2. Experimental invariant cross section of protons for 4°Ca (4°Ca, 4°Ca + p) reaction, represented in the (Vp~r,Vper) plane. Contour plot: Monte Carlo simulation of the target decay and of the proton pick-up break-up.
0.00
I
-120
,
"~.%~...
I
0
,
hb
I
120
O~ Figure 3. Angular correlations for neutrons feeding the GS of the 5rNi daughter nuclei in the 5SNi(4°Ar, 4°Ar + n) reaction.
system. Besides an almost isotropic component which could result from the decay of the target, a very strong peak is observed around +40 ° on the same side of the beam as the ejectile. This component is thus not compatible with the target decay which should either be isotropic or show a symmetry around the recoiling target direction, around -80 °. It is not compatible either with the pick-up break-up nor with the knock out processes expected respectively around 0 ° and -80 °. Azimuthal angular correlations could also be extracted for the reaction 4°Ar + SSNi, and it was observed that the ejectiles detected in coincidence had about the same azimuthal angle as the particle detected on the same side of the horizontal plane. This strong correlation between the proton and the ejectile seems to demonstrate that the proton has been pulled out of the target as the projectile passed by, thus the name given to this mechanism: the towing mode. Contrarily to the pick-up break-up process, where we assume a transfer followed by a statistical decay of the A+I ejectile, the particle does not stick to the projectile long enough to get fully boosted to the projectile velocity. The velocity of the observed light particles are not centered around the ejectile velocity. 3.3.
Calculation
A calculation has been performed to infer the evolution of a particle wave function when two potentials brush past each other. The time dependent SchrSdinger equation was solved in a three dimensional space using Wood-Saxon potentials. It describes the evolution of a wave function initially in the target potential at rest when the projectile passes by at a given impact parameter. Figure 4 shows the density probability for a 3s wave function initially bound in the target potential by 8.7 MeV, when the projectile has passed by at an impact parameter of 8 Fermi at 44 MeV per nucleon. We observe that besides the large probability that the particle remains in the target (73%) and some
J.A. Scarpaci /Nudear Physics A649 (1999) 225c-234c
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probability that it is transfered to the projectile (1.4%), there is a sizeable probability (21%) of particle emission at an angle around 40 ° on the same side of the beam as the projectile, reproducing the experimental observation.
\GR Inclusiveinelasticspectrum ~ / Targetexcitation o~ / / Knock-out TowingMode
o: N / Z
P ~ Q-
10;
I i;; i'--. !
0 Figure 4. Result of the time dependent SchrSdinger calculation (see text for more details).
I
hm
20
I
I
II
40
~'% L
60
"1 I
10"
80 IO0 E* (MeV)
Figure 5. Inclusive inelastic spectrum for the ~SNi (4°Ar, 4°Ar') reaction, decomposed in its differents reaction mechanisms.
3.4. C o n t r i b u t i o n t o t h e inelastic s p e c t r u m The contribution of the new mechanism was extracted by comparing the inelastic specmm~ in coincidence with particles emitted in the forward direction with the one in coincklcnce with backward emitted particles. In the former, both the target decay and the new mechanism contribute whereas in the later one only target decay is present. The contribution of the new mechanism to the inelastic spectrum is centered around 30 MeV ['or both particle emission. Figure 5 shows the inclusive inelastic spectrum (histogram). All components contributing to this spectrum are shown. The inelastic spectrum in coincidence with backward eufission of neutrons or protons normalized to 4rr reflects the excitation of the target. This contribution, shown with open circles, dominates the spectrum up to excitation encrgics of about 30 MeV. The contribution of the new mechanism sets in above 20 MeV and its cross section is of the same order as the target excitation for excitation energies above 40 MeV. The large plateau observed around 60 MeV comes from the neutron pickup break-up contribution[14] and the knock out process gives rise to a peak around 25 MeV. The full inelastic cross section has been disentangled in four reaction mechanisms.
J.A. Scarpaci /Nuclear Physics A649 (1999) 225c-234c
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Target excitations, pick-up break-up, knock-out and towing mode. In order to study target excitations and decays it is clear that we should concentrate on backward emitted nucleons. The decay of highly excited target states will now be investigated, in order to search for clues of multiphonon excitations. 4. D i r e c t d e c a y o f G R s - S i g n a t u r e o f t h e t w o - p h o n o n
GQR
To explain in detail the procedure, we will present the data obtained for the 4°Ca + 4°Ca reaction. In Fig. 6a), the 4°Ca inelastic spectrum in coincidence with backward emitted protons is displayed. Proton multiplicity calculated with CASCADE is also shown [11] and the spectrum corrected for this multiplicity is displayed in fig. 6b). In this coincidence spectrum a very prominent structure at twice the GQR excitation energy shows up, which is barely visible in the inclusive spectrum (not shown). 4o 40 ~o Ca( Ca Ca+p)
;~ (
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Figure 6. a) Inelastic spectrum in coincidence with backward emitted protons. The solid line is the multiplicity correction (see text); b) Inelastic spectrum after correction for multiplicity. The solid and dashed line are arbitrary backgrounds; c and d) spectrum after background subtraction. The solid line is a gaussian fit.
lO
~
3O Emiss (Mev )
Figure 7. Missing energy spectra for the decay of the GR in 4°Ca (a), and the decay of the double phonon region (b). Solid histograms are the calculated statistical contribution. (c) is a simulation of the direct decay expected for the double phonon.
In order to estimate the characteristics of this structure, several polynomial fits of the background were subtracted. Two examples of backgrounds are shown as solid and dashed lines in Fig. 6(b), and the result of their subtraction from the spectrum, fitted by
JA. Scarpaci/Nuclear Physics .4649 (1999) 225c-234c
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Gaussians, are displayed on Fig. 6(c) and Fig. 6(d). From these two subtracted spectra, the energy of the structure is found to be 34.8 + 0.5 MeV, the FWHM 8.8 +2 MeV and the cross section 15+8 times smaller than the giant resonance cross section. These characteristics are compatible with the multiphonon model[15] which predicts a two-phonon state at twice the energy of the GR, a width equal to v ~ times the width of the onephonon state and a cross section ratio of about 20 between the GR and the double phonon [16]. However, theoretical calculations for this energy region predict the presence of both the two-phonon state and other high lying giant resonances[17]. Although, the structure observed appears to be a good candidate for a double quadrupole phonon excitation, a detailed study of its decay and a comparison with the direct decay pattern of the GQI~, is needed to confirm this hypothesis. Fig. 7a). shows the missing energy spectrum for the region of the GQR. As discussed before, direct decay to the ground and first excited state in 39K 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. 7b) 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 aSAr, 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 38At. This is precisely the picture expected for the direct decay of a two-phonon state (cf. discussion of fig. 1). A simulation of such a two phonon direct decay has been done with the following 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. 7a), 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 38Ar). 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 and also for 30% direct decay. The results of the simulation are presented in fig. 7c). The various decay combinations give rise to ten peaks, the positions of which are shown by bars. After convolution by tile experimental resolution and the GR width, the final result exhibits only 4 peaks which are in remarkable agreement with those observed in the experimental missing energy spectrum (Fig. 7b). For the simulation performed with 30% direct decay, the peaks still persist but are less pronounced. This comparison conclusively demonstrates the presence of two-phonon strength.
J..A. Scarpaci/Nuclear Physics A649 (1999) 225c-234c
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4.1. D i r e c t d e c a y e x t r a c t i o n One should be aware that the extraction of the percentage of direct decay is not an unambiguous task. There are many reasons for that, the main reason being the background under the GR. Indeed, the percentage of direct decay that we extract from the GR region can be written as: bg
o'~o~
GR
atoe
where %~0 and %DO are the percentage of direct decay of the background and the GR respectively, eba, aria and atot are the cross section of respectively the background, the GR and the sum of background plus GR. In case the background has the same direct decay behaviour as the GR, the extracted value for the direct decay of the GR region (see Fig.7(a)) is the correct GR direct decay percentage. If on the contrary the background decays purely statistically, then the GR direct decay should be %DD = %~D ..... which in case of the 4°Ca + 4°Ca reaction would cr R be twice as much as the extracted va~ue of 30%, since the background accounts for half of the cross section in the GR region. Futhermore, one should take into account the fact that we only measure protons above 4 MeV due to experimental threshold problems. How the low energy protons will affect the precentage? Are they statistical proton? Finally the normalization of the Cascade statistical calculation is optimize to never overshoot the data, which gives an upper limit for the statistical decay contribution, hence a lower limit for the direct decay. This shows that the extraction of the direct decay percentage is a very hazardous business, and the value to be use for the direct decay simulation remains a very open question.
4.2. T w o - p h o n o n s t r e n g t h in 48Ca a n d 9°'94Zr In the case of 4SCa and 9°'94Zr, which decay predominantly by neutron emission, the same method was applied, replacing the proton detection system by the EDEN neutron array. Figure 8 shows the inelastic spectra in coincidence with backward emitted neutrons for 9°'94Zr. A peak is clearly present at 27 MeV excitation energy in 94Zr, which is twice the excitation energy of the GR. As for 9°Zr, a peak is observed which can be fitted by two peaks, one at 22 MeV and the other at 28 MeV. The latter is at the position expected for the double phonon. Figure 9a) shows the missing energy spectrum for the GR region in 48Ca and 9°'94Zr, along with the corresponding statistical decay calculations. A small direct decay branch is observed, to the ground state only for 4SCa and 9°Zr, but also to excited states around 4 MeV for 94Zr. The missing energy spectrum for the doublephonon region is shown in Fig. 9b) together with the simulation. For 4SCa and 9°Zr, the simulation shows two main structures in good agreement with the experimental data, providing the fingerprint of the two-phonon state in these nuclei. For 94Zr, the signature is less clear. This is mainly due to the direct decay of the GR which feeds several states in 93Zr, blurring the decay pattern for the two phonon decay. The ~8Ni decay was also studied through both neutron and proton, but the results suffer the same problem as for 94Zr since the GR decays through several unresolved states of 57Ni and 57C0 respectively, leading to a structureless direct decay component. This shows another limit of the method which needs not only a sizeable direct decay branch but also well separated hole states in the daughter nuclei.
J.A. Scarpaci/Nuclear Physics A649 (1999) 225c-234c
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Figure 8. Inelastic spectra in coincidence with backward emitted neutrons for 9°'94Zr o
1o E"ca(MeV)
,
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Figure 9. Missing energy spectra for the decay of the GR in 4SCa (a), 9°Zr (b) and 94Zr (c), and the decay of the double phonon regions (c,d,e).
5. C O N C L U S I O N S
AND PERSPECTIVES
Inelastic scattering of medium energy heavy ions have provided a large amount of data which gives a coherent picture of the properties and decay of two-phonon excitations. The excess of cross section in the missing energy spectra is well reproduced by a simulation of the two-phonon direct decay based on the measured direct decay Of the giant resonance providing an elegant proof of its existance. Furthermore, these inelastic measurements in coincidence with light emitted particles have allowed for the first time to fully disentangled the inclusive inelastic scattering spectrum in the different reaction mechanisms. The main challenge of the multiphonon 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. It seems however a general belief that these three-phonon states should be looked for since they would give us a better handle on the anharmonic-
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J.A. Scarpaci /Nuclear Physics A649 (1999) 225c-234c
ity of the nucleus. Amongst the methods employed for the two-phonon studies, double charge exchange reactions cannot excite triple phonon states because of trivial selection rules. The branching ratio of triple 7 decay would be much too small, making a three 0/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 4~r 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[18]. 6. A C K N O W L E D G E M E N T S I wish to thank my colleagues D. Beaumel, Y. Blumenfeld, N. Frascaria, I. Lhenry, V. Pascalon-Rozier, L. Petizon, J.C. Roynette and T. Suomij/irvi from Orsay and also my friends and colleagues from GANIL, Ph. Chomaz, D. Lacroix and P. Roussel-Chomaz for their constant involvement in the GANIL experimental (and theoretical) program and for innumerable discussions. I would like to acknowledge particularly our very fruitful collaboration with Adriaan van der Woude from KVI. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
Ph. Chomaz and N. Frascaria, Phys. Rep. 252 (1995) 275. T. Aumann, B.F. Bortignon and H. Emling Annu. Rev. Nucl. Part. Sci. 1998, Vol. 48 D. Beaumel and Ph. Chomaz, Ann. Phys. (N.Y.) 213 (1992) 405. R.A. Broglia et al., Phys. Lett. 61B (1978) 331. J.A. Scarpaci et al., Phys. Rev. Lett. 71 (1993) 3766. J. Ritman et al., Phys. Rev. Lett. 70 (1993) 533. R. Schmidt et al., Phys. Rev. Lett. 70 (1993) 1767. S. Mordechai and C. F. Moore, Nature 352 (1991) 393. A. van der Woude, Prog. Part. Nucl. Phys. 18 (1987) 217. L. Bianchi et al. Nucl. Inst. Meth. A276 (1989) 509. J.A. Scarpaci et al., Phys. Rev. C56, 3187 (1997) H. Laurent et al. Nucl. Inst. Meth. A326 (1993) 517. J.A. Scarpaci et al., Phys. Lett. B428 (1998) 241. J.A. Scarpaci et al., Phys. Lett. B258 (1991) 279. Ph. Chomaz and N.V. Giai, Phys. Lett. B282 (1992) 13. F. Cataraet al., Nucl. Phys. A471 (1987) 661. Y. Blumenfeld and Ph. Chomaz, Phys. Rev. C38 (1988) 2157. J. Pouthas et al., Nucl. Inst. Meth. A357 (1995) 418.