Evidence for a Three-Phonon Giant Resonance State in 40 Ca Nuclei M. Fallot, 1, * J. A. Scarpaci, 1 N. Frascaria, 1 Y. Blumenfeld, 1 A. Chbihi, 2 Ph. Chomaz, 2 P. De´sesquelles, 1 J. Frankland, 2 E. Khan, 1 J. L. Laville, 2 E. Plagnol, 1 E. C. Pollacco, 3 P. Roussel-Chomaz, 2 J. C. Roynette, 1 A. Shrivastava, 1 and T. Zerguerras 1 1 Institut de Physique Nucle´aire d’Orsay, IN2P3-CNRS-Universite´ Paris Sud, 91406 Orsay cedex, France 2 GANIL (CEA/DSM-CNRS/INP), BP 5027 F-14076 Caen Cedex 5, France 3 SPhN, DAPNIA, CEA Saclay 91191 Gif sur Yvette Cedex, France (Received 4 April 2006; revised manuscript received 27 October 2006; published 15 December 2006) Inelastic scattering of 40 Ca on 40 Ca at 50 MeV=A has been measured in coincidence with protons at the GANIL facility. The SPEG spectrometer was associated with 240 CsI(Tl) scintillators of the INDRA 4 array, allowing for the measurement of complete decay events. The missing energy method was applied to these events. For events with excitation energy between 42 and 55 MeV, a direct decay branch by three protons towards the low energy states of 37 Cl gives the first evidence for a 3-phonon state built with giant resonances. DOI: 10.1103/PhysRevLett.97.242502 PACS numbers: 24.30.Cz, 25.70.Bc, 25.70.Ef, 27.40.+z Collective behavior is mainly prevalent in macroscopic systems, but is also widespread in microscopic systems. Of particular interest are collective motions interpreted in terms of vibrations. In the context of quantum mechanics, vibrational collective modes are associated with boson degrees of freedom, even when considering excitations of fermionic systems [1]. These bosons can be understood as being built from fermion pairs which carry boson quantum numbers. However, the number of possible pairs must be large enough to insure that the Pauli exclusion principle does not introduce significant deviations from a boson behavior. In small fermionic systems antisymmetrization imposes constraints which cannot be well accounted for when using a boson representation. An important question is to understand the transition from small to many-body macroscopic systems. Collective oscillations have been observed in mesoscopic systems such as the surface plas- mons in metallic clusters [2], interpreted as the collective vibration of electrons against ions. The nucleus is known to exhibit collective vibrations which are usually called pho- nons. The giant dipole resonance (GDR) corresponds to a collective motion of protons against neutrons, akin to the plasmons in metal. The monopole vibration is a compres- sion mode analogous to the zero sound in Fermi liquids and the giant quadrupole resonance (GQR) is a surface vibra- tion which resembles the wave at the interface of two liquids. The study of the nucleus can thus give unique insight into the behavior of vibrations in small systems [3,4]. Giant resonances are understood as a first quantum of vibration. The existence of two-phonon states built with the GDR and the GQR as a general property of nuclei has been unambiguously demonstrated. Three complementary methods were used. Two-phonon states built with the GDR were excited through double charge-exchange reactions such as (  ,   )[5], and through Coulomb excitation using relativistic heavy ion beams at about 1 GeV=A [6]. Two-phonon states built with the GQR were excited through the nuclear interaction using heavy ion collisions at intermediate energy (about 50 MeV=A)[7,8]. The double phonon states were observed at an excitation energy close to twice that of the one-phonon state with a width close to the quadratic sum of the widths of the individual phonons. These features point towards a harmonic picture of the phonon excitation. However, the measured cross sections were found unexpectedly higher than in harmonic predictions. Theoretical calculations show that these ob- servations can be explained by invoking small anharmo- nicities and nonlinear effects due to interactions between phonons [4]. As nonlinear effects are expected to increase with the number of excited phonons, the observation of a 3-phonon state is of primary interest for the understanding of large amplitude collective motion in mesoscopic sys- tems. Such a measurement is not easily accessible. The double charge-exchange reaction is limited to the study of the double GDR. Optimal conditions to excite the triple GDR are given by electromagnetic excitation using rela- tivistic heavy ion collisions, but the signature of the three- phonon state would require the coincident detection of three high energy  rays, inaccessible with present de- tection efficiencies due to the small gamma branching ratio of the GDR. Heavy ion collisions at intermediate energy are the most promising probe to observe a 3-phonon state. An unambiguous signature of the 2-phonon GQR was previously provided by particle decay in [7,8]. The missing energy method used to sign the presence of the multi- phonon strength in the spectra is based on the direct decay of the giant resonance [3,7]. In the former 40 Ca  40 Ca experiment at 50 MeV=A, the direct decay pattern of the 2- phonon state could be built, using protons detected in coincidence with the 40 Ca ejectile in an array cover- ing only 3% of the total solid angle. Only one proton among the two protons emitted by a 2-phonon state by direct decay could be measured. But in the case of a PRL 97, 242502 (2006) PHYSICAL REVIEW LETTERS week ending 15 DECEMBER 2006 0031-9007= 06=97(24)=242502(4) 242502-1 © 2006 The American Physical Society