ELSEVIER Nuclear Physics A73 1 (2004) 175-l 87

www.elsevier.comllocate/npe

Multiphonon states built with giant resonances

J.A.Scarpaci a

a Institut de Physique Nucleaire, INzPs - CNRS, 91406 Orsay, France

The two-phonon states built with giant resonances have been observed through a large variety of experiments. A new experiment studying the inelastic scattering of 40Ca on 40Ca at 50 A.MeV has been measured at GANIL by detecting scattered 40Ca in coincidence with light charged particles. For the first time, the SPEG spectrometer was associated to 240 CsI(T1) scintillators of the INDRA 4n: array. The direct decay method, successfully used in previous experiments to sign the presence of multiphonon states, is applied to the excitation energy region of the GQR, the double and the triple GQR. The previous results concerning the GQR and the 2-phonon state built with the GQR are confirmed. Evidence is given for the excitation of a 3-phonon state, characterized by its 3 proton direct decay branch and indication are given for a four-phonon state.

1. INTRODUCTION

In the past decade numerous experimental efforts have been devoted to the search for multiphonon excitations. A number of them have been conclusive and the existence of the two-phonon states built with the most collective giant resonances (the isovector GDR and the isoscalar giant quadrupole GQR) has been unambiguously demonstrated [1,2]. In particular, it has been shown that multiphonon states essentially built with the GQR can be excited by the strong nuclear field present in heavy ion reactions and that different members of the two-GDR multiplet can be populated by relativistic Coulomb excitation with heavy targets or double charge exchange reactions.

In this paper we will briefly summarize the results gathered for the observation of the second phonon with various probes. Then we will present results for a new experiment performed at the GANIL facility aiming at the observation of higher order multiphonons [3,4]. Evidence will be presented for the excitation of the three-phonon state and indications for a four-phonon state through the study of their direct decay is also presented.

2. EXPERIMENTAL OBSERVATIONS OF THE TWO-PHONON STATE

Several experiments have provided evidence for the excitation of the two-phonon state from

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176 LA. Scarpaci/Nuclear Physics A731 (2004) 175-187

double charge exchange reactions, (n+,rc-) and (TC-,rc+) [5], that have consistently observed the double dipole phonon in a series of nuclei running from 12C to 197Au, to relativistic heavy ion scattering which showed evidence for two-phonon excitations in Xe, Pb and U. The double gamma decay of the two-phonon GDR excited in Pb, which has a very low branching ratio, was measured [6]. The exclusive measurements where the neutrons from the decay together with the gamma rays and the residual nucleus were also measured for all the three nuclei [7]. Finally the study of the fission fragment distribution in the case of U could only be understood if some strength was present in the energy range of the double phonon [g]. The giant quadrupole resonance (GQR) and its double excitation was in turn observed in different nuclei, 40Ca, 48Ca, 58,64Ni, 90,94Zr in experiments performed at Ganil at incident energies where the nuclear excitation dominates [9]. It this case the direct decay of the second phonon was shown to exhibit a pattern consistent with that of the GQR.

3. WHAT CAN BE LEARNED FROM THE MULTIPHONON EXCITATIONS - ANHARMONICITIES

In addition to confirming the vibrational nature of GRs, the observation and investigation of the multiphonon will teach us about the anharmonicities of nuclear excitations. For the harmonic potential we expect the n-phonon to be at n times the excitation energy of the first phonon. On the contrary, anharmonicity should be reflected in a shift of the excitation energies. However the predictions are that the energies should be different from the harmonic case by only a few hundred keV at most which is within the energy resolution of the majority of the experiments [lo]. However, models predict that anharmonicities should change by 10 to 30% the excitation cross sections and that quantity is measurable [ 1 l-131. We will show some evidence of such a feature both in relativistic heavy ion experiments and in lower energy experiments.

3.1 Relativistic beam experiments Excitation cross section was observed at energies around the second giant dipole resonance

region [7]. A deconvolution of the spectra was performed and the expected strengths were found for the excitation of the giant dipole resonance (GDR) and the GQR. At higher excitation energy, additional strength was observed consistent with the excitation of a double GDR. For the Pb and the Xe nuclei even an excess of strength was measured compared to the harmonic calculation in the order of 30 to 50% respectively. This is shown in fig.1 that plots the ratio between the measurement and the expected value in the harmonic picture. If anharmonicities were to be included in the calculation we would expect larger ratio shown by the stars. According to microscopic calculation performed by Lanza et al. [I l] not only the double GDR should be excited in this region but also the GDR coupled to the GQR. If this contribution is subtracted from the experimental measurement, the GDR cross section represented by the black dots agrees nicely with the anharmonic calculation. These data seems to indicate that the lighter the nucleus the more anharmonic its potential. What would be the result for an even lighter nucleus? Data were acquired at lower incident energies for

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40Ca and will now be presented after introducing the microscopic calculation by Andres et al. [ 131 and their prediction for this nucleus.

/ ,,f,,,,, ,*o 140 160 lee 200 220 20

Fig. 1 : Experimental DGDR cross sections relative to their harmonic values prior to (open circles) and after ( filled circles) subtraction of contributions from two-phonon states of type GDRxGQR for the three measured nuclei. Star symbols (connected by a dashed line) reflect the increase of cross section due to an anharmonic dipole response relative to the harmonic

response.

3.2. Intermediate energy experiments Microscopic calculations by Andres et al. were performed using the RPA states and

including anharmonicity in the Hamiltonian - by introducing couplings between one and two phonon states - as well as a quadratic term in the excitation field. The calculation included both the nuclear and the Coulomb interaction and enabled the extraction of the cross section for excitations of one and two-phonon states. This calculation found an increase in cross section of about 40% in the 28 to 38 MeV region with respect to a harmonic calculation. Fig.2 shows both calculations, with (solid line) and without (dashed line) anharmonicities and non linearities. These calculation are compared on an absolute cross section scale with experimental data for the 40Ca + 40Ca reaction at 50 MeV per nucleon at the Ganil facility [14] where coincidences between the 40Ca ejectile and one proton were measured. The agreement is rather good below 36 MeV indicating that the 40Ca nucleus demonstrates some anharmonicities. However at excitation energies above 40 MeV, experimental data show a larger cross section than the calculation. This is a region were higher order multiphonon states are expected. To obtain realistic predictions above 40 MeV, calculations should be extended to a basis including three- and four-phonon states, which could also slightly change the cross section for the two-phonon region [ 1.51.

4. NEW RESULTS FOR THE GQR BASED MULTIPHONONS

The previous experiment presented above was performed with a charged particle detector covering only 3% of the total solid angle. This allowed for coincidences between the ejectile and only one proton at a time. In order to obtain a more complete set of data and to be able to detect all the protons of the decaying nucleus the use of a 47~ detector for the emitted

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particles seemed required. Only then a signature of the existence of a three-phonon state could be obtained.

Fig.2 : Excitation cross section for the microscopic calculation including several one and two phonon states, with (plain line) and without (dashed line) anharmoncities and non

linearities. Dots are data measured at GANIL.

4.1. Experimental set-up A considerable improvement has been performed by using a large angular coverage

detector for the emitted charged particles. 240 CsI of the INDRA detector [16] were used (ring 6 to ring 17), covering angles from 14” to 176” in the laboratory frame. The reaction 40Ca (40Ca, 40Ca + xp) at 50 MeV/A was performed at GANIL. The 40Ca ejectile was identified in the SPEG [17] detection array where its kinetic energy and scattering angle allowing for the reconstruction of the inelastic spectra were measured. The angular acceptance of the spectrometer ran from 0.5” to 5” in the horizontal plane and from -2” to 2” in the vertical plane. Coincidences of several charged particles together with the ejectile could be measured allowing for the measurement of complete decay events.

4.2. Inelastic spectra 4.2.1. Inclusive inelastic spectrum

The inclusive inelastic spectrum is shown in fig.3. Several peaks are observed between 0 and 8 MeV excitation energy. The giant quadrupole resonance (GQR) is located between 12 and 20 MeV. At energies above 20 MeV, in addition to inelastic target excitation, several reaction mechanisms contribute to this inclusive inelastic spectrum. The pick-up break-up process where a nucleon is transferred from the target to the projectile and then re-emitted in flight gives rise to a flat contribution at apparent excitation energies between 30 and 90 MeV. The towing mode [18, 191 for which a nucleon from the target is extracted and towed along the projectile trajectory has a contribution which peaks around 25 MeV and extends up to 100 MeV. The knock-out of one particle of the target by the interaction with one nucleon

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of the projectile gives a contribution between 20 and 30 MeV in the inelastic spectrum. However all these above mentioned mechanisms that include the participation of the projectile give rise to particles emitted in the forward hemisphere in the laboratory frame. For a target excitation, its decays occurs in all direction and by requiring a coincidence with one proton emitted in the backward direction we select the target excitations in the inelastic spectrum. All the experimental data presented in the following chapters are gated on the presence of backward -emitted protons except when indicated. -

5000 Wa at 50 AMeV

d 0 10 30 30 40 50 60 70

Energy (Mel’)

Fig.3 : Inclusive inelastic spectrum.

4.2.2. Inelastic spectrum in coincidence with one proton The inelastic spectrum in coincidence with at least one proton emitted in the backward

hemisphere is presented in fig.4 left. In this case the proton detector is effectively reduced to 27~ in solid angle and correction is required to account for the varying proton multiplicity with the excitation energy and thus the varying probability to measure the coincidence. Using a Monte Carlo statistical decay code and the geometry of the detectors we obtained the correction functions presented in the figure. The dashed curve is the result when only the backward detectors are used. The raw experimental data is divided by the latter correction spectrum and the result is presented in the central figure. A clear change of slope is observed at about 25 MeV excitation energy. Fig.4 right is the result after the subtraction of an arbitrary background. It shows a nice bump located at about 35 MeV and of 11 MeV FWHM. This bump is a perfect candidate for a second phonon in 40Ca and its decay as well as the decay of the giant resonance and of higher excitation energy regions are presented in the following.

The microscopic calculation by Andres et al. [ 131 predicts that several states contribute to the two-phonon energy region. They are listed in table 1 with their energy and their cross section in the anharmonic and non linear case and in the linear and harmonic case. It can be noted that only 6 states have a cross section above 5% of the total and only two states, the double GQR and the GMR coupled to the GQR are able to emit two protons through direct decay. By studying the three fold events where two protons are detected in coincidence with

180 LA. Scarpaci/Nuclear Physics A731 (2004) 175-187

the ejectile we mainly study the decay more than 80% of the cross section.

4Lm. I . . : . *. mm.

!

10 30 30 40 50 60 70 80 90 10 Etw-gy (MeV)

of the double GQR that is predicted to account for

-~~~~~~

30 30 40 50 60 70 80 90 10 30 30 40 50 60 70 Enel-gy (MeV) E-w Wev)

Fig.4 : Inelastic spectrum in coincidence with at least one backward emitted proton. Raw data are presented in the left panel (dots) with the multiplicity correction spectra for

backward detectors (dashed line). Middle panel shows the same data corrected for the multiplicity spectrum (dashed line) together with a background. Right panel shows the result

of the subtraction of the background from the corrected data.

Table 1 : Excitation energies of all the states predicted in the 28-38 MeV region for a harmonic and linear case (right columns) and for the anharmonic and nolinear case (left columns).

Anharm. Nonlinear Harmon. Linear E* Cross section Cross section

WV) (mb) (MYV) (mb) GMRI x GMRl 36,6 0,0100 36,s 0,012o ISGQR x ISGQR 34,0 2,47OO 33,8 1,370d GDRl x GDRl 35,l 0,020o 35,6 0,0017

LEORI x HEOR 36,l 0,300o 36,3 IVGQR x LEORl 34,3 0,0024 34,5 GDRl x ISGQR 34,7 0,050o 34,7 GMRl x GDRl 35,9 0,0079 36,0

IVGQR 29,l 0,0314 29,5 GDRZ x LEORZ 31,4 0,0014 31,7 GMRI x ISGQR 35,2 0,450o 35,2 LEORI x HEOR 36,2 0,350o 36,3

HEOR 30,8 2,200o 31,3 GMRZ x LEORZ 32,3 0,240O 32,2 IVGQR x LEORI 34,4 0,0015 34,5

0,250O 0,002s 0,026O 0,0055 0,030o 0,OOll 0,230o 0,340o 2,lOOO 0,044o 0,0008

Total cross section

6,1346 4,4136

4.3. Proton decay and missing energy spectra The decay of the GQR is studied by constructing the missing energy spectrum (Emiss =

E* - Er). Fig.5 shows the missing energy spectrum for an excitation energy between 12 and 20 MeV. The ground state of 3gK as well as the first excited states are fed by the decay of the GQR. The statistical decay code CASCADE [20] was used to infer the contribution of the

LA. Scarpaci/Nuclear Physics A731 (2004) 175-187 181

compound nucleus decay for this excitation energy region and is shown as a solid line. It has been run for every 200 keV bin in energy and weighted by the coincidence spectrum before summing all the calculations. The normalization was maximized to the experiment so as to never overshoot the data. The cross section excess for the feeding of the ground state and the first excited states can be attributed to the direct decay of the GQR. It accounts for about 30% of the total decay,

The missing energy spectrum was extracted for the 28-38 MeV region where the peak has been observed in the inelastic spectrum (fig.4) for events where the two protons were detected and is presented in fig.6. The ground state and the first excited states of 38Ar are observed.

Fig.5 : Missing energy spectrum for the excitation energy of the GQR (12-20 MeV). The plain line is the statistical calculation CASCADE.

The statistical calculation was performed for initial angular momenta from 0 to 4 and summed with the weights predicted by the M.V. Andres et al. [13] calculation. As shown in fig.6 by the solid line it does not fully reproduce the measured cross section.

The missing energy spectrum was also extracted for the 42-55 MeV region where the three-phonon state is expected and for events where three protons are detected in the 43t solid angle and is presented in flg.7. Here again the ground state and the first excited states of 37C1 are observed. The statistical calculation was performed for this energy region. Here the relative feeding of the levels in 37C1 does not depend on the initial angular momentum. Fig.7 shows that the statistical decay does not fully account for the measured cross section living some space for the direct decay.

182 J.A. Scarpaci/Nucleau Physics A731 (2004) 175-187

-

I 1C

Fig.6 : Missing energy spectrum for the excitation energy region of 28-38 MeV for events where the two protons are detected. The plain line is the statistical calculation CASCADE.

Black bars represent the result of the direct decay simulation (see text). The histogram is the simulation convoluted by a 1 MeV gaussian.

20 50

Fig.7 : Missing energy spectrum for the excitation energy region of 42-55 MeV for events where three protons are detected. The plain line is the statistical calculation CASCADE.

Black bars represent the result of the direct decay simulation (see text).

A simulation was then performed to infer the contribution of the direct decay of a two and three-phonon state built with the GQR. This simulation assumes that the multiphonons decay independently with the same percentage of direct decay than the one measured for the GQR of 40Ca. This decay pattern is presented in fig.8 for a one, a two and a three-phonon state together with the states fed through the decay in the daughter nuclei. The result of this simulation in the missing energy spectra is presented in the figures 6 and 7 as black bars with an arbitrary normalization. The excess of cross section compared to the statistical decay calculation is qualitatively reproduced by this simulation which confirms that we are

LA. Scarpaci/Nucleav Physics A731 (2004) 175-187 183

observing the direct decay of a two-phonon state (fig.6) and a three-phonon state in the 42 to 55 MeV energy region (fig.7). The direct decay simulation gives the expected feeding of the daughter nuclei (37C1 in the case of the direct decay of the third phonon) as presented in the missing energy spectra of fig.7 but it also gives the path through which the direct decay occurs. In other words it predicts the intermediate states that are fed during the decay. In order to experimentally observe these states we should construct the missing energy spectra with one proton out of two or three emitted protons. If the detected proton is the first emitted we shall directly see the states fed in 39K. In any case the missing energy spectra will present an excess in cross section for the protons of the direct decay.

Fig.8 : Direct decay scheme of the GQR, the two-phonon state and the three-phonon state according to the simulation (see text).

Fig.9 shows the missing energy spectrum calculated with the energy of one proton for events where two protons are detected and for the two-phonon region. For each measured event two values are obtained for the missing energy calculated with each proton. The CASCADE calculation shown as a solid line has been normalized with the same factor as for the missing energy spectrum calculated with the two protons (fig.6). An excess of cross section is observed and is reasonably well reproduced by the same simulation of the direct decay of a two-phonon state as shown before given us some confidence about the picture of two GQRs going through a direct decay.

The missing energy spectrum has also been extracted for the 42-55 MeV region, again for complete events where three protons are detected in the 4n solid angle. For each physical event the missing energy spectrum is incremented three times, one for each proton. Fig.10 shows the result together with the statistical calculation and the result of the simulation.

184 LA. Scarpaci/Nuclear Physics A731 (2004) 175-187

Peaks are observed experimentally and their location is well reproduced by the simulation calculated with the same ingredients as for fig.7. This shows that the three-phonon state is excited in this region since its direct decay pattern is observed in both the missing energy spectrum constructed with the three protons and the missing energy spectrum constructed with one of the three protons.

Fig.9 : Missing energy spectrum calculated with one proton whenever two protons are detected and for the 28-38 MeV region. Plain line is the CASCADE calculation. Black bars are the predicted values given by the direct decay simulation. Dashed line is the prediction

of the simulation convoluted.

Fig. 10 : Missing energy spectrum calculated with one proton whenever three protons are detected and for the 42-55 MeV region. Plain line is the CASCADE calculation. Black bars

are the predicted values given by the direct decay simulation.

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4.5. Hints for the direct decay of the 4’h phonon The energy region between 56 and 70 MeV has been studied as it corresponds to the

excitation energy region where the fourth-phonon state built with the GQR is expected. Due to a lack of statistics on the five-fold events, only the missing energy spectrum calculated with one proton emitted in the 471 solid angle was built for events where at least three protons are detected. It is presented in fig. 11. Again, some peaks are present as predicted by the simulation performed for the direct decay of a four-phonon state.

40 45 50 55 60 65 70 Etlliss (MN

Fig. 11 : Missing energy spectrum calculated with one proton for events where at least three protons are detected. Grey bars are the simulation for the direct decay

4.6. Alpha particle direct decay Alpha particle decay was measured and the missing energy spectrum for the GQR

region was compared to the statistical decay and is shown in the left panel of fig.12. The calculation does not reproduce the feeding of the ground state and the first excited states. For the first time a non-statistical alpha decay branch was found for the GQR amounting to 16% of the total decay. A previous study through (e, e’) scattering has shown that the data were consistent with a purely statistical decay through alpha particle emission [21]. However error bars in this experiment were such that this result is not in contradiction with our finding. This non-statistical decay could be the indication of an alpha-particle clusterization in the wave function of the GQR.

The energy region of the second phonon was also studied through the two-alpha emission and the missing energy spectrum constructed with the two alpha particles is presented in the right panel of fig.12. The statistical calculation reproduces the experimental data. This could be the indication of a non clusterized 36Ar nucleus. However further study should be performed, in particular the proton plus alpha-particle decay channel yield further important information.

186 JA. Scarpaci/Nuclear Physics A731 (2004) 175-187

4 6 8 70 12 74 76 Q,, (MeW

35 E,,, NW

Fig. 12 : Missing energy spectrum calculated for the 12 to 20 MeV excitation energy region (left) and for the 28 to 38 MeV region (right) decaying through alpha particle. The plain line

is the statistical calculation performed with the code CASCADE.

5. CONCLUSION AND OUTLOOK

Multiphonon states built with giant resonances have now been observed in many different experiments. Recently, a study of nuclear excitations at GANIL energies was performed using a 4rr array for the detection of the decay charged particles. The second and the third multiphonon states built with the GQR were clearly observed through their specific direct decay. Evidence for the direct decay of a fourth phonon was presented but statistics are lacking for 5fold events in which the ejectile together with 4 protons were detected. A simulation of the direct decay pattern of multiphonon states qualitatively reproduces the missing energy spectra that were extracted. However this simulation contains many simplifications. First the giant resonance in the daughter nuclei may exhibit different characteristics as for 40Ca and decay differently. Second, calculations predict that other multiphonon states are excited that do not involve only GQR. A more complex simulation including multiphonons built with the excitation of a low energy state (7 MeV) and the GQR was performed by M.Fallot [3,4] and showed a fairly good reproduction of the data. Third, anharmonicities could shift the excitation energies of the multiphonons. To gain some more information on GQR excited in 3gK and 38Ar and their direct decay further studies could focuss on these nuclei. From the theoretical point of view, calculations need to be completed to infer the excitation cross section in a space where three and four phonons would be taken into account.

ACKNOWLEDGMENTS

I thank my colleagues for allowing me to present our recent results prior to publication : Y. Blumenfeld, A. Chbihi, Ph. Chomaz, P. Desesquelles, J. Frankland, N. Frascaria, E. Khan, J.L. Laville, E. Plagnol, E.C. Pollacco, P. Roussel-Chomaz, J.C. Roynette, A.

JA. Scarpaci/Nucleau Physics A731 (2004) 175-187 187

Shrivastava and T. Zerguerras. I acknowledge particularly M. Fallot who performed most of the analysis of the new data I presented here.

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